Microsoft Word - cet-01.docx CHEMICAL ENGINEERING TRANSACTIONS VOL. 46, 2015 A publication of The Italian Association of Chemical Engineering Online at www.aidic.it/cet Guest Editors: Peiyu Ren, Yancang Li, Huiping Song Copyright © 2015, AIDIC Servizi S.r.l., ISBN 978-88-95608-37-2; ISSN 2283-9216 Optimized Signal De-noising Algorithm for Acoustic Emission Leakage Wang Xin-Hua*a,b, Yang Jiea, Jiao Yu-Linb, Niu Yong-Chaoc a Wuhan University of Technology, Wuhan 430063, China b Shangqiu Vocational and Technical College, Shangqiu 476000, China c Shangqiu Jinpeng Industrial Co.,Ltd., Shangqiu 476000,China gyxxwxh@163.com Traditional wavelet denoising method cannot eliminate complex high-pressure pipe signals effectively. In the updated wavelet adaptive algorithm, this thesis defines the constraints in order to reconstruct the signals accurately. According to the minimum mean square error criterion, the results predict the weight coefficient and get the optimal linear predictive value. Adopting the improved algorithm under the same condition, this thesis concluded that Db6 increased the complexity of wavelet algorithm by 50% by comparative experiments. It will be more conducive to the realization of hardware and the feasibility of real-time denoising. Dual adaptive wavelet denoising method improved SNR by 50%. This denoising method will play a key role in the detection rate of high-pressure pipe in the online leakage detection system. 1. Introduction Acoustic emission signal contains abundant of information related to defect nature and various types of interferences and noises simultaneously. It has been long a technical problem to recognize the weak defect signal from the background noise. The impulse interference noise caused by occasional factors can be wiped off easily through amplitude limiting filter method, median filter method and arithmetic method (Heo, G., 2012) ,(Haiying, C., 2015). But the background noise distributed randomly in the time domain created inside the tested material will bring problematic difficulties to the defect detection. Especially in some noise material such as carbon fiber composite, welded joint and laminate material, this noise has similar frequency distribution feature with acoustic emission wave in the reflection inside the material due to the internal structure of these materials (such as scatterers as grain, carbon fiber and so on). Thus it is hard to use the mentioned method above to isolate the background noise from the frequency domain or time domain. Besides, noises are very easy to be brought in every links of the acoustic emission wave propagation. The noises include loop noise caused by detection system and other causes. And the electronic noise caused by pre-amplifier and the frictional noise caused by relative mechanical sliding in the loading procedure. These complicated noises have severer effects on acoustic emission signal. The problem of signal to noise ratio (SNR) worsening is severer as well. Due to all this the false drop rate and omission rate in acoustic emission detection increase. This has already been one of the key factors that influence the improvement of reliability of acoustic emission detecting and evaluating technologies (Dai, Q., 2012),(Wang, X. H., 2015) . Therefore, acoustic emission signal de- noising is one important step of acoustic emission signal disposal. 2. De-noising method for acoustic emission signal based on wavelet analysis There are many methods to conduct the de-noising of digital signals which include time domain method, frequency domain method and time-frequency domain method. Every method has different range of application and application effect. For stable signal, frequency domain analysis is generally adopted. Through Fourier transform the frequency feature of signals is extracted (Ghertner, D. A., 2007). And for unstable signal, wavelet analysis method is adopted in most situations so far (Eaton, M. J., 2012). DOI: 10.3303/CET1546169 Please cite this article as: Wang X.H., Yang J., Jiao Y.L., Niu Y.C., 2015, Optimized signal de-noising algorithm for acoustic emission leakage, Chemical Engineering Transactions, 46, 1009-1014 DOI:10.3303/CET1546169 1009 Acoustic emission signal is featured with unstable randomness and it belongs to one-dimensional signal. The de0-noising model of one-dimensional signal proposed by K. Fujita is (Hao, S., 2011): ( ) ( ) ( )x n s n u nσ= + ⋅ (1) In the equation, ( )x n is the observed signal of noise and ( )s n is the true signal. ( )u n is the Gaussian white noise signal while σ is the noise intensity. Signal de-noising means to acquire the optimum value of assessment ˆ( )s n of the original signal ( )s n from the observed signal ( )x n . This thesis adopts wavelet threshold value noise method to deal with de-noising of acoustic emission signal without exception. Through scatter binary row wavelet transformation conducted to acoustic emission signal and then wavelet threshold value de-noising method is also conducted to the acoustic emission signal de- noising. The specific processes are: 1), confirm a wavelet basic function, conduct wavelet decomposition to signals at the appropriate decomposition dimension, calculate the wavelet decomposition coefficient of noise signal at this dimension; 2), estimate the noise level of high-frequency coefficients at each dimension and then set up a threshold value, use the threshold value method to modify relevant wavelet coefficient; 3), conduct wavelet inverse transformation and signal re-construction to low-frequency coefficients and the modified high- frequency coefficients and thereafter gain the signal estimated value after de-noising process. 3. Based on lifting de-noising algorithm for acoustic emission signal of wavelet Since the construction of wavelet in time domain is directly realized, the complexity of lifting algorithm is only half of the original convolution method. The structure of algorithm is simple and the calculation is speedy. Thus the lifting method has become mainstream method of calculating scatter wavelet transformation (Chambers, W. M., 2004). The traditional wavelet transformation algorithm (Mallat algorithm) adopts a method of convoluting input signal and high plus low pass filters to realize separation of high frequency and low frequency information. However, the coefficients of wavelet filter are all decimals. Among intermediate results some are decimals and if take the integer of decimals, tons of information will be lost and the re-construction and de-composition will be irreversible. Consequently reconstruction cannot be realized accurately. But in the lifting scheme, integer transform is operable and it will not affect accurate reconstruction. Due to all these advantages mentioned above of lifting wavelet and to deal with existing problems of acoustic emission wavelet de-noising method, this chapter proposed a based on lifting de-noising algorithm for acoustic emission signal of wavelet, steps are as follow: (1) Confirm lifting frame type and lifting steps of signals, conduct lifting wavelet decomposition to the data; (2) Extract low frequency smooth signal and high frequency detail signal coefficient at each step, that is to acquire new approximate dimension coefficient and wavelet coefficient and then conduct condition analysis to wavelet coefficient which is to estimate noises of high-frequency coefficients at each step; (3) According to the noise estimation, combine the threshold value algorithm adopted, set up threshold value and modify high-frequency coefficients at each step; (4) Conduct lifting inverse calculation to low-frequency coefficients and modified high-frequency coefficients. The reconstructed signals are estimated values of noise signal. Figure 1: De-noising process based on lifting wavelet acoustic emission signal Processes of acoustic emission signal lifting wavelet de-noising are as shown in Fig 1. During the de-noising processes, selecting proper framework type and optimizing threshold value are two important factors to determine de-noising effect, like traditional scatter wavelet de-noising. During the de-noising processes, picking threshold value and conducting threshold value optimization are very important links. The selection of threshold form needs not only to remove the noise, but also to protect useful signals from being harmed. This thesis adopts medium-soft threshold value method. This method can dispose wavelet coefficient with hard threshold value or soft threshold value respectively according to the practical acoustic emission data features. 1010 Besides lifting steps need to be considered comprehensively. During the lifting calculation process, the length of signal coefficient will be halved gradually as the lifting goes on. After certain number of steps, the number of signal coefficient declines to 1. So the number of steps should not be too large. And in the noise estimation of decomposition coefficient at each level, the length of signal should not be too short; otherwise the noise level would not be estimated correctly. Moreover the number of lifting steps cannot be too small. Every framework structure in the lifting wavelet transform is like the wavelet basis function in the traditional wavelet analysis. Different framework structure will generate different results in the signal de-noising. Thus the lifting frame should also be optimized while using lifting method to conduct wavelet de-noising. During this process, the number of lifting steps is three, and they all need the same threshold value calculation method. 4. Self-adaptive lifting wavelet de-noising algorithm For one-dimensional acoustic emission signal, due to the diversity of its generation mechanisms, signals in different region have different features. For example, carbon fiber composite acoustic emission signal that needs to be disposed in this thesis is unstable random signal. It has two models: bending wave and spreading wave. It includes smooth region and mutational region. Therefore, the selection of decision criterion should be appropriate. The forecasted weighting coefficient should be adjusted to make weighting coefficient match feature region self-adaptively. To settle this Lei, Cuihong et al. proposed the self-adaptive lifting algorithm (El- Amin, M. F., 2008) ,(Keum, C. M., 2012). Self-adaptive lifting algorithm first analyzes the signal sequence, selecting corresponding update operator and prediction operator according to the sequence’s local features. After that it disposes the signals. It is thus clear that this transformation method thinks completely from the perspective of signal, self-adaptively choosing different filters according to signal features in de-noising processes. This method can conduct a complete reconstruction to the signals so that it can finish de-noising disposal to the signals effectively. Researches of Zhou, Donghua H et al. have proven this point and given an updated self-adaptive algorithm (Wang, X. H., 2015). In practical application, for some signals of fixed features, two methods can be adopted generally to realize the self-adaptive filtering to signals: the first one is the combination of fixed prediction filter and updated self-adaptive algorithm and the second one is the combination method of fixed updated algorithm and self- adaptive prediction filtering. The acoustic emission signal studied in this thesis demonstrates feature of being unstable along with the change of time. The sampled signal in every experiment demonstrates a feature of randomness. So to acquire better de-noising effects, a dual self-adaptive lifting wavelet transformation algorithm is adopted to conduct de-noising disposal which is to adopt self-adaptive filtering method in both updating link and predicting link (Roetzel, W., 1994). 4.1 Updated self-adaptive algorithm Adopt self-adaptive lifting algorithm proposed in literature (Ghosh, S., 2011)Qingli as the updated self-adaptive algorithm in this paper, its principle structure is as demonstrated in Fig 2: Figure 2: Self-adaptive updating principle In picture 2, ,x y and 'x , y are low-frequency coefficients and high- frequency coefficients respectively before and after updating, D is decision function, dU is update operator, d⊕ is generalized additive operator. Being different from the updating process of standard lifting method, update operator dU here and additive operator are not fixed. They are picked self-adaptively by the discrimination function D on the basis of information of odd-even sequence. At the moment the low-frequency coefficient is: [ ] [ ] { }' ( )d dx n x n U y n= ⊕ (2) [ ]( , )nd D x y n= (3) 1011 Here nd is the discrimination functional value at n point, the definition of discrimination function ( , )D x y is: [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] 1 1 ( , ) 0 1 = 1 1 x n y n x n y n D x y n x n y n x n y n x n y n x n y n − − − < − = − − −  − − < − (4) Then the expression of update operator is: [ ] [ ] [ ] [ ]d 1 1 1 U ( = ( 1 ) 0 2 ( ) 1 y n d y n y n y n d y n d  − = −   − + =  = ） (5) From equation (4) it can be seen that the symbol of nd is determined by the value of equation [ ] [ ] [ ] [ ]1x n y n x n y n− − < − . The derivation from this is that the discrimination function is determined by the following gradient vectors: [ ] [ ]( ) [ ] [ ] [ ] [ ]( ), 1 ,x n w n x n y n y n x n= − − − (6) Then: ( )[ ] [ ] [ ]( ) [ ] [ ] [ ] [ ]( ), , 1 ,D x y n d v n w n d x n y n y n x n= = − − − (7) In the equation, d represents mapping function, and different discrimination principles reflect different gradient values. Update operator dU is defined as: [ ] [ ] [ ]( ) ( 1 ) ( )d d dU y n y n y nδ ϕ= − + (8) Additive operator d⊕ is defined as: [ ] [ ] [ ] [ ]( ) ( ( ))d d d dx n U y n x n U y nα⊕ = ⊕ (9) Low-frequency coefficients are obtained according to equations (2), (8) and (9). [ ] [ ] [ ] [ ]' 1d d dx n x n y n y nα β γ= + − + (10) Here define 1d d dα β γ+ + = ( ) ( )( ) ( ) ( )( ) ( ) 0 1 v n w n T d v n w n v n w n T  + ≤+ =  + > (11) The constraint conditions of equation (11) can ensure that the signals can be reconstructed accurately. 4.2 Self-adaptive forecasting algorithm Forecasting algorithm predicts signal odd sequence through signal even sequence. The more accurate the forecasting is, the smaller are the high-frequency coefficients acquired and then the better is the forecasting effect. This method adopted in this thesis conducts updating first and then forecasting. The process of forecasting does not have any effects on the updating process. So the accuracy of this algorithm can be improved on. The specific forecasting algorithm is: [ ] [ ] [ ]{ }2 1 2D n x n P x n= + Θ (12) In the equation, ( )D n represents high-frequency coefficients in the lifting method, the definitions of operators P , Θ are: [ ] [ ] [ ]( 2 ) ( 2 1 ) ( 2 )P x n x n x nδ ϕ= + + (13) [ ] [ ] [ ] [ ]2 1 ( 2 ) 2 1 ( 2 )x n P x n x n P x n+ Θ = + − (14) By substituting equations (13) and (14) into equation (12), the linear prediction equation is acquired as below: ( ) [ ] [ ] [ ]2 1 2 2 2D n x n x n x nδ ϕ= + − + − (15) 1012 From the forecasting equation, the key to construct linear prediction filter is to calculate the values of prediction weighting coefficients δ and ϕ . To make sure that the forecast error is the least and then the high- frequency coefficients in the lifting algorithm are the least, the odd sequence prediction must be accurate. According to the minimum mean square error principle, the optimized linear prediction value can be acquired. The follow should be satisfied: [ ] [ ] [ ] [ ]{ }2 1 ( 2 2 ) 2 ) 0E x n x n x n x nδ ϕ+ − + + = (16) From equation (16), the prediction weighting coefficients δ and ϕ can be calculated. To dispose acoustic emission signal, the absolute value of difference value between two adjacent sampling points are picked to be discrimination principle in this paper. The signal sequence is divided into smooth and mutational regions. Minimum mean square error calculation is conducted to the signal samplings in two regions respectively. Then the prediction weighting coefficients in these two regions are calculated as well. At last self-adaptive forecasting is realized. 5. Simulation experiment and analysis In order to verify the effectiveness of the algorithm, traditional wavelet (Db6), lifting algorithm constructed wavelet (Db6) and dual self-adaptive lifting wavelet are adopted respectively to conduct de-noising experiments to the broken lead acoustic emission signal based on the acoustic emission signal de-noising steps discussed above in the paper. Table 1 and picture 3 give different wavelet de-noising algorithm results. Table1. Performance of different de-noising algorithms de-noising algorithm SNR RMSE traditional wavelet (Db6) 8.9762 3.5182 lifting wavelet (Db6) 9.5485 2.6936 dual self-adaptive lifting wavelet 18.998 2.7853 From the data in table 1, the signal to noise ratios of de-noising signals of noisy acoustic emission signal, traditional wavelet transformation and lifting algorithm (Db6) wavelet transformation are basically close, being 8.9762dB and 9.5485dB respectively. The signal to noise ratio of signal de-noised by dual self-adaptive lifting method is 18.998dB, being enhanced considerably. That proves that the dual self-adaptive lifting method has better de-noising effects than the other two methods. From picture 3 it can be seen that based on the combination method of lifting wavelet and medium-soft threshold value de-noising retains the peak value feature of composite acoustic emission signal effectively. The method also demonstrates good smooth feature in the process of tending to be steady. For wavelet basis function (Db6) of the same kind, adopting lifting algorithm wavelet and traditional wavelet have no obvious differences in enhancing signal to noise ratio. However, the complexity of lifting algorithm is only half of that of Mallat algorithm. So the lifting wavelet de-noising algorithm introduced in this thesis has advantages in calculation speed and storage space. It is in favor of hardware implementation. Figure 3: De-noising results of different acoustic emission signals of wavelet (a) Original signal (b) de-noising of traditional wavelet db6(c) de-noising of lifting wavelet db6 (d) de-noising of self-adaptive wavelet 6. Conclusion This paper conducted a deep research to wavelet de-noising methods of acoustic emission signal, analysing the selection of threshold value function and optimization of threshold value in de-noising processes. It also analysed the key technologies such as confirmation of wavelet basis function and evaluation standards of de- noising effects. Moreover, it proposed a de-noising method for acoustic emission based on lifting method to deal with problems that traditional wavelet de-noising method is not in favour of hardware implementation. And considering the features of acoustic emission signal, the paper also proposed a combination method of least 1013 square method and wavelet de-noising to improve de-noising algorithm for acoustic emission signal of wavelet, adopting dual self-adaptive lifting algorithm to conduct de-noising of acoustic emission signal.Due to the flexibility of lifting algorithm, this de-noising algorithm is not constraint by signal integral construction but designs different wave filters to deal with features of different parts of signals during the signal disposal processes. In comparison with traditional wavelet transformation method, this method not only enhances signal to noise ratio effectively but also has advantageous features like: the structure is simple; the calculation is fast. These features are good for the hardware implementation and are beneficial for the real-time online application of this algorithm in acoustic emission heater leakage fault detection. 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