Fault Diagnosis of Rolling Bearings Based on Path Graph Laplacian Norm and Mahalanobis Distance

Abstract

Abstract: In order to extract fault features of vibration signals of rolling bearings effectively, the graph signal processing technology was introduced into fault diagnosis of rolling bearings. Vibration signals of a rolling bearing was firstly transformed into path graph signal. Then, the path graph Laplacian norm was calculated as characteristic parameters, and the standard feature space was obtained. Finally, the Mahalanobis distance of test samples and the standard feature space were used to identify fault patterns of the rolling bearings. Analytic results of the practical vibration signals of rolling bearings demonstrate that the proposed method may be used to diagnose the rolling bearing faults effectively.

Key words: signal processing, Laplacian operator, rolling bearing, fault diagnosis

摘要： 为有效提取滚动轴承振动信号的故障特征，将图信号处理技术引入故障诊断领域。首先根据滚动轴承振动信号构造路图，获得路图信号；再将计算得到的路图拉普拉斯算子范数作为特征参数，构造不同故障的标准特征空间；最后通过测试样本与标准特征空间的马氏距离实现不同故障模式的识别。实测滚动轴承振动信号的分析结果表明，该方法能有效诊断轴承故障。

关键词: 信号处理, 拉普拉斯算子, 滚动轴承, 故障诊断

CLC Number:

TH165.3

YANG Hanjian1, 2;YU Dejie1;GAO Yiyuan1. Fault Diagnosis of Rolling Bearings Based on Path Graph Laplacian Norm and Mahalanobis Distance[J]. China Mechanical Engineering.

杨汉键1, 2;于德介1;高艺源1. 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.

References

[1]PRABHAKAR S，MOHANTY A R，SEKHAR A S. Application of Discrete Wavelet Transform for Detection of Ball Bearing Race Faults[J]. Tribology International，2002，35(12)：793-800.
[2]SREEJITH B，VERMA A K，SRIVIDYA A. Fault Diagnosis of Rolling Element Bearing Using Time-domain Features and Neural Networks[C]//IEEE Region 10 and the Third International Conference on Industrial and Information Systems.Kharagpur：IEEE，2009：1-6.
[3]YANG H，MATHEW J，MA L. Intelligent Diagnosis of Rotating Machinery Faults—a Review[C]//The 3rd Asia-Pacific Conference on Systems Integrity and Maintenance. Cairns：ACSIM，2002：385-392.
[4]JARDINE A K S，LIN D，BANJEVIC D.A Review on Machinery Diagnostics and Prognostics Implementing Condition-based Maintenance[J]. Mechanical Systems & Signal Processing，2006，20(7)：1483-1510.
[5]TSE P W，PENG Y H，YAM R.Wavelet Analysis and Envelope Detection for Rolling Element Bearing Fault Diagnosis—Their Effectiveness and Flexibilities[J]. Journal of Vibration & Acoustics，2001，123(3)：303-310.
[6]ALTMANN J，MATHEW J. Multiple Band-pass Autoregressive Demodulation for Rolling-element Bearing Fault Diagnosis[J]. Mechanical Systems & Signal Processing，2001，15(5)：963-977.
[7]KLEIN R，INGMAN D，BRAUN S. Non-stationary Signals：Phase-energy Approach Theory and Simulations[J]. Mechanical Systems & Signal Processing，2001，15(6)：1061-1089.
[8]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.
[9]ZHOU Y，Chen J，Dong G M，et al.Wigner-Ville Distribution Based on Cyclic Spectral Density and the Application in Rolling Element Bearings Diagnosis[J]. Journal of Mechanical Engineering Science，2011，225(12)：2831-2847.
[10]CHEBIL J，NOEL G，MESBAH M，et al. Wavelet Decomposition for the Detection and Diagnosis of Faults in Rolling Element Bearings[J]. Jordan Journal of Mechanical & Industrial Engineering，2009，3(4)：260-267.
[11]SHUMAN D I， NARAN G S K， FROSSAD P， et al.The Emerging Field of Signal Processing on Graphs[J].IEEE Signal Processing Magazine，2013，30(3)：83-98.
[12]SHUMAN D I， RICAUD B， VANDERGHEYNST P. Vertex-frequency Analysis on Graphs[J]. Applied & Computational Harmonic Analysis，2013，40(2)：260-291.
[13]THANOU D，SHUMAN D，FROSSARD P. Learning Parametric Dictionaries for Signals on Graphs[J]. IEEE Transactions on Signal Processing，2014，62(15)：3849-3862.
[14]SANDRYHAILA A， MOURA J M F. Discrete Signal Processing on Graphs[J]. IEEE Transactions on Signal Processing，2012，61(7)：1644-1656.
[15]VENKITARAMAN A，CHETTERJEE S，HNDEL P. On Hilbert Transform of Signals on Graphs[C]//11th International Conference on Sampling Theory and Applications.Washington DC：IEEE，2015：1-5.
[16]HU W，CHEUNG G，ORTEGA A，et al.Multiresolution Graph Fourier Transform for Compression of Piecewise Smooth Images [J]. IEEE Transactions on Image Processing，2014，24(1)：419-33.
[17]HU W，CHEUNG G，ORTEGA A. Intra-prediction and Generalized Graph Fourier Transform for Image Coding[J]. IEEE Signal Processing Letters，2015，22(11)：1913-1917.
[18]SANDRYHAILA A， MOURA J M F. Discrete Signal Processing on Graphs：Graph Fourier Transform[C]//IEEE International Conference on Acoustics, Speech and Signal Processing. Vancouver：IEEE，2013：6167-6170.
[19]任玲辉，刘凯，张海燕.基于图像处理技术的机械故障诊断研究进展[J].机械设计与研究，2011，27(5)：21-24.
REN Linghui，LIU Kai，ZHANG Haiyan. Progress on Mechanical Fault Diagnosis Based on Image Processing[J]. Machine Design and Research，2011，27(5)：21-24.
[20]欧璐，于德介. 路图傅里叶变换及其在滚动轴承故障诊断中的应用[J]. 机械工程学报，2015，51(23)：76-83.
OU Lu，YU Dejie. Path Graph Fourier Transformation and Its Application to Rolling Bearing Fault Diagnosis[J]. Journal of Mechanical Engineering，2015，51(23)：76-83.
[21]NAUMANN U， SCHENK O. Combinatorial Scientific Computing[M].Boca Raton：CRC Press，2012.
[22]XIANG S， NIE F，ZHANG C. Learning a Mahalanobis Distance Metric for Data Clustering and Classification[J]. Pattern Recognition，2008，41(12)：3600-3612.
[23]SCHLKOPF B，WARMUTH M K. Learning Theory and Kernel Machines[C]//16th Annual Conference on Learning Theory and 7th Kernel Workshop.Washington DC：Springer，2003：746-746.
[24]ZHOU D， SCHLKOPF B.A Regularization Framework for Learning from Graph Data[C]//International Conference on Machine Learning.Banff：Workshop on Statistical Relational Learning，2004：132-137.
[25]TAGUCHI G， JUGULUM R.The Mahalanobis-Taguchi Strategy：a Pattern Technology System[M].Hoboken：Wiley Online Library，2007.
[26]ZHAO X， YE B.Convolution Wavelet Packet Transform and Its Applications to Signal Processing[J]. Digital Signal Processing，2010，20(5)：1352-1364.
[27]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.