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

doi:10.3901/JME.2021.21.138

Abstract

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

CLC Number:

TH165
TH17

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.

References

[1] WANG Huaqing, HOU Wei, TANG Gang, et al. Fault detection enhancement in rolling element bearings via peak-based multi-scale decomposition and envelope demodulation[J]. Mathematical Problems in Engineering, 2014(1):135-142.
[2] 陈祥龙, 冯辅周, 张兵志, 等. 基于平方包络谱相关峭度的最优共振解调诊断滚动轴承故障[J]. 机械工程学报, 2018, 54(21):90-100. CHEN Xianglong, FENG Fuzhou, ZHANG Bingzhi, et al. Rolling bearing fault diagnosis with optimal resonant frequency band demodulation based on squared envelope spectral correlated kurtosis[J]. Journal of Mechanical Engineering, 2018, 54(21):90-100.
[3] 李华, 伍星, 刘韬, 等. 变分模态分解和改进的自适应共振技术在轴承故障特征提取中的应用[J]. 振动工程学报, 2018, 31(4):718-726. LI Hua, WU Xing, LIU Tao, et al. Application of variational mode decomposition and improved adaptive resonance technology in bearing fault feature extraction[J]. Journal of Vibration Engineering, 2018, 31(4):718-726.
[4] 李华, 伍星, 刘韬, 等. 基于信息熵优化变分模态分解的滚动轴承故障特征提取[J]. 振动与冲击, 2018, 37(23):219-225. LI Hua, WU Xing, LIU Tao, et al. Research on bearing fault feature extraction based on information entropy optimized variational modal decomposition[J]. Journal of Vibration and Shock, 2018, 37(23):219-225.
[5] 崔玲丽, 王鑫, 王华庆, 等. 基于改进开关卡尔曼滤波的轴承故障特征提取方法[J]. 机械工程学报, 2019, 55(7):44-51. CUI Lingli, WANG Xin, WANG Huaqing, et al. Feature extraction of bearing fault based on improved switching Kalman filtering[J]. Journal of Mechanical Engineering, 2019, 55(7):44-51.
[6] GOLAFSHAN R, SANLITURK K Y. SVD and Hankel matrix based de-noising approach for ball bearing fault detection and its assessment using artificial faults[J]. Mechanical Systems and Signal Processing, 2016, 70-71(3):36-50.
[7] LAUB A J. The singular value decomposition:Its computation and some applications[J]. Automatic Control IEEE Transactions on, 1980, 25(2):164-176.
[8] KANJIL P P, PALIT S, SAHA G. Fetal ECG extraction from single-channel maternal ECG using singular value decomposition[J]. Biomedical Engineering, IEEE Transactions on, 1997, 44(1):51-59.
[9] 杨文献, 任兴民, 姜节胜. 基于奇异熵的信号降噪技术研究[J]. 西北工业大学学报, 2001, 19(3):368-371. YANG Wenxian, REN Xingmin, JIANG Jiesheng. On improving the effectiveness of the new noise reduction technique based on singularity spectrum[J]. Journal of Northwestern Polytechnical University, 2001, 19(3):368-371.
[10] 赵学智, 叶邦彦, 陈统坚. 奇异值差分谱理论及其在车床主轴箱故障诊断中的应用[J]. 机械工程学报, 2010, 46(1):100-108. ZHAO Xuezhi, YE Bangyan, CHEN Tongjian. Difference spectrum theory of singular value and its application to the fault diagnosis of headstock of lathe[J]. Journal of Mechanical Engineering, 2010, 46(1):100-108.
[11] 王树青, 林裕裕, 孟元栋, 等. 一种基于奇异值分解技术的模型定阶方法[J]. 振动与冲击, 2012, 31(15):87-91. WANG Shuqing, LIN Yuyu, MENG Yuandong, et al. Model order determination based on singular value decomposition[J]. Journal of Vibration & Shock, 2012, 31(15):87-91.
[12] LI Hua, LIU Tao, WU Xing, et al. Research on bearing fault feature extraction based on singular value decomposition and optimized frequency band entropy[J]. Mechanical Systems and Signal Processing, 2019, 118:477-502.
[13] 汤宝平, 蒋永华, 张详春. 基于形态奇异值分解和经验模态分解的滚动轴承故障特征提取方法[J]. 机械工程学报, 2010, 46(5):37-42. TANG Baoping, JIANG Yonghua, ZHANG Xiangchun. Feature extraction method of rolling bearing fault based on singular value decomposition-morphology filter and empirical mode decomposition[J]. Journal of Mechanical Engineering, 2010, 46(5):37-42.
[14] 张超, 陈建军, 徐亚兰. 基于EMD分解和奇异值差分谱理论的轴承故障诊断方法[J]. 振动工程学报, 2011, 24(5):539-545. ZHANG Chao, CHEN Jianjun, XU Yalan. A bearing fault diagnosis method based on EMD and difference spectrum theory of singular value[J]. Journal of Vibration Engineering, 2011, 24(5):539-545.
[15] 张晓涛, 唐力伟, 王平, 等. 基于SVD与Fast Kurtogram算法的滚动轴承声发射故障诊断[J]. 振动与冲击, 2014, 33(10):101-105. ZHANG Xiaotao, TANG Liwei, WANG Ping, et al. Acoustic emission fault diagnosis of rolling bearings based SVD and Fast Kurtogram algorithm[J]. Journal of Vibration & Shock, 2014, 33(10):101-105.
[16] 王建国, 李健, 万旭东. 基于奇异值分解和局域均值分解的滚动轴承故障特征提取方法[J]. 机械工程学报, 2015, 51(3):104-110. WANG Jianguo, LI Jian, WAN Xudong. Fault feature extraction method of rolling bearings based on singular value decomposition and local mean decomposition[J]. Journal of Mechanical Engineering, 2015, 51(3):104-110.
[17] HAN Te, JIANG Dongxiang, WANG Nanfei. The fault feature extraction of rolling bearing based on EMD and difference spectrum of singular value[J]. Shock and Vibration, 2016, 2016(13):1-14.
[18] WILLIAM P E, HOFFMAN M W. Identification of bearing faults using time domain zero-crossings[J]. Mechanical Systems and Signal Processing, 2011, 25(8):3078-3088.
[19] LIU Tao, CHEN Jin, DONG Guangming, et al. The fault detection and diagnosis in rolling element bearings using frequency band entropy[J]. Proceedings of Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science, 2013, 227(1):87-99.
[20] WANG Biao, LEI Yaguo, LI Naipeng, et al. A hybrid prognostics approach for estimating remaining useful life of rolling element bearings[J]. IEEE Transactions on Reliability, 2020, 69(1):401-412.