关键词: 多分辨SVD, 多分辨分析, 奇异性检测, 奇异值分解, 特征提取, 信号处理

Abstract: The concept of multi-resolution singular value decomposition (MRSVD) is put forward. Based on the principle of dichotomy and recursion creation of matrix, a signal is decomposed into a series of approximation and detail signals with different resolution by singular value decomposition, and then the overview and detail features of original signal can be shown at different levels. The decomposition and reconstruction algorithm of MRSVD is given, and the property of multi-resolution analysis of this method is proved theoretically. The signal processing results show that MRSVD can detect the accurate position of singular point in signal, thus the defect of wavelet detection, i.e. the position deviation of singular point, is overcome. In addition, MRSVD can achieve good noise reduction effect without phase shift and distortion. Another function of MRSVD is to extract the faint fault feature, and the processing result for a bearing vibration signal shows that the hidden periodical impulses are well extracted by MRSVD, and then the fault of bearing is precisely diagnosed. The comparative study carried out with wavelet transform demonstrates that MRSVD has good application prospect in signal processing and fault diagnosis domain.

Key words: Feature extraction, Multi-resolution analysis, Multi-resolution SVD, Signal processing, Singular value decomposition, Singularity detection