关键词: 奇异值分解, 曲率谱, 最大转折点, 最大峰值, 信号处理

Abstract:

In order to realize the automatic selection of effective singular values,the method of curvature spectrum of singular values is proposed.The characteristic of the singular values of both ideal signals and noise signals is studied.It is discovered that there is a big turning point in the singular value curve of ideal signals,but not in the one of noise signals.Then the concept of curvature spectrum of singular value is put forward to describe the turning point of singular values of noisy signals,and some problems relating to the computation of curvature spectrum are analyzed.The results show that the number of effective singular values can be determined according to the position of the maximum peak of curvature spectrum.Specifically,this number is k if the singular value curve is convex in the coordinates k of the maximum peak,and is k-1 if the curve is concave.The effective singular values of a bearing vibration signal are well determined by the proposed method,and a modulation phenomenon caused by the small pits in the rolling track is extracted,according to which the number of the small pits is reliably diagnosed.

Key words: singular value decomposition, curvature spectrum, maximum turning point, maximum peak, signal processing