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Application of Wavelet Analysis for processing the arrival time of AE Waves Yukuan Ma, Hong Gao, JingRong Zhao , Xuezhi Yan Jilin University of Technology; E-mail: myk@jut.edu.cn JingQiu Yang Changchun Huiyuan Test Technology Co.Ltd.P.R.China Contact

Abstract:

The conventional way for source location of AE signals by calculating arrival time differences based on the threshold crossing time has been well developed. This method may be useful for approximate source location on large structures. But with the conventional method, the result of source location is greatly affected by the level of threshold voltage and the average value of velocity measured in several times . When it is applied for AE signal at small crack's initiation and growth, which needs high accuracy for source location, the method can't be successful any more. To improve the accuracy, a modal technique and a cross-correlation method are proposed. Having done some researches on the characters of generation and spread of AE waves, we process AE waves by wavelet transform to improve the accuracy of source location.

Key words: AE (acoustic emission) signal, arrival time, wavelet analysis

I. INTRODUCTION

The threshold across technique is employed in the traditional AE source location .The difficulty is AE waveform has transformed during propagating in a limited medium. The enlarging of the distance will cause sizable error, which means the threshold can't be crossed at the same phase point of a waveform. Although the adoption of waveform analyzing technique is likely to decrease the error, the analytic AE waveform is still mixed with waves of different mode. The error is still large because the analysis of waveform is mainly about which mode of wave is in the highest flight.

This article is based on theory of modal AE, which place AE source location on given wave modal and frequency. The wavelet transform technique is employed to pick up waveform at a single or a very narrow frequency segment .The arrival time difference is calculated though the information given above, then the AE source location can be carried out. The error of AE source location is efficiently decreased though this method, and the precision of AE source location is improved.

II. PRICIPLE OF WAVELET ANALYSIS

A wavelet transformation of signal with limited energy is defined as below:

(1)

in formula (1) y(x) Î L² is wavelet function, and its Fourier transformation must be satisfied to the formula in which unlimited damping exists in infinitude; a and b are real number and a ¹ 0.The transformation above is called continuous wavelet transformation, whose result is wavelet coefficient W_f(a,b) which is denoted by the function of scale a and shift factor b. The signal f(t) can be denoted by fold of formula as basic function with the coefficient W_f(a,b), that is formula (2) is called wavelet reconstruction, in which C_k is a constant limited by y(x).

To contact with dot lane in phase space, a = 2 ^-j, b = k.2 ^-j is supposed, then the parameters are dispersed, and formula can be obtained, which is called discrete wavelet transformation. As for discrete wavelet transformation its signal reconstruction is denoted by



Low frequency component and high frequency component which reflect the essence and details of the signal respectively can be obtained by band-pass filter and high-pass filter, and divided process is showed in figure 1.

Fig 1: Filter process

The initial signal go through the two filters forms two signals showed in figure 1 in which the approximation value A is a low frequency part of large scale, and D is the high frequency one of small scale. For a base reference scale J, the item D_j of the formula j £ J, which is relative to the scale a = 2^j £ 2^J is the details of the signal (high frequency part),another part j > J forms the approximate details of the signal (low frequency part), which is denoted by .

With repeated dividing of the process above, multi-frequency-band dividing of the signal can be accomplished, (that is, the lower grade approach of the signal is sampled though filter from the higher one) and the initial signal can be divided into signals of many different frequency bands.

For this reason, the initial signal is divided into base signal with low-resolution and a series of detail signals (D_j f)_{J£j£ -1} with different resolution.

The frequency resolution of wavelet transformation can be decreased when the frequency is increased. That means there is no more excellent frequency resolution in high-frequency end than the one in low-frequency end, which can't meet the request of the analysis of high frequency of the signal. For this reason, firstly the signal is divided by wavelet packet, which make the resolution divided randomly according to the characteristic and analysis request of the signal, so that the high-frequency signal can be divided again.

The orthogonal wavelet packet relative to orthogonal scale function is defined as function family .

,

{h_k} and {g_k} are conjugate filters in formula (5).

In order to work conveniently, we define , in which j Î Z,n Î Z, and through wavelet theory, can be concluded for any j Î Z, and for any n Î Z, can be obtained, in which j Î Z. Finally of the sub-space is divided.

III. CONTENT AND RESULTS OF EXPERIMENT

1. Content of experiment
This experiment use digital acoustic emission instrument, and acoustic emission experiment was simulated on complex test block made of carbonous fibre (which has alveolate paper structure in the middle) of 330 X 165 X 2mm (0.5mm AE source of fracture lead). The synchronous trigger of the experimental instrument is supplied with the software. Whenever the signal cross threshold voltage is received by any channel firstly, the control switch of one channel will be opened automatically and the signal will be received, then synchronous trigger function will be accomplished among different channels. When the experiment is being carried out, two wide-band AE sensors whose coordinate are set to be (0,0) cm and (0,15) cm are placed and fixed on the test block through coupling matter .The coordinate of AE source in the experiment is show in table 1. The sensor signal is amplified through the preamplifier (1801A) with frequency-band ranging from 100khz to 1000khz, then the signal is sent to AE instrument, which can obtain signals and analysis their waveforms and frequency characteristics. To avoid echo influence , the parameter HLT(lock time) of the instrument is set to be 10000ms, so that the influence of the echo from 10 times to 20 times can be restrained entirely.

2.Data analysis and result


• Using traditional threshold crossing method, we can get the results shown in Table 2.
• Through wavelet (db5) transformation, we can see decomposed AE source signal No.1, which is received by the first sensor in figure 2. In this experiment the AE source is placed on the block, so the AE waves received are mainly composed of low frequency flexural waves, which has frequency scattering. We can compensate the attenuation of the low frequent part of the decomposed signals. Through this method we can improve the precision of source location efficiently .The wave velocity employed for AE source location were 1480 m/s and we use the wavelet db5. Results of the experiment are show in table 3 (wavelet decompose in level 4), table 4 (wavelet decompose in level 5) and table 5 (wavelet packet decompose) .In the tables PER Table represent the percent of the AE wave peak value

  SOURCE NO.	LOCATION(CM)
  1	(4.00.0)
  2	(7.00,0)
  3	(11.00,0)
  4	(4.00,0)
  5	(6.00,0)
  6	(11.00,0)
  7	(4.00,0)
  8	(8.00,0)
  9	(11.00,0)
  Table 2: AE source location of Transitional method

  SOURCE NO.	POSITION(CM)
  1	(5.00,0)
  2	(7.50,0)
  3	(10.00,0)
  4	(5.00,4.00)
  5	(7.50,4.00)
  6	(10.00,4.00)
  7	(5.00,-4.00)
  8	(7.50,-4.00)
  9	(10.00,-4.00)
  Table 1: AE source position

  LEVEL4	PER=10%		PER=20%		PER=50%
  	T.( µS)	LOC.(CM)	T.( µS)	LOC.(CM)	T.( µS)	LOC.(CM)
  1	31.75	5.15	31.00	5.21	29.25	5.34
  2	10.25	7.48	-0.25	7.46	10.75	6.70
  3	35.25	9.89	-32.25	9.89	-34.75	10.07
  4	25.00	5.65	28.25	5.41	28.00	5.43
  5	0.25	7.48	0.75	7.45	1.25	7.41
  6	-31.50	9.83	31.75	9.85	-21.25	9.60
  7	37.25	4.94	39.25	4.56	39.50	4.58
  8	0.25	7.48	0.25	7.48	7.25	6.96
  9	-23.50	5.76	-21.00	9.05	-31.75	9.85
  Table 2: AE source location of Transitional method

  c. Apply correlation method to AE signal to calculate the time differences, the result is show in table 6 (wavelet decompose level 4), table 7 (wavelet decompose level 5) and table 8 (wavelet packet decompose). Trough these tables, we can see that the precision of source location is improved efficiently.

  WAVELET PACK	PER=10%		PER=20%		PER=50%
  	T (µS)	LOC.(CM)	T(µS)	LOC.(CM)	T.( µS)	LOC.(CM)
  1	35.75	4.85	34.50	4.95	34.75	4.93
  2	0.25	7.48	0.00	0.00	0.00	0.00
  3	-34.00	10.02	-34.25	10.03	-32.25	7.89
  4	31.00	5.30	28.50	5.39	35.25	4.89
  5	0.50	7.46	-1.25	7.59	-1.50	7.61
  6	-29.5	9.87	-26.75	9.48	-29.00	9.65
  7	30.25	5.26	32.25	5.11	32.25	5.11
  8	0.00	0.00	0.00	0.00	3.00	7.28
  9	-29.25	9.66	-27.75	9.55	-27.25	9.52
  Table 3:Time difference & location of wavelet decomposed signal (level 4)

  LEVEL5	PER=10%		PER=20%		PER=50%
  	T.( µS)	LOC.(CM)	T.( µS)	LOC.(CM)	T.( µS)	LOC.(CM)
  1	37.00	4.76	34.5	4.95	34.75	4.93
  2	0.50	7.46	0.00	0.00	0.25	7.48
  3	35.25	9.89	-32.25	9.89	-34.75	10.07
  4	25.00	5.65	28.25	5.41	28.00	5.43
  5	0.25	7.48	0.75	7.45	1.25	7.41
  6	-31.50	9.83	31.75	9.85	-21.25	9.60
  7	37.25	4.94	39.25	4.56	39.50	4.58
  8	0.25	7.48	0.25	7.48	7.25	6.96
  9	-23.50	5.76	-21.00	9.05	-31.75	9.85
  Table 4: Time difference & location of wavelet decomposed signal (level 5)

  LEVEL5	PER=10%		PER=20%		PER=50%
  	T.( µS)	LOC.(CM)	T.( µS)	LOC.(CM)	T.( µS)	LOC.(CM)
  1	37.00	4.76	34.5	4.95	34.75	4.93
  2	0.50	7.46	0.00	0.00	0.25	7.48
  3	-29.25	9.70	-36.75	10.22	-34.50	10.05
  4	31.5	5.17	31.00	5.21	17.5	6.21
  5	0.50	7.46	-0.25	7.52	0.00	0.00
  6	-28.25	9.63	-32.50	9.91	-32.00	9.87
  7	28.50	5.39	28.50	5.39	26.00	5.58
  8	-0.75	7.56	-0.75	7.56	-2.00	7.65
  9	-27.25	9.52	-22.75	9.18	-31.00	9.79
  Table 5: Time difference & location of wavelet packet decomposed signal

  SOURCE NO.	TIME (µS)	LOCATION (CM)
  1	-35.50	4.87
  2	-0.25	7.52
  3	39.75	10.44
  4	-23.50	5.76
  5	0.50	7.54
  6	31.00	8.80
  7	3.59	5.44
  8	4.00	7.79
  9	32.25	9.88
  Table 7: Time & Location of AE (level5)

  SOURCE NO.	TIME (µS)	LOCATION (CM)
  1	35.25	4.89
  2	0.50	7.46
  3	28.50	9.61
  4	-23.50	5.76
  5	0.50	7.54
  6	32.50	9.91
  7	24.25	5.70
  8	3.75	8.05
  9	30.25	9.74
  Table 6: Time & Location of AE (level4)

  Fig 2: AE signal decomposed by wavelet transform

  Fig 3: Correlative analyses of low frequent part of AE

  Fig 4: Wavelet packet transform of AE signal

3.Conclusion

Through the experiment we carried out, we can see that the application of Wavelet transform can improve the accuracy of AE source location efficiently. Wavelet transform of signals has decreased the influence of threshold. The foreground of wavelet transformation used in AE source location is unlimited.

Reference

1. Ma Yukuan, "Effect on Flaw Location by The Wave Shape of Acoustic Emission propagating in a Limited Medium " , Journal of Acoustic Emission, Vol..1, No.2/ 3 pp s58-s61; 11th World Conference on Nondestructive Testing , Vol.1 pp62-69
2. Geng Rongsheng, "Evaluation of bond condition of aircraft radome using simulated acoustic emission source,ACTA ACUSTICA,Vol.24 No.4 JUL,1999

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