Thermography pattern analysis and separationBin Gao, Libing Bai, W. L. Woo, and Guiyun Tian

Citation: Applied Physics Letters 104, 251902 (2014); doi: 10.1063/1.4884644 View online: http://dx.doi.org/10.1063/1.4884644 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/104/25?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Eddy current step heating thermography for quantitatively evaluation Appl. Phys. Lett. 103, 194101 (2013); 10.1063/1.4828889 Defect characterization by inductive heated thermography AIP Conf. Proc. 1430, 483 (2012); 10.1063/1.4716266 An Experimental Study of Defect Determination using Pulsed Thermal NonDestructive Testing AIP Conf. Proc. 1017, 215 (2008); 10.1063/1.2940630 TONE BURST EDDYCURRENT THERMOGRAPHY (TBET) AIP Conf. Proc. 975, 544 (2008); 10.1063/1.2902708 Integrated active transient thermography for rapid nondestructive analysis of sputtering target bond integrity J. Vac. Sci. Technol. A 24, 1100 (2006); 10.1116/1.2210950

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Thermography pattern analysis and separation

Bin Gao,1,a) Libing Bai,1 W. L. Woo,2 and Guiyun Tian2,1

1School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu, China2School of Electrical and Electronic Engineering, Newcastle University, England, United Kingdom

(Received 11 May 2014; accepted 10 June 2014; published online 23 June 2014)

Analysis of thermography spatial-transient patterns has considerable potential to enable automatic

identification and quantification of defects in non-destructive testing and evaluation. This Letter

proposes a non-negative pattern separation model for eddy current pulsed thermography to

automatically extract important spatial and time patterns according to the transient thermal

sequences without any pre-training or prior knowledge. In particular, the method is scale-invariant,

such that large differences in surface emissivity, hot spots, and cool areas with dynamic range of

thermal contrast can be extracted. Finally, an artificial slot in a steel sample with shining, black

strip on the surface is tested to validate the proposed method. VC 2014 AIP Publishing LLC.

[http://dx.doi.org/10.1063/1.4884644]

Infrared thermography methods have reached a prominent

status as a non-destructive testing and evaluation (NDT&E)

method due to both ease and speed of inspection.1–4 The ther-

mography based defect detection methods still pose two chal-

lenges. First, the variation of surface emissivity introduces

spurious temperature inhomogeneity and can result in false

alarm of defect detection. Second, the need to cope with the

growing demands for advanced methods that enable automatic

identification of defects. To deal with above issues, Shepard5

proposed thermographic signal reconstruction (TSR) based on

flash thermography to reduce the influence of the thermal

emissivity. Maldague and Marinetti6 inhibited the influence of

thermal emissivity variation by using the pulse phase infrared

thermography method. Chatterjee and Tuli7 removed the influ-

ence of non-uniform heating and surface emissivity variation

using a Fourier transformation based image reconstruction

algorithm. In addition, algorithms based on Principal

Component Analysis (PCA) and Independent Component

Analysis (ICA)8,9 have been used to automatically detect

flaws. All the aforementioned methods, however, cannot effi-

ciently perform automatic defect identification and simultane-

ously overcome the problem of large dynamic differences in

emissivity. The obtained results are acceptable but generally

not predictable.

Eddy current pulsed thermography (ECPT)10 is an

emerging infrared thermography method for conductive ma-

terial. It has recently gaining popularity with an increasing

span of applications. Compared with other thermography

methods,11 the heat of ECPT is not limited to the sample sur-

face; rather it can penetrate a certain depth, which is gov-

erned by the skin depth of eddy current. Furthermore, ECPT

concentrates the heat on the defect due to eddy current dis-

tortion, which increases the temperature contrast between

the defective region and defect-free areas. In our previous

work,12,13 we have proposed a PCA/ICA source separation

algorithm on ECPT for automatic crack detection and identi-

fication. However, the method did not consider the interfer-

ence from surface emissivity. In addition, the previous

model cannot efficiently separate the thermal patterns which

have a large dynamic range of thermal contrast. In this paper,

we proposed a new separation method based on the smooth

Itakura-Saito non-negative matrix factorization (s-ISNMF)14

to analyze the thermal patterns of ECPT and automatically

identify the thermal pattern that relates to a defect region.

The method has the unique property of scale-invariance,15,16

whereby a lower thermal contrast pattern can be treated with

equal importance as a higher one. Experimental studies have

been conducted to show the efficiency of pattern extraction.

Fig. 1 shows the diagram of ECPT. The excitation signal

generated by the excitation module is a short period of high

frequency current. It is driven to the coil on the conductive

material. The current in the coil will subsequently induce

eddy currents and generate the resistive heat in the conduc-

tive material. The heat will diffuse in time until it reaches an

equilibrium state in the material. If a defect (e.g., crack) is

present in the conductive material, eddy current distribution

or the heat diffusion process will vary. Consequently, the

spatial distribution of temperature on the surface of the mate-

rial, and the temperature transient response will show the

variation, which is captured by an infrared camera.

Specifically, when the eddy current encounters a discontinu-

ity, e.g., a slot or notch, they are forced to divert, leading to

areas of increased and decreased eddy current density.17

Therefore, in the heating phase, different areas have different

heat generation rates. Hot spots are observed around the slot

tips while the cool areas are located at both sides of the slot.

In the cooling phase, the heat diffuses from the high

FIG. 1. ECPT diagram.

a)Author to whom correspondence should be addressed. Electronic mail:

bin_gao@uestc.edu.cn

0003-6951/2014/104(25)/251902/5/$30.00 VC 2014 AIP Publishing LLC104, 251902-1

APPLIED PHYSICS LETTERS 104, 251902 (2014)

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temperature area to the low temperature area, and reduces

the thermal contrast. In addition, there are areas which inevi-

tably suffer from the interference of emissivity.

The infrared camera records both the spatial and tran-

sient response of temperature variation on the specimen and

can be represented as a spatial-transient tensor �Y with the

dimensions Nx � Ny|fflfflfflffl{zfflfflfflffl}Spatial

� NTransient

. A typical temperature tran-

sient response for a point on the surface of material is shown

in Fig. 1. It can be divided into two phases: heating phase

and cooling phase.

The analysis of ECPT thermal patterns (hot spots, cool

area, emissivity, and so on) is very useful for automatic

defect detection and identification. As can be seen in Fig. 1,

the hot spot pattern directly reveals the location of slot and

can be used to quantify the size of the defect. However, dur-

ing the recording by the infrared camera, the different ther-

mal patterns at different rates are mixed together. There are

different thermal patterns which have resulted in different

spatial thermal distribution. On the other hand, there are dif-

ferent heating and cooling rates of the transient characteris-

tics. This is illustrated in Fig. 5. Therefore, the recorded

thermal sequences from the thermal camera can be modelled

as a composition of different thermal patterns. Thus, the

issue of how to automatically separate different thermal pat-

terns from the IR images poses a crucial challenge. The char-

acteristics of different thermal patterns are described as

follows: In terms of emissivity, according to Stefan-

Boltzmann law, the energy emitted by a black body per sec-

ond per unit of area is proportional to the fourth power of its

absolute temperature. This can be described as

j� ¼ rsbT4; (1)

where rsb¼ 5.67� 10� 8 W/(m2 � k4) is the Stefan-

Boltzmann constant and T is the absolute temperature. When

the temperature of the material changes slightly, the radia-

tion power will cause a large change. The radiance of the

actual object depends on the properties of the material and

the surface preparation besides the temperature. This differ-

ence can be described by the emissivity 0 � e � 1 which

denotes the ratio of radiation of actual object with respect to

the black body. Thus, the Stefan-Boltzmann law which is

applied to the actual object can be described as

j� ¼ ersbT4: (2)

In ECPT testing, the samples under test possibly have oil,

oxide, and other stains on the surface. Oil and oxide can

drastically increase the thermal radiation and results in

unwanted spurious high temperature in the infrared images.

In terms of the hot and cool areas, when the eddy current

encounters a discontinuity, e.g., a slot or notch, it is forced to

divert, leading to areas of increased and decreased eddy cur-

rent density and the resultant hot and cool areas due to Joule

heating. Therefore, the hot spots are observed around the slot

tips which can be used to locate as well as sizing the defect,

while the cool areas are located at both sides of the slot.

Once the test sample with mixture of areas with strong

emissivity gradient to another (e.g., black stains on the sur-

face) and defect (e.g., slot which consists of cool and hot

spots areas), the task of separating different thermal patterns

becomes a difficult challenge. Generally, the temperature of

hot spots is three times higher than the cool area. However,

the temperature of a black stain region can be as high as ten

times higher than at the cool area due to the high emissivity.

In this case, the hot spots around the slot tip cannot be

observed, and this directly reduces the probability of detect-

ing the defects.

It is very promising to be able to separate thermal pat-

terns because of the potential to automatically identify the

defects and remove unwanted interference. To achieve this,

we consider the following mixing model:

YðtÞ ¼XNs

i¼1

miXiðtÞ: (3)

Mathematically, the thermography image at t transient time

captured by the infrared camera is considered as a mixing

observation signal image YðtÞ. The term mi is the mixing pa-

rameter which describes the contribution of the ith position

(thermal pattern) to the induced recorded thermography

image and Ns denotes the number of thermal patterns. The

visual representation of Eq. (3) is shown in Fig. 2.

Based on the mixing model of Eq. (1), it is expecting to

separate the thermal patterns XiðtÞ. There are many forms of

matrix factorization that can separate patterns, and to name a

few, these are PCA, ICA,18 and Non-negative Matrix

Factorization (NMF).19 Comparing with PCA and ICA,

NMF gives an unique decomposition under certain condi-

tions making it unnecessary to impose the constraints in the

form of orthogonality and statistical independence. In this

paper, as all elements in thermal video have non-negative

values, the s-ISNMF will be developed for separating the

thermal patterns. The method has two prominent characteris-

tics which benefit the separation. First, it is scale-invariant in

the sense that thermal distribution that is characterized by

large dynamic range (high and low temperature) can be

extracted more efficiently. Second, it imposes a smoothness

constraint on the solution to enhance the spatial resolution of

thermal patterns. The matrix form of tensor representation of

FIG. 2. Mathematical representation of

mixing model of thermal patterns.

251902-2 Gao et al. Appl. Phys. Lett. 104, 251902 (2014)

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�Y can be expressed as Y0 ¼ ½vecðYðtÞÞ; vecðYðtþ 1ÞÞ;…;vecðYðtþ N � 1ÞÞ�T, where “T” denotes the transpose oper-

ator and “vec” denotes the vectorization operator. The

specific steps of transformation procedure can be found in

Ref. 14. Thus, the NMF factorizes this matrix into a product

of two non-negative matrices as

Y0 ¼MX0 ; (4)

where M ¼ ½m1;…;mNs� represents the mixing matrix

and mi ¼ ½mi;1;…;mi;N�1�T is the ith mixing vector.

X0 ¼ ½x1; x2;…; xNs�T; where xi ¼ vecðXiÞ denotes the pat-

tern basis matrix and xi ¼ ½xi;1;…; xi;L�T and L ¼ Nx

�Ny � 1. The b-divergence was introduced in Ref. 14 which

is defined as

dbðajbÞ¼

1

bðb�1Þ abþðb�1Þbb�babb�1� �

b2< 0;1f g

a loga� logbð Þþ b�að Þ b¼ 1

a

b� log

a

b�1 b¼ 0

:

8>>>>>><>>>>>>:

(5)

The term b is defined as the divergence choice which has

been used for optimization of NMF. It is interesting to note

that for b ¼ 2, we obtain the Euclidean distance expressed

by Frobenius norm and, for b ¼ 1, the generalized Kullback-

Leibler (KL) divergence is defined. For b ¼ 0, this results in

the Itakura-Saito (IS) divergence.15 As noted by F�evotte,14 a

noteworthy property of the b-divergence is its behaviour

with respect to the scale, as the following equation holds for

any value of b:

dbðcajcbÞ ¼ cbdbðajbÞ: (6)

It implies that factorizations obtained with b > 0 (such as

with the Euclidean distance or the Kullback–Leibler diver-

gence) will rely more heavily on the predominant large value

data (i.e., these are the high power components). By the

same token, less precision is expected in the estimation of

the low-power components, i.e., dLSðcajcbÞ ¼ c2dLSðajbÞ and

dKLðcajcbÞ ¼ cdKLðajbÞ. For the case of b ¼ 0, this results

in the IS divergence which is scale-invariant, i.e., dISðcajcbÞ¼ dISðajbÞ and is the only one in the family of b-divergences

to possess this property. The IS divergence was mainly used

as a measure of the goodness of fit between two spectra.

Recently, IS divergence has received renewed interest in the

NMF. The IS divergence leads to desirable statistical inter-

pretations of the NMF problem. Most significantly, NMF

with IS divergence can provide scale invariant property

which enables low energy components of Y0 to bear the

same relative importance as high energy ones. This is rele-

vant to situations in which the coefficients of Y0 have a large

dynamic range such as thermal patterns which simultane-

ously consist of both extreme high and low temperature

region. The un-penalized IS divergence NMF algorithm is

based on surrogate auxiliary functions (local majorizations

of the cost function). The majorization-minimization (MM)

algorithm can be derived by optimizing these auxiliary func-

tions, which result in efficient multiplicative updates. The

monotonicity of the cost function can be proven by leverag-

ing on techniques in Ref. 14. The smoothness constraint is

encoded in the form of Markov chains, namely,

pðX0 Þ ¼YNs

i¼1

YL

l¼2

pðx0i;ljx0i;ðl�1ÞÞpðx0i;1Þ; (7)

where the Markov kernel pðx0i;ljx0i;ðl�1ÞÞ is a probability den-

sity function (pdf) defined on the non-negative orthant, with

mode at x0i;ðl�1Þ. The specific steps for S-ISNMF can be

found in Ref. 14, and Table I summarizes the thermal pattern

separation method.

The experimental set-up is shown in Fig. 3. An Easyheat

224 from Cheltenham Induction Heating is used for coil ex-

citation. The Easyheat has a maximum excitation power of

2.4 kW, a maximum current of 400 Arms and an excitation

frequency range of 150–400 kHz (200 Arms and 256 kHz are

used in this study). The system has a quoted rise time (from

the start of the heating period to full power) of 5 ms, which

was verified experimentally. Water cooling of coil is imple-

mented to counteract direct heating of the coil. The IR cam-

era, SC7500 is a Stirling cooled camera with a 320� 256

array of 1.5–5 lm InSb detectors. This camera has a sensitiv-

ity of <20 mK and a maximum full frame rate of 383 Hz,

with the option to increase frame rate with windowing of the

image.20 A rectangular coil is constructed to apply direc-

tional excitation. This coil is made of inner diameter

6.35 mm high conductivity hollow copper tube. In the

experiment, only one edge of the rectangular coil is used to

stimulate eddy current to the underneath sample. In this

study, the frame rate is 383 Hz, and 2 s videos are recorded

in the experiments.

A steel sample (0.24 mm� 45 mm� 100 mm) with a

slot of 10 mm length, 2 mm width is prepared (Fig. 3(b)).

There are equally spaced shinning and black stripes on the

sample surface. The shinning strips are the polished area,

while the black strips are the area sprayed black painting. A

100 ms heating duration is selected for inspection, which is

long enough to elicit an observable heat pattern. The cooling

TABLE I. Thermal pattern separation.

Input: matrix representation of ECPT thermal video Y0

Output: thermal pattern basis X0 and mixing matrix M

Procedure:

Initial X0 and M non-negative values

Compute V_

¼MX0

for k¼ 1: maximum iteration number

Z ¼ X0TðY0Y0 :�2Þ; Q ¼ X0TY0�1

Update m1(solving Ns order 2 polynomials

for s¼ 2:S� 1

mðkÞs ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffimðk�1Þsð Þ2zsþkm

ðkÞs�1

qsþk=mðk�1Þsþ1

sEnd

Update mS(solving Ns order 2 polynomials

Compute V_

¼MX0

X0 ¼ X0½ðV_�2

Y0ÞMT�=½V_�1

MT�Compute V

_

¼MX0

Normalize X0 and M

End

251902-3 Gao et al. Appl. Phys. Lett. 104, 251902 (2014)

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time is 1.9 s, which is long enough to ensure the sample

reaching a new thermal equilibrium state. The excitation coil

is placed at the back of the sample.

During the ECPT testing—when eddy current encoun-

ters a discontinuity, e.g., a slot or notch—it is forced to

divert, leading to areas of increased and decreased eddy cur-

rent density and resulting in hot and cool areas due to Joule

heating. Fig. 4(a) shows the temperature distribution at the

end of heating (0.1 s). Due to the high emissivity of the black

area, there is no obvious high temperature region around the

slot tips. The high temperature can only be observed at the

black area above the coil. In addition, Fig. 4(b) shows

the temperature distribution at the cooling phase (1.6 s). The

high temperature still can only be observed at the black strip

area because of both high emissivity and heat diffusion. The

transient temperature behavior at different positions is shown

in Fig. 5. Pos 1 is at the crack side with black strip (high

emissivity), Pos 2 is at the black strip where the area is far

away from the excitation, Pos 3 is at the crack tip with the

shinning strip, and Pos 4 is at the crack side with shinning

strip above the coil.

As can be seen in Fig. 5, different position behaves with

different temperature transient characteristics. However, Pos

1, as well as other similar black strip area (above the coil),

exhibits extreme high temperature transient in both heating

and cooling phase in which other thermal patterns have been

over-shadowed, and therefore, they cannot be distinguished.

This issue is difficult to tackle in defect detection using the

ECPT method where the hot spot around defect tips cannot

be taken as an indicator of defects especially for small

cracks. Notwithstanding this, it will lead to error when both

black stain and cracks are present on the surface of the test

sample. In order to solve this issue, the proposed thermal pat-

tern separation method is conducted. Fig. 6 shows the sepa-

ration results.

Fig. 6 shows the results by setting the number Ns of ther-

mal patterns equal to three. Figs. 6(a–c), 6(d–f), and 6(g–h)

are the separation results by using non-negative matrix sepa-

ration, PCA, and ICA, respectively. The separation results

highlight three complementary thermal patterns: (a), (d), and

(g) highlights the cool area with black strip (emissivity). The

transient characteristic of this area is as similar as position

one (Pos 1) which can be seen in Figure 5. Specifically, all

three separation methods exhibit their ability to obtain this

pattern of cool area, and the NMF perform the best, whereas

the separated pattern by using PCA does not tightly resemble

the cool area, and the ICA pattern somehow mixes the hot

spots around the tips. (b), (e), and (h) highlight the hot spots

where the transient characteristic of this thermal pattern is as

similar as position three in Figure 5. In comparison, the

NMF fully recovered both sides of the hot spots around the

defect tips. However, both PCA and ICA only clearly

emphasize the right side of a hot spot but neglect the left

one. The reason of this is that the proposed NMF method has

the unique property of scale-invariance where low energy

components can be precisely estimated, and they bear the

same relative importance as the high energy ones. While

PCA and ICA emphasize decorrelation and statistical inde-

pendence in pattern separation, respectively, they cannot

guarantee the accuracy of low energy separated patterns. The

identification of hot spots can be directly used to locate and

size the slot defect. The width and length of the slot can be

measured by counting the pixels of the width and the length

of the hot spots, respectively. The depth of the slot cannot be

directly measured by the hot spots pattern because the cap-

ture infrared image is a two dimensional image. In order to

measure the depth of the slot, we can process the proposed

method to test different standard depth slot samples, such as

2 mm, 4 mm, 6 mm, 8 mm depth slot samples, to measure

their value of hot spots and generate the relationship between

standard depth with the relative value of hot spots to measure

FIG. 3. (a) Experiment platform and (b) test sample.

FIG. 4. (a) Original infrared image at 0.1 s (the end of heating phase) and

(b) original infrared image at 1.6 s (the cooling phase).

FIG. 5. Original transient responses of different positions.

251902-4 Gao et al. Appl. Phys. Lett. 104, 251902 (2014)

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the depth. Figures 6(c), 6(f), and 6(i) highlight the the area

with black strip (emissivity) besides excitation coil where

the transient characteristic of this thermal pattern is as simi-

lar as position two in Figure 5. In comparison, both NMF

and PCA fully recovered the thermal patterns with high

emissivity (excitation coil are not included). However, ICA

does not completely separate this pattern and still mixes the

patterns of both black strip and shinny part.

In this Letter, thermal pattern analysis using ECPT has

been discussed. Both physics and mathematical interpreta-

tions have been developed. The NMF-based pattern separa-

tion algorithm has been proposed. It holds two desirable

properties of scale invariant and smoothness constraint.

Conclusions can be drawn as follows: (i) The separated ther-

mal patterns have the potential to directly identify the defects

and remove the interface such as emissivity. (ii) The pro-

posed method has been verified by using a steel sample with

a slot and mixed with equally spaced shinning and black

stripes on the sample surface. (iii) Future study will be con-

ducted to test the proposed model in natural defect specimen

with stain or oil on the surface, and the comparison with dif-

ferent separation methods will be analyzed.

The work was supported by National Natural Science

Foundation of China (Grant No. 51377015), FP7 HEMOW

IRSES project 269202, China Post Doctoral Program (No.

136413) and the Science & Technology Department of

Sichuan Province, China (Grant No. 2013HH0059).

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FIG. 6. Separated thermal patterns

using NMF (a)–(c), PCA (d)–(f), and

ICA (g)–(i).

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