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Pulsed inductive thermal wave radar (PI-TWR) using cross correlation matched filtering in eddy current thermography
Infrared Physics & Technology 71 (2015) 469–474
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Infrared Physics & Technology journal homepage: www.elsevier.com/locate/infrared
Pulsed inductive thermal wave radar (PI-TWR) using cross correlation matched filtering in eddy current thermography Ruizhen Yang a,⇑, Yunze He b,⇑ a b
Department of Civil and Architecture Engineering, Changsha University, Changsha 410022, PR China College of Mechatronics Engineering and Automation, National University of Defense Technology, Changsha 410073, PR China
h i g h l i g h t s Pulsed inductive thermal wave radar is proposed through matched filtering. Cross correlation (CC) phase and CC peak phase delay are used as features. Dynamic range and resolution for detection depth have a significant improvement. Surface emissivity variation can be reduced by the proposed method. Detectability of subsurface defects and inside delamination can be improved.
a r t i c l e
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Article history: Received 20 April 2015 Available online 14 June 2015 Keywords: Eddy current pulsed thermography Thermal wave radar Cross correlation Nondestructive testing Carbon fibre reinforced polymer
a b s t r a c t Major problems in eddy current thermography include the compromise between depth dynamic range and resolution, the influence of surface emissivity variation and the low defect detectability. This paper presents pulsed inductive thermal wave radar (PI-TWR) by introducing the cross correlation (CC) matched-filtering in eddy current pulsed thermography (ECPT). CC phase and CC peak phase delay are used as characteristic features. The proposed method was verified through numerical and experimental studies, where steel sample and carbon fibre reinforced polymer (CFRP) sample were tested under transmission and reflection modes. The results illustrate a significant improvement in the dynamic range, depth resolution, emissivity variation reduction and detectability of subsurface defects and inside delamination for the nondestructive testing applications. Ó 2015 Elsevier B.V. All rights reserved.
1. Introduction Eddy current thermography (ECT), also known as inductive thermography is an emerging active infrared thermography specifically for conductive materials from metal to carbon fibre reinforced plastic (CFRP), which combines the advantages of eddy current testing and IR thermography, such as non-contact, fast and high resolution [1–3]. Just like general thermography [4], it can be applied in terms of pulsed thermography, step heating thermography, lock-in thermography and pulsed phase thermography. Various eddy current thermography methods have been developed, such as thermal-inductive [5], electromagnetic-thermal [6], tone burst eddy current thermography (TBET) [7], and eddy current pulsed thermography (ECPT) [8–10]. They are all focused on the surface-breaking defect evaluation since the used principle is ⇑ Corresponding authors. Tel.: +86 731 84261208 (R. Yang), +86 13467698133 (Y. He). E-mail addresses: [email protected] (R. Yang), [email protected] (Y. He). http://dx.doi.org/10.1016/j.infrared.2015.06.004 1350-4495/Ó 2015 Elsevier B.V. All rights reserved.
based on the eddy current field interruption [11,12], just like eddy current testing [13,14]. In order to improve the dynamic range of detection depth, Yang and He proposed longitudinal heat conduction to qualify and quantify the subsurface defects in steel [15,16]. In addition, He proposed eddy current step heating thermography (ECSHT) to quantify the subsurface defects in steel [17]. Busse et al. proposed eddy current lock-in thermography (ECLT) [18] and the depth dynamic range can be decided by modulated frequency. Also, He proposed eddy current pulsed phase thermography (ECPPT) technique for subsurface defect quantitatively evaluation in steel [19,20] and delamination evaluation in CFRP [21]. The results from ECLT and ECPPT have illustrated that the non-uniform heating effect can be eliminated and defect detectability can be significantly improved through phasegram or phase information. In addition, several signal processing and blind source separation methods, such as principal components analysis (PCA), independent components analysis (ICA), were used to improve the defect detectability [9,22–25]. Nevertheless, the
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dynamic range and resolution for detection depth are still not satisfactory. In photothermal radiometry, Mandelis et al. proposed thermal-wave radar (TWR) combining linear frequency modulated continuous wave excitation and matched-filtering processing based on Hilbert transform to detect human dental demineralization lesions and osteoporotic bone loss [26], which suggests a significant improvement in depth-resolution dynamic range of subsurface defect [27,28]. This approach has been introduced in thermography nondestructive testing. In 2014, Liu used thermal-wave radar imaging (TWRI) for CFRP inspection [29]. Mulaveesala highlights the Hilbert transform-based time domain phase analysis scheme introduced for testing and evaluation of sub-surface defects in a mild steel sample [30]. Also, Mandelis et al. proposed truncated-correlation photothermal coherence tomography (TC-PCT) based on Hilbert transform and matched-filtering, which enabled three-dimensional visualization of subsurface features [31–33]. However, the variable eddy current excitation signals and advanced radar processing methods have not been used in eddy current thermography to solve the discrepancy between dynamic range and depth resolution or to improve the defect detectability. In the in-situ application, the materials under test (MUT) may have oil, coating, or an oxidation layers on their surface, which changes the thermal emissivity significantly and then introduces illusory temperature inhomogeneity and results in false alarms. To remove the influence of surface emissivity variation is vital and several solutions were attempted in previous studies. Firstly, inductive excitation is an emissivity-independent way of sub-surface heating depending on the induction frequency and the electrical properties of MUT, which remove the effect of emissivity variation in heating process. Except for spraying water or paint, Bai proposed a two heat balance states-based normalization method to remove the influence of surface emissivity variation [34]. He proposed inductive pulsed phase thermography (IPPT) technique to reduce the variation of surface emissivity [35]. However, the advanced cross-correlation phase was not investigated in inductive thermography, although the cross correlation phase in thermal-wave radar is a powerful emissivity-normalized parameter [26,28]. In this paper, a powerful pulsed inductive thermal wave radar (PI-TWR) is proposed by introducing the cross correlation matched filtering in eddy current pulsed thermography. Section 2 introduces the basic theory of the proposed method. Sections 3 and 4 provide the simulations and experimental results, respectively, which suggest a significant improvement in the dynamic range, depth resolution, emissivity reduction and defect detectability. Finally, Section 5 addresses the conclusions and future works. 2. Theory 2.1. Time domain feature extraction The principle and diagram of ECPT were shown in detail in previous works [24,25,36]. The excitation signal is a small period of high frequency current. The temperature response captured by IR camera is like a pulse, which can be divided into two phases: heating phase and cooling phase. In conventional ECPT testing, the signal process and feature extraction were carried out in time domain. Different absolute contrast (DAC) is defined as
CðtÞ ¼ sðtÞ refðtÞ
ð1Þ
where s(t) is detected signal, ref(t) is reference signal for a non-defective area. Two features are usually extracted from C(t). One is peak value, which is maximum value of the different
absolute contrast; another is time to peak, which is the time when DAC reaches the peak value. According to thermal wave conduction theory, peak value is proportional to the cube of the defect depth and is damped quickly while time to peak can be used to quantify the defect depth. 2.2. CC based feature extraction The schematic for the proposed method based on cross correlation (CC) matched filtering is shown in Fig. 1. The CC matched filtering is originated from radar sciences in the early 1940s to detect deterministic signals within highly noised channels and to augment range resolution. This methodology localizes the energy of the received signal under a single peak located at a delay time. In order to calculate the CC of two signals ref(t) and s(t), it would be more convenient to use the Fourier transform in frequency domain, as shown in Eq. (2), rather than the time domain formula
CCðsÞ ¼ F 1 fREFðxÞ SðxÞg
ð2Þ
where REF(x) and S(x) are the Fourier transforms of the reference signal, ref(t), and the detected signal, s(t). * and F 1 denote the complex conjugate and inverse Fourier transform operators, respectively. The variable s determines the time delay between two signals ref(t) and s(t). After getting the CC responses for all pixels, two features CC peak amp and CC peak amp delay are extracted. CC peak amp means the peak value of CC, and CC peak amp delay means the time delay when CC reaches the peak value. The amplitude of the CC peak amp strongly depends on the amplitude of the received signal and then emissivity variation. CC peak amp delay is linked to the depth of the signal source. To select a reference signal CCref, the differential CC (DCC) can be calculated easily using differential technique shown in Eq. (3) [37].
DCC ¼ CC CCref
ð3Þ
And then, DCC peak amp and DCC peak amp delay can be also extracted from DCC. DCC peak amp means the peak value of DCC, and DCC peak amp delay means the time delay when DCC reaches the peak value. One can further calculate the CC phase (h) according to Eq. (4)
hðsÞ ¼
F 1 fREFðxÞ SðxÞg F 1 f½isgnðxÞREFðxÞ SðxÞg
ð4Þ
where sgn(x) and i are the signum function and the imaginary unit, respectively. The expression inside the square bracket in the denominator is the Fourier transform of the quadrature reference signal, obtained through the Hilbert transform and then Fourier transforms as shown in Fig. 1. The significance of CC phase is that the emissivity is cancelled out and as a result the CC phase is an emissivity normalized quantity [26]. Two features CC peak phase and CC peak phase delay are extracted from the response of CC phase. CC peak phase means the peak value of CC phase and CC peak phase delay means the time delay when CC phase reaches the peak value. Just like DCC, the differential CC phase (DCC phase), can be calculated according to Eq. (5)
Dh ¼ h href
ð5Þ
where href is reference CC phase signal. Correspondingly, DCC peak phase and DCC peak phase delay can be also extracted from DCC phase. 3. Simulation results for depth quantification Numerical studies were conducted using COMSOL Multiphysics 3.5a. The 3D Finite Element Modelling (FEM) consists of specimen (steel), coil and subsurface defect (air’s parameters), as shown in
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Fig. 1. Signal processing block diagram for the proposed method.
Table 1 Parameters of FEM model.
Fig. 2. FEM model.
Fig. 2. Table 1 shows the material parameters which were used in the simulations [15,20]. According to coordinate system, the specimen size was constant as 150 60 10 mm3. Subsurface defects were constructed by 9 rectangular blocks with the same length (60 mm) and width V (6 mm) but different depths d from 1 to 5 mm in the step of 0.5 mm. Accordingly, their size-to-depth ratio v = V/d was respectively 6–1.2. The coil was placed above the defect-free side. The distance between coil and sample was 1 mm. The excitation frequency and current were set as 256 kHz and 380 A. The heating period was set as 0.1 s and the recorded time after inductive heating was set as 2.65 s. Then, the temperature responses s(t) on the surface (defect-free side) of the specimen was recorded. The different absolute contrast C(t) responses for all defects were calculated using Eq. (1). Peak value and time to peak were extracted and their dependences on depths are shown in Fig. 3(a). It is noticed that time to peak has an approximate linear relationship with depth till 5 mm, but, the depth resolution is not satisfactory. For example, there are the same time to peak for depth 2.5 and 3 mm, the same time to peak for depth 3.5 and 4 mm, and time to peak for depth 4.5 and 5 mm. The responses of DCC and DCC phase for these defects were calculated using Eqs. (2)–(5). Both DCC peak amp and DCC peak amp delay were extracted from DCC response. These dependences on defects’ depths are shown in Fig. 3(b). DCC peak amp is similar with peak value and the defect with 5 mm depth is not detectable due to its quick damping. In contrast, DCC peak amp delay has a monotonous increase with depth till 5 mm. Not like time to peak, there is no equal value between adjacent depths. This means the enhanced depth resolution for DCC peak amp delay at an enhanced dynamic depth range till 5 mm. The dependences of DCC peak
Parameters
Air
Steel
Conductivity (S/m) Relative Permeability Density (kg/m3) Heat capacity (J/(kg K)) Thermal conductivity (W/(m k)) Thermal diffusivity (m2/s)
0 1 1.205 1.005e3 0.0257 2.12e5
4.03e6 100 7850 475 44.5 1.1934e5
phase and DCC peak phase delay are shown in Fig. 3(c). The similar phenomenon can be observed. DCC peak phase delay has a monotonous linear increase with depth till 5 mm. This means the enhance depth resolution for DCC peak phase delay. It is concluded that, (1) peak value, DCC peak amp and DCC peak phase is not suitable to size the depth due to quick damping and their dependence on heating energy; (2) DCC peak amp delay, and DCC peak phase delay can be used as the characteristic features to quantify the defect’s depth, which have an optimal depth resolution and depth dynamic range over time to peak. 4. Experimental results 4.1. Experimental system The experimental system of ECPT was developed in previous works [11,12,38]. A precision induction heating device, Easyheat 224 from Cheltenham Induction Heating, Ltd was used for induction heating, with a maximum excitation power of 2.4 kW, a maximum current of 400 Arms and an excitation frequency range of 150–400 kHz. The excitation coil was made of 6.35 mm high-conductivity hollow copper tubing. In order to fit the sample under test, the excitation coil was designed as a rectangular shape in plane. The state-of-the-art infrared camera Flir SC7500 was used to record the temperature change, which is a Stirling cooled camera with a 320 256 array of 1.5–5 lm InSb detectors. The pitch between detectors is 30 lm. And it has a sensitivity of <20 mK, a maximum full frame rate of 383 Hz. The radiation of the object was sampled using software Altair and the unit of radiation was digital level (DL), which was used as the unit of temperature in experimental studies. 4.2. Elimination of surface emissivity variance A steel sample (0.24 45 100 mm3) with a slot of 10 mm length, 2 mm width was prepared, as shown in Fig. 4(a). There are equally spaced shinning and black stripes with 5 mm width on the sample surface. The shinning strips are the polished area, while the black strips are the area sprayed with black painting. They illustrate different emissivity. The emissivity of the black region is about 1, while, the emissivity of the shinning are is about
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Fig. 3. (a) The dependences of peak value and time to peak on defect’s depth; (b) the dependences of DCC peak amp and DCC peak amp delay on defect’s depth; (c) the dependences of DCC peak phase and DCC peak phase delay on defect’s depth.
Fig. 4. (a) The steel sample with a slot and strips, (b) thermogram at 0.1 s, (c) image formed by DCC amp at 0.1 s delay, (d) image by DCC phase at 0.1 s delay, and (e) image by DCC peak phase delay.
0.16. In the experiments, coil was located on the backside of steel while IR camera was placed on the front side, presenting transmission mode [39]. The coil was perpendicular to the slot and across the slot centre. Only one edge of the rectangular coil was used to stimulate eddy current in the sample. The heating duration was set as 0.1 s and the cooling time after heating was 1.9 s. The sampling frequency was 383 Hz. Fig. 4(b) shows the original thermogram at 0.1 s. During inductive thermography testing, when an eddy current encounters a discontinuity, e.g. a slot or a notch, they are forced to divert, leading to areas of increased and decreased eddy current density resulting in relatively hotter and cooler areas due to Joule heating. However, due to the high emissivity of the black area, there is no obvious high temperature region around the slot tips. The responses of DCC and DCC phase for the tested area were calculated. Fig. 4(c) shows the image formed by DCC amp at 0.1 s delay. The similar phenomenon with Fig. 4(b) can be observed. Fig. 4(d) shows the image formed by DCC phase at 0.1 s delay and Fig. 4(e) shows the image formed by DCC peak phase delay. The results are interesting. The temperature difference caused by emissivity variation is totally removed and the temperature characteristic by defect is remarkable. The tip of defect has the highest temperature, whereas the defect side has the lowest temperature. These are in line with the results in previous works [24,40]. To sum up, the surface emissivity variation can be perfectly removed using the CC phase features.
4.3. Improvement of subsurface defect detection A steel sample providing three subsurface defects was tested. As shown in Fig. 5(a), the defects have the same width (6 mm) but different depths (1, 2, and 4 mm, respectively). Their size-to-depth ratio v is respectively 6, 3, and 1.5. During the experiments, both coil and IR camera were located on the back side of sample, presenting reflection mode. The heating time was set as 0.1 s and the whole record time is 2 s. Three defects were tested individually
under the same conditions. Fig. 5(b) shows the thermograms at 0.1 s, which is composed by three thermograms for defects. The subsurface defects are marked by three dashed boxes. It is noticeable that only shallowest defect with 1 mm depth lead to hot spots along the coil. Fig. 5(c) shows the image formed by DCC phase at 1 s delay and Fig. 5(d) shows the image by DCC peak phase delay. Comparing experimental results in Fig. 5, it is noticed that both DCC phase at 1 s delay and DCC peak phase delay are better than the original thermograms to identify the subsurface defects although the 4 mm depth defect with size-to-depth ratio smaller than 2 is still hardly detectable. This illustrates that the proposed method has a significant improvement in defect detectability for subsurface defects.
4.4. Improvement of delamination detectability in CFRP The CFRP sample with lateral dimension 300 10 mm2 was tested. Several man-made delaminations were manufactured by inserting a polytetrafluoroethylene film between fibre layers. One delamination with 100 mm2 lateral size, shown in Fig. 6(a) was tested. The distances of delamination to front side and back side are 0.5 mm and 2.5 mm, respectively. In the experiment, coil was located on the backside while IR camera was placed on the front side, presenting transmission mode. The heating time is 200 ms followed by 800 ms recording time. Fig. 6(b) and (c) shows the thermograms at 25 ms and 500 ms, respectively. The delamination area is marked by a 1red dashed box. Clearly in Fig. 6(b), the fibre woven structure can be observed from the hot and dark patterns. In detail, the carbon fibre is highlighted, because the EC directly heat the carbon fibre. In Fig. 6(c), as the heat diffuses laterally, the carbon fibre structure is blurred and a dark area appears. However, the delamination is hardly detectable. Fig. 6(d) shows the image by 1 For interpretation of color in ‘Fig. 6’, the reader is referred to the web version of this article.
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Fig. 5. (a) The steel sample with subsurface defects; (b) thermogram at 0.1 s; (c) image by DCC phase at 0.1 s delay; and (d) image by DCC peak phase delay.
Fig. 6. (a) Photo of CFRP with a delamination inside; (b) thermogram at 25 ms; (c) thermogram at 500 ms; (d) image by DCC phase at 0.6 s delay; and (e) image by DCC peak phase delay.
DCC phase at 0.6 s delay. The temperature difference caused by carbon structure is removed and the temperature characteristic by defect is remarkable. Fig. 6(e) shows the image by DCC peak phase delay. The delamination area is identified except the area on its left side. This illustrates that the new proposed method has a significant improvement in defect detectability for inside delamination.
5. Conclusions This paper presents pulsed inductive thermal wave radar (PI-TWR) by introducing the cross correlation matched-filtering in eddy current pulsed thermography (ECPT). Simulation results demonstrate that the proposed method have an optimal depth resolution and dynamic range for detection depth over conventional time domain feature. Experimental studies, where steel sample and CFRP sample were tested under transmission and reflection modes, illustrate that the proposed method has a significant improvement in the emissivity variation reduction and defect detectability for subsurface defects and inside delamination. The
future works include defect depth quantification, tomography for specific depth, and comparison studies with frequency domain features. Conflict of interest The authors declare that there is no conflict of interests regarding the publication of this article. Acknowledgements The work was supported by National Natural Science Foundation of China (Grant No. 51408071). The authors would like to thank Professor Gui Yun Tian’s guide and lead in the research and career. References [1] A. Yin, B. Gao, G.Y. Tian, W.L. Woo, K. Li, Physical interpretation and separation of eddy current pulsed thermography, J. Appl. Phys. 113 (2013) 064101.
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[2] B. Gao, A. Yin, Y. He, Inductive Thermography Pattern Separation, LAP Lambert Academic Publishing, Saarbrücken, Germany, 2014. [3] L. Cheng, G.Y. Tian, Transient thermal behavior of eddy-current pulsed thermography for nondestructive evaluation of composites, IEEE Trans. Instrum. Meas. 62 (2013) 1215–1222. [4] X.P. Maldague, Theory and Practice of Infrared Technology for Nondestructive Testing, John Wiley Interscience, New York, 2001. [5] B. Oswald-Tranta, Thermo-inductive crack detection, Nondestruct. Test. Eval. 22 (2007) 137–153. [6] N. Tsopelas, N.J. Siakavellas, Experimental evaluation of electromagneticthermal non-destructive inspection by eddy current thermography in square aluminum plates, NDT and E Int. 44 (2011) 609–620. [7] N. Biju, N. Ganesan, C.V. Krishnamurthy, K. Balasubramaniam, Simultaneous estimation of electrical and thermal properties of isotropic material from the Tone-Burst Eddy Current Thermography (TBET) time–temperature data, IEEE Trans. Magn. 47 (2011) 2213–2219. [8] L. Cheng, G. Tian, Surface crack detection for Carbon Fibre Reinforced Plastic (CFRP) materials using pulsed eddy current thermography, IEEE Sens. J. 11 (2011) 3261–3268. [9] M. Pan, Y. He, G.Y. Tian, D. Chen, F. Luo, Defect characterisation using pulsed eddy current thermography under transmission mode and NDT applications, NDT and E Int. 52 (2012) 28–36. [10] I.Z. Abidin, G.Y. Tian, J. Wilson, S. Yang, D. Almond, Quantitative evaluation of angular defects by pulsed eddy current thermography, NDT and E Int. 43 (2010) 537–546. [11] R. Yang, Y. He, B. Gao, G.Y. Tian, J. Peng, Lateral heat conduction based eddy current thermography for detection of parallel cracks and rail tread oblique cracks, Measurement 66 (2015) 54–61. [12] J. Wilson, G.Y. Tian, I.Z. Abidin, S. Yang, D. Almond, Pulsed eddy current thermography: system development and evaluation, Insight: Non-Destruct. Test. Cond. Monit. 52 (2010) 87–90. [13] Y. He, F. Luo, M. Pan, Defect characterisation based on pulsed eddy current imaging technique, Sens. Actuat. A 164 (2010) 1–7. [14] Y. He, F. Luo, M. Pan, X. Hu, J. Gao, B. Liu, Defect classification based on rectangular pulsed eddy current sensor in different directions, Sens. Actuat. A 157 (2010) 26–31. [15] R. Yang, Y. He, Logarithmic analysis of eddy current thermography based on longitudinal heat conduction for subsurface defect evaluation, Infrared Phys. Technol. 67 (2014) 467–472. [16] Y. He, M. Pan, F. Luo, Defect characterisation based on heat diffusion using induction thermography testing, Rev. Sci. Instrum. 83 (2012) 104702. [17] Y. He, M. Pan, D. Chen, G.Y. Tian, H. Zhang, Eddy current step heating thermography for quantitatively evaluation, Appl. Phys. Lett. 103 (2013) 194101. [18] G. Riegert, A. Gleiter, G. Busse, Potential and limitation of eddy current lockinthermography, in: Thermosense XXVIII, SPIE, Orlando, 2006. [19] Y. He, G.Y. Tian, M. Pan, D. Chen, Eddy current pulsed phase thermography and feature extraction, Appl. Phys. Lett. 103 (2013) 084104. [20] Y. He, M. Pan, G.Y. Tian, D. Chen, Y. Tang, H. Zhang, Eddy current pulsed phase thermography for subsurface defect quantitatively evaluation, Appl. Phys. Lett. 103 (2013) 144108. [21] R. Yang, Y. He, Eddy current pulsed phase thermography considering volumetric induction heating for delamination evaluation in carbon fiber reinforced polymers, Appl. Phys. Lett. (2015) (revised). [22] B. Gao, L. Bai, W.L. Woo, G. Tian, Thermography pattern analysis and separation, Appl. Phys. Lett. 104 (2014) 251902.
[23] B. Gao, A. Yin, G. Tian, W.L. Woo, Thermography spatial-transient-stage mathematical tensor construction and material property variation track, Int. J. Therm. Sci. 85 (2014) 112–122. [24] B. Gao, L. Bai, W.L. Woo, G.Y. Tian, Y. Cheng, Automatic defect identification of eddy current pulsed thermography using single channel blind source separation, IEEE Trans. Instrum. Meas. 63 (2014) 913–922. [25] L. Cheng, B. Gao, G.Y. Tian, W.L. Woo, Impact damage detection and identification using eddy current pulsed thermography through integration of PCA and ICA, IEEE Sens. J. 14 (2014) 1655–1663. [26] N. Tabatabaei, A. Mandelis, B.T. Amaechi, Thermophotonic radar imaging: an emissivity-normalized modality with advantages over phase lock-in thermography, Appl. Phys. Lett. 98 (2011) 163706. [27] S. Kaiplavil, A. Mandelis, Highly depth-resolved chirped pulse photothermal radar for bone diagnostics, Rev. Sci. Instrum. 82 (2011) 074906. [28] N. Tabatabaei, A. Mandelis, Thermal coherence tomography using match filter binary phase coded diffusion waves, Phys. Rev. Lett. 107 (2011) 165901. [29] J. Gong, J. Liu, L. Qin, Y. Wang, Investigation of carbon fiber reinforced polymer (CFRP) sheet with subsurface defects inspection using thermal-wave radar imaging (TWRI) based on the multi-transform technique, NDT and E Int. 62 (2014) 130–136. [30] V. Arora, J. Siddiqui, R. Mulaveesala, A. Muniyappa, Hilbert transform-based pulse compression approach to infrared thermal wave imaging for sub-surface defect detection in steel material, Insight Non-Destruct. Test. Cond. Monit. 56 (2014) 550–552. [31] S. Kaiplavil, A. Mandelis, Truncated-correlation photothermal coherence tomography for deep subsurface analysis, Nat. Photonics 8 (2014) 635–642. [32] S. Kaiplavil, A. Mandelis, B.T. Amaechi, Truncated-correlation photothermal coherence tomography of artificially demineralized animal bones: two- and three-dimensional markers for mineral loss monitoring, J. Biomed. Opt. 19 (2014). [33] S. Kaiplavil, A. Mandelis, X. Wang, T. Feng, Photothermal tomography for the functional and structural evaluation, and early mineral loss monitoring in bones, Biomed. Opt. Exp. 5 (2014) 2488–2502. [34] L. Bai, S. Tian, Y. Cheng, G.Y. Tian, Y. Chen, K. Chen, Reducing the effect of surface emissivity variation in eddy current pulsed thermography, IEEE Sens. J. 14 (2014) 1137–1142. [35] R. Yang, Y. He, B. Gao, G.Y. Tian, Inductive pulsed phase thermography for reducing or enlarging the effect of surface emissivity variation, Appl. Phys. Lett. 105 (2014) 184103. [36] Y. He, G.Y. Tian, M. Pan, D. Chen, H. Zhang, An investigation into eddy current pulsed thermography for detection of corrosion blister, Corros. Sci. 78 (2014) 1–6. [37] Y. He, G.Y. Tian, H. Zhang, M. Alamin, A. Simm, P. Jackson, Steel corrosion characterisation using pulsed eddy current systems, IEEE Sens. J. 12 (2012) 2113–2120. [38] G. Tian, Y. He, L. Cheng, P. Jackson, Pulsed eddy current thermography for corrosion characterisation, Int. J. Appl. Electromagnet Mech 39 (2012) 269– 276. [39] Y. He, G. Tian, M. Pan, D. Chen, Impact evaluation in carbon fiber reinforced plastic (CFRP) laminates using eddy current pulsed thermography, Compos. Struct. 109 (2014) 1–7. [40] J. Wilson, G.Y. Tian, I.Z. Abidin, S. Yang, D. Almond, Modelling and evaluation of eddy current stimulated thermography, Nondestruct. Test. Eval. 25 (2010) 205–218.
Contents lists available at ScienceDirect
Infrared Physics & Technology journal homepage: www.elsevier.com/locate/infrared
Pulsed inductive thermal wave radar (PI-TWR) using cross correlation matched filtering in eddy current thermography Ruizhen Yang a,⇑, Yunze He b,⇑ a b
Department of Civil and Architecture Engineering, Changsha University, Changsha 410022, PR China College of Mechatronics Engineering and Automation, National University of Defense Technology, Changsha 410073, PR China
h i g h l i g h t s Pulsed inductive thermal wave radar is proposed through matched filtering. Cross correlation (CC) phase and CC peak phase delay are used as features. Dynamic range and resolution for detection depth have a significant improvement. Surface emissivity variation can be reduced by the proposed method. Detectability of subsurface defects and inside delamination can be improved.
a r t i c l e
i n f o
Article history: Received 20 April 2015 Available online 14 June 2015 Keywords: Eddy current pulsed thermography Thermal wave radar Cross correlation Nondestructive testing Carbon fibre reinforced polymer
a b s t r a c t Major problems in eddy current thermography include the compromise between depth dynamic range and resolution, the influence of surface emissivity variation and the low defect detectability. This paper presents pulsed inductive thermal wave radar (PI-TWR) by introducing the cross correlation (CC) matched-filtering in eddy current pulsed thermography (ECPT). CC phase and CC peak phase delay are used as characteristic features. The proposed method was verified through numerical and experimental studies, where steel sample and carbon fibre reinforced polymer (CFRP) sample were tested under transmission and reflection modes. The results illustrate a significant improvement in the dynamic range, depth resolution, emissivity variation reduction and detectability of subsurface defects and inside delamination for the nondestructive testing applications. Ó 2015 Elsevier B.V. All rights reserved.
1. Introduction Eddy current thermography (ECT), also known as inductive thermography is an emerging active infrared thermography specifically for conductive materials from metal to carbon fibre reinforced plastic (CFRP), which combines the advantages of eddy current testing and IR thermography, such as non-contact, fast and high resolution [1–3]. Just like general thermography [4], it can be applied in terms of pulsed thermography, step heating thermography, lock-in thermography and pulsed phase thermography. Various eddy current thermography methods have been developed, such as thermal-inductive [5], electromagnetic-thermal [6], tone burst eddy current thermography (TBET) [7], and eddy current pulsed thermography (ECPT) [8–10]. They are all focused on the surface-breaking defect evaluation since the used principle is ⇑ Corresponding authors. Tel.: +86 731 84261208 (R. Yang), +86 13467698133 (Y. He). E-mail addresses: [email protected] (R. Yang), [email protected] (Y. He). http://dx.doi.org/10.1016/j.infrared.2015.06.004 1350-4495/Ó 2015 Elsevier B.V. All rights reserved.
based on the eddy current field interruption [11,12], just like eddy current testing [13,14]. In order to improve the dynamic range of detection depth, Yang and He proposed longitudinal heat conduction to qualify and quantify the subsurface defects in steel [15,16]. In addition, He proposed eddy current step heating thermography (ECSHT) to quantify the subsurface defects in steel [17]. Busse et al. proposed eddy current lock-in thermography (ECLT) [18] and the depth dynamic range can be decided by modulated frequency. Also, He proposed eddy current pulsed phase thermography (ECPPT) technique for subsurface defect quantitatively evaluation in steel [19,20] and delamination evaluation in CFRP [21]. The results from ECLT and ECPPT have illustrated that the non-uniform heating effect can be eliminated and defect detectability can be significantly improved through phasegram or phase information. In addition, several signal processing and blind source separation methods, such as principal components analysis (PCA), independent components analysis (ICA), were used to improve the defect detectability [9,22–25]. Nevertheless, the
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dynamic range and resolution for detection depth are still not satisfactory. In photothermal radiometry, Mandelis et al. proposed thermal-wave radar (TWR) combining linear frequency modulated continuous wave excitation and matched-filtering processing based on Hilbert transform to detect human dental demineralization lesions and osteoporotic bone loss [26], which suggests a significant improvement in depth-resolution dynamic range of subsurface defect [27,28]. This approach has been introduced in thermography nondestructive testing. In 2014, Liu used thermal-wave radar imaging (TWRI) for CFRP inspection [29]. Mulaveesala highlights the Hilbert transform-based time domain phase analysis scheme introduced for testing and evaluation of sub-surface defects in a mild steel sample [30]. Also, Mandelis et al. proposed truncated-correlation photothermal coherence tomography (TC-PCT) based on Hilbert transform and matched-filtering, which enabled three-dimensional visualization of subsurface features [31–33]. However, the variable eddy current excitation signals and advanced radar processing methods have not been used in eddy current thermography to solve the discrepancy between dynamic range and depth resolution or to improve the defect detectability. In the in-situ application, the materials under test (MUT) may have oil, coating, or an oxidation layers on their surface, which changes the thermal emissivity significantly and then introduces illusory temperature inhomogeneity and results in false alarms. To remove the influence of surface emissivity variation is vital and several solutions were attempted in previous studies. Firstly, inductive excitation is an emissivity-independent way of sub-surface heating depending on the induction frequency and the electrical properties of MUT, which remove the effect of emissivity variation in heating process. Except for spraying water or paint, Bai proposed a two heat balance states-based normalization method to remove the influence of surface emissivity variation [34]. He proposed inductive pulsed phase thermography (IPPT) technique to reduce the variation of surface emissivity [35]. However, the advanced cross-correlation phase was not investigated in inductive thermography, although the cross correlation phase in thermal-wave radar is a powerful emissivity-normalized parameter [26,28]. In this paper, a powerful pulsed inductive thermal wave radar (PI-TWR) is proposed by introducing the cross correlation matched filtering in eddy current pulsed thermography. Section 2 introduces the basic theory of the proposed method. Sections 3 and 4 provide the simulations and experimental results, respectively, which suggest a significant improvement in the dynamic range, depth resolution, emissivity reduction and defect detectability. Finally, Section 5 addresses the conclusions and future works. 2. Theory 2.1. Time domain feature extraction The principle and diagram of ECPT were shown in detail in previous works [24,25,36]. The excitation signal is a small period of high frequency current. The temperature response captured by IR camera is like a pulse, which can be divided into two phases: heating phase and cooling phase. In conventional ECPT testing, the signal process and feature extraction were carried out in time domain. Different absolute contrast (DAC) is defined as
CðtÞ ¼ sðtÞ refðtÞ
ð1Þ
where s(t) is detected signal, ref(t) is reference signal for a non-defective area. Two features are usually extracted from C(t). One is peak value, which is maximum value of the different
absolute contrast; another is time to peak, which is the time when DAC reaches the peak value. According to thermal wave conduction theory, peak value is proportional to the cube of the defect depth and is damped quickly while time to peak can be used to quantify the defect depth. 2.2. CC based feature extraction The schematic for the proposed method based on cross correlation (CC) matched filtering is shown in Fig. 1. The CC matched filtering is originated from radar sciences in the early 1940s to detect deterministic signals within highly noised channels and to augment range resolution. This methodology localizes the energy of the received signal under a single peak located at a delay time. In order to calculate the CC of two signals ref(t) and s(t), it would be more convenient to use the Fourier transform in frequency domain, as shown in Eq. (2), rather than the time domain formula
CCðsÞ ¼ F 1 fREFðxÞ SðxÞg
ð2Þ
where REF(x) and S(x) are the Fourier transforms of the reference signal, ref(t), and the detected signal, s(t). * and F 1 denote the complex conjugate and inverse Fourier transform operators, respectively. The variable s determines the time delay between two signals ref(t) and s(t). After getting the CC responses for all pixels, two features CC peak amp and CC peak amp delay are extracted. CC peak amp means the peak value of CC, and CC peak amp delay means the time delay when CC reaches the peak value. The amplitude of the CC peak amp strongly depends on the amplitude of the received signal and then emissivity variation. CC peak amp delay is linked to the depth of the signal source. To select a reference signal CCref, the differential CC (DCC) can be calculated easily using differential technique shown in Eq. (3) [37].
DCC ¼ CC CCref
ð3Þ
And then, DCC peak amp and DCC peak amp delay can be also extracted from DCC. DCC peak amp means the peak value of DCC, and DCC peak amp delay means the time delay when DCC reaches the peak value. One can further calculate the CC phase (h) according to Eq. (4)
hðsÞ ¼
F 1 fREFðxÞ SðxÞg F 1 f½isgnðxÞREFðxÞ SðxÞg
ð4Þ
where sgn(x) and i are the signum function and the imaginary unit, respectively. The expression inside the square bracket in the denominator is the Fourier transform of the quadrature reference signal, obtained through the Hilbert transform and then Fourier transforms as shown in Fig. 1. The significance of CC phase is that the emissivity is cancelled out and as a result the CC phase is an emissivity normalized quantity [26]. Two features CC peak phase and CC peak phase delay are extracted from the response of CC phase. CC peak phase means the peak value of CC phase and CC peak phase delay means the time delay when CC phase reaches the peak value. Just like DCC, the differential CC phase (DCC phase), can be calculated according to Eq. (5)
Dh ¼ h href
ð5Þ
where href is reference CC phase signal. Correspondingly, DCC peak phase and DCC peak phase delay can be also extracted from DCC phase. 3. Simulation results for depth quantification Numerical studies were conducted using COMSOL Multiphysics 3.5a. The 3D Finite Element Modelling (FEM) consists of specimen (steel), coil and subsurface defect (air’s parameters), as shown in
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Fig. 1. Signal processing block diagram for the proposed method.
Table 1 Parameters of FEM model.
Fig. 2. FEM model.
Fig. 2. Table 1 shows the material parameters which were used in the simulations [15,20]. According to coordinate system, the specimen size was constant as 150 60 10 mm3. Subsurface defects were constructed by 9 rectangular blocks with the same length (60 mm) and width V (6 mm) but different depths d from 1 to 5 mm in the step of 0.5 mm. Accordingly, their size-to-depth ratio v = V/d was respectively 6–1.2. The coil was placed above the defect-free side. The distance between coil and sample was 1 mm. The excitation frequency and current were set as 256 kHz and 380 A. The heating period was set as 0.1 s and the recorded time after inductive heating was set as 2.65 s. Then, the temperature responses s(t) on the surface (defect-free side) of the specimen was recorded. The different absolute contrast C(t) responses for all defects were calculated using Eq. (1). Peak value and time to peak were extracted and their dependences on depths are shown in Fig. 3(a). It is noticed that time to peak has an approximate linear relationship with depth till 5 mm, but, the depth resolution is not satisfactory. For example, there are the same time to peak for depth 2.5 and 3 mm, the same time to peak for depth 3.5 and 4 mm, and time to peak for depth 4.5 and 5 mm. The responses of DCC and DCC phase for these defects were calculated using Eqs. (2)–(5). Both DCC peak amp and DCC peak amp delay were extracted from DCC response. These dependences on defects’ depths are shown in Fig. 3(b). DCC peak amp is similar with peak value and the defect with 5 mm depth is not detectable due to its quick damping. In contrast, DCC peak amp delay has a monotonous increase with depth till 5 mm. Not like time to peak, there is no equal value between adjacent depths. This means the enhanced depth resolution for DCC peak amp delay at an enhanced dynamic depth range till 5 mm. The dependences of DCC peak
Parameters
Air
Steel
Conductivity (S/m) Relative Permeability Density (kg/m3) Heat capacity (J/(kg K)) Thermal conductivity (W/(m k)) Thermal diffusivity (m2/s)
0 1 1.205 1.005e3 0.0257 2.12e5
4.03e6 100 7850 475 44.5 1.1934e5
phase and DCC peak phase delay are shown in Fig. 3(c). The similar phenomenon can be observed. DCC peak phase delay has a monotonous linear increase with depth till 5 mm. This means the enhance depth resolution for DCC peak phase delay. It is concluded that, (1) peak value, DCC peak amp and DCC peak phase is not suitable to size the depth due to quick damping and their dependence on heating energy; (2) DCC peak amp delay, and DCC peak phase delay can be used as the characteristic features to quantify the defect’s depth, which have an optimal depth resolution and depth dynamic range over time to peak. 4. Experimental results 4.1. Experimental system The experimental system of ECPT was developed in previous works [11,12,38]. A precision induction heating device, Easyheat 224 from Cheltenham Induction Heating, Ltd was used for induction heating, with a maximum excitation power of 2.4 kW, a maximum current of 400 Arms and an excitation frequency range of 150–400 kHz. The excitation coil was made of 6.35 mm high-conductivity hollow copper tubing. In order to fit the sample under test, the excitation coil was designed as a rectangular shape in plane. The state-of-the-art infrared camera Flir SC7500 was used to record the temperature change, which is a Stirling cooled camera with a 320 256 array of 1.5–5 lm InSb detectors. The pitch between detectors is 30 lm. And it has a sensitivity of <20 mK, a maximum full frame rate of 383 Hz. The radiation of the object was sampled using software Altair and the unit of radiation was digital level (DL), which was used as the unit of temperature in experimental studies. 4.2. Elimination of surface emissivity variance A steel sample (0.24 45 100 mm3) with a slot of 10 mm length, 2 mm width was prepared, as shown in Fig. 4(a). There are equally spaced shinning and black stripes with 5 mm width on the sample surface. The shinning strips are the polished area, while the black strips are the area sprayed with black painting. They illustrate different emissivity. The emissivity of the black region is about 1, while, the emissivity of the shinning are is about
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Fig. 3. (a) The dependences of peak value and time to peak on defect’s depth; (b) the dependences of DCC peak amp and DCC peak amp delay on defect’s depth; (c) the dependences of DCC peak phase and DCC peak phase delay on defect’s depth.
Fig. 4. (a) The steel sample with a slot and strips, (b) thermogram at 0.1 s, (c) image formed by DCC amp at 0.1 s delay, (d) image by DCC phase at 0.1 s delay, and (e) image by DCC peak phase delay.
0.16. In the experiments, coil was located on the backside of steel while IR camera was placed on the front side, presenting transmission mode [39]. The coil was perpendicular to the slot and across the slot centre. Only one edge of the rectangular coil was used to stimulate eddy current in the sample. The heating duration was set as 0.1 s and the cooling time after heating was 1.9 s. The sampling frequency was 383 Hz. Fig. 4(b) shows the original thermogram at 0.1 s. During inductive thermography testing, when an eddy current encounters a discontinuity, e.g. a slot or a notch, they are forced to divert, leading to areas of increased and decreased eddy current density resulting in relatively hotter and cooler areas due to Joule heating. However, due to the high emissivity of the black area, there is no obvious high temperature region around the slot tips. The responses of DCC and DCC phase for the tested area were calculated. Fig. 4(c) shows the image formed by DCC amp at 0.1 s delay. The similar phenomenon with Fig. 4(b) can be observed. Fig. 4(d) shows the image formed by DCC phase at 0.1 s delay and Fig. 4(e) shows the image formed by DCC peak phase delay. The results are interesting. The temperature difference caused by emissivity variation is totally removed and the temperature characteristic by defect is remarkable. The tip of defect has the highest temperature, whereas the defect side has the lowest temperature. These are in line with the results in previous works [24,40]. To sum up, the surface emissivity variation can be perfectly removed using the CC phase features.
4.3. Improvement of subsurface defect detection A steel sample providing three subsurface defects was tested. As shown in Fig. 5(a), the defects have the same width (6 mm) but different depths (1, 2, and 4 mm, respectively). Their size-to-depth ratio v is respectively 6, 3, and 1.5. During the experiments, both coil and IR camera were located on the back side of sample, presenting reflection mode. The heating time was set as 0.1 s and the whole record time is 2 s. Three defects were tested individually
under the same conditions. Fig. 5(b) shows the thermograms at 0.1 s, which is composed by three thermograms for defects. The subsurface defects are marked by three dashed boxes. It is noticeable that only shallowest defect with 1 mm depth lead to hot spots along the coil. Fig. 5(c) shows the image formed by DCC phase at 1 s delay and Fig. 5(d) shows the image by DCC peak phase delay. Comparing experimental results in Fig. 5, it is noticed that both DCC phase at 1 s delay and DCC peak phase delay are better than the original thermograms to identify the subsurface defects although the 4 mm depth defect with size-to-depth ratio smaller than 2 is still hardly detectable. This illustrates that the proposed method has a significant improvement in defect detectability for subsurface defects.
4.4. Improvement of delamination detectability in CFRP The CFRP sample with lateral dimension 300 10 mm2 was tested. Several man-made delaminations were manufactured by inserting a polytetrafluoroethylene film between fibre layers. One delamination with 100 mm2 lateral size, shown in Fig. 6(a) was tested. The distances of delamination to front side and back side are 0.5 mm and 2.5 mm, respectively. In the experiment, coil was located on the backside while IR camera was placed on the front side, presenting transmission mode. The heating time is 200 ms followed by 800 ms recording time. Fig. 6(b) and (c) shows the thermograms at 25 ms and 500 ms, respectively. The delamination area is marked by a 1red dashed box. Clearly in Fig. 6(b), the fibre woven structure can be observed from the hot and dark patterns. In detail, the carbon fibre is highlighted, because the EC directly heat the carbon fibre. In Fig. 6(c), as the heat diffuses laterally, the carbon fibre structure is blurred and a dark area appears. However, the delamination is hardly detectable. Fig. 6(d) shows the image by 1 For interpretation of color in ‘Fig. 6’, the reader is referred to the web version of this article.
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Fig. 5. (a) The steel sample with subsurface defects; (b) thermogram at 0.1 s; (c) image by DCC phase at 0.1 s delay; and (d) image by DCC peak phase delay.
Fig. 6. (a) Photo of CFRP with a delamination inside; (b) thermogram at 25 ms; (c) thermogram at 500 ms; (d) image by DCC phase at 0.6 s delay; and (e) image by DCC peak phase delay.
DCC phase at 0.6 s delay. The temperature difference caused by carbon structure is removed and the temperature characteristic by defect is remarkable. Fig. 6(e) shows the image by DCC peak phase delay. The delamination area is identified except the area on its left side. This illustrates that the new proposed method has a significant improvement in defect detectability for inside delamination.
5. Conclusions This paper presents pulsed inductive thermal wave radar (PI-TWR) by introducing the cross correlation matched-filtering in eddy current pulsed thermography (ECPT). Simulation results demonstrate that the proposed method have an optimal depth resolution and dynamic range for detection depth over conventional time domain feature. Experimental studies, where steel sample and CFRP sample were tested under transmission and reflection modes, illustrate that the proposed method has a significant improvement in the emissivity variation reduction and defect detectability for subsurface defects and inside delamination. The
future works include defect depth quantification, tomography for specific depth, and comparison studies with frequency domain features. Conflict of interest The authors declare that there is no conflict of interests regarding the publication of this article. Acknowledgements The work was supported by National Natural Science Foundation of China (Grant No. 51408071). The authors would like to thank Professor Gui Yun Tian’s guide and lead in the research and career. References [1] A. Yin, B. Gao, G.Y. Tian, W.L. Woo, K. Li, Physical interpretation and separation of eddy current pulsed thermography, J. Appl. Phys. 113 (2013) 064101.
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[2] B. Gao, A. Yin, Y. He, Inductive Thermography Pattern Separation, LAP Lambert Academic Publishing, Saarbrücken, Germany, 2014. [3] L. Cheng, G.Y. Tian, Transient thermal behavior of eddy-current pulsed thermography for nondestructive evaluation of composites, IEEE Trans. Instrum. Meas. 62 (2013) 1215–1222. [4] X.P. Maldague, Theory and Practice of Infrared Technology for Nondestructive Testing, John Wiley Interscience, New York, 2001. [5] B. Oswald-Tranta, Thermo-inductive crack detection, Nondestruct. Test. Eval. 22 (2007) 137–153. [6] N. Tsopelas, N.J. Siakavellas, Experimental evaluation of electromagneticthermal non-destructive inspection by eddy current thermography in square aluminum plates, NDT and E Int. 44 (2011) 609–620. [7] N. Biju, N. Ganesan, C.V. Krishnamurthy, K. Balasubramaniam, Simultaneous estimation of electrical and thermal properties of isotropic material from the Tone-Burst Eddy Current Thermography (TBET) time–temperature data, IEEE Trans. Magn. 47 (2011) 2213–2219. [8] L. Cheng, G. Tian, Surface crack detection for Carbon Fibre Reinforced Plastic (CFRP) materials using pulsed eddy current thermography, IEEE Sens. J. 11 (2011) 3261–3268. [9] M. Pan, Y. He, G.Y. Tian, D. Chen, F. Luo, Defect characterisation using pulsed eddy current thermography under transmission mode and NDT applications, NDT and E Int. 52 (2012) 28–36. [10] I.Z. Abidin, G.Y. Tian, J. Wilson, S. Yang, D. Almond, Quantitative evaluation of angular defects by pulsed eddy current thermography, NDT and E Int. 43 (2010) 537–546. [11] R. Yang, Y. He, B. Gao, G.Y. Tian, J. Peng, Lateral heat conduction based eddy current thermography for detection of parallel cracks and rail tread oblique cracks, Measurement 66 (2015) 54–61. [12] J. Wilson, G.Y. Tian, I.Z. Abidin, S. Yang, D. Almond, Pulsed eddy current thermography: system development and evaluation, Insight: Non-Destruct. Test. Cond. Monit. 52 (2010) 87–90. [13] Y. He, F. Luo, M. Pan, Defect characterisation based on pulsed eddy current imaging technique, Sens. Actuat. A 164 (2010) 1–7. [14] Y. He, F. Luo, M. Pan, X. Hu, J. Gao, B. Liu, Defect classification based on rectangular pulsed eddy current sensor in different directions, Sens. Actuat. A 157 (2010) 26–31. [15] R. Yang, Y. He, Logarithmic analysis of eddy current thermography based on longitudinal heat conduction for subsurface defect evaluation, Infrared Phys. Technol. 67 (2014) 467–472. [16] Y. He, M. Pan, F. Luo, Defect characterisation based on heat diffusion using induction thermography testing, Rev. Sci. Instrum. 83 (2012) 104702. [17] Y. He, M. Pan, D. Chen, G.Y. Tian, H. Zhang, Eddy current step heating thermography for quantitatively evaluation, Appl. Phys. Lett. 103 (2013) 194101. [18] G. Riegert, A. Gleiter, G. Busse, Potential and limitation of eddy current lockinthermography, in: Thermosense XXVIII, SPIE, Orlando, 2006. [19] Y. He, G.Y. Tian, M. Pan, D. Chen, Eddy current pulsed phase thermography and feature extraction, Appl. Phys. Lett. 103 (2013) 084104. [20] Y. He, M. Pan, G.Y. Tian, D. Chen, Y. Tang, H. Zhang, Eddy current pulsed phase thermography for subsurface defect quantitatively evaluation, Appl. Phys. Lett. 103 (2013) 144108. [21] R. Yang, Y. He, Eddy current pulsed phase thermography considering volumetric induction heating for delamination evaluation in carbon fiber reinforced polymers, Appl. Phys. Lett. (2015) (revised). [22] B. Gao, L. Bai, W.L. Woo, G. Tian, Thermography pattern analysis and separation, Appl. Phys. Lett. 104 (2014) 251902.
[23] B. Gao, A. Yin, G. Tian, W.L. Woo, Thermography spatial-transient-stage mathematical tensor construction and material property variation track, Int. J. Therm. Sci. 85 (2014) 112–122. [24] B. Gao, L. Bai, W.L. Woo, G.Y. Tian, Y. Cheng, Automatic defect identification of eddy current pulsed thermography using single channel blind source separation, IEEE Trans. Instrum. Meas. 63 (2014) 913–922. [25] L. Cheng, B. Gao, G.Y. Tian, W.L. Woo, Impact damage detection and identification using eddy current pulsed thermography through integration of PCA and ICA, IEEE Sens. J. 14 (2014) 1655–1663. [26] N. Tabatabaei, A. Mandelis, B.T. Amaechi, Thermophotonic radar imaging: an emissivity-normalized modality with advantages over phase lock-in thermography, Appl. Phys. Lett. 98 (2011) 163706. [27] S. Kaiplavil, A. Mandelis, Highly depth-resolved chirped pulse photothermal radar for bone diagnostics, Rev. Sci. Instrum. 82 (2011) 074906. [28] N. Tabatabaei, A. Mandelis, Thermal coherence tomography using match filter binary phase coded diffusion waves, Phys. Rev. Lett. 107 (2011) 165901. [29] J. Gong, J. Liu, L. Qin, Y. Wang, Investigation of carbon fiber reinforced polymer (CFRP) sheet with subsurface defects inspection using thermal-wave radar imaging (TWRI) based on the multi-transform technique, NDT and E Int. 62 (2014) 130–136. [30] V. Arora, J. Siddiqui, R. Mulaveesala, A. Muniyappa, Hilbert transform-based pulse compression approach to infrared thermal wave imaging for sub-surface defect detection in steel material, Insight Non-Destruct. Test. Cond. Monit. 56 (2014) 550–552. [31] S. Kaiplavil, A. Mandelis, Truncated-correlation photothermal coherence tomography for deep subsurface analysis, Nat. Photonics 8 (2014) 635–642. [32] S. Kaiplavil, A. Mandelis, B.T. Amaechi, Truncated-correlation photothermal coherence tomography of artificially demineralized animal bones: two- and three-dimensional markers for mineral loss monitoring, J. Biomed. Opt. 19 (2014). [33] S. Kaiplavil, A. Mandelis, X. Wang, T. Feng, Photothermal tomography for the functional and structural evaluation, and early mineral loss monitoring in bones, Biomed. Opt. Exp. 5 (2014) 2488–2502. [34] L. Bai, S. Tian, Y. Cheng, G.Y. Tian, Y. Chen, K. Chen, Reducing the effect of surface emissivity variation in eddy current pulsed thermography, IEEE Sens. J. 14 (2014) 1137–1142. [35] R. Yang, Y. He, B. Gao, G.Y. Tian, Inductive pulsed phase thermography for reducing or enlarging the effect of surface emissivity variation, Appl. Phys. Lett. 105 (2014) 184103. [36] Y. He, G.Y. Tian, M. Pan, D. Chen, H. Zhang, An investigation into eddy current pulsed thermography for detection of corrosion blister, Corros. Sci. 78 (2014) 1–6. [37] Y. He, G.Y. Tian, H. Zhang, M. Alamin, A. Simm, P. Jackson, Steel corrosion characterisation using pulsed eddy current systems, IEEE Sens. J. 12 (2012) 2113–2120. [38] G. Tian, Y. He, L. Cheng, P. Jackson, Pulsed eddy current thermography for corrosion characterisation, Int. J. Appl. Electromagnet Mech 39 (2012) 269– 276. [39] Y. He, G. Tian, M. Pan, D. Chen, Impact evaluation in carbon fiber reinforced plastic (CFRP) laminates using eddy current pulsed thermography, Compos. Struct. 109 (2014) 1–7. [40] J. Wilson, G.Y. Tian, I.Z. Abidin, S. Yang, D. Almond, Modelling and evaluation of eddy current stimulated thermography, Nondestruct. Test. Eval. 25 (2010) 205–218.