REAL-TIME DENOISING OF AE SIGNALS BY SHORT TIME FOURIER TRANSFORM AND WAVELET TRANSFORM

Transcription

1 REAL-TIME DENOISING OF AE SIGNALS BY SHORT TIME FOURIER TRANSFORM AND WAVELET TRANSFORM KAITA ITO and MANABU ENOKI Department of Materials Engineering, The University of Tokyo, Hongo, Bunkyo, Tokyo , Japan Abstract Laser AE method is a non-contact AE detection technique, which utilizes laser interferometer as sensor. This method is less subjected to environmental difficulties and can be adaptive for wider target than conventional PZT sensors. However, laser AE method has to improve its sensitivity because the noise level of laser interferometer is higher than PZT sensors. In this study, a method to reduce the noise component of output signal of laser interferometer is investigated. Output signals from laser interferometer were recorded continuously with 1-MHz sampling frequency and transformed into spectrogram (time-frequency-magnitude data) by time-frequency analysis method. After noise component in this spectrogram is cut, inverse transform is applied to obtain clear AE signals in time domain. Whole signal processing can be done in real time. Simulated AE detection test was conducted to confirm the effectiveness of this noise reduction scheme. In the result, weak AE signals buried in noise could be recovered and the improvement of sensitivity of laser AE system was demonstrated. Current real-time processing can extract about events/s. Keywords: Noise reduction, continuous waveform recording, short-time Fourier transform, wavelet transform Introduction Conventional PZT AE sensors are difficult to use under some of severe environments. For example, conventional AE sensor needs waveguide or some of heat avoidance mechanism if the testing temperature is higher than the Curie temperature of PZT. In another case, PZT sensors often cannot be attached to the target material during manufacturing process. Therefore, laser AE method [1] has been developed to realize a direct AE measurement under such severe environments by non-contact detection of AE with laser interferometer [2, 3]. However, laser AE method has to improve the sensitivity because the noise component of output signals from a laser interferometer is larger than the conventional PZT sensors. Frequency filtering is one of the most important techniques to improve the sensitivity. However, conventional analog filter is not so effective for the output waveform of laser interferometer because the noise component is closed to the frequency range of effective signal component. Digital signal processing (DSP) system can do more powerful and flexible noise reduction than analog system. In this study, a high performance method for noise reduction of the output signal from laser interferometer was investigated. The waveform from laser interferometer was continuously sampled and once transformed into spectrogram by time-frequency analysis methods. Effective noise reduction process was examined using this spectrogram. J. Acoustic Emission, 25 (7) Acoustic Emission Group

2 Analytical Method Time-Frequency Analysis Time-frequency analysis is a method to convert a waveform (time-voltage data) into a spectrogram (time-frequency-magnitude data). In this study, short time Fourier transform (STFT) and wavelet transform (WT) were used as time-frequency analysis techniques. In STFT method, a long waveform is split into short sections and each section is processed by Fourier transform using the following formula: F ( f ) s() t w( t ) + 2 tf = e dt,, (1) where s(t) is the sectioned waveform, w(t- ) is window function, f is frequency and F(, f) is the result of STFT. Meanwhile, in wavelet transform method, the original signal is expressed as summation of scaling and shift of certain short waveform called mother wavelet as W * ( a b) s() t h () t +, = dt, (2) a, b where h(t) is mother wavelet, a is the scaling factor, b is the shifting factor and W(a, b) is the result of WT. Fourier transform loses the time information in the transform section because it supposes ordinary wave. Then, if the section length becomes shorter, the time resolution of STFT improves, but the frequency resolution degrades. Thus, the overall resolution of STFT cannot be so high by this trade-off relationship. Meanwhile, wavelet transform can get high resolution, but the calculation amount is larger than STFT, so wavelet transform of very long continuous waveform is not realistic. Thus, less-intensive calculation and low-resolution STFT is better for rough estimation of long waveform, and intensive calculation and high-resolution wavelet transform is better for strict estimation of short waveform. Tactful use of both methods is important. Noise reduction Figure 1 shows a spectrogram of output waveform of laser interferometer and contains two main components as discrete AE signal component and continuous noise component. The noise appeared in a broad frequency range between about khz and 5 khz, and this range partially overlaps with the effective signal component. Furthermore, often the noise component is larger than the effective signal component in laser AE methods. In such a waveform, conventional frequency filter which utilizes moving average or pulse reaction is ineffective. In this study, pruning method and soft-thresholding methods are adopted as noise reduction process. This combination of the two processes was already reported in voice processing and ultrasonic testing area [4]. At first the spectrogram of recorded waveform is filtered by pruning method: for f < f1, f > f 2 W 2( f, t) =, (3) W 1( f, t) for f1 < f < f 2 where W 1 is waveform before processing, W 2 is waveform after the processing, f is frequency, t is time, f 1 and f 2 is cut-off frequency. Pruning method works as frequency filter and cuts off sharply. After that, remained white noise component was cut by soft-thresholding method: W 2 ( f, t) = W 1 for W1( f, t) ( f, t) for W ( f, t) 1 <, (4) where is the threshold of noise and signal. Originally, these methods are used for wavelet transform result; however, it can be used for STFT result too. After these noise reduction 248

3 khz7 Frequency, f / Time, t /ms Fig. 1 Sample spectrogram of output signal of laser interferometer. processes, the spectrogram was reconverted into waveform by inverse STFT or inverse WT. Real time signal processing The CWM system basically can do a real-time noise reduction process based on the above theories by a combination of high-speed STFT and high-resolution WT. At first, the whole recorded waveform is converted into spectrogram by STFT. The noise component in the spectrogram is reduced by pruning method and soft-thresholding method. Then, the processed spectrogram is reverted by inverse-stft with Hanning window function to connect smoothly at the connection points of inverse-stft period. After that, AE events are extracted from the noise reduced time domain data. However, the time resolution of this waveform may not be enough because this waveform is processed by STFT-based method. Therefore, a waveform with a few milliseconds length is clipped out from as-recorded waveform around AE event and processed again by WT-based method to get precise time information. The WT-based method is the same manner as the STFT-based method. In particular, the current CWM system with two 2.2 GHz processor (Athlon64 X2 Processor, AMD Inc.) can process 2-channel AE waveforms of 1-MHz sampling in real time by STFT-based method and can extract about events/s by WT-based method. Fig. 2 Experimental equipments of simulated AE signal detection. 249

4 Experimental Procedures Simulated AE detection test was conducted to confirm the above noise reduction method. Figure 2 shows the experimental equipment. Specimen was SUS34 disk of 3 mm in diameter and 5 mm in thickness. Simulated AE was generated by thermal stress of pulse YAG laser system (Tempest-2, New Wave Research, Inc.), measured by He-Ne laser heterodyne interferometer (AT36S and AT22, Graphtec Corp.) and analyzed by our CWM system [5]. The output power of YAG laser was 4 mj/pulse or 2 mj/pulse and pulse length was about 4 ns. The maximum detectable frequency of the laser interferometer was about 4 khz. CWM sampled the output signal of AT36S continuously during the whole test with 1-MHz frequency and 12-bit resolution. The noise level was about 3 mv in RMS. Results and Discussion Figure 3 shows the result of 4-mJ pulse. The pulse was strong enough to register as an AE event from as-recorded waveform (Fig. 3(a)). The spectrogram (Fig. 3(c)) of this waveform also contained strong signal component and weak noise component between khz and 5 khz. In order to reduce this noise component, only a frequency range between khz and 25 khz remained after applying pruning method. The white noise was reduced by soft-thresholding method with 6% of maximum magnitude as the threshold value (Fig. 3(d)). A clear waveform (Fig. 3(b)) was obtained by inverse STFT in comparison to the original waveform. Fig. 3 Noise reduction of simulated AE signal by 4-mJ pulse; (a) recorded waveform, (b) processed waveform, (c) STFT result of recorded waveform, (d) spectrogram after noise reduction. Figure 4 shows the result of 2-mJ pulse. Pulse was very weak and AE event was not visible in as-recorded waveform (Fig. 4(a)). However, a weak signal component was discernible in 25

5 the STFT result (Fig. 4(b)). Therefore, only a frequency range between 75 khz and 175 khz was remained by pruning method, and the white noise was reduced by soft-thresholding method with 6% of maximum magnitude as the threshold value. The processed waveform (Fig. 4(c)) could be detected as AE event. Fig. 4 Noise reduction of simulated AE signal by 2mJ pulse; (a) recorded waveform, (b) STFT result of recorded waveform, (c) noise reduced waveform. (a) Voltage, V / mv (c) Frequency, f / khz % 5% % (b) Voltage, V / mv (d) Frequency, f / khz % Fig. 5 Noise reduction of simulated AE signal by 4-mJ pulse; (a) recorded waveform, (b) noise reduced waveform, (c) WT result of recorded waveform, (d) spectrogram after noise reduction. 5% % The noise-reduction processing was also conducted with WT. Figures 5 and 6 show the waveform and spectrogram of the same AE event in Fig. 3. The noise component below khz was relatively strong in the spectrogram of the as-recorded waveform, but this noise can be cut by pruning method (Fig. 5(d)). The noise-reduced waveform (Fig. 5(b)) is clear in the time domain and the major characteristics of waveform are kept as the original waveform. Figure 6 shows the comparison of a rising waveform by the STFT-based and WT-based noise-reduction processes. WT shows sharper rising waveform than STFT. This good time resolution of WT is effective for the location of AE events. 251

6 Conclusion Fig. 6 Results of (a) STFT-based and (b) WT-based noise reduction process. A noise-reduction process to improve the sensitivity of laser AE method was investigated. The output signal of laser interferometer was continuously recorded and the recorded waveform was processed to reduce noise component by time-frequency analysis and combination of pruning method and soft-thresholding method. Simulated AE detection test was conducted to confirm the effectiveness of the noise reduction process. Weak AE signals buried in noise can be recovered and the improvement of sensitivity of laser AE system was demonstrated. Current CWM system can process 2-channel AE waveforms of 1-MHz sampling in real time, extracting about events/s. References 1. M. Enoki, M. Watanabe, P. Chivavibul and T. Kishi, Sci. Technol. Adv. Mater., 1,, M. Watanabe, M. Enoki and T. Kishi, Mater. Sci. Eng. A, 359, 3, S. Nishinoiri, M. Enoki, T. Mochizuki and H. Asanuma, Mater. Trans., 45, 4, A. Abbate, S. C. Schroeder and P. Das, IEEE Trans. on Ultrasonics, Ferroelectronics, and Frequency Control, 44, 1997, K. Ito and M. Enoki, Mater. Trans., 48, 7,