The Quantitative Study of TOFD influenced by the Frequency Window of Autoregressive Spectral Extrapolation

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19 th World Conference on Non-Destructive Testing 016 The Quantitative Study of TOFD influenced by the Frequency Window of Autoregressive Spectral Extrapolation Da KANG 1, Shijie JIN 1, Kan ZHANG 1,

$The time of flight diffraction (TOFD) technique can be employed to measure flaw height by use of the time lag of diffraction signals which come from the top and bottom edges of defect.$ However, the small flaw size or the poor temporal resolution will lead to signal aliasing in time domain, so it is hard to quantify the defect.

However, the small flaw size or the poor temporal resolution will lead to signal aliasing in time domain, so it is hard to quantify the defect.

1 19 th World Conference on Non-Destructive Testing 016 The Quantitative Study of TOFD influenced by the Frequency Window of Autoregressive Spectral Extrapolation Da KANG 1, Shijie JIN 1, Kan ZHANG 1, Zhongbing LUO 1, Shuxiao ZHANG, Lili LIU, Donghui ZHANG, Yunlong FANG, Li LIN 1* 1 NDT & E Laboratory, Dalian University of Technology, Dalian, China China Nuclear Industry 3 Construction Co., Ltd., Beijing, China, Contact linli@dlut.edu.cn Abstract. The time of flight diffraction (TOFD) technique can be employed to measure flaw height by use of the time lag of diffraction signals which come from the top and bottom edges of defect. However, the small flaw size or the poor temporal resolution will lead to signal aliasing in time domain, so it is hard to quantify the defect. To separate the mixed signals, Autoregressive Spectral Extrapolation (ARSE) technique takes advantage of the data in frequency window, which has a high signal-to-noise radio(snr), to estimate the data outside this frequency window by prediction error principle. Particularly, the choice of frequency window plays an important role in the above process. In this paper, combining ARSE technique with TOFD, the cracks with the height of 1.00mm, 1.0mm and 1.50mm in depth of 50.0mm were detected quantitatively in carbon steel block whose thickness was 10.0mm. Meanwhile, the influence of frequency window to the detection result was studied by simulation and experiment methods, and different quantitative results of crack height were presented. The relative error was less than 5% when the maximum in frequency spectrum of reference signal decreased 6dB or 7dB. 1. Introduction TOFD technique is applied to the sizing of crack height by diffracted waves generated from the interaction between the ultrasonic wave and crack tips [1]. However, several factors, such as pulse width, will affect the crack sizing []. When the diffracted waves are overlapped with each other, the time resolution becomes worse. To solve the above problem, the signal processing techniques, such as pulse compression technique [3] and split-spectrum processing technique [4], are applied to the TOFD detection. Besides, the deconvolution technique is also employed so as to improve the time resolution [5,7]. Sin [6] compared the advantages and feasibility of different deconvolution techniques (containing Wiener filtering, minimum variance and curve-fitting method, etc) in ultrasonic detection, and the simulation result shown that the Wiener filtering had a better performance. Furthermore, Farhang [8,9] proposed a technique named Autoregressive Spectral Extrapolation (ARSE) which combined the deconvolution in frequency domain and the autoregressive model. ARSE technique improves the time resolution of ultrasonic signals by expanding the data of frequency band with high SNR, and the pulse width is compressed in time domain. During this process, the choice of reference signal and frequency window has a significant influence on the processing results of ARSE. Sinclair [9, 10] conducted the research on reference signal, and suggested that it should be linked with the change of incident angles, so as to avoid the lost of useful information. However, the choice of frequency window has no specific principle [11], and the optimum cannot be guaranteed for the extrapolated data which did not lose significant frequency components or was not interfered by the License: 1 More info about this article:

2 miscellaneous signals. Once this phenomenon happens, the quantitative error of flaw will be larger. In this paper, the ARSE technique and TOFD detection were combined to research the relationship between the choice of frequency window and the sizing of crack height. The quantitative results corresponding to the decrease of maximum in frequency domain from db to 10dB were presented respectively. The comparison and analysis were carried out to provide some basis for the application in TOFD detection and parameter optimization of ARSE.. Principle The ultrasonic TOFD signal, y(t), can be written as the form of convolution, and it can be represented by [8] y( t) h( t) x( t) n( t) (1) where * denotes the convolution operator, h(t) is the system impulse response(named as reference signal), x(t) is defect impulse response, and n(t) is the additive noise in the system. The Wiener filtering is applied to Eq.(1) in the frequency domain, and the result can be stated as [1] X( ) Y( ) H ( ) H( ) S ( ) / S ( ) Where Y(), H(), X() and N() are the Fourier transforms of y(t), h(t), x(t) and n(t), H * ()is the complex conjugate of H(), S n ()and S x () are the power spectral density functions of n(t) and x(t), respectively. It is difficult to measure the amplitude of noise signal and real defect signal, so S n ()/S x () is set as a frequency-independent constant, called noise desensitizing factor. Generally. The origin formula can be rewritten as Q 10 H( ) max X( ) n Y( ) H ( ) H( ) Fig. 1 presents the frequency spectrums of ultrasonic signal, reference signal and deconvolved signal, respectively. The data with high SNR in frequency domain is chosen before the processing of ARSE. Q x () (3) (a) (b) (c) Fig. 1.Frequency spectrum of different signals: (a) ultrasonic signal; (b) reference signal; (c) deconvolved signal. Comparing Fig. 1(a), (b) and (c), it is observed that the high SNR portions of signals are similar to each other, so the frequency band can be chosen from the frequency spectrum of reference signal. By doing so, the spectrum analysis of deconvolved signal can be avoided. Usually, a frequency window corresponding to a certain db drop of the maximum

3 amplitude of spectrum is taken for the extrapolation (as shown in Fig. ). Then, the AR coefficients and model order can be calculated by fitting AR model with the data selected from the frequency window. Fig..Schematic diagram of frequency window. The forward and backward data are predicted by combining AR coefficients and the data chosen from the frequency window. The whole data with high SNR will be obtained by taking advantage of the Eq. (4) and (5) [8] p f i ak Xik( i=n+1,, N ) (4) k1 p b * i ak Xik( i =1,,, m-1 ) (5) k1 X X where ak and p are AR coefficients and AR model order, respectively, and a k is the complex conjugate of a k. The inverse Fourier transform is applied to the whole obtained frequency data to get defect signal in time domain which can be written as ~ x( t) IFFT( X) (6) In the end, the transmit time lag of diffracted waves can be acquired by the processing of normalization, and the flaw height is achieved by Eq. (7) 1 h c t t s c t s (7) where h is the flaw height, t is transmit time of diffracted signal from upper tip of flaw, Δt is the time lag of diffracted waves, s is the probe center separation, and c is the velocity of longitudinal wave. 3. Simulation and Experiment 3.1 Simulation As shown in Fig. 3, the detection model was established in CIVA based on the acoustic and elastic characteristics of carbon steel, in which the thickness was 10.0mm, velocity of longitudinal wave was 5.89km/s and density was 7.80g/cm 3. The cracks with the height of 1.00mm, 1.0mm and 1.50mm were set in the depth of 50.0mm. The center frequency of TOFD probes were 5MHz, the sizing of chip was 6.0mm and the angle of refraction was 45 in carbon steel. 3

4 Fig. 3.Schematic diagram of detection model. The B-scan was operated in the area containing cracks. Taking the 1.00mm crack for example, Figure. 4(a) and (b) presented the signals of A-scan and the processed result of ARSE, respectively. As shown in Fig. 4(a), the diffracted signals from the crack tips were mixed with each other, so the crack height was hard to be achieved. With the processing of ARSE, the time resolution had a significant improvement, and the mixed signals could be separated effectively. Furthermore, the processing of normalization was applied (as presented in Fig. 4(c)), and the crack height was accurately obtained from the time lag of diffracted waves Δt. (a) (b) (c) Fig. 4.The testing results of 1.00mm crack: (a) A-scan signal; (b) processing of ARSE; (c) processing of normalization. This processing was applied to TOFD detection for the three cracks in the model, and the data corresponding to different frequency windows =,3 10dB were chosen for the ARSE process. Based on the transmit time lags of diffracted waves from crack tips, the results of crack heights and quantitative errors were shown in Fig. 5. 4

(a) (b) (c) Fig. 5.The quantitative results and errors for different frequency windows and cracks: (a) height of 1.00mm; (b) height of 1.0mm; (c) height of 1.50mm.

with the increasing, and reached the minimum (less than 5%), when was equal to 6dB or 7dB; With the further increase of frequency window, the relative error was getting high again, and there was a

The instrument for TOFD detection was OmniScan MX, and detection parameters were the same as simulation except for the encoder having 0.5mm/step.

5 (a) (b) (c) Fig. 5.The quantitative results and errors for different frequency windows and cracks: (a) height of 1.00mm; (b) height of 1.0mm; (c) height of 1.50mm. Based on the calculation of quantitative errors, it was easy to find that the relative error was very high (even more than 40%), when the frequency window was narrow; The relative error decreased with the increasing, and reached the minimum (less than 5%), when was equal to 6dB or 7dB; With the further increase of frequency window, the relative error was getting high again, and there was a fluctuation within small scope. 3. Experiment. One crack with the height of 1.00mm was made in 50.0mm depth of carbon steel block. The instrument for TOFD detection was OmniScan MX, and detection parameters were the same as simulation except for the encoder having 0.5mm/step. The B-scan was applied, and the A-scan signal was extracted from the position of crack. The processing of ARSE was adopted with the data corresponding to different frequency windows =, 3 10dB, and the crack heights and quantitative errors were obtained. Fig. 6 presented the results, in which the maximum of heights was 1.43mm and the minimum was 0.9mm. Fig. 6.The quantitative results and errors of 1.00mm crack for different frequency windows. 5

6 3.3 Analysis and Discussion The histogram of quantitative errors of 1.00mm crack obtained by simulation and experiment was given in Fig. 7. It was shown that the sizing result was linked to the selection of frequency window, and the simulation and experiment results were in good agreement. After the calculation, it was presented that the quantitative error decreased with the increasing range of frequency window in the beginning, and the relative error was less than 5% when was equal to 6dB or 7dB. Beyond this range, the relative error increased and the fluctuation trend became gently. The reasons are stated as follows: the data with high SNR is insufficient when the frequency window is narrow. The lost useful information is unable to represent the characteristic of diffracted signals and will increase the quantitative error. On the other hand, when the frequency window is too wide to avoid the miscellaneous information mixed in the selected data, the interference signals lead to the reduction of time resolution and accuracy of sizing. Besides, the coupling condition and surface roughness also have influence on the experimental result, so the quantitative error of experiment is higher than that of simulation. Fig. 7.The quantitative errors of 1.00mm crack for different frequency windows by simulation and experiment. 4. Conclusion Combining ARSE technique with TOFD detection, the time resolution of detection signals can be improved obviously. On this basis, the relationship between the choice of frequency window and the sizing of crack height in the processing of ARSE was studied by simulation and experiment. The results showed that the relative quantitative errors of different cracks were less than 5%, when was equal to 6dB or 7dB. Acknowledgements This work has been supported by National Basic Research Program of China (973 program) under Grant No. 015CB and Fundamental Research Funds for the Central Universities under Grant No. DUT14RC(3)135. References [1] Hatanaka H, Ido N, Furikoma M, et al. Application of ultrasonic TOFD method for welds of LNG storage tanks[j]. IHI engineering review. 00, 35(4):

7 [] Manjula K, Vijayarekha K, Venkatraman B, et al. Ultrasonic time of flight diffraction technique for weld defects: a review[j]. Research Journal of Applied Sciences Engineering & Technology, 01, 4(4): [3] Gang T, Sheng Z Y, Tian W L. Time resolution improvement of ultrasonic TOFD testing by pulse compression technique[j]. Insight-Non-Destructive Testing and Condition Monitoring. 01, 54(4): [4] Muthumari S, Singh A, Sharma A P. DE-NOISING ULTRASONIC TOFD SIGNALS: A COMPARATIVE STUDY OF WAVELET PACKET METHOD USING SURE WITH SSP TECHNIQUE[J]. Journal of Theoretical and Applied Information Technology. 01, 37(1), [5] Olofsson T, Stepinski T. Minimum entropy deconvolution of pulse-echo signals acquired from attenuative layered media[j]. The Journal of the Acoustical Society of America. 001, 109(6): [6] Sin S, Chen C. A comparison of deconvolution techniques for the ultrasonic nondestructive evaluation of materials[j]. Image Processing, IEEE Transactions on. 199, 1(1): [7] van der Baan M. Time-varying wavelet estimation and deconvolution by kurtosis maximization[j]. Geophysics. 008, 73(): V11-V18. [8] Honarvar F, Sheikhzadeh H, Moles M, et al. Improving the time-resolution and signal-to-noise ratio of ultrasonic NDE signals[j]. Ultrasonics. 004, 41(9): [9] Sinclair A N, Fortin J, Shakibi B, et al. Enhancement of ultrasonic images for sizing of defects by time-of-flight diffraction[j]. NDT & E International. 010, 43(3): [10] Honarvar F, Yaghootian A Reference wavelets used for deconvolution of ultrasonic time-of-flight diffraction (ToFD) signals[c]. //17th World Conference on Nondestructive Testing. 008: 1-9. [11] Karslı H. Further improvement of temporal resolution of seismic data by autoregressive (AR) spectral extrapolation[j]. Journal of Applied Geophysics. 006, 59(4): [1] Guo J, Xin Y. Reconstructing outside pass-band data to improve time resolution in ultrasonic detection[j]. NDT & E International. 01, 50:

Reference wavelets used for deconvolution of ultrasonic time-of-flight diffraction (ToFD) signals

$Reference wavelets used for deconvolution of ultrasonic time-of-flight diffraction (ToFD) signals$ 17th World Conference on Nondestructive Testing, 25-28 Oct 2008, Shanghai, China Reference wavelets used for deconvolution of ultrasonic time-of-flight diffraction (ToFD) signals Farhang HONARVAR 1, Amin