非零奇异值数量的理论分析及其在滑动轴承-转子振动特征提取应用

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振动与冲击 ›› 2019, Vol. 38 ›› Issue (15) : 17-26.

论文

杨期江1，赵学智2，汤雅连3，李伟光2，滕宪斌1，郭明军1

作者信息 +

Theoretical analysis for number of non-zero singular values and its application in vibration feature extraction of a sliding bearing-rotor system

YANG Qijiang1,ZHAO Xuezhi2,TANG Yalian1,LI Weiguang2,TENG Xianbin1, GUO Mingjun1

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文章历史 +

摘要

首先实验分析了Hankel矩阵下非零奇异值数目与信号中的频率个数成两倍的数量关系，验证了奇异值成对出现规律，当构造的m×n的Hankel矩阵行数与列数充分接近时，信号中同一频率下的两个非零奇异值会紧密排列在一起。根据Hankel矩阵的构造方式，从理论上证明了非零奇异值与频率之间的数量关系规律：对于一个含有固定频率数目的确定性信号，利用其构造m×n的 Hankel 矩阵，当矩阵维数大于信号中频率个数的两倍之后，非零奇异值数目始终是与频率个数成2倍的数量关系，且非零奇异值数目是与幅值和相位无关的。将Hankel矩阵下非零奇异值的这一规律应用于旋转机械中的滑动轴承-转子振动信号的特征提取，实现了对转子不对中故障轴心轨迹的准确提纯。

Abstract

Here, firstly the quantitative relation that the number of non-zero singular values of Hankel matrix is 2 times of the number of frequencies in a signal was analyzed with tests.It was shown that the law that singular values appear in pairs is verified; when the number of rows and that of columns in a m×n Hankel matrix are sufficiently close, two non-zero singular values corresponding to one frequency in a signal are closely spaced; according to the construction mode of Hankel matrix, the quantitative relation between its non-zero singular values and frequencies in a signal is theoretically proved, this relation is that using a deterministic signal with a fixed number of frequencies, a m×n Hankel matrix is constructed, after the matrix’s dimensions are more than twice the number of frequencies in the signal, the number of non-zero singular values is always 2 times of the number of frequencies, the former is unrelated to the signal’s amplitude and phase.This relation law was applied in vibration feature extraction for a sliding bearing-rotor system to realize correct extraction of a rotor axial center’s misalignment fault trajectory.

导出引用

杨期江1，赵学智2，汤雅连3，李伟光2，滕宪斌1，郭明军1. 非零奇异值数量的理论分析及其在滑动轴承-转子振动特征提取应用[J]. 振动与冲击, 2019, 38(15): 17-26

YANG Qijiang1,ZHAO Xuezhi2,TANG Yalian1,LI Weiguang2,TENG Xianbin1, GUO Mingjun1. Theoretical analysis for number of non-zero singular values and its application in vibration feature extraction of a sliding bearing-rotor system[J]. Journal of Vibration and Shock, 2019, 38(15): 17-26

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