Optimized Signal De-noising Algorithm for Acoustic Emission Leakage

Transcription

1 1009 A publication of CHEMICAL ENGINEERING TRANSACTIONS VOL. 46, 2015 Guest Eitors: Peiyu Ren, Yancang Li, Huiping Song Copyright 2015, AIDIC Servizi S.r.l., ISBN ; ISSN The Italian Association of Chemical Engineering Online at DOI: /CET Optimize Signal De-noising Algorithm for Acoustic Emission Leakage Wang Xin-Hua* a,b, Yang Jie a, Jiao Yu-Lin b, Niu Yong-Chao c a Wuhan University of Technology, Wuhan , China b Shangqiu Vocational an Technical College, Shangqiu , China c Shangqiu Jinpeng Inustrial Co.,Lt., Shangqiu ,China gyxxwxh@163.com Traitional wavelet enoising metho cannot eliminate complex high-pressure pipe signals effectively. In the upate wavelet aaptive algorithm, this thesis efines the constraints in orer to reconstruct the signals accurately. Accoring to the minimum mean square error criterion, the results preict the weight coefficient an get the optimal linear preictive value. Aopting the improve algorithm uner the same conition, this thesis conclue that Db6 increase the complexity of wavelet algorithm by 50% by comparative experiments. It will be more conucive to the realization of harware an the feasibility of real-time enoising. Dual aaptive wavelet enoising metho improve SNR by 50%. This enoising metho will play a key role in the etection rate of high-pressure pipe in the online leakage etection system. 1. Introuction Acoustic emission signal contains abunant of information relate to efect nature an various types of interferences an noises simultaneously. It has been long a technical problem to recognize the weak efect signal from the backgroun noise. The impulse interference noise cause by occasional factors can be wipe off easily through amplitue limiting filter metho, meian filter metho an arithmetic metho (Heo, G., 2012),(Haiying, C., 2015). But the backgroun noise istribute ranomly in the time omain create insie the teste material will bring problematic ifficulties to the efect etection. Especially in some noise material such as carbon fiber composite, wele joint an laminate material, this noise has similar frequency istribution feature with acoustic emission wave in the reflection insie the material ue to the internal structure of these materials (such as scatterers as grain, carbon fiber an so on). Thus it is har to use the mentione metho above to isolate the backgroun noise from the frequency omain or time omain. Besies, noises are very easy to be brought in every links of the acoustic emission wave propagation. The noises inclue loop noise cause by etection system an other causes. An the electronic noise cause by pre-amplifier an the frictional noise cause by relative mechanical sliing in the loaing proceure. These complicate 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 rop rate an omission rate in acoustic emission etection increase. This has alreay been one of the key factors that influence the improvement of reliability of acoustic emission etecting an evaluating technologies (Dai, Q., 2012),(Wang, X. H., 2015). Therefore, acoustic emission signal enoising is one important step of acoustic emission signal isposal. 2. De-noising metho for acoustic emission signal base on wavelet analysis There are many methos to conuct the e-noising of igital signals which inclue time omain metho, frequency omain metho an time-frequency omain metho. Every metho has ifferent range of application an application effect. For stable signal, frequency omain analysis is generally aopte. Through Fourier transform the frequency feature of signals is extracte (Ghertner, D. A., 2007). An for unstable signal, wavelet analysis metho is aopte in most situations so far (Eaton, M. J., 2012). Please cite this article as: Wang X.H., Yang J., Jiao Y.L., Niu Y.C., 2015, Optimize signal e-noising algorithm for acoustic emission leakage, Chemical Engineering Transactions, 46, DOI: /CET

2 1010 Acoustic emission signal is feature with unstable ranomness an it belongs to one-imensional signal. The e0-noising moel of one-imensional signal propose by K. Fujita is (Hao, S., 2011): x( n) = s( n) + σ u( n) In the equation, x( n) is the observe signal of noise an sn ( ) is the true signal. un ( ) is the Gaussian white noise signal whileσ is the noise intensity. Signal e-noising means to acquire the optimum value of assessment sn ˆ( ) of the original signal sn ( ) from the observe signal x( n ). This thesis aopts wavelet threshol value noise metho to eal with e-noising of acoustic emission signal without exception. Through scatter binary row wavelet transformation conucte to acoustic emission signal an then wavelet threshol value e-noising metho is also conucte to the acoustic emission signal enoising. The specific processes are: 1), confirm a wavelet basic function, conuct wavelet ecomposition to signals at the appropriate ecomposition imension, calculate the wavelet ecomposition coefficient of noise signal at this imension; 2), estimate the noise level of high-frequency coefficients at each imension an then set up a threshol value, use the threshol value metho to moify relevant wavelet coefficient; 3), conuct wavelet inverse transformation an signal re-construction to low-frequency coefficients an the moifie highfrequency coefficients an thereafter gain the signal estimate value after e-noising process. 3. Base on lifting e-noising algorithm for acoustic emission signal of wavelet Since the construction of wavelet in time omain is irectly realize, the complexity of lifting algorithm is only half of the original convolution metho. The structure of algorithm is simple an the calculation is speey. Thus the lifting metho has become mainstream metho of calculating scatter wavelet transformation (Chambers, W. M., 2004). The traitional wavelet transformation algorithm (Mallat algorithm) aopts a metho of convoluting input signal an high plus low pass filters to realize separation of high frequency an low frequency information. However, the coefficients of wavelet filter are all ecimals. Among intermeiate results some are ecimals an if take the integer of ecimals, tons of information will be lost an the re-construction an e-composition will be irreversible. Consequently reconstruction cannot be realize accurately. But in the lifting scheme, integer transform is operable an it will not affect accurate reconstruction. Due to all these avantages mentione above of lifting wavelet an to eal with existing problems of acoustic emission wavelet e-noising metho, this chapter propose a base on lifting e-noising algorithm for acoustic emission signal of wavelet, steps are as follow: (1) Confirm lifting frame type an lifting steps of signals, conuct lifting wavelet ecomposition to the ata; (2) Extract low frequency smooth signal an high frequency etail signal coefficient at each step, that is to acquire new approximate imension coefficient an wavelet coefficient an then conuct conition analysis to wavelet coefficient which is to estimate noises of high-frequency coefficients at each step; (3) Accoring to the noise estimation, combine the threshol value algorithm aopte, set up threshol value an moify high-frequency coefficients at each step; (4) Conuct lifting inverse calculation to low-frequency coefficients an moifie high-frequency coefficients. The reconstructe signals are estimate values of noise signal. (1) Figure 1: De-noising process base on lifting wavelet acoustic emission signal Processes of acoustic emission signal lifting wavelet e-noising are as shown in Fig 1. During the e-noising processes, selecting proper framework type an optimizing threshol value are two important factors to etermine e-noising effect, like traitional scatter wavelet e-noising. During the e-noising processes, picking threshol value an conucting threshol value optimization are very important links. The selection of threshol form nees not only to remove the noise, but also to protect useful signals from being harme. This thesis aopts meium-soft threshol value metho. This metho can ispose wavelet coefficient with har threshol value or soft threshol value respectively accoring to the practical acoustic emission ata features.

3 1011 Besies lifting steps nee to be consiere comprehensively. During the lifting calculation process, the length of signal coefficient will be halve graually as the lifting goes on. After certain number of steps, the number of signal coefficient eclines to 1. So the number of steps shoul not be too large. An in the noise estimation of ecomposition coefficient at each level, the length of signal shoul not be too short; otherwise the noise level woul not be estimate 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 traitional wavelet analysis. Different framework structure will generate ifferent results in the signal e-noising. Thus the lifting frame shoul also be optimize while using lifting metho to conuct wavelet e-noising. During this process, the number of lifting steps is three, an they all nee the same threshol value calculation metho. 4. Self-aaptive lifting wavelet e-noising algorithm For one-imensional acoustic emission signal, ue to the iversity of its generation mechanisms, signals in ifferent region have ifferent features. For example, carbon fiber composite acoustic emission signal that nees to be ispose in this thesis is unstable ranom signal. It has two moels: bening wave an spreaing wave. It inclues smooth region an mutational region. Therefore, the selection of ecision criterion shoul be appropriate. The forecaste weighting coefficient shoul be ajuste to make weighting coefficient match feature region self-aaptively. To settle this Lei, Cuihong et al. propose the self-aaptive lifting algorithm (El- Amin, M. F., 2008),(Keum, C. M., 2012). Self-aaptive lifting algorithm first analyzes the signal sequence, selecting corresponing upate operator an preiction operator accoring to the sequence s local features. After that it isposes the signals. It is thus clear that this transformation metho thinks completely from the perspective of signal, self-aaptively choosing ifferent filters accoring to signal features in e-noising processes. This metho can conuct a complete reconstruction to the signals so that it can finish e-noising isposal to the signals effectively. Researches of Zhou, Donghua H et al. have proven this point an given an upate self-aaptive algorithm (Wang, X. H., 2015). In practical application, for some signals of fixe features, two methos can be aopte generally to realize the self-aaptive filtering to signals: the first one is the combination of fixe preiction filter an upate self-aaptive algorithm an the secon one is the combination metho of fixe upate algorithm an selfaaptive preiction filtering. The acoustic emission signal stuie in this thesis emonstrates feature of being unstable along with the change of time. The sample signal in every experiment emonstrates a feature of ranomness. So to acquire better e-noising effects, a ual self-aaptive lifting wavelet transformation algorithm is aopte to conuct e-noising isposal which is to aopt self-aaptive filtering metho in both upating link an preicting link (Roetzel, W., 1994). 4.1 Upate self-aaptive algorithm Aopt self-aaptive lifting algorithm propose in literature (Ghosh, S., 2011)Qingli as the upate self-aaptive algorithm in this paper, its principle structure is as emonstrate in Fig 2: Figure 2: Self-aaptive upating principle In picture 2, xy, an ' x, y are low-frequency coefficients an high- frequency coefficients respectively before an after upating, D is ecision function, U is upate operator, is generalize aitive operator. Being ifferent from the upating process of stanar lifting metho, upate operatoru here an aitive operator are not fixe. They are picke self-aaptively by the iscrimination function D on the basis of information of o-even sequence. At the moment the low-frequency coefficient is: [ ] [ ] { ( )} ' x n x n U y n n = (2) = D x y n (3) (, )[ ]

4 1012 Here is the iscrimination functional value at n point, the efinition of iscrimination function (, ) n [ ] [ ] < [ ] [ ] 1 x n y n 1 < x n y n D( x, y) [ n] = 0 x n y n 1 = x n y n 1 x n y n 1 x n y n Then the expression of upate operator is: [ ] y n 1 = 1 1 U ( y n = ( y n 1 y n ) 0 2 yn ( ) = 1 Dxy is: [ ]) [ ] + [ ] = (5) From equation (4) it can be seen that the symbol of is etermine by the value of equation [ ] [ 1] [ ] [ ] x n y n < x n y n. The erivation from this is that the iscrimination function is etermine by the following graient vectors: ( x[ n], w[ n] ) ( x[ n] y[ n 1 ], y[ n] x[ n] ) Then: = (6) (, )[ ] ( [ ], [ ]) ( [ ] [ 1 ], [ ] [ ]) D x y n = v n w n = x n y n y n x n (7) In the equation, represents mapping function, an ifferent iscrimination principles reflect ifferent graient values. Upate operatoru is efine as: U( y[ n] ) = δ( y[ n 1) ] + ϕ( y[ n] ) (8) Aitive operator is efine as: [ ] [ ] α [ ] [ ] x n U ( y n ) = ( x n U ( y n )) (9) Low-frequency coefficients are obtaine accoring to equations (2), (8) an (9). ' x n = α x n + β y n 1 + γ y n (10) Here efine α + β + γ = 1 0 v( n) + w( n) T ( v( n) + w( n) ) = 1 v( n) + w( n) > T The constraint conitions of equation (11) can ensure that the signals can be reconstructe accurately. 4.2 Self-aaptive forecasting algorithm Forecasting algorithm preicts signal o sequence through signal even sequence. The more accurate the forecasting is, the smaller are the high-frequency coefficients acquire an then the better is the forecasting effect. This metho aopte in this thesis conucts upating first an then forecasting. The process of forecasting oes not have any effects on the upating process. So the accuracy of this algorithm can be improve on. The specific forecasting algorithm is: [ ] [ 2 1] { [ 2 ]} D n = x n + Θ P x n (12) In the equation, D ( n) represents high-frequency coefficients in the lifting metho, the efinitions of operators P, Θ are: ( [ 2 ]) δ( [ 2 1) ] ϕ( [ 2 ]) Px n = x n+ + x n (13) x 2n+ 1 Θ P( x 2 n ) = x 2n+ 1 P( x 2 n ) (14) By substituting equations (13) an (14) into equation (12), the linear preiction equation is acquire as below: ( ) [ 2 1] δ [ 2 2] ϕ [ 2 ] D n = x n+ x n+ x n (15) n (4) (11)

5 1013 From the forecasting equation, the key to construct linear preiction filter is to calculate the values of preiction weighting coefficientsδ anϕ. To make sure that the forecast error is the least an then the highfrequency coefficients in the lifting algorithm are the least, the o sequence preiction must be accurate. Accoring to the minimum mean square error principle, the optimize linear preiction value can be acquire. The follow shoul be satisfie: { [ ] δ [ ] ϕ [ ] [ ] } E x 2n+ 1 ( x 2n+ 2 ) + x 2 n x n ) = 0 (16) From equation (16), the preiction weighting coefficientsδ anϕ can be calculate. To ispose acoustic emission signal, the absolute value of ifference value between two ajacent sampling points are picke to be iscrimination principle in this paper. The signal sequence is ivie into smooth an mutational regions. Minimum mean square error calculation is conucte to the signal samplings in two regions respectively. Then the preiction weighting coefficients in these two regions are calculate as well. At last self-aaptive forecasting is realize. 5. Simulation experiment an analysis In orer to verify the effectiveness of the algorithm, traitional wavelet (Db6), lifting algorithm constructe wavelet (Db6) an ual self-aaptive lifting wavelet are aopte respectively to conuct e-noising experiments to the broken lea acoustic emission signal base on the acoustic emission signal e-noising steps iscusse above in the paper. Table 1 an picture 3 give ifferent wavelet e-noising algorithm results. Table1. Performance of ifferent e-noising algorithms e-noising algorithm SNR RMSE traitional wavelet (Db6) lifting wavelet (Db6) ual self-aaptive lifting wavelet From the ata in table 1, the signal to noise ratios of e-noising signals of noisy acoustic emission signal, traitional wavelet transformation an lifting algorithm (Db6) wavelet transformation are basically close, being B an B respectively. The signal to noise ratio of signal e-noise by ual self-aaptive lifting metho is B, being enhance consierably. That proves that the ual self-aaptive lifting metho has better e-noising effects than the other two methos. From picture 3 it can be seen that base on the combination metho of lifting wavelet an meium-soft threshol value e-noising retains the peak value feature of composite acoustic emission signal effectively. The metho also emonstrates goo smooth feature in the process of tening to be steay. For wavelet basis function (Db6) of the same kin, aopting lifting algorithm wavelet an traitional wavelet have no obvious ifferences in enhancing signal to noise ratio. However, the complexity of lifting algorithm is only half of that of Mallat algorithm. So the lifting wavelet e-noising algorithm introuce in this thesis has avantages in calculation spee an storage space. It is in favor of harware implementation. Figure 3: De-noising results of ifferent acoustic emission signals of wavelet (a) Original signal (b) e-noising of traitional wavelet b6(c) e-noising of lifting wavelet b6 () e-noising of self-aaptive wavelet 6. Conclusion This paper conucte a eep research to wavelet e-noising methos of acoustic emission signal, analysing the selection of threshol value function an optimization of threshol value in e-noising processes. It also analyse the key technologies such as confirmation of wavelet basis function an evaluation stanars of enoising effects. Moreover, it propose a e-noising metho for acoustic emission base on lifting metho to eal with problems that traitional wavelet e-noising metho is not in favour of harware implementation. An consiering the features of acoustic emission signal, the paper also propose a combination metho of least

6 1014 square metho an wavelet e-noising to improve e-noising algorithm for acoustic emission signal of wavelet, aopting ual self-aaptive lifting algorithm to conuct e-noising of acoustic emission signal.due to the flexibility of lifting algorithm, this e-noising algorithm is not constraint by signal integral construction but esigns ifferent wave filters to eal with features of ifferent parts of signals uring the signal isposal processes. In comparison with traitional wavelet transformation metho, this metho not only enhances signal to noise ratio effectively but also has avantageous features like: the structure is simple; the calculation is fast. These features are goo for the harware implementation an are beneficial for the real-time online application of this algorithm in acoustic emission heater leakage fault etection. At the en of paper, the broken lea analogy simulation experiment has verifie this analysis conclusion. Acknowlegements Founation item: Nature Science Founation of Henan Science an Technology Bureau (141008) (141080); Major science an technology research plan project in Henan province ( ); References Chambers, W. M., & Mortensen, N. M., Postoperative leakage an abscess formation after colorectal surgery. Best Practice & Research Clinical Gastroenterology, 18(5), Doi: /j.bpg Cheng, H. Y., Hu, Z. Y., Jia, L., Response surface methoology of foame bitumen expansion ratio. International Journal of Heat an Technology, 33(3), Doi: /ijht Dai, Q., Ng, K., Zhou, J., Kreiger, E. L., & Ahlborn, T. M., Damage investigation of single-ege notche beam tests with normal strength concrete an ultra-high performance concrete specimens using acoustic emission techniques. Construction an Builing Materials, 31, Doi: /j.conbuilmat Eaton, M. J., Pullin, R., & Holfor, K. M., Acoustic emission source location in composite materials using Delta T Mapping. Composites Part A: Applie Science an Manufacturing, 43(6), Doi: /j.compositesa El-Amin, M. F., & Kanayama, H., Bounary layer theory approach to the concentration layer ajacent to a ceiling wall at impinging region of a hyrogen leakage. International journal of hyrogen energy, 33(21), Doi: /j.ijhyene Ghertner, D. A., & Fripp, M., Traing away amage: Quantifying environmental leakage through consumption-base, life-cycle analysis.ecological Economics, 63(2), Doi: /j.ecolecon Ghosh, S., Mukhopahyay, D., & Saha, S. K., An experimental analysis of subcoole leakage flow through slits from high pressure high temperature pipelines. International Journal of Pressure Vessels an Piping, 88(8), Doi: /j.ijpvp Hao, S., Shuguang, J., Lanyun, W., & Zhengyan, W., Bulking factor of the strata overlying the gob an a three-imensional numerical simulation of the air leakage flow fiel. Mining Science an Technology (China), 21(2), Doi: /j.mstc Heo, G., & Lee, S. K., Internal leakage etection for feewater heaters in power plants using neural networks. Expert Systems with Applications, 39(5), Doi: /j.conbuilmat Keum, C. M., Bae, J. H., Kim, M. H., Choi, W., & Lee, S. D., Solution-processe low leakage organic fiel-effect transistors with self-pattern registration base on patterne ielectric barrier. Organic Electronics, 13(5), Doi: /j.orgel Roetzel, W., & Lee, D. W., Effect of baffle/shell leakage flow on heat transfer in shell-an-tube heat exchangers. Experimental Thermal an Flui Science, 8(1), Doi: / (94)90068-X Wang, X. H., Jiao, Y. L., Niu, Y. C., & Yang, J., Stuy on the acoustic emission features of leakage etection assiste by wave guie ros. International Journal of Heat an Technology, 33(2), Doi: /ijht Wang, X. H., Jiao, Y. L., Niu, Y. C., & Yang, J., Stuy on enhance heat transfer features of nanomagnetic flui heat pipe uner magnetic fiel. International Journal of Heat an Technology, 33(1), Doi: /ijht