矩阵奇异值分解算法及应用研究  

Research on Singular Value Decomposition of Matrix and Its Application

作　　者：韩孝明 HAN Xiao-ming(Fenyang Normal College,Lvliang University,Fenyang 032200,Shanxi,China)

机构地区：[1]吕梁学院汾阳师范分校,山西汾阳032200

出　　处：《兰州文理学院学报（自然科学版）》2021年第1期14-18,共5页Journal of Lanzhou University of Arts and Science(Natural Sciences)

摘　　要：矩阵奇异值分解在信号处理和统计中具有广泛的应用,针对矩阵奇异值分解算法及在信号降噪处理中的应用进行研究.首先给出了矩阵奇异值分解算法,指出分解得到的奇异值是矩阵的固有属性.然后给出了采用矩阵奇异值分解进行信号降噪处理的办法,同时给出了奇异值差分谱法、特征均值法、奇异值中值法3种降噪方法.最后采用3种降噪方法对实测滚动轴承振动信号的降噪处理进行实证分析,降噪结果表明奇异值中值法对实测信号的降噪效果最优,对奇异值分解在信号降噪处理中的应用具有一定的参考价值.Matrix singular value decomposition is widely used in signal processing and statistics.In this paper,the algorithm of matrix singular value decomposition and its application in signal denoising are studied.Firstly,the algorithm of matrix singular value decomposition is given,and it is pointed out that the singular value obtained by decomposition is the inherent property of matrix.Then,the method of signal denoising using singular value decomposition of matrix is given.At the same time,three denoising methods,singular value difference spectrum method,characteristic mean value method and singular value mean value method,are given.Finally,three kinds of noise reduction methods are used to deal with the actual rolling bearing vibration signals.The results show that the singular value median method has the best noise reduction effect.The research of this paper has a certain reference value for the application of SVD in signal denoising.

关 键 词：奇异值分解 信号降噪 奇异值 

分 类 号：O241.6[理学—计算数学]