Preliminary investigation of multi-wavelet denoising in partial discharge detection

Transcription

1 Preliminary investigation of multi-wavelet denoising in partial disharge detetion QIAN YONG Department of Eletrial Engineering Shanghai Jiaotong University 8#, Donghuan Road, Minhang distrit, Shanghai City CHINA HUANG CHENG-JUN Department of Eletrial Engineering Shanghai Jiaotong University 8#, Donghuan Road, Minhang distrit, Shanghai City CHINA JIANG XIU-CHEN Department of Eletrial Engineering Shanghai Jiaotong University 8#, Donghuan Road, Minhang distrit, Shanghai City CHINA Abstrat: - Partial disharge (PD) pulses deteted on site usually tae on various modes, and it is diffiult for wavelet to selet proper wavelet basis funtion in denoising. In partiular, in the ase of PD luster with multi-mode, onventional wavelet denoising an hardly give satisfied result. Multi-wavelet is the new development of wavelet theory, extending the idea of wavelet by representing a signal with more than one saling funtion, and outperforms wavelet in signal proessing. In this ontribution, we employ multi-wavelet to detet the partial disharge, investigating its denoising performane. For PD pulse of single-mode or PD luster of multi-mode, we run massive simulations, using both multi-wavelet denoising and wavelet denoising. The results obtained demonstrate that, in omparison with wavelet, multi-wavelet denoising an preserve more signal features while removing noise from the measured data. In addition, multi-wavelet denoising needs no (or less) prior nowledge of partial disharge. Key-Words: - Multi-wavelet, Wavelet, Partial disharge, Vetor threshold, Denoising 1 Introdution Partial disharge deteting tehnology is important for insulation assessment of power apparatus, and a great deal of wor has been done in this field over the past deades. Partial disharge is wea eletri signal, apt to be interfered by various noises existing on site, and usually the noises are so strong that PD signals are buried ompletely. Therefore, for analyzing the partial disharge orretly, first of all, noises must be suppressed in a proper way[1]. At present, the most ommonly used method for noise suppression is wavelet denoising. Wavelet analysis, famous for its multi-resolution analysis (MRA), an usually give good results in signal proessing. However, in pratial appliation, there still exist some problems, of whih the well-nown is the seletion of wavelet basis funtion. The seletion of wavelet basis funtion is appliation dependent, mainly based on waveform mathing, and different wavelet basis funtion usually means different result. And it is the same ase in denoising PD data. Differene in wavelet basis funtions result in differene in denoised PD signals, and sometimes this differene is signifiant. For seleting the optimal wavelet basis funtion, Ma et al in [] proposed a method based on ross orrelation oeffiient, however, this method needs prior nowledge of PD pulse waveform. In addition, PD pulses, subet to different disharge mehanisms, defet positions, propagation routes and

2 detetion iruits, usually tae on different waveforms[3]. How an we determine the optimal wavelet basis funtion when the deteted PD pulses have more than one mode? For solving the problems mentioned above, a onept of wavelet subset was proposed reently [3], expeting lessening the effet of wavelet basis funtion by using several wavelet basis funtions simultaneously. However, with this algorithm, another problem about PD signal reonstrution was brought. Multi-wavelet is a relative newomer in the word of wavelet. It extends the idea of the wavelet by representing a signal with more than one saling funtion. And these saling funtions an be designed to be simultaneously symmetri, orthogonal, have short supports and high vanishing moments, whih annot be ahieved at the same time for wavelet using only one saling funtion[4]. Thus, multi-wavelet offers the possibility of superior performane in signal proessing appliations, ompared with wavelet. In this ontribution, we employ multi-wavelet to extrat PD pulses overwhelmed by noise, and investigate its performane in omparison with wavelet. The organization of this ontribution is as follows. Setion gives a short introdution to multi-wavelet. Setion 3 explains how multi-wavelet based denoising wors. Setion 4 disusses the performane of multi-wavelet based denoising for PD of various modes and shows some experiment results. And the final setion draws the onlusion and points out the wor in the future. Basi theory of multi-wavelet Multi-wavelet is introdued as an extension to salar wavelets, and many similarities exist between them, here we are about to introdue it briefly. The multi-wavelet basis uses translations and dilations of r ( r ) saling funtions φ 1, φ,, φ M and r mother wavelet funtions ψ 1, ψ,, ψ M.If we write Φ = ( φ, φ,..., φ ) T 1 M and Ψ = ( ψ1, ψ ( ) ( ) ( )) T 1 x, ψ x,..., ψ M x, then we have L 1 Φ = H Φ( x ) (1) = L 1 = = G Φ( x ) Ψ () where H and G denote r r filter matries, whereas L and r are the number of saling oeffiients and the multipliity of multi-wavelet, respetively. For the sae of larity, we use S = S, (, T S,,...,S r, ) and ( ) T = D1,,D,,...,Dr, D to represent the low-pass and high-pass oeffiients. The forward and inverse multi-wavelet transform an be reursively alulated by[5,6] + 1, = L 1 H ns n+ n= + 1, = L 1 G ns n+ n= L 1 T T = H n S + 1, + n + G n D + 1, + n n= S (3) D (4) ( ) S (5) where denotes the resolution level. With the development of multi-wavelet theory over the past deade, multi-wavelet GHM, CL and SA4 et., were onstruted in suession by Geronimo, Chui et al[7-9]. In this ontribution, as preliminary researh, only the ommonly used CL multi-wavelet ( r = ) is onsidered, orresponding filter matries of CL an be found in literature[8]. 3 Multi-wavelet denoising sheme 3.1 Preproessing of multi-wavelet The filters of multi-wavelet transform are in the form of matrix, and this demands the input signals must be in the form of vetor, and therefore, salar signals must be mapped into vetor signals by preproessing. Correspondingly, the denoised results must be mapped ba into salar signals by post-proessing. The flowhart of multi-wavelet denoising is depited in Fig.1[5]. Fig.1 Flow hart of multi-wavelet denoising Preproessing an be done in two ways: one is using the prefilter[6, 1], and the other is balaned multi-wavelet basis[11]. Beause prefilter an enable the resulting filterban to possess desired approximation power and property suh as orthoglnality, in pratie it is preferred. For multi-wavelet transform, prefilter is not unique, proper seletion of prefilter is important for the suess in denoising. Aording to literature[4, 1, 13], together with our massive simulations, best denoising performane an be obtained with repeated row prefilter and approximation prefilter. 1) Repeated row prefilter In this ase, the given salar input of length N is

3 mapped to a sequene of N length-vetor. () y, f y, = = (1) y, δf where denotes the initial deomposition level and δ is a onstant. The onstant δ is hosen so that the output from the highpass multi-filter is zero. ) Approximation prefilter The salar input of length N, by preproessing with this filter, an be mapped to a sequene of N/ length- vetor. M f ( m+ ) y, = Pm m= f ( m+ ) + 1 where P are matries. m Both repeated row prefilter and approximation prefilter do well in pratie. However, in omparison with the former, the latter omputes less omplexity, and hene in the suessive setions only the latter is onsidered. Prefiltering proess is invertible, and a post-filter an do the opposite proess, i.e., mapping the data from multiple streams into one stream. The prefilter and post-filter used in our wor an be found in literature [14]. 3. Vetor thresholding Proper seletion of threshold is ritial to the suess of multi-wavelet denoising. In the past years, numerous wor have been reported in this field[4, 13-17], in whih the results of Downie is signifiant. Based on Downie s wor, thresholding an be lassified into two ategories: salar thresholding and vetor thresholding. Results reported in literature [5, 1, 14-17] and simulations we run indiate that vetor thresholding is superior, and therefore in the following setions only vetor thresholding is onsidered. A vetor based thresholding sheme an be summarized as follows[1, 14]: 1) Compute multi-wavelet oeffiients D ) Compute the ovariane matrix V used for deorrelating multi-wavelet oeffiients. V is the distribution parameter of noise oeffiients at resolution level. It an be obtained by robust ovariane estimation[1], or by deflator defined in [14], in the suessive setions the latter is preferred. T 1 3) Define a new quantity θ = D V D, in the presene of only white noise, θ will have a χ distribution with freedom equal to r [1]. 4) Estimate threshold λ. Threshold estimator models, suh as universal threshold estimator[14], vetor threshold estimator[1], SURE estimator[13], LGCV estimator[15] and optimal threshold estimator[16], et., are well suited to eliminate white noise. For suppressing indeterminate noise, a robust threshold estimator should be adopted: λ = m ln n /.6745 [], where λ, n and m are threshold value, number of oeffiients, median value of oeffiients at level, respetively. 5) Thresholding. For a given threshold λ, the thresholding rule is D ˆ = D f ( θ, λ ), where f ( ) denotes the onventional hard thresholding or soft thresholding. Hard thresholding produes an improved PD signal to noise ratio in omparison with soft thresholding[]. And therefore, in the suessive setions, only hard thresholding is onsidered. 4 Multi-wavelet based denoising In order to evaluate the performane of multi-wavelet denoising in PD detetion, the results of wavelet denoising are provided as well. 4.1 Various modes of PD pulses Due to different disharge mehanisms, defet positions, propagation routes and detetion iruits, a omplex power apparatus usually generate PD pulses of various modes[3, 18]. In theory researh, 4 analytial expression are usually adopted to simulate these different PD pulses: damped single-exponent pulse (DSEP), damped resonant single-exponent pulse(drsep), damped double-exponent pulse (DDEP), and damped resonant double-exponent pulse(drdep)[18]. t / τ mode1 f1 ( t) = A1e (8) t / τ mode f ( t) = Ae sin( f πt) (9) 1.3t / τ.t / τ mode3 f 3 ( t) = A3 ( e e ) (1) 1.3t τ.t τ f 4 ( t) = A4 ( e e ) mode4 sin( f πt ) (11) where A denotes the amplitude, whereas τ and f are time onstant and resonant frequeny, respetively. The waveform orresponded with the 4 typial PD pulses are shown in Fig..

4 frequeny f is 1MHz, unless otherwise speified, sampling frequeny is 1MHz. The white noise superimposed has the normal distribution N (,.3 ), and the length of the simulation data is 14. For either mode displayed in Fig., with the parameters above, we run the simulation 1 times independently, and final result is the mean of 1 observations, see Fig.3-6. Fig. Typial PD pulse shapes: (a) DSEP, (b) DRSEP, () DDEP, and (d) DRDEP For PD pulse of any mode shown in Fig., we an selet orresponding optimal wavelet basis funtion by using the method suggested in[]. However, in the ase of multi-wavelet, as it possesses several basis funtions and its filterban is in the form of matrix, we annot alulate the ross relation oeffiient between PD pulse and the basis funtions. At present, no method is available for us to ompare the denoising performane of multi-wavelet and wavelet diretly, to our nowledge.the obetive of denoising is to remove noise from the measured data as effetively as possible while preserving the signal features essential to the appliation[]. In this sense, we adopt Mean square Error (MSE) as the riterion to measure denoising performane, together with massive simulations. As to wavelet based denoising, we hoose db and db8 as the wavelet basis funtion, whih are optimal in most ases[], and wavelet oeffiients are to be hard thresholded with the threshold λ = m ln n / proposed in[]. 4. Denoising PD pulses of single-mode Eletrial interferene on site an be lassified into three ategories: white noise, disrete spetrum interferene(dsi), and periodi pulsive noise, in whih white noise is the most ommon interferene, and as preliminary study, in this ontribution, the main interferene to be suppressed is white noise. In this setion, the main obetive is to investigate the denoising performane of multi-wavelet for PD pulse of single mode. PD is in the form of pulse with very wide frequeny band. In aordane with this high frequeny attenuation harateristi, in simulation, we set the time onstant τ in the range of 1ns~.5us, with simulation step equal to 5ns; the pea value of eah PD pulse is 1mV, and resonant Fig.3 Multi-wavelet vs. wavelet in denoising PD of DSEP Fig.4Multi-wavelet vs. wavelet in denoising PD of DRSEP

5 Fig.5 Multi-wavelet vs. wavelet in denoising PD of DDEP Fig.6 Multi-wavelet vs. wavelet in denoising PD of DRDEP From Fig.3 and Fig.4, it an be seen learly that, for PD of mode1, denoising performane with db is better than that with db8, but when dealing with PD of mode, db8 is superior to db. This observation is onsistent with the onlusion obtained in literature[]. In Fig.5 and Fig.6, omparing the denoising performane of db and db8, however, it is diffiult to determine whih is better. Suh as in Fig.6, when time onstant lies between 8ns and 1.us, db seems better, however, when time onstant falls into the area above 1.5us, db8 turns to be superior. In fat, from this, we an find a problem that ross relation oeffiient annot determine an optimal wavelet basis funtion absolutely. It is beause that ross relation oeffiient is alulated only from a typial and alibrated waveform of PD pulse, with the variety of time onstant and resonant frequeny, suh a typial PD pulse in fat an hardly exist, in other words, ross relation oeffiient annot ustify the performane in all ases. Now, we ompare the denoising performane of multi-wavelet and wavelet. From Fig.3-6, it is obvious that for PD pulse of any mode, multi-wavelet CL is superior to wavelet db or db8 in the suppression of white noise. In summary, from the results above we an onlude that: for PD pulse of any mode(shown in Fig.), the denoising performane of multi-wavelet CL outperforms that of wavelet db and db Denoising PD pulses of multi-mode In the previous setion, the denoising results for PD pulse of single mode are provided, and in this setion, we will give the results for PD pulses of multi-mode. It aims to further onfirm the denoising performane of multi-wavelet, what is more, investigate the performane under different noise level. In the simulation, 4 PD pulses of different modes, either in one form of Fig., are seleted and arranged in sequene, orresponding time onstants are 1µs, 1µs,.5µs,.5µs, respetively. Pulse pea value of either pulse is 1mV, with resonant frequeny and sampling frequeny is the same as previous setion. The interval between two suessive pulses is 51 points and the length of the simulation data is 48. The interferene superimposed is white noise with standard deviation ranging from.1 to.5mv (step equal to.1mv). It is the same as before, simulations are onduted repeatedly independently 1 times, and the eventual result is the mean of 1 observations, see Fig.7. Fig.7 Multi-wavelet vs. wavelet in denoising PD luster under different noise level From Fig.7, it an be seen that, with the inrease of noise level, the denoising performane degrades. However, the denoising performane of multiwavelet CL outperforms wavelet db and db8 all the while. 4.4 A typial instane For the sae of larity, we give an instane (see Fig.8 (a)), typial for multi-mode PD signals. The original PD signal and orresponding simulation parameters an be found in literature[3], and in the interest of onision, the parameters are no more provided here. Consistent with [3], besides white noise, we add DSI to the original PD signal. Furthermore, the interferenes added are muh stronger than those in [3]. (a) White noise has a N (,.4 ) distribution, (b) DSI an be formulated as: f DSI ( t) =.3 (sin( 6 π + sin( 85 π + sin(1.1m π + sin(1.5m π

6 (11) The PD pulses, superimposed by DSI and white noise, are shown in Fig.8 (b), with signal-to-noise ratio equal to -11.4dB.The length of the data is 48. Fig.9 Multi-wavelet vs. wavelet in denoising data of HSB-1 monitoring system: (a) original on-site data; (b) denoised result with db wavelet; () denoised result with db8 wavelet; (d) denoised result with CL multi-wavelet. Fig.8 Multi-wavelet vs. wavelet in denoising typial multi-mode PD luster: (a) simulation PD pulses; (b) orrupted signal; () denoised result with db wavelet; (d) denoised result with db8 wavelet; (e) denoised results with CL multi-wavelet. From the denoised results above, it an be observed that, multi-wavelet CL an preserve omplete information of PD pulses in omparison to wavelet db and db Proessing of on-site data The on-site data is derived from the PD monitoring system installed on the generators of BaoGang power plant[1]. The wor group led by Huang has developed two types of online PD monitoring systems, HSB-1 and HSB-, suessively from the late of last entury until now. The sampling frequeny of HSB-1 is 6.67MHz, and that of HSB- is 5MHz. In the following proess, we selet one data set from either system, the data length of HSB-1 is 819, and that of HSB- is The original data and the proessed results are illustrated in Fig.9 and Fig.1. In either plot, results obtained by using wavelet db, wavelet db8 and multi-wavelet CL are provided together. From Fig.9 and Fig.1, it an be observed that CL multi-wavelet an preserve more PD pulses when suppressing the interferene in omparison to wavelet db or db8. Although not as muh obvious, it is onsistent with the result obtained in the previous setion. Fig.1 Multi-wavelet vs. wavelet in denoising data of HSB- monitoring system: (a) original on-site data; (b) denoised result with db wavelet ; () denoised result with db8 wavelet; (d) denoised result with CL multi- wavelet. 5 Conlusion and future wor Multi-wavelet is the new development of wavelet theory, and possesses more advantages than lassial wavelet in signal proessing. In this ontribution, we employ it to detet the partial disharges overwhelmed by interferenes, mainly by white noise. Through massive simulation, together with on-site data proessing, it an be onluded that: 1) Compared with wavelet, multi-wavelet based method needs no (or less) prior nowledge of PD pulses, ) Compared with wavelet (db or db8), multi-wavelet (CL), depending less on the waveform of the PD pulses, exels in extrating PD pulses of various modes,

7 3) From the results obtained, multi-wavelet (CL) outperforms wavelet at least in the suppression of white noise. With the development of multi-wavelet, various new multi-wavelets have been reported, whih is optimal and how to determine it demand further researh. Besides, in this ontribution, we deal mainly with the suppression of white noise; in pratie, DSI is another important interferene, how to eliminate it with multi-wavelet transform still need muh more wor. Referenes: [1] Huang hengun, Study of partial disharge on-line monitoring system for large tubrine generators based on wavelet analysis, Shanghai:Shanghai Jiaotong University,. [] Ma, X., C. Zhou, and I.J. Kemp, Automated wavelet seletion and thresholding for PD detetion, IEEE Eletrial Insulation Magazine, Vol.18,No.,,pp [3] Xu Jian,Huang Chengun, Shao Zhenyu et al, Researh on a wavelet-based algorithm for extrating PD luster of diversiform features, Automation of Eletri Power Systems, Vol.8, No.16, 4,pp [4] Strela, V., et al., The appliation of multi-wavelet filterbans to image proessing, Image Proessing, IEEE Transations on,vol.8,no.4, 1999,pp [5] Bui, T.D. and G. Chen, Translation-invariant denoising using multi-wavelets, IEEE Transations on Signal Proessing, Vol.46, No.1,1998,pp [9]6 Xia, X.-G., et al., Design of prefilters for disrete multi-wavelet transforms. Signal Proessing, IEEE Transations on [see also Aoustis, Speeh, and Signal Proessing, IEEE Transations on],vol.44,no.1, 1996,pp [6]7 Geronimo, J.S., D.P. Hardin, and P.R. Massopust, GHM Fratal funtions and wavelet expansions based on several funtions, J. Approx. Theory, Vol., No.78, 1994, pp [7]8 Chui, C.K. and J.-a. Lian, Study of orthonormal multi-wavelets, Applied Numerial Mathematis, Vol.,No.3,1996,pp [8]9 Shen, L., H.H. Tan, and J.Y. Tham, Symmetri -antisymmetri orthonormal multi-wavelets and related salar wavelets,applied and Computational Harmoni Analysis, Vol.8, No.3,,pp [1] Xia, X.-G., A new prefilter design for disrete multi-wavelet transforms. Signal Proessing, IEEE Transations on [see also Aoustis, Speeh, and Signal Proessing, IEEE Transations on],vol.46, No.6,1998, pp [11] Lebrun, J. and M. Vetterli, High-order balaned multi-wavelets: theory, fatorization, and design. Signal Proessing, IEEE Transations on [see also Aoustis, Speeh, and Signal Proessing, IEEE Transations on], Vol.49,No.9, 1, pp [1] Downie, T.R. and B.W. Silverman, The Disrete Multiple Wavelet Transform and Thresholding Methods,IEEE Transations on signal proessing, Vol.46,No.9, 1998, pp [13] Bala, E. and A. Ertuzun, Appliations of multi-wavelet tehniques to image denoising, International Conferene on Image Proessing,. [14] V. Strela and A. T. Walden, Signal and Image Denoising via Wavelet Thresholding: Orthogonal and Biorthogonal, Salar and Multiple Wavelet Transforms, Imperial College, Statistis Setion, Tehnial Report TR-98-1,1998. [15] Hsung, T.-C. and D.P.-K. Lun, Generalized ross validation for multi-wavelet shrinage. Signal Proessing Letters, IEEE, Vol.11, No.6, 4, pp [16] Hsung, T.-C., D.P.-K. Lun, and K.C. Ho, Optimizing the multi-wavelet shrinage denoising, IEEE Transations on Signal Proessing, Vol.53, No.1,5,pp [17] Chen, G.Y. and T.D. Bui, Multi-wavelets denoising using neighboring oeffiients. Signal Proessing Letters, IEEE, Vol.1,No.7, 3, pp [18] Huang Chengun,Yu Weiyong. Study of adaptive filter algorithm based on wavelet analysis in suppressing PD's periodi narrow bandwidth noise,proeedings of the CSEE, Vol.3,No.1, 3,pp