路图傅里叶变换及其在滚动轴承故障诊断中的应用

doi:10.3901/JME.2015.23.076

机械工程学报 ›› 2015, Vol. 51 ›› Issue (23): 76-83.doi: 10.3901/JME.2015.23.076

扫码分享

路图傅里叶变换及其在滚动轴承故障诊断中的应用

欧璐, 于德介

湖南大学汽车车身先进设计制造国家重点实验室长沙 410082

收稿日期:2014-12-15 修回日期:2015-07-11 出版日期:2015-12-05 发布日期:2015-12-05
通讯作者: 于德介，男，1957年出生，博士，教授，博士研究生导师。主要研究方向为机械系统动力学、设备状态监测与故障诊断、动态信号分析与处理、振动与噪声控制等。
作者简介:欧璐，男，1986年出生，博士研究生。主要研究方向为机械故障诊断、动态信号分析与处理。 E-mail：oulu@hnu.edu.cn
基金资助:
国家自然科学基金资助项目(51275161)

Path Graph Fourier Transformation and Its Applications to Rolling Bearing Fault Diagnosis

OU Lu, YU Dejie

State Key Laboratory of Advanced Design and Manufacture for Vehicle Body, Hunan University, Changsha 410082

Received:2014-12-15 Revised:2015-07-11 Online:2015-12-05 Published:2015-12-05

摘要/Abstract

摘要： 图信号处理(Graph signal processing, GSP)是由谱图理论发展起来的新研究领域。图傅里叶变换(Graph Fourier transformation, GFT)是图信号关于图拉普拉斯矩阵特征函数的展开，也是GSP的基础。对路图的GFT进行分析，发现GFT得到的特征值谱与经典的傅里叶变换(Fourier transformation, FT)频谱有一一对应关系，同时，特征值谱的幅值与特征矢量也有对应关系。将GFT引入滚动轴承故障诊断，提出基于GFT特征提取和K-均值聚类的滚动轴承故障诊断方法。该方法先用GFT将滚动轴承的路图信号变换到特征值谱域；再计算特征值谱的统计量作为故障特征；最后运用K-均值聚类分类器识别滚动轴承的故障类型。对实际轴承振动信号的分析结果表明，基于GFT和K-均值聚类的故障诊断方法能准确有效地识别滚动轴承故障。

关键词: K-均值聚类, 故障诊断, 滚动轴承, 路图, 图傅里叶变换

Abstract: The graph signal processing (GSP) is a new research field, which is derived from the spectral graph techniques. The foundation of GSP is the graph Fourier transformation (GFT), which is the expansion of a graph signal in terms of the eigenfunctions of graph Laplacian matrix. The GFT on path graph is analyzed. It is found that the eigenvalue spectra obtained by GFT and the frequency spectra obtained by the classical Fourier transformation (FT) have a one to one correlation. Meanwhile, the amplitude of an eigenvalue is correlated with the amplitude of the corresponding eigenvector. The GFT is introduced into the fault diagnosis of rolling bearings and a fault diagnosis method based on the GFT and the K-means clustering is proposed. The path graph signal of the vibration signal of a rolling bearing is transformed by GFT into the eigenvalue spectrum domain. The statistical quantities of eigenvalues are calculated for fault feature extraction. The K-means clustering classifier is used to identify the work condition and fault patterns of the roller bearing. The analysis results of the practical vibration signals of rolling bearings demonstrate that the diagnosis approach based on the GFT and the K-means clustering can be used to identify the fault patterns of roller bearings accurately and effectively.

Key words: fault diagnosis, graph Fourier transformation, K-means clustering, path graph, rolling bearing

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 Applications to Rolling Bearing Fault Diagnosis[J]. Journal of Mechanical Engineering, 2015, 51(23): 76-83.

参考文献

[1] JIANG Quansheng，JIA Minping，HU Jianzhong，et al. Machinery fault diagnosis using supervised manifold learning[J]. Mechanical Systems and Signal Processing，2009，23(7)：2301-2311.
[2] JIANG Quansheng，LU Jiayun，JIA Mimping. Nonlinear manifold learning based fault classification method[C]// Proceedings of the 29th Chinese Control Conference，Beijing，China，July 29-31，2010. Beijing，2010：2972-2976.
[3] JOLLIFFE I T. Principal component analysis[M]. New York：Springer，1986.
[4] BALAKRISHNAMA S，GANAPATHIRAJU A. Linear discriminant analysis：A brief tutorial[M]. MS：Institute for Signal and Information Processing，1998.
[5] KOHONEN T. Self-organization and associative memory[M]. London：Springer，1988.
[6] CHUNG F R. Spectral graph theory[M]. New York：AMS Bookstore，1997.
[7] SPIELMAN D. Spectral graph theory[M]. New Haven：Yale University Press，2009.
[8] DAVID I S，SUNIL K N，PASCAL F，et al. The emerging field of signal processing on graphs：Extending high-dimensional data analysis to networks and other irregular domains[J]. Signal Process Mag.，2013，30(3)：83-98.
[9] DAVID I S，BENJAMIN R，PIERRE V. Vertex-frequency analysis on graphs[J]. In. ArXiv，2013，1307.5708.
[10] ZHU X，MICHAEL R. Approximating signals supported on graphs[C]// International Conference on Acoustics，Speech，and Signal Processing (ICASSP)，Kyoto，Japan，Mar. 25-30，2012. ICASSP，2012：3921-3924.
[11] SANDRYHAILA A，MOURA J M F. Discrete signal processing on graphs[J]. Transactions on Signal Processing，2013，61(7)：1644-1656.
[12] SANDRYHAILA A，MOURA J M F. Discrete signal processing on graphs：Graph Fourier transform[C]// International Conference on Acoustics，Speech，and Signal Processing (ICASSP)，Vancouver，BC，Canada，May 26-31. ICASSP，2013.
[13] SANDRYHAILA A，MOURA J M F. Discrete signal processing on graphs：Frequency analysis[J]. IEEE Trans. Signal Processing，2014，62(12)：3042-3054.
[14] ANIL K J．Data clustering：50 years beyond K-means[J]．Pattern Recognition Letters，2010，31(8)：651-666.
[15] LEI Yaguo，HE Zhengjia，ZI Yingying. EEMD method and WNN for fault diagnosis of locomotive roller bearings[J]. Expert Systems with Applications，2011，38(6)：7334-7341.
[16] YIAKOPOULOUS C T，GRYLLIAS K C，ANTONIADIS I A. Rolling element bearing fault detection in industrial environments based on a K-means clustering approcah[J]. Expert System with Applications，2011，38(3)：2888-2911.
[17] KANG S，RYU J，LEE J. Analysis of spacetimennd adaptive processing performance using K-means clustering algorithm for normalisation method in non-homogeneity detector process[J]. IET Signal Processing，2011，5(2)：113-120.
[18] LEE J W，PARK R H，CHANG S. Local tone mapping using the K-means algorithm and automatic gamma setting[J]. IEEE Transactions on Consumer Electronics，2011，57(1)：209-217.
[19] Bearing Data Center. Case western reserve university[EB/OL]. [2014-04-10]. http：//csegroups. case. edu/bearingdatacenter/pages/download-data-file.
[20] 彭富强，于德介，罗洁思，等. 基于多尺度线调频基稀疏信号分解的轴承故障诊断[J]. 机械工程学报，2010，47(7)：88-95. PENG Fuqiang，YU Dejie，LUO Jiesi，et al. Sparse signal decomposition method based on multi-scale Chirplet and its application to bearing fault diagnosis[J]. Journal of Mechanical Engineering，2010，47(7)：88-95.

路图傅里叶变换及其在滚动轴承故障诊断中的应用

Path Graph Fourier Transformation and Its Applications to Rolling Bearing Fault Diagnosis

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价

[1]	狄子钧, 袁东风, 李东阳, 梁道君, 周晓天, 信苗苗, 曹凤, 雷腾飞. 基于多尺度-高效通道注意力网络的刀具故障诊断方法[J]. 机械工程学报, 2024, 60(6): 82-90.
[2]	严如强, 许文纲, 王志颖, 朱启翔, 周峥, 赵志斌, 孙闯, 王诗彬, 陈雪峰, 张军辉, 徐兵. 航空发动机燃油控制系统故障诊断技术研究进展与挑战[J]. 机械工程学报, 2024, 60(4): 3-31.
[3]	张军辉, 刘施镐, 徐兵, 黄伟迪, 吕飞, 黄晓琛. 轴向柱塞泵智能化关键技术研究进展及发展趋势[J]. 机械工程学报, 2024, 60(4): 32-49.
[4]	丁孺琦, 熊文杰, 程敏, 徐兵. 智能化阀口独立电液控制系统安全性能评估[J]. 机械工程学报, 2024, 60(4): 101-112.
[5]	王志颖, 李天福, 许文纲, 孙闯, 张军辉, 徐兵, 严如强. 降噪混合注意力变分自编码器及其在轴向柱塞泵故障诊断中的应用[J]. 机械工程学报, 2024, 60(4): 167-177.
[6]	邵海东, 林健, 闵志闪, 明宇航. 分布外样本干扰下基于改进半监督原型网络的齿轮箱跨域故障诊断[J]. 机械工程学报, 2024, 60(4): 212-221.
[7]	潘海洋, 徐海锋, 郑近德, 童靳于, 张飞斌. 基于双加权不平衡矩阵分类器的机械故障诊断方法[J]. 机械工程学报, 2024, 60(3): 170-180.
[8]	赵轲, 叶敏, 王瑞欣, 陆海, 刘孟孟, 邵海东. 基于模糊域自适应的源自由域旋转机械故障诊断方法[J]. 机械工程学报, 2024, 60(18): 43-52.
[9]	李志鹏, 马天雨, 刘金平, 向青松, 唐俊杰. 基于非对称性对抗训练的多源域自适应智能故障诊断方法[J]. 机械工程学报, 2024, 60(18): 76-88.
[10]	汪煜坤, 易彩, 汪浩, 周秋阳, 冉乐, 王靖元. PSD引导的自适应频带划分方法及其在轴承故障诊断中的应用[J]. 机械工程学报, 2024, 60(17): 179-193.
[11]	高帅, 韩勤锴, 褚福磊. 具备实时动态稳定性监测特性的高速混合陶瓷摩擦电滚动轴承[J]. 机械工程学报, 2024, 60(15): 80-88.
[12]	刘一龙, 李心远, 陈银萍, 成玮, 陈雪峰. 基于峭度曲面极大值的电机轴承保持架故障诊断方法[J]. 机械工程学报, 2024, 60(15): 89-99.
[13]	于小洛, 杨阳, 杜明刚, 何清波, 彭志科. 机械传动系统含偏差频率分量协同检测与分解方法[J]. 机械工程学报, 2024, 60(15): 100-112.
[14]	黄包裕, 张永祥. 一种基于三步法的轴承故障诊断方法[J]. 机械工程学报, 2024, 60(14): 51-68.
[15]	陈钱, 陈康康, 董兴建, 皇甫一樊, 彭志科, 孟光. 一种面向机械设备故障诊断的可解释卷积神经网络[J]. 机械工程学报, 2024, 60(12): 65-76.