基于不完全Cholesky分解相关熵双谱的轴承故障诊断

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振动与冲击 ›› 2022, Vol. 41 ›› Issue (11) : 123-140.

论文

李辉1,郝如江2

作者信息 +

Bearing fault diagnosis based on incomplete Cholesky decomposition correntropy and bi-spectrum

LI Hui1, HAO Rujiang2

Author information +

文章历史 +

摘要

针对传统双谱难以有效处理强噪声干扰以及相关熵运算量大的问题，提出了一种基于不完全Cholesky分解相关熵和双谱分析的轴承故障诊断方法。该方法在不求出核矩阵的情况下，首先利用不完全Cholesky分解算法和核函数，计算核矩阵的低秩分解下三角矩阵；其次，利用Gini指数选取下三角矩阵的主分量，利用下三角矩阵的主分量计算核矩阵的低秩近似矩阵，进而计算信号的相关熵；最后，计算振动信号相关熵的双谱，根据相关熵的双谱特征识别轴承故障。通过不完全Cholesky分解算法和Gini指数计算信号的相关熵，不仅压缩了数据量，突出了轴承故障瞬态冲击特征，有效抑制了噪声的影响，而且提高了计算效率，减少了计算机内存占用量。通过仿真和实验轴承故障振动信号分析结果表明：强背景噪声会造成传统双谱故障诊断方法失效，而基于相关熵和双谱分析的轴承故障诊断方法，能在强噪声干扰背景中提取轴承故障瞬态冲击特征，准确识别轴承故障，其性能优于传统双谱和小波变换域双谱，为一种轴承故障诊断的有效方法。

Abstract

Aiming at the problem that the traditional bispectrum is difficult to deal with the strong noise interference and the lower computational efficiency of correntropy, a bearing fault diagnosis method based on incomplete Cholesky decomposition correlation correntropy and bispectrum analysis is proposed. Firstly, the incomplete Cholesky decomposition algorithm and kernel function are used to calculate the lower triangular matrix of the kernel matrix. Secondly, the Gini index is exploited to select the principal components of the lower triangular matrix. Thirdly, the lower rank approximation matrix of the kernel matrix is calculated using the principal components and the correntropy of the signal is obtained. Finally, the bispectrum based on correntropy of the vibration signal is computed and the bearing fault can be recognized according to the bispectrum feature of correntropy. The incomplete Cholesky decomposition algorithm and Gini index are used to calculate the correntropy of the vibration signal, which not only compresses the amount of data, highlights the transient impact characteristics of bearing fault, effectively suppresses the impact of noise, but also improves the calculation efficiency and reduces the computer memory consumption. The results of simulation and experiment show that the strong background noise will cause the failure of traditional bispectrum fault diagnosis method, while the proposed method based on correntropy and bispectrum analysis can extract the transient impact characteristics of bearing fault in the background of strong noise interference, and accurately identify bearing fault. Its performance is better than that of the traditional bispectrum and wavelet threshold denoising based bispectrum. The proposed correntropy based bispectrum method of is an effective method for bearing fault diagnosis.

导出引用

李辉1,郝如江2. 基于不完全Cholesky分解相关熵双谱的轴承故障诊断[J]. 振动与冲击, 2022, 41(11): 123-140

LI Hui1, HAO Rujiang2. Bearing fault diagnosis based on incomplete Cholesky decomposition correntropy and bi-spectrum[J]. Journal of Vibration and Shock, 2022, 41(11): 123-140

参考文献

[1] 于湘涛,褚福磊,郝如江.基于柔性形态滤波和支持矢量机的滚动轴承故障诊断方法[J].机械工程学报,2009, 45(7):75-80.
YU Xiangtao,CHU Fulei,HAO Rujiang.Fault diagnosis approach for rolling bearing based on support vector machine and soft morphological filters[J].Journal of Mechanical Engineering,2009,45(7):75-80.
[2] 杨江天,陈家骥,曾子平.双谱分析及其在机械诊断中的应用[J].中国机械工程,2000,11(4):424-426.
YANG Jiangtian,CHEN Jiaji, ZENG Ziping. Bispectral analysis and its application in machinery diagnosis[J]. China Mechanical Engineering,2000,11(4):424-426.
[3] BOUILLAUT L,SIDAHMED M. Cyclostationary approach and bilinear approach: comparison, applications to early diagnosis for helicopter gearbox and classification method based on HOCS[J].Mechanical Systems & Signal Processing,2001,15(5):923-943.
[4] Antoniadis I,Glossiotis G. Cyclostationary analysis of rolling-element bearing vibration signals[J].Journal of Sound and Vibration,2001,248(5):829-845.
[5] 王宏超,陈进,霍柏琦, 等.强抗噪时频分析方法及其在滚动轴承故障诊断中的应用[J].机械工程学报,2015,51(1): 90-96.
WANG Hongchao, CHEN Jin, HUO Baiqi. Noise-resistant time-frequency analysis method and its application in fault diagnosis of rolling bearing[J].Journal of Mechanical Engineering,2015,51(1):90-96.
[6] 鄢小安,贾民平.基于改进奇异谱分解的形态学解调方法及其在滚动轴承故障诊断中的应用[J].机械工程学报, 2017,53(7):104-112.
YAN Xiaoan,JIA Minping. Morphological demodulation method based on improved singular spectrum decomposition and its application in rolling bearing fault diagnosis [J].Journal of Mechanical Engineering, 2017,53 (7):104-112.
[7] 胥永刚,张志新,马朝永,等.改进奇异谱分解及其在轴承故障诊断中的应用[J].振动工程学报,2019,55 (3):540-547.
XU Yonggang, ZHANG Zhixin, MA Chaoyong, et al. Improved singular spectrum decomposition and its applications in rolling bearing fault diagnosis[J].Journal of Vibration Engineering,2019,55 (3):540-547.
[8] 胡超凡,王衍学.基于张量分解的滚动轴承复合故障多通道信号降噪方法研究[J].机械工程学,2019,55(12):50-57.
HU Chaofan, WANG Yanxue. Research on multi-channel signal denoising method for multiple faults diagnosis of rolling element bearings based on tensor factorization[J]. Journal of Mechanical Engineering,2019,55(12):50-57.
[9] 熊良才,史铁林,杨叔子.基于双谱分析的齿轮故障诊断研究[J].华中科技大学学报,1999,27(3):6-8.
XIONG Liangcai, SHI Tielin, YANG Shuzi. A method for extracting mechanical faults features based on higher order statistics [J].Journal of Huazhong University of Science and Technology,1999,27(3):6-8.
[10] 李军伟,韩捷,李志农,等.小波变换域双谱分析及其在滚动轴承故障诊断中的应用[J].振动与冲击,2006,25 (5):92-95.
LI Junwei, HAN Jie, LI Zhinong, et al. Bispectrum analysis in the wavelet transform domain and its application to the fault diagnosis of rolling bearings [J].Journal of Vibration and Shock,2006,25(5): 92-95.
[11] SAIDI L, ALI J B, FNAIECH F. Bi-spectrum based-EMD applied to the non-stationary vibration signals for bearing faults diagnosis[J].Isa Transactions,2014,53(5):1650-1660.
[12] 唐贵基,王晓龙.基于局部均值分解和切片双谱的滚动轴承故障诊断研究[J].振动与冲击,2013,32(24):83-88.
TANG Guiji, WANG Xiaolong. Fault diagnosis of roller bearings based on local mean decomposition and slice bispectrum[J].Journal of Vibration and Shock,2013, 32(24):83-88.
[13] 李辉,郑海起,唐力伟.基于倒双谱分析的轴承故障诊断研究[J].振动、测试与诊断,2010,30(4):353-356.
LI Hui, ZHENG Haiqi, TANG Liwei. Application of bi-cepstrum technique to bearing fault detection[J]. Journal of Vibration Measurement & Diagnosis,2010,30 (4):353-356.
[14] RAAD A, SIDAHMED M. Gear fault diagnosis using cyclic bispectrum[J].IFAC Proceedings Volumes,2002, 35(1):431-436.
[15] 朱忠奎,孔凡让,王建平,等.循环双谱及其在齿轮箱故障识别中的应用研究[J].振动工程学报,2004,17(2): 224-227.
ZHU Zhongkui, KONG Fanrang, WANG Jianping. Study on the applications of cyclic bispectrum in gearbox fault diagnosis[J].Journal of Vibration Engineering,2004,17(2): 224-227.
[16] 周宇,陈进,董广明,等.基于循环双谱的滚动轴承故障诊断[J].振动与冲击,2012,31(9):78-81.
ZHOU Yu,CHEN Jin,DONG Guangming, et al, Fault diagnosis of rolling element bearing based on cyclic bispectrum[J]. Journal of Vibration and Shock,2012, 31(9):78-81.
[17] 陈进,姜鸣.高阶循环统计量理论在机械故障诊断中的应用[J].振动工程学报,2001,14(2):125-134.
CHEN Jin, JIANG Ming.The state-of-art of the application of the higher-order cyclostationary statistics in mechanical fault diagnosis[J].Journal of Vibration Engineering,2001, 14(2):125-134.
[18] SANTAMARIA I, POKHAREL P P, PRINCIPE J C.Generalized correlation function: definition, properties, and application to blind equalization[J]. IEEE Transactions on Signal Processing,2006,54(6):2187-2197.
[19] LIU W, POKHAREL P P, PRINCIPE J C. Correntropy: properties and applications in non-gaussian signal processing[J].IEEE Transactions on Signal Processing, 2007,55(11): 5286-5298.
[20] GUNDUZ A, PRINCIPE J C. Correntropy as a novel measure for nonlinearity tests[J]. Signal Processing,2009, 89(1):14-23.
[21] 李辉,郝如江.基于循环多核相关熵的故障检测方法及应用[J].仪器仪表学报,2020,41(5):252-260.
LI Hui，HAO Rujiang. Fault detection based on cyclic multiple kernel correntropy and its application[J].Chinese Journal of Scientific Instrument,2020,41(5):252-260.
[22] 李辉.循环相关熵谱密度估计高效算法研究[J].电子与信息学报,2021,43(2):310-318.
LI Hui. Study on high efficient algorithm for cyclic correntropy spectral analysis [J].Journal of Electronics and Information Technology, 2021,43(2):310-318.
[23] BACH F R, JORDAN M I. Predictive low-rank decomposition for kernel methods[C]. Machine Learning, Proceedings of the Twenty-Second International Conference, Bonn, Germany, August 7-11,2005.
[24] HURLEY N, RICKARD S. Comparing measures of sparsity[J].IEEE Transactions on Information Theory, 2009,55(10):4723-4741.
[25] ANTONI J. Cyclic spectral analysis in practice [J]. Mechanical Systems and Signal Processing,2007,21(2): 597-630.
[26] SMITH W A, RANDALL R B. Rolling element bearing diagnostics using the Case Western Reserve University data: A benchmark study[J]. Mechanical Systems & Signal Processing,2015,64-65:100-131.