Application of Multifractal Detrended Fluctuation Analysis to Severity Identification of Rolling Bearing Damages

Abstract

Abstract:

The multifractal spectrum of bearing vibration data was estimated using MFDFA. As a result, the shapes and positions of the multifractal spectrum could be largely determined by the left-end, right-end and extreme points of the multifractal spectrum. Subsequently, coordinates of these characteristic points were used as characteristic parameters for describing dynamic properties of the bearings.MFDFA, together with four conventional temporal statistical parameters, wavelet transform(WT) and empirical mode decomposition(EMD), was exploited to recognize severity of damage of bearing balls and outer-races separately. Each of the Mahalanobis-distance(MD), BP neural network and support vector machine (SVM) algorithms was employed to classify the feature parameters derived from each of WT, EMD and MFDFA. Moreover, the effectiveness of these algorithms in severity identification of bearing damage was compared. The results show that the methods associating MD with MFDFA and associating SVM with WT or EMD perform better than the others. The conclusions drawn in the early work seem to be further confirmed.

Key words: multifractal detrended fluctuation analysis(MFDFA), rolling bearing, damage, severity identification

摘要：

为了评估多重分形去趋势波动分析(MFDFA)在滚动轴承损伤程度识别中的性能，采用MFDFA计算了轴承故障信号的多重分形谱，多重分形谱的左右端点和极值点可以近似描述多重分形谱的形状和位置，提取这三个特征点的坐标作为刻画轴承动力学行为的特征参数。将MFDFA、4个常用的时域统计参数、小波变换(WT)方法和经验模态分解(EMD)方法分别用于识别轴承滚动体和外圈损伤的严重程度，然后分别采用马氏距离判别法、BP神经网络和支持向量机对WT、EMD和MFDFA所提取的特征参数进行分类，并比较了这些方法在故障分类中的效果。结果表明，马氏距离判别法与MFDFA的组合以及支持向量机与WT或EMD的组合可以获得较好的轴承损伤程度识别结果。研究结果进一步验证了早期工作的结论。

关键词: 多重分形去趋势波动分析, 滚动轴承；损伤；程度识别

CLC Number:

TH113

Lin Jinshan, Chen Qian. Application of Multifractal Detrended Fluctuation Analysis to Severity Identification of Rolling Bearing Damages[J]. China Mechanical Engineering, 2014, 25(13): 1760-1765.

林近山, 陈前. 多重分形去趋势波动分析在滚动轴承损伤程度识别中的应用[J]. 中国机械工程, 2014, 25(13): 1760-1765.

References

[1]Randall R B, Antoni J. Rolling Element Bearing Diagnostics—a Tutorial[J]. Mechanical Systems and Signal Processing, 2011, 25(2)： 485-520.
[2]Demoura E P，Souto C R，Silva A A，et al. Evaluation of Principal Component Analysis and Neural Network Performance for Bearing Fault Diagnosis from Vibration Signal Processed by RS and DF Analysis[J]. Mechanical Systems and Signal Processing，2011，25(5)： 1765-1772.
[3]Lin Jinshan, Chen Qian, Tian Xiange, et al. Fault Diagnosis of Rolling Bearings Using Multifractal Detrended Fluctuation Analysis and Mahalanobis Distance Criterion[C]//Proceedings of the 18th International Conference on Automation & Computing. Leicestershire, UK, 2012：152-157.
[4]郝如江，卢文秀，褚福磊.形态滤波器用于滚动轴承故障信号的特征提取[J]. 中国机械工程，2009，20(2)：197-201.
Hao Rujiang, Lu Wenxiu,Chu Fulei. Morphological Filters in Feature Extraction for Rolling Bearing Defect Signals[J]. China Mechanical Engineering, 2009, 20(2): 197-201.
[5]何正嘉，陈进，王太勇，等. 机械故障诊断理论及应用[M].北京：高等教育出版社，2010.
[6]Wang Huaqing，Li Ke，Sun Hao，et al. Feature Extraction Method Based on Pseudo-Wigner-Ville Distribution for Rotational Machinery in Variable Operating Conditions[J].Chinese Journal of Mechanical Engineering，2011，24(4)：661-668.
[7]Rafiee J，Rafiee M A，Tse P W. Application of Mother Wavelet Functions for Automatic Gear and Bearing Fault Diagnosis[J]. Expert Systems with Applications，2010， 37(6)：4568-4579.
[8]Yu Dejie，Cheng Junsheng，Yang Yu. Fault Diagnosis Approach for Roller Bearings Based on Empirical Mode Decomposition Method and Hilbert Transform[J]. Chinese Journal of Mechanical Engineering，2005，18(2)：267-270.
[9]Huang N E，Shen Z，Long S R. The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Non-stationary Time Series Analysis[J]. Proceedings of the Royal Society of London Series A，1998，454(1971)：903-995.
[10]程军圣，张亢，杨宇. 局部均值分解方法及其在滚动轴承故障诊断中的应用[J]. 中国机械工程，2009， 20(22)：2711-2717.
Cheng Junsheng, Zhang Kang, Yang Yu. Local Mean Decomposition and Its Application to Roller Bearing Fault Diagnosis[J].China Mechanical Engineering, 2009, 20(22): 2711-2717.
[11]Peng C K，Buldyrev S V，Havlin S，et al. Mosaic Organization of DNA Nucleotides[J]. Physical Review E, 1994, 49(2)：1685-1689.
[12]Kantelhardt J W，Zschiegner S A，Koscielny-Bunde E，et al. Multifractal Detrended Fluctuation Analysis of Nonstationary Time Series[J]. Physica A，2002，316(1)：87-114.
[13]Zhang Shuqing，Zhao Yuchun，Zhang Liguo，et al. Mechanical Fault Diagnosis Based on Band-phase-randomized Surrogate Data and Multifractal[J]. Chinese Journal of Mechanical Engineering，2011，24(5)：885-890.
[14]郝研，王太勇，万剑，等. 基于经验模式分解和广义维数的机械故障诊断[J]. 吉林大学学报(工学版)，2012, 42(2)：392-396.
Hao Yan，Wang Taiyong，Wan Jian，et al. Mechanical Fault Diagnosis Based on Empirical Mode Decomposition and Generalized Dimension[J]. Journal of Jilin University(Engineering and Technology Edition)，2012，42(2)：392-396.
[15]Lui Yangqing，Gao Jianmin，Jiang Hongquan，et al. Condition Recognition of Complex Systems Based on Multi-fractal Analysis[C]//Proceedings of IEEE Conference on Annual Reliability and Maintainability Symposium.Lake Buena Vista，New Jersey, 2011：32-37.
[16]唐静远，师奕兵，张伟，等. 非线性模拟电路故障诊断的MF-DFA方法[J]. 计算机辅助设计与图形学学报，2010，22(5)：852-857.
Tang Jingyuan，Shi Yibing，Zhang Wei，et al. Nonlinear Analog Circuit Fault Diagnosis Based on MF-DFA Method[J]. Journal of Computer-Aided Design & Computer Graphics，2010，22(5)：852-857.
[17]Lin Jinshan, Chen Qian. Fault Diagnosis of Rolling Bearings Based on Multifractal Detrended Fluctuation Analysis and Mahalanobis Distance Criterion[J]. Mechanical Systems and Signal Processing, 2013, 38(2): 515-533.
[18]Mahalanobis P C. On the Generalized Distance in Statistics[J]. Proceedings of the National Institute of Sciences of India，1936，2(1)：49-55.
[19]焦李成. 神经网络系统理论[M]. 西安：西安电子科技大学出版社, 1990.
[20]殷震. 基于BP神经网络的电力变压器内部故障诊断方法研究[D]. 天津: 天津大学, 2007.
[21]张学工. 统计学习理论的本质[M]. 北京: 清华大学出版杜, 2000.
[22]Cristianini N, Shawe-Taylor J. 支持向量机导论[M]. 李国正，王猛，曾华军，译. 北京：电子工业出版社，2006.
[23]Sonar R, Deshmukh P R. Multiclass Classification: a Review[J]. International Journal of Computer Science and Mobile Computing, 2014, 3(4): 65-69.
[24]Qian Xiyuan，Gu Gaofeng，Zhou Weixing. Modified Detrended Fluctuation Analysis Based on Empirical Mode Decomposition for the Characterization of Anti-persistent Processes[J]. Physica A，2011，390(23/24)：4388-4395.
[25]Moktadir Z，Kraft M，Wensink H. Multifractal Properties of Pyrex and Silicon Surfaces Blasted with Sharp Particles[J]. Physica A，2008，387(8/9)：2083-2090.