• CN：11-2187/TH
• ISSN：0577-6686

• 仪器科学与技术 •

### 奇异值分解中考虑频率因素的矩阵维数

1. 华南理工大学机械与汽车工程学院 广州 510640
• 收稿日期:2019-01-26 修回日期:2019-07-02 出版日期:2019-08-20 发布日期:2019-08-20
• 作者简介:赵学智,男,1970年出生,博士,教授,博士研究生导师。主要研究方向为信号处理与机械故障诊断。E-mail:mezhaoxz@scut.edu.cn
• 基金资助:
国家自然科学基金（51375178、51875216）和广东省自然科学基金（No.2018A030310017）资助项目。

### Matrix Dimension Considering Frequency Factor in Singular Value Decomposition

ZHAO Xuezhi, SHAO Qipeng, YE Bangyan, CHEN Tongjian

1. School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou 510640
• Received:2019-01-26 Revised:2019-07-02 Online:2019-08-20 Published:2019-08-20

Abstract: The dimension of Hankel matrix has a very important influence on the signal processing effect of singular value decomposition (SVD). The traditional matrix dimension does not consider the frequency components in the signal and this is unreasonable. A least common multiple method is put forward to determine the matrix dimension based on the analysis for the frequency factor, and in this method, the least common multiple of the periods of the all frequency components in the original signal is used as a base number, and the row and column number of Hankel matrix must be the integer multiple of this base number, under this necessary condition, the dimension of Hankel matrix should be maximized, and then the optimal row number and column number are obtained by the optimization computation. The processing examples of simulation signal and rotor vibration signal are provided, which show that, under the matrix dimension determined by the least common multiple method, the calculation amount of SVD is much smaller, but waveform error of the decomposition results is much smaller than the ones of the traditional maximum dimension method.