为了实现有效奇异值的自动选择,提出了奇异值曲率谱方法.首先分析了Hankel矩阵方式下理想信号和噪声信号的奇异值特点,发现理想信号的奇异值曲线存在一个很大的转折点,噪声信号的奇异值曲线则很平坦.然后提出了奇异值曲率谱的概念,并利用它来描述含噪信号奇异值曲线的转折点情况,分析了曲率谱计算时需注意的问题.研究结果表明,根据曲率谱的最大峰值位置可以确定有效奇异值个数：如果奇异值曲线在曲率谱最大峰值的位置坐标k处是凸出的,则有效奇异值的个数为k;如果奇异值曲线在k处是凹进的,则有效奇异值的个数为k-1.利用此方法来确定轴承振动信号的有效奇异值,提取到了由于滚道损伤而引起的调制现象,据此可靠地判断出了滚道剥落坑总数.

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.