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Defect detection in CFRP structures using pulsed thermographic data enhanced by penalized least squares methods
Composites Part B 79 (2015) 351e358
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Composites Part B journal homepage: www.elsevier.com/locate/compositesb
Defect detection in CFRP structures using pulsed thermographic data enhanced by penalized least squares methods Kaiyi Zheng, Yu-Sung Chang, Yuan Yao* Department of Chemical Engineering, National Tsing Hua University, Hsinchu 30013, Taiwan, ROC
a r t i c l e i n f o
a b s t r a c t
Article history: Received 28 December 2014 Received in revised form 22 March 2015 Accepted 29 April 2015 Available online 8 May 2015
Pulsed thermography (PT) is a widely used non-destructive testing (NDT) method for detecting defective regions in carbon fiber reinforced polymers (CFRP) structures. In order to improve the spatial and temporal resolution of thermographic data, thermographic signal reconstruction (TSR) is often adopted for data processing and analysis. However, TSR only performs data filtering along the time direction, while the spatial information is not exploited for noise reduction. In addition, TSR cannot handle the non-uniform backgrounds commonly existing in thermal images. To get around these problems, this paper extends the utilization of the penalized least squares methods to defect detection in CFRP structures. The experiment results show that, with the aid of penalized least squares, the defective regions in thermal images are characterized more clearly, while the signal-to-noise ratio (SNR) values are increased significantly. © 2015 Elsevier Ltd. All rights reserved.
Keywords: A. Carbon fiber D. Non-destructive testing D. Thermal analysis Pulsed thermography
1. Introduction Due to the high chemical stability, high mechanical strength and low density, carbon fiber reinforced polymers (CFRP) have been widely used in the areas where high strength-to-weight ratio and rigidity are required, including aerospace, automotive, wind turbines, civil engineering, etc. However, various types of defects may exist in CFRP structures, such as fiber breaks, voiding, cracking, delaminating and interfacial debonding. These defects are often invisible at the part surface, but have negative effects on the strength and stiffness of CFRP products. Therefore, defect detection in CFRP structures is critical to product performance and safety. Generally, defect detection methods can be categorized as destructive and non-destructive. Due to the high cost of CFRP materials, non-destructive testing (NDT) methods including thermography [1e4], ultrasonic inspection [5e8], X-ray inspection [9e11], shearography [11,12], electronic speckle pattern interferometry [13,14], etc. are commonly applied. Among these methods, thermography is attractive for its low cost, easy operation and wide scanning scope. Thermography is a surface radiation measurement technique, which uses infrared camera to measure surface temperature of
* Corresponding author. Tel.: þ886 3 5713690; fax: þ886 3 5715408. E-mail addresses: [email protected] (K. Zheng), [email protected] (Y. Yao). http://dx.doi.org/10.1016/j.compositesb.2015.04.049 1359-8368/© 2015 Elsevier Ltd. All rights reserved.
target specimen and constructs thermal images for analysis. The thermographic NDT techniques can be divided into two categories: active thermography and passive thermography. The major difference between these two lies in the utilization of external energy source. In active thermography, an external energy source is required to produce a thermal contrast between the inspected parts and the surroundings. In contrast, no such external energy is supplied in passive thermography. As a result, active thermography are more robust to the influence of ambient temperature, and more widely used in defect detection of fiber reinforced polymers (FRP) [15,16]. In the past one or two decades, the use of pulsed thermography (PT), one of the most popular methods in active thermography, has increased dramatically for NDT of composite materials [17]. A major reason for this popularity is the quickness of the inspection relying on a thermal stimulation pulse [18]. In PT, the surface of a tested part is heated with a brief pulse of light usually from a high power source, e.g. photographic flashes. Then, the heat flux on the surface tends to diffuse into the material. The time-dependent surface temperature response is captured as a series of thermal images by an infrared camera connected to a computer. The temperature contrast between the defective and non-defective regions enables defect detection based on thermographic data. However, thermal images usually involve significant measurement noise and non-uniform backgrounds caused by uneven heating. As a result, it is difficult to recognize the defective regions
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clearly by naked eyes. Hence, different types of thermographic image analysis methods have been proposed for signal enhancement, e.g. thermographic signal reconstruction (TSR) [19,20], differential absolute contrast (DAC) [21,22], pulsed phase thermography (PPT) [23,24], principal component thermography (PCT) [25], etc., where TSR is frequently used for its performance in data compressing and noise reduction. Based on the Fourier diffusion equation, TSR applies polynomial filters to eliminate the noise contained in thermographic data. In addition, TSR can also use derivatives to further improve its defect detection ability. The major shortcomings of TSR are of the following two aspects. First, TSR only applies polynomial filters in time dimension to reduce noise, while the abundant spatial information contained in thermal images is not exploited. Therefore, the effectiveness of noise reduction is still not good enough. Especially, if time derivative is performed, the noise will be further amplified. Second, TSR cannot handle the non-uniform backgrounds well. To get around these problems, the statistical techniques of penalized least squares are adopted in this paper to better utilize the spatial information. Originally proposed by Whittaker [26], penalized least squares smoothers have become promising methods in the field of chemical data analysis [27], the ideology of which is to divide a noisy series into two parts, i.e. the signal and the noise, by solving a penalized optimization problem. Recently, Zhang et al. proposed an iteratively reweighted procedure based on penalized least squares to correct the baseline contained in chemical signals [28]. The penalized least squares smoothers have following attractive properties. (1) The programming is easy, especially in a MATLAB environment. (2) The boundaries of the data can be treated well in an automatic way. (3) Penalized least squares handles missing data. (4) The smoothness of the reconstructed signal obtained from decomposition can be controlled by tuning a single parameter. (5) The algorithms are efficient. Although with different dimensions, both thermographic data and chemical data consist of three critical elements: signals, backgrounds and noise. Inspired by such similarity, the penalized least squares methods are adopted in this paper to decompose the TSRtreated thermographic data and to extract the reconstructed images with least influence of non-uniform background and noise. By doing so, the defect detection efficiency of pulsed thermography can be significantly enhanced. The paper is organized as follows. In Section 2, the principle of pulsed thermography is briefly introduced. Then, the methodologies are presented in Section 3, including TSR, noise reduction with penalized least squares, and non-uniform background elimination. In Section 4, the experiment results show the effectiveness of the proposed method comparing to the conventional TSR method. Finally, conclusions are given in the Section 5.
2. Pulsed thermography The problem of heat diffusion through a solid specimen can be described by Fourier's law of heat diffusion:
1 vT ¼ 0: V2 T a vt
Q z2 ; Tðz; tÞ ¼ T0 þ pffiffiffiffiffi exp 4at e pt
where Q is the energy absorbed pffiffiffiffiffiffiffiffi by the specimen surface, T0 is the initial temperature, e ¼ krc is the effusivity, and T(z,t) is the material temperature at depth z and time t. In pulsed thermography, only the temperature of specimen surface is measurable, i.e. z ¼ 0. Accordingly, (2) can be simplified as:
Q TðtÞ ¼ T0 þ pffiffiffiffiffi : e pt
Here, V is the three-dimensional del operator, T is the temperature in the specimen, t is the time index, a ¼ k/(rc) is the material thermal diffusivity, k is thermal conductivity, r is the material density, and c is heat capacity. Under the circumstances of pulsed heating and thermal insulation, the one-dimensional solution of (1) in a semi-infinite homogeneous and isotropic solid can be expressed as follows [29].
(3)
After pulsed heating, the thermal front travels through the specimen as time elapses, while the surface temperature decreases uniformly over time if there is no defect. On the contrary, subsurface discontinuities caused by defects lead to resistances to heat flow, resulting in certain temperature patterns at the surface. Consequently, the abnormalities can be identified by the temperature contrast between defective and non-defective regions. However, as discussed in the introduction section, the useful information in thermographic data often hides behind measurement noise and non-uniform backgrounds caused by uneven heating. Therefore, effective processing methods are necessary for thermographic data analysis. 3. Methodologies To fully making use of both the temporal and spatial information in thermographic data analysis, the proposed method can be divided into two stages. In the first stage, the TSR algorithm is applied to the thermographic data, which reduces the noise using a time-directional filter. Then, in the second stage, penalized least squares algorithms are adopted to extract the reconstructed thermal images by further reducing noise and eliminating non-uniform backgrounds. In this stage, spatial information contained in each thermal image is utilized. 3.1. Thermographic signal reconstruction TSR assumes that the decay pattern of the surface temperature profile of a non-defective pixel can be described by (3) whose logarithmic form is as follows:
Q lnðDTÞ ¼ ln pffiffiffi 0:5lnðtÞ; e p
(4)
where DT ¼ T(t)T0. Although (4) is concise, it is only an approximation of the solution for the 3-D Fourier diffusion equation. In practice, the profile of the logarithmic thermographic data may diverge from the ideal linear equation for several reasons, such as poor camera calibration, reflection artifacts, convection and so on. Thus, in TSR, a polynomial function with m degree is used to fit the relationship between ln(DT) and ln(t), i.e.
lnðDTÞ ¼ a0 þ a1 ðln tÞ þ a2 ðln tÞ2 þ … þ am ðln tÞm : (1)
(2)
(5)
In a CFRP specimen, the thermal decay profiles belonging to intact regions behave approximately linear, while those of defective regions usually have different patterns. In order to make a good balance between data fitting and noise reduction, the value of m should be set properly. A too large value of m may cause overfitting, while a too small value may lead to model mismatch. Hence, it is suggested to set m as 4 or 5 [1]. In the following of this paper, the value of m is specified as 4. After acquiring the regression coefficients, the entire temperature profile can be compressed into
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m þ 1 coefficients, and the smoothed thermographic data can be reconstructed according to (5). Moreover, as stated in Ref. [19], differentiation can be conducted along time direction to further highlight the contrast between defective and non-defective regions. The first-order derivatives of the reconstructed data reflect the velocity of temperature decay, while the second-order time derivatives reflect the change rate of the velocity. The higher order derivatives are rarely adopted due to lack of physical interpretation. In addition, as observed in (4), the effects of uneven heating only appear in the constant term on the right side of the equation. Therefore, in theory, taking derivatives can remove the non-uniform backgrounds contained in thermographic data. However, due to mismatch between theoretical assumptions and practice, the background information may propagate to the high-order terms in (5). Meanwhile, the a0 term in (5) may involve a part of information related to defect detection as shown in the experiment section of this paper. Such information is lost in the derivative data. Therefore, in the proposed procedure, only the reconstructed thermographic data without derivation are subjected to the following steps.
3.2. Further noise reduction using penalized least squares smoothers After conducting TSR, the spatial information of each reconstructed thermal image is utilized for further noise reduction. To achieve this goal, penalized least squares smoothers are adopted. Since the data structure of each thermal image is two-dimensional, the smoothing is conducted sequentially to each row or column of a thermal image. For each row or column in the TSR-reconstructed image, the original data series x may be still too noisy. The target here is to find a smooth series z to fit x. During fitting, there are two issues to be considered: (1) roughness of z and (2) fidelity to x [27]. Differences between two successive data points, Dzi ¼ zi zi1, can be used to express roughness of the smoothed series. Thus, the overall roughness of z can be measured by summing the squares of the differences:
R1 ¼
n X
ðzi zi1 Þ2 ¼
i¼2
n X
(6)
1 1 « 0
0 1 « 0
/ / 1 /
0 0 « 1
3 0 07 7; «5 1
ðzi xi Þ2 ¼ kx zk2 :
(7)
(8)
i¼1
Usually, low roughness of z and high fidelity to x are desired. However, these two goals are conflict to each other. A smoother z deviates more from x. Hence, a balance should be made between fidelity and roughness. The following equation describes the balanced combination of both targets:
Q1 ¼ F1 þ l1 R1 ¼ kx zk2 þ l1 kDzk2 ;
(10)
Based on (10), z can be solved:
1 0 z ¼ I þ l1 D D x;
(11)
where I is the identity matrix. The noise is then reduced by replacing x with z in the reconstructed thermal images. 3.3. Non-uniform background elimination using adaptive iteratively reweighted penalized least squares After removing noise, the smoothed thermographic data are composed of signals (i.e. informative peaks) and non-uniform backgrounds (i.e. two-dimensional baselines), where the background information is not useful in defect detection and should be eliminated. Similar to the smoothing procedure, the background elimination algorithm is applied sequentially to each row or column of the smoothed thermal images. Here, the adaptive iteratively reweighted penalized least squares algorithm [28] is adopted. For each row or column of a smoothed thermal image, the partial least squares smoother can be revised to extract the nonuniform background y from the smoothed data series z. Fidelity of y to z is defined as:
F2 ¼
n X
0
wi ðzi yi Þ2 ¼ ðz yÞ Wðz yÞ;
(12)
i¼1
where the weight matrix W is diagonal with wi as its i-th diagonal element. At the positions corresponding to the peak segments of z, wi is set to zero. Accordingly, the objective function for background elimination becomes:
Q2 ¼ ðz yÞ Wðz yÞ þ l2 kDyk2 :
(13)
Thus, the background y can be calculated by minimizing Q2:
and kak indicates the Euclidean 2-norm of the vector a. The smaller the value of R1, the lower the roughness is. The fidelity can be quantified by the difference between z and x: n X
0 vQ1 0 ¼ 2ðz xÞ þ 2l1 D Dz ¼ 0: vz
i¼2
1 6 0 D¼6 4 « 0
F1 ¼
where l1 is a parameter adjusting the degree of importance of the two goals. Thus, the problem of smoothing is transformed to a penalized least squares problem. In order to minimize Q1, its partial derivative vector should be set to zeros, i.e.
0
Dz2i ¼ kDzk2 :
Here, n is the length of the series, D is a matrix with n1 rows and n columns:
2
353
(9)
1 0 y ¼ W þ l2 D D Wz:
(14)
Since it is difficult to identify the peak segments before background elimination, an adaptive iteratively reweighted procedure can be used to adjust the parameters in W [28]. In each iteration of the adaptive iteratively reweighted procedure, a weighted penalized least squares problem described in below is solved:
2 0 Q2k ¼ z yk W k z yk þ l2 Dyk ;
(15)
where k is the index of iteration. The initial value of W is set as W0 ¼ I, which means that the diagonal elements in W0 are all 1. In the k-th iteration, wki can be updated as:
wki
¼
8 > > > <0
zi yk1 i
kðzi yk1 Þ i > > > : e kdk k
zi < yk1 i
;
(16)
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Fig. 1. Preparation of a CFRP specimen with defects. (a) Simulating the defects using six Teflon square strips and a piece of insulating tape. (b) The specimen before resin infiltration. (c) The specimen after resin infiltration.
corresponding point yk1 in the background candidate yk1, such i data point is considered as part of an informative peak, i.e. signal. Therefore, its weight is set to zero, so that the point will be ignored in the next iteration of background fitting. By doing so, the recognized signal does not affect the calculation of the fidelity F2 of the background y to the raw data z. Hence, the background can be identified in a gradual and automatic way. Such iteration can be terminated either when the maximum iteration times is reached or when the termination criterion is achieved. The termination criterion can be defined as:
k d < 0:001kyk:
After estimating y, the signal less affected by either noise or background can be obtained by z y.
Fig. 2. Illustration of the defect positions in the CFRP specimen.
where yk1 is the i-th data point in yk1, and dk consists of negative i elements of the differences between z and yk1, i.e.
o n dk ¼ z yk1 :
(18)
4. Experiment and results 4.1. Experiment description
(17)
In the above equations, yk1 is a candidate of the background fitted in the (k1)-th iteration. If the value of zi is larger than the
In the experiment, the CFRP specimen with size of 12 cm 9.5 cm was manufactured by vacuum assisted resin transfer molding (VARTM) technique [30], which was strengthened
Fig. 3. Raw thermal images of the CFRP specimen collected at the 1st (a), 2nd (b), 3rd (c) and 4th (d) seconds after pulsed heating.
K. Zheng et al. / Composites Part B 79 (2015) 351e358
355
Fig. 4. Thermal images corresponding to the 1st (a), 2nd (b), 3rd (c) and 4th (d) seconds after pulsed heating, which were treated by TSR.
with multiple layers of carbon fiber sheets. The thickness of each fiber sheet was 0.26 cm. To simulate the defects, six Teflon square strips with different areas were inserted into the fiber sheets before executing VARTM. Additionally, another defective rectangle with size of 1.4 cm 0.6 cm was also constructed using a piece of insulating tape. Therefore, the CFRP specimen contained totally seven defective regions. In the photo shown in Fig. 1(a), the Teflon strips are in light color, while the color of the defect caused by the insulating tape is dark. The four defects on the left-hand side of the specimen were covered by a single layer of carbon fiber sheet, while the three defects on the right were under two layers of sheets (Fig. 1(b)). Therefore, these defects were at different depths, and were invisible by naked eyes after resin infiltration as shown in Fig. 1(c). Fig. 2 illustrates the position of each defective region. In this figure, Region A at the top left corner is the defect caused by
insulating tape. Regions B, C and D are the square defects with different sizes but all located under a single layer of carbon fiber sheet, the side lengths of which are 1.6 cm, 0.8 cm and 0.4 cm, respectively. Similarly, Regions E, F and G are all under two layers of carbon fiber sheets, with side lengths of 1.6 cm, 0.8 cm and 0.4 cm, respectively. For defect detection, pulsed thermography was performed. After the specimen was heated by a thermal pulse generated from a flash, an NEC infrared camera (type TAS-G100EXD) with a resolution of 320 240 pixels was used to collect the thermographic data, generating a series of thermal images. Then, image processing algorithms including TSR, noise reduction using penalized least squares smoothers, and background elimination were conducted as described in Section 3. All the algorithms were compiled and run on Matlab 2014a.
Fig. 5. The first derivative of the reconstructed data correspond to 1 s after pulsed heating without (a) and with (b) penalized least squares smoothing, and the second derivative of the reconstructed data correspond to 1.6 s after pulsed heating without (c) and with (d) penalized least squares smoothing.
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In order to evaluate the effectiveness of these algorithms, the index of signal-to-noise ratio (SNR) was adopted. Such index has been widely used in the comparison of pulsed thermographic data processing methods [1], which is defined in the following way:
SNR ¼
Mdef Min ; sin
(19)
where Mdef is the average signal in defective regions, Min is the average signal in intact regions, and sin is as the standard deviation of the signal in intact regions. Such index reflects thermal contrast between defective and non-defective areas, which can be increased by effective noise reduction (i.e. decreasing sin) and background elimination. Fig. 6. An image reconstructed using the constant terms a0 in the TSR fitted polynomials.
4.2. Results and discussions Fig. 3 shows the raw thermal images collected at the 1st, 2nd, 3rd and 4th seconds after pulsed heating. As observed in
Fig. 7. Thermal images corresponding to the 1st (a), 2nd (b), 3rd (c) and 4th (d) seconds after pulsed heating, which were treated by TSR and penalized least squares smoothing.
Fig. 8. Thermal images corresponding to the 1st (a), 2nd (b), 3rd (c) and 4th (d) seconds after pulsed heating, which were treated by TSR, penalized least squares smoothing and background elimination.
K. Zheng et al. / Composites Part B 79 (2015) 351e358
this figure, sub-plots (a) and (b) only provide obscure indications of the shallow defects, i.e. defects A, B, C and D, while almost all the information in sub-plots (c) and (d) is masked by noise, due to the low contrast between defective and nondefective areas in the raw thermal images. Furthermore, it can be noticed that the non-uniform backgrounds are very significant especially in the horizontal direction, which was caused by uneven heating. For better identification of the defects, TSR was executed to enhance the signal and reduce the noise, during which the degree of the polynomial function fitting the relationship between ln(DT) and ln(t) at each pixel was fixed to be 4. Fig. 4 shows the reconstructed thermal images after TSR. Comparing to Fig. 3, all the thermal images after TSR better revealed the defect information. Especially, the performance of the images corresponding to the 3rd and 4th seconds after pulsed heating was improved significantly because of noise reduction. The first and second-order derivatives of the reconstructed data formed the images in Fig. 5(a) and Fig. 5(c). Please note that only the images with the highest SNR values after differentiation are plotted. Fig. 5(b) and (d) are the further denoised version of Fig. 5(a) and (c) after penalized least squares smoothing. Perhaps a little surprisingly, the reconstructed thermal images after differentiation performed worse than the TSR-treated images without differentiation. The reasons are of two aspects. First, the differentiation increases the effects of noise. Second, during differentiation, the constant terms a0 in the polynomials are removed. However, as shown in Fig. 6, the a0 terms may contain important information of defective regions. Furthermore, as observed in Fig. 5, the differentiations cannot remove the non-uniform backgrounds contained in thermal images entirely. In the following processing steps, the TSR-treated images without differentiation were utilized. Before background elimination, the penalized least squares smoothers were applied for further noise reduction. During smoothing, an overlarge value of l1 may cause over-smoothness that is adverse to the detection of small defects. In this experiment, the value of l1 was uniformly selected to be 1. The images after smoothing are shown in Fig. 7. Compared to Fig. 4, the noise contained in each image is reduced in large extent, while the defective areas become much easier to identify. Nevertheless, the non-uniform backgrounds still exist. Especially, the effects of backgrounds make the region in the top right corner more like a defect than the real defective region E. Therefore, background elimination is necessary. To achieve this, adaptive iteratively reweighted penalized least squares introduced in Section 3.3 was adopted, where the values of l2 were set to be 50 and 200 for the horizontal and vertical direction in each image, respectively. The results are shown in Fig. 8. In each sub-plot, the image background became much more uniform after conducting adaptive iteratively reweighted penalized least squares. In especial, the significant non-uniform backgrounds in the top right corner of each image are not found in Fig. 8. All the seven defective regions, including both the swallow and deep defects, can be identified clearly in the processed images. For further investigating the effectiveness of different thermal image processing methods, the SNR values of each image under different treatments were computed and plotted in Fig. 9. Compared to raw images without any pretreatment, all the three processing methods can increase the SNR values. Meanwhile, in most of the sub-plots, the proposed processing method involving TSR, penalized least squares smoothing, and background elimination significantly outperformed other methods, highlighting the necessity of utilizing the spatial information in thermal image processing.
357
5. Conclusions In this paper, the concepts of penalized least squares are introduced to the field of pulsed thermographic data processing for defect detection in CFRP structures. By doing so, the spatial information contained in each thermal image can be fully utilized. As a result, the defect detection efficiency is improved comparing to the conventional TSR method. The effectiveness of the developed method was verified with the experiment results. Although proposed for pulsed thermography of CFRP, the method developed in this paper has the potential to be extended to other NDT applications using the thermography. For example, literature show that the active thermography technique has been adopted to detect debonding defects in the FRP-concrete systems [31], where the detection results also suffer from noise and nonuniform backgrounds contained in thermal images. Therefore, it will be promising to extend the utilization of the proposed method to such applications.
Fig. 9. SNR values of the thermal images with different types of processing for each defective region: (a) Region A, (b) Region B, (c) Region C, (d) Region D, (e) Region E, (f) Region F, (g) Region G, and (h) all the defective regions. (Red curve: No pretreatment; blue curve: TSR; green curve: TSR þ penalized least squares smoothing; black curve: TSR þ penalized least squares smoothing þ background elimination).(For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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In addition, despite that this paper focuses on the shape recognition of defects, the defect depth information may be explored by finding the time point when the deviation between the thermal responses of the defective region and the intact region begins. There is a relationship between this time point and the defect depth as discussed in the literature [32]. Such issue will be studied in our future research. Acknowledgments This work was supported in part by Ministry of Science and Technology, ROC under Grant No. MOST104-3113-E-007-004-CC2. References [1] Ibarra-Castanedo C, Piau J-M, Guilbert S, Avdelidis NP, Genest M, Bendada A, et al. Comparative study of active thermography techniques for the nondestructive evaluation of honeycomb structures. Res Nondestruct Eval 2009;20: 1e31. [2] Pickering S, Almond D. Matched excitation energy comparison of the pulse and lock-in thermography NDE techniques. NDT E Int 2008;41:501e9. [3] Schmutzler H, Alder M, Kosmann N, Wittich H, Schulte K. Degradation monitoring of impact damaged carbon fibre reinforced polymers under fatigue loading with pulse phase thermography. Compos Part B Eng 2014;59: 221e9. €llig M, Kunert M. Char[4] Maierhofer C, Myrach P, Reischel M, Steinfurth H, Ro acterizing damage in CFRP structures using flash thermography in reflection and transmission configurations. Compos Part B Eng 2014;57:35e46. [5] Stone DEW, Clarke B. Ultrasonic attenuation as a measure of void content in carbon-fibre reinforced plastics. Non Destr Test 1975;8:137e45. [6] Scarponi C, Briotti G. Ultrasonic technique for the evaluation of delaminations on CFRP, GFRP, KFRP composite materials. Compos Part B Eng 2000;31: 237e43. [7] Raisutis R, Ka zys R, Zukauskas E, Ma zeika L. Ultrasonic air-coupled testing of square-shape CFRP composite rods by means of guided waves. NDT E Int 2011;44:645e54. [8] Fahim AA, Gallego R, Bochud N, Rus G. Model-based damage reconstruction in composites from ultrasound transmission. Compos Part B Eng 2013;45: 50e62. [9] Hanke R, Fuchs T, Uhlmann N. X-ray based methods for non-destructive testing and material characterization. Nucl Instrum Methods Phys Res Sect A Accel Spectrom Detect Assoc Equip 2008;591:14e8. € gl S, Bichler S, Lemesch G, Ramsauer F, Ladsta €tter W, et al. New [10] Lenko D, Schlo approaches towards the investigation on defects and failure mechanisms of insulating composites used in high voltage applications. Compos Part B Eng 2014;58:83e90. pez-Arraiza A, Lizaranzu M, Aurrekoetxea J. [11] Amenabar I, Mendikute A, Lo Comparison and analysis of non-destructive testing techniques suitable for delamination inspection in wind turbine blades. Compos Part B Eng 2011;42: 1298e305.
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Defect detection in CFRP structures using pulsed thermographic data enhanced by penalized least squares methods Kaiyi Zheng, Yu-Sung Chang, Yuan Yao* Department of Chemical Engineering, National Tsing Hua University, Hsinchu 30013, Taiwan, ROC
a r t i c l e i n f o
a b s t r a c t
Article history: Received 28 December 2014 Received in revised form 22 March 2015 Accepted 29 April 2015 Available online 8 May 2015
Pulsed thermography (PT) is a widely used non-destructive testing (NDT) method for detecting defective regions in carbon fiber reinforced polymers (CFRP) structures. In order to improve the spatial and temporal resolution of thermographic data, thermographic signal reconstruction (TSR) is often adopted for data processing and analysis. However, TSR only performs data filtering along the time direction, while the spatial information is not exploited for noise reduction. In addition, TSR cannot handle the non-uniform backgrounds commonly existing in thermal images. To get around these problems, this paper extends the utilization of the penalized least squares methods to defect detection in CFRP structures. The experiment results show that, with the aid of penalized least squares, the defective regions in thermal images are characterized more clearly, while the signal-to-noise ratio (SNR) values are increased significantly. © 2015 Elsevier Ltd. All rights reserved.
Keywords: A. Carbon fiber D. Non-destructive testing D. Thermal analysis Pulsed thermography
1. Introduction Due to the high chemical stability, high mechanical strength and low density, carbon fiber reinforced polymers (CFRP) have been widely used in the areas where high strength-to-weight ratio and rigidity are required, including aerospace, automotive, wind turbines, civil engineering, etc. However, various types of defects may exist in CFRP structures, such as fiber breaks, voiding, cracking, delaminating and interfacial debonding. These defects are often invisible at the part surface, but have negative effects on the strength and stiffness of CFRP products. Therefore, defect detection in CFRP structures is critical to product performance and safety. Generally, defect detection methods can be categorized as destructive and non-destructive. Due to the high cost of CFRP materials, non-destructive testing (NDT) methods including thermography [1e4], ultrasonic inspection [5e8], X-ray inspection [9e11], shearography [11,12], electronic speckle pattern interferometry [13,14], etc. are commonly applied. Among these methods, thermography is attractive for its low cost, easy operation and wide scanning scope. Thermography is a surface radiation measurement technique, which uses infrared camera to measure surface temperature of
* Corresponding author. Tel.: þ886 3 5713690; fax: þ886 3 5715408. E-mail addresses: [email protected] (K. Zheng), [email protected] (Y. Yao). http://dx.doi.org/10.1016/j.compositesb.2015.04.049 1359-8368/© 2015 Elsevier Ltd. All rights reserved.
target specimen and constructs thermal images for analysis. The thermographic NDT techniques can be divided into two categories: active thermography and passive thermography. The major difference between these two lies in the utilization of external energy source. In active thermography, an external energy source is required to produce a thermal contrast between the inspected parts and the surroundings. In contrast, no such external energy is supplied in passive thermography. As a result, active thermography are more robust to the influence of ambient temperature, and more widely used in defect detection of fiber reinforced polymers (FRP) [15,16]. In the past one or two decades, the use of pulsed thermography (PT), one of the most popular methods in active thermography, has increased dramatically for NDT of composite materials [17]. A major reason for this popularity is the quickness of the inspection relying on a thermal stimulation pulse [18]. In PT, the surface of a tested part is heated with a brief pulse of light usually from a high power source, e.g. photographic flashes. Then, the heat flux on the surface tends to diffuse into the material. The time-dependent surface temperature response is captured as a series of thermal images by an infrared camera connected to a computer. The temperature contrast between the defective and non-defective regions enables defect detection based on thermographic data. However, thermal images usually involve significant measurement noise and non-uniform backgrounds caused by uneven heating. As a result, it is difficult to recognize the defective regions
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clearly by naked eyes. Hence, different types of thermographic image analysis methods have been proposed for signal enhancement, e.g. thermographic signal reconstruction (TSR) [19,20], differential absolute contrast (DAC) [21,22], pulsed phase thermography (PPT) [23,24], principal component thermography (PCT) [25], etc., where TSR is frequently used for its performance in data compressing and noise reduction. Based on the Fourier diffusion equation, TSR applies polynomial filters to eliminate the noise contained in thermographic data. In addition, TSR can also use derivatives to further improve its defect detection ability. The major shortcomings of TSR are of the following two aspects. First, TSR only applies polynomial filters in time dimension to reduce noise, while the abundant spatial information contained in thermal images is not exploited. Therefore, the effectiveness of noise reduction is still not good enough. Especially, if time derivative is performed, the noise will be further amplified. Second, TSR cannot handle the non-uniform backgrounds well. To get around these problems, the statistical techniques of penalized least squares are adopted in this paper to better utilize the spatial information. Originally proposed by Whittaker [26], penalized least squares smoothers have become promising methods in the field of chemical data analysis [27], the ideology of which is to divide a noisy series into two parts, i.e. the signal and the noise, by solving a penalized optimization problem. Recently, Zhang et al. proposed an iteratively reweighted procedure based on penalized least squares to correct the baseline contained in chemical signals [28]. The penalized least squares smoothers have following attractive properties. (1) The programming is easy, especially in a MATLAB environment. (2) The boundaries of the data can be treated well in an automatic way. (3) Penalized least squares handles missing data. (4) The smoothness of the reconstructed signal obtained from decomposition can be controlled by tuning a single parameter. (5) The algorithms are efficient. Although with different dimensions, both thermographic data and chemical data consist of three critical elements: signals, backgrounds and noise. Inspired by such similarity, the penalized least squares methods are adopted in this paper to decompose the TSRtreated thermographic data and to extract the reconstructed images with least influence of non-uniform background and noise. By doing so, the defect detection efficiency of pulsed thermography can be significantly enhanced. The paper is organized as follows. In Section 2, the principle of pulsed thermography is briefly introduced. Then, the methodologies are presented in Section 3, including TSR, noise reduction with penalized least squares, and non-uniform background elimination. In Section 4, the experiment results show the effectiveness of the proposed method comparing to the conventional TSR method. Finally, conclusions are given in the Section 5.
2. Pulsed thermography The problem of heat diffusion through a solid specimen can be described by Fourier's law of heat diffusion:
1 vT ¼ 0: V2 T a vt
Q z2 ; Tðz; tÞ ¼ T0 þ pffiffiffiffiffi exp 4at e pt
where Q is the energy absorbed pffiffiffiffiffiffiffiffi by the specimen surface, T0 is the initial temperature, e ¼ krc is the effusivity, and T(z,t) is the material temperature at depth z and time t. In pulsed thermography, only the temperature of specimen surface is measurable, i.e. z ¼ 0. Accordingly, (2) can be simplified as:
Q TðtÞ ¼ T0 þ pffiffiffiffiffi : e pt
Here, V is the three-dimensional del operator, T is the temperature in the specimen, t is the time index, a ¼ k/(rc) is the material thermal diffusivity, k is thermal conductivity, r is the material density, and c is heat capacity. Under the circumstances of pulsed heating and thermal insulation, the one-dimensional solution of (1) in a semi-infinite homogeneous and isotropic solid can be expressed as follows [29].
(3)
After pulsed heating, the thermal front travels through the specimen as time elapses, while the surface temperature decreases uniformly over time if there is no defect. On the contrary, subsurface discontinuities caused by defects lead to resistances to heat flow, resulting in certain temperature patterns at the surface. Consequently, the abnormalities can be identified by the temperature contrast between defective and non-defective regions. However, as discussed in the introduction section, the useful information in thermographic data often hides behind measurement noise and non-uniform backgrounds caused by uneven heating. Therefore, effective processing methods are necessary for thermographic data analysis. 3. Methodologies To fully making use of both the temporal and spatial information in thermographic data analysis, the proposed method can be divided into two stages. In the first stage, the TSR algorithm is applied to the thermographic data, which reduces the noise using a time-directional filter. Then, in the second stage, penalized least squares algorithms are adopted to extract the reconstructed thermal images by further reducing noise and eliminating non-uniform backgrounds. In this stage, spatial information contained in each thermal image is utilized. 3.1. Thermographic signal reconstruction TSR assumes that the decay pattern of the surface temperature profile of a non-defective pixel can be described by (3) whose logarithmic form is as follows:
Q lnðDTÞ ¼ ln pffiffiffi 0:5lnðtÞ; e p
(4)
where DT ¼ T(t)T0. Although (4) is concise, it is only an approximation of the solution for the 3-D Fourier diffusion equation. In practice, the profile of the logarithmic thermographic data may diverge from the ideal linear equation for several reasons, such as poor camera calibration, reflection artifacts, convection and so on. Thus, in TSR, a polynomial function with m degree is used to fit the relationship between ln(DT) and ln(t), i.e.
lnðDTÞ ¼ a0 þ a1 ðln tÞ þ a2 ðln tÞ2 þ … þ am ðln tÞm : (1)
(2)
(5)
In a CFRP specimen, the thermal decay profiles belonging to intact regions behave approximately linear, while those of defective regions usually have different patterns. In order to make a good balance between data fitting and noise reduction, the value of m should be set properly. A too large value of m may cause overfitting, while a too small value may lead to model mismatch. Hence, it is suggested to set m as 4 or 5 [1]. In the following of this paper, the value of m is specified as 4. After acquiring the regression coefficients, the entire temperature profile can be compressed into
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m þ 1 coefficients, and the smoothed thermographic data can be reconstructed according to (5). Moreover, as stated in Ref. [19], differentiation can be conducted along time direction to further highlight the contrast between defective and non-defective regions. The first-order derivatives of the reconstructed data reflect the velocity of temperature decay, while the second-order time derivatives reflect the change rate of the velocity. The higher order derivatives are rarely adopted due to lack of physical interpretation. In addition, as observed in (4), the effects of uneven heating only appear in the constant term on the right side of the equation. Therefore, in theory, taking derivatives can remove the non-uniform backgrounds contained in thermographic data. However, due to mismatch between theoretical assumptions and practice, the background information may propagate to the high-order terms in (5). Meanwhile, the a0 term in (5) may involve a part of information related to defect detection as shown in the experiment section of this paper. Such information is lost in the derivative data. Therefore, in the proposed procedure, only the reconstructed thermographic data without derivation are subjected to the following steps.
3.2. Further noise reduction using penalized least squares smoothers After conducting TSR, the spatial information of each reconstructed thermal image is utilized for further noise reduction. To achieve this goal, penalized least squares smoothers are adopted. Since the data structure of each thermal image is two-dimensional, the smoothing is conducted sequentially to each row or column of a thermal image. For each row or column in the TSR-reconstructed image, the original data series x may be still too noisy. The target here is to find a smooth series z to fit x. During fitting, there are two issues to be considered: (1) roughness of z and (2) fidelity to x [27]. Differences between two successive data points, Dzi ¼ zi zi1, can be used to express roughness of the smoothed series. Thus, the overall roughness of z can be measured by summing the squares of the differences:
R1 ¼
n X
ðzi zi1 Þ2 ¼
i¼2
n X
(6)
1 1 « 0
0 1 « 0
/ / 1 /
0 0 « 1
3 0 07 7; «5 1
ðzi xi Þ2 ¼ kx zk2 :
(7)
(8)
i¼1
Usually, low roughness of z and high fidelity to x are desired. However, these two goals are conflict to each other. A smoother z deviates more from x. Hence, a balance should be made between fidelity and roughness. The following equation describes the balanced combination of both targets:
Q1 ¼ F1 þ l1 R1 ¼ kx zk2 þ l1 kDzk2 ;
(10)
Based on (10), z can be solved:
1 0 z ¼ I þ l1 D D x;
(11)
where I is the identity matrix. The noise is then reduced by replacing x with z in the reconstructed thermal images. 3.3. Non-uniform background elimination using adaptive iteratively reweighted penalized least squares After removing noise, the smoothed thermographic data are composed of signals (i.e. informative peaks) and non-uniform backgrounds (i.e. two-dimensional baselines), where the background information is not useful in defect detection and should be eliminated. Similar to the smoothing procedure, the background elimination algorithm is applied sequentially to each row or column of the smoothed thermal images. Here, the adaptive iteratively reweighted penalized least squares algorithm [28] is adopted. For each row or column of a smoothed thermal image, the partial least squares smoother can be revised to extract the nonuniform background y from the smoothed data series z. Fidelity of y to z is defined as:
F2 ¼
n X
0
wi ðzi yi Þ2 ¼ ðz yÞ Wðz yÞ;
(12)
i¼1
where the weight matrix W is diagonal with wi as its i-th diagonal element. At the positions corresponding to the peak segments of z, wi is set to zero. Accordingly, the objective function for background elimination becomes:
Q2 ¼ ðz yÞ Wðz yÞ þ l2 kDyk2 :
(13)
Thus, the background y can be calculated by minimizing Q2:
and kak indicates the Euclidean 2-norm of the vector a. The smaller the value of R1, the lower the roughness is. The fidelity can be quantified by the difference between z and x: n X
0 vQ1 0 ¼ 2ðz xÞ þ 2l1 D Dz ¼ 0: vz
i¼2
1 6 0 D¼6 4 « 0
F1 ¼
where l1 is a parameter adjusting the degree of importance of the two goals. Thus, the problem of smoothing is transformed to a penalized least squares problem. In order to minimize Q1, its partial derivative vector should be set to zeros, i.e.
0
Dz2i ¼ kDzk2 :
Here, n is the length of the series, D is a matrix with n1 rows and n columns:
2
353
(9)
1 0 y ¼ W þ l2 D D Wz:
(14)
Since it is difficult to identify the peak segments before background elimination, an adaptive iteratively reweighted procedure can be used to adjust the parameters in W [28]. In each iteration of the adaptive iteratively reweighted procedure, a weighted penalized least squares problem described in below is solved:
2 0 Q2k ¼ z yk W k z yk þ l2 Dyk ;
(15)
where k is the index of iteration. The initial value of W is set as W0 ¼ I, which means that the diagonal elements in W0 are all 1. In the k-th iteration, wki can be updated as:
wki
¼
8 > > > <0
zi yk1 i
kðzi yk1 Þ i > > > : e kdk k
zi < yk1 i
;
(16)
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Fig. 1. Preparation of a CFRP specimen with defects. (a) Simulating the defects using six Teflon square strips and a piece of insulating tape. (b) The specimen before resin infiltration. (c) The specimen after resin infiltration.
corresponding point yk1 in the background candidate yk1, such i data point is considered as part of an informative peak, i.e. signal. Therefore, its weight is set to zero, so that the point will be ignored in the next iteration of background fitting. By doing so, the recognized signal does not affect the calculation of the fidelity F2 of the background y to the raw data z. Hence, the background can be identified in a gradual and automatic way. Such iteration can be terminated either when the maximum iteration times is reached or when the termination criterion is achieved. The termination criterion can be defined as:
k d < 0:001kyk:
After estimating y, the signal less affected by either noise or background can be obtained by z y.
Fig. 2. Illustration of the defect positions in the CFRP specimen.
where yk1 is the i-th data point in yk1, and dk consists of negative i elements of the differences between z and yk1, i.e.
o n dk ¼ z yk1 :
(18)
4. Experiment and results 4.1. Experiment description
(17)
In the above equations, yk1 is a candidate of the background fitted in the (k1)-th iteration. If the value of zi is larger than the
In the experiment, the CFRP specimen with size of 12 cm 9.5 cm was manufactured by vacuum assisted resin transfer molding (VARTM) technique [30], which was strengthened
Fig. 3. Raw thermal images of the CFRP specimen collected at the 1st (a), 2nd (b), 3rd (c) and 4th (d) seconds after pulsed heating.
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355
Fig. 4. Thermal images corresponding to the 1st (a), 2nd (b), 3rd (c) and 4th (d) seconds after pulsed heating, which were treated by TSR.
with multiple layers of carbon fiber sheets. The thickness of each fiber sheet was 0.26 cm. To simulate the defects, six Teflon square strips with different areas were inserted into the fiber sheets before executing VARTM. Additionally, another defective rectangle with size of 1.4 cm 0.6 cm was also constructed using a piece of insulating tape. Therefore, the CFRP specimen contained totally seven defective regions. In the photo shown in Fig. 1(a), the Teflon strips are in light color, while the color of the defect caused by the insulating tape is dark. The four defects on the left-hand side of the specimen were covered by a single layer of carbon fiber sheet, while the three defects on the right were under two layers of sheets (Fig. 1(b)). Therefore, these defects were at different depths, and were invisible by naked eyes after resin infiltration as shown in Fig. 1(c). Fig. 2 illustrates the position of each defective region. In this figure, Region A at the top left corner is the defect caused by
insulating tape. Regions B, C and D are the square defects with different sizes but all located under a single layer of carbon fiber sheet, the side lengths of which are 1.6 cm, 0.8 cm and 0.4 cm, respectively. Similarly, Regions E, F and G are all under two layers of carbon fiber sheets, with side lengths of 1.6 cm, 0.8 cm and 0.4 cm, respectively. For defect detection, pulsed thermography was performed. After the specimen was heated by a thermal pulse generated from a flash, an NEC infrared camera (type TAS-G100EXD) with a resolution of 320 240 pixels was used to collect the thermographic data, generating a series of thermal images. Then, image processing algorithms including TSR, noise reduction using penalized least squares smoothers, and background elimination were conducted as described in Section 3. All the algorithms were compiled and run on Matlab 2014a.
Fig. 5. The first derivative of the reconstructed data correspond to 1 s after pulsed heating without (a) and with (b) penalized least squares smoothing, and the second derivative of the reconstructed data correspond to 1.6 s after pulsed heating without (c) and with (d) penalized least squares smoothing.
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In order to evaluate the effectiveness of these algorithms, the index of signal-to-noise ratio (SNR) was adopted. Such index has been widely used in the comparison of pulsed thermographic data processing methods [1], which is defined in the following way:
SNR ¼
Mdef Min ; sin
(19)
where Mdef is the average signal in defective regions, Min is the average signal in intact regions, and sin is as the standard deviation of the signal in intact regions. Such index reflects thermal contrast between defective and non-defective areas, which can be increased by effective noise reduction (i.e. decreasing sin) and background elimination. Fig. 6. An image reconstructed using the constant terms a0 in the TSR fitted polynomials.
4.2. Results and discussions Fig. 3 shows the raw thermal images collected at the 1st, 2nd, 3rd and 4th seconds after pulsed heating. As observed in
Fig. 7. Thermal images corresponding to the 1st (a), 2nd (b), 3rd (c) and 4th (d) seconds after pulsed heating, which were treated by TSR and penalized least squares smoothing.
Fig. 8. Thermal images corresponding to the 1st (a), 2nd (b), 3rd (c) and 4th (d) seconds after pulsed heating, which were treated by TSR, penalized least squares smoothing and background elimination.
K. Zheng et al. / Composites Part B 79 (2015) 351e358
this figure, sub-plots (a) and (b) only provide obscure indications of the shallow defects, i.e. defects A, B, C and D, while almost all the information in sub-plots (c) and (d) is masked by noise, due to the low contrast between defective and nondefective areas in the raw thermal images. Furthermore, it can be noticed that the non-uniform backgrounds are very significant especially in the horizontal direction, which was caused by uneven heating. For better identification of the defects, TSR was executed to enhance the signal and reduce the noise, during which the degree of the polynomial function fitting the relationship between ln(DT) and ln(t) at each pixel was fixed to be 4. Fig. 4 shows the reconstructed thermal images after TSR. Comparing to Fig. 3, all the thermal images after TSR better revealed the defect information. Especially, the performance of the images corresponding to the 3rd and 4th seconds after pulsed heating was improved significantly because of noise reduction. The first and second-order derivatives of the reconstructed data formed the images in Fig. 5(a) and Fig. 5(c). Please note that only the images with the highest SNR values after differentiation are plotted. Fig. 5(b) and (d) are the further denoised version of Fig. 5(a) and (c) after penalized least squares smoothing. Perhaps a little surprisingly, the reconstructed thermal images after differentiation performed worse than the TSR-treated images without differentiation. The reasons are of two aspects. First, the differentiation increases the effects of noise. Second, during differentiation, the constant terms a0 in the polynomials are removed. However, as shown in Fig. 6, the a0 terms may contain important information of defective regions. Furthermore, as observed in Fig. 5, the differentiations cannot remove the non-uniform backgrounds contained in thermal images entirely. In the following processing steps, the TSR-treated images without differentiation were utilized. Before background elimination, the penalized least squares smoothers were applied for further noise reduction. During smoothing, an overlarge value of l1 may cause over-smoothness that is adverse to the detection of small defects. In this experiment, the value of l1 was uniformly selected to be 1. The images after smoothing are shown in Fig. 7. Compared to Fig. 4, the noise contained in each image is reduced in large extent, while the defective areas become much easier to identify. Nevertheless, the non-uniform backgrounds still exist. Especially, the effects of backgrounds make the region in the top right corner more like a defect than the real defective region E. Therefore, background elimination is necessary. To achieve this, adaptive iteratively reweighted penalized least squares introduced in Section 3.3 was adopted, where the values of l2 were set to be 50 and 200 for the horizontal and vertical direction in each image, respectively. The results are shown in Fig. 8. In each sub-plot, the image background became much more uniform after conducting adaptive iteratively reweighted penalized least squares. In especial, the significant non-uniform backgrounds in the top right corner of each image are not found in Fig. 8. All the seven defective regions, including both the swallow and deep defects, can be identified clearly in the processed images. For further investigating the effectiveness of different thermal image processing methods, the SNR values of each image under different treatments were computed and plotted in Fig. 9. Compared to raw images without any pretreatment, all the three processing methods can increase the SNR values. Meanwhile, in most of the sub-plots, the proposed processing method involving TSR, penalized least squares smoothing, and background elimination significantly outperformed other methods, highlighting the necessity of utilizing the spatial information in thermal image processing.
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5. Conclusions In this paper, the concepts of penalized least squares are introduced to the field of pulsed thermographic data processing for defect detection in CFRP structures. By doing so, the spatial information contained in each thermal image can be fully utilized. As a result, the defect detection efficiency is improved comparing to the conventional TSR method. The effectiveness of the developed method was verified with the experiment results. Although proposed for pulsed thermography of CFRP, the method developed in this paper has the potential to be extended to other NDT applications using the thermography. For example, literature show that the active thermography technique has been adopted to detect debonding defects in the FRP-concrete systems [31], where the detection results also suffer from noise and nonuniform backgrounds contained in thermal images. Therefore, it will be promising to extend the utilization of the proposed method to such applications.
Fig. 9. SNR values of the thermal images with different types of processing for each defective region: (a) Region A, (b) Region B, (c) Region C, (d) Region D, (e) Region E, (f) Region F, (g) Region G, and (h) all the defective regions. (Red curve: No pretreatment; blue curve: TSR; green curve: TSR þ penalized least squares smoothing; black curve: TSR þ penalized least squares smoothing þ background elimination).(For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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In addition, despite that this paper focuses on the shape recognition of defects, the defect depth information may be explored by finding the time point when the deviation between the thermal responses of the defective region and the intact region begins. There is a relationship between this time point and the defect depth as discussed in the literature [32]. Such issue will be studied in our future research. Acknowledgments This work was supported in part by Ministry of Science and Technology, ROC under Grant No. MOST104-3113-E-007-004-CC2. References [1] Ibarra-Castanedo C, Piau J-M, Guilbert S, Avdelidis NP, Genest M, Bendada A, et al. Comparative study of active thermography techniques for the nondestructive evaluation of honeycomb structures. Res Nondestruct Eval 2009;20: 1e31. [2] Pickering S, Almond D. Matched excitation energy comparison of the pulse and lock-in thermography NDE techniques. NDT E Int 2008;41:501e9. [3] Schmutzler H, Alder M, Kosmann N, Wittich H, Schulte K. Degradation monitoring of impact damaged carbon fibre reinforced polymers under fatigue loading with pulse phase thermography. Compos Part B Eng 2014;59: 221e9. €llig M, Kunert M. Char[4] Maierhofer C, Myrach P, Reischel M, Steinfurth H, Ro acterizing damage in CFRP structures using flash thermography in reflection and transmission configurations. Compos Part B Eng 2014;57:35e46. [5] Stone DEW, Clarke B. Ultrasonic attenuation as a measure of void content in carbon-fibre reinforced plastics. Non Destr Test 1975;8:137e45. [6] Scarponi C, Briotti G. Ultrasonic technique for the evaluation of delaminations on CFRP, GFRP, KFRP composite materials. Compos Part B Eng 2000;31: 237e43. [7] Raisutis R, Ka zys R, Zukauskas E, Ma zeika L. Ultrasonic air-coupled testing of square-shape CFRP composite rods by means of guided waves. NDT E Int 2011;44:645e54. [8] Fahim AA, Gallego R, Bochud N, Rus G. Model-based damage reconstruction in composites from ultrasound transmission. Compos Part B Eng 2013;45: 50e62. [9] Hanke R, Fuchs T, Uhlmann N. X-ray based methods for non-destructive testing and material characterization. Nucl Instrum Methods Phys Res Sect A Accel Spectrom Detect Assoc Equip 2008;591:14e8. € gl S, Bichler S, Lemesch G, Ramsauer F, Ladsta €tter W, et al. New [10] Lenko D, Schlo approaches towards the investigation on defects and failure mechanisms of insulating composites used in high voltage applications. Compos Part B Eng 2014;58:83e90. pez-Arraiza A, Lizaranzu M, Aurrekoetxea J. [11] Amenabar I, Mendikute A, Lo Comparison and analysis of non-destructive testing techniques suitable for delamination inspection in wind turbine blades. Compos Part B Eng 2011;42: 1298e305.
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