IEEE SENSORS JOURNAL, VOL. 14, NO. 5, MAY 2014

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Impact Damage Detection and Identification Using Eddy Current Pulsed Thermography Through Integration of PCA and ICA Liang Cheng, Student Member, IEEE, Bin Gao, Member, IEEE, Gui Yun Tian, Senior Member, IEEE, Wai Lok Woo, Senior Member, IEEE, and Gerard Berthiau

Abstract— Eddy current pulsed thermography (ECPT) is implemented for detection and separation of impact damage and resulting damages in carbon fiber reinforced plastic (CFRP) samples. Complexity and nonhomogeneity of fiber texture as well as multiple defects limit detection identification and characterization from transient images of the ECPT. In this paper, an integration of principal component analysis (PCA) and independent component analysis (ICA) on transient thermal videos has been proposed. This method enables spatial and temporal patterns to be extracted according to the transient response behavior without any training knowledge. In the first step, using the PCA, the data is transformed to orthogonal principal component subspace and the dimension is reduced. Multichannel morphological component analysis, as an ICA method, is then implemented to deal with the sparse and independence property for detecting and separating the influences of different layers, defects, and their combination information in the CFRP. Because different transient behaviors exist, multiple types of defects can be identified and separated by calculating the cross-correlation of the estimated mixing vectors between impact the ECPT sequences and nondefect ECPT sequences. Manuscript received May 6, 2013; revised November 25, 2013; accepted January 5, 2014. Date of publication January 17, 2014; date of current version March 24, 2014. This work was supported in part by the National Natural Science Foundation of China under Grant 51377015, in part by the Sichuan Science and Technology Department under Grant 2013HH0059, in part by the University of Electronic Science and Technology of China, in part by the National Research Center of Sensors Engineering, in part by Shenyang Academy of Instrumentation Company Ltd., in part by Health Monitoring of Offshore Wind Farms, in part by Cognitive-Networks-Enabled Transnational Proactive Healthcare, in part by the Engineering and Physical Sciences Research Council (EPSRC), U.K., under Grant EP/F06151X/1, and in part by FP7 Health Monitoring of Offshore Wind Farms (HEMOW, FP7-PEOPLE2010-IRSES-269202). L. Cheng and B. Gao contributed equally to this work. The associate editor coordinating the review of this paper and approving it for publication was Dr. Lorenzo Lo Monte. (Corresponding author: B. Gao.) L. Cheng and G. Y. Tian are with the School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 610051, China, and also with the School of Electrical and Electronic Engineering, Newcastle University, Newcastle upon Tyne NE1 7RU, U.K. (e-mail: [email protected]; [email protected]). B. Gao is with the School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 610051, China (e-mail: [email protected]). W. L. Woo is with the School of Electrical and Electronic Engineering, Newcastle University, Newcastle upon Tyne NE1 7RU, U.K. (e-mail: [email protected]). G. Berthiau is with the Institute of Research in Electrical Engineering of Nantes-Atlantique, University of Nantes, Nantes 44300, France (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JSEN.2014.2301168

Index Terms— Eddy current pulsed thermography, non-destructive evaluation, principal component analysis, independent component analysis, impact damage, spatialtemporal pattern separation.

I. I NTRODUCTION

E

DDY current pulsed thermography (ECPT), combining EC and thermography, involves the application of a high current electromagnetic pulse to the conductive material under inspection for a short period. Eddy currents will be induced in the material, leading to the heating of the material itself. The existence of any defects distorts the propagation of the eddy current leading to a variation in material temperature that can be emphasised with thermography. After the period of eddy current heating, the non-homogeneity of carbon fibre reinforced plastic (CFRP) in the cooling phase also affect the diffusion of heat. Therefore, the mixed phenomena of induction heating dominating in the heating phase and the diffusion of this dominating in the cooling phase and their specific behaviours are useful for the quantitative nondestructive evaluation of non-homogeneity of a given material. Different from other thermography techniques such as flash and laser thermography, ECPT focuses the heat generation at the defects, at not only the surface but also subsurface. In this paper, impact damage, one of the most common defects in CFRP, is under investigation using ECPT. ECPT has been used to inspect metallic parts [1]–[4]. Abidin et al. [1] evaluated the angular slots in metal through simulation and experiment. Features, e.g. maximum temperature amplitude, slope inclination etc., were extracted to quantify the angle of the slot. Oswald-Tranta et al. [3] investigated the temperature distribution around a crack with different penetration depths using FEM modelling and compared with experimental measurements on metallic materials. The results showed that lower temperatures are exhibited at the surface edge of a crack and higher temperatures at the bottom in nonmagnetic materials with a large penetration depth. Compare to defects in metal, those in composite materials were rarely investigated. Ramdane et al. [5] detected inserted delaminations using induction-heating thermography. The experimental studies were undertaken in transmission mode (the inductor and infrared camera are on the different sides of the sample), which is normally not applicable in the

1530-437X © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

1656

in-situ inspection. Moreover, the inspection period is around 80 seconds. He et al. [6] combined transmission and reflection mode for wall thinning defect and inner defect based on heat diffusion. Through 1D analytical model, 3D numerical model and experimental results, suitable detection mode for those defects was identified, and the location in thickness of the defects was quantified. All the above works are limited by the manual selection of proper contrast frames or investigated area. In addition, the transient response features suffer from noise. To enhance the flaw contrast and improve noise rejection qualities, pattern based image enhancement has been conducted by introducing the raw data upon a set of orthogonal basis functions. Fourier transform was applied to pulsed thermography, and enhanced the flaw-contrast significantly using phase map [14]. Influence of non-uniform heating and surface emissivity variation was removed by using a Fourier transformation based image reconstruction algorithm [15]. Instead of a prescribed set of basis functions, Principal Component Analysis (PCA) and Independent Component Analysis (ICA) are used to enhance the contract of defective region and sound area (non-defect region) in thermal image sequence. Marinetti et al. [9] compared the efficiency of PCA to thermography features extraction by considering the initial sequence as either a set of images or a set of temporal profiles. Khan et al. [10] identified water leakage in dikes from thermometric data using PCA and ICA. Rajic [11] employed PCA to improve the flaw detection ability of thermography, and characterised the surface flaw depth using characteristic time estimated from Principle Component (PC) vector. Sophian et al [12] and Yang et al. [13] implemented PCA and ICA for defect classification based on PEC signals. The statistical kurtosis was used as standard to select Independent Components (ICs) for feature extraction. In addition, the liftoff effect on defects was classified. Bai et al. [14] proposed ICA to highlight the anomalous patterns of ECPT video for crack in metallic specimen. Estimated mixing vector using ICA in heating and cooling phase around crack tips were used for automatic identification of cracks. However, most above mentioned works only employ the analysis separately as a signal processing tool. The mathematical reasons why these algorithms can enhance an image and how these techniques are connected to physical models are not provided in detail. In addition, the separation of multiple defects as well as fibre texture is limited, especially for nonhomogeneous composite samples. Moreover, an especially important case is not discussed when the defect region is highly sparse, meaning that it is rarely active within the whole surround background. In this paper, an integrative method is developed to extract anomalous and sparse patterns from transient thermal videos. This method can automatically highlight and separate the defects in the spatial components and the temporal components. The rest of this paper will be organised as follows: Section II introduces the PCA and ICA algorithms used for transient thermal videos. The experimental system and sample are illustrated in Section III. The results and comparison using

IEEE SENSORS JOURNAL, VOL. 14, NO. 5, MAY 2014

Fig. 1.

Impacted sample.

PCA and ICA are reported in Section IV. The conclusion and future work are represented in Section V. II. T HEORETIC C ONCERNS The composite sample with impact damage point is shown in Fig. 1. From the figure, it can be seen that the area of defect in the sample is much less than those of the surrounding, which indicates the sparse property of inspected sample. Here, ‘sparseness’ refers to a representational scheme where only a few units (out of a large population) are effectively used to represent typical data vectors [15]. The indecency of material property at defects refers to the decrease of electric conductivity and increase of thermal conductivity at impact damage [16]. This directly results in the transient temperature response at impact damage region, independent to those in sound area. The impact can also generate delamination at the backside of the sample when the impact energy is large enough. Delamination causes the discontinuity of both electric and thermal conductivity in thickness direction, where the transient temperature response is also independent to those in sound area. Fig. 2 illustrates the procedure of defect identification and separation by using ECPT video sequences. Firstly, the data is transformed to orthogonal PC subspace and the dimension is reduced by using PCA. Multichannel Morphological Component Analysis (MMCA) is then implemented to deal with the sparse and independence property for detecting impact damage and delamination in CFRP. By using MMCA, the different characteristics of transient responses related to the impact damage, delamination, and area without defects can be separated. Subsequently, the cross-correlation of the estimated mixing vectors derived from MMCA for both thermal transient video with defect and the one without defect are calculated. The maximum/minimum correlation value of correlation value can be used to identify the influence of the impact damage, delamination and non-defect factors. Fig. 2 shows the flow diagram for the proposed method. In the figure, the defect and non-defect thermal videos are recorded by using the same material sample (at the defective area and non-defective area, respectively). The record area and relevant coil position in detail will be presented in Section III. In following subsections, the individual algorithms for PCA and MMCA are introduced and investigated. A. PCA Algorithm PCA is a multivariate analysis technique, transforming the original measured data into new uncorrelated variables, as

CHENG et al.: IMPACT DAMAGE DETECTION AND IDENTIFICATION USING ECPT

Fig. 2.

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Procedure for defect identification and separation.

termed Principal Components (PC). The original measured data are treated as independent variables. Each PC is a linear combination of the original variables. These PCs form the basis of the respective vector space and they are arranged in order of decreasing variance. Thus, the first PC carries the most of information regarding the original data and so on. Use of PCA methods in PEC testing can be found in previous work [12] and [17], and in this paper will be used for defect highlighting and classification of ECPT images. To conduct PCA on the N input signals, eigenvalue decomposition of the covariance of the input 2D matrix I M is used. After decomposition, I M can be transformed into uncorrelated sources. The covariance of I M can be expressed as E{I M ITM } = EDET , where E is the orthogonal matrix of eigenvectors and D = di ag(λ1 , . . . , λ N ). λ1 ≥ . . . ≥ λ N are the decent eigenvalues. Thus, the covariance of I M is N × F matrix where F is the product of row and column of image (e.g. 320 × 256 = 81920) where this can be rewritten as: E{I M ITM } = EDET = ED1/2 D1/2 ET T

−1 = E{W−1 PC A X PC A W PC A W PC A } T

−1 = W−1 PC A E{X PC A W PC A }W PC A T

−1 = W−1 PC A W PC A . T

T

(1)

In Equation (1), E{.} is expectation operation, T E{X PC A WPC A } = I where I is identity matrix. Therefore, W PC A = (ED1/2 )−1 = D1/2 ET and whitening can be written as: X PC A = W PC A I M

(2)

where W PC A is the estimated de-correlation matrix and X PC A is the uncorrelated sources by using PCA. The mixing matrix M PC A = W−1 PC A = [m1 , m2 , . . . , m N ] and mn are the mixing vectors of PCA. By using PCA, N orthogonal signals can be derived to from the ECPT video. For the thermal sequence, the aim of using PCA is to maximise the contrast between defective region and sound region. In addition, the dimension of data is reduced to P, rather than N = 383. Here the selection of P number of PC can be implemented by using threshold based approach which can be found in [14] and this procedure is summarized in Fig. 3. Because PCA cannot guarantee the statistical independence of above regions, whereas the PCA is not an ideal tool for separating the different types of defect

Fig. 3.

PCA procedure on the thermal videos.

as well as non-defect regions in one go. Therefore, ICA is subsequently proposed to overcome these problems since its aims to find the independent signals rather than orthogonal ones. B. MMCA Algorithms The ICA learning algorithm searches for the linear transformation to make the components as statistically independent as possible. MMCA is used as an ICA algorithm in this paper for separation purpose. MMCA takes advantage of the sparse representation of multichannel data in large overcomplete dictionaries to separate features in the data based on their morphology, even with noise [18]. The defect in CFRP meets the sparse property criterion since the pixel number of informational data at defective region is much smaller than that of the overall image. After the dimension reduction using PCA, the measurement I M is re-sized as IM with dimensional P × F, which can be written as a multiplying of estimated decorrelation matrix X I C A and mixing matrix M I C A plus noise: IM = M I C A X I C A + Nnoice .

(3)

The row vectors of IM , X I C A and M I C A are ip , x p and m p ( p = 1, . . . , P), respectively. Each x p can be described as xTp = p a p with an over-complete dictionary p and a sparse representation a p . The estimation of X I C A and M I C A is governed by following equation [18]: ˆ I C A, X ˆ I C A } = arg min IM − M I C A X I C A 2 {M Fro M I C A ,X I C A + λ p x p + (4) p p

1

where M2Fro = trace (MT M), here ‘Fro’ denotes the frobenius norm. + in the next iteration; λ p p is the updated p + denotes the sparse parameters and x p p forms the L 1 1 norm regularization. From equation (4), by minimising the objective function with respect to x p when m p is fixed, it can

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IEEE SENSORS JOURNAL, VOL. 14, NO. 5, MAY 2014

be derived through equation (5) [18]: λp 1 +T x p = 2 [mTp Im − sign(x p + p ) p 2 m p 2 1 m p = 2 Im xTp (5) m p 2 where Im = IM − p = p m p x p . The MMCA algorithm is presented as follows [18]: 1. Set number of iterations L max & threshold ∀ p, δ p = L max λ p /2 Fig. 4.

2. While δ p > λ p /2, For p = 1, . . . , P • •

– – – – – •

–

ECPT system diagram.

Re-normalise m p and x p Update x p assuming all x p = p andm p are fixed Compute the residual Im = IM − p = p m p x p Project Im : x˜ p = 1 2 mTp Im m p 2 Compute α p = x˜ p + p Soft threshold α p with threshold δ p , yielding α˜ p T Reconstruct x p by x p = α˜ p + p Update m p assuming all x p and m p = p are fixed: m p = 1 2 Im xTp x p 2

Lower the thresholds: δ p = δ p − λ p /2

III. E XPERIMENTAL S YSTEM AND S AMPLE P REPARATION A. Experimental System The diagram of ECPT system is illustrated in Fig. 4. In the system, the excitation signal generated by the excitation module is a small period of high frequency current, as shown in Fig. 4. It is driven to the coil on the conductive material. Then, the current in the coil will induce the eddy currents and generate the resistive heat in the conductive material. The heat will diffuse as the time delay till the heat balance in material. If there is a defect in conductive material, eddy current distribution or heat diffusion process will be obstructed. Consequently, the temperature distribution on the surface of material will show the variation, which is captured by an infrared camera. As shown in Fig. 5 at Newcastle University, an Easyheat 224 from Cheltenham Induction Heating is used for coil excitation. The Easyheat has a maximum excitation power of 2.4 kW, a maximum current of 400 Arms and an automatic resonant excitation frequency range of 150 kHz - 400 kHz (values of 380Arms and 256 kHz are used in the experiments for rectangular coil). In general, high excitation frequencies will lead to high thermal contrast (or high temperature rise). The time domain information will allow the derivation of defect profile information. 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 the coil is implemented to counteract direct heating of the coil. The Flir

Fig. 5.

Experimental setting-up at Newcastle University.

SC7500 is a Stirling cooled camera with a 320 × 256 array of 1.5 − 5 μm InSb detectors. The camera has a sensitivity of

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Impact Damage Detection and Identification Using Eddy Current Pulsed Thermography Through Integration of PCA and ICA Liang Cheng, Student Member, IEEE, Bin Gao, Member, IEEE, Gui Yun Tian, Senior Member, IEEE, Wai Lok Woo, Senior Member, IEEE, and Gerard Berthiau

Abstract— Eddy current pulsed thermography (ECPT) is implemented for detection and separation of impact damage and resulting damages in carbon fiber reinforced plastic (CFRP) samples. Complexity and nonhomogeneity of fiber texture as well as multiple defects limit detection identification and characterization from transient images of the ECPT. In this paper, an integration of principal component analysis (PCA) and independent component analysis (ICA) on transient thermal videos has been proposed. This method enables spatial and temporal patterns to be extracted according to the transient response behavior without any training knowledge. In the first step, using the PCA, the data is transformed to orthogonal principal component subspace and the dimension is reduced. Multichannel morphological component analysis, as an ICA method, is then implemented to deal with the sparse and independence property for detecting and separating the influences of different layers, defects, and their combination information in the CFRP. Because different transient behaviors exist, multiple types of defects can be identified and separated by calculating the cross-correlation of the estimated mixing vectors between impact the ECPT sequences and nondefect ECPT sequences. Manuscript received May 6, 2013; revised November 25, 2013; accepted January 5, 2014. Date of publication January 17, 2014; date of current version March 24, 2014. This work was supported in part by the National Natural Science Foundation of China under Grant 51377015, in part by the Sichuan Science and Technology Department under Grant 2013HH0059, in part by the University of Electronic Science and Technology of China, in part by the National Research Center of Sensors Engineering, in part by Shenyang Academy of Instrumentation Company Ltd., in part by Health Monitoring of Offshore Wind Farms, in part by Cognitive-Networks-Enabled Transnational Proactive Healthcare, in part by the Engineering and Physical Sciences Research Council (EPSRC), U.K., under Grant EP/F06151X/1, and in part by FP7 Health Monitoring of Offshore Wind Farms (HEMOW, FP7-PEOPLE2010-IRSES-269202). L. Cheng and B. Gao contributed equally to this work. The associate editor coordinating the review of this paper and approving it for publication was Dr. Lorenzo Lo Monte. (Corresponding author: B. Gao.) L. Cheng and G. Y. Tian are with the School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 610051, China, and also with the School of Electrical and Electronic Engineering, Newcastle University, Newcastle upon Tyne NE1 7RU, U.K. (e-mail: [email protected]; [email protected]). B. Gao is with the School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 610051, China (e-mail: [email protected]). W. L. Woo is with the School of Electrical and Electronic Engineering, Newcastle University, Newcastle upon Tyne NE1 7RU, U.K. (e-mail: [email protected]). G. Berthiau is with the Institute of Research in Electrical Engineering of Nantes-Atlantique, University of Nantes, Nantes 44300, France (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JSEN.2014.2301168

Index Terms— Eddy current pulsed thermography, non-destructive evaluation, principal component analysis, independent component analysis, impact damage, spatialtemporal pattern separation.

I. I NTRODUCTION

E

DDY current pulsed thermography (ECPT), combining EC and thermography, involves the application of a high current electromagnetic pulse to the conductive material under inspection for a short period. Eddy currents will be induced in the material, leading to the heating of the material itself. The existence of any defects distorts the propagation of the eddy current leading to a variation in material temperature that can be emphasised with thermography. After the period of eddy current heating, the non-homogeneity of carbon fibre reinforced plastic (CFRP) in the cooling phase also affect the diffusion of heat. Therefore, the mixed phenomena of induction heating dominating in the heating phase and the diffusion of this dominating in the cooling phase and their specific behaviours are useful for the quantitative nondestructive evaluation of non-homogeneity of a given material. Different from other thermography techniques such as flash and laser thermography, ECPT focuses the heat generation at the defects, at not only the surface but also subsurface. In this paper, impact damage, one of the most common defects in CFRP, is under investigation using ECPT. ECPT has been used to inspect metallic parts [1]–[4]. Abidin et al. [1] evaluated the angular slots in metal through simulation and experiment. Features, e.g. maximum temperature amplitude, slope inclination etc., were extracted to quantify the angle of the slot. Oswald-Tranta et al. [3] investigated the temperature distribution around a crack with different penetration depths using FEM modelling and compared with experimental measurements on metallic materials. The results showed that lower temperatures are exhibited at the surface edge of a crack and higher temperatures at the bottom in nonmagnetic materials with a large penetration depth. Compare to defects in metal, those in composite materials were rarely investigated. Ramdane et al. [5] detected inserted delaminations using induction-heating thermography. The experimental studies were undertaken in transmission mode (the inductor and infrared camera are on the different sides of the sample), which is normally not applicable in the

1530-437X © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

1656

in-situ inspection. Moreover, the inspection period is around 80 seconds. He et al. [6] combined transmission and reflection mode for wall thinning defect and inner defect based on heat diffusion. Through 1D analytical model, 3D numerical model and experimental results, suitable detection mode for those defects was identified, and the location in thickness of the defects was quantified. All the above works are limited by the manual selection of proper contrast frames or investigated area. In addition, the transient response features suffer from noise. To enhance the flaw contrast and improve noise rejection qualities, pattern based image enhancement has been conducted by introducing the raw data upon a set of orthogonal basis functions. Fourier transform was applied to pulsed thermography, and enhanced the flaw-contrast significantly using phase map [14]. Influence of non-uniform heating and surface emissivity variation was removed by using a Fourier transformation based image reconstruction algorithm [15]. Instead of a prescribed set of basis functions, Principal Component Analysis (PCA) and Independent Component Analysis (ICA) are used to enhance the contract of defective region and sound area (non-defect region) in thermal image sequence. Marinetti et al. [9] compared the efficiency of PCA to thermography features extraction by considering the initial sequence as either a set of images or a set of temporal profiles. Khan et al. [10] identified water leakage in dikes from thermometric data using PCA and ICA. Rajic [11] employed PCA to improve the flaw detection ability of thermography, and characterised the surface flaw depth using characteristic time estimated from Principle Component (PC) vector. Sophian et al [12] and Yang et al. [13] implemented PCA and ICA for defect classification based on PEC signals. The statistical kurtosis was used as standard to select Independent Components (ICs) for feature extraction. In addition, the liftoff effect on defects was classified. Bai et al. [14] proposed ICA to highlight the anomalous patterns of ECPT video for crack in metallic specimen. Estimated mixing vector using ICA in heating and cooling phase around crack tips were used for automatic identification of cracks. However, most above mentioned works only employ the analysis separately as a signal processing tool. The mathematical reasons why these algorithms can enhance an image and how these techniques are connected to physical models are not provided in detail. In addition, the separation of multiple defects as well as fibre texture is limited, especially for nonhomogeneous composite samples. Moreover, an especially important case is not discussed when the defect region is highly sparse, meaning that it is rarely active within the whole surround background. In this paper, an integrative method is developed to extract anomalous and sparse patterns from transient thermal videos. This method can automatically highlight and separate the defects in the spatial components and the temporal components. The rest of this paper will be organised as follows: Section II introduces the PCA and ICA algorithms used for transient thermal videos. The experimental system and sample are illustrated in Section III. The results and comparison using

IEEE SENSORS JOURNAL, VOL. 14, NO. 5, MAY 2014

Fig. 1.

Impacted sample.

PCA and ICA are reported in Section IV. The conclusion and future work are represented in Section V. II. T HEORETIC C ONCERNS The composite sample with impact damage point is shown in Fig. 1. From the figure, it can be seen that the area of defect in the sample is much less than those of the surrounding, which indicates the sparse property of inspected sample. Here, ‘sparseness’ refers to a representational scheme where only a few units (out of a large population) are effectively used to represent typical data vectors [15]. The indecency of material property at defects refers to the decrease of electric conductivity and increase of thermal conductivity at impact damage [16]. This directly results in the transient temperature response at impact damage region, independent to those in sound area. The impact can also generate delamination at the backside of the sample when the impact energy is large enough. Delamination causes the discontinuity of both electric and thermal conductivity in thickness direction, where the transient temperature response is also independent to those in sound area. Fig. 2 illustrates the procedure of defect identification and separation by using ECPT video sequences. Firstly, the data is transformed to orthogonal PC subspace and the dimension is reduced by using PCA. Multichannel Morphological Component Analysis (MMCA) is then implemented to deal with the sparse and independence property for detecting impact damage and delamination in CFRP. By using MMCA, the different characteristics of transient responses related to the impact damage, delamination, and area without defects can be separated. Subsequently, the cross-correlation of the estimated mixing vectors derived from MMCA for both thermal transient video with defect and the one without defect are calculated. The maximum/minimum correlation value of correlation value can be used to identify the influence of the impact damage, delamination and non-defect factors. Fig. 2 shows the flow diagram for the proposed method. In the figure, the defect and non-defect thermal videos are recorded by using the same material sample (at the defective area and non-defective area, respectively). The record area and relevant coil position in detail will be presented in Section III. In following subsections, the individual algorithms for PCA and MMCA are introduced and investigated. A. PCA Algorithm PCA is a multivariate analysis technique, transforming the original measured data into new uncorrelated variables, as

CHENG et al.: IMPACT DAMAGE DETECTION AND IDENTIFICATION USING ECPT

Fig. 2.

1657

Procedure for defect identification and separation.

termed Principal Components (PC). The original measured data are treated as independent variables. Each PC is a linear combination of the original variables. These PCs form the basis of the respective vector space and they are arranged in order of decreasing variance. Thus, the first PC carries the most of information regarding the original data and so on. Use of PCA methods in PEC testing can be found in previous work [12] and [17], and in this paper will be used for defect highlighting and classification of ECPT images. To conduct PCA on the N input signals, eigenvalue decomposition of the covariance of the input 2D matrix I M is used. After decomposition, I M can be transformed into uncorrelated sources. The covariance of I M can be expressed as E{I M ITM } = EDET , where E is the orthogonal matrix of eigenvectors and D = di ag(λ1 , . . . , λ N ). λ1 ≥ . . . ≥ λ N are the decent eigenvalues. Thus, the covariance of I M is N × F matrix where F is the product of row and column of image (e.g. 320 × 256 = 81920) where this can be rewritten as: E{I M ITM } = EDET = ED1/2 D1/2 ET T

−1 = E{W−1 PC A X PC A W PC A W PC A } T

−1 = W−1 PC A E{X PC A W PC A }W PC A T

−1 = W−1 PC A W PC A . T

T

(1)

In Equation (1), E{.} is expectation operation, T E{X PC A WPC A } = I where I is identity matrix. Therefore, W PC A = (ED1/2 )−1 = D1/2 ET and whitening can be written as: X PC A = W PC A I M

(2)

where W PC A is the estimated de-correlation matrix and X PC A is the uncorrelated sources by using PCA. The mixing matrix M PC A = W−1 PC A = [m1 , m2 , . . . , m N ] and mn are the mixing vectors of PCA. By using PCA, N orthogonal signals can be derived to from the ECPT video. For the thermal sequence, the aim of using PCA is to maximise the contrast between defective region and sound region. In addition, the dimension of data is reduced to P, rather than N = 383. Here the selection of P number of PC can be implemented by using threshold based approach which can be found in [14] and this procedure is summarized in Fig. 3. Because PCA cannot guarantee the statistical independence of above regions, whereas the PCA is not an ideal tool for separating the different types of defect

Fig. 3.

PCA procedure on the thermal videos.

as well as non-defect regions in one go. Therefore, ICA is subsequently proposed to overcome these problems since its aims to find the independent signals rather than orthogonal ones. B. MMCA Algorithms The ICA learning algorithm searches for the linear transformation to make the components as statistically independent as possible. MMCA is used as an ICA algorithm in this paper for separation purpose. MMCA takes advantage of the sparse representation of multichannel data in large overcomplete dictionaries to separate features in the data based on their morphology, even with noise [18]. The defect in CFRP meets the sparse property criterion since the pixel number of informational data at defective region is much smaller than that of the overall image. After the dimension reduction using PCA, the measurement I M is re-sized as IM with dimensional P × F, which can be written as a multiplying of estimated decorrelation matrix X I C A and mixing matrix M I C A plus noise: IM = M I C A X I C A + Nnoice .

(3)

The row vectors of IM , X I C A and M I C A are ip , x p and m p ( p = 1, . . . , P), respectively. Each x p can be described as xTp = p a p with an over-complete dictionary p and a sparse representation a p . The estimation of X I C A and M I C A is governed by following equation [18]: ˆ I C A, X ˆ I C A } = arg min IM − M I C A X I C A 2 {M Fro M I C A ,X I C A + λ p x p + (4) p p

1

where M2Fro = trace (MT M), here ‘Fro’ denotes the frobenius norm. + in the next iteration; λ p p is the updated p + denotes the sparse parameters and x p p forms the L 1 1 norm regularization. From equation (4), by minimising the objective function with respect to x p when m p is fixed, it can

1658

IEEE SENSORS JOURNAL, VOL. 14, NO. 5, MAY 2014

be derived through equation (5) [18]: λp 1 +T x p = 2 [mTp Im − sign(x p + p ) p 2 m p 2 1 m p = 2 Im xTp (5) m p 2 where Im = IM − p = p m p x p . The MMCA algorithm is presented as follows [18]: 1. Set number of iterations L max & threshold ∀ p, δ p = L max λ p /2 Fig. 4.

2. While δ p > λ p /2, For p = 1, . . . , P • •

– – – – – •

–

ECPT system diagram.

Re-normalise m p and x p Update x p assuming all x p = p andm p are fixed Compute the residual Im = IM − p = p m p x p Project Im : x˜ p = 1 2 mTp Im m p 2 Compute α p = x˜ p + p Soft threshold α p with threshold δ p , yielding α˜ p T Reconstruct x p by x p = α˜ p + p Update m p assuming all x p and m p = p are fixed: m p = 1 2 Im xTp x p 2

Lower the thresholds: δ p = δ p − λ p /2

III. E XPERIMENTAL S YSTEM AND S AMPLE P REPARATION A. Experimental System The diagram of ECPT system is illustrated in Fig. 4. In the system, the excitation signal generated by the excitation module is a small period of high frequency current, as shown in Fig. 4. It is driven to the coil on the conductive material. Then, the current in the coil will induce the eddy currents and generate the resistive heat in the conductive material. The heat will diffuse as the time delay till the heat balance in material. If there is a defect in conductive material, eddy current distribution or heat diffusion process will be obstructed. Consequently, the temperature distribution on the surface of material will show the variation, which is captured by an infrared camera. As shown in Fig. 5 at Newcastle University, an Easyheat 224 from Cheltenham Induction Heating is used for coil excitation. The Easyheat has a maximum excitation power of 2.4 kW, a maximum current of 400 Arms and an automatic resonant excitation frequency range of 150 kHz - 400 kHz (values of 380Arms and 256 kHz are used in the experiments for rectangular coil). In general, high excitation frequencies will lead to high thermal contrast (or high temperature rise). The time domain information will allow the derivation of defect profile information. 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 the coil is implemented to counteract direct heating of the coil. The Flir

Fig. 5.

Experimental setting-up at Newcastle University.

SC7500 is a Stirling cooled camera with a 320 × 256 array of 1.5 − 5 μm InSb detectors. The camera has a sensitivity of