多分辨奇异值分解理论及其在信号处理和故障诊断中的应用

Theory of Multi-resolution Singular Value Decomposition and Its Application to Signal Processing and Fault Diagnosis

提出多分辨奇异值分解(Multi-resolution singular value decomposition,MRSVD)的概念,基于矩阵二分递推构造原理,利用奇异值分解(Singular value decomposition,SVD)获得具有不同分辨率的近似和细节信号,以多分辨率来展现信号不同层次的概貌和细部特征。给出MRSVD的分解和重构算法,并从理论上证明这种分解方式的多分辨分析特性。研究结果表明,MRSVD可以精确地检测出信号中的奇异点位置,克服小波检测时的奇异点偏移缺陷,并具有优良的消噪能力,可实现零相移消噪,此外还具有微弱故障特征提取能力,在对一个轴承振动信号的处理中,提取到其中隐藏的周期性冲击特征,实现对轴承损伤的准确诊断。相应地与小波变换结果进行比较,证明MRSVD在信号处理和故障诊断领域是一种很有应用前景的方法。

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.