Research On Key Technology Of Signal Processing Based On Singular Value Decomposition

Singular value decomposition(SVD) is an effective signal processing method for non-linear and non-stationary signals. In this article, some key issues of signal processing base on SVD is deeply researched and discussed, the segment SVD algorithm and wavelet packet energy spectrum(WPES)-SVD algorithm are proposed, and they are applied to feature extraction.Firstly, the signal processing principle of SVD based on Hankel matrix mode is studied, the singular value distribution of the oringal signal and noisy signal is analysised. According to the contribution rate of signal and noise, the big singular values are selected to reconstruct the matrix by the difference spectrum of singular values, so the original signal can be separated from the noisy signal.Secondly, the cost of the SVD’s numerical calculation is computed, due to the large order of Hankel matrix constructed by long sequence signal, the SVD of it is time-consuming and memory occupancy. To solve the problem, two segment SVD algorithms by dividing the signal into severl segements are proposed, the proposed algorithms can greatly reduce the computation and effectively shorten time of signal processing.Then, the principle component analysis(PCA) is applied to signal processing and compared with SVD. The signal processing theory of PCA is introduced, and the difference spectrum theory of eigenvalue is proposed to select the principal components. The first sigular value is greater than the other sigular value when the signal contains direct(DC) component, the zero-mean normalization of signal is proposed to eliminate the influence of the DC component of sigular values.Finally, the WPES-SVD algorithm combined wavelet packet decomposition and SVD is proposed for fault feature extraction in heavy noise. Firstly, wavelet packet decomposition is used to decompose the signal, then the signal processing based on SVD is applied to the signal of the maximum energy. Finally, envelope analysis is applied to feature extraction for the de-noised signal. The method is applied to feature extraction of the rotor vibration signal and bearing vibration signal, and good results are obtained.