外文原文-脈沖渦流檢測中的頻域缺陷特征

International Journal of Applied Electromagnetics and Mechanics 45 (2014) 621625621 DOI 10.3233/JAE-141885 IOS Press Frequency-domain defect characterization in pulsed eddy current testing Zhiwei Zeng, Yansong Li, Lin Huang and Minfang Luo Department of Aeronautics, Xiamen University, Xiamen, Fujian, China Abstract. Pulsed eddy current (PEC) testing has attracted researchers interest because the pulsed excitation comprises a broad band of frequencies and the response signal provides more information about defect than traditional eddy current testing. Various features have been extracted from PEC signal for defect characterization. In this paper, we extract frequency-domain features and propose defect characterization scheme for identifying defects location, radius, and height. Keywords: Pulsed eddy current testing, defect characterization, feature 1. Introduction In pulsed eddy current (PEC) testing, the coil is excited by pulsed waveform, typically rectangular wave,as illustrated in Fig.1.PECtesting hasmanyadvantagesovertraditional eddycurrent(EC) testing, such as better fi eld penetration and less sensitive to liffoff 1. More importantly, induced currents in the test sample have a wide band of frequency components. Due to the skin effect, different frequency components have different penetration depths. Therefore the response signal in PEC testing provides richer depth information about defect than that of traditional EC testing. As a result, there are more options for defect characterization in PEC testing. In the recent years, studies of PEC testing have been focused to the extraction of features from the transient response signal, which is critical to defect characterization. He et al. presented time-domain analysis method, which extracts time-domain features of transient signal after difference processing, as shown in Fig. 2 2. Tian et al. developed wavelet-based principal component analysis (PCA) method, which applies PCA to the wavelet coeffi cients of PEC signal to extract dominant features 3. Some re- searchers transformed PEC signals to the frequency domain and performed spectral analysis. Vasi c et al. analyzed signal spectra but did not use frequency-domain features for defect classifi cation 4. Lebrun et al. used a particular frequency, namely characteristic frequency, as a feature to characterize defect length 5. Yang et al. computed energy of signal in the low-frequency band and used it as a feature 6. Both 5,6 combined frequency-domain features with time-domain features for defect characterization. Basedon the fact that different frequencycomponentshavedifferent penetrationdepths,it is advisableto study PEC defect characterization with all the features being spectral features, which has more physical Corresponding author: Zhiwei Zeng, Department of Aeronautics, Xiamen University, Xiamen 361005, Fujian, China. E-mail: 1383-5416/14/$27.50 c ? 2014 IOS Press and the authors. All rights reserved 622Z. Zeng et al. / Frequency-domain defect characterization in pulsed eddy current testing r h Magnetic field sensor Fig. 1. Pulsed eddy current testing. O t Peak value Zero-crossing time Differential output Fig. 2. Typical PEC transient signal and time-domain features. signifi cance than the other characterization schemes. He et al. transformed transient signal to the fre- quency domain and select high-frequency components as features 1,7. However, this characterization scheme will lose deeply hidden defects which are detectable only by low-frequency components. In this paper, we attempt to fully exploit frequency-domain information of PEC signal for defect char- acterization. More specifi cally, not only high-frequency component, but also low-frequency component and middle-frequency information are extracted. Simulation results show that the frequency-domain features are promising to identify defects location, size, and depth. The idea is different from multi- frequency eddy current (MEC) testing. In MEC testing 810, optimization of frequencies in terms of quantifying defect depth is impossible as defect depth is not known a prior in real situation. On the contrary, appropriate frequency components of PEC signal can be selected from the spectrum to best characterize defect parameters. 2. Finite element analysis The signals used in the paper are generated by numerical simulation using the fi nite element method. The Fourier transform method is utilized for obtaining transient signal and its spectrum. 2.1. Geometry and parameters In Fig. 1, the air-core coil has inner radius of 6 mm, outer radius of 10 mm, height of 13 mm, and liftoff of 1 mm. The coil has 312 turns and is excited by rectangular wave of 100 Hz, 50% duty ratio, and 0.333 A amplitude. The sample is 4 mm thick. The conductivity and relative permeability of the sample are 58.6 %IACS and 1, respectively. Defect (assumed cylindrical type in the paper) is characterized by three parameters: location (top or bottom, or surface or subsurfacein other words), radiusr, and heighth.We use notationTrh(Brh) to denote top (bottom) defect with radiusrand heighth. The unit ofrandhis mm. 2.2. Fourier transform method Transient modeling using the Fourier transform method is straightforward. Firstly transform transient source current into harmonics. Then compute complex response (normal component of magnetic fl ux density, denoted byBz ) of each frequency component using axisymmetric frequency-domain fi nite ele- ment model. The complex responses form the spectrum of PEC signal. Finally the transient signal can be obtained by taking inverse Fourier transform of the spectrum. The transient signal and part of its amplitude spectrum for defect-free case are shown in Fig. 3. Z. Zeng et al. / Frequency-domain defect characterization in pulsed eddy current testing623 (a)(b) Bz (T) Amplitude Time (s)Frequency (Hz) Fig. 3. Normal component of magnetic fl ux density Bz(T) for defect-free case. (a) Transient signal. (b) Part of amplitude spectrum. (a)(b) ? ? ? ? ? ? Frequency (Hz) Amplitude difference ? ? ? ? ? ? Frequency (Hz) Amplitude difference Fig. 4. Part of differential amplitude spectra. (a) Defect height fi xed at 2 mm. (b) Defect radius fi xed at 4 mm. 3. Frequency-domain defect characterization 3.1. Frequency-domain features The following steps are performed to analyze frequency-domain characteristics of PEC signals. 1. Get amplitude spectrum of response signal. 2. Get differential amplitude spectrum using the amplitude spectrum of no defect as reference. 3. Take odd harmonics and plot spectrum. Figure 4(a) shows part of differential amplitude spectra for various defect radii when fi xing defect height at 2 mm. Figure 4(b) shows part of differential amplitude spectra for various defect heights when fi xing defect radius at 4 mm. Observing Figs 4(a) and (b), we fi nd the following interesting phenomena. 1. At high frequency(e.g.8 kHz),amplitude difference in the presenceofsubsurfacedefectconverges to 0; whereas amplitude difference in the presence of surface defect does not. This can be easily 624Z. Zeng et al. / Frequency-domain defect characterization in pulsed eddy current testing (a)(b) ? ? ? ? ? ? ? ? ? Feature 1 Feature 2 ? ? ? ? ? ? ? ? ? Feature 2 Feature 3 Fig. 5. Feature plots. (a) For surface defects. (b) For subsurface defects. explainedbythe skineffect.Thatis,high-frequencycomponentsofeddycurrentonlyaffectsurface defects and do not affect subsurface defects. 2. When surface defect is present, values of amplitude difference for fi xed defect height but various defect radii have different values at high frequency. The value increases with the increase of de- fect radius (see Fig. 4(a). Nonetheless, values of amplitude difference for fi xed defect radius but various defect heights have almost the same values at high frequency (see Fig. 4(b). This is be- cause high-frequency components of eddy current focus to the surface and is therefore insensitive to defect height. 3. When subsurface defect is present, values of amplitude difference for fi xed defect height but var- ious defect radii have almost the same values of zero-crossing frequency (the frequency at which the amplitude difference crosses0). The zero-crossing frequencies for B32,B42, and B52 are 2623 Hz, 2546 Hz, and 2464 Hz, respectively. On the other hand, values of amplitude difference for fi xed defect radius but various defect heights have very different values of zero-crossing fre- quency. The zero-crossing frequencies for B42, B42.5, and B43 are 2546 Hz, 3743 Hz, and 6757 Hz, respectively. These results tell us that zero-crossing frequency is largely determined by defect depth. Based on the above observations, we propose to use three frequency-domain features for defect char- acterization. Feature 1 is the amplitude difference at high frequency (8 kHz). Feature 2 is the peak value of amplitude difference, which occurs at low frequency (about 500 Hz). Feature 3 is zero-crossing fre- quency for subsurface defects, which is regarded as middle frequency information. 3.2. Defect characterization Using the proposed features, we can characterize defect by the following procedure. 1. Use feature 1 to identify defect location (surface or subsurface). 2. For surface defects, use feature 1 again to identify defect radius (see Fig. 4(a), then use feature 2 to identify defect height (see Fig. 4(b). 3. For subsurface defects, use feature 3 to identify defect height (see Fig. 4(b), then use feature 2 to identify defect radius (see Fig. 4(a). Z. Zeng et al. / Frequency-domain defect characterization in pulsed eddy current testing625 Feature plots for surface defects and subsurface defects are shown in Figs 5(a) and (b), respectively. Obviously surface defects with same radius have similar values of feature 1. Then defects with same radius butdifferent heights are discriminated by feature 2. Likewise,subsurfacedefects with sameheight have similar values of feature 3. Then defects with same height but different radii are discriminated by feature 2. 4. Conclusions Frequency-domain features exploiting the broad-band characteristic of PEC signal are extracted. The features include low, middle, and high frequency information. Simulation results show that defect char- acterization using the proposed features is promising. Validation with measurement data is to be per- formed. Acknowledgments This work is supported by the National Science Foundation of China under Grant 51277154,Program for New Century Excellent Talents in University under Grant NCET-09-0682,the Research Fund for the Doctoral Program of Higher Education under Grant 20120121110026, and the Fundamental Research Funds for the Central Universities under Grant 2012121036. References 1 Y. He, M. Pan, F. Luo and G. Tian, Reduction of lift-off effects in pulsed eddy current for defect classifi cation, IEEE Transactions on Magnetics 47 (2011), 47534760. 2 Y. He, F. Luo, M. Pan, X. Hu, J. Gao and B. Liu, Defect classifi cation based on rectangular pulsed eddy current sensor in different direction, Sensors and Actuators A: Physical 157 (2010), 2631. 3 G. Tian, A. Sophian, D. Taylor and J. Rudlin, Wavelet-based PCA defect classifi cation and quantifi cation for pulsed eddy current NDT, IEE Proceedings: Science, Measurement & Technology 152 (2005), 141148. 4D. Vasi c, V. Bilas and D. Ambru, Pulsed eddy current nondestructive testing of ferromagnetic tubes, Instrumentation and Measurement Technology Conference, Vail, USA, (May 2003), 11201125. 5B. Lebrun