A Novel Partial Discharge Signal Denoising Method Based on Sparse Decomposition
Bowen Wang · 2015
In order to analyzing the noise suppression of partial discharge (PD) signal, a PD signal denoising method based on sparse decomposition was proposed in this research. Through the analysis of partial discharge signal time-frequency characteristics, the PD signal correlated atom and PD signal correlated overcomplete dictionary were designed. The newly created PD signals were correlated to the original PD signal while uncorrelated or weak-correlated to the noise signal. In our research, we made use of the sparse decomposition method which is based on matching pursuit algorithm and correlation ratio iteration termination condition, to denoise the PD signal. The rational behind this is that only the original PD signal can be expressed by the best atoms extracted from the PD signal correlated overcomplete dictionary, thus achieve the goal of denoising. Moreover, the searching progress of best atoms can be further accelerated by quantum genetic algorithm. The denoising method presented in this paperpaper has been applied on the simulated, laboratory measured as well as field detected PD signals. The results of our detecting method are critical compared with denoising method based on db2 and db8 wavelet transform in the sense that it can effectively papersuppress the PD signal noise jamming and the denoising effect is superior to traditional wavelet methods, which has less amplitude error as well as litter waveform destination. Introduction INSULATION defeat is one of the main causes for electrical equipment failure. Partial discharge (PD) measurements can effectively identify potential insulation failure of electrical equipment [1], which has become a major task of electrical equipment online monitoring. However, since the PD signal is weak while the electromagnetic noise in PD measuring site is strong, the major bottleneck affecting PD monitoring effect is noise jamming. Noise suppression is one of the key links for PD measurements . Digital denoising method has become a research hotpot and main method for PD signal interference suppression [2-9], mainly including FFT threshold filter [2], adaptive filter [3], empirical mode decomposition (EMD) [4], [5], wavelet transform [6-9] and so on. Providing a new analysis tool implemented in both the time and frequency domains [6], wavelet transform PD signal denoising method has beenwidely used in recently years. However, due to the diversity of partial discharge signals, it is difficult to select a singlewavelet basis function that is perfectly suitable for all PD signals [7]. What’s more, the unreasonable selection of threshold method will also affect the denoising effect seriously [8], [9]. Conventional signal expression methods, such as Fourier transform and wavelet transform, obtain a widespread application. However, in order to express the signal to a known transform domain, these signal expression methods map the signal into finite complete orthogonal basis functions without fully considering the characteristics of the signal itself [10]. Therefore, these signal expression methods are insufficient in expressing signals especially expressing those with large range of time and frequency domains [11], such as PD signal. Consequently, the PD signal denoising results based on traditional signal expression signal methods are deficient. Sparse decomposition [12] has become a hot research area in signal expression methods. Using few atoms from overcomplete dictionary to express signals, sparse decomposition avoids the defect of the conventional signal expression methods and it has been International Conference on Information Sciences, Machinery, Materials and Energy (ICISMME 2015) © 2015. The authors Published by Atlantis Press 1754 widely used in the field of image compression [13], image denoising [14] , signal recognition [15] and so on. In this paperpaper, a novel PD signal denoising method based on sparse decomposition was proposed. The principles of this method are signal sparse decomposition and its matching pursuit (MP) algorithm. Firstly, the PD signal matching atom and PD signal matching overcomplete dictionary was given, which were only correlated to original PD signal but uncorrelated or weakcorrelated to the noise signal. Based upon this, the noisy signal can be sparse decomposed by MP algorithm in this dictionary to search the best correlative atoms. What’ more, the quantum genetic algorithm (QGA) was used to accelerate the searching progress. Using correlation ratio iteration termination condition, only a few atoms can be extracted which can only express the original PD signal. Compared with the denoising results based on db2 and db8 wavelet transform, the simulated, laboratory and filed detected PD signals were used to verify the denoising effect of this method. Sparse Decomposition & Matching Pursuit Algorithm Basic Principle of Sparse Decompositon Based on the analysis of wavelet theory, Mallet and Zhang firstly proposed expressing signals by adaptively selecting atoms that most similar to a given signal from a overcomplete dictionary, while limiting the number of the atoms as little as possible. Hence, this method developed into the signal sparse decomposition theory [12]. The basic principles of sparse decomposition are as follows Let N = H R be a Hilbert space. The atom q g is a unit vector of H, and the overcomplete dictionary Q N × ∈ D R is composed by q g , i.e., { } , 1,2, , q g q Q = = D , where Q N � . A signal x ∈ H can be denoted as a sparse linear combination of atoms from the overcomplete dictionary ( ) 1 m q q q I x g α ∈ = ∑ where q α is the expansion coefficient of q g , m I is subscript set of q. Here ( ) m card I m = and m Q � . Since D is overcomplete, the atoms gq do not satisfy the orthogonality. Therefore, the representation method of equation (1) is not unique. The aim of sparse decomposition is to find out the sparsest decomposition coefficients or to hunt for the minimum value of m from a variety of possible decomposition methods. Matching pursuit algorithm Matching pursuit (MP) algorithm [12] is the main method for sparse representation. Taking maximum inner product as the optimization principle, MP is an iterative greedy algorithm and it can be explained as follows Let f ∈ H be the signal to be decomposed, and 0 q g be the best matching atoms selected form overcomplete dictionary D. 0 q g satisfied the requirement of equation (2) ( ) 0 , sup , 2 q q q I f g f g ∈ = where , q f g donates the inner product of f and 0 q g .Shown as equation (2), 0 q g is the atom that closest to the signal direction in the Hilbert space N = H R selected from the dictionary D, namely 0 q g is the best atom that match for the signal f. Therefore, the signal f can be decomposed as ( ) 0 0 1 , 3 q q f f g g R f = + where 0 0 , q q f g g is the projection in 0 q g of f , 1 R f is the residue signal after the first decomposition. Repeat the above process for the residual signal ( ) 1 , 4 k k k k k q q R f R f g g R f + = + after N steps we can get the following decomposition of the original signal f ( ) 1 0 , 5 k k K k K q q k f R f g g R f −