In order to extract the non-stationary and non-linear fault features of rolling bearing vibration signals more accurately and effectively, complex network and graph signal processing (GSP) techniques were introduced into the field of mechanical fault diagnosis, and a method of rolling bearing fault diagnosis based on the graph spectrum amplitude entropy of visibility graph(GSAEVG) was proposed.Firstly, the vibration signal of rolling bearing was transformed into visibility graph signal; then, the visibility graph signal was transformed from vertex domain to graph spectrum domain by graph Fourier transform (GFT), and graph spectrum amplitude entropy (GSAE) was calculated as the fault characteristic parameter; finally, Mahalanobis distance (MD) discriminant function was used as a classifier to recognize different types of faults.From the analysis results of actual rolling bearing vibration signals, it can be seen that the fault diagnosis method based on the graph spectrum amplitude entropy of visibility graph can be used to identify rolling bearing faults accurately and effectively.
陈芒，于德介，高艺源. 基于可视图图谱幅值熵的滚动轴承故障诊断方法[J]. 振动与冲击, 2021, 40(4): 23-29.
CHEN Mang，YU Dejie，GAO Yiyuan. Fault diagnosis of rolling bearings based on graph spectrum amplitude entropy of visibility graph. JOURNAL OF VIBRATION AND SHOCK, 2021, 40(4): 23-29.
[1] Jiang Q, Jia M, Hu J, et al. Machinery fault diagnosis using supervised manifold learning[J]. Mechanical Systems & Signal Processing, 2009, 23(7): 2301-2311.
[2] Jardine A K S, Lin D, Banjevic D. A review on macinery diagnostics and prognostics implementing conditionbased maintenance[J]. Mechanical Systems & Signal Processing, 2006, 20(7): 1483-1510.
[3] Dong H, Qi K, Chen X, et al. Sifting process of EMD and its application in rolling element bearing fault diagnosis[J]. Journal of Mechanical Science & Technology, 2009, 23(8): 2000-2007.
[4] 何正嘉. 机械故障诊断理论及应用[M]. 北京：高等教育出社，2010:1-10.
HE Zhengjia. Theory and Application of Mechanical Fault Diagnosis [M]. Beijing: Higher Education Press, 2010:1-10.
[5] Sandryhaila A, Moura J M F. Discrete Signal Processing on Graphs[J]. IEEE Transactions on Signal Processing, 2013, 61(7): 1644-1656.
[6] Hammond D K, Vandergheynst P, Gribonval R.Wavelets on graphs via spectral graph theory[J]. Applied & Computational Harmonic Analysis, 2011, 30(2): 129-150.
[7] Shuman D I, Ricaud B, Vandergheynst P. Vertex-Frequency Analysis on Graphs[J]. Applied and Computational Harmonic Analysis, 2016, 40(2):260-291.
[8] Tremblay N, Borgnat P, Flandrin P. Graph Empirical Mode Decomposition[C]. Signal Processing Conference, 2014.
[9] Zhang B, Wang J, Fang W. Volatility behavior of visibility graph EMD financial time series from Ising interacting system[J]. Physica A Statistical Mechanics & Its App-lications, 2015, 432: 301-314.
[10] Sandryhaila A, Moura J M F. Big Data Analysis with Signal Processing on Graphs: Representation and processing of massive data sets with irregular structure[J]. IEEE Signal Processing Magazine, 2014, 31(5): 80-90.
[11] Wei H, Cheung G, Ortega A. Intra-Prediction and Gen-eralized Graph Fourier Transform for Image Coding[J]. IEEE Signal Processing Letters, 2015, 22(11): 1913-1917.
[12]杨汉键,于德介,高艺源.基于路图拉普拉斯算子范数和马氏距离的滚动轴承故障诊断[J].中国机械工程,2017,28(20):2493-2499,2519.
YANG Hanjian,YU Dejie,GAO Yiyuan. Fault Diagnosis of Rolling Bearings Based on Path Graph Laplacian Norm and Mahalanobis Distance[J]. China Mechanical Engineering, 2017,28(20):2493-2499,2519.
[13] Lacasa L, Luque B, Luque J, et al. The visibility graph: A new method for estimating the Hurst exponent of fractional Brownian motion[J]. Epl, 2009, 86(3).
[14] Gao Z K, Cai Q, Yang Y X, et al. Visibility Graph from Adaptive Optimal Kernel Time-Frequency Representation for Classification of Epileptiform EEG[J]. International Journal of Neural Systems, 2017, 27(4): 1750005.
[15] Supriya S, Siuly S, Wang H, et al. Weighted Visibility Graph With Complex Network Features in the Detection of Epilepsy[J]. IEEE Access, 2016, 4(99): 6554-6566.
[16] Zhuang E, Small M, Feng G. Time series analysis of the developed financial markets’ integration using visibility graphs[J]. Physica A: Statistical Mechanics and its Applications, 2014, 410: 483-495.
[17] 孙斌, 梁超, 崔彬彬. 基于可视图网络节点重要性度量的离心泵振动故障诊断方法[J]. 热能动力工程, 2014, (03): 320-325+347.
SUN Bin,LIANG Chao,CUI Binbin. Vibration Fault Diagnosis Method of Centrifugal Pump Based on Visibility Graph Network Node Importance Measure[J]. Journal of Engineering for Thermal Energy and Power, 2014(03): 320-325+347.
[18] 陈安华, 潘阳, 蒋玲莉. 基于复杂网络社团聚类的故障模式识别方法研究[J]. 振动与冲击, 2013, 32(20):129-133.
CHEN Anhua, PAN Yang, JIANG Lingli. Failure pattern recognition method research based on complex network community clustering algorithm [J]. Journal of Vibration and Shock, 2013, 32(20): 129-133.
[19] 王小玲,陈进,从飞云. 基于时频的频带熵方法在滚动轴承故障识别中的应用[J].振动与冲击,2012,31(18):29-33.
WANG Xiaoling,CHEN Jin,CONG Feiyun. Application of spectral band entropy method in rolling bearing fault diagnosis based on time-frequency analysis[J]. Journal of Vibration and Shock, 2012, 31(18): 29-33.
[20] Xiang S, Nie F, Zhang C. Learning a Mahalanobis distance metric for data clustering and classification[J]. Pattern Recognition, 2008, 41(12): 3600-3612.
[21] Ou L, Yu D, Yang H. A new rolling bearing fault diagnosis method based on GFT impulse component extraction[J]. Mechanical Systems and Signal Processing, 2016, 81: 162-182.
[22] 欧璐. 图谱理论在齿轮箱故障诊断中的应用研究[D]. 长沙：湖南大学, 2016.
OU Lu. Research on the application of graph spectrutheory in gearbox fault diagnosis[D]. Changsha: Hunan University, 2016.
[23] Shannon C E. A mathematical theory of communi-cation[J]. Bell Systems Technical Journal, 1948, 27(4): 623-656.
[24] Tian Y, Wang Z , Lu C. Self-adaptive bearing fault diagnosis based on permutation entropy and manifold-based dynamic time warping[J]. Mechanical Systems and Signal Processing, 2012, 114: 658-673.
[25] WU, S D, WU C W, Wu, T Y, et al, Multi-Scale Analysis Based Ball Bearing Defect Diagnostics Using Mahalanobis Distance and Support Vector Machine[J].Entropy,2013, 15(2) :416-433.
