基于奇异值分解的液压信号时域分解方法

张小明,唐建,张梅军

振动与冲击 ›› 2017, Vol. 36 ›› Issue (16) : 93-99.

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振动与冲击 ›› 2017, Vol. 36 ›› Issue (16) : 93-99.
论文

基于奇异值分解的液压信号时域分解方法

  • 张小明,唐建,张梅军
作者信息 +

Hydraulic Signal Decomposition Method based on Singular Value Decomposition

  • Zhang Xiao-ming   Tang Jian   Zhang Mei-jun
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文章历史 +

摘要

为了抑制模态混叠和降低分量中的噪声含量,提出了一种基于奇异值分解的液压信号时域分解方法。根据奇异值分解的两点特性:一是每个频率成分对应两个大小相当的奇异值,二是各频率对应的奇异值的大小与该频率的振幅呈正相关,该方法先选取原信号中的某一频率,向其中叠加频率相同、振幅已知的周期信号,使叠加信号中该频率的振幅最大,这样与其对应的奇异值一定位于对角矩阵的前两阶,解决了原信号该频率的奇异值阶数无法确定的问题,继而选取前两阶奇异值重构,再减去前步加入的周期信号,即还原出原信号中该频率的时间序列。同样,对于原信号中的其他频率用相同方法处理,最终获得一组分量。经实验,该方法较EMD不仅能有效消除模态混叠,而且降低了分量中的噪声含量。

Abstract

In order to restrain the mode aliasing phenomenon and reduce noise composition, a signal decomposition method in time domain based on singular value decomposition (SVD) is proposed. Based on two features of SVD, firstly each frequency corresponds to two sizeable singular values, secondly singular values are positively related to the amplitude of its corresponded frequency. The method is conducted by adding a known simulation sine signal with an appropriate amplitude to make the location of singular values easier to be identified. Then reconstruct time series by choosing related singular values. Finally, the time series of a certain frequency can be achieved by subtracting added simulation signal. By comparing with EMD, it is effectively confirmed that the method can both eliminate mode aliasing and reduce noise composition.

关键词

奇异值分解 / 构造信号 / 叠加信号 / 模态混叠 / 噪声含量

Key words

singular value decomposition / construct signals / add signals / mode aliasing / noise composition

引用本文

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张小明,唐建,张梅军. 基于奇异值分解的液压信号时域分解方法[J]. 振动与冲击, 2017, 36(16): 93-99
Zhang Xiao-ming Tang Jian Zhang Mei-jun. Hydraulic Signal Decomposition Method based on Singular Value Decomposition[J]. Journal of Vibration and Shock, 2017, 36(16): 93-99

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