分量形成方式对奇异值分解信号处理效果的影响

上海交通大学学报（自然版） ›› 2011, Vol. 45 ›› Issue (03): 368-0374.

• 无线电电子学、电信技术 • 上一篇下一篇

分量形成方式对奇异值分解信号处理效果的影响

赵学智，叶邦彦

（华南理工大学机械与汽车工程学院，广州 510640）

收稿日期:2010-01-05 出版日期:2011-03-30 发布日期:2011-03-30
基金资助:
国家自然科学基金资助项目(50875086)，中央高校基本科研业务费专项资金资助项目(2009ZM0287)，广州市科技计划项目(2008J1C101)

The Influence of Formation Manner of Component on Signal Processing Effect of Singular Value Decomposition

ZHAO Xue-Zhi, YE Bang-Yan

(School of Mechanical and Automotive Engineering, South China University of Technology,
Guangzhou 510640, China)

Received:2010-01-05 Online:2011-03-30 Published:2011-03-30

摘要/Abstract

摘要： 针对奇异值分解后分量信号的形成方式，研究了简便法和平均法的信号处理效果差异，根据Hankel矩阵的特点，提出了一种简单的求平均算法.证明了2种方式都可将原始信号分解为一系列分量信号的线性叠加，并提出一个损失率参量来评价其分解效果.研究结果表明：对于正弦信号，2种方式的信号处理效果相同；对于变频信号，平均法优于简便法；2种方式都可从轴承复杂振动信号中提取到因滚道损伤而引起的调制特征，但平均法计算量大.除变频信号外，对于一般信号，推荐使用简便法.

关键词: 奇异值分解, 简便法, 平均法, 信号处理, 轴承振动

Abstract: Aimed at the formation manner of component signal in singular value decomposition (SVD), the difference of signal processing effect between the simple manner and the average manner was studied. Firstly, for the average manner, a convenient algorithm to get the average of matrix elements is proposed according to the characteristic of Hankel matrix. Secondly, it is proved that the original signal can be decomposed into the linear sum of a series of component signals by SVD with both manners, and a parameter called loss ratio is proposed to evaluate the signal processing effect of both manners. The studying results show that for sine signals, there is no difference between the processing effects of the two manners, while for frequency change signals, the average manner has the advantage of the simple one, however, both manners have extracted the modulated signal caused by the damage in roll track from the complicated vibration signal of a bearing, but the computation amount of the average manner is much larger than that of the simple one. It is recommended that except frequency change signal, for other common signals the simple method should be prior used.

Key words: singular value decomposition, simple manner, average manner, signal processing, bearing vibration

中图分类号:

TN911.7

赵学智, 叶邦彦. 分量形成方式对奇异值分解信号处理效果的影响[J]. 上海交通大学学报（自然版）, 2011, 45(03): 368-0374.

ZHAO Xue-Zhi, YE Bang-Yan. The Influence of Formation Manner of Component on Signal Processing Effect of Singular Value Decomposition[J]. Journal of Shanghai Jiaotong University, 2011, 45(03): 368-0374.

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分量形成方式对奇异值分解信号处理效果的影响

The Influence of Formation Manner of Component on Signal Processing Effect of Singular Value Decomposition

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