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
1.School of Marine Engineering, Guangzhou Maritime Institute, Guangzhou 510725, China;
2.School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou 510640, China;
3.Department of internet Finance & lnformation Engineering, Guangdong University of Finance, Guangzhou 510521, China
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.
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. JOURNAL OF VIBRATION AND SHOCK, 2019, 38(15): 17-26.
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