基于小波包和FCM多分类器组的轴承故障诊断
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摘要
滚动轴承是各种旋转机械中应用最广泛的一种通用机械部件，其工况监控与故障诊断具有重要意义。本文研究基于小波包的轴承故障特征提取及基于模糊C均值(Fuzzy C-Means，简称FCM)多分类器组的故障识别方法，以提高轴承故障诊断系统的准确率。
首先，对滚动轴承的故障机理进行了分析，并分别采用时域和基于傅里叶变换的频域方法对轴承振动信号的特征进行提取与分析。分析结果表明，基于时域和傅里叶变换的频域方法对信号的故障特征描述各有局限性。进而，本文采用基于小波包的信号能量特征提取方法。
其次，由于多分类器组的鲁棒性较好，能克服因某些原因造成的数据失真或缺失引起的误判或漏判。在故障识别中采用FCM多分类器对故障特征进行分类识别，得到各类的聚类中心及各个故障样本对于各故障类型的隶属度，从而实现模糊聚类划分。FCM算法具有较高的搜索能力，但它是一种局部搜索算法，且对聚类中心的初值十分敏感，并容易陷入局部极值。为避免分类时陷入局部最优，本文利用粒子群优化(Particle Swarm Optimization，简称PSO)算法的全局搜索能力对FCM的聚类中心进行优化，进而得到一种基于PSO优化的FCM多分类器组故障特征识别方法。
最后，在进行FCM多分类器组融合时采用模糊积分(Fuzzy Integral，简称FI)融合方法，用以提高多分类器融合系统的分类精确率。在基于FI的多分类器融合系统中，模糊测度对融合系统的性能有很大的影响，通常情况模糊测度为预先人为给定。因此，本文同样采用PSO算法优化模糊测度，改进基于FI融合的多分类器组的分类精度和分类效率。仿真研究表明基于小波包和FCM多分类器组的故障诊断方法能够有效地提高轴承故障诊断的识别准确率。
The rolling bearing is the most widely used mechanical components in a variety ofrotating machinery, its condition monitoring and fault diagnosis possess significance. Inorder to improve the accuracy of the bearing fault diagnosis system, bearing fault featureextraction based on wavelet packet and fault recognition based on FCM classifier group.
First of all, the analysis of the failure mechanism of rolling bearing, time domain andfrequency domain based on Fourier transform are used in the bearing vibration signalfeature extraction and analysis. The analysis showed that the failure characteristics of thesignal based on time domain and Fourier transform have their own limitations.Furthermore, using the signal energy feature extraction methods based on wavelet packet.
Secondly, for the robustness, multiple classifier group is able to overcome the falsepositives caused by data distortion or missing due to some reason. Using multipleclassifiers of FCM achieve the classification of fault characteristics in the faultidentification. FCM algorithm has better search capabilities which is a local searchalgorithm and so sensitive to the initial value of the cluster center that is easy to fall intolocal minima. In order to avoid the local optimum, using Particle Swarm Optimizationalgorithm, which of the global search ability optimize the cluster centers of FCM andachieve the failure feature recognition method of FCM classifier group based on PSO.
Finally, in order to improve the classification accuracy rate of multiple classifiersfusion system and the robustness of the system, fuzzy integral fusion method is usedduring the FCM classifier group fusion. Based on fuzzy integral classifier fusion system,fuzzy measure has a great impact on the performance of the fusion system and is given onthe pre-anthropogenic. Therefore, the PSO algorithm is used to optimize the fuzzymeasure and improve the classification accuracy and efficiency based on fuzzy integralfusion group. Simulation studies show that the fault diagnosis method based on waveletpacket and FCM classifier group is effectively improve the recognition accuracy.
首先，对滚动轴承的故障机理进行了分析，并分别采用时域和基于傅里叶变换的频域方法对轴承振动信号的特征进行提取与分析。分析结果表明，基于时域和傅里叶变换的频域方法对信号的故障特征描述各有局限性。进而，本文采用基于小波包的信号能量特征提取方法。
其次，由于多分类器组的鲁棒性较好，能克服因某些原因造成的数据失真或缺失引起的误判或漏判。在故障识别中采用FCM多分类器对故障特征进行分类识别，得到各类的聚类中心及各个故障样本对于各故障类型的隶属度，从而实现模糊聚类划分。FCM算法具有较高的搜索能力，但它是一种局部搜索算法，且对聚类中心的初值十分敏感，并容易陷入局部极值。为避免分类时陷入局部最优，本文利用粒子群优化(Particle Swarm Optimization，简称PSO)算法的全局搜索能力对FCM的聚类中心进行优化，进而得到一种基于PSO优化的FCM多分类器组故障特征识别方法。
最后，在进行FCM多分类器组融合时采用模糊积分(Fuzzy Integral，简称FI)融合方法，用以提高多分类器融合系统的分类精确率。在基于FI的多分类器融合系统中，模糊测度对融合系统的性能有很大的影响，通常情况模糊测度为预先人为给定。因此，本文同样采用PSO算法优化模糊测度，改进基于FI融合的多分类器组的分类精度和分类效率。仿真研究表明基于小波包和FCM多分类器组的故障诊断方法能够有效地提高轴承故障诊断的识别准确率。
The rolling bearing is the most widely used mechanical components in a variety ofrotating machinery, its condition monitoring and fault diagnosis possess significance. Inorder to improve the accuracy of the bearing fault diagnosis system, bearing fault featureextraction based on wavelet packet and fault recognition based on FCM classifier group.
First of all, the analysis of the failure mechanism of rolling bearing, time domain andfrequency domain based on Fourier transform are used in the bearing vibration signalfeature extraction and analysis. The analysis showed that the failure characteristics of thesignal based on time domain and Fourier transform have their own limitations.Furthermore, using the signal energy feature extraction methods based on wavelet packet.
Secondly, for the robustness, multiple classifier group is able to overcome the falsepositives caused by data distortion or missing due to some reason. Using multipleclassifiers of FCM achieve the classification of fault characteristics in the faultidentification. FCM algorithm has better search capabilities which is a local searchalgorithm and so sensitive to the initial value of the cluster center that is easy to fall intolocal minima. In order to avoid the local optimum, using Particle Swarm Optimizationalgorithm, which of the global search ability optimize the cluster centers of FCM andachieve the failure feature recognition method of FCM classifier group based on PSO.
Finally, in order to improve the classification accuracy rate of multiple classifiersfusion system and the robustness of the system, fuzzy integral fusion method is usedduring the FCM classifier group fusion. Based on fuzzy integral classifier fusion system,fuzzy measure has a great impact on the performance of the fusion system and is given onthe pre-anthropogenic. Therefore, the PSO algorithm is used to optimize the fuzzymeasure and improve the classification accuracy and efficiency based on fuzzy integralfusion group. Simulation studies show that the fault diagnosis method based on waveletpacket and FCM classifier group is effectively improve the recognition accuracy.
引文
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[2]王冬云,张文志.基于小波包变换的滚动轴承故障诊断[J].中国机械工程, 2012, 23(3):295-298.
[3]黄坤,李洪儒.小波分析在轴承故障诊断中的应用[J].科学技术与工程,2006, 6(23): 356-359.
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[6] Yesilun I. Fault detection and location in gears by the smoothed instantaneous power spectrumdistribution[J]. NCT&E Internation, 2003(36): 535-542.
[7] Jones D L, Parks T W. A resolution comparison of several time-frequency representations[J]. IEEETransactions on Signal Processing, 1992, 40(2): 413-420.
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[10] Sadeghian. A, Ye. Z, Wu. B. Online detection of broken rotor bars in induction motors by waveletpacket decomposition and artificial neural networks[J]. IEEE Transactions on Instrumentation andMeasurement, 2009, 58(7):2253-2263.
[11] Wang W J, McFadden P D. Application of orthogonal wavelet to early gear damage detection[J].Mechanical Systems and Signal Processing, 1995, 9(5): 497–507.
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[14]朱启兵,刘杰等.基于小波能量和RBF网络的钢水下渣自动检测[J].振动、测试与诊断, 2005,25(3): 30-32.
[15]郭健,陈勇等.基于多传感器信息融合的结构损伤识别研究[J].振动工程学报, 2006,18(2):155-160.
[16]周福昌,陈进等.基于小波滤波与循环平稳度分析的滚动轴承早期故障诊断方法[J].振动与冲击, 2006, 5(4): 9l-93.
[17] Ye. Z, Sadeghian. A, Wu. B. Mechanical fault diagnostics for induction motor with variable speeddrives using Adaptive Neuro-fuzzy Inference System[J]. Electric Power Systems Research, 2006,76(9):181-189.
[18] Rodriguez P. V. J, Negrea, Arkkio.A. A simplified scheme for induction motor conditionmonitoring[J]. Mechanical Systems and Signal Processing, 2008, 22(5):1216-1236.
[19] Gunal. S, Gokhan Ece. D, Nezih Gerek. O. Induction machine condition monitoring usingnotch-filtered motor current[J]. Mechanical Systems and Signal Processing, 2009,23(8):2658-2670.
[20] Widodo. A, Yang. B. S. Wavelet support vector machine for induction machine fault diagnosisbased on transient current signal[J]. Expert Systems with Application, 2008,35(1):307-316.
[21] Lee. S. H, Cheon. S. P, Kim. Y. Fourier and wavelet transformations for the fault detection ofinduction motor with stator current. Lecture Notes in Computer Science Springer,2006(4114):557-569.
[22] Suen C Y, Nadal C, Mai T A, et al. Recongnition of Totally Unconstrained Handwriting NumeralsBased on the concept of Multiple Experts[A]. Suen C Y. Frontiers in HandwritingRecognition[C]//Montreal Canada: International Workshop on Frontiers in HandwritingRecognition, 1990: 131-143
[23] Mubeccel D, Hakan A. Plurality voting-based multiple classifier systems: statistically independentwith respect to dependent classifier sets. Pattern Recognition, 2002, 35(11): 2365-2379.
[24] Hull J J, Commike A, Ho. T K Multiple algorithms for handwritten character recognition[C]//ProcInt workshop frontiers in handwriting recognition, Montreal, Canada, 1990: 117-129.
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[26] Josef K, Mohamad H, Robert P, et al. On Combining Classifiers[J]. Pattern Analysis and MachineIntelligence, 1998(20): 226-239.
[27]谢华,夏顺仁,张赞超.医学图像识别中多分类器融合方法的研究进展[J].国际生物医学工程杂志, 2006, 29(3):152-157.
[28]张德国,胡海虹.基于模糊积分的图像分割算法融合[J].系统工程与电子技术, 2006,28(10):1480-1483.
[29]孔志周.多分类器融合框架下的模糊积分方法[J].统计与决策, 2007(10):137-139.
[30] Loparo. K. A. Bearings vibration data set[DB/OL]. Case Western Reserve University.http://www.eecs.edu/laboratory/bearing/.
[31]侯帅,韩中庚,黄洁等.基于Sugeno模糊积分的多分类器融合方法在多属性决策中的应用[J].信息工程大学学报, 2010, 11(1): 124-128.
[32] David Ben-Arieh, Deep Kumar Gullipalli. Data Envelopment Analysis of clinics with sparse data:fuzzy clustering approach[J]. Computers and Industrial Engineering, 2012, 63(1):13-21.
[33] Tamalika Chaira. A novel intuitional fuzzy c means clustering algorithm and its application tomedical images[J]. Applied Soft Computing, 2011, 11(2):1711-1717.
[34] Aihong Tang, Youmei Zhang, Jiazeng Wei, et al. A multi sensor information fusion method basedon fuzzy clustering and artificial immune[J]. Energy Procedia, 2011(13):5415-5420.
[35] Keh-Shih Chuang, Hong-Long Tzeng, Sharon Chen, et al. Fuzzy c means clustering with spatialinformation for image segmentation[J]. Computerized Medical Imaging and Graphics,2006(30):9-15.
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[37] Yuksel Ozbay, Rahime Ceylan, Bekir Karlik. Integration of type-2 fuzzy clustering and wavelettransform in a neural network based ECG classifier[J]. Pattern Recognition, 2011,38(1):1004-1010.
[38] Francois Caron, Emmanuel Duflos, Denis Pomorski, et al. GPS/IMU data fusion usingmulti-sensor kalman filtering: introduction of contextual aspects[J]. Information Fusion, 2006,7(2):221-230.
[39] Jeffrey K. U. Covariance consistency methods for fault tolerant distributed data fusion[J].Information Fusion, 2003, 4(3):201-215.
[40] Hung-Ta Pai, Jing Deng, Yunghsiang S. Han. Time slotted voting mechanism for fusion dataassurance in wireless sensor networks under stealthy attacks[J]. Computer Communications, 2010,33(13):1524-1530.
[41] Faouzi. N. E, Henry Leung, Ajeesh Kurian. Data fusion in intelligent transportation systems:Progress and challenges-A survey[J]. Information Fusion, 2011, 12(1):4-10.
[42] Gang Niu, Bo-Suk Yang. Intelligent condition monitoring and prognostics system based on datafusion strategy[J]. Expert Systems with Applications, 2010, 37(12):8831-8840.
[43] Kaihong Guo, Wenli Li. Combination rule of D-S evidence theory based on the strategy of crossmerging between evidence[J]. Expert Systems with Application, 2011, 38(10):13360-13366.
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[2]王冬云,张文志.基于小波包变换的滚动轴承故障诊断[J].中国机械工程, 2012, 23(3):295-298.
[3]黄坤,李洪儒.小波分析在轴承故障诊断中的应用[J].科学技术与工程,2006, 6(23): 356-359.
[4]戴冲.基于小波和混沌的微弱信号检测[D].成都:西南交通大学,2008: 1-3.
[5]朱大奇,刘永安.故障诊断的信息融合方法[J].控制与决策, 2007, 22(12): 1321-1328.
[6] Yesilun I. Fault detection and location in gears by the smoothed instantaneous power spectrumdistribution[J]. NCT&E Internation, 2003(36): 535-542.
[7] Jones D L, Parks T W. A resolution comparison of several time-frequency representations[J]. IEEETransactions on Signal Processing, 1992, 40(2): 413-420.
[8] McFadden P D, Wang W J. Analysis of gear vibration signatures by the weighted Wigner-Villedistribution[J]. Vibration in Rotating Machinery, Processing of the Institution of MechanicalEngineers, 1992: 393-397.
[9] Lin J, Zuo M J. Gearbox fault diagnosis using adaptive wavelet filter[J]. Mechanical Systemsand Signal Processing, 2003, 17(6): 1259–1269.
[10] Sadeghian. A, Ye. Z, Wu. B. Online detection of broken rotor bars in induction motors by waveletpacket decomposition and artificial neural networks[J]. IEEE Transactions on Instrumentation andMeasurement, 2009, 58(7):2253-2263.
[11] Wang W J, McFadden P D. Application of orthogonal wavelet to early gear damage detection[J].Mechanical Systems and Signal Processing, 1995, 9(5): 497–507.
[12]程军圣,于德介等.尺度-小波能量谱在滚动轴承故障诊断中的应用[J].振动工程学报, 2004,17(1): 82-85.
[13]王国锋,王子良等.基于小波包和径向基神经网络轴承故障诊断[J].北京科技大学学报,2004, 26(2): 184-187.
[14]朱启兵,刘杰等.基于小波能量和RBF网络的钢水下渣自动检测[J].振动、测试与诊断, 2005,25(3): 30-32.
[15]郭健,陈勇等.基于多传感器信息融合的结构损伤识别研究[J].振动工程学报, 2006,18(2):155-160.
[16]周福昌,陈进等.基于小波滤波与循环平稳度分析的滚动轴承早期故障诊断方法[J].振动与冲击, 2006, 5(4): 9l-93.
[17] Ye. Z, Sadeghian. A, Wu. B. Mechanical fault diagnostics for induction motor with variable speeddrives using Adaptive Neuro-fuzzy Inference System[J]. Electric Power Systems Research, 2006,76(9):181-189.
[18] Rodriguez P. V. J, Negrea, Arkkio.A. A simplified scheme for induction motor conditionmonitoring[J]. Mechanical Systems and Signal Processing, 2008, 22(5):1216-1236.
[19] Gunal. S, Gokhan Ece. D, Nezih Gerek. O. Induction machine condition monitoring usingnotch-filtered motor current[J]. Mechanical Systems and Signal Processing, 2009,23(8):2658-2670.
[20] Widodo. A, Yang. B. S. Wavelet support vector machine for induction machine fault diagnosisbased on transient current signal[J]. Expert Systems with Application, 2008,35(1):307-316.
[21] Lee. S. H, Cheon. S. P, Kim. Y. Fourier and wavelet transformations for the fault detection ofinduction motor with stator current. Lecture Notes in Computer Science Springer,2006(4114):557-569.
[22] Suen C Y, Nadal C, Mai T A, et al. Recongnition of Totally Unconstrained Handwriting NumeralsBased on the concept of Multiple Experts[A]. Suen C Y. Frontiers in HandwritingRecognition[C]//Montreal Canada: International Workshop on Frontiers in HandwritingRecognition, 1990: 131-143
[23] Mubeccel D, Hakan A. Plurality voting-based multiple classifier systems: statistically independentwith respect to dependent classifier sets. Pattern Recognition, 2002, 35(11): 2365-2379.
[24] Hull J J, Commike A, Ho. T K Multiple algorithms for handwritten character recognition[C]//ProcInt workshop frontiers in handwriting recognition, Montreal, Canada, 1990: 117-129.
[25] Ali K M, Pazzani M J. On the link between error correlation and error reduction in decision treeensembles[R]. Technical report, ICS-UCI, 1995: 95-98.
[26] Josef K, Mohamad H, Robert P, et al. On Combining Classifiers[J]. Pattern Analysis and MachineIntelligence, 1998(20): 226-239.
[27]谢华,夏顺仁,张赞超.医学图像识别中多分类器融合方法的研究进展[J].国际生物医学工程杂志, 2006, 29(3):152-157.
[28]张德国,胡海虹.基于模糊积分的图像分割算法融合[J].系统工程与电子技术, 2006,28(10):1480-1483.
[29]孔志周.多分类器融合框架下的模糊积分方法[J].统计与决策, 2007(10):137-139.
[30] Loparo. K. A. Bearings vibration data set[DB/OL]. Case Western Reserve University.http://www.eecs.edu/laboratory/bearing/.
[31]侯帅,韩中庚,黄洁等.基于Sugeno模糊积分的多分类器融合方法在多属性决策中的应用[J].信息工程大学学报, 2010, 11(1): 124-128.
[32] David Ben-Arieh, Deep Kumar Gullipalli. Data Envelopment Analysis of clinics with sparse data:fuzzy clustering approach[J]. Computers and Industrial Engineering, 2012, 63(1):13-21.
[33] Tamalika Chaira. A novel intuitional fuzzy c means clustering algorithm and its application tomedical images[J]. Applied Soft Computing, 2011, 11(2):1711-1717.
[34] Aihong Tang, Youmei Zhang, Jiazeng Wei, et al. A multi sensor information fusion method basedon fuzzy clustering and artificial immune[J]. Energy Procedia, 2011(13):5415-5420.
[35] Keh-Shih Chuang, Hong-Long Tzeng, Sharon Chen, et al. Fuzzy c means clustering with spatialinformation for image segmentation[J]. Computerized Medical Imaging and Graphics,2006(30):9-15.
[36] Mitchell T M.机器学习[M].北京:机械工业出版社, 2005: 40-45.
[37] Yuksel Ozbay, Rahime Ceylan, Bekir Karlik. Integration of type-2 fuzzy clustering and wavelettransform in a neural network based ECG classifier[J]. Pattern Recognition, 2011,38(1):1004-1010.
[38] Francois Caron, Emmanuel Duflos, Denis Pomorski, et al. GPS/IMU data fusion usingmulti-sensor kalman filtering: introduction of contextual aspects[J]. Information Fusion, 2006,7(2):221-230.
[39] Jeffrey K. U. Covariance consistency methods for fault tolerant distributed data fusion[J].Information Fusion, 2003, 4(3):201-215.
[40] Hung-Ta Pai, Jing Deng, Yunghsiang S. Han. Time slotted voting mechanism for fusion dataassurance in wireless sensor networks under stealthy attacks[J]. Computer Communications, 2010,33(13):1524-1530.
[41] Faouzi. N. E, Henry Leung, Ajeesh Kurian. Data fusion in intelligent transportation systems:Progress and challenges-A survey[J]. Information Fusion, 2011, 12(1):4-10.
[42] Gang Niu, Bo-Suk Yang. Intelligent condition monitoring and prognostics system based on datafusion strategy[J]. Expert Systems with Applications, 2010, 37(12):8831-8840.
[43] Kaihong Guo, Wenli Li. Combination rule of D-S evidence theory based on the strategy of crossmerging between evidence[J]. Expert Systems with Application, 2011, 38(10):13360-13366.
[44] Xiao-feng Fan, Ming J. Zuo. Fault diagnosis of machines based on D-S evidence theory. Part 1:D-S evidence theory and its improvement[J]. Pattern Recognition Letters, 2006, 27(5):366-376.
[45] Xiao-feng Fan, Ming J. Zuo. Fault diagnosis of machines based on D-S evidence theory. Part 2:Application of the improved D-S evidence theory in gearbox fault diagnosis[J]. PatternRecognition Letters, 2006, 27(5):377-385.
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