相关奇异值比的SVD在轴承故障诊断中的应用

doi:10.3901/JME.2021.21.138

机械工程学报 ›› 2021, Vol. 57 ›› Issue (21): 138-149.doi: 10.3901/JME.2021.21.138

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Application of SVD Based on Correlated Singular Value Ratio in Bearing Fault Diagnosis

LI Hua^1,2, LIU Tao², WU Xing^2,3, LI Shaobo¹

1. State Key Laboratory of Public Big Data, Guizhou University, Guiyang 550025;
2. Yunnan Provincial Key Laboratory of Advanced Equipment Intelligent Manufacturing Technology, Kunming University of Science and Technology, Kunming 650500;
3. Yunnan Vocational College of Mechanical and Electrical Technology, Kunming 650203

Received:2020-10-14 Revised:2020-12-28 Online:2021-11-05 Published:2021-12-28

摘要/Abstract

摘要： 基于Hankel矩阵的奇异值分解（Singular value decomposition，SVD）方法在信号处理、故障诊断领域得到了广泛应用。其降噪性能受选取的重构分量、Hankel矩阵结构、分析的数据点数的影响，对此进行了系统的研究，提出了基于相关奇异值比的SVD （Correlated singular value ratio SVD，C-SVR SVD）方法，并成功应用于轴承故障诊断。首先，针对SVD的重构分量的确定问题，提出了奇异值比（Singular value ratio，SVR）和互相关系数相结合的方法；其次，对Hankel矩阵的结构进行研究，提出了基于SVR和峭度指标的结构优化方法。然后，对分析的数据点数进行了分析讨论，给定了约束。最后，将C-SVR SVD方法应用于轴承故障仿真信号和实际轴承故障案例分析，验证了C-SVR SVD方法的有效性和优越性。

关键词: 奇异值分解, 重构分量确定, 奇异值比, 互相关系数, Hankel矩阵结构, 滚动轴承

Abstract: The SVD method based on Hankel matrix is widely used in signal processing and fault diagnosis. Its noise reduction performance is affected by the selected reconstruction component, the structure of the Hankel matrix, and the number of points of the analysis data. Based on this, a systematic research is carried out, and the SVD based on correlated singular value ratio (C-SVR SVD) is proposed, and successfully applied to bearing fault diagnosis. First, for the problem of determining the reconstruction components of SVD, a method combining singular value ratio (SVR) and cross-correlation coefficient is proposed; secondly, the structure of Hankel matrix is studied, and a structure optimization method based on SVR and kurtosis indicator is proposed. The structure optimization method of the indicator. Then, the number of analyzed data points was analyzed and discussed, and constraints were given. Finally, the C-SVR SVD method is applied to the analysis of the bearing fault simulation signal and the actual bearing fault signal, which verifies the effectiveness and superiority of the C-SVR SVD method.

Key words: singular value decomposition, reconstructed component determination, singular value ratio, cross-correlation coefficient, Hankel matrix structure, rolling bearing

中图分类号:

TH165
TH17

李华, 刘韬, 伍星, 李少波. 相关奇异值比的SVD在轴承故障诊断中的应用[J]. 机械工程学报, 2021, 57(21): 138-149.

LI Hua, LIU Tao, WU Xing, LI Shaobo. Application of SVD Based on Correlated Singular Value Ratio in Bearing Fault Diagnosis[J]. Journal of Mechanical Engineering, 2021, 57(21): 138-149.

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