establishment of artificial neural network for suspension spring

1

ESTABLISHMENT OF ARTIFICIAL NEURAL NETWORK FOR SUSPENSION SPRING FATIGUE LIFE PREDICTION USING STRAIN AND ACCELERATION DATA

Von der Fakultät für Ingenieurwissenschaften, Abteilung Maschinenbau und Verfahrenstechnik der

Universität Duisburg-Essen

zur Erlangung des akademischen Grades

eines

Doktors der Ingenieurwissenschaften

Dr.-Ing.

genehmigte Dissertation

von

YAT SHENG KONG aus

Klang, Malaysia

1. Gutachter: Prof. Dr.-Ing Dieter Schramm 2. Gutachter: Prof. Ir. Dr. Shahrum Abdullah Tag der mündlichen Prüfung: 19.02.2019

ESTABLISHMENT OF ARTIFICIAL NEURAL NETWORK FOR SUSPENSION

SPRING FATIGUE LIFE PREDICTION USING STRAIN AND

ACCELERATION DATA

KONG YAT SHENG

THESIS SUBMITTED IN FULFILMENT FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

FACULTY OF ENGINEERING AND BUILT ENVIRONMENT

UNIVERSITI KEBANGSAAN MALAYSIA

BANGI

2019

DECLARATION

I hereby declare that the work in this thesis is my own except for quotations and

summaries which have been duly acknowledged.

08 April 2019 KONG YAT SHENG

P78155

ACKNOWLEDGEMENT

Author would like to express his sincere gratitude and appreciation to thesis

supervisor Prof. Ir. Dr. Shahrum Abdullah and Prof. Dr.-Ing. Dieter Schramm for

providing valuable guidance, supervision and mentoring as well as encouragement for

carrying this research.

Also, author would like to express my high appreciation to my co-supervisor

Prof. Dr. Mohd Zaidi Omar and Associate Prof. Dr. Sallehuddin Mohd. Haris for

providing valuable comment, support and guidance throughout the course and

research.

Author would like to thank all post graduate students of UKM structure

integrity group for their help, friendship, and creating a pleasant working environment

throughout his years in UKM.

Importantly, author would like to express his heartfelt thanks to his beloved

parent for their lifelong encouragement.

Last but not least, author gratefully acknowledge financial support provided by

MyBrain 15 and DAAD 2016. Without their support, author could not finish his

research in time.

v

ABSTRACT

This study presents establishment of multiple input prediction model for automotive

coil spring fatigue life estimation to shorten automotive suspension design process.

Automotive suspension design is a lengthy work where any changes of the design lead

to repetition of the entire process. It was hypothesised that the established model could

be used to predict the spring design fatigue life without using any strain measurements.

To initiate this model establishment, five sets of strain and acceleration measurement

across different road conditions were collected and used for validations. To include

spring stiffness as a parameter, a quarter car model was generated to obtain the force

time histories from spring and vertical vibration of vehicle mass. In addition, artificial

road profiles of road classes “A” to “D” were also generated for the quarter car

simulation. Through adjusting the spring stiffness in the quarter car model, the spring

and vehicle responses were varied. The simulated force time histories were used to

predict springs’ fatigue life while acceleration time histories were used to calculate

ISO 2631 ride-related vertical vibration. Subsequently, multiple linear regression

approach was applied to determine the relationship between vehicle body frequency,

ISO 2631 ride-related vertical vibration and spring fatigue life. The obtained

regression had shown significance to the spring fatigue life with coefficient of

determination of 0.8320. Reciprocally, multiple linear regression models were also

used to predict the ISO 2631 ride-related vertical vibration with a coefficient of

determination at 0.8810 and mean squared error values below 0.3430. To optimise the

prediction results, artificial neural network was trained for the fatigue and vibration

prediction purposes. The architectures of the artificial neural network were designed

in terms of number of neurons and hidden layers to achieve a higher coefficient of

determination of 0.9926 and lower mean squared error of 0.0824. For vibration

prediction, the vehicle body frequency and spring fatigue life has shown a significant

coefficient of determination to the ISO 2631 weighted vertical vibration, reaching

0.9579 with mean squared error of 0.0004. Based on the experimental strain and

acceleration results, the predicted fatigue lives of multiple linear regression models

were correlated well with the experimental results with coefficient of determination

value of 0.9275. Meanwhile, the maximum difference of vibration prediction to

experimental value using multiple linear regression models was only 18%. For

artificial neural network predictions, the fatigue lives were mostly distributed within

1:2 or 2:1 life correlation and vibration prediction results were within 12%. For a good

prediction, the target correlation value was above 0.80 to demonstrate a good fitted

curve and the difference below 20%. The trained artificial neural network has shown

outstanding capability in fatigue life or ride-related vertical vibration predictions. In

this research, the main novelty was the trained artificial neural network for spring

fatigue life or ride-related vertical vibration predictions which serve to reduce some

procedures of automotive suspension design. The outcome of this study can be used to

provide a new knowledge towards the field of fatigue research as well as vehicle ride

dynamics. This research contributes to automotive industries especially in suspension

spring design where the analysis of fatigue and ride-related vibration are provided.

iv

PENUBUHNAN RANGKAIAN NEURAL BUATAN UNTUK JANGKAAN

HAYAT LESU SISTEM AMPAIAN PEGAS DENGAN DATA

TERIKAN DAN DATA PECUTAN

ABSTRAK

Kajian ini membentangkan pembangunan model ramalan pelbagai input untuk

jangkaan hayat lesu pegas gegelung automotif supaya proses reka bentuk sistem

ampaian automotif disingkatkan. Proses reka bentuk sistem ampaian automotif adalah

memakan masa dan segala perubahan reka bentuk akan mengakibatkan pengulangan

proses tersebut. Hipotesis kajian ini ialah model yang dibangunkan boleh digunakan

untuk meramalkan hayat lesu reka bentuk pegas gegelung dengan tanpa menggunakan

sebarang isyarat terikan. Sebagai permulaan, lima isyarat terikan dan pecutan yang

dicerap daripada keadaan jalan yang berbeza telah digunakan sebagai kes kajian.

Untuk merangkumi kekakuan pegas sebagai parameter, model kereta sukuan dibina

untuk memperolehi isyarat beban pada pegas dan pecutan menegak kenderaan.

Sebagai tambahan, profil jalan buatan kelas "A" hingga "D" juga dijana untuk

simulasi kereta sukuan. Dengan melaraskan kekakuan pegas dalam model kereta

sukuan, tindak balas pegas dan badan kenderaan telah berubah. Isyarat beban simulasi

yang dijana digunakan untuk meramalkan hayat lesu pegas gegelung manakala isyarat

pecutan digunakan untuk mendapatkan indeks getaran menegak yang berkaitan

dengan ISO 2631. Seterusnya, kaedah regresi linear berganda telah digunakan untuk

menentukan hubungan antara frekuensi badan kereta, getaran menegak ISO 2631 dan

hayat lesu pegas gegelung. Perkaitan yang diperolehi telah menunjukkan nilai pekali

penentuan setinggi 0.8320. Sebaliknya, model regresi linear berganda yang digunakan

untuk meramal getaran menegak ISO 2631 mempunyai pekali penentuan minimum

0.8810 dan min kuasa dua ralat di bawah 0.3430. Untuk mengoptimunkan prestasi

ramalan, rangkaian neural buatan telah dilatih untuk tujuan ramalan yang sama. Seni

bina rangkaian neural buatan telah direka dari segi bilangan neuron dan lapisan

tersembunyi untuk mencapai pekali penentuan setinggi 0.9926 dan min kuasa dua

ralat tertinggi 0.0824. Untuk ramalan getaran menegak, frekuensi kereta dan hayat

lesu pegas telah menunjukkan pekali penentu yang tinggi terhadap getaran menegak

ISO 2631, nilai 0.9579 telah dicapai dengan min kuasa dua ralat serendah 0.0004.

Ramalan hayat lesu model regresi linear berganda mempunyai korelasi yang baik

dengan keputusan eksperimen dengan pekali penentu setinggi 0.9275. Ramalan

getaran menegak menggunakan model regresi linear berganda adalah dalam julat 18%.

Bagi rangkaian neural buatan, ramalan hayat lesu kebanyakan berada dalam korelasi

hayat julat 1:2 atau 2:1 manakala perbezaan hasil ramalan getaran menegak kepada

ujikaji adalah dalam julat 12%. Untuk ramalan yang baik, nilai korelasi sasaran ialah

sekurang-kurangnya 0.80 bagi penyesuaian lengkung yang baik dan perbezaannya di

bawah 20%. Rangkaian neural buatan yang terlatih telah menunjukkan keupayaan

yang baik dalam meramalkan hayat lesu pegas atau penunggangan automotif. Dalam

kajian ini, hasil utama ialah rangkaian neural buatan yang terlatih untuk ramalan hayat

lesu pegas atau kesan menunggang supaya prosedur reka bentuk sistem ampaian

automotif dapat dikurangkan. Hasil kajian ini dijangka memberikan pengetahuan

ilmiah baharu terhadap bidang penyelidikan lesu dan penunggangan dinamik

kenderaan. Kerja ini menyumbang kepada industri automotif yang terbabit dengan

reka bentuk sistem ampaian di mana analisis kelesuan dan getaran yang berkaitan

dengan reka bentuk pegas gegelung kenderaan telah dirangkumi.

vi

TABLE OF CONTENTS

Page

DECLARATION ii

ACKNOWLEDGEMENT iii

ABSTRACT iv

ABSTRAK v

TABLE OF CONTENTS vi

LIST OF TABLES ix

LIST OF FIGURES xii

LIST OF ABBREVIATIONS xx

CHAPTER I INTRODUCTION

1.1 Overview of Fatigue Life Assessment 1

1.2 Durability of Automotive Suspension System 3

1.3 Problem Statement 6

1.4 Research Objectives 7

1.5 Scope of Works 8

1.6 Research Hypothesis 9

1.7 Significance of Research 9

CHAPTER II LITERATURE REVIEW

2.1 Introduction 11

2.2 Automotive Suspension System 12

2.2.1 Types of Automotive Suspension Systems 12

2.2.2 Mechanism of Suspension Components 14

2.2.3 Coil Spring Design and Characteristics 20

2.3 Durability Analyses 23

2.3.1 Introduction to Durability Analysis 24

2.3.2 Types of Loading Signals 27

2.3.3 Cycle Counting Methods 34

2.3.4 Fatigue Life Analysis 36

2.3.5 Linear Damage Cumulative Rule 42

2.4 Ride Related Vibration Analysis 44

2.4.1 Introduction to Ride Analysis 44

vii

2.4.2 Road Roughness as Excitation Sources 47

2.4.3 Vehicle Suspension System Modelling 50

2.4.4 International Ride Standards 54

2.5 Data Analysis 56

2.5.1 Introduction to Data Analysis 56

2.5.2 Regression Analysis 59

2.5.3 Neural-Network based Regression Analysis 63

2.5.2 Validation Analysis 67

2.6 Summary 70

CHAPTER III METHODOLOGY

3.1 Introduction 71

3.2 Durability Characterisation of the Suspension System 72

3.2.1 Perform Analysis on Spring 72

3.2.2 Collection of Strain and Acceleration Signals 77

3.2.3 Characterisation of Fatigue and ISO 2631

Vertical Vibration 82

3.3 Establishment of Multiple Linear Regression 89

3.3.1 Generating Artificial Road Profiles 89

3.3.2 Extract Data from Simulated Quarter Car Model 92

3.3.3 Perform Spring Stiffness Sensitivities 97

3.3.4 Establishment of Multiple Linear Regression for

Fatigue Life 99

3.4 Predicting the Spring Fatigue Life 101

3.4.1 Design the Artificial Neural Network Architecture 101

3.4.2 Optimise the Spring Fatigue Life 107

3.5 Validation of the Prediction 108

3.4.1 Validation using Normality Test 108

3.4.2 Validation using Experimental Data 111

3.6 Summary 113

CHAPTER IV RESULTS AND DISCUSSION

4.1 Introduction 114

4.2 Determining the Durability Characteristics 115

4.2.1 Finite Element Analysis of Coil Spring 115

4.2.2 Observing Signal Characteristics 117

4.2.3 Regression Analysis for fatigue life 130

4.3 Data For Modelling 136

viii

4.3.1 Artificial Road Profiles 136

4.3.2 Quarter Car Model Simulation Results 140

4.3.3 Spring Stiffness Sensitivity Analysis 151

4.3.4 Fatigue Life and Vibration Data 153

4.4 Multiple Input Regression 155

4.4.1 Analysis for Life Regression 155

4.4.2 Analysis for Vibration Regression 167

4.5 Implementation of Artificial Neural Network for Prediction 175

4.4.2 Fatigue Life Prediction 175

4.5.2 ISO 2631 Vertical Vibration Prediction 199

4.6 Prediction Validation 208

4.7 Summary 217

CHAPTER V CONCLUSION

5.1 Conclusion 218

5.1.1 Establishment of the Durability Relationships 218

5.1.2 Optimisation of the Durability Relationships 219

5.1.3 Validation of the Durability Relationships 219

5.2 Research Contribution 220

5.3 Recommendations 221

REFERENCES 222

APPENDICES

A Spring Failure Report by TheAAA 250

B Mesh Sensitivity 251

C Optimised Multilayer ANN architecture 253

D Artificial Road Simulated Time Histories 256

E Measured Road Simulated Time Histories 263

F Fatigue Life and Vibration Data 271

G MSE Data For Single Layer ANN 274

H MSE For Three Layer ANN 275

I Data for Error Histogram 278

J Curve Fitting For ANN 281

K Weights and Biases for ANN 285

L List of Publications 289

ix

LIST OF TABLES

NO. TABLE PAGE

Table 2.1 Chronology of published automobile suspension

durability analysis

26

Table 2.2 Literature of types of VAL in automotive

applications

33

Table 2.3 Chronology of vehicle ride analysis 45

Table 2.4 Objective ride and preferred countries 54

Table 2.5 Researches on generation of MLR-based model 64

Table 3.1 Measured geometrical properties of the spring 75

Table 3.2 Monotonic and cyclic properties of the spring

material

76

Table 3.3 Vehicle speed during signal collection 81

Table 3.4 Guide for assessing the effects of vibration on

comfort

86

Table 3.5 Frequency-weighting curves for principal

weighting

87

Table 3.6 Suitability of fit for coefficient of determination

value

89

Table 3.7 Parameter for ISO 8608 road profile generation 91

Table 3.8 Classification of road roughness proposed by

ISO 8608

91

Table 3.9 k value for ISO 8608 road roughness

classification

91

Table 3.10 Function of each block in quarter car model 94

Table 4.1 Range of the measured strain time histories 118

Table 4.2 Statistics for the measured strain time histories

at different type of roads

119

Table 4.3 Statistics for the measured acceleration time

histories at lower arm

120

Table 4.4 Statistics for the measured acceleration time

histories at top mount

121

Table 4.5 RMSE between sprung and un-sprung mass

acceleration time histories

130

x

Table 4.6 ISO 2631 vertical accelerations and spring

fatigue lives

132

Table 4.7 Regression predicted and experimental fatigue

lives

136

Table 4.8 Statistical parameters of artificial generated road

classes

139

Table 4.9 Spring stiffness parameter sensitivity analysis 152

Table 4.10 Predicted fatigue life and ISO 2631 weighted

acceleration from class “A” road

154

Table 4.11 Predicted fatigue life and ISO 2631 weighted

acceleration from highway road

154

Table 4.12 F-test for vibration-life regression analysis 160

Table 4.13 t-test of vibration-life datasets for various

approaches

160

Table 4.14 Standardised coefficients of independent

variables

161

Table 4.15 Coffin-Manson MLR-based fatigue life

predictions

165

Table 4.16 Morrow MLR-based fatigue life predictions 165

Table 4.17 SWT MLR-based fatigue life predictions 165

Table 4.18 F-test of fatigue-vibration datasets for various

approaches

169

Table 4.19 t-test of fatigue-vibration datasets for various

approaches

169

Table 4.20 Coffin-Manson MLR predicted ISO 2631

vertical vibrations

173

Table 4.21 Morrow MLR predicted ISO 2631 vertical

vibrations

173

Table 4.22 SWT MLR predicted ISO 2631 vertical

vibrations

174

Table 4.23 R2 value for all approaches with single hidden

layer ANN

180

Table 4.24 MSE for various approaches and datasets with

single hidden layer ANN

180

Table 4.25 R2 value for all approaches with two hidden

layers ANN

184


two hidden layers ANN

184

xi

Table 4.27 R2 value for all approaches with three hidden

layers ANN

188


three hidden layer ANN

188

Table 4.29 The best performance ANN architecture for

vibration-life predictions

191

Table 4.30 MLR and ANN predicted Coffin-Manson

fatigue lives

191

Table 4.31 MLR and ANN predicted Morrow fatigue lives 192

Table 4.32 MLR and ANN predicted SWT fatigue lives 192

Table 4.33 MSE for different trained vibration prediction

ANN

200

Table 4.34 MLR and ANN Coffin-Manson predicted ISO

2631 vertical vibration

203

Table 4.35 MLR and ANN Morrow predicted ISO 2631

vertical vibration

204

Table 4.36 MLR and ANN SWT predicted ISO 2631

vertical vibration

204

Table 4.37 Difference between experimental and MLR

vibration-life prediction for Coffin-Manson

datasets

211


vibration-life prediction for Morrow datasets

211


vibration-life prediction for SWT datasets

211

Table 4.40 Difference between experimental and ANN

vibration-life prediction for Coffin-Manson

datasets

215


vibration-life prediction for Morrow datasets

216


vibration-life prediction for SWT datasets

216

xii

LIST OF FIGURES

NO. FIGURE PAGE

Figure 2.1 Solid axle dependent suspension 13

Figure 2.2 Types of independent suspension system: (a)

Macpherson strut, (b) double wishbone, (c)

multi-link, (d) trailing arm

14

Figure 2.3 Schematic diagram of a quarter car model

under road excitation

15

Figure 2.4 Schematic diagram of spring: (a) uniaxially

loaded spring, (b) free body diagram

16

Figure 2.5 Mechanism of a damper: (a) rebound, (b)

compression, (c) hysteresis loop

17

Figure 2.6 Schematic diagram of a tyre model based on a

linear spring damper with SAE coordinate

system

18

Figure 2.7 Mechanism of a lower arm: (a) initial

condition, (b) when wheel is hitting a bump

19

Figure 2.8 Chronology of spring materials development 22

Figure 2.9 Accident investigation due to leaf spring

failure: (a) scene of accident, (b) damaged leaf

spring

25

Figure 2.10 V cycle fatigue design for automotive

suspension system

25

Figure 2.11 “Five Box Trick” durability model 27

Figure 2.12 Classification of signals 28

Figure 2.13 Representation of CAL in different forms: (a)

time series, (b) peak-valley reversals

29

Figure 2.14 Representation of VAL in different forms: (a)

time series, (b) peak-valley reversals

31

Figure 2.15 Strain signals at different mean values: (a)

SAEBKT with zero mean value, (b) SAESUS

with negative mean value, (c) SAETRN with

positive mean

32

Figure 2.16 Rainflow cycle counting algorithm: (a) – (f)

sequence of the method, (g) cycles derived

from Rainflow cycle counting method

35

Figure 2.17 Typical S-N curve of steel 37

Figure 2.18 A typical ɛ-N curve of steel 38

xiii

Figure 2.19 Procedures for Palmgren-Miner damage

summation

43

Figure 2.20 Vehicle ride dyanmic system 44

Figure 2.21 Example of profilometer measured road

roughness profile

47

Figure 2.22 PSD as a function of spatial frequency of

various classes of road

49

Figure 2.23 Input and output of a linear vehicle system 50

Figure 2.24 Schematic diagram of a 2 D.O.F quarter car

model

52

Figure 2.25 Group of data mining technique 57

Figure 2.26 A basic model of a single node ANN 65

Figure 2.27 An example of multilayer feed forward ANN

architecture

66

Figure 2.28 Residuals normality assessment graph: (a)

error histogram, (b) scatter plot

68

Figure 2.29 Schematic diagram of scatter band for fatigue

life using generated data

69

Figure 2.30 Schematic diagram of correlation between

prediction and experimental data

70

Figure 3.1 Part 1: Process flow of the research

methodology

73

Figure 3.2 Part 2: Process flow of the research

methodology

74

Figure 3.3 CAD of the coil spring 75

Figure 3.4 Experimental setup for strain and acceleration

signals collection

80

Figure 3.5 Highway road conditions: (a) road preview, (b)

route map

81

Figure 3.6 UKM campus road conditions: (a) road

preview, (b) route map

81

Figure 3.7 Hilly road conditions: (a) road preview, (b)

route map

81

Figure 3.8 Residential road conditions: (a) road preview,

(b) route map

82

Figure 3.9 Rural road conditions: (a) road preview, (b)

route map

82

xiv

Figure 3.10 Flowchart for statistical analysis using

Glyphworks®

83

Figure 3.11 Flowchart for spectrum analysis using

Glyphworks®

84

Figure 3.12 Flowchart for nCode Glyphwork®-based strain

life fatigue assessment

85

Figure 3.13 Procedures for ISO 2631 vibration assessment 86

Figure 3.14 Procedures for ISO 8608 road profile

generation

90

Figure 3.15 Setup of quarter car model in SimulationX®:

(a) diagram view, (b) 3D view

94

Figure 3.16 CAD of Macpherson un-sprung mass

components: (a) rim, (b) brake caliper, (c) disc

brake, (d) hub, (e) knuckle, (d) lower arm

95

Figure 3.17 Procedures for quarter car model simulation 96

Figure 3.18 Spring fatigue life prediction using nCode

DesignLife®

99

Figure 3.19 Process flow for establishment multiple linear

regression

100

Figure 3.20 Flowchart to determine single hidden layer

ANN architecture with the lowest MSE

103

Figure 3.21 Flowchart to determine two hidden layer ANN

architecture with the lowest MSE

104

Figure 3.22 Flowchart to determine three hidden layer

ANN architecture with the lowest MSE

106

Figure 3.23 ANN architecture for optimised Coffin-

Manson vibration-life predictions

108

Figure 3.24 Validation of the established multiple linear

regression

109

Figure 3.25 Validation of the ANN predictions 110

Figure 3.26 Process flow for validation of the ANN

predictions

112

Figure 4.1 Stress distribution of the coil spring under

axial loading

116

Figure 4.2 Stress distribution of the coil spring under

combination of axial and torsional loading

116

Figure 4.3 Fatigue life contour of the coil spring 117

xv

Figure 4.4 Strain time histories of spring collected from

various road conditions: (a) highway, (b)

campus, (c) hill, (d) residential, (e) rural

118

Figure 4.5 Time histories of the measured acceleration

from lower arm under various roads: (a)

highway, (b) campus, (c) hill, (d) residential,

(e) rural

120

Figure 4.6 Time histories of the measured acceleration

from top mount under various roads: (a)

highway, (b) campus, (c) hill, (d) residential,

(e) rural

121

Figure 4.7 Damage histogram of spring strain time history

under highway road using various strain life

approaches: (a) Coffin-Manson, (b) Morrow,

(c) SWT

124


under UKM campus road using various strain

life approaches: (a) Coffin-Manson, (b)

Morrow, (c) SWT

125


under hilly road using various strain life


(c) SWT

126


under residential road using various strain life


(c) SWT

127


under rural road using various strain life


(c) SWT

128

Figure 4.12 PSD of collected strain and acceleration time

histories for various roads: (a) highway, (b)

campus, (c) hill, (d) residential, (e) rural

131

Figure 4.13 Correlation of spring fatigue life and ISO 2631

vertical vibration in power form

133

Figure 4.14 Correlation of spring fatigue life and ISO 2631

vertical vibrations in linear form

135

Figure 4.15 Correlation analysis for fatigue life using

various fatigue approaches: (a) Coffin-

Manson, (b) Morrow, (c) SWT

137

Figure 4.16 Classification of measured road profile

according to ISO 8608

138

xvi

Figure 4.17 ISO 8608 road profile in form of spatial

frequency for generated road classes: (a) class

A, (b) class B, (c) class C, (d) class D

140

Figure 4.18 ISO 8608 road profile in form of temporal

frequency for various road classes: (a) class A,

(b) class B, (c) class C, (d) class D

141

Figure 4.19 Simulated force time histories under road class

“A” for different spring stiffness: (a) k14, (b)

k16, (c) k18, (d) k20, (e) k22, (f) k24, (g) k26,

(h) k28, (i) k30, (j) k32

143

Figure 4.20 Simulated acceleration time histories under

road class “A” for different spring stiffness: (a)

k14, (b) k16, (c) k18, (d) k20, (e) k22, (f) k24,

(g) k26, (h) k28, (i) k30, (j) k32

146

Figure 4.21 Simulated force time histories under highway

road for different spring stiffness: (a) k14, (b)

k16, (c) k18, (d) k20, (e) k22, (f) k24, (g) k26,

(h) k28, (i) k30, (j) k32

148

Figure 4.22 Simulated acceleration time histories under

highway road for different spring stiffness: (a)

k14, (b) k16, (c) k18, (d) k20, (e) k22, (f) k24,

(g) k26, (h) k28, (i) k30, (j) k32

150

Figure 4.23 Spring design variants with different bar

diameter

152

Figure 4.24 Multiple linear regression for fatigue life

prediction using various approaches: (a)

Coffin-Manson, (b) Morrow, (c) SWT

157

Figure 4.25 Normal Probability-Probability plot of

vibration-life regression standardised residual

for various approaches: (a) Coffin-Manson, (b)

Morrow, (c) SWT

162

Figure 4.26 Error histogram of vibration-life regression

standardised residual for various approaches:

(a) Coffin- Manson, (b) Morrow, (c) SWT

163

Figure 4.27 Scatter plot of vibration-life regression



164

Figure 4.28 Correlation analysis of MLR fatigue life: (a)


166

Figure 4.29 Response surface plot for ISO 2631 vertical

vibration prediction using various approaches:

(a) Coffin-Manson, (b) Morrow, (c) SWT

168

xvii

Figure 4.30 Normal Probability-Probability plot of

vibration regression standardised residual for

various approaches: (a) Coffin-Manson, (b)

Morrow, (c) SWT

171

Figure 4.31 Error histogram of vibration regression



172

Figure 4.32 Scatter plot of vibration prediction regression



172

Figure 4.33 MSE of trained neural network with single

hidden layer for various approaches: (a)


178

Figure 4.34 Curve fitting of trained Coffin-Manson

vibration-life ANN approach with single

hidden layer for various datasets: (a) all, (b)

training, (c) validation, (d) ANN test

179

Figure 4.35 Error histogram of single hidden layer

vibration-life ANN for various approaches: (a)


181

Figure 4.36 MSE of trained vibration-life ANN with two

hidden layers for various approaches: (a)


183


vibration-life ANN with two hidden layers for

various datasets: (a) all, (b) training, (c)

validation, (d) ANN test

184

Figure 4.38 Error histogram of two hidden layers



185

Figure 4.39 MSE of trained Coffin-Manson vibration-life

ANN first hidden layer with various number of

neurons: (a) 1, (b) 2, (c) 3, (d) 4, (e) 5, (f) 6, (g)

7, (h) 8, (i) 9, (j) 10

187


vibration-life ANN with three hidden layers

for various datasets: (a) all, (b) training, (c)

validation, (d) ANN test

189

Figure 4.41 Error histogram of three hidden layers



190

xviii

Figure 4.42 Correlation curve for Coffin-Manson target

fatigue life using various approaches: (a)

ANN, (b) MLR

194

Figure 4.43 Correlation curve for Morrow target fatigue

life using various approaches: (a) ANN, (b)

MLR

195

Figure 4.44 Correlation curve for SWT target fatigue life

using various approaches: (a) ANN, (b) MLR

196

Figure 4.45 Linear regression analysis for prediction and

target Coffin-Manson fatigue life using

various approaches

197


target Morrow fatigue life using various

approaches: (a) ANN, (b) MLR

198


target SWT fatigue life using various


199

Figure 4.48 Curve fitting of trained vibration prediction

ANN for various approaches: (a) Coffin-

Manson, (b) Morrow, (c) SWT

202

Figure 4.49 Error histogram of three hidden layers

vibration prediction ANN for various


(c) SWT

203

Figure 4.50 Correlation between Coffin-Manson predicted

and target vertical vibration using various


206

Figure 4.51 Correlation between Morrow predicted and

target vertical vibration using various


207

Figure 4.52 Correlation between SWT predicted and target

vertical vibration using various approaches: (a)

ANN, (b) MLR

208

Figure 4.53 Correlation curve for three vibration-life

regressions: (a) Coffin-Manson, (b) Morrow,

(c) SWT

210

Figure 4.54 Difference between prediction and experiment

ISO 2631 vertical vibration for various

approaches

212

xix

Figure 4.55 Correlation curve of three vibration-life ANN

prediction and target fatigue life using various


(c) SWT

214

Figure 4.56 Difference between prediction and experiment

ISO 2631 vertical vibration for various strain

life approaches

216

xx

LIST OF ABBREVIATIONS

r.m.s Root mean square

FFT Fast Fourier transform

PSD Power spectral density

VAL Variable amplitude loadings

D.O.F Degree of freedom

S-N Stress-life

b Fatigue strength exponent

c Fatigue ductility exponent

ɛ-N Strain-life

ɛ’f Fatigue ductility coefficient

σ’f Fatigue strength coefficient

E Modulus elasticity

L Spring coil diameter

d spring bar diameter

Di Accumulated fatigue damage

R Stress ratio

σ Stress

V Vehicle speed

fc Centre frequency

m Sprung mass

Aw Frequency weighted acceleration

Wk ISO 2631 vertical weighting factor

r Pearson coefficient

R2 Coefficient of determination

ISO International Standardisation Organisation

MLR Multiple linear regression

ANN Artificial neural network

MSE Mean square error

Sf Tangent sigmoid activation function

VIF Variance inflation factor

ANOVA Analysis of variance

xxi

RMSE Root mean square error

SWT Smith-Watson-Topper

a Regression coefficient

br Regression exponent

NCM_power Power regression predicted Coffin-Manson fatigue life

NMorrow_power Power regression predicted Morrow fatigue life

NSWT_power Power regression predicted SWT fatigue life

Wa ISO 2631 vertical weighted acceleration

NCM_linear Linear regression predicted Coffin-Manson fatigue life

NMorrow_linear Linear regression predicted Morrow fatigue life

NSWT_linear Linear regression predicted SWT fatigue life

k ISO 8608 proposed road waviness

QCM Quarter car model

Pn ANN prediction outcome

f Sigmoidal activation function

NCM_MLR Multiple linear regression predicted Coffin-Manson fatigue life

NMorrow_MLR Multiple linear regression predicted Morrow fatigue life

NSWT_MLR Multiple linear regression predicted SWT fatigue life

Suspension natural frequency

ISO 2631 vertical acceleration input

P-P Probability-Probability

Wij Weights for ANN

Bij Biases for ANN

ks Spring stiffness

SAE Society of Automotive Engineers

1

CHAPTER I

INTRODUCTION

1.1 OVERVIEW OF FATIGUE LIFE ASSESSMENT

Mechanical failures have caused many injuries and property losses. However, the

mechanical failures can only be minimised rather than eliminated. Large numbers of

properly designed mechanical components and structures have successfully minimised

the mechanical failure of mechanical structures, such as aircraft (Zhu, Zhang & Xia

2015), turbines (Song et al. 2017), automotive dampers (Coutinho, Landre, &

Magalhaes 2016). There is a category of mechanical failure that is caused by continuous

loads, either constant or variable, causing the loss of material ductility, cracks, and

failure of a component (Ye, Su & Han 2014). Such failure is known as fatigue failure.

At least half of the mechanical failures are due to fatigue (Dowling 2004; Ye,

Su & Han, 2014). Fatigue failure does not only cause loss of property but also leads to

catastrophic accidents that may cost lives. Hence, it is important to understand the

chronology and recent development of fatigue analysis to perform a durable product

design. The concept of fatigue failure was properly addressed in 1850 when a German

engineer, August Wöhler, first introduced a stress-life (S-N) curve using smooth

cylindrical specimens under constant loadings. The proposed S-N curve has proven as

a great step towards understanding the materials fatigue properties (Liu et al. 2016).

Another significant contribution was the invention of a force measurement tool to

measure service loads of a freight passenger vehicle. A zinc plate with lever mechanism

was designed and attached to the freight vehicle for axle deflection measurement. The

project successfully measured the deflection signal of the freight vehicle for 22,000 km

between Breslau and Berlin. This measurement has led to the future invention of strain

2

gauges. A strain gauge is an electronic device used to measure the strain value of a

component under dynamic conditions and regarded as very useful for fatigue life

analysis (Xia & Quail 2016).

During the operating conditions, most of the mechanical components are

exposed to vibration loadings in which the loadings were randomly set at varying mean

stresses (Repetto & Torrielli 2017). Such conditions require the use of a strain gauge to

measure the strain while identifying the mean stresses. W. Gerber in 1874 proposed a

parabolic method to model the boundary line for mean stress corrections in order to

measure the mean stresses. In 1910, Basquin transformed the finite life region of

Wöhler’s curve into log form. Gerber’s model was then modified by J. Goodman and

C.R. Soderberg, as reported by Zhu et al. (2016). The mean stress correction models

were normally applied together in S-N fatigue analysis. However, the S-N method

neglected the difference of stress-strain behaviour between monotonic and cyclic

loadings which deviated from the real fatigue behaviour.

Due to the shortfall, the Bauschinger effect was introduced by J. Bauschinger

which highlighted the changing material’s elastic limit after repeated cyclic loading (Hu

et al. 2016). The Bauschinger effect also mentioned the cyclic hardening and softening

underwent by the material under cyclic loading which led to the development of the

Coffin-Manson model in 1954. The Coffin-Manson model is a strain life model which

explains the fatigue crack growth in terms plastic strain. The establishment of Basquin

model, Bauschinger effects and Coffin-Manson model have further contributed to the

development of the Morrow model in 1968 and the Smith-Watson-Topper model in

1970 which considered the non-zero mean stress effects.

The earliest cycle counting algorithm for fatigue life prediction was first

introduced in 1955. Nevertheless, the most popular cycle counting method was the

rainflow cycle counting method developed by M. Matsuishi and T. Endo in 1968. This

robust method enables the reduction of complex varying spectrum into a set of simple

stress reversals. The simplified stress reversals were adopted into Palmgren-Miner

linear cumulative fatigue damage rule in the estimation of components’ fatigue life

when subjected to complex loading. Fatigue testing of a component using the repeating

3

strain time histories is time consuming as the loadings need to be continuously applied

on the specimen until failure occurs (Stanzl-Tschegg 2014). The fatigue test could be

accelerated by transforming the strain time histories into frequency domain using a

transfer function (Mrnik, Slavic & Boltezar 2016).

The importance of fatigue analysis has prompted many industries to perform

fatigue studies in their product designs. Industries which utilised fatigue analyses

include automotive (Coutinho, Landre & Magalhaes 2016), aviation (Zhu, Zhang & Xia

2015), and offshore industry (Song et al. 2017). Nevertheless, it was proven difficult to

have a general model (Ye, Su & Han 2014) due to the complexity of fatigue phenomena.

In aviation industry, the aircrafts are exposed to aerodynamics or turbulences while

offshore components are subjected to vibrations caused by ocean waves. Meanwhile,

the analysis for automotive vehicles is often subjected to variable driving conditions

such as the users and the driving environments. Dynamic driving environment may end

with failure caused by fatigue during their operations and these dynamical properties

are heavily influenced by its suspension system design.

1.2 DURABILITY OF AUTOMOTIVE SUSPENSION SYSTEMS

Durability of an automotive component is influenced by many factors namely the

manufacturing process and design. Most of the automotive mechanical components

were treated with heat treatment or shot peening process to prolong its fatigue life before

being released to the market (Fragoudakis et al. 2014). The treatment is necessary

because a passenger car is regarded as a complex dynamical system that travels on the

ground. Response of the vehicle depends mostly on the collision and contact of tyres

towards the road surfaces which may change rapidly. The dynamic interaction induces

a certain amount of vibration to the vehicle components and causes the components to

fail. Hence, the relevant manufacturing process associated with fatigue failure causing

vibrations must be considered during the design stage of automotive components

(Moon, Chu & Yoon 2011).

Sources of vibration in a vehicle originate from engine, driveline and road

excitations (Pandra 2016). Road induced vibration is the most critical cause for

4

component fatigue (Dimitris 2016). In such a case, isolation of road induced vibration

is advantageous. Thus, a system for automotive vehicles was established to isolate the

road vibrations, known as suspension system. A suspension system does not only serve

to filter road disturbances and provide ride comfort, but also reduces the probability of

fatigue failure among the supported automotive components. In general, a suspension

system consists of a set of spring damper which supports the car body and allows the

wheel to translate in vertical direction. Although the tyre is also a part of the suspension

system, it is regarded as a tear and wear component in which periodic change of the

component is required (Ganjian, Khorami & Maghsoudi 2009). Constant inspection on

the tyre draws more attentions on spring fatigue analysis because the spring is expected

to last until the end of its durability targeted warranty period for at most six years

(Huang, Huang & Ho 2017).

When the wheel travels across uneven terrain, the spring is compressed or

expanded to absorb the vibration energy. Hence, the spring will interactively react to

the road profiles. During the spring compression, the spring experiences principal stress

in various directions due to its circular geometry. The complex stress state complicates

the fatigue analysis process. In order to analyse the coil spring fatigue characteristics,

experimental testing using a fatigue testing machine was performed (Pyttel et al. 2014).

The research investigated the effects of material state and spring wire diameter of coil

springs on fatigue life. In the research, a total of 1400 springs were utilised to study the

spring fatigue parameters. The spring fatigue test is a destructive test considering the

spring to be destroyed during the experiment. Hence, the experiment was deemed as

very cost ineffective and the number of samples could be reduced with a good fatigue

simulation tool.

Fatigue simulation is a very convenient tool to predict spring fatigue life when

all the relevant information for fatigue prediction are available. The information

includes material cyclic properties, loading time histories and a fatigue model. Kamal

and Rahman (2014) conducted a fatigue prediction of automotive coil spring using

strain life approach with a SAESUS loading time history to obtain an approximate

fatigue life prediction. The analyses also provide the fatigue results of the spring under

different stress states. Sedlák et al. (2014) investigated the complex stress state of a

5

spring in relation to material phase composition and fatigue resistance. However,

realistic loading time histories are needed to obtain a good fatigue simulation result of

a spring. When the actual measurement is not available, simple life testing for

components is applied by using constant amplitude loading (CAL) or block cycle testing

test that are similar to the test conducted by most automotive component manufacturers

on their products (Giannakis, Malikoutsakis & Savaidis 2016).

Understanding the importance of time history measurement towards spring

fatigue analysis, Putra (2016) proposed a novel acceleration to strain conversion using

a simulation approach. The strain time histories of a spring could be obtained from

acceleration measurements while acceleration time histories could be converted into

strain time histories. Strain time histories were usually used to predict the fatigue life of

spring while acceleration time histories were used to obtain an indicator for vehicle ride

comfort. Pawar Prasant and Saraf (2009) performed an analysis on vehicle ride and

durability based on a new system to measure a road profile. In their research, they

pointed out that both vehicle durability and ride were mainly based on the road profile

excitations.

Road excitation does not only cause fatigue to a vehicle coil spring, but also

affects the ride quality. Rough road conditions contribute to less comfortable vehicle

ride. However, it is impossible to change the road conditions in order to improve the

vehicle ride. Hence, the suspension system is designed to compensate with the

vibrations caused by the road conditions (Mitra & Benerjee 2015). A quarter car model

was constructed to simulate the vehicle ride. Vehicle vertical acceleration amplitudes

that are generated by a series of spring stiffness and damping coefficient values were

determined in order to propose an optimised parameter. Thite (2012) proposed a method

to refine a vehicle quarter model for ride analysis. A simplified equation was developed

to estimate the damping effects towards vehicle ride.

Since road profiles are the key component to vehicle ride and durability, efforts

to reconstruct the road defects and roughness were performed using artificial neural

networks (Ngwangwa et al. 2014). Three sprung mass vertical accelerations for ride

analyses were used to train a neural network model for a road profile estimation. A set

6

of measurement data was used for the neural network model validation. On the other

hand, Paraforos, Griepentrog and Vougioukas (2016) developed a sensor frame to

acquire road and field profiles in absolute geo-referenced coordinate for agricultural

machine hitch fatigue life prediction. Based on these two recent literature studies,

different modelling methods were proposed to predict vehicle ride and durability using

a generated road profile with consideration of the vehicle suspension systems. Although

the modelling methods are different, the concept consistently aims to provide faster

solution to durability or ride analysis.

1.3 PROBLEM STATEMENTS

Nowadays, car buyers do not only demand for a durable vehicle system but also request

for excellent riding characteristics. Automotive industries have been focusing much

attention to satisfy the customers’ needs in the quest to sustain their competency.

Henceforth, a good automotive suspension design is compulsory to achieve this target.

Unfortunately, the automotive suspension design process is a time-consuming process

which entails selecting the appropriate vehicle level target, system architecture, hard

points, bushing rates, suspension load analysis, spring rates, shock absorber

characteristics, structure integrity on each component, and analysis on the vehicle

dynamics of the design results (Saurabh et al. 2016). Each of these steps involves many

human efforts, time and resources to ensure the suspension design is sufficient to

withstand the repeated road vibrations without premature failure while providing good

vehicle ride characteristics.

Vehicle vertical vibration contributes the most to vehicle ride performance

(Shao, Xu & Liu 2018). Recent literature highlighted the potential redundancy caused

by the separate suspension analyses on the durability and vertical vibration analysis of

an automotive. Upon the completion of suspension structure integrity analysis, the

effects of suspension design towards vehicle ride dynamic were analysed to ensure they

provide good ride characteristics. Therefore, Scheiblegger et al. (2017) utilised hydro

mounts in a car simulation model to obtain durability loads for ride and durability

analyses. The proposed method has a drawback as the modelling is complex and every

tuning on the suspension generates a new transfer function. These processes need to be

7

repeated until both the fatigues strength of the suspension components and ride

dynamics are balanced to achieve optimal design. This repeating process is time

consuming and produces little engineering value. After all, there is still the possibility

of unavailability or error in the simulation or measurement that may hinder analysis of

the desired results (Gu 2017). In a worst-case scenario, it may cause a delay of product

launching and affect the reputation of the company.

It is significant to have a robust and simple method to quickly perform the design

analysis and serve as a guideline to reduce unnecessary works. In addition, all the

valuable durability test data for old vehicle variants were wasted after investing lots of

workmanships and monetary costs. The problem that arises now is how to allow the

information from actual vehicle generation to be used in the next vehicle generation so

that the development process would not be repeated. Eventually, the complete solution

for this issue has not yet been found. Although the road load analysis was extensively

conducted, the ride dynamics were not considered in the integrity structure which were

closely related to suspension components. Hence, there is a need to determine the

relationship between ride comfort and durability of an automobile suspension design

for design assistances. To the best of the author’s knowledge, no solution was offered

to solve this matter which leads to the contribution of this research.

1.4 RESEARCH OBJECTIVES

The aim of the current research is to establish an automotive spring durability

relationship for vehicle ISO 2631 vertical vibration prediction with the consideration of

road surface profiles. Several specific objectives have been determined to achieve the

aim of the research. The specific objectives are as follows:

1. To determine a multiple input durability relationship that predicts the vehicle

ISO 2631-1 weighted vertical vibration using quarter car model simulations with

different spring stiffness variants.

2. To establish the fatigue life predictions using multilayer perceptron artificial

neural network through the determination of the architecture with the lowest

mean square error.

8

3. To validate the durability characteristic with ISO 2631-1 weighted vertical

vibration using actual vehicle measurement data.

1.5 SCOPE OF WORK

This study focuses on mathematical analysis of developed spring durability relationship

for automotive ISO 2631 vertical vibration. The scope is defined according to the three

objectives:

Objective 1: A computer aided software is used to model the coil spring while a

finite element (FE) software is applied to determine the stress-strain

characteristics of the coil spring. Strain signals are measured at the

point with the highest stress of the actual spring while acceleration

signals are measured at the vehicle lower arm using two different

data acquisition systems. The strain signals are used to calculate the

spring fatigue life using strain life models while acceleration signals

are used to obtain ISO 2631 vertical vibration. A multi component

kinematic quarter car model is created and simulated using road

input. Altering the spring stiffness provides a series of spring

variants associated with fatigue and ISO 2631 vertical vibrations.

The parameters are graded using power and multiple linear

regression approaches. The goodness of relationship between the

parameters and normality of the residuals are analysed using

statistical approaches.

Objective 2: To optimise the fatigue life prediction, an artificial intelligence is

used with the neurons ranging from one to ten and the hidden layers

up to three. A looping process is implemented to find the optimised

artificial intelligent in which the artificial intelligent with the lowest

mean squared error (MSE) was determined. The goodness of fitting

for artificial intelligent is analysed using statistical parameters

including the coefficient of determination and residuals. In addition,

9

the normality of the residual is tested using a suitable statistical

approach.

Objective 3: The regression relationships and artificial intelligence are validated

using strain and acceleration measurement data from an actual

vehicle running on different roads. The fatigue life prediction

relationship is subsequently validated via a conservative fatigue life

correlation method. Meanwhile, the ISO 2631 vertical vibrations are

validated using experimental acceleration data. Errors of the

outcome are analysed to ensure the accuracy of the regression as the

results contribute to the overall body of knowledge.

1.6 RESEARCH HYPOTHESES

Prior to the research works, several hypotheses related to the objectives have been

identified as follows:

Hypothesis 1: If the suspension frequencies, ISO 2631 vertical vibrations and

spring fatigue lives are related to each other, then the established

regressions possess high coefficients of determination and low

mean squared error values.

Hypothesis 2: If a suitable artificial intelligence was applied, then the performance

of predictions in terms of mean square error shall be improved.

Hypothesis 3: If a set of independent validation data fits nicely into the created

solutions, the solutions could be used to estimate the spring fatigue

behaviour with acceptable accuracy.

1.7 SIGNIFICANCE OF RESEARCH

This research contributes new understandings to several branches of mechanical

engineering such as durability, vehicle dynamics, artificial intelligence or machine

10

learning, mechanical design, and engineering mathematics. This research presents a

development of a durability relationship for automotive vertical vibrations according to

ISO 2631 standard. Firstly, the durability of the automotive spring was assessed using

different road conditions. The road profile measurement data are precious and

significant for a realistic fatigue life prediction. Without these measurements, the

fatigue assessment of springs could only be performed using constant amplitude (CA)

tests which are much deviated from the actual environment. Secondly, the relative

vehicle ISO 2631 vertical vibration was also performed. It is also important to know the

quality of the current suspension design in providing road excitation filtering.

In addition, this research bridges the gap between spring durability and vehicle

ride dynamics using an artificial intelligence modelling method. A series of neural

network architectures have been proposed throughout the modelling process. The

application of neural network to find these parameters is novel and serves as a new

contribution to knowledge. For application, the process to design a suspension spring

with good durability and vertical vibration characteristics is time consuming and

requires lots of efforts. Therefore, this prediction of durability and ride characteristic

for automotive suspension is crucial to shorten the time frame because no simulation

model is needed. The established relationship usage is quite user friendly and the results

could be interpreted immediately, hence the prediction results are always robust. The

generated prediction relationships with acceptable accuracy are the novel and main

contribution of this research.

11

CHAPTER II

LITERATURE OVERVIEW

2.1 INTRODUCTION

This chapter presents the relevant theory and research trends according to the current

research scope and topic that are related directly to the literature of automotive

suspension system. The mechanisms of different suspension systems were reviewed by

focusing on coil spring designs and characteristics which served as the main case study

component of this research. As coil spring design plays a key role in vehicle component

durability and automobile ride, the discussions concentrate on durability analysis which

is the main parameter of this research. The trends of coil spring failure from 2009 to

2012 reported by the British motoring company, the automotive association is listed in

Appendix A. The first discussion deliberates on the various types of loading signals

that contribute to automobile fatigue life, followed by cycle counting methods, fatigue

life analysis and damage cumulative rule. The suitable fatigue life models for

determining automobile suspension component analysis are also highlighted.

In the following section, ride related vertical vibrations of an automobile

involving road roughness excitations, simulation models and vibration standards were

reviewed. A contemporary design of coil spring significantly affects the automobile

vertical vibration and its fatigue life because of varying suspension mechanisms. In

order to have an insight on the direct relationship between spring fatigue life and vertical

vibration to the mechanism of automotive suspension system, the following section

focuses on the data analysis method which serve as a connecting medium to bridge those

parameters. The data analysis section studies the trends of recent methods in regression

modelling and data mining techniques which also includes neural network analysis.

12

Validation of the regression residuals such as normality test and scatter band approach

are also literally studied. Lastly, the summary of this chapter is provided in Section 2.6.

2.2 AUTOMOTIVE SUSPENSION SYSTEM

2.2.1 Types of Automotive Suspension Systems

Developments of automotive suspension system have drastically increased over the

years. Continuous developments have been conducted on all types of suspension

systems. The suspension systems could be classified into three classes which are active,

semi-active and passive. An active suspension system consists of coil spring and damper

which could dissipate or add energy to the system in a controllable way while semi-

active suspension systems allow variable damping with a fixed spring characteristic

(Pionke & Bocik 2011). Nevertheless, the most widely used suspension system is the

simplest passive suspension system due to its simplicity (Rizvi et al. 2016) whereby a

passive suspension system consists of a pair of spring and damper with predefined

characteristics. For the advance suspension system, Mercedes Benz utilised a

suspension system with continuous variable damping while the Porsche Panamera

implemented air springs for varying spring and damper characteristics (Aboud, Haris,

Yaacob 2014).

In general, passive suspension systems could be categorised into three groups

which are dependent, semi-dependent and independent. Wheel motion of a dependent

suspension system depends on the motion of its partner on the other side of the wheel

as both the right and left wheel are attached to a same solid axle. When one wheel of

the dependent suspension hits a bump, its upward movement causes a slight tilt of the

other wheel. One of the most well-known dependent suspensions is Hotchkiss

suspension system as shown in Figure 2.1 (Jazar 2014). Advantages of this dependent

passive suspension are its ability to assure constant camber that is suitable for heavy

load vehicles. For a semi-dependent suspension, rigid connections between a pair of

wheel are replaced by a compliant link. An example of this type of suspension system

is a trailing twist axle suspension. The main difference between dependent and semi-

13

dependent suspension systems is the number of compliant links which are connected to

the left and right wheels.

For an independent suspension system, wheels on the same axle could move

independently of each other. Independent suspension systems are beneficial in

packaging and provide greater design freedom compared to dependent suspension

system. The most well-known examples of independent suspension system are

Macpherson strut, double wishbone, multilink and trailing arm as shown in Figure 2.2.

A Macpherson strut consists of one strut with a combination of spring and shock

absorber and connects the wheel to the frame of a vehicle. The Macpherson suspension

system is recognised for its lightweight and compact size as well as lower cost because

it comprises lesser components (Purushotham 2013).

Figure 2.1 Solid axle dependent suspension system

Source: Jazar 2014

Double wishbone and multilink suspension systems provide greater

performance and adjustability compared to the Macpherson suspension system

(Purushotham 2013). The double wishbone suspension system usually possesses two

lateral unequal length control arms along with a coil spring and shock absorber as shown

in Figure 2.2(a). On the other hand, the multilink suspension utilises a five-link

mechanism with five connecting links as shown in Figure 2.2(c). As the number of

connecting point increases, the design parameters also increase and prompt the dynamic

and kinematic complexity of the suspension system which is actually good for handling

properties (Yarmohamadi & Berbyuk 2013).

14

However, a higher number of links may increase the cost due to the additional

components. Trailing arm is widely applied in heavy vehicle such as military trucks due

to the existence of solid axle in the vehicle (Naeem & Jagtap 2017) and usually applied

by connecting an axle to pivot point as shown in Figure 2.2(d). Selection of suitable

suspension system type is based on vehicle type, performance target and allocated costs.

Selecting an appropriate suspension system for vehicle design requires thorough

understanding on the mechanism of suspension.

(a) (b)

(c) (d)

Figure 2.2 Types of independent suspension system: (a) MacPherson strut, (b) double wishbone,

(c) multi-link, (d) trailing arm

Source: Jazar 2014

2.2.2 Mechanism of Suspension Components

The mechanism of a suspension system is used to specify the kinematics of the wheel

in vertical and lateral movements when the vehicle is travelling on a road. When the

wheels of the vehicle travel across different terrains, uneven road surfaces will cause

the wheel to move up and down, as shown in the schematic diagram in Figure 2.3. In

Figure 2.3, Z is the vehicle body response, c is the damper’s damping coefficient, and

Zg is the road surface excitation. Movements of the wheels are perpendicular to the road

15

surface. Movement of the wheel is carried on a reflection which further stretch or

compress the coil spring of the suspension system. The spring absorbs the energy and

then releases it gradually. The remaining excitation loads are then transmitted to the

vehicle body and create a body dynamic response. This mechanism is the same for most

suspension systems in filtering road disturbances.

Figure 2.3 Schematic diagram of a quarter car model under road excitations

Source: Blundell & Harty 2004

When the wheel moves, the attached coil spring moves relatively to the wheel.

The relationship between spring and wheel displacement is known as motion ratio (MR)

(Uberti et al. 2015). Bhatt (2010) suggested to maintain the MR value of a vehicle at

one to ensure the sustainability of the vehicle balance during roll for the frontal

suspension. Since the tyre was modelled as linear spring element and connected in series

to the coil spring and hence, the ride rate (kr) could be defined as follows (Cao, Rakheja

& Su 2008):

kr = kskt

(ks+ kt) (2.1)

A coil spring is also known as helical spring and compressed when pressure is applied.

The mechanism of spring compression is shown in Figure 2.4. When the spring is

compressed, the wire is subjected to a direct and torsional shear (T) as shown in Figure

2.4(b). For a coil spring, the fundamental of Hooke’s law is used as follows (Kreyszig

2011):

Zg

Time (s)

Z

Sprung mass Mass

s

Vehicle body response

c

Spring

and

damper Ground input

kr

16

𝑘 = 𝐹

𝑥 (2.2)

where k is the spring stiffness, F is the applied force, x is the spring displacement.

Hooke’s law is widely used in coil spring design and it exists for more than 300 years

(Choube 2016).

(a) (b)

Figure 2.4 Schematic diagram of spring: (a) uniaxially loaded spring, (b) free body

Source: Sequeira, Singh & Shetti 2016

A spring returns the mass to its original position to achieve equilibrium. When

sudden impact is imposed, the spring bounces and vibrates until all the energy is spent.

A suspension system built on springs alone is extremely bouncy and bad for ride.

Implementation of a shock absorber reduces the vibration of the coil spring because the

kinetic energy is turned into heat that could be dissipated through hydraulic fluid (Dixon

2007). Mechanism of a shock absorber could be divided into two, rebound and

compression as shown in Figure 2.5(a) & (b). The damping is usually resulted by

viscous effects. The viscous damping of a shock absorber is normally proportional to

velocity and can be defined as follows:

d = F

x (2.3)

where d is the damping coefficient and is the velocity. As shown in Figure 2.5(c), the

damping curve of a shock absorber consists of hysteresis effects due to the valve

17

compressing the oil on the damper (Cossalter et al. 2010). The positive damper force

indicating the compression of the damper while the negative damper force shows the

rebound condition of damper (Schramm, Hiller & Bardini 2014).

(a) (b)

(c)

Figure 2.5 Mechanism of a damper: (a) rebound, (b) compression, (c) hysteresis loop

Source: Skagerstand 2014; Schramm, Hiller & Bardini 2014

Besides spring and shock absorber, tyre is also an important part of automotive

suspension system, especially in the vehicle dynamic properties. Simulating the ride

properties of a vehicle requires knowledge of tyre properties. The required properties

for vehicle ride simulations are vertical stiffness and damping. Normally, the tyre is

modelled as a linear spring damper system as shown in Figure 2.6 where mt is the wheel

mass, kz is the tyre vertical stiffness, cz is the vertical damping coefficient of the tyre, P

is the contact point, δz is the vertical deflection of the tyre, Xsae is the longitudinal axis

and Zsae is the vertical axis according to the SAE coordinate system.

18

A linear spring and damper tyre model is sufficient to simulate most of passenger

vehicles (Koch et al. 2010). The tyre of a passenger car is quite lightly damped and the

running vehicle motions are usually dominated by wheel hop (Blundell & Harty 2011).

When a heavy vehicle is considered, the linear tyre model needs to be extended into

nonlinear model due to large deflection. Suspension tyre could be modelled using either

Kelvin-Voigt-type or Maxwell model. Kelvin-Voigt-type model consisted of a

Newtonian damper and Hookean elastic spring connected in parallel while Maxwell

model can be represented by a viscous damper and elastic spring connected in series.

Hackl et al. (2016) proposed that the Kelvin-Voigt model worked well with tyre under

fixed a fixed operating point but not for manoeuvre.

Figure 2.6 Schematic diagram of a tyre model based on a linear spring damper with SAE

coordinate system

Source: Blundell & Harty 2011

The control arm is a hinged suspension link between the chassis and the upright

suspension that carries the wheel. The end of the control arm to the chassis is attached

by a single pivot bushing that controls the position of the end in a single degree of

freedom (D.O.F) and maintains the radial distance from the inboard as shown in Figure

2.7. When the tyre is travelling across uneven terrain, the lower arm swings in a constant

radius and brings the movement of the wheel into an arc. The control arm plays an

important rule for vehicle stability and ride comfort where the movement of wheel is

controlled by the control arm (Mahmoodi-Kaleibar 2013). Meanwhile, Genetic

19

algorithm (GA) was proposed to find the optimised design of suspension lower arm in

terms of length to minimise the vehicle lateral force. The weight of the control arm has

also lead to some improvement on vehicle dynamics. Kim et al. (2014) proposed a

design of carbon fibre reinforced on the composite lower to reduce the suspension

weight while maintaining the strength.

(a) (b)

Figure 2.7 Mechanism of a lower arm: (a) initial condition, (b) when wheel is hitting a bump

Source: Skagerstand 2014

The purpose of suspension components is usually the same for most of the

passenger cars. However, different setup of suspension systems provides different

dynamic characteristics for the automobile. The most favourable suspension systems

are Macpherson and double wishbone suspension systems as listed in many vehicle

specifications (Kavitha et al. 2018). As reported by Purushotham (2013), Macpherson

suspension system was applied on high performance car, such as Porsche 911 and BMW

3-series. Meanwhile, many locally manufactured car also applied the Macpherson

suspension system as their vehicle front suspension system. Therefore, many studies

aimed to analysis the Macpherson suspension system design on vehicle dynamics

through simulations (Reddy et al. 2016; Kavitha et al. 2018).

20

2.2.3 Coil Spring Design and Characteristics

Both Macpherson and double wishbone suspension systems utilise a coil spring

as the main component to absorb impact. Coil spring designs are usually dependent on

the stiffness target for the designated suspension natural frequency. Meanwhile, the

maximum and minimum (Fmax, Fmin) forces acting on a spring during wheel travel are

also considered in which the force mean and amplitude (Fm, Fa) loadings could be

defined as follows (Valsange 2012):

Fm= (Fmax + Fmin)

2 (2.4)

Fa= (Fmax − Fmin)

2 (2.5)

The mean (τm) and amplitude (τa) shear stress could then be obtained as follows

(Valsange 2012):

τm = ks (8FmD

πd3

) (2.6)

τa = 𝑊𝑤𝑎ℎ𝑙 (8PaD

πd3

) (2.7)

where WWahl is the Wahl factor and ks is spring design constant and could be obtained

from the equation as below (Gandomi 2015):

ks = 1 + 0.5

C (2.8)

WWahl = 4C − 1

4C − 4 +

0.615

C (2.9)

where C is the spring index as below (Gandomi 2015):

21

C = L

d (2.10)

where L is the inner diameter of the spring and d is the spring wire diameter.

Stress distributions of coil spring designs are important for design perspective

where the design is validated. Analysis of stress distribution of coil spring has been

widely adopted in spring industry. The approximate spring design stressing for different

spring material is shown in Figure 2.8. In a review by Rathore & Joshi (2013), the FEA

method well fits the stress analysis of different kinds of coil springs. Khurd et al. (2016)

performed an FEA analysis to validate the stress levels of different coil spring designs.

Under certain assumptions, the stress and strain possessed a linear relationship known

as Hooke’s law. The linear relationship is maintained by the material within its elastic

limit. If the proposed conditions are satisfied, the following linear relationship of stress

and strain could be applied:

σ = Eε (2.11)

where E is the material modulus elasticity, σ is the stress and ε is the strain. Under linear

elastic condition, the spring could return to its original position after the load is removed.

A component design is not always linear and within elastic limit and gives rise

to the need to create a non-linear stress-strain relationship for plastic design application,

such as car body and components (Evin et al. 2014). In 1943, W. Ramberg and W.R.

Osgood proposed an equation to describe the nonlinear behaviour between stress and

strain. The original form of Ramberg-Osgood equation could be written as follows:

ε = σ

E + (

σ

K')

1

n'

(2.12)

where K’ is the cyclic strain coefficient and n’ is the cyclic strain hardening exponent.

The first part of the model defines the elastic relationship between stress and strain

while the second part defines the plasticity of material. The incremental reversals with

22

respect to a reference turning point are calculated based on Masing’s model as follows

(Lee, Barkey & Kang 2012):

∆𝜀 =∆𝜎

𝐸 + 2 (

∆𝜎

2𝐾′)

𝑛′

(2.13)

Most of the automotive components failed after damage accumulation in plastic limit

due to strain hardening effects (Upadyaya & Sridhara 2012).

Figure 2.8 Chronology of spring materials development

Source: Prawoto et al. 2008

The transition of elastic to plastic properties is known as yield. In case of simple

stress state analysis, the principle stress theory was utilised for component design

especially for brittle material. However, von Mises yield criterion is always applied

when dealing with complex stresses for ductile material (Aygül, Al-Emrani &

Urushadze 2012). The von Mises yield criterion could be written as follows (Juvinall &

Marshek 2017):

σi = √3𝐽2

=√(σ11 - σ22)2 + [σ22 - σ33]2 + [σ33 - σ11]2 + 6(σ12

2 + σ232 + σ31

2)

2

(2.14)

23

where J2 is the Cauchy stress tensor component which was named after Augustin-Louis

Cauchy in 1827, as reported by Barulich, Godoy and Dardati (2017) as below:

σ = [

σ11 σ12 σ13

σ21 σ22 σ23

σ31 σ32 σ33

] = [

σx τxy τxz

τyx σy τyz

τzx τzy σz

] (2.15)

The von Mises stress criterion is still widely used in automotive applications such as

analysis of twin helical springs (Kaoua et al. 2011) and normal automotive coil springs

(Lavanya, Rao & Pramod Reddy 2014). This method is still popular because many

experiments have been conducted to prove its accuracy for stress estimation (Coppola,

Cortese & Folgarait 2009).

When the stress of a component exceeds the ultimate tensile strength of the

material, the component will fail instantly. This type of failure is known as static failure.

Nevertheless, literature on the failure of automotive springs (Zhu, Wang & Huang 2014;

Vukelic & Brcic 2016; Shevale & Khaire 2016) claimed that the failure of automotive

coil springs was never due to static issues. Their investigations showed that the failure

of a coil spring was due to repeated cyclic loading as a coil spring is always able to

withstand a single applied load but the loadings toward automotive suspension systems

were repeatedly. Hence, durability analysis was usually performed to estimate the

fatigue life of the design in order to prevent the coil spring from failing before the

desired lifespan.

2.3 DURABILITY ANALYSIS

Durability analysis is a crucial element in automotive industry where fatigue failure

could cause catastrophic losses. In case of ground vehicle, fatigue failure of suspension

components could lead to a road accident. As published by the Institute for Traffic

Accident Research and Data Analysis (ITARDA) Japan in 2005, one of the most

common road accident cases was due to fatigue failure of a spring. Usually when the

driver saw a car coming from the opposite direction, the driver would shift to the left to

let the car pass. However, the truck may tilt to the left and deprive the driver of control,

and eventually rolled over on the passenger side. The scene of accident is shown in

24

Figure 2.9(a). The accident was caused by fatigue and break down of the leaf spring.

The broken leaf spring is shown in Figure 2.9(b). Such accident may cause monetary

loss due to the damage of the vehicle and goods, as well as injuries of the driver. Hence,

study of fatigue of automotive suspension component is compulsory to prevent potential

failure and promote safety.

2.3.1 Introduction to Durability Analysis

Acknowledging the significance of fatigue assessment, automotive industries and

engineering researchers put lots of efforts into fatigue area to improve the component

designs. V cycle was implemented on automotive suspension component fatigue design

as shown in Figure 2.10. The V cycle aims to convert the customer idea into vehicle

design requirements, before breaking down the requirements into subsystems and

component targets. The design of the suspension components was then validated using

experimental results. Once a good understanding on fatigue requirement was obtained,

the component design could be optimised to reduce unnecessary material and

maintenance costs (He et al. 2010).

Computer aided engineering (CAE) durability analysis is usually performed

using a commercial software to predict the fatigue life of a component based on

geometry, material properties and service loads as input. These processes are known as

“Five Box Trick” durability model as shown in Figure 2.11 (Karthik, Chaitanya &

Sasanka 2012). The geometry is used to determine the critical region of stress

concentration and fatigue life distribution. Besides, the correct boundary conditions

reflect the actual specimen setup for experimental fatigue testing and provide

meaningful analysis. Material properties and service loads are used in conjunction with

geometry for fatigue analysis. Selection of an appropriate fatigue analysis algorithm

leads to a more accurate result.

Throughout the years, many durability models have been applied in automobile

suspension fatigue design. A chronology of published studies on the durability analysis

of automobile suspension components in high impact journals is illustrated in Table 2.1

to facilitate better understanding on the trends of the analysis. Based on this chronology,

25

numerous researches are found to use virtual simulation to predict fatigue life of

automobile suspension components. Recently, a few simulations were assisted with

metaheuristic or evolutionary algorithm to perform fatigue design optimisation of

automotive suspension components (Yildiz & Lekesiz 2017; Huang, Luo & Yi 2013).

The objective was to reduce component weight while maintaining the fatigue

characteristic.

(a)

(b)

Figure 2.9 Accident investigation due to leaf spring fatigue: (a) scene of accident, (b) damaged

leaf spring

Source: http://www.itarda.or.jp/itardainfomation/english/info59/next06.html

Figure 2.10 V cycle fatigue design for automotive suspension system

Source: Thomas, Bignonnet & Perroud 2005

26

Table 2.1 Trends of published automobile suspension component durability analysis

Author Year Contribution Component

Luo, Huang

& Zhou 2018

Applied Multi-Gaussian fitting and long short-

term memory neural network for automotive

suspension durability analysis Torsion beam

Yildiz &

Lekesiz 2017

Performed fatigue optimisation of an

automobile lower arm using hybrid charged

system search algorithm Lower arm

Kulkarni,

Ranjha &

Kapoor

2016

Assessed the durability and life cycles for a

damper of an electric vehicle using measured

strain signals Damper

Darban,

Nosrati &

Djavanroodi

2015

Applied multiaxial fatigue algorithm to predict

fatigue life of a stranded wire coil spring Coil spring

Nam, Shin &

Choi 2014

Evaluated the fatigue life of vehicle subframe

using nonlinear suspension model Vehicle subframe

Huang, Luo

& Yi 2013

Evaluated fatigue life of an automobile torsion

beam suspension using radial basis function

neural network simulated loading time histories Torsion beam

suspension

Klemenc,

Janezic &

Fajdiga

2012

Predicted strain-life curves of automotive

spring steel with combination of material

influential parameter, such as testing

temperature and specimen diameter using

hybrid neural network

Coil spring

Zonfrillo &

Rossi 2011

Predicted strain-life curves of spring steel with

combination of material influential parameter

like testing temperature and specimen diameter

using fuzzy approach Coil spring

Knapcyzk &

Maniowski 2010

Optimising the durability of suspension

bushing with a dynamic criterion using multi-

criteria goal function

Bushings of 5 rod

suspension

Bae et al. 2005

Investigated the shot peening effects on

automobile leaf spring’s fatigue strength Leaf spring

Nakano et al. 2000

Developed high strength spring materials with

consideration of corrosion effects Coil spring

Qian &

Fatemi 1995

Investigated the durability effects of ion-

nitriding process of spring steels using strain

block loadings

Spring steel

Takechi 1990

Investigated the effects of non-metallic

inclusion of automotive steels in affecting their

fatigue life

Spring steel

Tanaka et al. 1985

Predicted the fatigue life of spring steel under

fretting condition Spring steel

27

Figure 2.11 Durability model-based “Five Box Trick”

Source: Karthik et al. 2012

Meanwhile, integrations of artificial intelligence into fatigue analysis are also

observed. Those works mainly focused on applying data mining techniques on fatigue

data, such as artificial neural network (ANN) or fuzzy approach for fatigue life

prediction purpose. Apart from that, methods to determine road loadings for fatigue life

prediction are also of huge interest. Those researches aim to construct reality road

loading profiles to simulate fatigue life of automotive suspension components.

2.3.2 Types of Loading Signals

Signal is a function of independent variables that carry information in the form

of service load. It is important to understand the details of every type of signal,

especially in durability and automotive ride analysis. In general, signals are divided into

two categories known as analog and digital. A digital signal is a discrete time signal

generated by digital modulation while an analog signal is a continuous signal which

represents physical measurements (Gazi 2017). As proposed by Lee et al. (2004), the

strain signal measured using a strain gauge is in analog form and processed into digital

signal using analog-to-digital (A-D) converter for computer reading purpose. The

correct recording method of the loading signal leads to accurate analysis of durability

and ride.

In order to study the dynamic properties of a vehicle, the characteristics of the

measured signal are first to be statistically determined. Fatigue behaviour of an

automotive component depends on the strain signal behaviour (Zakaria et al. 2014). In

the first step, the signal is classified into a few classifications. The classifications are

Material properties Geometry Service loads

Durability model

Fatigue life

28

displayed in an organisation chart as shown in Figure 2.12. A deterministic signal

possesses a complete specific function of time and does not vary over time which can

be completely represented by a mathematical equation, e.g.

y = Asin(2πfot+ θ) (2.16)

where A is the amplitude, fo is the frequency and θ is the phase angle. Deterministic

signals can be further classified into periodic and non-periodic. Periodic signals

complete a pattern within a measurable time frame while non-periodic signals do not

repeat the pattern over time.

Figure 2.12 Classification of signals

Source: Norton & Karczub 2007

A simple periodic signal contains only a single frequency while a complex

periodic signal contains multiple frequencies. A nonperiodic signal can also be

interpreted as quasi-periodic signal and can be defined as a periodic signal that has

infinite lengthy period. A transient signal is a signal which lasts within a limited period.

For fatigue cyclic loading, there are two major categories of signal type, known as

constant amplitude loading (CAL) and variable amplitude loading (VAL). CAL is also

a type of periodic loading signal. Two example forms of CAL are shown in Figure 2.13.

29

The CALs repeat under the same pattern over time. In automotive industry,

manufacturers rely on the CALs to predict components’ fatigue life (Karthik, Chaitanya

& Sasanka 2012) as the equivalent CALs are easier to implement for component testing

in lab.

(a) (b)

Figure 2.13 Representation of CAL in different forms: (a) time series, (b) peak-valley reversals

Source: de Jesus & da Silva 2010

Non-deterministic signals are classified into two types which are stationary and

non-stationary. Non-deterministic signals represent random physical phenomena that

could not be described by means of mathematical rules. Variable amplitude loading

(VAL) is a type of non-deterministic loading histories which is widely applied in

automotive industries. Non-deterministic loading signals could be stationary or non-

stationary. Many strain time histories for fatigue analysis exhibit non-stationary

behaviour (Capponi et al. 2017). Karlsson (2007) applied the stationary road load data

to generate cyclic load for automobile fatigue life prediction. Meanwhile, Chaari et al.

(2013) applied nonstationary loadings to study dynamic response of an automobile

planetary gear. In the actual automobile operating conditions, most of the loadings are

non-stationary because road surfaces always consist of potholes or bumps (Lennie et al.

2010).

For cyclic loading, it is important to know the amplitude and mean stress of the

signal. In terms of CAL cyclic loading, the stress amplitude is expressed as follows:

σ = Δσ

2 (2.17)

30

and the stress range, Δσ is as follows:

Δσ = σmax − σmin (2.18)

where 𝜎𝑚𝑎𝑥 is the maximum stress and 𝜎𝑚𝑖𝑛 is the minimum stress. The mean stress,

𝜎𝑚𝑒𝑎𝑛 is defined as follows:

σmean= σmax − σmin

2 (2.19)

For the CAL fatigue application, alternating loads with mean stress are usually applied

on the component. Stress ratio (R) is used to represent the mean stress where it could be

defined as the ratio of minimum stress to maximum stress in one cycle of loading in a

fatigue test as follows:

R = σmin

σmax

(2.20)

Different stress ratios were often used to obtain fatigue life of high strength steel for S-

N curve construction (Gao 2017).

For CAL, it is easier to determine the stress ratio for fatigue analysis while

observing other parameters toward fatigue. Kovaci et al. (2016a) determined the effects

of two parameters which were plasma nitriding time and temperature on fatigue crack

growth of nitride steels under CAL. They have also pointed out that the VAL was less

significant for their studies since the applied loading was an independent variable.

However, most of the loading signals in real life have involved stress amplitudes that

change in irregular manner and exhibit variable characteristics. Fatigue life of a

component under VAL is totally different from CAL.

VAL is a cyclic load oscillating between the variable maximum and minimum

amplitudes that consist of no specific pattern as shown in Figure 2.14. Mottitschka et al.

(2010) conducted an experimental investigation to study the effects of fatigue life using

CAL and VAL. The results revealed that the fatigue life of a component is lower under

31

the VAL when compared to CAL at equivalent stress range. For VAL, a low-high-low

block loading with different R was applied to the specimen. For detailed VAL and load

interaction effects on fatigue crack, an experiment to determine the fatigue crack growth

under overload (OL), underload (UL), OL + UL and UL + OL was performed. When

an OL was applied, the total fatigue crack life was increased which is known as crack

retardation. When an UL was applied, the total life was decreased, and crack

acceleration occurred (Dore & Maddox 2013). The application of VAL for crack

initiation and fatigue crack growth is quite different because the higher tensile stresses

initiate cracks while it prevents fatigue crack growth in FCG. Load sequence effects of

low-high-low block loading have generated a “memory” effect on the material (Lu &

Liu 2011). If the loading sequence is different, the “memory” effect will be different.

These effects cause the lower amplitude cycles to be more damaging when they were

applied after high cycle amplitude.

(a) (b)

Figure 2.14 Representation of VAL in different forms: (a) time series, (b) peak-valley reversals

Source: de Jesus & da Silve 2010

In the engineering fields, VALs are considered as part of the design requirement.

All the steps of the design procedure should be consistent with each other in terms of

damage. For efficiency, robustness and capitalisation purpose, VAL could be converted

into a damage equivalent loading because VAL analysis and experiments are time

consuming and expensive (Thomas, Bignonnet & Perroud 2005). SAE fatigue design

and evaluation (FD&E) committee has conducted a test to provide a set of basic data to

determine the validity and fatigue life of various automobile component. Three VAL

load histories were obtained from vehicle suspension component, bracket, and

transmission system, respectively, as shown in Figure 2.15. The suspension VAL

32

(SAESUS) was obtained from the bending moment of a suspension system component

driven over an accelerated durability course by Wetzel in 1977, as reported by Oh

(2001). The SAE bracket loading history was obtained from a vibration with nearly

constant mean load over a rough road while the transmission was measured from the

transmission torque measured on a tractor engaged in front end loader where drastic

change of mean has been observed.

VAL was widely used in automotive industry for fatigue characteristic studies

of automotive suspension components (Facchinetti 2018; Anes et al. 2017; Kulkarni,

Ranjha & Kapoor 2016). Loading time histories applied in automotive industry exist in

different formats such as stress, strain or force. Literature trend of VAL in automotive

suspension component fatigue design over 30 years is tabulated into Table 2.2 to

highlight the usage of VAL in automotive suspension systems. Based on the trend, a

few researches focused on converting the VAL into CAL for automotive component

fatigue analysis. Some of the researches tried to use the outdoor-measured VAL in

indoor testing using equivalent spectrum. Different forms of loading time histories were

used in the study. This shows that suitable VAL is very significant in automotive

suspension durability analysis.

(a)

(b)

(c)

Figure 2.15 Strain signals at different mean values: (a) SAEBKT with zero mean value,

(b) SAESUS with negative mean value, (c) SAETRN with positive mean value

Source: C.S. Oh 2001

33

Table 2.2 Trend of types of VAL in automotive suspension applications

Authors Year Contribution Types of loading

Facchinetti 2018 Comparing the VAL and CAL loading

spectra for automotive chassis component Force VAL

Anes et al. 2017

Analysed the fatigue life of automotive

suspension steel and transformed the VAL

into CAL using stress scale factor Stress CAL & VAL

Kulkarni,

Ranjha &

Kapoor 2016 Predicted the fatigue life of a damper in

electric vehicle using strain life approach Stress VAL

Matteti, Molari

& Mertua 2015

Converted the acceleration VAL of a

wheel hub into displacement VAL and

applied on a four-poster test rig.

Force & Displacement

VAL

Zhao et al. 2014

Assessed fatigue life of rear axle

suspension with consideration of loading

below fatigue limit

Strain & Force VAL

Kowfie &

Rakhbar 2013 Derived a new damage summation model

based on the applied cyclic stress Strain VAL

Karthik,

Chaitanya &

Sasanka 2012

Predicted the fatigue life of a leaf spring

using SAE strain signals Strain VAL

Saoudi,

Bouzara &

Marceau 2011

Predicted the fatigue life of lower arm

using a quarter car model simulation Force VAL

Grujicic et al. 2010

Integrated first objective reliability method

and strain life approach to optimise fatigue

life of an automobile lower arm Force VAL

Ledesma et al. 2005

Developed a accelerated durability test rig

for commercial vehicle suspension

systems Force VAL

Fu & Cebon 2000

Proposed a new model for calculating the

probability density function of stress range

for bi-modal spectral densities using a case

study of trailing arm suspension Strain VAL

Yang et al. 1995

Designed a new force transducer and

correlated with axle strain measurements

for chassis applications Force VAL

Ramamurti &

Sujatha 1990

Applied random vibration concept to a

finite element model of bus chassis using

correlation of left and right tracks Strain and Acceleration

VAL

Dabell 1985

Discussed on the importance of service

loads on automotive suspension prototype

development Force & Strain VAL

34

2.3.3 Cycle Counting Methods

VAL time history varies according to time and behaves randomly. Hence, it is not easy

to define the cycle counts of a long VAL signal. A few cycle counting techniques were

proposed to summarise the irregular-load-versus time histories by providing the number

of time cycles across numerous sizes occurrences. The cycle counting method aims to

obtain equivalent constant amplitude cycles and consists of level crossing counting,

peak counting, simple range counting, range-pair counting, and Rainflow counting.

However, each method defines the cycle differently. Cycle counts could be applied in

all kinds of loading time history including force, stress, strain, acceleration, and torque

(ATSM E1049-85 2005).

Single parameter algorithms analyse a single parameter such as difference

between points to regenerate a simple cycle. Examples of single parameter cycle

counting methods are level crossing counting method, peak cycle counting, and simple

range cycle counting method. Range pair and Rainflow cycle counting methods are

classified as two parameter methods (ASTM E1049-85 2005). Among these methods,

Rainflow cycle counting method, developed by M. Matsuishi and T. Endo in 1968,

ranks as the most popular method. Downing and Socie developed the Rainflow

technique into vector-based using three-point criteria in 1982 (Marsh et al. 2016). The

procedures to perform Rainflow cycle counting are illustrated in Figure 2.16 in which

the loads were initially rearranged from the maximum or minimum peak, whichever is

greater in absolute magnitude.

Rainflow cycle counting provided the most acceptable results compared to other

methods (Roshanfar & Salimi 2015). This method could determine the cycles in a

complex loading sequence. Rainflow cycle counting was popular because it required

less storage and could be used for real-time monitoring. Besides, the accuracy of

Rainflow cycle counting has been verified through a wide range of industrial

applications (Marsh et al. 2016). The small cycles are individually extracted as shown

in Figure 2.16 (c) & (d). The large cycles are extracted at the end of the process. When

the cycles are extracted from the load time history, the mean value of each cycle are

also determined. However, Anes et al. (2014) pointed out that Rainflow cycle counting

35

technique is only acceptable for uniaxial loading but may yield a poor result under

multiaxial application. Nevertheless, Rainflow cycle counting technique is still widely

applied in automotive applications such as steering (Ligaj 2011) and suspension upper

arm due to its simplicity (Mrad et al. 2016). After extracting the cycles, this information

is used as input to the fatigue models to calculate the fatigue life of the components.

(a) (b)

(c) (d)

(e) (f)

Range Mean Counts Events

8 1 1 C – D

6 1 1 H – I

4 1 1 E – F

3 -0.5 1 A – B (g)

Figure 2.16 Rainflow cycle counting algorithm: (a) – (f) sequence of the method, (g) cycles

derived from Rainflow cycle counting method

Source: ASTM E1049-85 (2005)

36

2.3.4 Fatigue Life Analysis

Fatigue life could be defined as the number of stress cycles of a specified character that

a specimen sustains before failure of a specified nature occurs, as recited by Chetan,

Khushbu & Nauman (2012). Fatigue life assessment methods are generally divided into

two approaches which are high cycle fatigue (HCF) and low cycle fatigue (LCF).

Fatigue life occurring at above 1×104 cycles is usually called as HCF. LCF usually

occurs at condition below 1×104 cycles. For LCF, the total fatigue life of a component

includes the crack properties such as crack initiation and propagation. When the fatigue

life occurred beyond 1 × 107 cycles, it is defined as very high cycle fatigue (VHCF)

regime (Korhonen et al. 2017). Some components like turbine blades, rotating

components are designed using HCF because the components are expected to sustain

high numbers of cyclic load or high frequency vibrations (Tafti 2013).

In order to prevent failure due to fatigue, periodic maintenance of a structure

needs to be performed constantly (Pantazopoulus et al. 2014). This preventive method

is suitable for costly products such as aircraft or crane where the replacement cost of

these components is extremely expensive. Meanwhile, it is not feasible to perform

regular checking on small mass-produced components such as automobile engines,

steering part, and suspension components because lots of efforts are required. Hence,

an easier way to avoid fatigue failure is through replacing the cracked components after

the designated service period (Jiang & Murthy 2011). If the components are designated

to be replaced, the components are considered as fail when a crack is initiated. However,

a small crack opening of spring steel is harmless. Therefore, Takahashi et al. (2011)

investigated on crack length effect on fatigue failure of spring steel SUP 9A. They

proposed that any crack length below 0.2 mm could be rendered as harmless. In their

paper, defects smaller than 0.2 mm were non-damaging to the fatigue limit after

extensive number of experimental testing for different crack size.

Crack initiation is caused by stress concentration at a point and a fatigue feature

determined by means of the stress life (S-N) approach was used. The concept of S-N

was introduced by A. Wӧhler and still widely applied by current researchers (Sonsino,

2007). A typical S-N curve for steel is shown in Figure 2.17. Main critical parameters

37

for S-N approach are mean and amplitude stress. An earlier empirical model by W.

Gerber in 1874 was proposed to include mean stress effect on high cycle regime. The

shortfall of this proposed model is its ignorance of tension and compression. J.

Goodman modified the model into another more conservative form in 1914. C.R.

Soderberg in 1930 reformulated the Goodman model using yield strength, 𝜎𝑢𝑡𝑠 .

Soderberg model is very conservative and expects no fatigue failure nor yield to occur

(dos Santos, Auricchio & Conti 2012). As for Gerber, Goodman and Soderberg model,

the loading condition is only applicable to tensile loadings.

Figure 2.17 Typical S-N curve of steel

Source: ASTM E1049-85 2005

After the mean stress correction, the stress was used to predict the fatigue life of

the component. For Wӧhler’s S-N approach, the life prediction model is assumed to

follow a power relationship:

σ = σf'(2Nf))b (2.21)

where 𝜎𝑓′ is the fatigue strength coefficient while b is the fatigue strength exponent.

Goodman model was more conservative when loading sequence was tensile

predominant (Karthik, Chaitanya & Sasanka 2012). When it is a zero-mean loading, the

Gerber model is more conservative. Although the mean stress effect has been described,

the S-N method still has a drawback in terms of amplitude and mean stress at different

levels. Nevertheless, S-N approach is suitable for components which require higher

safety factor.

38

Mean stress effect is not capable to be estimated accurately with using solely

ultimate tensile strength. This has been proven by Dowling (2004) through the testing

on steel and aluminium specimens using S-N approaches. Using the ultimate tensile

strength of material to estimate the fatigue life of a component is far from sufficient.

However, S-N approach has a limited capability where the accuracy is good for

components with only high fatigue life, at approximately 105 life cycle (Ghafoori et al.

2015). This approach emphasises on the nominal stress of the specimen and it does not

consider the materials behaviour under time-variable loading, such as cyclic hardening

or softening in the middle cycle fatigue. Hence, a model to predict the localised fatigue

life with the consideration of cyclic hardening effects is in need. The approach which

considers the cyclic strain hardening effects is strain life (ε-N) method.

A ε-N approach is much more accurate to assess the fatigue life of a component

compared to traditional S-N approach. This is because ε-N approach considers plastic

deformation that exists in localised region where fatigue cracks begin (Ince & Glinka

2011). The example ε-N curve for steel is shown in Figure 2.18 where the ε-N model is

labelled as “Total” in the curve and derived from the plastic and elastic data. ε-N method

is applicable to ductile materials with low cycle fatigue of components within 103 cycles.

This method permits a more rational and handling of mean stress effects through

employing a local mean stress rather than nominal stress. There is a commonality

between S-N and ε-N approaches as both methods do not include crack growth.

Figure 2.18 A typical ε-N curve of steel

Source: Williams, Lee & Rilly 2003

39

ε-N approaches have the possibility to replace S-N approach due to its greater

accuracy (Fajdiga & Sraml 2009). In applying the ε-N approach, the S-N curves are

obtained from fatigue test under complete reversed cyclic loading between constant

strain limits using strain-controlled fatigue test standard which is ASTM E606. It is

significant to note that the there is a force-controlled fatigue test standard ASTM E46.

The force-controlled fatigue test serves to obtain the fatigue strength of metallic

material in the regime where the elastic strain is predominant throughout the test. For

the strain control, cyclic total strain is measured where the plastic strain is also known.

The number of cycles to failure is counted until there is a substantial crack on the

specimen. Cyclic strain-controlled fatigue test is recommended because the material

with the stress concentration of a component is subjected to cyclic plastic deformation

even the component behaves elastically during cyclic loading.

For the elastic linear relation of ε-N approach, the model is based on a

relationship from O.H. Basquin in 1910, as mentioned by Lee et al. (2005). In 1954,

S.S. Manson expressed a power relationship for low cycle regimes in terms of the plastic

strain range as follows:

εp = εf'(2Nf)

c (2.22)

where 𝜀𝑝 is the plastic strain, 𝜀𝑓′ is the fatigue ductility coefficient, c is the fatigue

ductility exponent.

After the plastic strain range relationship was proposed, the elastic and plastic

strains were combined to obtain a correlation between the fatigue life and strain known

as Coffin-Manson relationship. The Coffin-Manson relationship is the first ε-N

approach which could be written as follows:

εp = σf

'

E(2Nf)

b + εf

'(2Nf)c (2.23)

The original relationship performs the fatigue life assessment with an assumption of

zero-mean stress. Again, the mean stress effect is crucial for fatigue life estimation

40

whether using S-N or ε-N approach because the mean stress is part of the fatigue failure

criteria (Dowling 2004; Ghaffori et al. 2015).

The Coffin-Manson relationship was assessed and compared with other fatigue

models. Most of the comparisons show that this relationship could provide acceptable

results (Runciman et al. 2011). Due to the simplicity of this relationship, its application

has been expanded to ductile cast iron (Ricotta 2015). Gribbin et al. (2016) revealed

that when the plastic strain is small, Coffin-Manson relationship cannot fit the data well.

Hence, a bilinear model was used to improve the data fitting process. Thomas (2012)

proposed that this relationship provides the best means for predicting the high strength

steel for automotive chassis and suspension. In real life application, the components are

loaded with different mean stresses where the limitation of Coffin-Manson relationship

exhibits. Nevertheless, further development of ε-N models has led to a solution for this

drawback. In fatigue analysis, the tensile or positive mean stress tends to reduce fatigue

life while compressive or negative mean stress tends to increase fatigue life (Chiou &

Yang 2012; Taheri, Vincent & Le-roux 2013; Khan et al. 2014; Bruchhausen et al.

2015). Therefore, some automotive components were induced with compression tensile

stress to enhance fatigue life. An instance is the shot peening process that is often

applied on automotive component such as gears to prolong fatigue life of the component

(Zhang et al. 2016).

There is a model that could be used for applications involving mean stress effects

in 1968, as reported by Manson and Halford (2006), known as Morrow strain-life model.

This model stated that the ε-N curve could be adjusted using added mean stress effects.

J.D. Morrow added the mean stress, 𝜎𝑚𝑒𝑎𝑛 into the Coffin-Manson relationship and

could be rewritten as follows:

ε = σf

' − σmean

E(2Nf)

b + εf

'(2Nf)c (2.24)

The mean stress, 𝜎𝑚𝑒𝑎𝑛 is positive when the loading is tension and negative when the

loading is compression. Nevertheless, Coffin-Manson relationship correlated better

than Morrow model (Ertas & Sonmez 2008) in terms of spot weld joint fatigue analysis.

41

K.N. Smith, P. Watson and T.H. Topper proposed another mean stress corrected

ε-N model in 1970. This model is known as Smith-Watson-Topper (SWT) model. This

model is widely used as reported by Ince and Glinka (2011). The parameters considered

for fatigue prediction are the maximum stress and strain amplitude per cycles. These

SWT parameters were obtained from ε-N fatigue test data observed at various mean

stresses and stress or strain amplitudes. The mathematical model of SWT could be

written as follows:

σmaxε = (σf

')2

E(2Nf)

2b + σf

'εf

'(2Nf)

b + c (2.25)

where σmax is the maximum stress. SWT model has proven to be more robust compared

to Morrow model where the fatigue life prediction is higher and more conservative after

a wide range of materials were tested using this approach (Ince & Glinka 2011). Cui

(2002) suggested that the Morrow model is only acceptable for steel while SWT model

is better for general use.

For fatigue analysis, there is a group based on continuum damage mechanics in

which fatigue life was predicted through computing a damage parameter cycle by cycle

(Santechchia et al. 2016). In terms of fatigue crack analysis, the fatigue crack length of

specimen was usually measured. The recent interest of fatigue crack analysis includes

adding parameter for simulation. For example, Meneghetti et al. (2016) added mean

stress effects as additional parameter to heat energy-based approach for fatigue crack

simulation of steel specimens.

Controversy appears during the selection of a suitable model for automotive

component fatigue life prediction, especially when the component is made of steel.

Abdullah (2005) suggested that the SWT was more conservative for tensile loading

sequence while Morrow yields greater correlation during compression loading when

compared to SWT predicted fatigue life of a steel automotive lower arm. Ince & Glinka

(2011) mentioned that the SWT model gives better results and more flexibility for

fatigue life prediction for most of the applications. Although the Morrow and SWT

models consider mean stress effects, both of them are still applicable for zero mean

42

stress fatigue analysis (Karthik, Chaitanya & Sasanka 2012). When the mean stress is

zero, the Morrow model is the same as Coffin-Manson relationship. Each approach

gives certain interest range or mean strain amplitude to the fatigue damage. Then, the

total fatigue damage is required for the final fatigue life analysis. Hence, a method to

sum up the fatigue damage is required and proposed. The most acceptable damage

summation method is known as the Palmgren-Miner linear damage cumulative rule.

2.3.5 Linear Damage Cumulative Rule

Cumulative fatigue damage theory is obtained through summation of normal and shear

energy of peak valley in each block loading. A. Palmgren introduced the concept of

fatigue damage summation in 1924 while M.A. Miner proposed a linear cumulative

fatigue damage criterion in 1954 (Petaś, Mróz & Doliński 2013). This rule is known as

the Palmgren-Miner linear cumulative damage rule. The procedures for Palmgren-

Miner damage summation are shown in Figure 2.19. The linear damage summation rule

proposed by Palmgren-Miner and the damage of one cycle Di is expressed as:

1i

fi

DN

= (2.26)

where Nfi is the number of constant amplitude cycles to failure. A linear cumulative

fatigue damage calculation under VAL is defined in the equation:

1ii

fi

nD

n = = (2.27)

where Di is the cumulative fatigue damage, ni is the number of applied cycles, and nfi is

the number of constant amplitude cycles to failure. The failure occurs when the

summation of individual damage value caused by each cycle reaches the value of one

(Upadhyaya & Sridhara 2012).

Different range of damage summation indicates varying confidence probability.

The critical damage summation values were 0.08, 0.3 and 1 which show confidence

probability of 90, 50 and 10 %, respectively in 2002 (Beretta & Regazzi 2016).

43

Selection of damage summation value depends on the desired design target. However,

the failure occurs mostly at the damage summation of one (Fiedler & Vormwald 2016).

This proposed Palmgen-Miner rule consists of a few limitations. Under spectrum

loading, component failed during the portion of the duty cycle when the load is below

the endurance limit. Secondly, the Palmgren-Miner rule also underestimates the damage

because the damage of lower load is neglected. Thirdly, the Palmgren-Miner rule

neglected the load sequence effects. Experimental results showed that the damage

summation at failure are very different when the load is from high to low or low to high

(Shamsaei et al. 2010).

Therefore, many damage accumulative theorems have been proposed since 1945

as reported by Gao et al. (2014) and could be generally classified into six types including

linear damage summation, nonlinear damage curve, life curve modification to account

load sequence effects, crack growth concept based, continuum damage mechanics and

energy-based methods. Despite the shortcomings of Palmgren-Miner linear damage

summation rule, it is still dominantly used in design due to its simplicity and acceptable

accuracy (Sun, Dui & Fan 2014). Fatigue analysis using VAL and Palmgren-Miner rule

is usually consumed lots of time and many experimental works. Hence, accelerated

fatigue test or fatigue assessment in frequency domain has been introduced to shorten

the time domain fatigue analysis. The frequency domain fatigue analysis aims to

provide similar prediction results with the time domain.

Figure 2.19 Procedures for Palmgren-Miner damage summation

Source: Woo 2017

44

2.4 RIDE RELATED VIBRATION ANALYSIS

When an automobile travels at a certain speed, it experiences a broad spectrum of

vibrations. These vibrations are transmitted to the passengers by tactile or visual

excitations, commonly known as the term of “ride”. The spectrum of vibrations is

divided according to frequency, with frequency ranging from 0 to 25 Hz is classified as

ride (Rafael 2007). On the other hand, frequency ranged between 25 to 20,000 Hz is

classified as noise. The maximum of 25 Hz is the frequency limit of simpler vibrations

to all motor vehicles. Vibration environment is one of the most important criteria by

which people judge the design and construction criteria “quality” of an automobile.

Hence, the ride quality of a vehicle is judged mainly through the performance of the

suspension design. However, being judgemental is subjective in nature and give rises

to one of the greatest difficulties in developing objective engineering methods which is

to deal with ride as a performance mode of a vehicle.

2.4.1 Introduction to Ride Analysis

Subjective assessment of vehicle ride involved human response and was usually

conducted using questionnaires (Cossalter, Roberto & Rota 2010). Subjective ride

assessment is difficult to perform because it requires human as judges. Hence, objective

ride standards were developed to assess the vehicle ride based on human perception to

vibrations. Objectively define the vehicle quality requires measuring the vibration of a

vehicle through an automobile model in virtual environment. The standard procedure

to study the objective ride of a vehicle is shown in Figure 2.20. The first element to

study the vehicle ride is the excitation source where it plays the role as the input for

analysis. Subsequently, the vehicle dynamics responses are obtained and processed to

get the ride rating.

Figure 2.20 Vehicle ride dynamic system

Source: Wong 2008

Excitation

sources (road

roughness)

Vehicle

dynamic

response

Vibration Ride

perception

45

In order to study the trends of objective ride analysis, the trend of previous

research for the past 30 years related to this vehicle ride was tabulated in sequence into

Table 2.3. From the trend analysis, automotive ride analysis is found to be closely

related to automotive suspension system design. Numerous researches proposed to

optimise the vehicle ride by altering the suspension system design. The most important

finding in vehicle ride analysis is the road input for simulation model. The road profiles

are obtained either through measurement using sensors on actual vehicle or artificially

generated vehicle according to ISO 8608. Meanwhile, surface roughness of the road

profile could be classified into different levels. As for the ride indicator, different ride

standards or root mean square (r.m.s) vertical acceleration were used to quantify the

ride

The aim of the vehicle ride analysis is to optimise the suspension parameters for

better perceptions. The optimisation of ride was assisted by metaheuristic algorithms

such as genetic algorithm (Seifi, Hassannejad & Hamed 2016). The ride standard was

also used to determine the suitable suspension parameter like damping in affecting the

ride quality of a vehicle. Meanwhile, Abdelkareem et al. (2018) improved the ride

performance of a truck through optimised leaf spring design. The constructed vehicle

simulation model was also a critical element to perform the simulation for ride analysis.

Based on the trend analysis, quarter car model was widely used in performing the ride

simulation (Hassaan 2015; Burdzik & Koniczny 2013). Seifi, Hassannejad & Hamed

(2016) proposed that quarter car model is sufficient for ride analysis but not sufficient

for road holding and rollover capability assessments.

Table 2.3 Trend of vehicle ride analysis for the past 30 years

Authors (Year) Objective Road

excitation Ride indicator

Abdelkareem et al.

(2018)

To improve the truck ride

performance through

optimisation of leaf spring design

Artificial

generated road

profile

r.m.s. value of seat

body acceleration

Loprencipe & Zocalli

(2017)

To analyse the effects of ride

standards to a real road profile

Profilometer

measurements

ISO 2631, Michigan

ride quality index,

ASTM ride number

Continue…

46

Continued…

Seifi, Hassannejad &

Hamed (2016)

To optimise the suspension

system in terms of ride and

handling using GA

Deterministic

road profile

(Sine waves)

ISO 2631

Hassaan (2015)

To simulate ride comfort of an

automobile using quarter car

model under bump excitation

Simple

harmonic bump ISO 2631

Reza-Kashyzadeh,

Ostad-Ahmad-

Ghorabi & Arghavan

(2014)

Investigated the road roughness

effects on a semi-active

suspension system

Road class A to

E Vertical acceleration

Burdzik &

Konieczny (2013)

Investigated ride of a passenger

car under different damping

parameters

On-road test ISO 2631

Velmurugan,

Kumaraswamidhas &

Sankaranarayarasamy

(2012)

Reduced whole-body vibration of

trailer cabin Class B

Driver seat

acceleration

Barbosa (2011) Simulated frequency response of

a half vehicle model Class A Vertical acceleration

Pang et al. (2010) Optimised ride of a heavy truck

suspension system Class B ISO 2631

Goncalves &

Ambrosio (2005)

To optimise the ride, handling

and rollover parameter of a

vehicle

Profilometer

measurements ISO 2631

Stone & Demetriou

(2000)

To simulate vehicle ride and

handling performance during

braking and cornering events

Static

displacement Heave displacement

Cherry & Jones

(1995)

To analyse the application of

fuzzy logic in controlling vehicle

ride performance

Tyre force Sprung mass

acceleration

Elmadany (1990)

Optimised the ride performance

of a vehicle through load

levelling system

Derived road

surface based

on vehicle

velocity

Sprung mass

acceleration

Kamawura & Kaku

(1985)

To evaluate the effects of road

roughness on vehicle ride

Displacement

PSD

Acceleration at

vehicle centre of

gravity

47

2.4.2 Road Roughness as Excitation Sources

There are a few sources of excitation from which the vehicle is induced. These sources

generally fall into two major classes, known as road roughness and on-board sources.

The on-board sources arise from rotating components and include the tyre/wheel

assemblies, the driveline and the engine, while road roughness encompasses everything

from potholes resulting from localised surface failures to random deviations. Roughness

is defined as the elevation profile along the wheel tracks where the vehicle passes and

possibly obtained through measurement from a profilometer. An example of road

roughness measurement using a profilometer is shown in Figure 2.21. with international

roughness index (IRI) value. The IRI were divided into measurements from inner wheel

path (IWP) and outer wheel path (OWP).

Road profiles were fitted into category of “broad-band random signals” and

therefore, could be described either by the profile itself or its statistical properties. One

of the most useful representations is the power spectral density (PSD) function because

of randomness nature of the profile. Reza-Kashyzadeh et al. (2014) presented a quarter

car model with different road roughness in terms of PSD function to simulate the vehicle

vertical vibration response for automotive suspension component durability analysis.

Due to the randomness of road roughness, the instantaneous value of the function could

not be estimated in a deterministic manner.

Figure 2.21 Example of profilometer measured road roughness profile

Source: Abulizi et al. (2016)

48

However, some properties of random functions could be determined statistically

such as the mean or the r.m.s value. It could be determined by averaging the value while

the frequency content of the function could be obtained through Fourier transform. In

addition, road surface elevation is determined as stationary in which the statistical

properties derived from a portion of the surface profile could be used to define the entire

section of the road surface (Wong 2008). This meant that a small sampling of road

profile data could be repeated to represent the whole road profile. Since the mean value

of the signal remained constant when computed over different segment of samples, the

random road surface functions are also considered as ergodic.

Road roughness measurement requires a profilometer and an accelerometer

attached on a vehicle (Loprencipe et al. 2017). Considering the expensive cost to build

the experimental setup for rough roughness measurement, ISO committee proposed a

standard road roughness classification known as ISO 8608 (2016). The degree of

roughness, Sg(Ω), of a road could be obtained using range and geometric mean using

the equation as follows:

Sg(Ω) = CspΩ-N

(2.28)

where Csp and N are constants, Ω is the spatial frequency. Over the years, various

organisations attempted to classify the road roughness. ISO proposed a road roughness

classification (classes A – H) based on the PSD, as shown in Figure 2.22 for application

of vehicle dynamic analysis.

The mean value of road properties is often used to study the response of a vehicle

to road roughness. However, different road types with different surface qualities have

different spectral qualities (Mohammadi 2012). Cantisani & Loprencipe (2010)

established a speed related relationship between International Roughness Index (IRI) of

road and ISO 2631 vehicle vertical ride, Awz, model under a pavement road. This model

restrained to vehicle speed of 80 kmph due to Reference Average Rectified Slope

(RARS). RARS suggested that vehicle speed of 80 kmph is the best numerical index.

The wavelength of a vehicle with speed of 80 kmph is detectable by most road users

and covers all road frequencies.

49

The measurement of rough roughness required a profilometer attached to a

vehicle. Attaching profilometer for road roughness analysis is not convenient for

research purpose because it incurs extra cost and involves complex operation. Hence,

Du et al. (2014) developed a model to measure road roughness with a Z-axis

accelerometer and a global positioning system (GPS). They utilised a linear time

invariant (LTI) quarter vehicle model and regarded the pavement as a continuous

surface. A regression model to predict the IRI was proposed using PSD amplitude of

acceleration, LTI system and PSD of pavement roughness (Du et al., 2014). The model

was then expanded using multiple linear regression (MLR) to include both wheels. Du,

Liu and Wu (2016) proposed a speed correction factor to enhance the feasibility of the

regression model for different vehicle speeds.

Figure 2.22 PSD as a function of spatial frequency of various classes of road

Source: ISO 8608 2016

Acceleration road profile PSD could be converted to displacement or shifted

from acceleration to displacement (Du, Liu & Wu, 2016). Displacement PSD is

obtained through second integration of acceleration suggested as follows:

50

Sa(ω) = (ω

v)

4

Sx(ω) (2.29)

where Sa(ω) is the acceleration PSD, ω is the angular frequency, Sx is the displacement

PSD. This conversion aims to provide a more feasible input to vehicle simulation model

because the input for a vehicle simulation usually involves displacement (Loprencipe

& Zocalli 2017; Seifi, Hassannejad & Hamed 2016).

2.4.3 Vehicle Suspension System Modelling

Considering the unneglectable road surface irregularities, the ideal way to control

vehicle vibration response is through suspension isolation, particularly the motion of

vehicle body and axle (Wong 2008). In this case, the vehicle suspension system is

usually modelled as a linear system with a direct linear relationship, surface

irregularities and excitation input. The typical modelling process flow for a simulation

model is shown in Figure 2.23. The vehicle system is characterised by its transfer

function and converts the road surface irregularities input to vehicle vibration output.

In addition, a linear quarter car model was usually used in such ride analysis. Yu et al.

(2013) utilised a quarter car model to design an adaptive real-time road profile

estimation observer considering the vehicle vertical dynamics.

Figure 2.23 Input and output of a linear vehicle system

Source: Wong 2008

In terms of suspension modelling, the vehicle was modelled into a single D.O.F

system with nonlinearities. Surface irregularities were expressed as input while vehicle

vibrations were expressed as output (Naik & Singru 2011). In a basic level analysis, a

quarter car model consisted of a sprung mass supported by primary suspension applied

at each wheel. Dynamic behaviour of this system is the first level of isolation from the

road roughness. These dynamic characteristics are largely defined by ride rates (RR) as

follows (Shim & Velusamy 2007):

Surface

irregularities

(Sg(f))

Vehicle system

H(f)

Vehicle

Vibrations

Sv(f) = |H(f)|2Sg(f)

51

RR = KsKt

Ks + Kt

(2.30)

where Ks is the spring stiffness and Kt is the tyre stiffness. Implications of ride rate affect

four main vehicle modal dynamic characteristics like pitch, roll, yaw and bounce. A

conventional automobile has body bounce frequencies ranging from 1.0 to 1.5 Hz. In

this recommended frequency range, the road holding and ride properties are the most

compromised aspects.

In the absence of damping, the general bounce natural frequency of each

suspension system of the passenger car could be determined using the equation:

fn =

1

2π√

RR × g

W (2.31)

where fn is the bounce frequency, g is the gravity acceleration, and W is the corner

weight of the vehicle. When damping exists, the resonance occurs at damped natural

frequency, fd as follows:

fd = f

n√1- (ξs)

2 (2.32)

where fn is the undamped natural frequency, ξs is the damping ratio which is obtained

using the equation below:

ξs = Cs

√4KsM (2.33)

where Cs is the suspension damping coefficient. In order to maintain a good ride, the

suspension damping ratio usually falls on the range of 0.2 to 0.4. Since there is small

difference between the damped and undamped natural frequency, undamped natural

frequency is usually used to characterise vehicle (Wong 2008).

52

For a quarter car model, the suspension is modelled by using two simple

equations of motions as illustrated in Figure 2.24. The equation of motion for 2 D.O.F.

vehicle model is written as below (Satishkurma et al. 2014):

MsX2 + Cs(X2- X1) + Ks(X2 - X1) = 0 (2.34)

MuX1 + Kt(X2 - w) - Ks(X2 - X1) − Cs(X2 - X1) = 0 (2.35)

where Ms is the sprung mass, Mu is the un-sprung mass, 𝑋2, 2, 2 are the sprung mass

displacement and derivatives respectively, 1 , 1 , 𝑋1 are the un-sprung mass

acceleration and their derivatives respectively, Kt is the tyre stiffness, and w is the road

input. Application of quarter car model in vehicle ride analysis is very common. Sharma

et al. (2013) modelled a 2 D.O.F. car suspension system under state space representation

for vehicle ride study. State space suspension model is more widely used for active

suspension controller design than traditional transfer function method because the

applicability of nonlinearity. For example, Popovic et al. (2011) considered the

nonlinearity of actuator in the controller design of a vehicle suspension by using the

state space quarter car model.

Figure 2.24 Schematic diagram of a two D.O.F quarter car model

Source: Sathiskumar et al. 2014

It is known that increasing D.O.F of a simulation model leads to greater accuracy

but simultaneously causes complex model and heavy computation. Quarter car model

53

usually consists of two D.O.F while half car model has four D.O.F. Full vehicle models

are usually consisted of at least seven D.O.F. (Krauze & Kasprzyk 2016). For a half

vehicle model, bounce and pitch motion of the vehicle body are considered through

integrating bounce and pitch governed equation into the model (Shafiqur Rahman &

Kibria 2014). For vehicle model with bounce and pitch motion, lower front frequency

puts the bounce centre close to rear axle and the pitch centre forwards near the front

axle. This tuning process is known as the “Olley tuning” which could improve the ride

quality (Fu et al. 2013).

Full vehicle model is the most complex but complete model to study. The

number of D.O.F of vehicle model increases according to vehicle motion. A traditional

way to mathematically model a full vehicle is tedious and consumes lots of time and

effort (Ning, Zhao & Shen 2013). Over the years, many algorithms have been developed

to make multibody dynamics analysis more accessible. Nowadays, many commercial

multibody dynamics software have been introduced to help designers to promptly

perform vehicle modelling. Commercial multibody dynamics software serves better in

current fast pace automotive industry due to its effectiveness and ease of use. Ning,

Zhao and Shen (2013) performed a kinematic and dynamic analysis of vehicle

suspension using ADAMS/Car to seek for better ride comfort. Virtual analysis was

continuously conducted until the design met the expected ride index before processed

to prototype making.

Other than ADAMS, SimulationX is a lumped network simulation with

equation-based model objects for simulation. Due to low requirements in terms of

computing power, SimulationX is suitable to analyse complex dynamic systems

involving substantial number of components (Dor & Vielhaber 2015; Sim et al. 2017).

Sim et al. (2017) developed a LQR control algorithm for agricultural tractors hydro-

pneumatic cab suspension to increase the ride comfort. SimulationX was used to model

the hydro-pneumatic system that is installed at the left and right side of the vehicle to

provide suitable load and stabilise the tractor. Jin, Yu and Fu (2016) published a

research on vehicle ride driven by in-wheels motor. A road test was performed on the

selected car model with different added weight in un-sprung mass to represent the

additional weight to corroborate the 11 D.O.F simulation model. With the road

54

roughness excitation and constructed simulation model, the vehicle vibrations are

measured and suspension parameters are tuned to improve vehicle ride.

A frontal quarter car model has been used to conduct vehicle ride dynamics

analysis and the vehicle mass ratios and suspension parameters were tuned to improve

the vehicle ride (Unaune, Pawar & Mohite 2011). The choice is based on the simplicity

to model the quarter car model and sufficiency of front quarter suspension for simple

vehicle ride analysis. Sentil Kumar & Vijayarangan (2007) used a quarter car model to

optimise the vehicle ride through proportional-integral-derivative (PID) controller. The

ride performance of passive suspension was compared to active suspension in terms of

ride. A comparison between quarter, half and full vehicle model for vehicle ride was

also performed (Mahala, Gadkari & Anindya 2009). The research showed that the full

vehicle model yielded the highest accuracy followed by half and quarter vehicle model.

However, the research paper stated that the trends of the responses were similar and

acceptable for all three models (Mahala, Gadkari & Anindya 2009). The acceleration

responses obtained from quarter car, half car and full car model were in the same range.

2.4.4 International Ride Standards

Once the PSD function for acceleration of the vehicle was obtained, further analysis is

required to relate to it to potential ride comfort criterion. Numerous ride comfort criteria

have been proposed such as vertical vibration described in the Ride and Vibration Data

Manual J6a from the SAE, ISO 2631, BS 6841, Society of German Engineers VDI 2057,

Average Absorbed Power (AAP), NATO Reference Mobility Model. Each standard is

used by specific country or region as shown in Table 2.4. Every developed objective

ride standards provides different weightings to quantify the ride, but the concept is

virtually similar where the amplitude and frequency are considered.

Table 2.4 Objective ride and preferred countries

Standards Country Use

ISO 2631 Europe

BS 6841 United Kingdom

VDI 2057 Germany and Austria

AAP / NATO Reference Mobility Model United States of America

Source: Els 2005

55

AAP standard was developed by the US Army Tank Automotive Command in

1966. Under vibration, the human body behaves elastically and generates restoring

forces that are related to displacement. The generated restoring forces dissipate the

energy until they are imparted. Time rate of this energy absorption process is named as

absorbed power. The AAP standard computes the energy in frequency domain. It

proposed the frequency range of interest from 1 to 80 Hz. This standard emphasised the

frequency range from 4 to 5 Hz because the range is in resonance with human tissues.

Zhao and Schindler (2014) utilised AAP and ISO 2631 standard to calculate the ride

quality of a crawler chassis for suspension design. The need of off-road vehicle for ride

quality was also emphasised.

British Standards BS 6841 proposed the concept of vibration dose value (VDV)

in 1987. The frequency range of interest is from 0.5 – 80 Hz where the frequency of 0.5

Hz is to compensate the motion sickness. This standard modifies the frequency

weighting of Z-axis so that the results are closer to experimental findings. For the ride

comfort, they proposed the r.m.s of the weighted signal. This ride index is easily

comparable because the value is linear to the ride quality. Paddan et al. (2012) utilised

the BS 6841 standard to analyse the seat backrest towards ride perception. VDI standard

was initially published by Society of German Engineers in 1963 where it was the first

standard to quantify ride comfort. VDI standard was created using many human data

under sinusoidal vibrations with certain frequency and amplitude. In 1979, the VDI

adopted the tolerance curves of ISO 2631 but maintained the K-factor for subjective

comparison.

VDI standards was applied by Hohl in 1984 to assess vehicle ride, as reported

by Els et al. (2007). However, there is very limited recent publications on the use of

VDI standard. ISO 2631 standards extended the frequency range below 0.1 Hz in 1997.

The r.m.s value remained as the basis for ride assessment. Generally, the method of

assessment resembles the standard BS 6841. The main difference between ISO 2631

and BS 6841 is the vertical weighting factors. The ISO standard included the frequency

range for motion sickness in frequency range of 0.1 to 0.5 Hz that is not considered in

BS 6841 standard. Literature review has shown that the current trend for objective ride

56

rating of a vehicle mostly adopts the ISO 2631 standard. ISO 2631 was used to assess

the ride comfort of many vehicles because of its comprehensiveness and ease of use.

For example, it was used to assess the ride comfort of compact wheel loaders

(Zhao & Schindler 2014), motorcycles (Chen et al. 2009), passenger cars (Hassaan

2015), mining vehicles (Eger et al. 2008), bus (Sekulic et al. 2016), and agricultural

tractor (Loutridis et al. 2011). Compact wheel loaders, mining vehicles and agricultural

tractors are off-road vehicles which are used in harsh terrain with higher chance of

exposure to vibrations compared to normal passenger vehicle. Long-time exposure of

vibration is detrimental to operator’s health. ISO 2631 standard also illustrates the limit

of exposure to vibration. For passenger vehicle, the ISO 2631 standard has improved

the vehicle ride because passengers nowadays do not only demand for durability, but

also a greater ride vehicle.

For vehicle vibration, a complete vehicle model has many D.O.F. Specifically,

there is a seat suspension between the driver and the vehicle. Moreover, the random

input to the vehicle is always more than one because the passenger car has four wheels.

Each wheel possesses one random input. Interaction of the random inputs with each

other becomes important to determine the output of the system. Hence, cross-spectral

densities are essential. For cross spectral, time lag between the front and rear wheel

should be taken into consideration (Feng et al. 2013). The rear time delay could replicate

the response of the front. Understanding the front suspension state in principles allows

the rear suspension to also react to road profiles.

2.5 DATA ANALYSIS

2.5.1 Introduction to Data Analysis

Fatigue life of a product is scattered and has an acceptable variations range of 100%

(Shamsaei & MeKelvey 2014; Karolczuk 2016). Hence, it is not easy to interpret the

fatigue life in a direct manner. Better understanding on the fatigue characteristic of a

component requires data analysis to statistically define the fatigue life. For deeper

analysis, a specific field to identify the correlations and patterns within the data known

57

as “data mining” is introduced. The list of data mining techniques is shown in Figure

2.25. In general, there are six branches of data mining techniques. Application of data

mining techniques to build models and predict outcomes is called “Machine Learning”.

Machine learning is an application of artificial intelligence that provides the system the

capability to learn and improve without explicitly programming. Statistical theories

form the language of machine learning problems which are amenable to solve.

In the scope of durability, data analysis is an essential element due to the

randomness of the fatigue process (Schneider & Maddox 2003). Additionally, samples

for fatigue life test are often destructed and could not be practically used. In case of

fatigue test, the small standard coupon that is used to determine the fatigue behaviour

of material is generally known as specimen. For a fatigue loading time history, the

sample size is known as the number of data points in a measurement. The sample size

for fatigue analysis is usually high and depends on the sampling rate. When the

sampling size is large, fatigue data are characterised using statistical method because

value of a single point does not bring any significant meaning.

Figure 2.25 Groups of data mining technique

Source: Ngai et al. 2011

The eigenvalues of the observed data representing the statistical nature of a

sample can be classified into two categories: (1) the central position of data and (2)

dispersion of the data. Examples of central position data include the mean value while

dispersion of the data represent the standard deviation (𝜎𝑆𝐷) or variance. Mean and

Data mining

Classification

Clustering

Outlier detection

Prediction

Regression

Visualisation

58

standard deviation of strain signals were used in automotive component fatigue analysis

to determine when the strain signals were random and stationary (Kosobudzki 2014).

The mean value of a sample can be defined as follows:

x = 1

n∑ xi

n

i=1

(2.36)

where n is the sample size. The sample mean represents the centre position of the data.

Dispersion of a set of datasets is analysed using 𝜎𝑆𝐷. 𝜎𝑆𝐷 of less than 30 sample

is derived as follows:

σSD = √∑ (xi- x)2n

i=1

n - 1 (2.37)

where is the sample mean. Meanwhile, for any sample of more than 30, the 𝜎𝑆𝐷 is

obtained as below:

σSD = √∑ (xi - x)2n

i=1

n (2.38)

𝜎𝑆𝐷 is a crucial index to determine the dispersion of data. Greater value of 𝜎𝑆𝐷 indicates

larger dispersion of the observed data. However, Wang, Chen & Zhou (2016) proposed

that r.m.s was more frequently used in fatigue analysis because r.m.s shows the

vibration energy of every fatigue cycle. The r.m.s value of datasets is defined as below:

r.m.s = √∑ (xi)

2ni=1

n (2.39)

Yan, Wang and Zhang (2014) suggested the commonly used statistical

parameters in statistical analysis including skewness (λ) and kurtosis (γ). When λ and γ

exist in a sample data, the data are non-Gaussian distributed. λ is a measure of the

59

asymmetry of the probability distribution of a real-valued random variable about its

mean (Rizzi, Behnke & Przekop 2010). λ is expressed in the central of moment of the

probability density function (PDF) as follows:

λ = ∑ (xi - x)3n

i=1

n(r.m.s)3 (2.40)

γ denotes the “tailedness” of the probability distribution of a real-valued random

variable (Rizzi, Behnke & Przekop 2010). The γ is defined as follows:

γ = ∑ (xi - x)4n

i=1

n(r.m.s)4 (2.41)

Crest factor (CF) is often used in characterisation of vibration signal and indicator for

vehicle ride. It could be defined as follows:

CF = |𝑋max

r.m.s| (2.42)

where Xmax is the maximum amplitude of a time history.

2.5.2 Regression Analysis

Regression analysis is one of the data mining techniques involving a set of statistical

processes to estimate the relationships among variables. In case of a simple single

independent variable to dependent variable, the regression method is known as simple

linear regression. This type of regression method is considered as linear. Simple linear

regression is commonly seen in engineering applications, such as spring stiffness

calculation (Ryu et al. 2010), and loads and cycles to failure modelling for automobile

chassis (Thomas 2012). For the spring stiffness analysis, the dependent variable was the

load applied on spring while the independent variable was the spring displacement.

Load and cycles to failure were also modelled using linear regression after applying the

natural logarithm on fatigue life.

60

In 1880s, F. Galton originated the concept of correlation which was the

fundamental to linear regression, as mentioned by Dodge (2010). Linear regression is

used to fit with a linear curve. However, introduction of mathematical approximations

indicates the presence of uncertainty that occurs and causes deviations from the true

value. Hence, the standard “goodness of fitting” measure for a regression-type model

was introduced. This statistic indicator is called the coefficient of determination (R2).

The R2 indicates the proportion of variance in the dependent variable that is predictable

from the independent variable. Graphically, the measurement is used to determine how

well the regression line represents the data set.

For simple linear regression, the R2 value of a regression could be obtained using


R2 = 1 - ∑ (X1 - X2)2n

i=1

∑ (X1 - x)2ni=1

(2.43)

where X1 is the vector of true value and X2 is the vector of n predictions. The R2 value

ranges from 0 to 1. Higher R2 values indicate greater fitness of the regression with the

data. When the prediction is poor, uncertainty or error shall reflect a significance value

of the prediction. In statistics, mean squared error (MSE) could be used to measure the

average squares of the error. The MSE is defined as below:

MSE = ∑ (X1 - X2)2n

i=1

n (2.44)

As R could also provide negative value, root squaring the R value will obtain positive

value with more weight and smaller value.

When a set of parameters possesses linear relationship, least squares method

could be applied to obtain linear regression. Least square method has been used to

determine the fatigue characteristic and ultrasound (Padzi, Abdullah & Nuawi 2014).

The function of least squares method could be written as below:

61

y = bL + aLx (2.45)

where bL is the intercept value and aL is the slope. The aL and bL are obtained using the

following solutions:

aL=∑ xi

ni=1 y

i -

1

n∑ xi

ni=1 ∑ y

ini=1

∑ xi2n

i=1 - 1

n(∑ xi

ni=1 )2

(2.46)

bL = ∑ yi

ni=1

n -

aL ∑ xini=1

n (2.47)

A prerequisite to apply least squares linear fitting method is the linearity of data.

However, engineering components tend to exhibit both linear and non-linear

relationships. For nonlinear regression, the preferred methods are logarithmic, power,

exponential, polynomial and moving average (Skrobachi 2007). A logarithm is suitable

when the data grow rapidly, followed by a period where the period continues to increase

in slower pace. Polynomial regression is applied when the data fluctuates. When the

data values increased or decreased at very high rate, exponential regression model

should be applied. Exponential value could not be created when there is zero or negative

value without any intercept. Apart from these, moving average model uses average

value to smoothen out any fluctuating data to show pattern or trend.

Power regression model is suitable for data that increase at a specific rate and

commonly used in fatigue application because the fatigue nature of materials is in this

form. S-N curve proposed by O.H. Basquin in 1910 was based on this power function.

Meanwhile, power law was used to fit stress-strain behaviour of a steel under different

strain rate loading to represent flow (Gupta & Kumawat 2017) in which the obtained

fatigue data appear to have a power-law character. The power function shall be used to

represent the data and the function as found in Zielesny (2014) can be written as follows:

y = apxbp (2.48)

where ap and bp are obtained using the following equation (Zielesny 2014):

62

ap = exp [1

n∑ ln y

i - bp

∑ ln xini=1

n

n

i=1

] (2.49)

bp = ∑ ln xi ln(y

i) -

1

N(∑ ln xi)(∑ ln y

i)

(∑(ln xi)2) - 1

N(∑ ln xi)2

(2.50)

where i is the data number.

Amsterdam and Grooteman (2016) studied the fatigue stress crack length of

aluminium alloy using Paris law with power exponent to model the crack growth

variation. Carpinteri and Paggi (2009) proposed a study of relationship existing between

Wöhler’s and Paris’s representation of fatigue. According to dimensional analysis, the

Wöhler’s and Paris’s equation provides a rational interpretation to most of the empirical

power law criteria used in fatigue. Both the linear and power functions are only

applicable when a single independent variable is used to predict the value of a dependent

variable. When the independent variable is more than one, a method for multiple input

is required for the model construction and MLR should be applied.

In 1896, F. Galton and K. Pearson systemised the correlation analysis and

established a theory of correlation for three variables. This was the fundamental idea of

MLR in which MLR was used to model the predictor with one or more independent

variables. The general form of MLR is as follows (Stojanovic et al. 2013):

yi = β

o + xiβ1

+.. .+ xikβk + ei i = 1,2, ..., n (2.51)

where 𝛽𝑜 is a constant, xk is the regression coefficient, βk are the variables, and ei are

the residuals. The MLR is applied for prediction, explanation or theory building

purposes for the parameters. Dang et al. (2014) correlated vehicle handling with other

46 metrics, shifting each dataset to zero mean value in order to obtain good results. Du

et al. (2014) also applied this method to determine the IRI road roughness index with

left and right wheel acceleration measurements. The IRI is determined as the

63

dependence parameter while the left and right wheel accelerations mean values were set

as the independent parameters.

The application of MLR in the field of fatigue is not common because fatigue

usually exhibits nonlinear behaviour such as in forms of power (Amsterdam &

Grooteman 2016). Limited research publication has been found in fatigue life analysis.

A list of recent applications of MLR in creating fatigue life prediction model is shown

in Table 2.5. These research results focused on fatigue life prediction using

experimental data, either through geometry of specimen or loading conditions. The

advantage of using MLR models distributes in its ability to detect outliers. However,

this method has some limitations such as linear relationship, randomness and equal

variance variables (Kamer-Aimu & Marioara 2007).

2.5.3 Neural Network-based Regression Analysis

Soft computing is a collection of algorithms that are employed to solve a very complex

problem. The algorithms are like fuzzy logic, artificial neural network (ANN),

evolutionary algorithms and hybrid systems (Ibrahim 2013). Fuzzy system is a method

that is traceable using the fuzzy set theory that was developed by L. Zadeh in 1965. A

mathematical framework was provided to describe the vagueness of variables by

mapping a given input to output using fuzzy logic which is known as adaptive neural

fuzzy inference system (ANFIS). As for fatigue application, ANFIS was used to model

the S-N curve of polyester under CALs (Vassilopoulos, Georgopoulos, &

Dionysopoulos 2008). However, the performance of ANFIS was less accurate as

compared to ANN (Khademi et al. 2016; Tayyebi & Pijanowski 2014; Mas & Ahlfeld

2007; Elbayoumi, Yusof & Ramli 2015; Tosun, Aydin & Bilgili 2016).

ANN is a versatile methodology that can accurately approximate non-linear

functions, developed by W. McCulloch and W. Pitts in 1943 and inspired by human

brains neurons (Pospíchal & Kvasnička 2015). Neural networks resemble the human

brain as learning and knowledge are stored within the connected neurons. A basic model

for the node in ANN is shown in Figure 2.26 where xi is the input, wi are the weights, f

is the transfer function and y is the output. ANN is also divided into two categories

64

which are single and multi-layer. Single layer ANN consists of only one hidden layer

while multilayer ANN consists of two or more hidden layers.

Table 2.5 Researches on generation of fatigue related MLR-based model

Authors Year Research contributions

Dong,

Garbatov &

Soares

2018

Established a fatigue crack related notch of a cruciform weld joint using

weld leg and slit lengths

Mayén et al. 2017

Generated a crack prediction model using stress amplitude and number

of cycles as input.

Jin et al. 2016

Generated a multiple linear prediction model to correlate damage,

vibration and temperature of a highway bridge.

Rothleutner et

al. 2015

Created a shear stress model for hardened steel using fatigue life, carbon

content and normalised effective case depth as independent variables

(radius).

Bižal,

Klemenc &

Fajdiga

2014

Established a fatigue life model for aluminium using different porosity

level and manufacturing properties like die temperature and pressure.

Kanoje,

Sharma &

Harsha

2013

Established a natural frequency model of locomotive wheel using rim

geometry and loadings. The natural frequencies were then correlated to

fatigue life.

Kannappan &

Dhurai 2012

Modelled a relationship between tensile strength properties of fibre

reinforced composite with temperature, pressure and time as

independent parameter.

LeBozec &

Thierry 2010

Modelled corrosion cyclic test of automotive aluminium alloy with

parameters like concentration of salt, drying level, humidity cycle,

frequency of salt spray and temperature.

Shell,

Buchzeit &

Zoofan 2005

Modelled residual fatigue life of aluminium alloy with non-destructive

evaluation metrics.

Lu, Behling &

Halford 2000

Modelled total strain range as dependent variable with heating hold time

and cyclic life relation for stainless steel alloy SS409 which was widely

used in automotive exhaust system.

Atkins &

Gibeling 1995

Modelled a relationship of creep strain according to stress and

temperature for Al-SiC metal matrix composite.

Zhang, Bui-

Qouc &

Gomuc

1990

Modelled fatigue life of stainless steels with heating temperature and

strain rate effects under cyclic loadings.

Vinokur et al. 1985

Developed a multiple linear regression model to predict intensity of

wear with temperature and time conditions of tempering and hardening

65

Figure 2.26 A basic model of a single node ANN

Source: Livinstone 2008

An example of a multilayer neural network is shown in Figure 2.27 (Borah,

Sarma & Talukdar 2015). This example of multilayer neural network has two hidden

layers with four neurons in the first and second hidden layers. There are many types of

ANN available in the supervised and unsupervised learning. In general, the neural

network could be classified into two main types, namely the feed forward and feedback

ANN (Baykal & Yildirim 2013). Feed forward type is a type of straight forward ANN

with no loop, with an example of feed forward ANN is illustrated in Figure 2.27.

Architecture of feed forward ANN could be in single or multiple layers. Feed forward

type of neural network is also a static type ANN which has no feedback.

There is another type of ANN known as recurrent or feedback ANN. Recurrent

or feedback type of neural network is a type of ANN where the output provides feedback

to the neuron (Borah, Sarma & Talukdar 2015). This type of neural network is a type of

dynamic neural network where the output depends on the current input. One example

of a recurrent neural network is the Hopfield neural network where all the neurons were

fully interconnected (Hsu 2012). Another famous neural network architecture is the

radial basis function network invented by D. Broomhead and D. Lowe in 1988. The

radial basis function network is similar to feed forward neural network with exception

of its application of radial basis function as the activation function. When more than

one hidden layer is applied, the learning process is known as deep learning

(Schmidhuber 2014). Deep learning could be implemented in both feed forward and

feedback neural networks. ANN provides a very good prediction results because

numerical optimisation was applied to iteratively improve the regression (Hanke 2010).

This technique is used to optimise least square problems.

66

Figure 2.27 An example of multilayer feed forward ANN architecture

Source: Borah, Sarma & Talukdar 2015

Another one of the important parameters to improve the performance of an ANN

is the activation function. The activation function of ANN transforms the activation

level of a neuron into an output signal. There are various available activation functions

such as uni-polar sigmoid function, bipolar sigmoid function, hyperbolic tangent

function, radial basis function, conic section function (Karlik & Vehbi Olgac 2011).

Comparison between these activation functions has been widely performed. The bipolar

sigmoid function is the most applied function because of its computational efficiency.

Application of ANN is vast in engineering application. Many ANNs are involved in

recent advance applications such as adaptive robotics and control, handwriting

recognition, speech recognition, keyword spotting, music composition, attentive vision,

protein analysis, stock market prediction and many other sequence problems. Recurrent

neural network was particularly used in the recognition of handwriting (Graves 2011),

image, and speech (Graves, Mohamed & Hinton 2013). A recurrent neural network is

heavier than a feed forward neural network in terms of computing because it provides

feedback to the hidden or input layers to correct the weights and biases. Therefore,

recurrent neural network is suitable for the abovementioned complex analysis.

Application of feed forward neural network is common in fatigue applications

due to the straightforward data (Figueira Pujol & Andrade Pinto 2011). Al-Assadi, Kadi

and Deiab (2007) demonstrated the ability of different neural networks in predicting

fatigue life. The input parameters include volume fraction, tensile modulus, tensile

strength, applied load parameters, probability of failure, and statistical parameters of

fatigue life. The output was the logarithm of the fatigue life cycles. Kang et al. (2006)

67

utilised a feed forward neural network together with the critical plane method to predict

the multiaxial fatigue life of an automotive subframe. The results indicated that feed

forward ANN was appropriate in searching critical locations. In addition, neural

networks were applied to estimate the fatigue crack growth rate. ANN was also applied

to address the stochastic aspects of fatigue phenomenon. For example, Janežič,

Klemenc and Fajdiga (2010) implemented a feed forward neural network to model

cyclic stress-strain scatter using arbitrary selection of temperature, size of cross-section,

content of alloying elements, and loading rate as the inputs.

2.5.4 Validation Analysis

Once the regression models are generated, performances of the generated models will

be verified. Performance of a regression was usually analysed using residuals. The

residuals of a good regression prediction should be in normal distribution (Ghasemi &

Zahediasi 2012). There are two types of method to test for data normality, which are

graph assessment method and normality test. For the graph assessment, residuals were

plotted into error histogram and scatter plot (Francisco et al. 2006). An example of

residual histogram and scatter plot is shown in Figure 2.28(a) & (b), respectively. The

commonly used normality test method is Kolmogorov-Smirnov (KS) test. KS test is

widely used because it does not depend on the sample size.

Besides KS test, another well-known normality test is Lilliefors test. Lilliefors

(LF) test is an improvement of KS where the tails of probability distribution were

corrected. Lilliefors test is limited to up to 1000 sample size. The first step in Lilliefors

test is to obtain the individual z-scores (zi) for every member of the sample. The zi is

obtained as follows:

zi = xi - x

σSD

(2.52)

Subsequently, the next step is to calculate the test statistic which is empirical density

function based on the zi. The formula for Lilliefors test statistic is as follows:

68

Residual

LF = maxx|Dz(x) - Lz(x)| (2.53)

where Dz(x) is the theoretical standard normal distribution function, Lz(x) is the

empirical distribution density function of the zi value. The last step is to determine the

critical value for the test. When the number of sample is greater than 30, the critical

value (CV) for significance level, α = 0.05 (95 % confidence level) is obtained as

follows:

CV = 0.886

√n (2.54)

The null hypothesis (H0) is rejected when the test statistic is greater than the critical

value. The hypothesis for Lilliefors test is defined as below:

H0: Data are normally distributed

H1: Data are not normally distributed

(a) (b)

Figure 2.28 Residuals normality assessment graph: (a) error histogram, (b) scatter plot

Source: Francisco et al. 2006

In a regression analysis, the prediction value is always required to be in normal

distribution to ensure the value would not deviate too much from the real data. Razali

and Yap (2011) studied normality of regression and concluded that Lilliefors test is

Fre

quen

cy

Reg

ress

ion s

tand

aris

ed r

esid

ual

Regression standarised predicted value

69

suitable to test for normality among regression residuals. Normality test examines the

goodness of regression. However, scatter band is always applied to examine fatigue

results. Scatter band is often used in fatigue study to describe the difference of two result

sets, such as experimental and simulation results. Shamsaei et al. (2010) utilised this

method to compare Palmgren-Miner and Fatemi-Socie critical plane predicted fatigue

lives. For illustration purpose, a generated schematic diagram for this scatter band is

shown in Figure 2.29. Both the axes are logarithmic and the reference line is labelled as

1:1. The upper bound is labelled with 2:1 while the lower bound is labelled with 2:1

(Karolczuk 2016). When a datum locates beyond the 1:2 or 2:1 boundary from the

reference line, the datum is considered to have poor correlation.

Figure 2.29 Schematic diagram of scatter band for fatigue life using generated data

For standard validation of test data, correlation between experimental and

predicted data is usually performed. The correlation between predicted data and

experimental data is determined using R2 value as shown in Figure 2.30. R2 value above

0.50 is considered as acceptable. R2 value above 0.80 is considered as good while any

value above 0.90 is considered as very good. A good correlation indicates the prediction

results are closely associated with the experimental data. Meanwhile, Huang and Griffin

(2014) used this correlation method in vibration analysis to study how good the

vibration model prediction as compared to experimental results. A good validated

mathematical model is applicable for prediction so that conclusions could be drawn.

Log – Experimental fatigue lives (cycles)

Lo

g –

Pre

dic

ted

fat

igue

lives

(cycl

es)

70

Figure 2.30 Schematic diagram of correlation between prediction and experimental data

2.6 SUMMARY

This chapter discusses the related research works that had been done by researchers in

the fields of fatigue and automotive ride. The focus of this chapter is on the development

of durability and vehicle ride in terms of statistical and mathematical modelling. The

discovery of fatigue had begun since 1837 while the vehicle ride standard was first

introduced by Society of German Engineering in 1963. The literature trends have also

shown extensive publications of vehicle ride analysis in recent years. Both durability

and ride analysis were directly linked to the automotive suspension design. As for the

vehicle ride and durability analysis, regression and neural network analysis are

frequently found in the literature and illustrates the significance of the data analysis

approaches in automobile ride and durability analysis.

Based on the findings of this literature study, it is found that the fatigue life

estimation in automotive suspension design still requires some improvements because

the spring fatigue life analysis and automotive ride were previously conducted

independently. Fatigue life prediction process in automobile spring design consisted of

a scientific gap in the aspect of spring design’s effects towards vehicle ride which

required additional efforts during the spring design phase. Generation of mathematical

models to shorten the automotive suspension design process has become the motivation

of the current research works. In Chapter III, details of the methodology employed in

this study are discussed. A comprehensive presentation of the specific methods used to

develop an original mathematical model as the novelty of this study is fully described.

Experimental data

Pre

dic

ted

dat

a

71

CHAPTER III

METHODOLOGY

3.1 INTRODUCTION

This chapter explains the methodology employed to achieve the aim of this research

which is the establishment of regression-based durability relationship for automobile

vertical vibration. In Figures 3.1 and 3.2 are the illustrations of the process flow of this

current study, dividing the methodologies according to the three objectives. In order to

achieve the first objective which was characterisation of durability relationship, coil

spring design from a local automobile was analysed with collected strain and

acceleration time histories. Statistical analysis was performed to understand the spring

responses under different road conditions. In obtaining additional datasets, artificial

road data and quarter car models were employed to generate new datasets. The

simulation outcomes were used to predict spring fatigue life and ISO 2631 vertical

vibration. Subsequently, a new regression relationship was obtained with vehicle body

frequency of quarter car model, spring fatigue life and ISO 2631 vertical vibration as

the parameters. This proposed regression was used to predict fatigue life of spring.

For the second objective, the steps involved the establishment of the regression-

based durability relationship which led to the novelty of current research. This step

included utilisation of artificial neural network (ANN) to train the datasets. Based on

the literature review carried out by author, ANN was suitable to perform regression

analysis for linear and nonlinear data. In this analysis, ANN performed high

dimensional and multimodal search space to determine the optimised iterations with a

few sets of weights and biases. In addition, the improvised ANN architecture led to

better performance in terms of MSE and coefficient of determination (R2) value.

72

Therefore, different ANN architectures with varying hidden layers and neurons were

analysed. Through these processes, the output of the ANN predictions was the

optimised fatigue life of coil spring.

Lastly, the third objective was to validate the regression and ANN-based

durability regressions. Five sets of strain and acceleration measurement data from an

actual vehicle were processed and put into the generated fatigue life prediction

regression and ANN. The accuracy of the prediction was analysed using statistical

methods such as R2 value and conventional fatigue life scatter band. The conventional

fatigue life scatter band approach was found to be suitable for fatigue life prediction

between simulation and experimental. Meanwhile, the normality of the prediction

residuals was assessed according to Lilliefors test. The obtained R2 value for the

regression and experimental results indicated the level of correlation between

simulation and experimental results.

3.2 DURABILITY CHARACTERISATION OF THE SUSPENSION

SYSTEM

3.2.1 Perform Analysis on Spring

Macpherson suspension system was used as the case study to establish the durability

regression because this type of suspension system had a simple architecture and

required lesser space which is suitable for the application of most passenger cars

(Mahmoodi-Kaleibar et al. 2013). Thus, a frontal coil spring of a local passenger car

was used to perform the regression establishment. The Macpherson suspension system

suits well for this type of vehicle application because of the simplicity of suspension

design when compared to a double wishbone suspension system (Mahmoodi-Kaleibar

et al. 2013). Both the Macpherson and double wishbone suspension systems possess

good strength and durability. However, Macpherson type suspension system is simple

and requires less components such as control arms.

73

Figure 3.1 Process flow of the research methodology: Part 1

OBJECTIVE 1:

Determine a multiple-linear regression

analysis with fatigue life as the response

Spring stiffness

sensitivities

OBJECTIVE 2:

Establish the spring fatigue life

prediction using ANN

Collect and analyse the strain and acceleration

signals on various road conditions:

a) highway

b) hilly

c) residential

d) UKM campus

e) Rural (gravel)

Characterise durability of the suspension system

Force time history Acceleration time histories

Generate artificial data according to

Road class “A” to “D”

class “A” to “D”

Continue to

Figure 3.2

Vehicle body

frequency Spring fatigue life ISO 2631 vertical

vibration

Determine multiple linear regression for fatigue life prediction

Perform CAD and CAE

on spring geometry

Extract data from simulated quarter car model

simulation

74

Figure 3.2 Process flow of the research methodology: Part 2

Analyse the prediction outcomes using

statistical method

OBJECTIVE 3:

Validate the regression-based and ANN

durability predictions

Input experimental data into

regression-based and ANN durability

relationship

Normality test

Continued

from Figure

3.2

Determine the number of neurons Determine the number of layers

Set number of neurons: 1:10 Set number of layers: 1: 3

Analysis of number of neurons and layers

Determine the suitable architecture for

fatigue life prediction

Obtain the suitable fatigue life

NOVELTY:

Integrated vibration-life relationships

Scatter band

Validate established relationship

Design the ANN architecture

Suitability of fitting

Note:

bold letter: objectives

bold & italic letter: novelty

75

The selected automobile suspension system was from a Proton SAGA BLM

1300 cc with kerb weight of 1085 kg which consisted of a set of spring and damper with

the spring geometry listed in Table 3.1. These data were obtained from measurement

and observation on an actual spring. The spring stiffness was calculated as 20,000 N/m

while the spring index was 9.833. Optimum spring index ranged from 4.00 to 20.00

where the spring index out of this range would lead to extra cost and tolerance during

manufacturing (Taktak et al. 2014). The weight of this coil spring was determined at

2.64 kg, with maximum shear stress of a helical spring usually occurred in the spring

inner surface. For this spring, the Wahl shear stress correction factor was calculated to

be 1.15 in which this value was applied in spring shear stress design (Chiu et al. 2016).

The geometry design of the coil spring as shown in Figure 3.3 was produced

using a computer aided design (CAD) software by means of the CATIA software

package. The geometry of this spring was created and used as input to determine the

stress distribution using FEA approach in SIMULIA ABAQUSTM software.

Subsequently, the FEA stress-strain model was applied for fatigue life analysis using

the nCode DesignLife®.

Figure 3.3 CAD of the coil spring

Table 3.1 Measured geometrical properties of the spring

Geometry MacPherson spring values

Spring free length (mm) 385

Mean coil diameter (mm) 130

Material diameter (mm) 12

Number of active coils 6

76

In terms of material, the SAE 5160 carbon steel was given and this material is

known as the most common spring steel with high yield strength and elasticity (Lopez-

Garcia et al. 2016). Based on the carbon content, the spring steel was classified as low-

medium carbon steel with the carbon content ranged from 0.3 to 0.6 % (Rasyidi &

Pratiwi 2015). Monotonic and cyclic mechanical properties of this spring steel are listed

in Table 3.2. The cyclic properties of this carbon steel were obtained through fatigue

test of heat treated specimens and documented in nCode material database, as reported

by Bhanage and Padmanabhan (2015).

Initial design process of a coil spring involved calculation of spring stiffness

including measurements of material properties, boundary and loading conditions for

target stiffness (Arjun & Peter 2014). Once these parameters were determined, the study

continued with static stress analysis to prevent design static failure based on the FEA

procedures. Initially, the coil spring was meshed with three-dimensional (3D)

hexahedra (Hex) elements. This type of element was selected because 3D Hex elements

provided more accurate results compared to 3D tetrahedrical and two-dimensional (2D)

quadrilateral elements (Anitua et al. 2009). A mesh sensitivity analysis was conducted

as listed in Appendix B. Considering the bar size of the coil spring, the element size of

2 mm was suitable for the meshing because the model consists of 6 elements across the

thickness level (Gokhale et al. 2008). In this case, the spring model consisted of 9227

nodes and 7170 3D Hex elements. In the case of boundary conditions, the top of the

spring was fixed where no movement was allowed and the loads were applied at the

opposite of the spring.

Table 3.2 Monotonic and cyclic properties of the spring material

Properties Values

Ultimate tensile strength (MPa) 1,584

Modulus of elasticity (GPa) 207

Yield strength (MPa) 1,487

Fatigue strength coefficient (MPa) 2,063

Fatigue strength exponent -0.08

Fatigue ductility exponent -1.05

Fatigue ductility coefficient 9.56

Cyclic strain hardnening exponent 0.05

Cyclic strength coefficient (MPa) 1,940

Poisson ratio 0.3

Source: Bhanage & Padmanabhan 2015

77

Considering the weight of fully loaded passenger car is about 1,200 kg, the static

load on each suspension is about 300 kg. The assumption that the loads were evenly

distributed in all four wheels was made (He et al. 2010). Hence, an axial force of 3000

N was applied on the bottom of the spring. For torsional loading, same amount of torque

load was also applied on spring material as proposed by Akiniwa et al. (2008). The

torque load was applied on the same spot of coil spring but in X-axis according to SAE

coordinate system to simulate bending moment because the wheel is moving in arc

direction (Ryu et al. 2010). All the values and directions of force, material properties,

and mesh qualities could affect the accuracy of the FEA results (Gokhale et al. 2008).

Extra cares were needed when meshing the spring CAD. On the other hand, linear static

analysis was conducted in the calculation due to its simplicity to determine the stress

distribution (Putra 2016). From the static analysis, results of the spring FEA results

indicated the maximum stress region of the spring where the critical location for strain

time histories measurement was indicated. Furthermore, the effects of axial and

combination of axial and torsional of the spring in stress level were analysed because

the loads of spring could come from various directions due to the arc movement of

wheel (Liu et al. 2008).

3.2.2 Collection of Strain and Acceleration Signals according to Road Surface

Once the critical region of the spring was identified, the measurements of strain time

histories on the vehicle were conducted using a set of strain gauges. In automotive

industry, the required strain time histories were obtained by driving the vehicle

equipped with prototype components for durability evaluation known as a

“development mule” (Sashikumar et al. 2017). The desired loading time histories of the

prototype vehicle components were collected for driving behaviour and road surface

effects analyses. In this work, the required loading signals were strain time histories of

the coil spring and acceleration time histories of the vehicle sprung and un-sprung mass.

The strain data collection process could be generally divided into two stages which were

instrument installation and signal collection stages.

The equipment for the strain measurement were a 2 mm uniaxial strain gauge, a

SoMAT eDAQ data acquisition system, and a computer with TCE software package

78

(SoMAT 2002). Meanwhile, the applied uniaxial strain gauge was a rectangular, planar

strain gauge. This type of rectangular uniaxial strain gauge was used when the direction

of principal strains was unknown (Vishay 2005a). For this type of strain gauge, the

gauge factor of 2.07 ± 1.0% was obtained as listed in the purchase packaging. In

addition, the gauge resistance was 120 Ω and this resistance range is the lowest among

the commercial strain gauge because the strain gauge with lower gauge resistance

possess lower errors (He, Yi & Sun 2016). These constants defined the properties of

strain gauge sensors where the generated voltage from Wheatstone bridge were scaled

according to these constants. These constants were also part of the inputs to SoMAT

software.

Meanwhile, the accelerometers used in the analysis were piezoelectric type

from PCB PIEZOTRONICSINC. The measurement range and frequency of the

accelerometer were required to be higher than the vehicle vibration level to capture the

road induced vibration. The selected accelerometers had the sensitivity of 1.02

mV/(m/s2), measurement range of ± 4900 m/s2 and frequency range of 0.5 – 10 kHz.

The vibration level of an automobile was usually below 8 m/s2 and frequency of 500

Hz (Burdzik 2014). Hence, this type of accelerometer was suitable in automobile

vibration data collection because it was able to capture all the required information of

the suspension vibrations. In this case, the accelerometer was attached at the top mount

for ride assessment because the generated quarter car model did not take the seat into

consideration (Ahmed et al. 2015; Phalke & Mitra 2016).

Attachment of a strain gauge to the coil spring was the main factor that directly

affected the accuracy of the collected data (Vishay 2005b). The surface of the

attachment point must be flat and clean. Prior to the measurement, the desired surface

of the coil spring was scrubbed with a sand paper of grade 400 to ensure polished surface

(ASTM E112-96 2004). As for the attaching material, a specific glue cynoacrilite (CC-

33A) was used to attach the strain gauges. The adhesive glue can withstand heat up to

80 oC as heat dissipation was an important parameter for data collection (Radhakrishna

& Gurmukhdas 2013).

79

An experimental setup flow for strain and acceleration data collection is shown

in Figure 3.4. The strain gauge sensor was attached at the coil spring hotspot while

another end of the strain gauge was connected to a data acquisition system. Gauge factor

of 2.07 were set into the Somat data acquisition software. On the other hand,

acceleration time histories of the vehicle were measured using single axis

accelerometers. One accelerometer was attached at the lower arm of the vehicle to

collect un-sprung mass vibration while another accelerometer was attached at the top

mount of the suspension strut to collect sprung mass vibration. Both accelerometers

were attached to the components using a strong adhesive material.

The accelerometers were then connected to a data acquisition system NI 9234

and the data were previewed and recorded using NI LabVIEW®. Once the instruments

were installed, the vehicle was driven across five different road conditions to collect

both the strain and acceleration time histories. The selected area for data measurement

were highway, UKM campus, hilly, residential, and rural road surfaces. During the

testing, the vehicle speeds varied across the different road conditions as listed in Table

3.3. Although the driver tried to maintain constant speed for all road conditions, there

were some uncertainties on the road, such as sudden vehicle lane changes or extreme

rough road surfaces which lead to varying vehicle speed.

For the selection of sensor locations, the accelerometer was attached as close as

possible to the top mount to collect the transmitted vibration response while the

accelerometer at the lower arm was collected at the lower arm which close to the damper

strut for un-sprung mass excitations. Meanwhile, the strain gauge attachment point was

determined based on the FEA stress hot-spot referred to Section 3.2.1. The

accelerometers and strain gauge were calibrated according to the calibration certificate

and the initial value was reset into zero before experiment. The proposed vehicle speed

was 80 kmph according to RARS but due to the harsh road conditions, the driver has to

reduce the vehicle speed which lead to the varying vehicle speed in Table 3.3.

During the vehicle test, various road conditions in Malaysia were identified for

data collection with the route as shown in Figure 3.5 – 3.9. The road conditions were

selected based on the common usage of Malaysians. Different road profiles contributed

80

to distinct fatigue behaviour of the automotive components. For example, Ozmen et al.

(2015) collected data from a harsh road using different leaf spring to develop a new in-

lab fatigue test bench. In addition, Kubo et al. (2015) investigated the influence of shock

absorbers on leaf spring fatigue behaviour using pothole tracks. These literatures

justified the significance of road profile effects on automotive durability analysis

Figure 3.4 Experimental setup for strain and acceleration signals collection

Accelerometer

81

Table 3.3 Vehicle speed during signal collection

Selected Road Vehicle speed (kmph)

Highway 80 – 100

UKM campus 60 – 80

Hilly 40 – 80

Residential 40 – 50

Rural 30 – 40

(a) (b)

Figure 3.5 Highway road conditions: (a) road preview, (b) route map

(a) (b)

Figure 3.6 UKM campus road conditions: (a) road preview, (b) route map

(a) (b)

Figure 3.7 Hilly road conditions: (a) road preview, (b) route map

82

(a) (b)

Figure 3.8 Residential road conditions: (a) road preview, (b) route map

(a) (b)

Figure 3.9 Rural road conditions: (a) road preview, (b) route map

3.2.3 Characterisation of Fatigue and ISO 2631 Vertical Vibration

After data collection, both collected strain and acceleration signals were characterised

to seek for the current spring design durability and performance. In order to understand

the characteristics of time histories, statistical properties of the signal were analysed

because the fatigue and vibration time histories were generally non-stationary in nature.

In this case, four commonly used statistical parameters in fatigue analysis namely the

mean value, standard deviation (SD), root mean square (r.m.s), and kurtosis were

applied and listed in Equations 2.36, 2.37, 2.38 and 2.39. The mean value of a strain

signal identified the vibrations experienced by the coil spring, either in tensile or

compression depending on the positive or negative signs of the mean value.

83

The statistical parameters were obtained using the nCode GlyphWorks®

software with the process flow as shown in Figure 3.10. In addition, the acceleration

signals were analysed in the frequency domain utilising the fast Fourier transform (FFT)

and power spectral density (PSD). Frequency spectrum setup in nCode GlyphWorks®

was used to determine the FFT and PSD of the signals and the flowchart for spectrum

analysis is shown in Figure 3.11. Frequency domain analysis was performed to

determine the energy content inside a time history where these energy contents were

related to vehicle ride and spring fatigue life.

Figure 3.10 Flowchart for statistical analysis using Glyphworks®

The fatigue analysis of the spring using nCode GlyphWorks® was conducted as

shown in Figure 3.12. The GlyphWorks® strain life fatigue assessment predicted the

fatigue life of the spring using material cyclic properties and strain variable amplitude

loadings (VAL) as inputs. All three Coffin-Manson, Morrow and Smith-Watson-

Topper (SWT) approaches were used to predict the fatigue life of the coil spring because

these models considered different mean stress effects. The cyclic hardening effects were

also considered when applying the Ramberg-Osgood relationship and Masing’s model

which could be referred to Equations 2.12 and 2.13. The Ramberg-Osgood and

Start

Input strain or acceleration time

histories

Select statistic function block

Calculate the statistic parameters

Display the results

Stop

Are the results within

acceptable range?

Yes

No

84

Masing’s model considered the total strain (elastic and plastic) for fatigue life

assessment.

Figure 3.11 Flowchart for spectrum analysis using Glyphworks®

Applying the strain life approaches in this analysis is suitable because coil spring

was a small component. When a crack was initiated on the spring, the spring was

considered as failed and replacement must be immediately done. In addition, application

of strain life approaches to predict fatigue life was common in automotive components

such as spring (Karthik et al. 2012), disc brake (Pevec et al. 2014), and truck cab (Fang

et al. 2015). Although both stress and strain approaches are considered localisation

effects, stress-life approaches had a very high safety factor and was not suitable for

components that could be easily replaced. Hence, strain life approach was selected to

perform fatigue life prediction for coil springs.

After analysing the fatigue life of spring using measured strain time histories,

the ISO 2631 vertical vibration of the vehicle associated with the coil spring was

obtained using Matlab® R2015a software package. The procedures to obtain the ISO

Start

Input strain or acceleration time

histories

Select spectrum analysis block

Calculate the PSD of time histories

Display and save the results

Stop

Is the PSD range

positive?

Yes

No

85

2631 objective vertical vibration are shown in Figure 3.13. Firstly, the collected

acceleration signals were transformed into frequency domain PSD and a series of

discrete frequencies within the range of interest was selected. Determining the mean

square value of acceleration at a given frequency (fc) requires integration of the obtained

PSDs over a one-third octave band. In other words, the centre frequency band of 0.89 –

1.12 fc was applied where the r.m.s value of acceleration at each centre frequency, fc

was obtained. The Sv(f) was the amplitude of the acceleration PSD for vehicle sprung

mass while ar.m.s was the r.m.s acceleration.

Figure 3.12 Flowchart for nCode Glyphwork®-based strain life fatigue assessment

Subsequently, the ISO 2631 weighting factors were obtained by multiplying the

acceleration amplitude of one third centre frequencies with the amplitude of ISO 2631

proposed vertical weighting factors. In Figure 3.13, Aw is the frequency weighted r.m.s

acceleration, Wi is the weighting factor for the ith one-third octave band, and ai is the

r.m.s acceleration for the ith one-third octave band. The obtained Aw were used to assess

the comfort level of the vehicle using the guide proposed by ISO 2631 as listed in Table

3.4 while the applied weighting factors proposed by ISO 2631 (1997) are listed in Table

3.5. According to ISO 2631, the frequency of interest for human ranged from 0.1 to 80

Start

Input strain time history

Calculate fatigue damage and life

Display and save the results

Stop

Select strain-life function block

Is the fatigue life > 1

and damage < 1?

Yes

No

86

Hz. In this case, the vertical weighting factors, wk from Table 3.5 was applied in the one

third octave band to obtain the vibration index.

Figure 3.13 Procedures for ISO 2631 vibration assessment

Table 3.4 Guide for assessing the effects of vibration on comfort

Range of weighted acceleration Comfort level

Less than 0.315 m/s2 Not uncomfortable

0.315 – 0.63 m/s2 A little uncomfortable

0.5 – 1 m/s2 Fairly uncomfortable

0.8 – 1.6 m/s2 Uncomfortable

1.25 – 2.55 m/s2 Very uncomfortable

Greater than 2 m/s2 Extremely uncomfortable

Source: ISO 2631-1 1997

Measured acceleration

Transform the acceleration time histories into PSDs

Transform PSD into one-third octave band

𝑎𝑟𝑚𝑠 = ቌ න 𝑆𝑣ሺ𝑓ሻ𝑑𝑓

1.12𝑓𝑐

0.89𝑓𝑐

ቍ

12

Apply ISO 2631 vertical weighting factors

𝑎𝑤 = ሺ𝑊𝑖𝑎𝑖ሻ2

𝑖

൩

12

Apply integration

Obtain vertical vibration index

Analyse the vibration index

Start

Stop

87

Table 3.5 Frequency-weighting curves for principal weighting

Frequency, Hz Wk

0.100 31.2

0.125 48.6

0.160 79.0

0.200 121

0.250 182

0.315 263

0.400 352

0.500 418

0.630 459

0.800 477

1.000 482

1.250 484

1.600 494

2.000 531

2.500 631

3.150 804

4.000 967

5.000 1039

6.300 1054

8.000 1036

10.000 988

12.500 902

16.000 768

20.000 636

25.000 513

31.500 405

40.000 314

50.000 246

63.000 186

80.000 132

Source: ISO 2631-1 1997

The weighting factors of ISO 2631 (1997) were regarded as the most

comprehensive standard in which the lowest frequency was 0.1 Hz. The frequency from

0.1 to 0.5 Hz covered the motion sickness of the passengers. Upon the completion of

the ride related vertical vibration and fatigue analysis, linear regression was performed

to determine the relationship between these two parameters under this fixed suspension

system configuration so that the fatigue life could be expressed in terms of ISO 2631

vertical vibration. The effective method to perform these tasks was through a simple

regression method.

There were many existing types of regression approaches for engineering

application. Nevertheless, power law was commonly applied in fatigue analyses of

materials (Amin Yavari et al. 2016). A power law is a functional relationship between

88

two quantities in which a relative change in one quality results in a relative change of

the other quantity as a power of another, independent of the initial size of those

quantities. There were also a few types of nonlinear power curve characterisations, such

as polynomial, exponential, cubic and approximate cubic. Still, power law is the most

commonly used for fatigue analysis (Carrillo et al. 2013).

The relationship between fatigue damage and ISO 2631 vertical vibration was

determined using power law because the fatigue level of material was nonlinear in

nature. The applied power law regression possessed the relationship between two

parameters in the form as follows (Amitrano 2012):

𝑦 = 𝑎𝑥𝑏 (3.1)

where a and b are coefficients with fitted least squares and defined as below:

b = n ∑ (ln xi - ln y

i)n

i=1 − ∑ ሺln xiሻni=1 ∑ (ln y

i)n

i=1

n ∑[ሺln xሻ2] − ሺ∑ ln xሻ2 (3.2)

a = ∑ሺln yሻ − b ∑ሺln xሻ

n (3.3)

Here, n is the number of data, x is the spring fatigue life, and y is the ISO 2631 vertical

acceleration.

In determining the goodness of fitting of the model, coefficient of determination

(R2) was used. The R2 was used to determine the proportion of the variance in the

dependent variable that was predicted from the independent variable and defined as

follows:

R2= [∑ ln xi ln y

i-

1n

∑ ln xi ln yi]

2

[- ሺ∑ ln xiሻ2

n] (ln y

i)

2-

(∑ ln yi)

2

n൩

(3.4)

89

Apart from R2, MSE was used to find the line of best fit. The classification of goodness

of fit using R2 value is listed in Table 3.6. Adopting the power law curve fitting, the

dependent variable was the weighted ISO 2631 vertical acceleration while the

independent variable was the fatigue life. The data were fitted using Matlab® curve

fitting tool. These predictions were limited to a single spring fatigue life and ISO 2631

weighted vertical acceleration without the consideration of suspension parameters

effects. In actual, different coil spring designs exhibit different effects in spring

durability and vehicle vertical vibration characteristics.

Table 3.6 Suitability of fit for coefficient of determination value

Obtained R2 value Goodness of fitting

0.90 Very good

0.80 Good

0.60 Acceptable

Source: Sivák and Ostertagová 2012

The novelty of this research was to determine the relationship between spring

fatigue life and ISO 2631 vertical vibration. Nevertheless, the suitability of the fitting

was important because it affected the consistency of predictions. This proposed power

law regression only took a single parameter which was the ISO 2631 vertical vibration

as the independent variable. In consideration of the spring design, a vehicle quarter car

model was constructed to extract the effects of spring stiffness. A regression method

with multiple inputs were used to build the relationship between these parameters.

3.3 ESTABLISHMENT OF MULTIPLE LINEAR REGRESSION

3.3.1 Generating Artificial Road Profiles

To simulate a quarter car model, realistic road profiles were required to simulate actual

road conditions. However, the measurement data of road conditions was very limited

due to time constraints. In agreement with ISO 8608 road profiles, it was possible to

generate road profiles with stochastic representation in the form of PSD of vertical

displacements. Fundamental idea of the ISO 8608 was spatial frequency, road profile

and PSD. ISO 8608 proposed the description of the road roughness profile through the

calculation of PSD of vertical displacement as a function of spatial frequency. For

90

comparing different road roughness profiles, a classification based on their PSD was

conducted by calculating the conventional values of spatial frequency.

A total of four classes of road roughness were generated according to ISO 8608

as shown in Figure 3.14 and the parameters are defined in Table 3.7. The road profiles

were regarded as simple harmonic function and geometric mean values of the road

roughness profile were used to formulate the road profile according to road roughness

and waviness functions as listed in Table 3.8 and 3.9, respectively. The random phase

angle was assumed to follow a uniform probabilistic distribution within the 0 - 2π range.

The road profile was then converted into time domain with consideration of vehicle

speed. The waviness function was programmed into Matlab to construct the different

classes of road profile under a vehicle speed of 80 kmph because this speed was the

standard value for road roughness (Kropac & Mucka 2007).

Figure 3.14 Procedures for ISO 8608 road profile generation

Determine the required road class

Generate the PSD according to degree of roughness

as listed in Table 3.8

𝐺𝑑ሺ𝑛ሻ = 𝐺𝑑ሺ𝑛𝑜ሻ. ൬𝑛

𝑛𝑜൰

−2

Start

Stop

Applied the waviness function with k value in Table 3.9

ℎሺ𝑥ሻ = ξ𝛥𝑛. 2𝑘 . 10−3. ቀ𝑛𝑜

𝑖. 𝛥𝑛ቁ . 𝑐𝑜𝑠ሺ2𝜋. 𝑛𝑖. 𝑥 + 𝜑ሻ

𝑁

𝑖=0

Convert spatial to temporal domain

𝑆𝑔ሺ𝑡ሻ = 𝑆𝑑ሺ𝑑ሻ

𝑉

91

According to the ISO 8608 standard, four of ISO 8608 road classes (Class A to

D) were generated for sprung mass acceleration and spring force time histories

extraction. These road classes were selected due to their suitability for automobile

application based on reasonable roughness, as reported by Agostinacchio et al. (2014),

Patil et al. (2016), and Koulocheris et al. (2016). Road classes “A” and “B” were

classified as smooth runway and highway while road class “C” was gravel road. The

class “D” was the rough runway which had a very rough surface profile (Balmos et al.

2014). The researches have reported that road classes of E and above were too harsh for

automobile analysis. Hence, road classes A to D were generated and applied for quarter

car model simulations.

Table 3.7 Parameter for ISO 8608 road profile generation

Parameter Definition

Gd(no) Degree of roughness value as listed in Table 3.7

no Spatial frequency

n Road length data point

h(x) Amplitude of the vertical displacement

Ai Amplitude which obtained from the mean square value of the component for the

spatial frequency

𝜑 Phase angle

ni Generic spatial frequency

x Abscissa of road length from 0 to L, Δn = 1/L, N = L/B

B Sampling frequency

k Constant value depending on ISO 8608 road classification as depicted in Table 3.8

Sg(d) Road profile in terms of road length

V Vehicle speed

Source: ISO 8608 2016

Table 3.8 Classification of road roughness proposed by ISO 8608

Road Class Degree of roughness

Lower limit Upper limit Geometric mean

A 8 32 16

B 32 128 80

C 128 512 320

D 512 2048 1280

Source: ISO 8608 (2016)

Table 3.9 k values for ISO 8608 road roughness classification

Road class k value

A 2

B 3

C 4

D 5

Source: Agostinacchio et al. (2014)

92

3.3.2 Extract Data from Simulated Quarter Car Model

After obtaining the generated artificial road profile, a vehicle suspension quarter model

was constructed using a modelling methodology based on object orientation and

equations solving. Computer based modelling is a powerful tool to perform analysis

across multiple disciplines. One of this computer-based modelling commercial software

is SimulationX®. SimulationX® is a multibody dynamics commercial software

developed by ITI GmbH. This software was used to model the quarter car model

through a simple graphical user interface. Function blocks of the component were

dragged and connected in a diagram view. Furthermore, movement of the vehicle

system was visualised in a 3D view.

For practical purpose, a vehicle quarter car model was constructed to study the

dynamic interaction between vehicle and road roughness profile. The generated quarter

car model was including the kinematic properties because the compression of spring

was not directly perpendicular to the ground as shown in Figure 3.15 (Balike, Rakheja

& Stiharu 2013). Variation of the mass values, spring stiffness and damping properties

of the quarter car model made it possible to model any type of ground vehicle: car, truck

or bus using these equations of motion (Agostinacchio et al. 2014). The vehicle’s

response along a road section with uniformly distributed roughness was determined by

the study of the model forced oscillations. Due to the oscillations, the vertical force

exchanged with the road was not constant with time but in sinusoidal variation. For this

simulation, SimulationX® was selected because of its capability to simulate these

stochastic road profiles as the amplitude changed drastically.

For the visualisation of the quarter car model in SimulationX®, a block diagram

view of the linear three-dimensional (3D) quarter car model was built and shown in

Figure 3.15. From Figure 3.15(a), a total of 11 main blocks inside SimulationX®

interface were connected to build the quarter car model for mimicking the selected

Macpherson suspension system. Functions of the blocks are tabulated into Table 3.10.

Block 1 was a signal source with curve sets as input. It defined any types of excitation

profiles in the simulation. In this case, the generated ISO 8606 road profiles were

applied in this block. Block 2 was a spatial spring-damper element. The spring force Fs,

93

the damper force, Fd, and the internal force, Fi were computed for each spatial direction.

In this analysis, the Block 2 represented the tyre and a stiffness value of 105,000 N/m

was assigned (Wu et al. 2015). Block 3 was a set of cylinder element which was

visualised as a cylinder, hollow cylinder or pipe. This component was used to model

the lower arm in 3D view as shown in Figure 3.15(b). Movement of the wheel was

visualised across the simulation period to ensure the correct mechanism of the

suspension model. Block 4 and 5 were cylinder elements which represented the tie rod

attachments. Block 6 was a linear translation mass which modelled the knuckle.

Block 7 was also a spring element which was implemented with elastic

behaviour for coil spring model while Block 8 is force-damping element for damper

model. Block 8 represented the spring and damper of the suspension system in which

the damping coefficient was 2000 Ns/m for compression and 6000 Ns/m for rebound

(Jugulkar et al. 2016). The internal forces Fi, the spring force Fs, and the damper force

Fd were computed using the following formulas:

𝐹𝑠 = 𝑘. 𝛥𝑥 (3.5)

𝐹𝑑 = 𝑏. 𝛥𝑣 (3.6)

𝐹𝑖 = 𝐹𝑠 + 𝐹𝑑 (3.7)

where b is the damping coefficient, k is the spring stiffness, x is the displacement, and

v is the velocity. The change of potential energy in this element was calculated using


𝑃𝑝 = 𝐹𝑠 . 𝛥𝑣 (3.8)

The power loss of the damper Pl is calculated as follows:

𝑃𝑙 = 𝐹𝑑 . 𝛥𝑣 (3.9)

94

(a)

(b)

Figure 3.15 Setup of quarter car model in SimulationX®: (a) diagram view, (b) 3D view

Table 3.10 Function of each block in quarter car model

Blocks Function

1 Input the road profile

2 Input the tyre stiffness

3 Define the lower arm connectivity

4 Define the tie rod part 1

5 Define the tie rod part 2

6 Define the knuckle

7 Input the spring stiffness

8 Input the damping coefficients

9 Define the damper rod

10 Define the damper tube

11 Input the sprung mass

95

Block 9 and 10 were two cylindrical elements which modelled the damper road

and tube for visualisation purpose. In this case, all the cylindrical elements served to

define the weights of un-sprung mass. The total wheel mass of the suspension system

considered the geometry of rim, brake calliper, disc brake, hub, knuckle and lower arm

using CAD with material density as shown in Figure 3.16. The mass of the components

in Figure 3.16(a) – (e) was the input to Block 6 while Figure 3.16(f) was the input to

Block 3. With the density of the material as the input, mass of these components was

obtained. On the other hand, sprung mass of 350 kg was applied into Block 11. Two

spherical joints and one revolute joint were defined in the model to connect the knuckle,

lower arm and tie rod. The prismatic joints which allowed only translation movement

were assigned on sprung mass and tie rod. Upon completion of quarter car model setup,

the model was ready for a dynamic simulation.

Figure 3.16 CAD of Macpherson un-sprung mass components: (a) rim, (b) brake calliper, (c) disc

brake, (d) hub, (e) knuckle, (f) lower arm

(a) (b)

(c) (d)

(e) (f)

96

After determining the quarter car model parameters, the simulations were

performed as shown in Figure 3.17. During the simulation, the model was defined in

forms of ordinary differential equation (ODE) and solved using a numerical algorithm

(Roman et al. 2014). SimulationX® offered the solution of ODE using backward

differentiation formula (BDF) for transient simulation (ITI 2009) while transient

simulation was performed in time domain. BDF solvers were suitable for non-stiff or

stiff model with eigenfrequencies in wide range (Zheng & Zhou 2014). This algorithm

is a predictor-corrector method with automatic control of step size and order. With this

kind of implicit multistep method, the current value was extrapolated from every state

variable (1 ≤ k ≤ 6).

Figure 3.17 Procedures for quarter car model simulations

Select the suitable function blocks

Connect the function blocks according to suspension

system configuration

Start

Stop

Input the road profile, tyre stiffness, sprung and un-sprung mass

weights, spring stiffness and damping coefficient

Request force and acceleration output from

spring and sprung mass

Define the road-wheel contacts

Run transient simulation

Check the kinematic of the suspension system

Extract and save the time history data

97

The model was simulated for a total duration of 90 s to ensure the signals were

sufficient to provide information on ISO 2631 vertical vibration and fatigue analysis.

The acceleration time histories of the vehicle body were extracted based on different

spring stiffness and damping coefficient. The optimal suspension stiffness for passenger

car ranged from 1 to 1.5 Hz (Shirahatt et al. 2008) while the suspension stiffness for

race car ranged from 2 to 2.5 Hz, as proposed by Sun et al. (2014). However, the

suspension natural frequencies for racing purpose were built to the range of 5 to 7 Hz.

In this case, the quarter car mass for this passenger car with Macpherson suspension

system was 300 kg. The original simulation of quarter car model was based on the actual

spring stiffness but this was restricted to a fixed value. In order to incorporate the spring

design into fatigue analysis, spring stiffness parameter sensitivities analysis was

required to determine the effect of spring design towards fatigue life and ISO 2631

vertical vibration.

3.3.3 Perform Spring Stiffness Sensitivities

Changing spring design usually involved spring geometry such as bar diameter, outer

diameter or number of active coils. The simplest way to obtain different spring stiffness

was by changing the bar size as different outer diameter and number of active coils was

usually done to revise the allocated space for suspension system in the chassis.

Changing the spring diameter increased the spring width while changing the number of

active coil increased the spring length under fixed material properties. Hence, changing

the bar size was the best option to find different spring stiffness.

In this analysis, spring stiffness parameter sensitivity analysis was performed to

seek for the effects of spring stiffness towards fatigue life and ISO 2631 vertical

vibration. The difference between the new designed springs were required to be as close

as possible to the calculations. Zhang et al. (2007) proposed that deviation below 10 %

is good while deviation below 20 % is acceptable. The spring stiffness was subsequently

decided based on the natural frequency of the suspension system using the modal

equation as below (Chen et al. 2014):

98

𝑓𝑛 = 1

2𝜋√

k𝑟

𝑚 (3.10)

where kr is the ride rate, m is the distributed vehicle mass on the spring, and fn is the

vertical vibration of vehicle body frequency. The kr value was obtained based on the

spring stiffness of FEA and constant tyre stiffness calculations as stated in Equation 2.1.

The original spring stiffness of the case study vehicle was 20,000 N/m and the

calculated natural frequency of 1.3 Hz was obtained. A series of spring variants for

passenger car spring stiffness were designed from 14,000 to 32,000 N/m to achieve the

designated frequency range of 1 to 1.5 Hz in the quest to examine the effects of spring

stiffness or natural frequency towards the ISO 2631 vertical vibration and spring fatigue

life. The option to alter the spring stiffness was either through using different spring

materials or distinctive design. In the current spring industry, most of the springs were

made of spring steel and alternative materials are not feasible for commercial use

(Abidin et al. 2013). Hence, the spring design changes were considered to achieve

various stiffness levels.

After the bar sizes for different spring stiffness were obtained, the CAD models

of spring for every size were prepared and processed with FEA. The FEA results of the

springs were used for fatigue life prediction. The setup of fatigue life prediction using

nCode DesignLife® and force time histories from the quarter car model are shown in

Figure 3.18. In Figure 3.18, there were 6 blocks used in setting up the fatigue simulation.

Block 1 was an FE input in which the FEA stress-strain simulation results of the springs

were applied. In the FE simulation, static force was applied so that the loadings were

scaled in DesignLife® for fatigue analysis. The scalar loading for scaling is shown in

block 2 as the force time histories were obtained from the quarter car model simulation.

Block 3 was a function block to perform strain-life fatigue analysis.

During the fatigue analysis, all three uni-axial strain life fatigue approaches

namely the Coffin-Manson, Morrow, and SWT were applied. Block 4 was the FE output

from the strain life fatigue simulation. This block contained the fatigue information of

each node of the spring models. The simulation results were visualised in Block 5.

99

Block 6 was the data value displaying the fatigue simulation results. Meanwhile, the

acceleration time histories of the vehicle sprung mass with different spring stiffness

were also extracted from quarter car model and processed into ISO 2631 vertical

vibration. For feasibility of model construction, the spring stiffness was converted into

suspension natural frequency based on the vehicle mass using Equations 2.1 and 3.10

so that the established model could be used for all types of ground vehicle. Once all the

required parameters were ready, the modelling process was subsequently conducted.

Figure 3.18 Spring fatigue life prediction using nCode DesignLife®

3.3.4 Establishment of Multiple Linear Regression for Fatigue Life

Multiple linear regression (MLR) is a type of regression approach with several

independent variables. In order to establish a relationship with more than one

independent variable, MLR method is one of the options to deal with multiple

independent variables as it is available in IBM® SPSS® Statistic software package. This

approach was different from the power law regression which only involved one

parameter. Applying the MLR method required a few assumptions (Krzanowski 2010).

Firstly, the dependent variable was measured on a continuous scale. The continuous

measurement involved any observation that fell anywhere on a continuum, such as

displacement or time. Secondly, two or more independent variables were continuous or

categorical. Categorical is also known as discrete as the data are obtained through

100

counting. Subsequently, a linear relationship needed to be established between the

dependent variable and the independent variable. Performing the MLR analysis

involved entering all 90 datasets and input into SPSS® data editor. The details for MLR

generation is shown in Figure 3.19.

Figure 3.19 Process flow for establishment of multiple linear regressions

Initially, the dependent and independent variables were determined. The

regression with the fatigue life as the dependent variable is known as “vibration-life”

while the regression with ISO 2631 vertical vibration as the dependent variable is

known as “life-vibration” regression. As for the vibration-life regression, the dependent

variable was spring fatigue life while the independent variables were vehicle body

Input the suspension frequencies, spring fatigue

lives and ISO 2631 vertical vibrations into SPSS®

Define the dependent and independent variables

Start

Stop

Request regression coefficients, model fit, scatter

plot, normal probability plot, error histogram

Run the multiple linear regression analysis according least

square estimate

𝐵 =

ێێێێێۍ𝛽0

𝛽1

.

.

.𝛽𝑘ۑ

ۑۑۑۑې

= ሺ𝑋′𝑋ሻ−1𝑋′𝑌

where B is the least square estimate, X’ is the transpose of X, Y

is the predicted value

Use the model summary to fit the regression into form:

𝑦𝑖 = 𝛽𝑜 + 𝑥𝑖𝛽1+. . . + 𝑥𝑖𝑘𝛽𝑘 + 𝑒𝑖 i = 1,2, …,n

where 𝛽𝑜 is a constant, xk is the regression coefficient, 𝛽𝑘 are the

variables, ei are the residuals.

101

frequency and ISO 2631 vertical vibration. As for life-vibration regression, the ISO

2631 vertical vibration was set as the dependent variable while the vehicle body

frequency and spring fatigue life were determined as the independent variables.

Once the multiple linear regressions were obtained, the R2 value for the

regression was examined to ensure the data fitted nicely. The limitation of this approach

was the linearity of the datasets where nonlinear data were not applicable. In addition,

this approach was very straightforward as the regression was obtained using a least

square estimate method (Krzanowski 2010). A more advance artificial intelligence

method known as the artificial neural network (ANN) was proposed to enhance the

prediction outcome.

3.4 PREDICITNG THE SPRING FATIGUE LIFE

3.4.1 Design the Artificial Neural Network Architecture

ANN is a supervised machine learning method to find the best iteration. The matrix

converged until the defined conditions were satisfied. In some circumstance, ANN

approach provided better prediction results than MLR method (Abyaneh 2014). The

difference between ANN and MLR method in determining the spring fatigue and ISO

2631 vertical vibration was tested using the same datasets to train an ANN architecture.

Before the training process, suitable types of ANN were determined. ANN with single

hidden layer was classified as a simple feedforward neural network and trained using

Matlab® ANN toolbox. ANN with more than one hidden layer was known as multilayer

perceptron neural network (Bogdan et al. 2011).

The multilayer perceptron neural network could be divided into feedforward and

hybrid neural network. The major difference between these two types of ANN was the

connectivity to the input neurons. The output neurons of hybrid neural networks were

connected to the front hidden layers and input neurons while feedforward output layer

was only connected to the prior layer. The hybrid neural network was applied because

of optimal time and acceptable accuracy of the method as compared to feedback neural

network (Welch et al. 2009). After determining the suitable type of neural network, the

102

first step to train a neural network was deciding the architecture of the neural network

in terms of neurons and hidden layer. Random selection of a few hidden neurons and

layers might cause either overfitting or under fitting (Ghana Sheela & Deepa 2013).

However, there was no established rule for neuron network architecture design and the

conventional way to determine the suitable neuron was based on trial and error.

There were a few proposals to determine the suitable number of neurons based

on mean square error (MSE). The neuron with the lowest MSE was usually determined

to be the most optimum architecture for a neural network (Salim et al. 2015). In this

analysis, the architecture of different ANN was constructed for MSE analysis. The

“perform” function in Matlab® was applied to the ANN test data in order to call the

MSE for ANN analysis. The MSE function is written as follows:

MSE = 1

n (f

i− y

i)

2

n

i=1

(3.11)

where n is the number of samples, and fi is the estimation of yi. The performance of the

neural network and MSE were plotted against the number of neurons to determine the

most suitable ANN architecture (Salim et al. 2015).

Adjusting the proper number of hidden layers and neurons is an empirical

exercise for every analysis (Lopez-Moreno et al. 2014). Increasing the number of

neurons was not necessary to obtain a better performance (Ghana Sheela & Deepa,

2013). Similar conditions applied to a number of hidden layers. Hence, an analysis to

determine the optimum number of neurons and hidden layers for neural network

architecture was performed in Matlab® environment. A “for” loop was used in Matlab

to continuously search for the optimum ANN architecture with minimum MSE. The

flowcharts for the searching loop were listed in Figures 3.20 – 3.22. Figure 3.20 shows

the loop for simple feedforward ANN with single hidden layer while Figures 3.21 – 22

depict the hybrid ANN with two and three hidden layers, respectively.

ANN with one to three hidden layers were analysed to determine the suitable

architecture with the lowest MSE. In Figure 3.20, the flowchart for determine the single

103

hidden layer ANN for fatigue life prediction is illustrated where nN1

was the number of

neurons to be applied in the hidden layer. A maximum of ten neurons was assigned

because the number of input and output was only three (Heaton 2015), as this number

of neurons provided the suitable results within the acceptable time frame (Salim et al.

2015). In addition, the proposed suitable number of neurons to train an ANN was the

mean value between input and output which indicated two neurons were sufficient in

training the ANN (Heaton 2015). For ANN with one hidden layer, the “for” loop was

applied to calculate the MSE of neuron number from one to ten and the loop was

terminated after reaching ten neurons. The MSE was calculated using Equation 2.44

where the ANN predictions were the output and the fatigue life data used to train the

ANN were the target. With the lowest MSE value, the suitable ANN architecture to

determine fatigue life was proposed.

Figure 3.20 Flowchart to determine single hidden layer ANN architecture with the lowest MSE

In Figure 3.21, an additional parameter nL was defined to add the number of

hidden layers. The input for constructing the two hidden layers ANN were number of

hidden layers and neurons (nL, nN

). The maximum number of neurons in the first and

Start

Set nL

nN1

≤ 10?

Stop

nL = n

L + 1

Yes

No

Determine fatigue life using ANN

Calculate MSE

Suggest suitable ANN

104

second hidden layer (nN2 & n

N1) were set to be ten and the maximum number of hidden

layer (nL) was determined as two. 100 sets of ANN architecture were simulated and the

ANN architecture with the lowest MSE were selected for further analysis. The output

of the loop process was the suitable ANN with two hidden layers for fatigue life

predictions.

Figure 3.21 Flowchart to determine two hidden layer ANN architecture with the lowest MSE

Start

nL = 2

Stop

Set new nN1

Set new nN2

NN2

= nN2

+ 1

NN1

= 10?

NN2

= 10?

NN1

= nN1

+ 1

No

Yes

No

Calculate MSE


Set nN1

= 1

Set nN2

= 1


Yes

105

After the two-hidden layer, ANN architecture was expanded to three hidden

layers. The process to find the lowest MSE ANN architecture with three hidden layers

is listed in Figure 3.22. In this case, the maximum hidden layer (nL) was set as three and

the maximum number of ANN hidden layers of this research was only three because

three hidden layers were able to handle many of the complex analysis with suitable

computational power (Bozorg-Haddad et al. 2016). Each hidden layer was also looped

up to ten neurons with a total of 1000 sets of ANN architectures to obtain a single

durability regression. The MSE for three hidden layers were determined and the lowest

MSE ANN architecture was analysed using statistical method. As the outcome, a most

suitable three hidden layers ANN for fatigue life prediction was accordingly obtained

for Coffin-Manson, Morrow, SWT strain life approaches.

Despite the possibility of better results by increasing the number of layers and

neurons, the computational time was shown to increase exponentially (Lopez-Moreno

et al. 2014). The computational power needed for ANN architectures was heavy because

there were many data and repeated simulations. Thus, a fast and appropriate architecture

as well as a training algorithm was needed. For training algorithm, Levenberg-Marquadt

algorithm was established as one of the quick and accurate algorithms for ANN training

(Cui et al. 2017; Kuruvilla & Gunavathi 2014). Levenberg-Marquadt algorithm

computed the solution through calculation of Jacobian matrix (Cui et al. 2017). Due to

its accuracy, this algorithm was used to train all the required ANN.

During the training process, the weights and biases were randomly generated

according to Nguyen-Widrow layer initialization function. After each training, the

information was applied to adjust the new weights and biases. The iterations converged

until no improvement was obtained. Hence, the hybrid ANN was optimised through this

back-propagation algorithm (Ibrahimy et al. 2013). For the vibration-life ANN,

suspension natural frequency and vertical vibration were used as inputs while the spring

fatigue life was the output. Contradictorily for vibration prediction ANN, the inputs

were vehicle body frequency and spring fatigue life while the output was ISO 2631

vertical vibration. The outcome of the ANN predicted vibration was also analysed using

error histogram and Lilliefors test.

106

Figure 3.22 Flowchart to determine three hidden layer ANN architecture with the lowest MSE

Start

nL = 3

Stop

Set new nN1

Set new nN2

NN2

= nN2

+ 1

NN1

= 10?

NN2

= 10?

NN1

= nN1

+ 1

Yes

No No

No

Calculate MSE


Set nN1

= 1

Set nN2

= 1

Set new nN3

Set nN3

= 1

NN1

= 10?

NN3

= nN3

+ 1

Yes

Yes


107

In the hidden layer, each neuron consisted of a weight and bias value. Before

proceeding to process output, the weighted value of the hidden layer was activated with

a transfer function. A hyperbolic tangent sigmoid (tansig) transfer function was applied

because of the importance of the training speed (Dorofki et al. 2012). The hyperbolic

tangent sigmoid transfer function is suitable for nonlinear function fitting ANN

(Dorofki et al. 2012) as the function is written as follows:

Sf = 2

ሺ1 + e-2nሻ - 1 (3.12)

where Sf is the hyperbolic tangent sigmoid activation function, and n is the mathematical

function of neuron.

After the suitable ANN architecture was determined, it was trained for the

durability predictions. The simulation data were randomised and split into training,

validation and testing datasets so as to facilitate training and testing of the ANN.

Training purposes used 70% of the data while 15% of the data were used for validation

purpose. The remaining 15% of the datasets were used for ANN test. There was no

specified rule for the percentage of data for training and validation purpose, but this

segregation was used for small number of datasets (<100), as mentioned by Chandwani

et al. (2015). Therefore, the separations of datasets based on 70% training, 15%

validation and 15% test were used when the number of datasets was below 100

(Chandwani et al. 2015). In this analysis, the total number of datasets were only 90 and

hence, the ratio of 70:15:15 was applied. The goodness of fitting R2 value of the training

were examined to ensure the trained ANN was good. The R2 of ANN architecture with

the lowest MSE was selected and analysed.

3.4.2 Optimising the Spring Fatigue Life

The ANN design process in Section 3.4.1 aimed to determine the most suitable

architecture in performing the prediction process of spring fatigue life by determining

the lowest MSE. The improvement process for fatigue life using Coffin-Manson ANN

is illustrated in Figure 3.23. The inputs were the suspension frequencies and ISO 2631

108

vertical vibrations while the output was the spring fatigue life. The designed ANN

architecture played the role as the function to optimise the spring fatigue life predictions

by providing the predictions with the lowest MSE. Subsequently, the optimised fatigue

life could be proceeded for validations. For Morrow and SWT fatigue life ANN, the

determined suitable architectures are listed into Appendix C. In addition, the determined

suitable ANN architecture for ISO 2631 vertical vibration predictions are also listed in

Appendix C.

Figure 3.23 ANN architecture for optimised Coffin-Manson vibration-life predictions

3.5 VALIDATION OF THE PREDICTION

3.5.1 Validation using Normality Test

Validating the established multiple linear regression requires accessing the value of R2

which represents the suitability of the data fitting. The validation process was followed

by a series of statistical evaluation methods as listed in Figure 3.24. The key to a

prominent prediction regression was normal distribution of the residuals. For regression

approaches, F-test was performed to test the normality of the residuals to ensure the

parameters have the same standard deviation (Smyth 2002; Palowitch et al. 2016). For

detail analysis, the normality of residuals was interpreted from the normal probability

plot (P-P) and F-test. If the residuals are normally distributed around zero in residual

Spring

fatigue life

ISO 2631-1

weighted

acceleration

Vehicle body

frequency

Input layer Second hidden layer First hidden layer Output layer

109

histogram, the expected value of the error term was zero. Residuals were significant in

MLR analysis because it biased the results by "pulling" or "pushing" the regression line,

thereby leading to biased regression coefficients. Often, excluding just a single extreme

case could yield a completely distinct set of results (Jaccard & Turrisi 2003).

Figure 3.24 Validation of the established multiple linear regression

The t-test was also applied to test the significance of individual independent

variables towards the dependent variable. In addition, multicollinearity was also

checked using tolerance and variance inflation factor (VIF). The proposed tolerance

value should be greater than 0.1 while the VIF value should be less than 10 to avoid

linearity between the independent variables (Mokhtari et al. 2013). When the VIF value

was within this range, the residuals were assumed to have a normal distribution (Ibrahim

Obtained the multiple linear regression

Check the coefficient of determination value

Start

Stop

Check the normality of the regression using normal

Probability-Probability plot

Check the t-test and F-test for parameter

significance

Check the residuals of the predictions

Error histogram Scatter plot

Check the

homoscedasticity

Validate the regression performance

110

2013). For regression validation, the normality of prediction residuals was validated

using F-test, normal P-P plot and VIF from ANOVA. Subsequently, residuals of the

regression predictions were investigated using an error histogram in which the

prediction error range was defined. The residuals were plotted into scatter plots for

homoscedasticity examinations with the standardised predicted value in X-axis while

the standardised residual value in Y-axis.

Different from the regression approach, ANN resorted to perform iteration

process instead of ANOVA analysis. Hence, a different performance validation process

was performed as shown in Figure 3.25. After the ANN training processes were

completed, the trained architecture with the weighting values were obtained in Matlab®

interface. Prior to that, the R2 value for all the separated datasets such as training,

validation and ANN test were analysed and the MSE of the ANN was plotted in a 3D

scatter plot for data visualisation. An error histogram was plotted to observe the

difference of the ANN trained output and target data. Lilliefors test was performed to

examine the normality of the residuals (Razali & Yap 2012). The critical value of

Lilliefors test was obtained and compared to test the statistical value. The null

hypothesis was rejected when the test statistic value was greater than the critical value.

Figure 3.25 Validation of the ANN predictions

Run the ANN analysis for various architecture

Optimise the ANN using separate data

Start

Stop

Examine the R2 value for all datasets

Examine the normality and errors of the predictions

Plot the MSE for all different ANN

111

However, the cross-validation process using the 30% validation and testing data

were only able to indicate how good the data were fitted and used to select the best

trained ANN. The accuracy of the selected ANN was yet to be clarified. This ANN was

then validated using a set of independent experimental data for accuracy and robustness

in predicting the actual fatigue life or ISO 2631 vertical vibration.

3.5.2 Validation using Experimental Data

For validation of the regression, a set of experimental measurement data was applied to

the MLR and ANN approaches. The validation data set was divided into two groups,

which were the strain and acceleration measurement signals from a case study vehicle

and the process is shown in Figure 3.26. The measured strain time histories were used

to calculate the spring fatigue life while the acceleration time histories were used to

obtain the ISO 2631 vertical vibration. For vibration-life validation, the ISO 2631

vertical vibrations were used as input to the MLR and ANN prediction approaches. The

output of the vibration-life approach was the spring fatigue life. The regression-based

relationship compared the fatigue life to experimentally obtained fatigue life using

coefficient of determination and RMSE.

For ANN based predicted fatigue life, a conservation fatigue life correlation

approach known as scatter band method was applied. The conventional scatter band was

constructed with boundary of 1:2 or 2:1 to validate the estimation results in which any

point distributed beyond the boundary was considered as conservative (Kim et al. 2002).

The point distributed beyond the boundary was known as non-conservative. For life-

vibration relationships, the validations were performed using the experimental strain

time histories predicted fatigue life as input. Together with the suspension natural

frequency, the ISO 2631 vertical vibrations were predicted and compared to the

experimental value. The difference between the regression prediction and experimental

results were obtained as follows:

112

Δs = (absሺ𝐴wm − 𝐴weሻ

𝐴we

) × 100% (3.13)

where Δs is the difference in percentage, Awm is the regression predicted ISO 2631

vertical vibration, and Awe is the experimentally obtained ISO 2631 vertical vibration.

Figure 3.26 Process flow for validation of the ANN predictions

For further comparison, root mean square error between experimental and

prediction ISO 2631 vertical vibrations was performed. The formula for RMSE is as

below:

Collected road vibration signals

Collected sprung mass

acceleration time histories

Start

Stop

Input to regression/ANN for

fatigue life predictions

Spring stiffness

ISO 2631 vertical

vibration

Vehicle body

frequency

Check the normality of residuals using

error histogram and Lilliefors test

Plot correlation between predicted and

experimental fatigue lives

113

RMSE = √(Ypred − Yexp)

2

N (3.14)

where Ypred is predicted ISO 2631 vertical vibration, Yexp is experimental ISO 2631

vertical vibration, and N is number of data. The difference between the regression

prediction and experimental results was ensured to be within 20% to indicate good

predictive results (Zhang et al. 2007).

3.6 SUMMARY

This chapter detailed the methodology employed to achieve the three objectives. This

work focused on two main novelties which were generation of multiple input

regression-based durability relationship and establishment of artificial neural network

(ANN) durability approach for predictions. The strain-life durability approaches were

fundamental for fatigue life prediction and combined with ISO 2631 vertical vibration

which indicated the vehicle ride level using multiple linear regression (MLR). A deep

learning hybrid artificial neural network was then proposed to optimise the regression

relationships. For validation, the conventional scatter band and error estimation method

were performed for both approaches.

In the following Chapter IV, the results which reflect the objectives and

novelties of this research are presented. The results are presented according to the

sequence of the three objectives which were characterisation of ISO 2631 vertical

vibration and spring fatigue life, establishment of multiple input regression-based

durability relationships, predictions using ANN and validations of the results. The

results were discussed to provide justifications to the novelty of this research.

114

CHAPTER IV

RESULTS AND DISCUSSION

4.1 INTRODUCTION

This chapter presents the details of the results according to the three research objectives.

The first objective was to establish a regression-based vibration-life relationship for

spring fatigue life and ISO 2631 vertical vibration predictions. In this research, the

preliminary results were the finite element analysis (FEA) of the coil spring under static

compression and torsion loading which were followed by the performance of global

statistical analysis of the experimental collected strain and acceleration time histories.

Next, the collected strain time histories were used to calculate fatigue life while the

acceleration signals were used to obtain ISO 2631 vertical vibration. Subsequently, a

simple power-law regression was applied to study the fatigue life and ISO 2631 vertical

vibration. The critical results that led to first novelty like generated artificial road

profile, quarter car simulation results, spring designs and estimated fatigue life were

subsequently presented and the evaluation of fatigue multiple linear regression-based

relationship which was related to the first objective was established. In addition, a

vibration-life regression was also developed to provide a prediction for ride related ISO

2631 vertical vibration.

Subsequently, the second objective was to optimise the fatigue and ISO 2631

vertical vibration predictions using artificial neural network (ANN). The selection

results of ANN in terms of different architecture were performed where the ANN-based

durability and vibration architecture with the lowest mean square error (MSE) were

determined. The ANN architecture with the improvised prediction outcome was the

second novelty of this research. Lastly, the third objective was to validate the

regression-based and ANN-based prediction approaches. The regression-based

115

vibration-life approaches were correlated to experimental data using coefficient of

determination (R2) while the vibration-life ANN was validated using a conservative 1:2

or 2:1 fatigue life correlation curve. For ISO 2631 vertical vibration prediction, the

difference between predictions and experimental data were analysed using root mean

square errors (RMSE) and coefficient of determination (R2).

4.2 DETERMINING THE DURABILITY CHARACTERISTICS

4.2.1 Finite Element Analysis of Coil Spring

The preliminary analysis of this work was FEA of a case study vehicle coil spring to

investigate on the stress distribution. This analysis was important because the fatigue

failure area corresponded directly to stress where the crack initiation occurred at the

peak stress region (Meneghetti, Guzella & Atzori 2014). A proper finite modelled

spring possessed details of the geometry captured with finite elements. After the static

analysis was performed, the von Mises stress distribution of the spring was provided in

colour stress contours as shown in Figure 4.1. The region with the highest stress level

is shown in red while the lowest stress region is shown in blue and the highest stress

region was distributed at the inner surface of the spring as similar findings in Del Llano-

Vizcaya, Rubio-Gonzalez and Mesmaque (2006). Although the coil spring is a simple

component, but when the torsional loading was exerted, the stress states of the spring

became complicated.

When a coil spring experiences combined axial and torsional loading, the stress

amplitude of the spring changes (Akiniwa et al. 2002). Stress contour of the case study

coil spring with the combination of axial and twisting load is shown in Figure 4.2. When

compared to the uniaxial loading, the critical point of the spring under combined

torsional and compression remained at the same inner region. Under linear condition,

the stress was proportional to the strain in which the strain was also the highest (Lee et

al. 2005). Even though the spring was loaded under multiaxial forces, the critical point

also remained at the same inner region (Zhu et al. 2014; Abidin et al. 2013). Although

a few high stress regions (FEA contour in red) were observed, the highest stress was

found in the element 41517. With the stress-strain FEA results, the fatigue life contour

of the coil spring was obtained as shown in Figure 4.3. The red contour indicates the

116

region with the lowest fatigue life while the blue contour shows the high fatigue life

regime. The region of spring with low fatigue life was the same with the region of high

stress concentration in uniaxial loading because the stress level has a direct effect on

the fatigue life. The localised fatigue life results were extracted from the highest stress

hot-spot which was 1.26 × 105 blocks to failure. The endurance limit of a steel alloy in

a S-N curve was 2 × 106 cycles under cyclic loadings (Závodská et al. 2016). Although

the fatigue life of the spring was obtained from simulation, the simulated fatigue life

was considered as acceptable because it was within the endurance limit.

Figure 4.1 Stress distribution of the coil spring under axial loading

Figure 4.2 Stress distribution of the coil spring under combination of axial and torsional loading

Stress 989.7 MPa

@ element 41517

Stress (MPa)

Stress 985.9 MPa

@ element 41517

117

Figure 4.3 Fatigue life contour of the coil spring

4.2.2 Observing Signal Characteristics

After determining the critical point of the spring using FEA, signal acquisitions were

performed on a case study passenger car by placing a strain gauge on the coil spring

with a sampling rate of 1000 Hz and same sampling frequency was also applied to the

acceleration measurements (Wang & Zhang 2010). The collected signals for both strain

and acceleration from the testing are obtained as shown in Figures 4.4, 4.5 and 4.6,

respectively. The lengths of strain signals are all at 90 s with 90,000 data points, and

they are sufficient for life assessment because it is repeated based on cycles and are

independent of time. The strain characteristics are tabulated into Table 4.1 and the four-

strain signal amplitude was high because of the extremely uneven road surfaces. The

measured strain amplitude of spring was closely related to the road profile because of

the motion ratio between the wheel and the spring (Patil & Sharma 2015). The

displacement of the wheel was directly linked to the spring response and produced an

equivalent strain of the spring surface (Zhang, Suo, Wang 2008). To characterise the

strain measurements, the statistical properties of the strain time histories were obtained

as shown in Table 4.2. As observed from Table 4.2, all the strain signals had a small

mean value. The positive sign of the strain time histories indicated the mean stress was

in tension while the negative sign was compression.

Fatigue life (blocks to failure)

Fatigue life: 1.264

× 105 @ element

41517

118

Table 4.1 Range of the measured strain time histories

Minimum strain amplitude (µε) Maximum strain amplitude (µε)

Highway -519 537

Campus -1357 1368

Hill -1525 1553

Residential -837 1367

Rural -1550 1770

(a)

(b)

(c)

(d)

(e)

Figure 4.4 Strain time histories of spring collected from various road conditions: (a) highway,

(b) campus, (c) hill, (d) residential, (e) rural

119

Table 4.2 Statistics for the measured strain time histories at different type of roads

Highway Campus Hill Residential Rural

Mean (µε) 58 6.1 4.4 3.0 -4.0

r.m.s (µε) 205.5 373.9 288.3 254.7 375.0

Kurtosis 3.0 3.0 3.4 4.4 5.7

During the data collection process, the rural road was observed to be the

roughest with numerous potholes. Hence, the rural road consisted of the highest SD

value, indicating that the strain amplitudes were distributed far away from the mean

value. Due to the small mean value, the r.m.s value of the strain time histories were

almost the same with the SD value. The r.m.s values indicated the vibration energy in

the strain signal where high energy content led to high fatigue damage that leads to the

fatigue failure (Kihm & Delaux 2013)

Kurtosis value was usually applied to analyse the fatigue damage with

explanation by John & Phillip (2012) higher kurtosis value lead to the greater

randomness of the time histories which contributes to higher fatigue damage. When the

kurtosis value of a time history was greater than a value of 3.0, the time history was

regarded as a non-stationary or non-Gaussian signal. The non-stationary time histories

were time varying spectra where the statistical properties, i.e. mean or SD of the time

histories were varying over time. In this case, the rural road strain time histories had

revealed a heavily non-stationary behaviour with a kurtosis value of 5.7. A few of the

sharp peaks were observed which caused the time histories to become non-stationary.

For the vibration analysis, the collected acceleration time histories from the

vehicle lower arm and top mount are depicted in Figures 4.5 and 4.6, respectively.

Acceleration of lower arm was regarded as the excitation of un-sprung mass while the

top mount of the suspension strut was considered as vibration of the vehicle sprung

mass (Heiβing & Ersoy 2011). The vibrations originated from the wheel of the vehicle

and transmitted through the suspension to the vehicle body. To describe the

characteristic of these vibration time histories, global statistical analysis results of the

lower arm and top mount vibration time histories were performed and tabulated into

Tables 4.3 and 4.4.

120

(a)

(b)

(c)

(d)

(e)

Figure 4.5 Time histories of the measured acceleration from lower arm under various roads:

highway, (b) campus, (c) hill, (d) residential, (e) rural

Table 4.3 Statistics for the measured acceleration time histories at lower arm


r.m.s 3.6 2.5 3.3 2.6 3.7

Kurtosis 3.4 758 14.3 9.7 4.0

Crest factor 6.7 72.2 12.7 12.3 10.9

121

(a)

(b)

(c)

(d)

(e)

Figure 4.6 Time histories of the measured acceleration from top mount under various roads:

(a) highway, (b) campus, (c) hill, (d) residential, (e) rural

Table 4.4 Statistics for the measured acceleration time histories at top mount


r.m.s 2.2 1.5 2.1 1.5 2.7

Kurtosis 3.1 47.6 14.3 3.9 3.4

Crest factor 4.5 31.5 21.1 5.6 6.7

122

In Tables 4.3 and 4.4, the SD value of the lower arm was higher than the top

mount which indicates that the vibrations of the un-sprung mass were higher than the

sprung mass. This implies that the suspension system has filtered part of the road

vibrations and the impacts were absorbed by the suspension system. For fatigue

analysis, another statistic parameter to be concerned with is the kurtosis value which is

a measurement of the sensitivity to spikes. The greatest spikes were observed at campus

road measurements with peaks observed at time 61 to 63 s. This happened because of

the pothole strike happened during a curve driving. These peaks led to the high kurtosis

value of the campus road acceleration measurement in both sprung and un-sprung mass.

Based on these observations, all the vibration measurements consisted of a

kurtosis value of higher than three. Thus, it is suggested that the time histories were

possessing non-stationary behaviour. However, the campus road acceleration time

histories were heavily non-stationary because the kurtosis value was much more

deviated from the value of 3.0. Meanwhile, the highway acceleration time histories had

short periods of changed statistics due to the presence of transient behaviour.

Nevertheless, the acceleration time histories from highway road had a kurtosis value

which was closest to 3.0. This meant that the acceleration time history was close to

stationary behaviour. When the kurtosis value above 3.0, the data were expected to

consist of stronger peak with rapid decay and heavy tails (Malik, Wang & Naseem

2017). When the kurtosis level of a time histories increases, the rapid decay and tails of

the histogram distributions were more obvious.

When comparing the acceleration and strain time histories, it was found that the

highway consisted of the lowest kurtosis value which was around 3.0. This implied that

the highway has a better road surface profile which induced less spikes on the

suspension systems. For the r.m.s value, both the strain and acceleration time histories

also revealed that the highest value was during the rural road data collection because

high amplitude was obtained during the testing. The rural road was an unpaved road

with stones and potholes which induced high vibration towards suspension system.

Meanwhile, the acceleration analysis depended on the time while the strain amplitude

was independent of time, which had led to the deviation of statistic parameter for

various road conditions.

123

The collected strain time histories were random and were unable to apply

directly for fatigue life prediction. One of the most famous approaches to analyse the

strain time histories was to decompose the strain time histories into simple stress

reversals which is known as the Rainflow cycle counting method, as reported by

Paraforos et al. (2014). This Rainflow cycle counting was applied to decompose the

collected strain time histories into simple reversal. The fatigue damage histogram of the

strain time histories under all five road conditions were plotted into Figures 4.7 to 4.11.

The x-axis represents the range of the strain, the y-axis represents the mean strain, and

the z-axis represents the fatigue damage to the number of fatigue cycles at the same

range and mean. The observed fatigue damage value was increased proportionally to

the value of strain range and mean value.

The maximum strain range contributed to the maximum fatigue damage, or the

tallest column with red contour, in the damage histogram plots. The fatigue damage

displayed on the histograms was the product of the fatigue damage at one cycle with

the corresponding strain range and mean value. The maximum fatigue damage strain

ranges were observed to have occurred at rural road measurement with fatigue damage

as high as 5.50 × 10-5. It is worth noting that the fatigue damage by calculation was

unitless. During the fatigue life prediction, a single fatigue damage strain range did not

provide significant meaning to the total spring fatigue life. Hence, the Palmgren-Miner

linear fatigue damage rule was applied to summarise all the contributed fatigue damage

because Palmgren-Miner is recognised as a simple but acceptable technique for damage

summation (Fernández-Canteli & Blasón 2014).

When considering these damage histograms, there were a few existing low strain

range cycles which did not contribute much to the fatigue damage. For comparison, the

strain time histories from rural road had obviously shown a few higher fatigue damages

than other road condition measurements. The fatigue damage histogram of highway

road has shown fewer fatigue damage in terms of frequency and amplitude leading to

the cause of the highway road to have a smoother surface and less impact on the

suspension system.

124

(a)

(b)

(c)

Figure 4.7 Damage histograms of spring strain time history under highway road using various

strain life approaches: (a) Coffin-Manson, (b) Morrow, (c) SWT

125

(a)

(b)

(c)

Figure 4.8 Damage histograms of spring strain time history under UKM campus road using

various strain life approaches: (a) Coffin-Manson, (b) Morrow, (c) SWT

126

(a)

(b)

(c)

Figure 4.9 Damage histograms of spring strain time history under hilly road using various strain

life approaches: (a) Coffin-Manson, (b) Morrow, (c) SWT

127

(a)

(b)

(c)

Figure 4.10 Damage histogram of spring strain time history under residential road using various


128

(a)

(b)

(c)

Figure 4.11 Damage histogram based for spring strain time history under rural road using various


129

When the measured strain time histories were analysed using the Rainflow cycle

counting technique, a long-time history was usually required to obtain a statistically

representative fatigue damage (Halfpenny & Kihm 2010). Hence, a field of fatigue

based on vibrations was introduced to provide an accelerated fatigue analysis. The

standard procedures to perform a vibration fatigue analysis were by firstly calculating

or estimating the frequency response functions of the structure (Mršnik, Slavi c &

Boltezar 2013). Furthermore, the vibration time histories in the form of PSD were given

as excitation input to obtain the fatigue life of the structures. Through exciting different

vibration modes of the structure, the spread of vibration energy over a frequency range

influences the fatigue damage on the structure. Thus, vibration loading histories play an

important role in fatigue analysis. Nevertheless, automobile vibrations affected not only

structures but also the drivers and passengers (Lakušić, Brčić & Lakušić 2011).

It was worth noting to mention that human perception on vehicle ride dynamics

was also related to the vibration induced by various sources, such as engine and road

profile (Burdzik & Doleček 2012). In some cases, vibration time histories were also

applied to study the structure integrity of automobile components instead of only

vehicle ride quality. The vibration of vehicle sprung mass indicates the level of comfort

provided by the vehicle during interaction between wheel and ground. Meanwhile, the

vibration of the lower arm has shown the excitations of the wheel when the vehicle deals

with the road excitations.

Vibration level of an automobile was analysed using PSD because area under

the curve of a PSD indicates the energy (Vinogradov et al. 2013). The comparison

between the acceleration PSD of lower arm and top mount are plotted into Figure 4.12.

Based on the obtained PSD, it was found that the high amplitude occurred at low

frequency which were below 10 Hz and the energy was decayed across frequency range.

As observed, the energy level in terms of amplitude from PSD of top mount was lower

than lower arm under all five road conditions. This was because of transmissibility and

isolation effects provided by the suspension system (Parekh et al. 2014). To determine

the transmissibility, root mean square error (RMSE) between the top mount and the

lower arm acceleration PSD were performed using Equation 3.14 and listed into Table

4.5. The RMSE value was significant to understand the behaviour of suspension in

https://en.wikipedia.org/wiki/Vibration

130

filtering the vibration where a high RMSE value indicates that more vibrations were

attenuated. The rural road contained the highest RMSE value at 0.0164 because the road

was rough, and the suspension system has worked more for the vibration attenuation.

For automotive suspension components, the interest frequency range for fatigue

analysis was 40 to 60 Hz and frequency above 100 Hz could be neglected (Sener 2012).

Nevertheless, the natural frequency of suspension system and seat was between 1 to 3

Hz (Bouazara, Richard, Rakheja 2006). The resonance frequencies range for engine part

was 20 to 200 Hz with engine speed range of 600 – 6000 rpm (Yu et al. 2001). The

proposed road excitation was below 10 Hz when the vehicle speed was 50 km/hr

(González et al. 2008). Nevertheless, based on the strain PSD under campus and hill

roads, peak was observed at frequency above 100 Hz where this frequency range was

also considered in spring fatigue analysis.

Table 4.5 RMSE between sprung and un-sprung mass acceleration time histories

Road Root mean square error (m/s2)2/Hz

Highway 0.0004

UKM Campus 0.0001

Hilly 0.0010

Residential 0.0007

Rural 0.0164

4.2.3 Regression Analysis for Fatigue Life

The acceleration time histories were used to calculate the vehicle ISO 2631 vertical

vibrations while the spring fatigue life were calculated using strain life approaches. The

results of spring fatigue life and ISO 2631 vertical vibrations were then tabulated into

Table 4.6, indicating that the rural road possessed the lowest fatigue life at 5.71 × 103

blocks to failure due to rough road surface. Meanwhile, the ISO 2631 vertical vibration

of automobile for sprung mass under rural road was the highest at 0.73 m/s2 which

indicates that the ISO 2631 has an inverse relationship towards fatigue life. In addition,

the ISO 2631 vertical vibration for highway road was low (0.57 m/s2) while the fatigue

life was high (3.52 × 104 blocks to failure) due to the smooth road surface. This also

implies that the negative correlation between the fatigue lives and ISO 2631 vertical

vibration were. When ISO 2631 vertical vibration amplitude was high, the vibrational

energy of the suspension was also high and lead to the reduction of fatigue life.

131

(a)

(b)

(c)

(d)

(e)

Figure 4.12 PSD of collected strain and acceleration time histories for various roads: (a) highway,

(b) campus, (c) hill, (d) residential, (e) rural

132

Table 4.6 ISO 2631 vertical accelerations and spring fatigue lives

Weighted

acceleration for

top mount

(m/s2)

Weighted

acceleration

for lower arm

(m/s2)

Coffin-

Manson

(blocks to

failure)

Morrow

(blocks to

failure)

SWT (blocks

to failure)

Highway 0.57 0.98 6.45 × 104 3.64 × 104 3.52 × 104

Campus 0.68 0.86 1.25 × 104 1.18 × 104 1.18 × 104

Hill 0.56 1.87 4.59 × 104 4.61 × 104 5.41 × 104

Residential 0.59 1.06 4.90 × 104 3.52 × 104 3.73 × 104

Rural 0.73 0.97 6.06 × 103 5.71 × 103 5.71 × 103

To investigate the relationship between fatigue life and ISO 2631 vertical

vibrations, a suitable regression approach was needed. Regression analysis is an

extraction of hidden predictive information from large databases with immense

potential to help in extracting the most valuable information in the data. One of the

methods to extract this information is known as linear regression method (Lewis-Beck

2015). This statistical technique is used to find the best-fitting linear relationship

between a dependent variable and its predictors. As prerequisite for the linear

regression, the dependent variable needed to have a linear relationship with the

independent variable.

The correlation study of vibration for durability and vehicle ride was significant

to reduce the number of testing. In nature, fatigue of material possesses a power

relationship with the applied loadings. The power law regression function was applied

to mathematical model of the spring fatigue life and ISO 2631 vertical vibration. The

fitted power curve is shown in Figure 4.13 and the generated power regression

relationships are shown as follows:

NCM_power = 1349Wa-6.523

(4.1)

NMorrow_power = 847Wa-6.859

(4.2)

NSWT_power = 606Wa-7.598

(4.3)

where Ncm_power, NMorrow_power and NSWT_power are the respective Coffin-Manson, Morrow

and SWT approaches with experimental predicted spring fatigue life with units blocks

to failure, Wa is the experimental ISO 2631 vertical vibration with the unit of m/s2. The

133

R2 value for Coffin-Manson vibration-life regression was 0.8419, 0.9433 for Morrow

and 0.9754 for SWT.

Figure 4.13 Correlation of spring fatigue life and ISO 2631 vertical vibration in power form

Equations 4.1 – 4.3 were used to predict the spring fatigue life using the ISO

2631 vertical vibration as input. Based on the R2 value, the relationship between spring

fatigue life and ISO 2631 vertical vibration possessed a strong negative relationship.

This was indicative that the weighted vertical vibration predicted the spring fatigue life

with good accuracy. Hence, these regression relationships were suitable to be proposed

to the automotive industry for spring design assistances. When considering including

additional parameters, the simple power form regression was difficult to handle due to

its non-linearity.

For the ease of use, the regression in power form was derived into linear form

to enable least square calculation (Hanaki et al. 2010). This was through applying

natural logarithm on calculated fatigue life. Subsequently, a linear regression analysis

was conducted on the spring fatigue life and ISO 2631 vertical vibration datasets after

applied natural logarithm and the results of the linear regression analysis are shown in

R2 = 0.8419

R2 = 0.9754

R2 = 0.9344

Fat

igue

life

(b

lock

s to

fai

lure

)

ISO 2631 vertical vibration (m/s2)

134

Figure 4.14. The R2 value for Coffin-Manson predicted that spring fatigue life and ISO

2631 vertical vibration was 0.9613 while the R2 value for Morrow and vertical vibration

was 0.9278. For SWT model, the linear regression fitted with R2 value of 0.9808. Based

on all the obtained R2 value, it could be clarified that the ISO 2631 vertical vibration

has a strong linear relationship with spring fatigue life after the natural logarithm was

applied to the fatigue life unit.

The gradient and intercept of linear regression vibration-life relationship was

obtained and written as follows:

NCM_linear = -5.828Wa + 8.056 (4.4)

NMorrow_linear = -4.699Wa + 7.206 (4.5)

NSWT_linear = -5.359Wa + 7.691 (4.6)

where Ncm_linear, NMorrow_linear, NSWT_linear are the Coffin-Manson, Morrow and SWT

approaches experimental predicted spring fatigue life respectively with the natural

logarithm of units of block to failure, Wa is the ISO 2631 vertical vibration with the unit

of m/s2. All these three approaches provided immediate fatigue life assessment using

ISO 2631 vertical vibration as input.

For Equations 4.4 – 4.6, the vibration-life regressions were linearised and hence,

the coefficients and constants were different from the power law form. The reason to

linearise the power regression approach was because it was easier to interpret the fatigue

life in a linear form than a nonlinear power form (Tomaszewki, Sempruch & Piatkowski

2014). With the high R2 value, it reflected also the quality and repeatability of the

analysis. Moreover, the strong correlation value was also indicative that the feasibility

of linear relationship between spring fatigue life and ISO 2631 vertical vibration. These

proposed new regressions have achieved part of the first objective which was the

establishment of spring vibration-life relationships.

135

Figure 4.14 Correlation of spring fatigue life and ISO 2631 vertical vibration in linear form

To validate the regression predictions, the linear regression predicted fatigue

lives were compared to experimental fatigue lives as shown in Table 4.7 using RMSE

as defined in Equation 3.14. The RMSE for Coffin Manson regression predicted and

experimental fatigue life was 0.0754 blocks to failure in natural logarithm while the

RMSE for predicted Morrow fatigue life was 0.0720 blocks to failure in natural

logarithm. In addition, the RMSE for predicted SWT fatigue life was 0.0507 blocks to

failure in natural logarithm. The suitability of the RMSE was usually compared with

the parameter range where the fatigue lives were ranged from 3.8 to 4.8 blocks to failure

in natural logarithm. Cárdenas et al. (2012) proposed that the suitable RMSE range

when compared with the parameter range was about 10% which indicates that the

proposed regression predictions were acceptable. The correlation studies of prediction

and experimental data for all three strain life models are shown in Figure 4.15 with the

lowest R2 value of 0.8328. According to Sivák and Ostertagová (2012), the R2 value for

fatigue correlation above 0.80 is considered as acceptable. Hence, it suggested that the

regression predicted fatigue life was acceptable.

R2 = 0.91

R2 = 0.95

R2 = 0.9613

R2 = 0.9278

R2 = 0.9808

Fat

igue

life

(b

lock

s to

fai

lure

)

ISO 2631 vertical vibration (m/s2)

136

Table 4.7 Regression predicted and experimental fatigue lives

Linear regression predicted fatigue life

(blocks to failure) Experimental fatigue life (blocks to failure)

Coffin-

Manson Morrow SWT

Coffin-

Manson Morrow SWT

5.42 × 104 3.37 × 104 4.33 × 104 6.45 × 104 3.64 × 104 3.52 × 104

1.24 × 104 1.02 × 104 1.11 × 104 1.25 × 104 1.18 × 104 1.18 × 104

6.20 × 104 3.75 × 104 4.90 × 104 4.59 × 104 4.61 × 104 5.41 × 104

4.14 × 104 2.71 × 104 3.38 × 104 4.90 × 104 3.52 × 104 3.73 × 104

6.33 × 103 6.00 × 103 6.01 × 103 6.06 × 103 5.71 × 103 5.71 × 103

4.3 DATA FOR MODELLING

4.3.1 Artificial Road Profiles

To achieve the first objective, which was establishing multiple input regression

relationships of fatigue life, ISO 2631 vertical vibration and vehicle body frequency,

additional data for analysis were required to expand the analysis. Without experimental

testing, a vehicle quarter car model was proposed and simulated where road inputs were

required to simulate the dynamical behaviour of the suspension. As for the road

acceleration measurements, there were only five acceleration time histories from

different road conditions which were insufficient. To resolve this issue, ISO 8608

artificial road profiles were proposed to generate the additional loading signals where

the fundamental ideas of ISO 8608 were spatial frequency, road displacement and PSD.

Road profile was the variations in height of the road surface which was measured on

single track parallel to the road. This proposed road profile assumed that the given road

was stationary where the statistic properties did not change over time. The generated

road surface was a combination of numerous long or fleeting period bumps with varying

amplitudes.

137

(a)

(b)

(c)

Figure 4.15 Correlation analysis for fatigue life using various fatigue approaches:


0.00E+00

1.00E+04

2.00E+04

3.00E+04

4.00E+04

5.00E+04

6.00E+04

7.00E+04

0.00E+001.00E+042.00E+043.00E+044.00E+045.00E+046.00E+047.00E+04

Lin

ear

regre

ssio

n f

atig

ue

life

(b

lock

s

to f

ailu

re)

Experimental fatigue lives (blocks to failure)

0.00E+00

5.00E+03

1.00E+04

1.50E+04

2.00E+04

2.50E+04

3.00E+04

3.50E+04

4.00E+04

4.50E+04

0.00E+00 1.00E+04 2.00E+04 3.00E+04 4.00E+04 5.00E+04

Lin

ear

regre

ssio

n f

atig

ue

life

(b

lock

s

to f

ailu

re)


0.00E+00

1.00E+04

2.00E+04

3.00E+04

4.00E+04

5.00E+04

6.00E+04

0.00E+00 1.00E+04 2.00E+04 3.00E+04 4.00E+04 5.00E+04 6.00E+04

Lin

ear

regre

ssio

n f

atig

ue

life

(b

lock

s

to f

ailu

re)


R2 = 0.8328

R2 = 0.9763

R2 = 0.9312

138

For classification, the PSD between measured road and ISO 8608 road profile

classifications were plotted into a graph as shown in Figure 4.16. The trend of the

measured road profile was different from the ISO 8608 road class because the actual

road excitations was varied, and the road was a combination of various classes due to

different roughness and vehicle speeds. The same trend was also reported by González

et al. (2008). As observed in Figure 4.16, the measured road profiles consisted of the

greatest roughness up to standard road class “D” and the lowest roughness as class “A”

were based on the ISO 8608 classification. The highway measured acceleration PSD

was classified as the class “A” road while the rural area measured acceleration was in

the class “D” road. As support for this classification, many previous researches have

also utilised ISO 8608 class “A” to “D” in quarter car model simulation (Loprencipe &

Zoccali 2017; Joshi et al. 2015). Road profiles beyond road class “D” were unrealistic

for passenger cars because the amplitudes were too high and the signals were considered

as heavily non-stationary with many high peaks from random effects (Chaari et al.

2013). The road class “E” was unrealistic because it simulated off-road conditions

(Balmos et al. 2014). In Figure 4.16, the measured road class was classified below class

“E” and hence the collected acceleration signals were suitable for quarter car model

simulations.

Figure 4.16 Classification of measured road profile according to ISO 8608

139

The generated road profiles in terms of spatial frequency are shown in Figure

4.17. The vehicle speed was determined to be 80 kmph because this was the average

vehicle speed for the objective ride analysis, as proposed by ISO 2631 (Nagarkar et al.

2016; Loprencipe & Zoccali 2017; Panta et al. 2014). When the vehicle speed effect

was not a parameter to be considered, the average vehicle speed of 80 kmph was usually

selected. Meanwhile, the quarter car model simulation required the input of

displacement in time domain so that the behaviour of suspension could be clearly

visualised. Hence, the generated road classes in temporal frequency for simulation were

performed using the generated temporal road profile as shown in Figure 4.18 where the

artificial generated road profiles were in the form of displacement versus time. As

observed, the generated road profiles were stochastic but generally stationary.

Meanwhile, the generated road profiles were also considered as non-deterministic

loading time histories.

To understand the characteristics of these generated road profiles, a statistic

evaluation was performed on the generated road profiles. The mean, r.m.s values and

respective fatigue life of the spring under these road classes were analysed and tabulated

into Table 4.8. The mean value of the road class increased from 4.71 ×10-7 to -1.51 ×

10-5 m across road class “A” to “D”. Nevertheless, the generated road profile contained

a very small mean value. The same trend implied on r.m.s value of the road profile from

road class “A” to “D” where the r.m.s value has been increased from 0.0046 to 0.0369

m. Moreover, the road class “D” contained the highest r.m.s. The r.m.s value indicating

the degree of rough of the generated road profile as well as the energy level. Higher

mean and r.m.s value produced a road class with a higher degree of roughness and

hence, led to lower fatigue life of the coil spring. Muc ka (2016) reported that the road

class “A” to “C” was typical road while class “D” above was unpaved road. After

examining the road characteristics, all four classes of generated road were then used as

input to quarter car simulation model for fatigue loading signal extractions.

Table 4.8 Statistical parameters of artificial generated road classes

Road Mean (m) r.m.s (m) CM Morrow SWT

Class A 4.71 ×10-7 0.0046 6.03 × 106 6.61 × 106 6.76 × 106

Class B -3.77 × 10-6 0.0092 9.33 × 105 1.07 × 106 7.08 × 105

Class C -7.54 × 10-6 0.0185 3.63 × 103 3.63 × 103 3.63 × 103

Class D -1.51 × 10-5 0.0369 2.19 × 102 2.19 × 102 2.19 × 102

140

(a)

(b)

(c)

(d)

Figure 4.17 Generated ISO 8608 road profile in form of spatial frequency for generated road

classes: (a) class A, (b) class B, (c) class C, (d) class D

4.3.2 Quarter Car Model Simulation Results

Quarter car model (QCM) was a vehicle simulation model that could be efficiently used

to study the dynamic interaction between vehicle and road roughness profile, and

therefore applied in this study of suspension dynamic behaviour. Through combining

the masses values, the stiffness and damping of the QCM, it was possible to model any

type of road vehicle (Agostinacchio et al. 2014). Using the QCM, the dynamic

responses of the vehicle were extracted. Two types of time history were extracted for

vibration and fatigue analysis which were force time histories induced on the coil spring

and acceleration time histories exerted on the vehicle mass under influence of different

road roughness.

141

(a)

(b)

(c)

(d)

Figure 4.18 ISO 8608 road profile in form of temporal frequency for various road

classes: (a) class A, (b) class B, (c) class C, (d) class D

An example results of simulated force time histories is shown in Figure 4.19.

This example force time histories were obtained from QCM simulation under road class

“A” with different spring stiffness. As observed, when the spring stiffness increased,

the magnitude of the simulated force time histories was also increased because the

spring force linearly depended on the displacement and spring stiffness according to the

Hooke’s law. Loading a spring with higher stiffness under a fixed displacement,

additional force was required to achieve the same height. Nevertheless, for road class

“A”, the displacement or road surface roughness was not high when compared to other

generated road classes. For other roads, the spring force time histories of other road

classes and measurements were listed in Appendix D. All the simulated spring force

142

time histories were within the range of 200 N and the range of force was drastically

increased after an increment of road class.

(a)

(b)

(c)

(d)

(e)

Continue…

Fo

rce

(N)

20 40 60 80

-200

200

0

20 40 60 80

-200

200

0

20 40 60 80

-200

200

0

20 40 60 80

-200

200

0

20 40 60 80

200

0

-200

143

Continued…

(f)

(g)

(h)

(i)

(j)

Time (s)

Figure 4.19 Simulated force time histories under road class “A” for different spring stiffness:

(a) k14, (b) k16, (c) k18, (d) k20, (e) k22, (f) k24, (g) k26, (h) k28, (i) k30, (j) k32

Fo

rce

(N)

20 40 60 80

-200

200

0

20 40 60 80

-200

200

0

20 40 60 80

-200

200

0

20 40 60 80

-200

200

0

20 40 60 80

-200

200

0

144

Apart from spring force time histories, QCM simulations have also provided the

acceleration of vehicle mass under various road classes. The accelerations of the vehicle

sprung mass under various spring stiffness were plotted into Figure 4.20. The

acceleration of vehicle mass was an indicator for passenger ride perception where high

amplitude reduced the vehicle ride quality. Based on the observations from Figure 4.20,

the acceleration levels were within the range of -1 to 1 m/s2. The acceleration level

under this class “A” road was not high when compared from classes “B” to “D”. The

results of acceleration for road classes “B” to “D” were listed in Appendix E.

The acceleration amplitude was also increased from road classes “A” to “D”

under the influence of road roughness. For measured acceleration simulation input, the

results of spring force time histories are shown in Figure 4.21 while the QCM simulated

acceleration time histories for sprung mass is shown in Figure 4.22. In Figure 4.21, the

spring force time histories were extracted from highway road acceleration input with

quarter car model simulation. The amplitude range for the quarter car model simulation

under highway road excitation was ranged from -200 to 200 N which was a very close

amplitude range to artificial road class “A” due to the similar road roughness

excitations.

In Figure 4.22, the quarter car simulation measured acceleration was collected

from the highway road with the acceleration amplitudes ranging from -0.5 to 0.5 m/s2

which was close to artificial road class “A”. The highway road had similar properties to

artificial road class “A” in terms of amplitude which led to the same extracted data

range. However, the measured road profiles were more dynamic than the artificial road

profile because there were many uncertainties in roads, such as the changing of vehicle

speed due to traffic, lane changes or pothole strikes. When associating the acceleration

amplitude with the ISO 2631 ride standard, the acceleration amplitude was considered

as not high. Hence, these low amplitudes suggest that highway roads provide good ride

quality to the automobile.

145

(a)

(b)

(c)

(d)

(e)

Continue…

Acc

eler

atio

n (

m/s

2)

20 40 60 80

-1

1

0

20 40 60 80 -1

0

1

20 40 60 80

-1

0

1

20 40 60 80 -1

0

1

1

20 40 60 80 -1

0

146

Continued…

(f)

(g)

(h)

(i)

(j)

Time (s)

Figure 4.20 Simulated acceleration time histories under road class “A” for different spring

stiffness: (a) k14, (b) k16, (c) k18, (d) k20, (e) k22, (f) k24, (g) k26, (h) k28, (i) k30,

(j) k32

Acc

eler

atio

n (

m/s

2)

1

20 40 60 80 -1

0

1

20 40 60 80

-1

0

1

20 40 60 80

-1

0

1

20 40 60 80 -1

0

1

20 40 60 80

0

-1

147

(a)

(b)

(c)

(d)

(e)

Continue...

Fo

rce

(N)

200

20 40 60 80

-200

0

200

20 40 60 80 -200

0

200

20 40 60 80 -200

0

20 40 60 80

20 40 60 80

200

-200

0

200

-200

0

148

Continued...

(f)

(g)

(h)

(i)

(j) Time (s)

Figure 4.21 Simulated force time histories under highway road for different spring stiffness:

(a) k14, (b) k16, (c) k18, (d) k20, (e) k22, (f) k24, (g) k26, (h) k28, (i) k30, (j) k32

Fo

rce

(N)

20 40 60 80

20 40 60 80

20 40 60 80

20 40 60 80

20 40 60 80

200

-200

0

200

-200

0

200

-200

0

200

-200

0

200

-200

0

149

(a)

(b)

(c)

(d)

(e)

Continue…

Acc

eler

atio

n (

m/s

2)

20 40 60 80 -1

1

0

20 40 60 80

20 40 60 80

20 40 60 80

20 40 60 80

-1

1

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-1

1

0

-1

1

0

-1

1

0

150

Continued…

(f)

(g)

(h)

(i)

(j)

Time (s)

Figure 4.22 Simulated acceleration time histories under highway road for different spring

stiffness: (a) k14, (b) k16, (c) k18, (d) k20, (e) k22, (f) k24, (g) k26, (h) k28, (i) k30,

(j) k32

Acc

eler

atio

n (

m/s

2)

20 40 60 80

20 40 60 80

20 40 60 80

20 40 60 80

20 40 60 80

-1

1

0

-1

1

0

-1

1

0

-1

1

0

-1

1

0

151

When considering the various road class in Appendix E, the simulated force and

acceleration time histories of other road conditions were higher than the highway road.

This was because the quarter car simulation has considered the dynamical condition of

hilly, UKM campus, residential and rural road where these road conditions consisted of

coarser road condition and produced higher vibration to the suspension system. The

higher force and acceleration amplitude proposed that these road conditions provide

less ride quality of the automobile.

4.3.3 Spring Stiffness Sensitivity Analysis

The change of a spring design was involving the parameters like spring geometry, bar

diameter, outer diameter or number of active coils (Valsange 2012). To obtain different

spring stiffness, one of the ways was through changing the bar size (SAE 1990). During

the simple regression analysis, the model was analysed with two variables which were

the spring fatigue life and ISO 2631 vertical vibration and, the suspension spring

stiffness was considered as a fixed parameter. In order to include the effects of spring

stiffness as a parameter, spring stiffness sensitivities were performed to obtain the

effects of different spring stiffnesses.

To determine the spring design variants, the adjustment of the bar diameter for

coil spring was performed as the stiffness of the spring increased when the bar diameter

increased (Valsange et al. 2012). However, different bar diameter led to various stress

levels which affected the spring fatigue life. Hence, a series of new spring design

variants were conducted. The examples of spring design variants are shown in Figure

4.23. The stiffest spring design have bar diameter of 13.3 mm which achieved the

maximum stiffness for automobile vehicle body frequency analysis with the

consideration of vehicle ride quality.

The results of all the coil spring diameter adjustment were tabulated into Table

4.9. All the new designed coil springs were obtained through simple calculation and

analysed using FEA. There were some deviations between calculated and FEA stiffness

according to the adjustment of the spring bar diameter. Hence, the difference between

the calculation and FEA simulations were analysed to ensure the validity of the spring

152

design. The maximum difference between the calculated and FEA analysis were

relatively small where the maximum error was only 5.3 %. Based on Zhang et al. (2007),

the acceptance of the FEA results with experimental data was 10 %. Therefore, the FEA

coil spring models were acceptable for fatigue analysis where a more realistic fatigue

life prediction was offered in accordance to spring design.

Figure 4.23 Spring design variants with different bar diameter

Table 4.9 Spring stiffness parameter sensitivity analysis

Bar

diameter

Calculated stiffness

(N/mm)

FEA based stiffness

(N/mm) Difference (%)

11.0 14.3 13.8 1.4

11.3 16.1 15.7 1.9

11.6 18.0 17.6 2.2

12.0 20.3 19.7 1.5

12.2 22.3 21.6 1.8

12.4 24.0 23.9 0.4

12.6 25.7 25.5 1.9

12.8 27.5 27.0 3.5

13.0 29.5 28.4 5.3

13.3 32.4 30.8 3.8

Note: Difference = |Calculated stiffness-FEA based stiffness

FEA based stiffness| ×100% (Equation 3.13)

This spring sensitivity analysis was crucial to determine the ISO 2631 vertical

vibration because the spring stiffness was proportional to the induced vehicle response

153

from ground uncertainties. During the spring sensitivity analysis, the spring stiffness

was adjusted to determine the effects of spring design to fatigue life. Adjusting the

spring stiffness in quarter car model led also to the variation in spring design. The

original nominal spring design did not represent the real fatigue life predictions with the

loading signals from the quarter car model when various spring stiffnesses were applied.

Without the spring sensitivity analysis, the fatigue life of spring could not be accurately

predicted, and the analysis were limited to a fixed spring parameter.

4.3.4 Fatigue Life and Vibration Data

When the spring force time histories and design variants were prepared, the prediction

of spring fatigue life was performed. The equivalent suspension natural frequency was

calculated according to different spring stiffness using Equation 3.10. The results of

spring fatigue life, suspension natural frequency and ISO 2631 vertical vibration under

class “A” were tabulated into Table 4.10 while the results of other road classes were

listed in Appendix F. As observed in Table 4.10, the ISO 2631 vertical acceleration

increased along with increasing the suspension natural frequency. For the other road

conditions, the same increasing trend has been observed. Sekulić and Dedović (2011)

proposed that when the natural frequency was increased, the vertical acceleration

response on the driver side was also increased.

The increasing trends were observed because the spring stiffness changes led to

the increment of suspension natural frequency where the road excitation was amplified.

In addition, the results for highway road simulation predicted fatigue life is shown in

Table 4.11. In Tables 4.10 and 4.11, the vehicle body frequency was ranged from 1.00

to 1.50 Hz because this frequency range was the optimal frequency for passenger cars

(Sekulić & Dedović 2011). The ISO 2631 vertical accelerations were obtained based on

the vehicle sprung mass acceleration through processing the signals with the ISO 2631

weighting values. This value was an indicator of vehicle vibration level and human

perception where the fatigue life of automobile spring was also affected by these

vibrations. When the natural frequencies were increased, the fatigue life of spring was

reduced. This was because the force exerted on the spring was increased according to

154

Hooke’s law. Under the same induced displacement, the force of the spring was higher

when the spring stiffness was increased.

In Tables 4.10 and 4.11, the nominal spring design was 1.20 Hz with spring bar

diameter 12 mm. For this spring stiffness, the obtained fatigue lives were ranged from

1.23 × 107 to 1.46 × 107 blocks to failure while the fatigue lives of spring under highway

road simulation were ranged from 9.80 × 105 to 4.36 × 107 blocks to failure. The

variation of spring during highway excitation was due to the nonlinear road conditions

like pothole striking or waviness which led to varying mean stresses. Kamal and

Rahman (2014) proposed that the fatigue life of a coil spring was about 5.16 × 107

blocks to failure where the predicted fatigue life was reasonable because it fall within

the same range with the proposed fatigue life.

Table 4.10 Predicted fatigue life and ISO 2631 weighted acceleration from Class “A” road

Vertical

frequency (Hz)

Weighted

vertical

acceleration

(m/s2)

Coffin-Manson

fatigue life

(blocks to

failure)

Morrow fatigue

life (blocks to

failure)

SWT fatigue life

(blocks to

failure)

1.00 0.1540 2.02 × 108 2.50 × 108 2.71 × 108

1.06 0.1548 1.69 × 108 1.99 × 108 2.14 × 108

1.13 0.1562 5.60 × 107 6.60 × 107 6.99 × 107

1.20 0.1574 1.23 × 107 1.39 × 107 1.46 × 107

1.25 0.1589 5.96 × 106 6.57 × 106 6.77 × 106

1.30 0.1606 2.83 × 106 3.03 × 106 3.11 × 106

1.36 0.1622 1.51 × 106 1.60 × 106 1.64 × 106

1.41 0.1644 7.69 × 105 7.98 × 105 8.13 × 105

1.45 0.1665 5.39 × 105 5.53 × 105 5.58 × 105

1.50 0.1689 3.93 × 105 3.98 × 105 3.99 × 105

Table 4.11 Predicted fatigue life and ISO 2631 weighted acceleration from highway road

Vertical

frequency (Hz)

Weighted

vertical

acceleration

(m/s2)

Coffin-Manson

fatigue life

(blocks to

failure)

Morrow fatigue

life (blocks to

failure)

SWT fatigue life

(blocks to

failure)

1.00 0.2863 2.68 × 107 6.70 × 109 2.79 × 108

1.06 0.3112 1.75 × 107 1.18 × 108 8.58 × 107

1.13 0.3255 5.26 × 106 2.00 × 107 2.61 × 107

1.20 0.3390 9.80 × 105 4.36 × 107 6.23 × 106

1.25 0.3525 4.22 × 105 7.46 × 106 1.32 × 107

1.30 0.3658 2.11 × 105 7.31 × 105 1.25 × 106

1.36 0.3792 1.22 × 105 2.62 × 105 6.64 × 105

1.41 0.3918 7.58 × 104 7.42 × 104 2.50 × 105

1.45 0.4046 5.52 × 104 5.39 × 104 1.82 × 105

1.50 0.4169 4.15 × 104 4.19 × 104 1.25 × 105

155

As observed from Table 4.11, the ISO 2631 vertical acceleration also increased

with increasing spring stiffness. The same increasing trend for the vertical vibration has

also been proposed by Chen et al. (2017). For fatigue life prediction, a decreasing trend

has been observed where the spring fatigue life was decreased with increased spring

stiffness due to higher amplitude. As reported by Sekulić & Dedović (2011), amplitude

of vertical acceleration increased drastically with spring stiffness of frequency 1.50 Hz

and above. Hence, the vehicle body frequency ranges up to 1.50 Hz was solely

considered in this work. Based on this frequency range, 90 datasets were prepared and

ready for multiple regression analysis which considered all three-spring fatigue life,

vehicle body frequency and ISO 2631 vertical vibrations parameters.

4.4 MULTIPLE INPUT REGRESSION

MLR is a common form of linear regression analysis which explains the relationship

between one dependent variable and two or more independent variables. This method

could be used to explore the relationship between more parameters where the spring

stiffness was included. Hence, this section proposed multiple linear regression for

fatigue life and ISO 2631 vertical vibration including spring stiffness that is related to

the first objective and led to part of the novelty of this research.

4.4.1 Analysis for Life Regression

When there is more than one independent variable (predictors or explanatory variable),

the simple linear method was not able to perform regression fitting because it fitted only

a single variable. Hence, a more complicated regression method known as multiple

linear regression was applied to overcome the limitation of numerous independent

variables. MLR is a type of supervised machine learning method where the target of the

regression approach is needed. This method produces a linear regression relationship

using least square estimate with partial coefficients. A total of 90 datasets were used

where 50 of the datasets were simulated from the measured acceleration while the other

40 datasets were obtained from artificial road profile. The measured acceleration

datasets were collected from various road classes with varying surface conditions.

156

For vibration-life regression approach, the spring fatigue life was applied as the

dependent variable while the ISO 2631 vertical vibration and suspension natural

frequency were set as the independent variables. This relationship is suggested to be

called ‘vibration-life’ analysis where all three strain life fatigue approaches were

applied, i.e. Coffin-Manson, Morrow and SWT. The regression response surfaces are

shown in Figure 4.24 for all three relationships. The yellow contour of the graph

indicates the parameter values with high fatigue life while the purple colour region

shows the area with the lowest fatigue life. The blue colour region shows the region

with middle fatigue life range.

As observed from the response surface plane in Figure 4.24, it is obvious that

the spring fatigue life reduced with increased ISO 2631 vertical acceleration, indicating

linear negative relationship with the spring fatigue life. Apart from that, increments in

suspension natural frequency led to the reduction of spring fatigue life, suggesting a

linear negative relationship between these two parameters. However, the effects of

vehicle body frequency on spring fatigue life were not drastic because the gradient of

the response surface for these two parameters were low. Increasing the spring stiffness

would also cause the spring fatigue life to be reduced.

For the vibration parameters, the increment of vehicle body frequency has led to

higher ISO 2631-1 vertical acceleration. After these relationship surface planes were

generated, the mathematical relationship in the forms of regression were obtained. The

obtained regressions were named as ‘vibration-life’ relationship which were part of the

novelty of this research. This vibration-life regression was created to predict spring

fatigue life with two parameters as input. The application of this regression-based

fatigue relationship to predict spring fatigue life was very straightforward. Conventional

durability analysis needed to measure the spring with strain gauges and performed strain

life calculations using materials cyclic properties. These processes were time

consuming and the data were rarely reusable (Yang & Xu 2012). Vibration-life

regression is intended to provide a solution to this issue through providing spring fatigue

life predictions using solely vibration measurements.

157

(a)

(b)

(c)

Figure 4.24 Multiple linear regression for fatigue life characteristics using various approaches:


158

Using the MLR method, the regression relationships in mathematical form were

also obtained through analysis of variance (ANOVA). For this purpose, ANOVA meant

to relate all three generated regressions for spring strain life predictions according to

Figure 4.24(a) – (c) are listed as follows:

NCM_MLR = 11.61 − 3.65.ωninput − 3.83.Wa_input (4.8)

NMorrow_MLR = 12.62 − 4.32.ωn_input − 4.12.Wa_input (4.9)

NSWT_MLR = 12.78 − 4.40.ωn_input − 4.14.Wa_input (4.10)

where NCM_MLR, NMorrow_MLR, NSWT_MLR are the Coffin-Manson, Morrow and SWT

multiple regression predicted fatigue life with the unit of blocks to failure in natural

logarithm respectively, 𝜔𝑛_𝑖𝑛𝑝𝑢𝑡 is the suspension natural frequency input with unit of

Hz, Wa_input is the ISO 2631 vertical acceleration input with unit of m/s2. In Section

4.2.3, NCM_power, NCM_Morrow, NSWT_power, NCM_linear, NMorrow_linear, NSWT_linear were proposed

to predict fatigue life using ISO 2631 weighted acceleration as input with units of blocks

to failure as output. However, the proposed regressions in Section 4.2.3 were only

applicable to the nominal spring design. In this section, the proposed MLR-based

fatigue life predictions considered the spring design variants which made the regression

more flexible for application.

The proposed coefficients from Equations 4.8 to 4.10 were un-standardised

coefficients from the MLR approach. Un-standardised coefficients indicated the amount

the dependent variable changed if the independent variables changed by one unit while

the other independent variables were kept constant. Un-standardised coefficients do not

eliminate the unit of measurement. Hence, it is not applied to rank the independent

variables (Darlington & Hayes 2016). For example, in Equation 4.8, it implied that for

every increase of a unit of fatigue life, the vehicle body frequency was reduced by 3.65

Hz and ISO 2631 vertical vibration was reduced by 3.83 m/s2 from a constant of 11.61.

The validity of these generated regression relationships was further examined using

analysis of variance (ANOVA), residual histograms, normal probability-probability (P-

P) plot and scatter plot for goodness of fitting, residuals’ normality and

homoscedasticity.

159

To examine the suitability of generated regression-based relationships as shown

in Figure 4.24, the R2 values of each regressions were analysed using ANOVA. The R2

was used to examine the goodness of the fitted data where a high value of R2 indicated

a good correlation (Asadi et al. 2014). With the high R2 value, the regressions were

considered as acceptable for spring fatigue life prediction. The range of acceptable R2

values and its definition is already listed in Table 3.6. In the current analysis, the R2

value show a confidence level of 83% for the developed Coffin-Manson vibration-life

regression with MSE of 0.5285 as shown in Figure 4.24(a). The confidence value is

88% for the Morrow vibration-life regression with MSE of 0.5855 (Figure 4.24(b)) and

83% for the SWT vibration-life regression with MSE of 0.7056 (Figure 4.24(c)). The

low MSE value indicated that the vibration-life regression relationships were acceptable

because the deviations of fatigue life prediction were low. Taghavifar & Mardani (2014)

utilised ANN to predict wheel-soil interaction of off-road vehicles with MSE of up to

0.996. This indicated that the obtained MSEs were within acceptable range. Although

the residuals were determined as normally distributed, it was significant to examine the

residuals using a scatter plot to ensure the homoscedasticity of the vibration-life

regression. The homoscedasticity meant that the variance around the regression line is

the same for all values of the independent variables where the error term was consistent

(Prieto et al. 2016). The homoscedasticity ensured the predictions of fatigue life were

consistent throughout the whole regression range.

The significance of the vibration-life regression in predicting the spring fatigue

life was examined using the F-test. The F-ratio in the ANOVA tested whether the

overall regressions were a good fit of data (Sheridan et al. 2008). The results have shown

that the independent variables were statistically significant in predicting the dependent

variable (Table 4.12). For the Coffin-Manson vibration-life regression, F-test results of

F(2, 87) = 313.5 with p < 0.05 were obtained. The Morrow vibration-life regression was

F(2, 87) = 321.3 with p < 0.05 while the SWT vibration-life regression possessed F(2,

87) = 215.7 with p < 0.05. The regression p-values have indicated that the regression

approaches were significant at an α-level of 0.05, confidence interval of 95 % (Sheridan

et al. 2008). Hence, all three generated regressions have good fit of data which

supported the strong linear relationships (Delijaicov et al. 2010).

160

Table 4.12 F-test for vibration-life regression analysis

Approaches Sample sizes, n Number of independent variables, k F-value P-value

Coffin-Manson 90 2 313.5 <0.05

Morrow 90 2 321.3 <0.05

SWT 90 2 215.7 <0.05

The F-test is used to test the equality of two populations while the t-test is used

to compared to related variables because t-test is a univariate hypothesis test. The t-

values of both predictors of all three regression approaches are listed in Table 4.13. The

higher the absolute t-value, the higher the significance levels of the predictor variable

(Delijaicov et al. 2010). When the p-values of t-test of variables were lower than 0.05,

the variables were considered as significance predictor in the model (Takemoto et al.

2016). Based on Table 4.13, the regression constants have the highest significance level

with the highest t-values while the ISO 2631 vertical vibration were the second. The

third predictors were suspension natural frequency. Nevertheless, all the three

predictors were significant with p-values below 0.05. This indicated that all two

independent variables and constant were significant in predicting spring fatigue life and

the significance level was directly related to the p-value. In this case, all the p-value was

below 0.05 which showed a great significance of the independent variables.

Table 4.13 t-test of vibration-life datasets for various approaches

Approaches

t-value

p-value Constant, α

Vehicle body

frequency, 𝝎𝒏

Weighted

acceleration, Wa

Coffin-Manson 25.85 -10.35 -21.35 <0.05

Morrow 27.27 -11.54 -20.65 <0.05

SWT 21.31 -9.33 -17.26 <0.05

To analyse the relationship between each individual parameter to fatigue life

parameter, standardised coefficients were used to compare the relative importance of

each coefficient in a regression as shown in Table 4.14. The standardised coefficient

was used to explain the relationship between spring fatigue life, vehicle body frequency

and ISO 2631 vertical vibration. For example, for each one standard deviation increase

in vehicle body frequency, predicted Coffin-Manson fatigue life went down by 0.390

of standard deviation. In addition, for each one standard deviation increase in ISO 2631

weighted acceleration, predicted Coffin-Manson fatigue life went down by 0.805 of

standard deviation. These standardised coefficients analysis were also applied to

Morrow and SWT regression approaches. The standardised coefficients explained each

161

parameter in terms of standard deviation and ignored the scale of units which made the

comparisons easy. It suggested that the ISO 2631 vertical vibration has higher influence

on fatigue life when considering the absolute value of standardised coefficients as listed

in Table 4.14.

Table 4.14 Standardised coefficients of independent variables

Approaches Standardised Coefficients

Vehicle body frequency, 𝝎𝒏 ISO 2631 Weighted acceleration, 𝝎𝒂

Coffin-Manson -0.390 -0.805

Morrow -0.432 -0.773

SWT -0.413 -0.764

The vibration-life regression approaches were evaluated using normal P-P plots

and residual histograms to ensure the normality of the datasets. In MLR analysis, there

is more than one explanatory variable making traditional plot impractical to represent

the data. Therefore, the predicted value versus the observed value for these applied

datasets were plotted in the form of normal P-P plots as shown in Figure 4.25. These

data nicely fitted and there was a strong correlation between the regression prediction

and actual results because the points were distributed around the regression line to form

a linear relationship. Meanwhile, the normal P-P plot of regression of these standardised

residuals for the dependent variable also indicated a relatively normal distribution where

the actual values lined up along the diagonal that goes from lower left to upper right

(Sheridan et al. 2008). In this case, the datasets were normally distributed and good

predictions of fatigue life were obtained because the predicted fatigue lives were

distributed between the mean value according to centre limit theorem and identically

distributed.

To examine whether there were existing outliers in the regressions, the residuals

of the regressions were analysed. The residuals were obtained by deducting the

predicted values from the observed values from the regression (Shaman et al. 2015).

The residuals were also significant to determine outliers and how good the regression

was in providing solutions. Therefore, the regression approaches needed to satisfy the

condition that the error terms were normally distributed. If the data followed a normal

distribution with mean µ and variance σ2, then a plot of the theoretical percentiles of the

normal distribution versus the observed sample percentiles were approximately linear

(Sheridan et al. 2008).

162

Apart from normal P-P plot, residual histogram plots of the vibration-life

regression approaches were used to define the error terms. The residual histograms were

plotted into Figure 4.26. As observed in Figure 4.26, the patterns have confirmed the

assumption that the residuals were normally distributed at each level of fatigue life and

constant in variance across all levels of the dependent variable. Since the deviations of

the datasets were small, the datasets were considered as acceptable for spring fatigue

life predictions because all the data were fitted nicely to the curve (Junior & Pires 2014).

(a) (b)

(c)

Figure 4.25 Normal Probability-Probability plot of vibration-life regression standardised

residual for various approaches: (a) Coffin-Manson, (b) Morrow, (c) SWT

The most useful way to plot the residuals was with predicted values from the

regression on the X-axis and standardised residuals on the Y-axis as shown in Figure

4.27. When the data distribution satisfied this random condition, the residuals

distribution in the scatter plot were almost symmetric, tending to cluster towards the

middle of the plot. When the data were homoscedastic, the residuals were

Observed cumulative probability

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approximately equal for all predicted dependent variable scores (Prieto et al. 2016). No

significant pattern was observed on any of the residual scatter plots that violated the

suitability of fit of the regression. The data was distributed evenly among the zero line

and no cluster was observed. To obtain information of the data dispersion, linear

analysis was performed on the regression standardised residual and standardised

predicted values. When a straight linear regression line was obtained, fatigue life

estimation was consistent for all the prediction range (Azadi & Karimi-Jashni 2016).

(a) (b)

(c)

Figure 4.26 Error histogram of vibration-life regression standardised residual for various

approaches: (a) Coffin- Manson, (b) Morrow, (c) SWT

The application of the regression was applied to the vehicle body frequency and

ISO 2631 vertical vibration as inputs with the Coffin-Manson, Morrow and SWT MLR-

based fatigue life predictions shown in Tables 4.15 – 4.17 respectively. The Coffin-

Manson MLR-based predicted fatigue life possessed a RMSE of 0.5165 when compared

with target fatigue life while the Morrow MLR-based predicted fatigue life had an

Regression standardised residual

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RMSE of 0.5274. Subsequently, the SWT MLR-based predicted fatigue life consisted

of RMSE of 0.3775. For the calculated RMSE of fatigue life, they were defined in

natural logarithm and the RMSE value was acceptable because the fatigue life range

was 2 to 8 (Cárdenas et al. 2012). As observed in Table 4.15, when the vehicle body

frequency and ISO 2631 vertical vibration were 1.00 Hz and 0.15 m/s2 respectively, the

fatigue life was high and the predicted fatigue life deviated a lot from the target value.

This was a limitation of regression approach on data range where its density shape

depended on the parameters that index the distribution (Ospina & Ferrari 2012). The

correlation study of predicted fatigue life was also performed using 1:2 or 2:1

correlation curve as shown in Figure 4.28. However, 10 out of 12 MLR predicted

Morrow fatigue lives distributed out beyond the conservative boundary due to the mean

stress effects. Morrow adjusted the mean stress for fatigue life calculation which led to

the varying results. Nevertheless, the Coffin-Manson and SWT was suitable in

predicting the fatigue life because most of the data points distributed within the

acceptable boundary.

(a) (b)

(c)

Figure 4.27 Scatter plot of vibration-life regression standardised residual for various approaches:


Regression standardised predicted value

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Table 4.15 Coffin-Manson MLR-based fatigue life predictions

Vehicle body frequency

(Hz)

ISO 2631 vertical

Acceleration (m/s2)

MLR-based fatigue life

(blocks to failure)

Target fatigue life

(blocks to failure)

1.25 0.35 5.09 × 105 4.27 × 105

1.25 0.67 3.03 × 104 1.20 × 104

1.45 0.75 2.79 × 103 5.75 × 103

1.25 0.66 3.31 × 104 9.55 × 103

1.50 0.73 2.18 × 103 5.75 × 103

1.50 0.40 4.01 × 104 2.82 × 104

1.00 0.15 2.43 × 107 2.04× 108

1.36 0.16 1.08 × 106 1.51 × 106

1.41 0.16 7.09 × 105 7.76 × 105

1.25 0.32 6.64 × 105 9.33 × 105

1.07 0.62 2.14 × 104 3.72 × 104

1.07 1.24 9.02 × 102 7.94 × 102

Table 4.16 Morrow MLR-based fatigue life predictions


(Hz)

ISO 2631 vertical

Acceleration (m/s2)


(blocks to failure)

Target fatigue life

(blocks to failure)

1.40 0.40 8.39 × 104 5.37 × 104

1.24 0.62 5.11 × 104 6.46 × 104

1.35 0.66 1.17 × 104 4.07 × 103

1.40 0.67 6.48 × 103 3.80 × 103

1.06 0.62 3.06 × 105 6.31 × 104

1.45 0.77 1.53 × 103 6.76 × 103

1.06 0.61 3.37 × 105 5.50 × 104

1.35 0.71 7.29 × 103 7.24 × 103

1.30 0.16 2.21 × 106 3.02 × 106

1.00 0.31 1.05 × 107 3.63 × 107

1.45 0.33 9.92 × 104 8.32 × 104

1.50 0.68 2.18 × 104 6.92 × 102

Table 4.17 SWT MLR-based fatigue life predictions


(Hz)

ISO 2631 vertical

Acceleration (m/s2)


(blocks to failure)

Target fatigue life

(blocks to failure)

1.30 0.62 2.82 × 104 1.29 × 104

1.41 0.66 6.45 × 103 5.62 × 103

1.30 0.69 1.45 × 104 8.71 × 103

1.07 0.57 4.45 × 105 1.26 × 105

1.19 0.61 9.25 × 104 1.38 × 104

1.13 0.31 2.89 × 106 4.17 × 106

1.19 0.33 1.32 × 106 1.17 × 106

1.25 0.34 6.59 × 105 5.89 × 105

1.36 0.36 1.83 × 105 1.82 × 105

1.45 0.39 5.61 × 104 9.12 × 104

1.50 0.4 3.10 × 104 7.24 × 104

1.00 0.15 4.81 × 107 2.69 × 108

Note: Difference = |MLR-based fatigue life - target fatigue life

target fatigue life| × 100% (Equation 3.13)

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(a)

(b)

(c) Figure 4.28 Correlation analysis for MLR fatigue life: (a) Coffin-Manson, (b) Morrow, (c) SWT

1.0E+02

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As for the vibration-life relationship, the suitability of the regression was

successfully established and evaluated using normal P-P and scatter plots as defined in

the first objective. The main challenges of regression analysis were not only to obtain

the fatigue life prediction relationship but also the consistency of the prediction

outcome. Hence, the normal P-P and scatter plots performed in this analysis were used

to illustrate the consistency of the established regression. The predicted fatigue life was

evaluated according to the target fatigue life. Nevertheless, the regression had a

limitation of wide data range predictions. This suggested vibration-life regression and

fatigue life predictions using ISO 2631 vertical vibration and vehicle body frequency is

the main idea for the novelty of this research which answered the first objective.

4.4.2 Analysis for Vibration Regression

ISO 2631 vertical vibration of vehicle mass associated to coil spring stiffness also

played a significant role in indicating vehicle ride. There was a need to perform

prediction of ISO 2631 vertical vibration using spring fatigue life which is known in

this thesis as vibration prediction. Using the MLR approach, the response surfaces of

regression approaches were obtained and shown in Figure 4.29. The regressions were

defined as follows:

Wa_CM = 2.59 - 0.76.ωninput - 0.22.NCM_MLR (4.11)

Wa_Morrow = 2.58 - 0.83.ωninput - 0.20.NMorrow_MLR (4.12)

Wa_SWT = 2.45 - 0.77.ωninput - 0.19.NSWT_MLR (4.13)

where Ncm_MLR, Nmorrow_MLR, NSWT_MLR are the Coffin-Manson, Morrow SWT fatigue life

input with unit blocks to failure in natural logarithm, 𝜔𝑛_𝑖𝑛𝑝𝑢𝑡 is the suspension natural

frequency with unit Hz having the same range for all three regressionsd, Wa_CM, WMorrow,

WSWT are the regressions estimated ISO 2631 vertical acceleration with unit m/s2 using

various fatigue approaches predicted fatigue life and suspension natural frequency as

input.

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(a)

(b)

(c)

Figure 4.29 Response surface plot for ISO 2631 vertical vibration prediction using various

approaches: (a) Coffin-Manson, (b) Morrow, (c) SWT

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The listed regressions were generated using un-standardised coefficients where

the units of the parameters remained. Hence, the unit for dependent variable was m/s2

while the independent variables were vehicle body frequency and fatigue life with units

of Hz and blocks to failure, respectively. Since MLR applied the unstandardized

coefficient, the units of the parameters varied because this regression approach served

to analyse the response change with predictors. When the standardised coefficient was

applied, the units of the parameters were unified with the unit of variance. The

unstandardized coefficients were more commonly used due to its simplicity (Darlington

& Hayes 2016).

The regressions were obtained from ANOVA where the F-test and t-test results

were analysed. For the F-test, the critical F-values were obtained as listed in Table 4.18.

The p-values for all the test were below 0.05 which indicated that the regressions were

significant. The significance levels of each independent variable were determined using

the t-test where the results are tabulated in Table 4.19. The significance of the parameter

depends on the t-test value where a higher t-test value showed greater effects of the

designated variable towards dependent variable. The highest t-value for all regression-

based vibration-life relationships were based on spring fatigue life parameter. This

indicated that the fatigue life played a significant role in defining the prediction

regressions, followed by the constant and vehicle body frequency respectively.

Table 4.18 F-test of fatigue-vibration datasets for various approaches

Approaches Sample sizes, n Number of independent variables, k F-value P-value

Coffin-Manson 90 2 232.1 <0.05

Morrow 90 2 218.8 <0.05

SWT 90 2 151.9 <0.05

Table 4.19 t-test of fatigue-vibration datasets for various approaches

Approaches

t-value

Constant, α Vehicle body

frequency, 𝝎𝒏 Fatigue life

Coffin-Manson 16.91 -7.93 -21.35

Morrow 16.86 -8.43 -20.65

SWT 13.62 -6.65 -17.26

The goodness of fit for the generated regression relationships were analysed and

shown in Figure 4.29. Based on Figure 4.29, there were acceptable correlation between

the regression prediction and actual results and these were supported by the high R2

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value. The R2 value for vibration prediction Coffin-Manson regression was 0.8420

while the R2 value for Morrow vibration regression was 0.8340. Lastly, the R2 value for

SWT vibration regression was 0.7877 which showed a confidence level of 78 % for ISO

2631 vertical vibration prediction. According to Sivák and Ostertagová (2012), these

models has shown a high correlation value which indicated the data fitted well into the

model as defined in Table 3.6.

Based on the ANOVA analysis, the normality of the datasets was analysed using

Normal P-P plots where the plots of the vibration regression approaches were obtained

as shown in Figure 4.30. When observing the Figure 4.30, the datasets were distributed

along the centre line which indicated the datasets were normally distributed. For the

MLR approach, normality of the datasets was a requirement to perform the analysis

because the assumptions of linearity between parameters were conducted.

Subsequently, examination of residuals was performed for vibration regression

relationship and plotted into error histograms as shown in Figure 4.31. As observed

from Figure 4.31, the residuals were distributed at the centre of the error histograms

which also suggested the normality of the residuals.

In Figure 4.31, the residuals ranged from -3 to 3 for Coffin-Manson vibration

regression with a standard deviation of 0.989. The residuals range of Morrow vibration

relationship predictions were from -3 to 3.2 while the range for SWT relationships were

also from -3 to 3. In this case, the dataset variations were considered as very high and

not suitable for ISO 2631 vertical vibration predictions which ranged from 1.0 to 1.5

m/s2. Indirect causal relationship mentioned that one of the variables exerted a causal

impact on the second variable but only through the impacts on a third variable (Jaccard

& Turrisi 2003). This caused the independent parameters to be less efficient in

predicting the ISO 2631 vertical vibrations.

After analysing the normality of the datasets, the homoscedasticity of the

obtained regressions was analysed using scatter plot as shown in Figure 4.32. As

observed in Figure 4.32, a linear regression with R2 value of zero was obtained at centre

line. When a linear regression lined up with zero and no clear pattern of data was

observed in a scatter plot, the regressions were assumed to be homoscedastic (Casson

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& Farmer 2014). In this case, the regressions were consistently predicting the ISO 2631

vertical vibrations where the deviations were within the acceptable range.



(a) (b)


(c)

Figure 4.30 Normal Probability-Probability plot of vibration regression standardised residual

for various approaches: (a) Coffin-Manson, (b) Morrow, (c) SWT

The results of ISO 2631 vertical vibration prediction using the MLR approach

and Coffin-Manson fatigue life input were obtained as shown in Table 4.20. In Table

4.20, there were a total of 12 sets of ISO 2631 vertical vibration predictions and targeted

value. The predicted ISO 2631 vertical vibrations were close to the targeted value with

a RMSE of 0.0875. For Morrow, the obtained RMSE was 0.1222 and the data for this

analysis is shown in Table 4.21. The RMSE for SWT predicted ISO 2631 vertical

vibration was 0.1279 with data as shown in Table 4.22. In Table 4.22, the high

difference of prediction up to 75.9% was obtained. This was mainly due to the limitation

of multiple linear regression in predicting the wide range data which induced higher

error range (Ospina & Ferrari 2012). Nevertheless, most of the predicted ISO 2631

vertical vibrations were still within acceptable range.

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(a) (b)


(c)

Figure 4.31 Error histogram of vibration regression standardised residual for various

approaches: (a) Coffin- Manson, (b) Morrow, (c) SWT

(a) (b)


(c)

Figure 4.32 Scatter plot of vibration prediction regression standardised residual for various


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The difference between MLR predicted and target ISO 2631 vertical vibration

values were mostly acceptable. Nevertheless, there were a few points which distributed

beyond the acceptable limit and the highest difference went up to 41.38% which was

far beyond the acceptable limit. The high percentage of difference was due to the tail

value of the distribution which was a limitation of MLR (Ospina & Ferrari 2012). In

this case, the highest percentage difference of 41.38% was predicted from the extreme

value like the smallest frequency value of 1.0 Hz and the highest fatigue life at 8.45

(2.82 × 108 blocks to failure). In most of the cases, the prediction range was within the

acceptable limit of 20% which indicated that the regression vibration predictions were

still acceptable (Manivel & Gandhinathan 2016).

Table 4.20 Coffin-Manson MLR predicted ISO 2631 vertical vibrations

Vehicle

body

frequency

(Hz)

Fatigue life

(blocks to failure in

natural logarithm)

MLR predicted

ISO 2631 vertical

vibration (m/s2)

Target ISO

2631 vertical

vibration

(m/s2)

Difference

(%)

1.13 6.72 0.25 0.33 24.24

1.25 5.63 0.40 0.35 14.28

1.41 4.88 0.44 0.39 12.82

1.19 5.14 0.55 0.59 6.77

1.50 3.72 0.63 0.68 7.35

1.30 3.96 0.73 0.69 5.79

1.50 3.76 0.62 0.73 15.07

1.19 5.68 0.21 0.27 22.22

1.25 6.78 0.15 0.16 6.25

1.30 5.65 0.36 0.32 12.50

1.50 4.68 0.42 0.34 23.5

1.19 3.77 0.86 0.63 36.50

Table 4.21 Morrow MLR predicted ISO 2631 vertical vibrations

Vehicle

body

frequency

(Hz)

Fatigue life


natural logarithm)

MLR predicted

ISO 2631

vertical

vibration (m/s2)

Target ISO

2631 vertical

vibration

(m/s2)

Difference

(%)

1.00 6.00 0.62 0.54 14.81

1.13 4.72 0.70 0.61 14.75

1.30 3.94 0.71 0.70 1.43

1.25 5.53 0.44 0.35 25.71

1.40 4.94 0.43 0.39 10.25

1.13 7.82 0.12 0.16 25.00

1.50 5.60 0.22 0.17 29.40

1.00 7.56 0.24 0.31 22.58

1.30 5.71 0.36 0.32 12.50

1.00 5.41 0.67 0.62 8.06

1.30 2.22 1.06 1.29 17.83

1.36 2.13 1.06 1.30 17.82

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Table 4.22 SWT MLR predicted ISO 2631 vertical vibrations

Vehicle

body

frequency

(Hz)

Fatigue life


natural logarithm)

MLR predicted

ISO 2631

vertical

vibration (m/s2)

Target ISO

2631 vertical

vibration

(m/s2)

Difference

(%)

1.00 8.45 0.17 0.29 41.38

1.00 5.11 0.71 0.54 31.48

1.40 3.79 0.64 0.73 12.33

1.07 5.10 0.66 0.57 15.78

1.36 3.02 0.83 0.70 18.57

1.07 6.89 0.32 0.30 6.67

1.36 5.26 0.40 0.36 11.11

1.07 8.33 0.10 0.15 33.33

1.07 7.23 0.25 0.31 19.35

1.00 5.38 0.66 0.62 6.45

1.36 3.19 0.80 0.65 23.07

1.40 3.02 0.79 0.66 19.70

Note: Difference = |MLR prediction - target ISO 2631 vertical vibration

target ISO 2631 vertical vibration| × 100% (Equation 3.13)

The novelty of this research was to integrate the spring fatigue life, ISO 2631

vertical vibration and vehicle body frequency into a regression relationship. The spring

fatigue life was processed using the loading signals obtained from simulation of the

quarter car model with material cyclic properties and coil spring stress-strain simulation

from FEA. Meanwhile, the acceleration signals from the vehicle sprung mass were

processed into ISO 2631 ride index. Lastly, the spring stiffness was used to calculate

the natural frequencies for different spring designs. In section 4.4, the regression to link

these three parameters was performed and their performances were evaluated.

In summary, this section has proposed regressions for fatigue life and ISO 2631

vertical vibration predictions using Coffin-Manson, Morrow and SWT strain life

approaches. The proposed regressions have predicted spring fatigue life or ISO 2631

vertical vibration with low RMSE when compared to targeted value. These regressions

were newly established with the purpose of assisting in automotive spring design

through reducing the processes. Hence, the outcome of this section has revealed the

novelty of this research and after an extensive study of literature, no similar proposal

has been found. These established regressions could play a significant role in the field

of fatigue and automotive ride dynamics. Nevertheless, the MLR prediction had some

restriction in predicting extreme values for ISO 2631 vertical vibrations.

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The first objective was successfully achieved with the determination of these

MLR fatigue life and ISO 2631 vertical vibration predictions. However, MLR is very

limited in capability. Based on a research of bus chassis shear stress prediction, the

capabilities of MLR and ANN approach in predicting the stress results were analysed

(Patel & Bhatt 2013). ANN method has been reported to have higher accuracy than

MLR predictions. Hence, to obtain a more robust prediction model, the same datasets

were proposed to train artificial neural networks (ANN). ANN consist of self-adjusting

capability in adjusting the gradient to obtain optimised fatigue life predictions which

led to the determination of the second objective.

4.5 IMPLEMENTATION OF ARTIFICIAL NEURAL NETWORK FOR

PREDICTION

The second objective of this research is to optimise the fatigue life and ISO 2631 vertical

vibration predictions using ANN. This section presents the results of ANN optimising

procedures, optimised fatigue life and ISO 2631 vertical vibration which was also part

of the novelty of this research because the optimised predictions provided higher

accuracy than the regression predictions. The subsection 4.5.1 depicts the optimised

fatigue life predictions while the subsection 4.5.2 illustrates the optimised ISO 2631

vertical vibration predictions.

4.5.1 Fatigue Life Prediction

To search for a method to optimise the spring fatigue life and automobile ISO 2631

vertical vibration, the same datasets from MLR were used to train ANNs. In this section,

the idea was to optimise the spring fatigue life predictions using ANN approach.

Initially, the feedforward type ANN was trained using Matlab® with Levenberg-

Marquadt training algorithm. The feedforward neural network was selected because the

optimised time and accuracy of the method when compared to other neural networks

(Welch et al. 2009). After determining the type of neural network, the next step was to

train a neural network with a suitable architecture.

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Random selection of several hidden neurons and layers caused either overfitting

or underfitting (Ghana Sheela & Deepa 2013). The number of neurons and layers were

highly dependent on the characteristics of the data. However, until now, there were no

established rules for ANN architecture design. Previous methods to determine the

suitable number of neurons and layers were based on trial and error (Ghana Sheela &

Deepa 2013). Due to this reason, there was a need to develop a new procedure to

determine the optimum prediction architecture which formed the novelty of this second

objective. For a single hidden layer feedforward neural network, the number of neurons

in the hidden layer was the most important parameter to determine the accuracy of the

trained ANN. The key to assess the goodness of the trained ANN was through analysing

the MSE. Hence, the MSE with one to ten neurons of Coffin-Manson, Morrow and

SWT ANN were selected for these ANN training processes because ten neurons were

sufficient to handle analysis with three parameters (Salim et al. 2015).

When the number of neurons increased or decreased, the MSE of the predictions

were also randomly varying. The results of the MSE across a number of neurons for

Coffin-Manson, Morrow and SWT trained feedforward ANN are plotted into Figure

4.33. The minimum MSE for trained Coffin-Manson datasets was detected at seven

neurons with the value of 0.0885, as shown in Figure 4.34(a). However, different results

were observed for Morrow and SWT ANN-based vibration-life approach. The lowest

MSE for trained Morrow ANN-based vibration-life approach was 0.0827 with nine

neurons in a hidden layer while the lowest MSE for trained SWT ANN-based vibration-

life approach was 0.1769 with only one neuron. The list of the MSE is shown in

Appendix G. When the number of neurons was reduced, the ANN has become simpler

with less weights and biases. Based on Heaton (2015), the minimum number of neurons

was the mean value for the input and output parameters. However, the process to

determine the most suitable number of neurons was an empirical exercise which

consumed a lot of effort. The benefit of ANN with less weights and biases was the

reduced computational power required. Nevertheless, the selection of number of

neurons depended on the MSE which defined the accuracy of predictions.

As observed in Figure 4.33(a), the maximum MSE happened at one neuron for

Coffin-Manson approach while the maximum MSE happened at six neurons for both

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Morrow and SWT approaches as shown in Figure 4.33(b) and (c), respectively. These

high MSE sets of neuron architecture should be avoided because it yielded great

deviation of predictions. The high MSE was due to the ANN generated random initial

weights that led to varying local minima. The initial weight is difficult to decide (Lee,

Geem & Suh 2016). After considering the MSE, the trained ANN architecture with the

lowest MSE was chosen to be analysed in terms of ‘goodness’ of fit. The total datasets

were divided into three main categories, which was training, validation and ANN test

set. The training set data consisted of 70% of the total data, validation and test set

consisted of 15% each of the total data respectively. This type of data separation was

considered as one of the most optimum when the number of datasets were below 100

(Takahashi et al. 2016). In this analysis, the training dataset was used to adjust the

weights on the ANN. The validation set was used to minimise overfitting while the test

set was used to test the final solution of the actual predictive results of the ANN.

The goodness of fit for the datasets were analysed using indicators known as

Pearson correlation coefficient (r) and the R2 value. The r value was used to present the

strength and direction of a linear relationship while the R2 value was used to show the

proportion of explained variance. The fitted curve for trained Coffin-Manson ANN is

shown in Figure 4.34 where the R2 of each fitting was shown. For Morrow and SWT

curve fitting, the results are listed in Appendix J. The R2 value was determined based

on the Pearson coefficient. All the fitted curves have shown good fit and the datasets

were well distributed along the line. In this case, fitted curve for ‘All’ spent all 90

datasets into weights adjustment have also shown a good agreement between the data.

The R2 value for ANN indicated how good the selected ANN was trained which could

directly affect the fatigue life predictions. A high R2 indicated that the ANN was

predicting with high accuracy and low MSE (Mia, Khan & Dhar 2017).

The summarised R2 value and datasets for all three approaches were tabulated

in Table 4.23. The R2 value for Coffin-Manson training, validation and ANN test dataset

was high and the ANN test was used to assess the performance or generalisation ability

of ANN (Kamp & Savenije 2006). For Coffin-Manson approach, the R2 value for ANN

test was 0.9322 while the R2 value for Morrow approach was 0.9732. This indicated

that the datasets fitted well into the trained ANN. The Morrow training datasets were

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even closer to the fitted ANN regression. On the other hand, the R2 value for trained

SWT ANN was 0.9502. Although the R2 value of the trained SWT vibration-life ANN

was not high as the Coffin-Manson and Morrow approaches, the datasets were

considered as acceptable. Nevertheless, as observed from all the three-curve fitted

ANN, the data were well distributed around the model line.

(a)

(b)

(c)

Figure 4.33 MSE of trained neural network with single hidden layer for various approaches:


Maximum MSE @ 6 neurons

Number of neurons

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re)

Maximum MSE @ 1 neuron

Maximum MSE @ 6 neurons

179

In Figure 4.34, the datasets for all training, validation and ANN tests were

trained according to data separation and the ‘ANN Output’ of ANN is labelled on the

vertical axis as the ANN predictions. Meanwhile, the horizontal axis is the ‘Target’

fatigue life which was the supervised learning response. Through this curve fitting, the

difference between ANN predictions and target value for various separated datasets

could be identified and the corresponding correlation between the prediction and target

value identified (Zadeh et al. 2010). These functions could be used to evaluate the

performance of trained ANN.

(a) (b)

(c) (d)

Figure 4.34 Curve fitting of trained Coffin-Manson vibration-life ANN approach with single

hidden layer for various datasets: (a) all, (b) training, (c) validation, (d) ANN test

Target

All: R2 = 0.9448

AN

N o

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Target

Training: R2 = 0.9467

AN

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Validation: R2 = 0.9520

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ANN Test: R2 = 0.9322

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Table 4.23 R2 value for all approaches with single hidden layer ANN

All Training Validation ANN Test

Coffin-Manson 0.9448 0.9467 0.9520 0.9322

Morrow 0.9700 0.9873 0.9748 0.9732

SWT 0.8885 0.8947 0.7305 0.9504

Table 4.24 summarises the MSE for all three sets of training, validation and

ANN test data where all 90 sets of training data for all three strain life models are listed.

The MSE for trained ANN-based Coffin-Manson vibration-life ANN was below

0.2000. The MSE was relatively low when compared to the datasets. The ANN-based

Morrow vibration-life approach also showed low MSE of below 0.0827. Nevertheless,

the SWT has shown a higher MSE when compared to ANN-based Coffin-Manson and

Morrow vibration-life approach. This was due to the fatigue data characteristics of the

SWT vibration-life approach. Morrow predicted the fatigue life better with compression

mean stress while SWT predicted the fatigue life in tension which led to deviation of

results between Coffin-Manson, Morrow and SWT (Ince & Glinka 2011).

Table 4.24 MSE for various approaches and datasets with single hidden layer ANN

Coffin-Manson Morrow SWT

All 0.1232 0.0839 0.3241

Training 0.1137 0.0753 0.3197

Validation 0.2001 0.1234 0.4911

Testing 0.0885 0.0827 0.1769

A good data fit of R2 value did not indicate that the trained ANN had a low MSE.

To study the error, error histograms of all three trained ANN vibration-life were plotted

into Figure 4.35 with details listed in Appendix I. The error range between the output

and targeted fatigue life of ANN-based Coffin-Manson vibration-life is shown in Figure

4.36(a) (-0.7316 to 0.3082). The error range of Morrow vibration-life ANN ranged from

-0.7621 to 0.6157 while the error range of SWT vibration-life ANN was from -0.7319

to 0.3858 as shown in Figures 4.35(b) & (c) respectively. In this ANN analysis, the

targeted value of fatigue lives was in the range of 2 to 8. This error range was relatively

small when compared to the fatigue life range 2 to 8 due to the optimisation process

loop. When compared to MLR method, the error of single hidden layer ANN has proven

to be lower where the SWT MSE dropped from 0.7056 to 0.1769. This suggests that

ANN provided a better fatigue life prediction because the ANNs were trained and

improved to deal with linear and non-linear dependence datasets.

181

Subsequently, normality test was performed on the residuals of all trained

vibration-life ANN outcome. Examining the normality of residuals is significant in

regression analysis because it implies consistency of predictions (Xie et al. 2017). The

normality of the data was tested using the Lilliefors test because it is one of suitable

methods to determine normality with a sample size of less than 100 (Ayinde et al. 2017).

The results have shown that all the predictions have failed to reject the null hyprothesis

and therefore, the residuals were normally distributed. Based on the Lilliefors test, it

indicated a failure to reject the null hypothesis at the default 5% significance level. The

alternate hypothesis was that the data did not come from a normal distribution. Based

on the Lilliefors test, all the residual datasets failed to reject the null hypothesis which

indicated that all the residuals were normally distributed.

(a) (b)

(c)

Figure 4.35 Error histogram of single hidden layer vibration-life ANN for various approaches:


The analysis of a single hidden layer in optimising the spring fatigue life is

shown in Section 3.4.2. This analysis was a discovery process where the ANN

architecture with the lowest MSE was initially defined. Furthermore, the predicted

182

fatigue lives were evaluated using normality test to ensure the consistency of

predictions. The process was repeated for two and three hidden layers until the most

satisfactory ANN architecture for fatigue life prediction was obtained and the second

objective was achieved.

Other than the number of neurons, the other way to enhance the prediction of

trained ANN was through adding more hidden layers (Hemmat Esfe et al. 2015). Hence,

an additional hidden layer was added to ANN architecture to train a model with

improved accuracy. This modified the ANN from a single hidden layer to become two

hidden layers. Subsequently, MSE analyses of the two hidden layers ANN were also

performed and plotted into Figure 4.36. Coffin-Manson vibration-life ANN with three

neurons in first hidden layer and seven neurons in second layer consisted of the lowest

MSE value of 0.0249. For Morrow vibration-life ANN, the lowest MSE was 0.0333

with eight neurons in first hidden layer and six neurons in second hidden layer. Lastly,

the trained SWT vibration-life ANN consisted of MSE value of 0.0945 with one and

six neurons in first and second hidden layers respectively.

Subsequently, curve fitting of trained Coffin-Manson ANN with two hidden

layers were also plotted into Figure 4.37 but the Morrow and SWT approaches were

plotted into Appendix J. The goodness of the fitted curve was determined using R2 value

and the results were tabulated in Table 4.25. As observed from Table 4.25, all the R2

value for trained Coffin-Manson ANN was above 0.8000 with minimum R2 value of

0.8703 which was considered as good. Based on the R2 value, the trained Morrow ANN

was considered as very good with all the R2 value above 0.9000. The R2 value of the

trained SWT ANN was higher than 0.8000 which was considered as good. All MSE of

these fitted ANNs was tabulated in Table 4.26. The minimum MSE for two-layer

Coffin-Manson ANN was 0.0249 in ANN test datasets while Coffin-Manson and

Morrow were 0.0333, 0.0945 respectively. The obtained MSE was considered as low

when compared to the fatigue life datasets with a range of 2 to 8.

183

(a) (b)

(c)

Figure 4.36 MSE of trained vibration-life ANN with two hidden layers for various approaches:


When compared to single hidden layer, the SWT vibration-life ANN also

possessed the highest MSE value of 0.0945 among all three approaches. Nevertheless,

the overall test datasets have shown some improvements with the reduction of MSE.

However, increasing the hidden layer of ANN did not guarantee with improvement of

the trained model (Ghana Sheela & Deepa 2013). Based on the observation between

single and two hidden layers ANN, adding another hidden layer improved the MSE of

trained ANN-based Coffin-Manson fatigue life from 0.0885 to 0.0249. The MSE of

trained ANN-based Morrow fatigue life dropped from 0.0827 to 0.0333 while the

trained ANN-based SWT fatigue life dropped from 0.1769 to 0.0945. The MSE of

fatigue life for all three trained ANN have shown significant improvements. In this

fatigue data ANN analysis, adding an additional hidden layer has helped to reduce the

test datasets MSE and enhanced fatigue life predictions.

184

(a) (b)

(c) (d)

Figure 4.37 Curve fitting of trained Coffin-Manson vibration-life ANN with two hidden layers for

various datasets: (a) all, (b) training, (c) validation, (d) ANN test

Table 4.25 R2 value for all approaches with two hidden layers ANN

all training validation test

Coffin-Manson 0.9426 0.9432 0.8703 0.9926

Morrow 0.9736 0.9657 0.9775 0.9918

SWT 0.8879 0.8943 0.8122 0.9732

Table 4.26 MSE for various approaches and datasets with two hidden layers ANN


All 0.1278 0.0738 0.3222

Training 0.1248 0.0823 0.2585

Validation 0.2441 0.0770 0.8316

ANN Test 0.0249 0.0333 0.0945

In Figure 4.37, the ANN output in vertical axis is the ANN predicted fatigue

life. The ‘Target’ is the response for supervised learning where the performance of each


Target

All: R2 = 0.9426 A

NN

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ANN test: R2 = 0.9926 A

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dataset (all, training, validation, test) could be evaluated using the regression. These

fitted curves served to evaluate the performance of ANN training with different datasets

as well as the stability of the ANN. The error range of test datasets for two hidden layers

were plotted into Figure 4.38 with details listed in Appendix I. For Coffin-Manson ANN

test datasets, the errors were distributed in the range of -0.2456 to 0.1578. The error

range for this Coffin-Manson vibration-life ANN predictions was low and acceptable

because the difference was only 10% from the original data range. Meanwhile, the error

range of trained Morrow test datasets were from -0.3460 to 0.2884. This error range

was wider than the trained Coffin-Manson ANN because of the fatigue data

characteristic. The width of error range was also related to the MSE which was an

indicator for accuracy. On the other hand, the trained SWT test datasets showed an error

range of -0.6605 to 0.2620. Based on the MSE, the error of SWT ANN fatigue life

prediction was expected to be higher than Coffin-Manson and Morrow. Nevertheless,

the distribution of the SWT vibration-life ANN error was still within the acceptable

range.

(a) (b)

(c)

Figure 4.38 Error histogram of two hidden layers vibration-life ANN for various approaches:


186

After ANN with single and two hidden layers were investigated, a third hidden

layer was also applied and analysed. The R2 of fitting for all the trained ANN-based

vibration-life is plotted into Table 4.27. All the R2 values were examined to ensure the

ANN-based vibration-life approaches were well fitted. The MSE results of each training

were tabulated into Table 4.28. As observed, the MSE of test datasets were lower than

training and validation datasets due to the back propagation of the training algorithm.

Combined with the varying number of neurons, the MSE of the trained three hidden

layers Coffin-Manson ANN were plotted and shown in Figure 4.39. The minimum MSE

of this trained Coffin-Manson ANN was 0.0356 according to the ANN test datasets.

The MSE of trained three hidden layers Morrow and SWT ANN fatigue life was listed

in Appendix H. Throughout this analysis, the minimum MSE for trained Morrow ANN

was identified as 0.0117 while the lowest MSE of SWT datasets was 0.0824. Three

hidden layers ANN exhibited a significant improvement in MSE when compared to

single or two hidden layers ANN. As observed in Figures 4.39(e), 4.39(i), there was a few

trained ANN with extra high MSE. In Figure 4.39(e), the high MSE architecture was five

neurons in the first hidden layer, ten neurons in the second hidden layer and five neurons in

the third hidden layer while another high MSE point in Figure 4.39(i) was nine neurons in the

first layer, nine neurons in the second layer and ten neurons in the third hidden layer.

This phenomenon demonstrated that the increasing number of neurons did not

guarantee the improvement in performance. These high MSE architecture were

explained via the iterative learning process in which data cases are presented to the

network one at a time, and the weights associated with the input values were adjusted

each time. After all cases were presented, the process often starts over again. During

this learning phase, the network learnt by adjusting the weights to be able to predict the

correct class label of input samples. The random generation on weights and biases have

caused the high MSE. It is significant to know that the initial weights were chosen

randomly. After that the training, or learning, began. The random MSE effects were

also reported by Salim et al. (2011) where they used a loop to determine the ANN

architecture with the lowest MSE and the MSE were fluctuating across different

neurons. The outcome of the MSE as shown in Figure 4.39 was a significant procedure

for exploration of the optimised fatigue life. Utilising the deep learning in fatigue life

prediction also contributed to the novelty of this analysis.

187

(a) (b)

(c) (d)

(e) (f)

(g) (h)

(i) (j)

Figure 4.39 MSE of trained Coffin-Manson vibration-life ANN first hidden layer with various

number of neurons: (a) 1, (b) 2, (c) 3, (d) 4, (e) 5, (f) 6, (g) 7, (h) 8, (i) 9, (j) 10

188

A superior performance of ANN training was mostly dependent on the data

characteristic where a suitable number of layers and neurons were required. To analyse

the trained ANN, a fitted curve of trained three hidden layer Coffin-Manson vibration-

life ANN is shown in Figure 4.40. The r value of all the datasets were considerably high

at above 0.9000. When considering ANN-based Morrow vibration-life ANN, the r

values were also very high, indicating a very good fit of the datasets. The curve fitting

of trained Morrow and SWT ANN using are shown in Appendix J. The trained

vibration-life ANN has also shown a good fitted behaviour of datasets with the lowest

r value of 0.9396. After ensuring the trained ANN fitted nicely, the residuals of the

trained ANN were analysed using error histograms.

In Figure 4.40, the function of ANN ‘Output’ is defined on the vertical axis

while the ‘Target’ is on the horizontal axis for all, training, validation and ANN test

datasets. The significance of the function was to provide a correlation closest to the

target value for ANN performance evaluation. The residuals of the trained ANNs were

plotted into error histograms shown in Figure 4.41 with details listed in Appendix I. As

observed in Figure 4.41(a), the range of residuals for Coffin-Manson vibration-life

ANN was from -0.4041 to 0.2188. The residuals for ANN-based Morrow vibration-life

ANN ranged from -0.0913 to 0.2732 while for the SWT vibration-life ANN, the errors

ranged from -0.4195 to 0.4739. When compared to the two hidden layer vibration-life

ANN, the range of error has shown a significant reduction. To check the normality of

the errors, the Lilliefors test was also applied. The test showed that it failed to reject

null hypothesis which indicated that the residuals were normally distributed for all three

trained three hidden layer ANN residuals.

Table 4.27 R2 value for all approaches with three hidden layers ANN

all training validation test

Coffin-Manson 0.9395 0.9403 0.8530 0.9912

Morrow 0.9811 0.9781 0.9839 0.9944

SWT 0.9017 0.8828 0.9610 0.9559

Table 4.28 MSE for various approaches and datasets with three hidden layers ANN


All 0.1425 0.0529 0.2831

Training 0.1514 0.0636 0.3636

Validation 0.2102 0.0465 0.1274

ANN Test 0.0356 0.0117 0.0824

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(a) (b)

(c) (d)

Figure 4.40 Curve fitting of trained Coffin-Manson vibration-life ANN with three hidden layers

for various datasets: (a) all, (b) training, (c) validation, (d) ANN test

Among these three approaches, the trained Morrow ANN has the lowest MSE

and the same trend applies for single and two hidden layers. The three hidden layers

ANN were much more complex than single and two hidden layers because additional

weights and biases as well as layer connectivity. Nevertheless, additional hidden layers

did not promise greater accuracy. The multilayer ANN were compared to single and

two hidden layers and results revealed that the trained ANN Coffin-Manson has fitted

greater with two hidden layers. The results of three hidden layers of Morrow and SWT

have shown better improvement with adding the third layer due to the lower MSE value.

All: R2 = 0.9395

Target

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Target

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Target

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Target

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(a) (b)

(c)

Figure 4.41 Error histogram of three hidden layers vibration-life ANN for various approaches:


As a summary for the ANN determination, the best performing ANN

architecture for one, two and three hidden layer vibration-life ANN were identified. The

best architecture among the layers are tabulated in Table 4.29 with the selected ANN

architectures in bold text. Table 4.29 illustrates the ANN architecture with the lowest

MSE for fatigue life prediction which is significant in deciding the most suitable ANN

architecture from one to three hidden layers. The lowest MSE was important to

determine the final ANN architecture among all the designed ANN architecture. This

again contributed to the novelty of this research. In Table 4.29, ANN-based Coffin-

Manson vibration-life ANN with two hidden layers has shown the lowest MSE of

0.0356 and this type of ANN architecture is a hybrid multilayer neural network where

all the hidden layers are interconnected to the output layer. The number of neurons

implied the number of weights in this ANN. For the ANN architecture, the weights and

biases of the ANN were defined in Appendix K. This trained ANN architecture

consisted of two input neurons and three neurons in input layer where inputs and first

hidden layer were connected.

191

Table 4.29 The best performance ANN architecture for vibration-life predictions

Single hidden layer Two hidden layers Three hidden layers

Coffin-Manson 0.0885 0.0356 0.0249

Morrow 0.0827 0.0333 0.0117

SWT 0.1769 0.0945 0.0824

For fatigue life comparisons, the Coffin-Manson, Morrow and SWT ANN-based

predicted fatigue lives using ANN and MLR were listed into Tables 4.30, 4.31 and 4.32

respectively. To compare between ANN and MLR predictions, the RMSE between

ANN and MLR predictions to target fatigue life was identified. The Coffin-Manson

RMSE for MLR-based prediction was 0.5165 blocks to failure in natural logarithm

while the ANN was 0.1578 blocks to failure in natural logarithm. The RMSE has

improved by a significant amount. For Morrow, the RMSE for MLR prediction was

0.5274 blocks to failure in natural logarithm while the ANN prediction was 0.1080

blocks to failure in natural logarithm This also showed a drastic improvement.

Furthermore, the RMSE for MLR SWT prediction was 0.3775 blocks to failure in

natural logarithm while the RMSE for ANN predictions was 0.2870 blocks to failure in

natural logarithm.

Table 4.30 MLR and ANN predicted Coffin-Manson fatigue lives

ANN-based predictions

(blocks to failure)

MLR-based predictions

(blocks to failure)

Target fatigue life

(blocks to failure)

3.27 × 105 5.09 × 105 4.27 × 105

1.07 × 104 3.03 × 104 1.20 × 104

3.13 × 103 2.79 × 103 5.75 × 103

1.17× 104 3.31 × 104 9.55 × 103

3.16 × 103 2.18 × 103 5.75 × 103

3.87 × 104 4.01 × 104 2.82 × 104

1.62 × 108 2.43 × 107 2.04× 108

1.34 × 106 1.08 × 106 1.51 × 106

7.44 × 105 7.09 × 105 7.76 × 105

2.38 × 107 5.93 × 106 3.16 × 107

5.03 × 105 6.64 × 105 9.33 × 105

5.63 × 104 2.14 × 104 3.72 × 104

9.91 × 102 9.02 × 102 7.94 × 102

Although the improvement of RMSE for Morrow was not as high as Coffin-

Manson and SWT, there was still a significant improvement in terms of RMSE. When

the RMSE was low, the predicted value was close to the target value (Kisi 2015). Based

on the obtained RMSE, it suggested that the established ANN has improved the fatigue

life prediction when compared to the MLR approach. This analysis has shown that the

192

ANN approach successfully improved fatigue life predictions when compared to the

MLR approach.

Table 4.31 MLR and ANN predicted Morrow fatigue lives


(blocks to failure)


(blocks to failure)

Target fatigue life

(blocks to failure)

7.06 × 104 8.39 × 104 5.37 × 104

6.73 × 103 5.11 × 104 6.46 × 104

4.66 × 103 2.33 × 104 5.13 × 103

4.25 × 103 1.17 × 104 4.07 × 103

2.94 × 103 6.48 × 103 3.80 × 103

6.70 × 104 3.06 × 105 6.31 × 104

6.15 × 103 1.53 × 103 6.76 × 103

8.23 × 104 3.37 × 105 5.50 × 104

7.66 × 103 7.29 × 103 7.24 × 103

2.54 × 106 2.21 × 106 3.02 × 106

4.11 × 107 1.05 × 107 3.63 × 107

9.88 × 104 9.92 × 104 8.32 × 104

1.36 × 104 2.18 × 104 6.92 × 102

Table 4.32 MLR and ANN predicted SWT fatigue lives


(blocks to failure)


(blocks to failure)

Target fatigue life

(blocks to failure)

6.84 × 103 2.82 × 104 1.29 × 104

2.61 × 103 6.45 × 103 5.62 × 103

2.96 × 103 1.45 × 104 8.71 × 103

4.20 × 105 4.45 × 105 1.26 × 105

7.62 × 104 1.68 × 105 9.33 × 104

2.86 × 104 9.25 × 104 1.38 × 104

9.19 × 106 2.89 × 106 4.17 × 106

2.64 × 106 1.32 × 106 1.17 × 106

8.96 × 105 6.59 × 105 5.89 × 105

1.94 × 105 1.83 × 105 1.82 × 105

7.18 × 104 5.61 × 104 9.12 × 104

5.13 × 104 3.10 × 104 7.24 × 104

1.68 × 108 4.81 × 107 2.69 × 108

For fatigue life analysis, 1:2 or 2:1 correlation curve was used for determining

the accuracy of predictions (Karolczuk 2016). The correlation for ANN-predicted and

target Coffin-Manson fatigue life is shown in Figure 4.42 while the Morrow fatigue life

is shown in Figure 4.43. Based on the Coffin-Manson fatigue life correlation curve, only

three points deviated from the 1:2 or 2:1 boundary while the MLR predicted results

have five deviations. Additionally, the Morrow predictions for ANN approach

possessed only a single point beyond the boundary while the MLR predictions have six

points lying beyond the boundary. Half of the points were outside the acceptability

margin according to the conservative fatigue life analysis. This was due to the mean

stress effects of the Morrow model. The SWT fatigue life correlations are depicted in

193

Figure 4.44 where three points of ANN predictions were beyond the boundary. The

MLR predicted SWT fatigue life has four points lying beyond the boundary. As

observed from all three strain life approaches, the ANN prediction has more points

distributed within the conservative region and the data points were distributed close to

the 1:2 or 2:1 boundary which implied that the predictions were close to the target value.

The MLR predicted fatigue lives were scattered far beyond.

For further analysis, the relationship between prediction and target fatigue lives

were evaluated using linear regression method as shown in Figures 4.45, 4.46 and 4.47.

In Figure 4.45, the R2 value for ANN prediction and target fatigue life was 0.9998 and

the MLR prediction was 0.9954. The R2 value for Morrow fatigue life using ANN was

0.9995 while the MLR prediction with target fatigue life was 0.9805. The R2 value for

ANN predicted SWT with target fatigue life was 0.9991 while the R2 value for MLR

predicted and target fatigue life was 0.9982. The obtained R2 value suggested that the

ANN and MLR prediction was closely related to the target fatigue life (Sivák &

Ostertagová 2012). Nevertheless, based on the fatigue life 1:2 or 2:1 correlation

analysis, the ANN prediction has revealed better accuracy than the MLR predictions

due to the higher number of data points fitted in the conservative boundary region.

In this section, the results of ANN architecture determination and process to find

the optimised spring fatigue life were obtained. The first novel aspect of this research

was the establishment of the prediction regression as discussed in Section 4.4. In this

section, the fatigue life prediction has been improved using ANN which was also the

second objective of this research. The improvised RMSE, R2 and correlation analysis of

the fatigue life predictions suggested that the ANN approach has successfully optimised

the fatigue life predictions. The improvement of fatigue life predictions using ANN

approach was also the novelty of the second objective. Apart from that, the same

procedures were also further analysed to determine the optimised ISO 2631 weighted

acceleration predictions.

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(a)

(b)

Figure 4.42 Correlation curve for Coffin-Manson target fatigue life using various approaches:

(a) ANN, (b) MLR

1.0E+03

1.0E+04

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(a)

(b)

Figure 4.43 Correlation curve for Morrow target fatigue life using various approaches:

(a) ANN, (b) MLR

1.0E+03

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(a)

(b)

Figure 4.44 Correlation curve for SWT target fatigue life using various approaches:

(a) ANN, (b) MLR

1.0E+03

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(a)

(b)

Figure 4.45 Linear regression analysis for prediction and target Coffin-Manson fatigue life using

various approaches: (a) ANN, (b) MLR

1.00E+02

1.00E+03

1.00E+04

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R2 = 0.9998

R2 = 0.9917

198

(a)

(b)

Figure 4.46 Linear regression analysis for prediction and target Morrow fatigue life using various


1.00E+02

1.00E+03

1.00E+04

1.00E+05

1.00E+06

1.00E+07

1.00E+08

1.00E+02 1.00E+03 1.00E+04 1.00E+05 1.00E+06 1.00E+07 1.00E+08

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1.00E+02

1.00E+03

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1.00E+05

1.00E+06

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1.00E+02 1.00E+03 1.00E+04 1.00E+05 1.00E+06 1.00E+07 1.00E+08

ML

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life

(b

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R2 = 0.9995

R2 = 0.9805

199

(a)

(b)

Figure 4.47 Linear regression analysis for prediction and target SWT fatigue life using various


4.5.2 ISO 2631 Vertical Vibration Prediction

Prediction of fatigue life using ANN has been successfully performed using vehicle

body frequency and ISO 2631 vertical vibration as input. This section presents the

improvement of ISO 2631 vertical vibration prediction for vehicle sprung mass using

trained ANN using vehicle body frequency and spring fatigue life as input. All three

Coffin-Manson, Morrow and SWT predicted spring fatigue lives were used as the input

to train ANN for optimised ISO 2631 vertical vibration prediction.

1.00E+02

1.00E+03

1.00E+04

1.00E+05

1.00E+06

1.00E+07

1.00E+08

1.00E+09

1.00E+02 1.00E+03 1.00E+04 1.00E+05 1.00E+06 1.00E+07 1.00E+08 1.00E+09

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1.00E+02

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R2 = 0.9991

R2 = 0.9982

200

To determine a suitable ANN architecture for ISO 2631 vertical vibration

predictions, the MSE for using all three strain life approaches were obtained through

using different numbers of neurons and hidden layers. In this case, ANN with

architecture from one to ten neurons and one to three hidden layers were constructed

and analysed. The results of the lowest MSE across varied number of neurons and

hidden layers were tabulated in Table 4.33. As observed from Table 4.33, the

architecture with three hidden layers has shown the lowest MSE for all three strain life

fatigue approaches. The lowest MSE for Coffin-Manson vibration prediction ANN

predicted ISO 2631 vertical vibration was 0.0007 m/s2 while the lowest MSE for

Morrow ANN predictions was 0.0004 m/s2. For SWT predicted ISO 2631 vertical

vibration the MSE was determined to be 0.0016 m/s2. The determination of suitable

ANN architecture highly depended on the lowest MSE because the accuracy of

predictions was directly influenced by the MSE. Hence, the proposed MSE was the

lowest obtained value which indicated the suitable architecture for this analysis.

Table 4.33 MSE for different trained vibration prediction ANN

Hidden layer Coffin-Manson Morrow SWT

1 0.0885 0.0025 0.0053

2 0.0016 0.0010 0.0031

3 0.0007 0.0004 0.0016

The detailed 3D scatter plot of MSE for all neurons and hidden layers are shown

in Appendix H. The same datasets from Section 4.3.4 were used to train these vibration-

life ANN. For data separation, a total of 72 datasets were used to train the ANN, 14

datasets for validation and 14 data were selected for ANN ‘test’. Curve fitting of the

trained Coffin-Manson ANN-based vibration-life prediction is shown in Figure 4.48

where the r value of 0.9912 for ANN ‘test’ was obtained. When the r value was squared,

R2 value of 0.9825 was obtained. For Morrow vibration prediction ANN, the r value of

ANN ‘test’ was 0.9983 and R2 as high of 0.9966 was obtained. Furthermore, the trained

SWT vibration prediction ANN consisted of r value 0.9787 which was equivalent to R2

value of 0.9579. In Figure 4.48, the obtained R2 value for Coffin-Manson, Morrow and

SWT were considered as very high which indicating the weights and biases of the ANN

were well trained and optimised for the prediction outcome (Sivák & Ostertagová

2012). The ordinate of Figure 4.48 revealed the ANN predicted ISO 2631 with respect

to the target trained value. When the obtained R2 value of ANN ‘test’ was high, the

201

designed ANN performed better (Atici 2011). Hence, the prediction of the ISO 2631

vertical vibration was expected to be greater with high R2 value.

The residuals of the trained ANN were analysed using error histograms as shown

in Figure 4.49. The residuals range of trained Coffin-Manson vibration prediction ANN

was from -0.0494 to 0.0315 m/s2. For Morrow vibration prediction ANN, the error range

was from -0.0385 to 0.0410 m/s2 while the SWT vibration prediction ANN possessed a

range of -0.0929 to 0.0420 m/s2. The original range of the ISO 2631 vertical vibration

was from 0.2900 to 1.3600 m/s2. Based on the obtained residuals, the range was

relatively small. The residuals were also normally distributed. The Lilliefors test

performed to verify the normality of the residuals indicated that the critical value was

greater than the statistic k value, pointing to a normal distribution. This also proved that

the outputs of the trained ANN were well-behaved and suitable to use for ISO 2631

vertical vibration prediction.

In this analysis, a three hidden layer architecture of the Coffin-Manson vibration

prediction ANN has shown the lowest MSE when compared to two hidden layer ANN.

When observing the t-test value for vibration prediction MLR, the t-value of the

parameters were varied when the dependent variables or independent variable were

interchanged. The t-test value expresses the functionality of the independent variable to

dependent variable (Prieto et al. 2017). When the spring fatigue life and ISO 2631

vertical vibration were exchanged, the R2 value and un-standardised coefficients were

also varied. Therefore, three hidden layers Coffin-Manson ANN has shown better

capability in ISO 2631 vertical vibration predictions instead of ANN with two hidden

layers as proposed in vibration-life analysis because the data characteristics were varied.

The selected ANN architectures are listed in Section 3.4.2. All the selected and

trained feedforward network was a hybrid ANN and the weights and biases for this

trained ANN are listed in Appendix K. With the weights and biases, the ANN could be

reproduced and used for optimised ISO 2631 vertical vibration prediction. ISO 2631

vertical vibration is an essential element in assessing vehicle ride (Sezgin & Arslan

2012). Excessive vertical vibration leads to discomfort for drivers and passengers

because human body parts resonate in low frequency range, and the cause of human

202

fatigue. Hence, the ISO 2631 vertical vibration is a main consideration in automotive

suspension design which is relevant to the durability analysis of a vehicle.

(a) (b)

(c)

Figure 4.48 Curve fitting of trained vibration prediction ANN for various approaches:


Utilising the designed ANN architecture as proposed in Section 3.4.2, the

predicted ISO 2631 vertical vibration using Coffin-Manson fatigue lives are shown in

Table 4.34. In addition, the predicted ISO 2631 vertical vibrations for Morrow and SWT

input are shown in Tables 4.35 and 4.36 respectively. In Table 4.34, the comparisons

between MLR and ANN predicted ISO 2631 vertical vibrations were performed. As

observed, the ANN predicted ISO 2631 vertical vibrations were closer in range to the

target value. This was proved by the RMSE between the predictions and target value

using Equation 3.14 where the Coffin-Manson ANN predictions RMSE was 0.0264

Target

AN

N o

utp

ut

AN

N o

utp

ut

AN

N o

utp

ut

Target

Target

203

m/s2. The MLR predicted ISO 2631 vertical vibration was 0.0875 m/s2 which was

higher than the ANN predictions.

(a) (b)

(c)

Figure 4.49 Error histogram of three hidden layers vibration prediction ANN for various


Table 4.34 MLR and ANN Coffin-Manson predicted ISO 2631 vertical vibration

ANN-based

predictions

(m/s2)

MLR-based

predictions

(m/s2)

Target ISO 2631

vertical

vibration (m/s2)

ANN

difference

(%)

MLR

difference

(%)

0.32 0.25 0.33 3.03 24.24

0.34 0.40 0.35 2.86 14.28

0.42 0.44 0.39 7.69 12.82

0.60 0.55 0.59 1.69 6.77

0.71 0.63 0.68 4.41 7.35

0.65 0.73 0.69 5.79 5.80

0.70 0.62 0.73 4.11 15.06

0.27 0.21 0.27 0.00 22.22

0.38 0.44 0.33 15.15 33.33

0.18 0.15 0.16 12.50 6.25

0.15 0.20 0.16 6.25 25.00

0.32 0.36 0.32 0.00 12.50

0.39 0.42 0.34 14.71 23.52

Errors

Inst

ance

Errors

Inst

ance

Errors

Inst

ance

204

Table 4.35 MLR and ANN Morrow predicted ISO 2631 vertical vibration

ANN-based

predictions

(m/s2)

MLR-based

predictions

(m/s2)

Target ISO 2631

vertical

vibration (m/s2)

ANN

difference

(%)

MLR

difference

(%)

0.58 0.62 0.54 7.41 14.81

0.61 0.75 0.61 0.00 22.95

0.62 0.70 0.61 1.64 14.75

0.65 0.71 0.70 7.14 1.43

0.32 0.17 0.30 6.67 43.33

0.36 0.44 0.35 2.86 25.71

0.38 0.43 0.39 2.56 10.26

0.16 0.12 0.16 0.00 25.00

0.15 0.21 0.17 11.76 23.53

0.34 0.24 0.31 9.68 22.58

0.34 0.36 0.32 6.25 12.50

0.61 0.67 0.62 1.61 8.06

1.30 1.06 1.29 0.78 17.83

Table 4.36 MLR and ANN SWT predicted ISO 2631 vertical vibration

ANN-based

predictions

(m/s2)

MLR-based

predictions

(m/s2)

Target ISO 2631

vertical

vibration (m/s2)

ANN

difference

(%)

MLR

difference

(%)

0.27 0.07 0.29 6.89 41.38

0.57 0.71 0.54 5.56 31.48

0.69 0.64 0.73 5.48 12.33

0.63 0.66 0.57 10.50 15.79

0.68 0.83 0.70 2.86 18.57

0.33 0.32 0.30 10.00 6.67

0.39 0.40 0.36 8.33 11.11

0.17 0.04 0.15 13.33 33.33

0.30 0.25 0.31 3.23 19.35

0.57 0.66 0.62 8.06 6.45

0.61 0.82 0.63 3.17 30.16

0.59 0.81 0.64 7.81 26.56

0.62 0.80 0.65 4.62 23.08

Note: Difference = |Predicted ISO 2631 vertical vibration - target ISO 2631 vertical vibration

target ISO 2631 vertical vibration| × 100% (Equation 3.13)

For Morrow predicted ISO 2631 vertical vibrations, the RMSE for ANN

predictions was 0.0207 m/s2 while the MLR predicted ISO 2631 vertical vibration was

0.1222 m/s2. The difference between RMSE also showed that the ANN predictions were

superior than the MLR predicted ISO 2631 vertical vibration. RMSE using SWT input

were 0.0423 and 0.1279 m/s2 with respect to ANN and MLR approaches where an

obvious improvement of RMSE has been observed. The RMSE is a method to validate

the predictions towards experimental data where a smaller RMSE indicate the

predictions are closer to the actual value (Beltramo et al. 2016). When considering the

difference in predictions, the maximum difference of ANN was 15.15% while the

maximum difference of MLR prediction was 41.38%. However, the acceptable limit for

deviation is only within 20% (Manivel & Gandhinathan 2016). Approximately, half of

205

the MLR predictions were beyond the proposed acceptable limit due to the regression

range error (Ospina & Ferrari 2012). Both the RMSE and difference results proposed

that the ANN have improved the ISO 2631 vertical vibration predictions.

The correlation between ANN prediction and target ISO 2631 vertical vibration

using Coffin-Manson fatigue life input was analysed as shown in Figure 4.50(a) while

the correlation for MLR prediction is shown in Figure 4.50(b). In this analysis, the

obtained R2 value for ANN and MLR predictions were 0.9767 and 0.8596 respectively.

The R2 value for Morrow ANN predictions and target vertical vibrations was 0.9938

while the MLR predictions R2 value was 0.8649 as depicted in Figure 4.51. On the other

hand, in Figure 4.52, the R2 value for ANN predictions using SWT input was 0.9539

and the R2 value MLR predictions was 0.8346. In overall terms, the ISO 2631 vertical

vibration prediction using ANN has shown significant improvement when compared

with the MLR approach according to the R2 value. Nevertheless, the ANN prediction

could be classified as “very good” while the MLR predictions was still considered as

good (Sivák and Ostertagová 2012).

In this subsection, multilayer ANN was successfully used to optimise the ISO

2631 vertical vibrations according to the reduced RMSE and R2 value which indicated

a greater correlation to the target value. This analysis aimed to determine the optimised

ISO 2631 vertical vibrations which was relevant to the second novel aspect of this

research. The results suggested that the second objective for prediction improvement

has been successfully achieved. Nevertheless, although most of the ANN predictions

nicely fitted, the accuracy of the predictions remained controversial because the data

used to generate the MLR and trained ANN were artificially generated. The capability

of the quarter-sized car model to predict actual conditions using strain or acceleration

data was unknown. Hence, there was a need to validate the approaches using actual

vehicle experimental data. Experimental validation using collected strain and

acceleration data were performed to verify the generated MLR and ANN based

regression, leading to the third objective.

206

(a)

(b)

Figure 4.50 Correlation between Coffin-Manson predicted and target vertical vibration using

various approaches: (a) ANN, (b) MLR

0

0.1

0.2

0.3

0.4

0.5

0.6

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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

AN

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m/s

2)

Target vertical vibration (m/s2)

0

0.1

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ML

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m/s

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R2 = 0.9767

R2 = 0.8596

207

(a)

(b)

Figure 4.51 Correlation between Morrow predicted and target vertical vibration using various


0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.2 0.4 0.6 0.8 1 1.2 1.4

AN

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vib

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m/s

2)


0

0.2

0.4

0.6

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1

1.2

1.4

0 0.2 0.4 0.6 0.8 1 1.2 1.4

ML

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vib

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R2 = 0.9938

R2 = 0.8649

208

(a)

(b)

Figure 4.52 Correlation between SWT predicted and target vertical vibration using various


4.6 PREDICTION VALIDATION

Prediction of automotive component fatigue life using measured strain time histories is

considered as one of the most acceptable methods due to its acceptable accuracy and

real time monitoring capability (Prakash, Nandi & Sivakumar 2016). Nowadays, many

researches are focusing on developing an algorithm with prediction outcome close to

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

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ML

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m/s

2)


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

ML

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vib

rati

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m/s

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R2 = 0.9539

R2 = 0.8346

209

the strain time history predicted fatigue life because strain life fatigue approaches

provided good accuracy (Slavi c et al. 2012; Ferreira et al. 2016). Hence, for this

regression validation, five sets of experimental measured data collected from the actual

vehicles were applied to the MLR and ANN approach. The validation datasets were

divided into two groups, which were strain and acceleration signals. Initially, the

measured strain time histories were used to calculate the spring fatigue life while the

acceleration time histories were used to obtain ISO 2631 vertical vibration. For

vibration-life regression validation, the experimental ISO 2631 vertical vibration and

vehicle body frequency were used as input for MLR fatigue lives prediction where the

outcome were plotted against experimental fatigue lives as shown in Figure 4.53. It is

noteworthy to mention that the proposed MLR-based regressions were obtained from

simulated data but more applicable than the NCM_linear and NCM_power and, hence only the

MLR regressions were validated.

As observed from Figure 4.53(a), the Coffin-Manson vibration-life regression

predicted fatigue life correlated well with experimental fatigue life and an R2 value of

0.9643 was obtained. The RMSE between prediction and experimental results was

0.4857 blocks to failure in natural logarithm. For Morrow vibration-life regression, an

R2 value of 0.9275 was obtained with the RMSE of 0.6401 blocks to failure in natural

logarithm. Meanwhile, SWT vibration-life regression has yielded a better correlation

compared to other generated regression with an R2 value of 0.9806. For SWT regression

prediction, the obtained RMSE value was 0.6240 blocks to failure in natural logarithm.

Although the generated SWT vibration-life regression consisted of higher RMSE, the

regression predictions have correlated well to the experimental strain time history

predicted fatigue life. Nevertheless, all the three vibration-life regressions have shown

a good correlation with high R2 value which was above 0.9000. Therefore, it is

suggested that the fatigue life predictions using vibration-life regression is closely

related to the experimental predicted spring fatigue life which is considered as

acceptable. Thus, these generated regressions are suitable for automotive applications.

210

(a)

(b)

(c)

Figure 4.53 Correlation curve for three vibration-life regressions: (a) Coffin-Manson, (b) Morrow,

(a) SWT

3.6

3.8

4

4.2

4.4

4.6

4.8

5

5.2

3.4 3.6 3.8 4 4.2 4.4 4.6 4.8 5Vib

rati

on

-lif

e r

eg

ress

ion

pre

dic

ted

fati

gu

e li

fe (

blo

cks

to f

ail

ure

)

Experimental strain predicted fatigue life (blocks to failure)

3.6

3.8

4

4.2

4.4

4.6

4.8

5

5.2

5.4

3.4 3.6 3.8 4 4.2 4.4 4.6 4.8

Vib

rati

on

-lif

e r

eg

ress

ion

pre

dic

ted

fa

tig

ue

life

(b

lock

s to

fail

ure

)


3.6

3.8

4

4.2

4.4

4.6

4.8

5

5.2

5.4

3.4 3.6 3.8 4 4.2 4.4 4.6 4.8Vib

rati

on

-lif

e r

eg

ress

ion

pre

dic

ted

fati

gu

e li

fe (

blo

cks

to f

ail

ure

)


R2 = 0.9642

R2 = 0.9275

R2 = 0.9806

211

The regressions for ISO 2631 vertical vibration predictions were validated using

the same experimental datasets. The results of the Coffin-Manson vibration prediction

regressions were plotted into Table 4.37. As seen from Table 4.37, the highest

difference between MLR predicted and experimental ISO 2631 vertical vibration was

17.86% with a RMSE value of 0.0933 m/s2. The percentage of difference between

Morrow regression-based predicted and experimental ISO 2631 vertical vibration is

illustrated in Table 4.38. The highest difference was 19.31% while the minimum error

was 14.40% with the RMSE of 0.1026 m/s2. Subsequently, the SWT predicted and

experimental ISO 2631 vertical vibration was tabulated in Table 4.39 where the highest

error was 17.52%. with RMSE of 0.0844 m/s2. In this analysis, all the RMSE was

calculated using Equation 3.14 where the difference between the MLR predicted and

experimental ISO 2631 vertical vibration was calculated. A high R2 value and low

RMSE indicated the correlation between prediction and experimental data was good

(Beltramo et al. 2016).

Table 4.37 Difference between experimental and MLR vibration-life prediction for

Coffin-Manson datasets

MLR predicted vibration (m/s2) Experimental vibration (m/s2) Difference (%)

0.63 0.57 10.09

0.78 0.68 15.34

0.66 0.56 17.86

0.65 0.59 10.81

0.85 0.73 16.92

Table 4.38 Difference between experimental and MLR vibration-life prediction for Morrow

datasets


0.68 0.57 19.31

0.78 0.68 14.40

0.66 0.56 17.78

0.68 0.59 15.76

0.84 0.73 15.20

Table 4.39 Difference between experimental and MLR vibration-life prediction for SWT

datasets


0.67 0.57 17.52

0.76 0.68 11.77

0.63 0.56 13.28

0.67 0.59 12.72

0.82 0.73 12.32

Note: Difference = |MLR predicted vertical vibration - Experimental vibration

Experimental vibration| × 100% (Equation 3.13)

212

The percentage of difference for regression predictions were obtained but this

gave rise to the question of how much difference between the predicted and

experimental value was acceptable in automotive applications. Manivel and

Gandhinathan (2016) proposed that the acceptable reliable statistical analysis of error

for regression analysis was below 20%. Additionally, Zhang et al. (2007) proposed that

the 20% deviation between experimental and simulation results was considered as

acceptable and 10% deviation was considered as good. In addition, the RMSE for all

the vibration prediction regression predictions were relatively low. To analyse the error,

the differences between all three vibration prediction regression predictions were

obtained and plotted into Figure 4.54. As observed, most of the outcomes were below

20%. Within the proposed acceptable range of 20%, the predictions of all generated

vibration prediction regressions were considered as acceptable. This demonstrated that

the vibration prediction regression has predicted the automobile ISO 2631 vertical

vibration with acceptable accuracy. This analysis corresponded to objective three of this

research which was the validation of the generated regression to integrate the all three-

fatigue life, vehicle body frequency and ISO 2631 vertical vibration parameters.

Figure 4.54 Difference between prediction and experiment ISO 2631 vertical vibration for various

approaches

0

5

10

15

20

25


Dif

fere

nce

(%

)

Coffin-Manson

Morrow

SWT

213

After the validation of the MLR approach, the validation analysis was performed

for the trained ANN. The following validation of trained ANN was performed using

strain-based experimental fatigue life data which were collected from different road

conditions. The correlation plots between ANN predicted and experimental fatigue lives

are shown in Figure 4.55. As observed from Figure 4.55(a), the ANN predicted Coffin-

Manson fatigue lives all fitted into the boundary of 1:2 or 2:1 life correlation graph.

This implied that the trained ANN has provided very good prediction of Coffin-Manson

fatigue life (Kim et al. 2002). For Morrow ANN predicted fatigue life (Figure 4.55(b)),

there were three fatigue life data points located beyond the boundary of life factor of 2.

These three data points were strain time histories from hill, residential and rural area.

Based on the observation, these three points have very low mean value of 4.4, 3.0 and

-4.0 µε when compared to the other two strain measurements. Morrow strain life model

is very sensitive to mean stress (Manson & Halford 2006). Hence, the predictions of

this fatigue life deviated from the experimental results.

In Figure 4.55(c), all the fatigue life predictions fitted into the 1:2 or 2:1 region

of fatigue life correlation graph. SWT vibration-life ANN has provided a better

prediction results than Morrow ANN even though both fatigue strain life model

considered the mean stress effects. Ince & Glinka (2011) has provided research results

through comparing Morrow and SWT strain life models where the results have shown

that the SWT model was superior in predicting fatigue life than Morrow model for steel

components. This was the reason that SWT vibration-life ANN provided nicely fitted

and accurate fatigue life predictions inside the fatigue life scatter band. When compared

to the MLR prediction, vibration-life ANN have shown a good improvement in fatigue

life prediction where the MSE dropped from 0.7056 to 0.1769. The reduction of MSE

suggested that the fatigue life prediction was improved. Although vibration-life ANN

was more accurate than MLR vibration-life method, the structure of ANN was much

more complex than MLR. Implementation of MLR regression was easier and the results

could be obtained through simple calculations.

214

(a)

(b)

(c)

Figure 4.55 Correlation curve of experimental and vibration-life ANN fatigue life predictions

using various approaches: (a) Coffin-Manson, (b) Morrow, (c) SWT

1.0E+03

1.0E+04

1.0E+05

1.0E+06

1.0E+03 1.0E+04 1.0E+05 1.0E+06

AN

N p

red

icu

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fa

tig

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life

(b

lock

s to

fail

ure

)

Experimental fatigue life (blocks to failure)

1:1 correlation

1:2 or 2:1

correlation

1.0E+03

1.0E+04

1.0E+05

1.0E+06

1.0E+03 1.0E+04 1.0E+05 1.0E+06

AN

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life

(b

lock

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fail

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)


1:1 correlation

1:2 or 2:1

correlation

1.0E+03

1.0E+04

1.0E+05

1.0E+06

1.0E+03 1.0E+04 1.0E+05 1.0E+06

AN

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(b

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)


1:1 correlation

1:2 or 2:1

correlation

215

For vibration-life ANN training results, the validation was performed using the

same experimental data. The results of validation for ISO 2631 vertical vibration

prediction using Coffin-Manson fatigue life as input was tabulated in Table 4.40. For

Coffin-Manson ANN predicted ISO 2631 vertical vibration, the highest difference

between prediction and experimental ISO 2631 vertical vibration results was 10.96%.

For Morrow vibration prediction ANN, the maximum difference was also 10.96% while

the SWT ANN for ISO 2631 vertical vibration was 11.69%. The results for Morrow

and SWT life vibration ANN are illustrated in Tables 4.41 and 4.42 respectively while

the percentage difference was plotted into a chart as shown in Figure 4.56. The

difference between ANN-based prediction and experimental ISO 2631 vertical

vibration was below 15% while the MLR approaches were below 20%. Based on

Manivel and Gandhinathan (2016), the prediction of vibration for experimental and

simulation within 20% were acceptable and below 10% was considered as good. Hence,

the ANN prediction was considered as good and the prediction results were also

improved from MLR approaches.

When compared to MLR, the percentage difference of trained ANN was lower

because the ANN has deeper learning with Levenberg-Marquadt algorithm.

Nevertheless, these functions also made the trained vibration-life ANN more complex

to handle than MLR method. ANN method has shown superior capability in

development and widely applied in recent automotive researches. For example, Patel

and Bhatt (2016) applied the ANN method for chassis identical stress predictions. ANN

was also introduced to predict the spine acceleration from road excitation signal of an

automobile (Gohari et al. 2014). The vehicle suspension system was then optimised

using metaheuristic algorithms. In this research, the proposed MLR relationship and

trained ANN were also applicable to automotive suspension system design. MLR

provided a less accurate solution but was easier to use. The trained ANN provided more

accurate predictions but knowledge of ANN was required when it was applied.

Table 4.40 Difference between experimental and ANN vibration-life prediction for

Coffin-Manson approach

ANN predicted vibration (m/s2) Experimental vibration (m/s2) Difference (%)

0.61 0.57 6.20

0.62 0.68 8.70

0.61 0.56 8.69

0.61 0.59 3.07

0.65 0.73 10.96

216

Table 4.41 Difference between experimental and ANN vibration-life prediction for Morrow

approach


0.63 0.57 10.53

0.63 0.68 7.35

0.62 0.56 10.71

0.63 0.59 6.78

0.65 0.73 10.96

Table 4.42 Difference between experimental and ANN vibration-life prediction for SWT

approach


0.63 0.57 11.35

0.60 0.68 11.69

0.62 0.56 10.11

0.63 0.59 7.36

0.65 0.73 10.96

Note: Difference = |ANN Predicted vertical vibration - Experimental vibration

Experimental vibration| × 100% (Equation 3.13)

Figure 4.56 Difference between prediction and experiment ISO 2631 vertical vibration for various

strain life approaches

In this section, validation of both MLR and ANN vibration-life approaches for

spring fatigue life and ISO 2631 vertical vibration predictions were performed. The

MLR regression predicted fatigue life has correlated to the experimental strain predicted

fatigue life while the ANN predicted fatigue life has correlated well with the

experimental fatigue life under a conservative fatigue scatter band approach. On the

other hand, the vibration prediction ANN has shown a significant improvement of ISO

2631 vertical vibration with percentage of difference below 11.69%. All this validation

processes suggested that the third objective has been successfully achieved where the

0

5

10

15

20


Dif

fere

nce

(%

)

Coffin-Manson

Morrow

SWT

217

proposed approaches were acceptable for spring fatigue life or ISO 2631 vertical

vibration predictions.

4.7 SUMMARY

This chapter has presented all the analysis results and discussions according to the

sequence of three objectives which led to the achievement of research novelty. There

were two main findings that contributed to the research novelty where the first was

regression-based prediction approaches for spring fatigue life, vehicle body frequency

and ISO 2631 vertical vibration. The integrated fatigue life regressions were analysed

using R2, normal P-P, F-test, t-test to show normality. The second novelty was

described by the second objective which was predictions of the fatigue life or ISO 2631

vertical vibration using ANN. The ANN approach with Levenberg-Marquadt algorithm

in training where the ANN method has the capability of adjusting weighting and

improvised the prediction results. The designed ANN were analysed using R2, error

histogram and the Lilliefors test to ensure that it had satisfactory performance which

served as the second novelty of this research.

Based on the validation results, the vibration prediction ANN have shown

significant improvement when compared with regression-based approaches according

to experimental data. The vibration prediction ANN have also shown a lower percentage

of MSE. Nevertheless, both regression and ANN-based vibration predictions were

acceptable due to the low percentage of differences. Overall, both proposed prediction

approaches contribute to the automotive industry through reducing spring or suspension

design process in field of fatigue and automobile ride. In the automotive industry,

suspension design process involved many steps including the spring fatigue life and

automobile ride analysis associated to the spring stiffness. In this thesis, the solutions

to assist these tedious processes have been proposed which are known as the vibration-

life approaches. This proposed MLR and ANN vibration-life approaches for optimised

spring fatigue life predictions have led to the novelty of this research.

218

CHAPTER V

CONCLUSION AND RECOMMENDATIONS

5.1 CONCLUSION

This thesis focuses on determining and establishing fatigue life prediction

relationships using vehicle body frequency and automotive ride as inputs. Multiple

linear regression relationships and trained ANNs were proposed for modelling these

parameters to simplify the automotive suspension design process through predictions.

This study was divided into the following three main stages:

1. Determination of multiple input regression-based fatigue relationships that

predict vehicle ISO 2631 weighted vibrations using quarter car model

simulations with different spring stiffness variants;

2. Establishment of fatigue life predictions using a multilayer perceptron ANN by

determining the architecture with the lowest mean squared error; and

3. Validation of the regression and ANN predictions using various experimental

data.

The execution of these stages produced the optimised durability relationships for

predicting the spring fatigue life or ISO 2631 vertical vibration with good and

acceptable accuracy, as well as repeatability.

5.1.1 Determination of Durability Relationships

The first objective of the current study is to determine a relationship that predicts the

spring fatigue life or vertical vibration with consideration of suspension parameter.

219

The characterisation of road measurement data successfully verified the feasibility of

the regression method. With the combination of the generated artificial road profile

and the acceleration inputs to the quarter car model simulation, spring force and

vehicle spring mass acceleration responses were obtained and processed into fatigue

life and ISO 2631 weighted acceleration, respectively. For the nominal spring design,

the simulated fatigue life was 6.23 × 106 blocks to failure while the weighted

acceleration was 0.3390 m/s2. Then, MLR approaches were used to model these

parameters with R2 value of 0.8320 and an MSE of 0.7056. Based on these

parameters, the proposed durability relationship was suitable for fatigue life and ISO

2631 vertical vibration predictions.

5.1.2 Establishment of Fatigue Life Prediction

The second objective is to establish the fatigue life prediction relationship using ANN.

ANNs performed better than the MLR predictions for vibration–life analyses. For the

Morrow vibration–life ANN, the R2 and MSE obtained were 0.9944 and 0.0117,

respectively. For the SWT vibration–life ANN, R2 and MSE values of 0.9926 and

0.0824 m/s2 were respectively obtained. For the life–vibration Morrow ANN, the

trained ANN possessed an R2 value of 0.9966 with a low MSE of 0.0004 m/s2. The

SWT fatigue–vibration ANN obtained an R2 value of 0.9580 with an MSE value of

0.0016 m/s2. The ANN exhibited greater improvement in terms of MSE compared

with the MLR method. From these findings, the life estimations can be established

using ANN through the analysis of vibration and strain data.

5.1.3 Validation of MLR- and ANN-Predicted Fatigue Life

The third objective of this study is to validate the regression and ANN predictions

using various experimental data. To achieve this goal, the predicted life of the

vibration–life MLR approach was correlated to the experimental strain results. The

correlations showed high R2 values of 0.9275 and 0.9806 for the Morrow and SWT

predictions. The fatigue life was considered following the trend of experimental

predictions. Meanwhile, the maximum difference of the predicted ISO 2631 vertical

vibrations using MLR was 19.31%. For vibration–life ANN, the fatigue lives were

220

correlated to the experimental data using a 1:2 or 2:1 correlation curve. Most of the

data were fitted within the boundary, and the outcome of the predictions was

considered acceptable. For fatigue life to ISO 2631 vertical vibration ANN, the

maximum deviation of the prediction was 11.69% which indicating that it is

acceptable. Finally, it suggested that the ANN predictions could be suitable for the

cases of ride-related vibration and life prediction in automotive suspension

applications.

5.2 RESEARCH CONTRIBUTIONS

The automotive suspension design process requires considerable and lengthy efforts.

Thus, this study established prediction relationships to provide a quick solution to

reduce the time and effort required. To the best of the author’s knowledge, the

established prediction relationship has yet to be found in previous works. With the

vehicle body frequency and ISO 2631 vertical vibration as inputs, spring fatigue lives

were predicted with acceptable accuracy. Conversely, the ISO 2631 vertical vibrations

were estimated using vehicle body frequency and spring fatigue life as inputs. This

study involved three academic disciplines of mechanical engineering, namely,

automotive suspension design, structure durability and vehicle ride analysis. The gap

of these three disciplines could be bridged using an advanced supervised learning

method. Considerable attention has been devoted to the improvement of predictions

using ANN architectures in the field of machine learning in terms of mechanical

engineering applications. The outcomes of this study could offer solutions to

automotive industries for addressing issues in prototyping costs and time. In addition,

academicians from the field of fatigue could better understand vehicle vibration to

analyse spring fatigue life.

221

5.3 RECOMMENDATIONS

There are some future works that can be furthered to improve this current work, which

are:

1. In real applications, the springs are subjected to multiaxial loadings because

they possess round and helical geometry where the stress states are complex.

In future, the fatigue life of the spring could be assessed using a multiaxial

fatigue model to obtain fatigue life. The proposed analysis was based on ISO

2631 vertical vibration as a ride indicator. This indicator could be expanded

into three axes where the lateral and longitudinal vibrations are also

considered.

2. This current strain life approaches do not take load sequence effects into

consideration. When the loading time histories are random and stochastic, the

fatigue life could deviate from the actual conditions. Effective strain damage

models could be used to enhance the predictions.

3. The quarter car simulation model was applied in this analysis to extract the

vehicle and spring responses. A half car or full car model could provide greater

accuracy of simulation because of the consideration of time-delayed input.

4. The developed prediction relationship could be further expanded with

additional parameters, such as variable damping coefficient of dampers, hard

points of the lower arm, tyre stiffness to perform a more feasible suspension

design. Additional variables could be added to train the ANN for a more

advanced application.

5. Recurrent neural network is a type of neural network where the output is

feedback to the input for weights and biases adjustment. This kind of neural

network is more complicated but provides greater accuracy. This type of

neural network is suggested for further analyses.

222

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Zonfrillo, G. & Rossi, A. 2012. A fuzzy approach for drawing S-N curves in the finite life

region. Fatigue and Fracture of Engineering Materials and Structures 34: 868 – 876.

250

APPENDIX A

SPRING FAILURE REPORTED BY THEAA

A.1 Reported coil spring breakdowns

Source: https://www.theaa.com/driving-advice/service-repair/coil-springs-breaking

https://www.theaa.com/driving-advice/service-repair/coil-springs-breaking

251

APPENDIX B

MESH SENSITIVITY

(a) (b)

(c) (d)

(e)

B.1 Element sizes: (a) 3.0, (b) 2.5, (c) 2.0, (d) 1.5, (e) 1.0 mm

252

(a) (b)

(c) (d)

(e)

B.2 Von Mises stress for various element sizes: (a) 3.0, (b) 2.5, (c) 2.0, (d) 1.5, (e) 1.0 mm

B.3 Mesh sensitivity results

Mesh Size (mm) Von Mises Stress (MPa) Required Time (minute)

3.0 1010 < 1

2.5 1002 < 1

2.0 990 2

1.5 988 4

1.0 987 25

253

APPENDIX C

OPTIMISED MULTILAYER ANN ARCHITECTURE

C.1 ANN architecture for optimised Morrow vibration-life predictions

C.2 ANN architecture for SWT vibration-life predictions

Spring fatigue

life

ISO 2631-1

weighted

acceleration

Characteristic

frequency

Input layer Second hidden layer First hidden layer Third hidden layer

Second hidden

layer Input First hidden

layer

Spring

fatigue life

Characteristic

frequency

ISO 2631-1

weighted

acceleration

Third hidden

layer Output

254

C.3 ANN architecture for Coffin-Manson ISO 2631 vertical vibration prediction

C.4 ANN architecture for Morrow ISO 2631 vertical vibration prediction

ISO 2631-1

weighted

acceleration

Second hidden

layer Input First hidden

layer

Spring

fatigue life

Characteristic

frequency

Third hidden

layer Output

ISO 2631

weighted

acceleration

Second hidden

layer

Input First hidden

layer

Spring

fatigue life

Suspension

frequency

Third hidden

layer Output

255

C.5 ANN architecture for SWT ISO 2631 vertical vibration prediction

ISO 2631

weighted

acceleration

Spring

fatigue life

Suspension

frequency

Second hidden

layer Input

First hidden

layer Third hidden

layer

Output

256

APPENDIX D

ARTIFICIAL ROAD SIMULATED TIME HISTORIES

D.1 Spring force time histories of road class “B” for various spring stiffness: (a) k14, (b) k16,

(c) k18, (d) k20, (e) k22, (f) k24, (g) k26, (h) k28, (i) k30, (j) k32

257

D.2 Spring force time histories of road class “C” for various spring stiffness: (a) k14, (b) k16,

(c) k18, (d) k20, (e) k22, (f) k24, (g) k26, (h) k28, (i) k30, (j) k32

258

D.3 Spring force time histories of road class “D” for (a) k14, (b) k16, (c) k18, (d) k20, (e) k22,

(f) k24, (g) k26, (h) k28, (i) k30, (j) k32

259

D.4 Vehicle acceleration time histories of road class “A” for (a) k14, (b) k16, (c) k18, (d) k20,

(e) k22, (f) k24, (g) k26, (h) k28, (i) k30, (j) k32

260

D.5 Vehicle acceleration time histories of road class “B” for (a) k14, (b) k16, (c) k18, (d) k20,

(e) k22, (f) k24, (g) k26, (h) k28, (i) k30, (j) k32

261

D.6 Vehicle acceleration time histories of road class “C” for (a) k14, (b) k16, (c) k18, (d) k20,

(e) k22, (f) k24, (g) k26, (h) k28, (i) k30, (j) k32

262

D.7 Vehicle acceleration time histories of road class “D” for (a) k14, (b) k16, (c) k18, (d) k20,

(e) k22, (f) k24, (g) k26, (h) k28, (i) k30, (j) k32

263

APPENDIX E

MEASURED ROAD SIMULATED TIME HISTORY

E.1 Spring force time histories of highway road for (a) k14, (b) k16, (c) k18, (d) k20, (e) k22,

(f) k24, (g) k26, (h) k28, (i) k30, (j) k32

264

E.2 Spring force time histories of campus road for (a) k14, (b) k16, (c) k18, (d) k20, (e) k22,

(f) k24, (g) k26, (h) k28, (i) k30, (j) k32

265

E.3 Spring force time histories of hill road for (a) k14, (b) k16, (c) k18, (d) k20, (e) k22, (f) k24,

(g) k26, (h) k28, (i) k30, (j) k32

266

E.4 Spring force time histories of residential road for (a) k14, (b) k16, (c) k18, (d) k20, (e) k22,

(f) k24, (g) k26, (h) k28, (i) k30, (j) k32

267

E.5 Simulated acceleration time histories of road class “D” for (a) k14, (b) k16, (c) k18, (d) k20,

(e) k22, (f) k24, (g) k26, (h) k28, (i) k30, (j) k32

268


(e) k22, (f) k24, (g) k26, (h) k28, (i) k30, (j) k32

269


(e) k22, (f) k24, (g) k26, (h) k28, (i) k30, (j) k32

270


(e) k22, (f) k24, (g) k26, (h) k28, (i) k30, (j) k32

271

APPENDIX F

FATIGUE LIFE AND VIBRATION DATA

F.1 Predicted fatigue life and ISO 2631 weighted acceleration from road Class “B”

Suspension

frequency (Hz)

Weighted

Acceleration

(m/s2)

Coffin-Manson

fatigue life

(blocks to

failure)

Morrow fatigue

life (blocks to

failure)

SWT fatigue life

(blocks to

failure)

1.00 0.3085 3.14 × 108 3.65 × 108 2.23 × 108

1.06 0.3109 2.44 × 107 2.79 × 107 1.69 × 107

1.13 0.3133 8.20 × 106 9.20 × 106 5.88 × 106

1.20 0.3160 1.87 × 106 2.12 × 106 1.40 × 106

1.25 0.3191 9.35 × 105 1.07 × 106 5.85 × 105

1.30 0.3224 4.42 × 105 5.14 × 105 3.47 × 105

1.36 0.3262 2.34 × 105 2.80 × 105 1.93 × 105

1.41 0.3303 1.00 × 105 1.25 × 105 9.17 × 104

1.45 0.3346 6.45 × 104 8.33 × 104 5.78 × 104

1.50 0.3392 4.78 × 104 5.00 × 104 3.79 × 104

F.2 Predicted fatigue life and ISO 2631 weighted acceleration from road Class “C”

Suspension

frequency (Hz)

Weighted

Acceleration

(m/s2)

Coffin-Manson

fatigue life

(blocks to

failure)

Morrow fatigue

life (blocks to

failure)

SWT fatigue life

(blocks to

failure)

1.00 0.6158 2.97 × 105 2.57 × 105 2.38 × 105

1.06 0.6201 3.72 × 104 3.41 × 104 3.26 × 104

1.13 0.6244 1.64 × 104 1.55 × 104 1.50 × 104

1.20 0.6298 5.84 × 103 5.75 × 103 5.67 × 103

1.25 0.6360 3.66 × 103 3.64 × 103 3.60 × 103

1.30 0.6433 2.30 × 103 2.30 × 103 2.28 × 103

1.36 0.6507 1.62 × 103 1.60 × 103 1.55 × 103

1.41 0.6587 1.08 × 103 1.06 × 103 1.05 × 103

1.45 0.6672 8.70 × 102 8.54 × 102 8.43 × 102

1.50 0.6771 6.89 × 102 6.98 × 102 6.89 × 102

F.3 Predicted fatigue life and ISO 2631 weighted acceleration from road Class “D”

Suspension

frequency (Hz)

Weighted

Acceleration

(m/s2)

Coffin-Manson

fatigue life

(blocks to

failure)

Morrow fatigue

life (blocks to

failure)

SWT fatigue life

(blocks to

failure)

1.00 1.234 2.48 × 103 2.48 × 103 2.47 × 103

1.06 1.241 7.95 × 102 8.05 × 102 8.05 × 102

1.13 1.251 5.11 × 102 5.15 × 102 5.17 × 102

1.20 1.262 2.86 × 102 2.86 × 102 2.87 × 102

1.25 1.274 2.19 × 102 2.18 × 102 2.18 × 102

1.30 1.288 1.68 × 102 1.67 × 102 1.67 × 102

1.36 1.303 1.37 × 102 1.36 × 102 1.35 × 102

1.41 1.319 1.28 × 102 1.06 × 102 1.06 × 102

1.45 1.335 9.31 × 101 9.26 × 101 9.21 × 101

1.50 1.356 8.15 × 101 8.11 × 101 8.11 × 101

272

F.4 Predicted fatigue life and ISO 2631 weighted acceleration from campus road

Suspension

frequency (Hz)

Weighted

vertical

acceleration

(m/s2)

Coffin-Manson

fatigue life

(blocks to

failure)

Morrow fatigue

life (blocks to

failure)

SWT fatigue life

(blocks to

failure)

1.00 0.4816 9.74 × 105 2.17 × 107 8.33 × 107

1.06 0.5350 8.77 × 105 8.62 × 105 1.02 × 107

1.13 0.5631 3.72 × 105 1.04 × 105 4.13 × 106

1.20 0.5861 1.38 × 105 2.26 × 105 5.41 × 104

1.25 0.6068 1.03 × 105 8.87 × 103 8.20 × 104

1.30 0.6249 7.85 × 104 6.49 × 103 1.30 × 104

1.36 0.6413 6.52 × 104 5.18 × 103 9.43 × 103

1.41 0.6563 5.30 × 104 4.03 × 103 5.62 × 103

1.45 0.6701 5.23 × 104 3.80 × 103 5.21 × 103

1.50 0.6819 5.26 × 103 3.66 × 103 4.93 × 103

F.5 Predicted fatigue life and ISO 2631 weighted acceleration from hilly road

Suspension

frequency (Hz)

Weighted

vertical

acceleration

(m/s2)

Coffin-Manson

fatigue life

(blocks to

failure)

Morrow fatigue

life (blocks to

failure)

SWT fatigue life

(blocks to

failure)

1.00 0.5391 2.92 × 105 9.92 × 105 1.29 × 105

1.06 0.5916 5.17 × 104 2.65 × 105 3.49 × 104

1.13 0.6202 3.01 × 104 6.03 × 104 2.28 × 104

1.20 0.6451 1.58 × 104 2.44 × 104 1.35 × 104

1.25 0.6678 1.19 × 104 1.59 × 104 1.07 × 104

1.30 0.6906 9.19 × 103 1.24 × 104 8.63 × 103

1.36 0.7115 7.75 × 103 1.01 × 104 7.40 × 103

1.41 0.7300 6.24 × 103 8.07 × 103 6.13 × 103

1.45 0.7489 5.75 × 103 7.35 × 103 5.71 × 103

1.50 0.7657 5.36 × 103 6.77 × 103 5.38 × 103

F.6 Predicted fatigue life and ISO 2631 weighted acceleration from residential road

Suspension

frequency (Hz)

Weighted

vertical

acceleration

(m/s2)

Coffin-Manson

fatigue life

(blocks to

failure)

Morrow fatigue

life (blocks to

failure)

SWT fatigue life

(blocks to

failure)

1.00 0.2740 2.93 × 107 3.50 × 107 4.63 × 107

1.06 0.2981 3.93 × 106 7.99 × 107 7.75 × 106

1.13 0.3122 1.72 × 106 3.30 × 107 4.18 × 106

1.20 0.3250 4.82 × 105 1.05 × 107 1.17 × 106

1.25 0.3374 2.37 × 105 9.82 × 105 5.92 × 105

1.30 0.3503 1.17 × 105 3.40 × 105 2.93 × 105

1.36 0.3630 7.35 × 104 1.87 × 105 1.81 × 105

1.41 0.3759 4.56 × 104 1.14 × 105 1.17 × 105

1.45 0.3888 3.56 × 104 8.77 × 105 9.17 × 104

1.50 0.4013 2.82 × 104 6.95 × 104 7.30 × 104

273

F.7 Predicted fatigue life and ISO 2631 weighted acceleration from rural road

Suspension

frequency (Hz)

Weighted

vertical

acceleration

(m/s2)

Coffin-Manson

fatigue life

(blocks to

failure)

Morrow fatigue

life (blocks to

failure)

SWT fatigue life

(blocks to

failure)

1.00 0.5040 2.98 × 105 1.04 × 106 8.47 × 105

1.06 0.5740 5.73 × 104 2.71 × 105 1.25 × 105

1.13 0.5919 2.56 × 104 5.55 × 104 9.43 × 104

1.20 0.6098 2.37 × 104 5.29 × 104 1.37 × 104

1.25 0.6619 9.55 × 103 1.24 × 104 4.12 × 103

1.30 0.6818 8.18 × 103 1.02 × 104 1.28 × 103

1.36 0.6990 7.05 × 103 8.71 × 103 1.05 × 103

1.41 0.7130 6.03 × 103 7.29 × 103 7.37 × 102

1.45 0.7236 5.86 × 103 6.98 × 103 6.97 × 102

1.50 0.7310 5.78 × 103 6.80 × 103 4.92 × 103

274

APPENDIX G

MSE FOR SINGLE LAYER ANN

G.1 MSE of trained neural network with single hidden layer for Coffin-Manson

Number of Neurons MSE

1 0.4490

2 0.1461

3 0.2691

4 0.1132

5 0.1418

6 0.1715

7 0.0885

8 0.1537

9 0.2114

10 0.2551

G.2 MSE of trained neural network with single hidden layer for Morrow


1 0.1430

2 0.2127

3 0.1230

4 0.1430

5 0.1372

6 0.3389

7 0.0905

8 0.1175

9 0.0827

10 0.1315

G.3 MSE of trained neural network with single hidden layer for SWT


1 0.1769

2 0.5395

3 0.1818

4 0.2106

5 0.3576

6 1.2619

7 0.6108

8 0.2437

9 0.2241

10 0.2404

275

APPENDIX H

MSE FOR THREE HIDDEN LAYER ANN

(a) (b)

(c) (d)

(e) (f)

(g) (h)

Continue…

276

Continued…

(i) (j)

H.1 MSE of trained Morrow vibration-durability first hidden layer ANN with various number of neurons:

(a) 1, (b) 2, (c) 3, (d) 4, (e) 5, (f) 6, (g) 7, (h) 8, (i) 9, (j) 10

(a) (b)

(c) (d)

(e) (f)

Continue…

277

Continued…

(g) (h)

(i) (j)

H.2 MSE of trained SWT vibration-durability first hidden layer ANN with various number of neurons: (a) 1,

(b) 2, (c) 3, (d) 4, (e) 5, (f) 6, (g) 7, (h) 8, (i) 9, (j) 10

278

APPENDIX I

DATA FOR ANN ERROR HISTOGRAM

I.1 Error histogram data for single

layer Coffin-Manson ANN


layer Morrow ANN

Data

points

Residuals Data

points Residuals

1 0.0192 1 0.1201

2 -0.0388 2 -0.1902

3 -0.1407 3 -0.0824

4 -0.7894 4 -0.1845

5 0.0201 5 -0.7051

6 0.0595 6 -0.2369

7 0.3660 7 -0.2758

8 0.3417 8 -0.3243

9 0.2170 9 -0.0489

10 0.0957 10 0.3004

11 -0.4284 11 0.4710

12 -0.2765 12 0.0951

13 -0.1489 13 -0.0838

14 -0.0388 14 -0.0340

I.3 Error histogram data for single layer SWT ANN

Data points Residuals

1 -0.7940

2 -0.6770

3 -0.0884

4 0.3144

5 -0.6802

6 0.0617

7 0.3868

8 0.3802

9 0.4321

10 0.2567

11 -0.1106

12 0.1764

13 0.4479

14 0.1560

279

I.4 Error histogram data for two

layers Coffin-Manson ANN

I.5 Error histogram data for two

layers Morrow ANN

Data

points

Residuals Data

points Residuals

1 -0.1149 1 -0.3812

2 -0.0495 2 0.0582

3 -0.2646 3 0.1013

4 0.0872 4 0.0028

5 -0.2610 5 -0.2983

6 0.1381 6 -0.0192

7 -0.0997 7 0.0901

8 -0.0533 8 0.1498

9 -0.0183 9 0.0040

10 -0.1237 10 0.1288

11 -0.2680 11 0.3236

12 0.1802 12 -0.1451

13 0.0961 13 -0.2092

14 0.1621 14 0.0345

I.6 Error histogram data for two layers SWT ANN


1 -0.7118

2 -0.4118

3 0.1854

4 0.2901

5 0.3072

6 0.2381

7 0.3133

8 -0.0183

9 0.0016

10 0.2048

11 0.2160

12 0.3070

13 0.0825

14 0.2992

280


layer Coffin-Manson ANN


layer Morrow ANN

Data

points

Residuals Data

points Residuals

1 -0.4387 1 0.1189

2 -0.1059 2 0.0182

3 0.0275 3 -0.0416

4 -0.0249 4 0.0188

5 0.0068 5 -0.1115

6 0.1061 6 0.0260

7 0.1081 7 -0.0408

8 0.0461 8 0.1753

9 -0.1317 9 0.0243

10 -0.0556 10 -0.0747

11 -0.3277 11 0.0539

12 -0.2755 12 0.0748

13 0.2534 13 0.2934

14 0.0243 14 0.0213

I.9 Error histogram data for single layer SWT ANN


1 -0.2752

2 -0.3334

3 -0.4692

4 0.5236

5 -0.0881

6 0.3157

7 0.3435

8 0.3515

9 0.1823

10 0.0268

11 -0.1038

12 -0.1502

13 -0.2055

14 0.1169

281

APPENDIX J

CURVE FITTING FOR ANN

(a) (b)

(c) (d)

J.1 Curve fitting of trained Morrow vibration- fatigue ANN model with single hidden layer for


(a) (b)

Continue…

282

Continued…

(c) (d)

J.2 Curve fitting of trained SWT vibration- fatigue ANN model with single hidden layer for


(a) (b)

(c) (d)

J.3 Curve fitting of trained Morrow vibration- fatigue ANN model with two hidden layers for


283

(a) (b)

(c) (d)

J.4 Curve fitting of trained SWT vibration- fatigue ANN model with two hidden layers for


(a) (b)

Continue…

284

Continued…

(c) (d)

J.5 Curve fitting of trained Morrow vibration- fatigue ANN model with three hidden layers for


(a) (b)

(c) (d)

J.6 Curve fitting of trained SWT vibration- fatigue ANN model with three hidden layers for


285

APPENDIX K

WEIGHTS AND BIASES FOR ANN

K.1 Weights of input layer for trained Coffin-Manson ANN

WIi,j WIi1 WIi2

WI1j -2.2843 0.6346

WI2j 4.0773 -1.1071

WI3j 0.0954 -2.1144

K.2 Weights of first hidden layer for trained Coffin-Manson ANN

W2i,j W2i1 W2i2 W2i3

W21j -0.4810 0.4841 0.5051

W22j 0.8562 1.1494 0.7742

W23j -0.4734 -0.5309 -0.6807

W24j 0.02823 -0.4950 0.3696

W25j -0.7406 0.8840 -0.4637

W26j 0.02554 -0.1258 -0.4063

W27j 1.0695 -0.7864 0.7782

K.3 Weights of second hidden layer for trained Coffin-Manson ANN

WOi,j WOi1 WOi2 WOi3 WOi4 WOi5 WOi6 WOi7

WO1j 0.0593 -1.1444 -0.1317

WO2j 1.4178 -1.3051 -0.5066 -1.0216 -0.9601 -0.5815 1.4264

K.4 Biases for trained Coffin-Manson ANN

Bi,j Bi1 Bi2

B1j -5.335 1.0025

B2j 0.2126 -1.1008

B3j -2.1111 -0.2645

B4j -0.6274

B5j -0.7800

B6j -0.4187

B7j 1.2197

K.5 Weights of input layer for trained Morrow ANN

WIij WIi1 WIi2

WI1j -1.6465 3.8170

WI2j -1.6633 -3.3086

WI3j -4.0989 -0.1864

WI4j -2.3028 4.1623

WI5j 2.2595 -3.3822

WI6j 1.942 1.9043

WI7j -0.9415 -4.3768

WI8j -2.2554 6.5517

WI9j 2.5697 -3.3467

286

K.6 Weights of first hidden layer for trained Morrow ANN

W1ij WIi1 W1i2 W1i3 W1i4 W1i5 W1i6 W1i7 W1i8 W1i9

W11j 0.9527 0.3362 0.5431 0.3380 0.0772 0.5009 0.6537 0.7318 0.2898

W12j 0.9181 0.3032 0.2514 0.5188 0.7691 0.8235 0.1485 0.5031 0.5786

W13j 0.6756 0.6931 0.4256 0.4646 0.7967 0.7466 0.8653 0.2610 0.4493

W14j 1.0211 1.0168 0.7203 0.2622 0.6877 0.7144 0.5856 0.5634 0.4557

W15j 0.5575 0.2048 0.4135 0.4912 0.6442 0.6290 0.4135 0.9610 0.0955

W16j 0.4864 0.7796 0.0204 0.7247 0.6901 0.5001 0.6143 0.2616 0.8713

W17j 0.9278 0.4753 0.9148 0.5578 0.4243 0.2143 0.0206 0.0110 0.2143

K.7 Weights of second hidden layer for trained Morrow ANN

W2ij W2i1 W2i2 W2i3 W2i4 W2i5 W2i6 W2i7 W2i8 W2i9

W21j 0.9332 0.3810 0.3960 0.9501 0.8211 0.3950 0.3167 0.0042 0.1904

W22j 0.4814 0.4829 0.7698 0.9784 0.1981 0.8531 0.6161 0.1351 0.9220

W23j 0.1289 0.6535 0.4215 0.5788 0.9862 0.5374 0.4559 0.2884 0.8550

W24j 0.4440 0.4556 0.1042 0.8450 0.6675 0.7242 0.5206

W25j 0.4704 0.5964 0.8376 0.6293 0.5061 0.3583 0.4967

W26j 0.9775 0.5690 0.0173 0.1312 0.1987 0.3375 0.0442

K.8 Weights of third hidden layer for trained Morrow ANN

W3ij W3i1 W3i2 W3i3 W3i4 W3i5 W3i6 W3i7 W3i8 W3i9

W31j 0.0939 0.6367 0.3584 0.2294 0.3612 0.6167 0.7527 0.4798 0.9156

W32j 0.9825 0.0487 1.2130 0.2337 0.0096 0.1908 1.0180

W33j 0.1490 0.1000 0.5146

K.9 Bias for trained Morrow ANN

Bij Bi1 Bi2

B1j 1.9779 1.4289

B2j 3.7479 -0.6773

B3j 1.5133 2.1153

B4j -1.6643 -0.2913

B5j 0.6234 0.2567

B6j 1.4991 0.1413

B7j -2.521 -0.9489

B8j 3.6138

B9j 4.2704

K.10 Weights of input layer for trained SWT ANN

WIij WIi1 WIi2

WI1j 2.6847 2.2466

WI2j -0.3294 -2.5249

WI3j -0.2808 0.9913

WI4j 1.1835 0.4237

287

K.11 Weights of first hidden layer for trained SWT ANN

W1ij W1i1 W1i2 W1i3 W1i4

W11j 0.6588 -0.2927 -0.7191 0.1382

W12j 0.6696 0.2984 0.753 -0.7009

W13j 0.8316 0.3809 -0.8153 0.0307

W14j 0.6308 -0.0236 0.3668 0.5656

W15j -0.127 -0.0644 0.7814 -0.7755

W16j -0.198 -0.2983 -0.2633 -0.8177

W17j 0.4486 0.2628 0.4799 0.3082

W18j 1.0334 0.9514 0.6678 -0.6896

W19j 0.1513 -0.2279 -0.1566 0.4566

W110j -0.817 -0.827 -0.0604 -0.2201

K.12 Weights of second hidden layer for trained SWT ANN: Part 1

W2ij W2i1 W2i2 W2i3 W2i4

W21j 0.0857 0.2385 0.6906 -0.7706

W22j 0.1564 -0.6227 0.3521 -0.3331

W23j 0.1215 -0.7911 0.5255 0.8570

W24j -0.4073 0.8366 -0.5305 -0.1828

W25j -0.4545 -0.8891 -0.841 0.1596

W26j -0.191 -0.5893 -0.5577 0.8493

W27j 0.2866 -0.7959 0.0447 0.6888

W28j -0.8247 -0.6177 0.2179 -0.5031

K.13 Weights of second hidden layer for trained SWT ANN: Part 2

W2ij W2i1 W2i2 W2i3 W2i4 W2i5 W2i6 W2i7

W21j 0.3651 -0.3194 0.2035 0.7496 -0.1942 0.2132 0.0255

W22j -0.2167 -0.0419 -0.1911 0.2413 0.2265 -0.9164 -0.0828

W23j 0.0575 -0.3303 0.8003 -0.3519 -0.2428 0.1589 0.0624

W24j -0.0277 -0.7334 0.4025 0.0536 0.0498 -0.8695 0.0366

W25j -0.5373 -0.1226 -0.1859 -0.5005 -0.3357 0.942 -0.0289

W26j 0.3062 -0.714 0.5921 -0.4777 0.9051 -0.8714 0.5242

W27j 0.529 -0.3133 -0.3739 0.237 0.425 -0.716 0.8697

W28j 0.8158 0.0935 0.1499 0.7025 -0.2701 0.0045 -0.8567

W2i8 W2i9 W2i10 W2i8 W2i9 W2i10

W21j -0.822 0.6717 0.2898 W28j -0.097 -0.7101 0.7193

W22j -1.0831 0.2174 -0.3881

W23j 0.0995 0.7386 -0.3866

W24j 0.7115 -0.0015 -0.2078

W25j 0.1601 -0.2957 -0.2848

W26j 0.534 -0.3738 0.8251

W27j 0.7373 -0.2374 -0.5994

K.14 Weights of third hidden layer for trained SWT ANN

Wij Wi1 Wi2 Wi3 Wi4 Wi5 Wi6 Wi7 Wi8

W1j -0.8055 0.5143 0.277 -0.6102

W2j 0.866 0.9021 -0.2945 0.8391 -0.4476 0.2799 -0.064 -0.4499

W3j -0.0019 -0.5066 -0.4311 0.5389 -0.5407 0.1726 -0.2061 0.8255

Wi9 Wi10

W2j -0.9228 -0.3769

288

K.15 Biases for trained SWT ANN

Bij Bi1 Bi2

B1j -2.9837 1.1637

B2j -1.1411 0.2212

B3j 0.1448 -0.2593

B4j 0.7207 0.9473

B5j -0.5979

B6j -0.7493

B7j -0.5716

B8j 0.3258

B9j -0.1556

B10j 0.4510

289

APPENDIX L

LIST OF PUBLICATIONS

1. Kong, Y.S., Abdullah, S., Omar, M.Z., Haris, S.M. 2016. Failure assessment of a

leaf spring eye design under various load cases. Engineering Failure Analysis 63:

146 – 159. (ISI Q2, Published)

2. Kong, Y.S., Abdullah, S., Omar, M.Z., Haris, S.M. 2016. Topological and

topographical optimization of automotive spring lower seat. Latin America Journal

of Solids and Structures 13(7): 1388 – 1405. (ISI Q2, Published)

3. Kong, Y.S., Abdullah, S., Omar, M.Z., Haris, S.M. 2016. Side force analysis of

suspension strut under various load cases. Jurnal Teknologi 78(6-10): 85 – 90.

(Scopus, Published)

4. Kong, Y.S., D. Schramm, Abdullah, S., Omar, M.Z., Haris, S.M. 2017. The

significance to establish a durability model for automotive ride. SAE Technical

Paper 2017-01-0347. (Scopus, Published)

5. Kong, Y.S., D. Schramm, Abdullah, S., Omar, M.Z., Haris, S.M., Bruckmann, T.

2017. Mission profiling of road data measurement for coil spring fatigue life.

Measurement 107: 99 – 110. (ISI Q2, Published)

6. Kong, Y.S., D. Schramm, Abdullah, S., Omar, M.Z., Haris, S.M. 2018. Vibration

fatigue analysis of carbon steel coil spring under various road excitations. Metals

8(8): 617 (ISI Q1, Published)

7. Kong, Y.S., D. Schramm, Abdullah, S., Omar, M.Z., Haris, S.M., Bruckmann, T.

2017. The need to generate a force time history towards life assessment of a coil

spring. Journal of Mechanical Engineering SI4 (5): 11 – 26. (Scopus, Published)

8. Kong, Y.S., D. Schramm, Abdullah, S., Omar, M.Z., Haris, S.M., Bruckmann, T.,

Kracht, F. 2018. Observing the durability effects of a Formula Student Electric Car

using acceleration and strain signals. Mobilität und digitale Transformation,

Springer Gabler. (Book Chapter, Published)

9. Kong, Y.S., D. Schramm, Abdullah, S., Omar, M.Z., Haris, S.M., Kracht, F. 2018.

Characterising spring durability for automotive ride using artificial neural network.

International Journal of Engineering and Technology 7: 47 - 53. (Scopus, Published)

10. Kong, Y.S., D. Schramm, Abdullah, S., Omar, M.Z., Haris, S.M. 2019.

Development of multi linear regression-based models for fatigue life evaluation of

automotive coil spring. Mechanical Systems and Signal Processing 118: 675 - 695

(ISI Q1, Published)

11. Kong, Y.S., D. Schramm, Abdullah, S., Omar, M.Z., Haris, S.M. 2018. Generation

of artificial road profile for spring durability analysis. Jurnal Kejuruteraan 30(2).

(ECSI, Published)

290

12. Kong, Y.S., D. Schramm, Abdullah, S., Omar, M.Z., Haris, S.M. 2018.

Optimisation of spring fatigue life prediction model for vehicle ride using hybrid

multi-layer perceptron artificial neural networks. Mechanical Systems and Signal

Processing 122: 597- 621 (ISI Q1, Published)

13. Kong, Y.S., D. Schramm, Abdullah, S., Omar, M.Z., Haris, S.M. 2018. Ride and

durability characterisation under road excitation in frequency domain.

Measurement. (ISI Q2, Minor corrections)

14. Kong, Y.S., D. Schramm, Abdullah, S., Omar, M.Z., Haris, S.M. 2018. Correlation

of uniaxial and multiaxial fatigue models for spring fatigue life assessment.

Experimental Techniques (ISI Q3, Major corrections)

15. Kong, Y.S., D. Schramm, Abdullah, S., Omar, M.Z., Haris, S.M. 2018. Design of

artificial neural network using particle swarm optimisation for spring durability.

Journal of Mechanical Science and Technology (ISI Q3, Under Review)

16. Kong, Y.S., D. Schramm, Abdullah, S., Omar, M.Z., Haris, S.M. 2018. Validation

of established predictive models for automotive ride and spring durability. Journal

of Mechanical Science and Technology (ISI Q3, Under Review)

17. Kong, Y.S., D. Schramm, Abdullah, S., Omar, M.Z., Haris, S.M. 2018. Evaluation

of regression-tree based durability models for spring fatigue life assessment.

ICMFM XI Porto (Scopus, Under Review)

18. Kong, Y.S., D. Schramm, Abdullah, S., Omar, M.Z., Haris, S.M. 2018. Determining

optimal suspension system parameters for spring fatigue life using design of

experiment. Mechanics and Industry (ISI Q4, Under Review)

19. Kong, Y.S., D. Schramm, Abdullah, S., Omar, M.Z., Haris, S.M. 2018. Evaluation

of automobile spring energy-based model for strrain signals generation. Metals (ISI

Q2, Submission)

20. Kong, Y.S., D. Schramm, Abdullah, S., Omar, M.Z., Haris, S.M. 2018. A

comparison of multiple linear regression and artificial neural network for

automobile vertical vibration predictions. Mechanical Systems and Signal

Processing (ISI Q1, Submission)

21. Kong, Y.S., Abdullah, S., Omar, M.Z., Haris, S.M. 2018. Kebolehtahanan terpecut

bagi komponen sistem ampaian dengan pelbagai ujaan jalan. (Book Chapter,

Submission)

22. Kong, Y.S., Abdullah, S., Omar, M.Z., Haris, S.M. 2018. Kaedah ujian jahitan bagi

kebolehtahanan komponen sistem ampaian kenderaan. (Book Chapter, Submission)

23. Kong, Y.S., D. Schramm, Abdullah, S., Omar, M.Z., Haris, S.M. 2018. K-Nearest

Neighbors Classification of Spring Strain Signal according to ISO 8608 using

Hilbert Huang Transform. Mechanical Systems and Signal Processing (ISI Q1,

Submission)

291

24. Kong, Y.S., Abdullah, S., Omar, M.Z., Haris, S.M. 2018. Prediction of automobile

spring fatigue life using support vector machine approach. (Scopus, Submission)

Diese Dissertation wird über DuEPublico, dem Dokumenten- und Publikationsserver derUniversität Duisburg-Essen, zur Verfügung gestellt und liegt auch als Print-Version vor.

DOI:URN:

10.17185/duepublico/70111urn:nbn:de:hbz:464-20190523-091034-1

Dieses Werk kann unter einer Creative Commons Namensnennung -Nicht kommerziell - Keine Bearbeitungen 4.0 Lizenz (CC BY-NC-ND 4.0) genutzt werden.

https://duepublico2.uni-due.de/

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establishment of artificial neural network for suspension spring

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