基于逻辑回归和高斯混合模型的设备故障诊断技术研究与应用
|
摘要
近年来,随着现代制造工业的发展,各种机械设备越来越广泛的应用于石化、电力等行业,而且它们本身还不断向大型化、智能化、高速化和复杂化等方面发展,这些发展极大的推动了社会生产力的发展。然而,一旦这类设备发生严重故障,不仅会给企业带来经济损失,严重时甚至还会造成人员伤亡。因此,研究设备故障诊断技术,确保它们的安全稳定运行,降低生产成本,已成为现代企业管理的重要目标之一。
本文在国家“十一五”科技支撑计划：“大型高参数高危险性成套装置长周期运行安全保障关键技术研究及工程示范”(项目编号：2006BAK02B02)的资助下开展研究,主要研究工作体现在以下几个方面：
(1)介绍了课题研究的背景、目的和意义,阐述了设备性能退化评估和设备故障模式识别的发展现状,明确了需要解决的问题。
(2)研究了信号处理、特征选择与特征提取技术,着重针对本研究中所涉及到的两种信号处理方法FFT和小波包分解,以及基于故障特征频率的特征选择方法和基于主成分分析(PCA)的特征抽取方法进行了研究。
(3)详细研究了本文研究中的重要模型,即逻辑回归和高斯混合模型。针对逻辑回归,对其进行了理论概述以及基于极大似然估计法的参数获取研究；针对高斯混合模型,介绍了模型理论以及EM参数估计方法,另外,对于使用EM算法进行参数估计时所遇到的初值设定和高斯混合数的确定问题进行了一定的探索研究。
(4)将逻辑回归和高斯混合模型引入到旋转机械设备的性能退化评估中。使用逻辑回归建立了滚动轴承运行性能退化评估模型,并用本实验室获取的实验数据和网上公开的CWRU数据进行了验证；使用高斯混合模型建立了离心压缩机运行性能退化状态评估模型,并用中国石油某炼化企业现场实际监测数据进行验证,取得良好效果。
(5)将高斯混合模型引入旋转机械设备的故障模式识别研究中。首先使用传统的基于贝叶斯极大似然分类器的模式分类方法,并在此基础上提出一种改进的基于特征空间重合度计算的模式分类方法,最后利用CWRU滚动轴承数据进行验证,取得良好效果。
In recent years, as modern manufacturing industry develops, various kinds of mechanical equipments have been widely utilized in petro-chemical, electricity industries and so on, while the equipments concerned have the trend towards large scale, intelligentization, high speed and integration, which greatly enhances the progress of the social productivity. However, if faults occur in these equipments, it will not only cause economic losses to the enterprises, but also will result in severe human casualties. As a result, to research equipment fault diagnosis technology and guarantee the safe and stable operation of the equipments has been of extreme significance to modern enterprises.
This paper is supported by National Key Technologies R& D Program of China:(2006BAK02B02), and the main jobs of this study are as follows:
(1) Introduced the background, goal and significance of this research, illustrated the current developing status of performance degradation assessment and fault pattern recognition method for equipments, and ascertained the problem to be solved.
(2) Researched signal processing, feature selection and feature extraction technology. Signal processing methods including FFT, Wavelet Transform and Wavelet Packet Decomposition are paid special attention to. Meanwhile, feature selection method based on fault characteristic frequency and feature extraction method based on principal component analysis are both thoroughly investigated.
(3) Investigated logistic regression and Gaussian mixture model that are theoretically essential in this paper. As for LR, its theoretical illustration and parameter estimation based on MLE (maximum likelihood estimation) are introduced; as for GMM, its theory and parameter estimation based on EM algorithm are introduced. In addition, this paper explored the problem of parameter initialization and optimal mixture number for GMM.
(4) Introduced LR and GMM into the performance degradation assessment research of rotating machinery. LR is used to assess the performance of bearing, and the method is validated by both experimental data and CWRU data; GMM is utilized to assess the performance of centrifugal compressor, which is validated by data acquired in the field of a chemical refinery enterprise of Petro China. Both the two methods have gained favorable effect.
(5) GMM is also introduced in the fault pattern recognition for rotating machinery. Firstly, traditional Bayesian classifier-based method is adopted, and then an improved method based on the overlap between GMMs is proposed, which have been validated by CWRU bearing data.
本文在国家“十一五”科技支撑计划：“大型高参数高危险性成套装置长周期运行安全保障关键技术研究及工程示范”(项目编号：2006BAK02B02)的资助下开展研究,主要研究工作体现在以下几个方面：
(1)介绍了课题研究的背景、目的和意义,阐述了设备性能退化评估和设备故障模式识别的发展现状,明确了需要解决的问题。
(2)研究了信号处理、特征选择与特征提取技术,着重针对本研究中所涉及到的两种信号处理方法FFT和小波包分解,以及基于故障特征频率的特征选择方法和基于主成分分析(PCA)的特征抽取方法进行了研究。
(3)详细研究了本文研究中的重要模型,即逻辑回归和高斯混合模型。针对逻辑回归,对其进行了理论概述以及基于极大似然估计法的参数获取研究；针对高斯混合模型,介绍了模型理论以及EM参数估计方法,另外,对于使用EM算法进行参数估计时所遇到的初值设定和高斯混合数的确定问题进行了一定的探索研究。
(4)将逻辑回归和高斯混合模型引入到旋转机械设备的性能退化评估中。使用逻辑回归建立了滚动轴承运行性能退化评估模型,并用本实验室获取的实验数据和网上公开的CWRU数据进行了验证；使用高斯混合模型建立了离心压缩机运行性能退化状态评估模型,并用中国石油某炼化企业现场实际监测数据进行验证,取得良好效果。
(5)将高斯混合模型引入旋转机械设备的故障模式识别研究中。首先使用传统的基于贝叶斯极大似然分类器的模式分类方法,并在此基础上提出一种改进的基于特征空间重合度计算的模式分类方法,最后利用CWRU滚动轴承数据进行验证,取得良好效果。
In recent years, as modern manufacturing industry develops, various kinds of mechanical equipments have been widely utilized in petro-chemical, electricity industries and so on, while the equipments concerned have the trend towards large scale, intelligentization, high speed and integration, which greatly enhances the progress of the social productivity. However, if faults occur in these equipments, it will not only cause economic losses to the enterprises, but also will result in severe human casualties. As a result, to research equipment fault diagnosis technology and guarantee the safe and stable operation of the equipments has been of extreme significance to modern enterprises.
This paper is supported by National Key Technologies R& D Program of China:(2006BAK02B02), and the main jobs of this study are as follows:
(1) Introduced the background, goal and significance of this research, illustrated the current developing status of performance degradation assessment and fault pattern recognition method for equipments, and ascertained the problem to be solved.
(2) Researched signal processing, feature selection and feature extraction technology. Signal processing methods including FFT, Wavelet Transform and Wavelet Packet Decomposition are paid special attention to. Meanwhile, feature selection method based on fault characteristic frequency and feature extraction method based on principal component analysis are both thoroughly investigated.
(3) Investigated logistic regression and Gaussian mixture model that are theoretically essential in this paper. As for LR, its theoretical illustration and parameter estimation based on MLE (maximum likelihood estimation) are introduced; as for GMM, its theory and parameter estimation based on EM algorithm are introduced. In addition, this paper explored the problem of parameter initialization and optimal mixture number for GMM.
(4) Introduced LR and GMM into the performance degradation assessment research of rotating machinery. LR is used to assess the performance of bearing, and the method is validated by both experimental data and CWRU data; GMM is utilized to assess the performance of centrifugal compressor, which is validated by data acquired in the field of a chemical refinery enterprise of Petro China. Both the two methods have gained favorable effect.
(5) GMM is also introduced in the fault pattern recognition for rotating machinery. Firstly, traditional Bayesian classifier-based method is adopted, and then an improved method based on the overlap between GMMs is proposed, which have been validated by CWRU bearing data.
引文
[1]高金吉.高速涡轮机械振动故障机理及诊断方法的研究[D].清华大学博士学位论文.1993.
[2]沈庆根,郑水英.设备故障诊断[M].北京：化学工业出版社,2006.
[3]雷金波.基于逻辑回归和支持向量机的设备状态退化评估与趋势预测研究[D].上海交通大学硕士学位论文.2008.
[4]杨国安.机械设备故障诊断实用技术[M].北京：中国石化出版社,2007.
[5]王道平,张义忠著.故障智能诊断系统的理论与方法[M].北京：冶金工业出版社,2001.
[6]肖涵.基于高斯混合模型与子空间技术的故障识别研究[D].武汉科技大学博士学位论文.2007.
[7]Lee J. Measurement of the machine performance degradation using a neural network model [J]. International Journal of Computers in Industry,1996,30 (3):193209.
[8]J.Lee, Jun Ni, Dragan Djurdjanovic, et al. Intelligent prognostic tools and e-maintenance [J]. Computers in Industry,2006,57:476-489.
[9]D. Djurdjanovica, J.Lee, J.Ni. Watchdog Agent-an infotronics-based prognostics approach for product performance degradation assessment and prediction [J]. Advanced Engineering Informatics,2003, (17):109-125.
[10]Poyhonen.S, Jover.P, Hyotyniemi.H. Signal processing of vibrations for condition monitoring of an induction motor [C]. First international symposium on control, communications and signal processing,2004,499-502.
[11]B.Gu, Z.Y.Wang, B.Y.Jing, Fault detection and diagnosis in chillers using artificial neural networks[C]. Proceedings of the 2003 International Conference on Cryogenics and Refrigeration,2003.
[12]L.Atlas, M.Ostendorf, G.D.Bernard, Hidden Markov models for monitoring machining tool-wear [C], Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing ICASSP,2000.
[13]Djurdjanovic D, Ni J, Lee J. Time-frequency based sensor fusion in the assessment and monitoring of machine performance degradation [C]. Proceeding of ASME IMEC&E 2002, New Orleans, LA. Paper number IMECE,2002.
[14]Zhang Lei. PCA-CMAC based machine performance degradation assessment [J]. Journal of Southeast University (English Edition),2005,21(3):299-303.
[15]Casoetto N, Djurdjanovic D, Mayor, D, Lee, J and Ni, J, Multi-sensor Process Performance Assessment Through the Use of Autoregressive Modeling and Feature Maps [J]. Journal of Manufacturing Systems,2003,22(1):64-72.
[16]Yuan S, Ge M, Qiu H, Lee J, Xu Y. Intelligent diagnosis in electromechanical operations systems [C]. Proceedings of 2004 IEEE international conference on robotics and automation, New Orleans,2004:2267-2272.
[17]Yan Jihong, Lee Jay, Degradation assessment and fault modes classification using logistic regression [J]. Journal of Manufacturing Science and Engineering, Transactions of the ASME, 2005,127(4):912-914.
[18]Vachtsevanos G, Wang P, Fault prognosis using dynamic wavelet neural networks [C]. AUTOTESTCON (Proceedings),2001:857-870.
[19]胡桥,张周锁,何正嘉.机械设备运行状态智能评估研究[J].振动工程学报,2004,17：313-316.
[20]董国金等.Elman神经网络在起重机安全状态评估中的应用[J].装备制造技术,2007,4：64-66.
[21]周炎涛等.RBF神经网络在电气设备状态评估中的应用[J],航空计算技术,2005,35(3)：1-4.
[22]朱义,陈进.基于HMM的设备性能退化评估方法的研究[J],振动与冲击,200827(8)：110-112.
[23]曾庆虎等.基于KPCA-HSMM设备退化状态识别与故障预测方法研究[J],仪器仪表学报,2009,30(7)：1341-1346.
[24]刘雨等.基于SVDD与信息融合技术的设备性能退化评估[J].振动与冲击,2009,28(9)：21-24.
[25]潘玉娜,陈进.基于二代小波包-支持向量数据描述的轴承性能退化评估研究[J].振动与冲击,2008,27(8)：299-301.
[26]刘伯运,欧阳光耀,常汉宝.基于神经网络和D_S证据理论的柴油机状态评估[J].车用发动机,2005,5：14-17.
[27]雷亚国等.基于特征评估和神经网络的机械故障诊断模型[J].西安交通大学学报,2006,40(5)：558-562.
[28]杨光正,吴眠,张晓莉.模式识别[M].合肥：中国科学技术大学出版社,2001.
[29]边肇棋,张学工等.模式识别(第二版)[M].北京：清华大学出版社,1999.
[30]R.O.Duda, P.E.Hart, D.G.Stor. Pattern Classification, second edition [M]. Wiley, New York, 2001.
[31]王奉涛,马孝江,邹岩琨.智能故障诊断技术综述[J].机床与液压,2003,4：6-8.
[32]Xu Y, Ge M. Hidden Markov model-based process monitoring system [J]. Journal of intelligent manufacturing,2004,15:337-350.
[33]Ye D. New method for faults diagnosis of rotating machinery based on 2-dimensional Hidden Markov Model [J]. Proceedings of the international symposium on precision mechanical measurement, Hefei, China,2002,4:391-395.
[34]Sppoerre J K. Application of the cascade correlation algorithm to bearing fault classification problems [J]. Computers in industry,1997,32:295-304.
[35]Wang C. C, Tao G. P. J. Rotating machine fault detection based on HOS and artificial neural networks [J]. Journal of Intelligent Manufacturing.2002,13,283-293.
[36]Tallam et al. Self-commissioning training algorithms for neural networks with applications to electric machine fault diagnosis [J]. IEEE transactions on Power Electronics. 2002,17:1089-1095.
[37]Sohn H, Worden K, Farrar C. R. Statistical damage classification under changing environment and operational conditions [J]. Journal of Intelligent Material Systems and Structures. 2002,13:561-574.
[38]Yang B. S, Han T. Kim Y. S. Integration of ART-Kohonen neural network and case-based reasoning for intelligent fault diagnosis [J]. Expert Systems with applications,2004, 26:387-395.
[39]Sampath S. Ogaji S. Singh R. Engine fault diagnostics:An optimization procedure [J]. Applied Energy,2002,73:47-70.
[40]Yang B. S, Jeong S. K, Oh Y. M. Case-based reasoning system with petri nets for induction motor fault diagnosis [J]. Expert Systems with applications,2004,27:301-311.
[41]唐贵基,田丽洁,田学航.人工神经网络在混合智能故障诊断技术中的应用研究[J].汽轮机技术,2005,47(5)：378-380.
[42]王志鹏,马孝江.基于RBF网络的旋转机械故障诊断方法[J].大连理工大学学报,2001,41(6)：696-699.
[43]刘占生等.基于遗传算法的旋转机械故障诊断方法融合[J].机械工程学报,2007,43(10)：227-233.
[44]张龙等.基于时变自回归模型与支持向量机的旋转机械故障诊断方法[J].中国电机工程学报,2007,27(9)：99-103.
[45]李志农,丁启全,吴昭同.旋转机械升降速过程的双谱-FHMM识别方法[J].振动工程学报,2003,(6)：172-174.
[46]苗强.基于隐马尔可夫模型的故障诊断系统研究[J].航空学报,2005,9：212-214.
[47]刘天雄,华宏星,李中付,陈兆能.基于分行集合状态检测方法的应用研究[J].机械工程学报,2001,5：234-237.
[48]肖涵,李友荣,吕勇.基于四分位偏差分型维与高斯混合模型的故障识别算法研究[J].振动工程学报.2008,21(1)：79-83.
[49]何正嘉.机械设备非平稳信号的故障诊断原理及应用[J].高等教育出版社,2001,11：169-171.
[50]彭斌,刘振全.基于改进小波神经网络的旋转机械故障诊断[J].振动、测试与诊断,2007,27,(1)：32-35.
[51]岳玉梅,毛雅丽,王家庆.高速旋转机械故障智能诊断系统的研究[J].沈阳建筑大学学报(自然科学版),2005,21(6)：770-773
[52]程佩青.数字信号处理(第二版)[M].北京：清华大学出版社,2001.
[53]胡广书.数字信号处理理论,算法与应用[M].清华大学出版社.2003
[54]彭玉华.小波变换与工程应用[M].北京：科学出版社,1999.
[55]张梅军.机械状态检测与故障诊断[M].北京：国防工业出版社,2008.
[56]孙传奇.基于小波包变换的谐波电能计量技术研究.湖南大学硕士学位论文[D].2006.
[57]W.J.Staszewski and GR.Tomlinson. Application of the wavelet transforms to fault detection in a spur gear [J]. Mechanical Systems and Signal Processing,1994,8(3):289-307.
[58]Philippe Ravier and Pierre Olivier Amblard. Wavelet Packets and de-noising based on higher-order-statistics for transient detection [J]. Signal Processing,2001,81:1909-1926.
[59]Yen, Lin. Wavelet packet feature extraction for vibration monitoring. Industrial Electronics [C], IEEE Transactions,2000,47(3),650-667.
[60]John Neter著,张勇,王国明,赵秀珍译.应用线性回归模型[M].北京：中国统计出版社,1988.
[61]王济川,郭志刚.Logistic回归模型——方法与应用[M].北京：高等教育出版社,2001.
[62]刘宝龙,樊晶光,陈胜.Logistic回归模型在尘肺发病预测与控制中的应用研究[J].中国安全科学学报,2001,11(1)：40-43.
[63]Hosmer, D. W, Lemeshow, S. Applied Logistic Regression [M](Wiley),1989.
[64]Spezzaferro, K. E. Applying logistic regression to maintenance data to establish inspection intervals. Proceedings of Annual Reliability and Maintainability Symposium,1996:296-300.
[65]Rego L. C, Menezes Campello de Souza. Improved estimation of left ventricular hypertrophy. IEEE Engineering in Medicine and Biology Magazine [J],2002,21(1):66-73.
[66]J.Yan, Muammmer.K, J.Lee. A prognostic algorithm for machine performance assessment and its application [J]. Production, Planning& Control,2004,15(8):796-801.
[67]崔桂香,丁晓明.基于GMM的说话人识别系统研究[J].北京电子科技学院学报,2004,12(4).
[68]Celeux, Gand Govaret. A classification EM algorithm for clustering and two stochastic versions [J]. Computational Statistics and Data Analysis,1992,14:315-332.
[69]S.W.Choi, J.H.Park, I.B.Lee. Process monitoring using a Gaussian mixture model via principal component analysis and discriminant analysis[J], Computers& Chemical Engineering,2004,28 (8):1377-1387.
[70]K.Krishnan Nair, Anne S. Kiremidjian. Time series based structural damage detection algorithm using Gaussian mixture model [J]. Journal of Dynamic Systems, Measurement and Control,2007,129(5):285-293.
[71]G. Schwarz. Estimating the dimension of a model [J]. The Annals of Statistics,1978, 6(2):461-464.
[72]G.J.Mclachlan (Ed.), Discriminant Analysis and Statistical Pattern Recognition [M]. Wiley, New York,1992.
[2]沈庆根,郑水英.设备故障诊断[M].北京：化学工业出版社,2006.
[3]雷金波.基于逻辑回归和支持向量机的设备状态退化评估与趋势预测研究[D].上海交通大学硕士学位论文.2008.
[4]杨国安.机械设备故障诊断实用技术[M].北京：中国石化出版社,2007.
[5]王道平,张义忠著.故障智能诊断系统的理论与方法[M].北京：冶金工业出版社,2001.
[6]肖涵.基于高斯混合模型与子空间技术的故障识别研究[D].武汉科技大学博士学位论文.2007.
[7]Lee J. Measurement of the machine performance degradation using a neural network model [J]. International Journal of Computers in Industry,1996,30 (3):193209.
[8]J.Lee, Jun Ni, Dragan Djurdjanovic, et al. Intelligent prognostic tools and e-maintenance [J]. Computers in Industry,2006,57:476-489.
[9]D. Djurdjanovica, J.Lee, J.Ni. Watchdog Agent-an infotronics-based prognostics approach for product performance degradation assessment and prediction [J]. Advanced Engineering Informatics,2003, (17):109-125.
[10]Poyhonen.S, Jover.P, Hyotyniemi.H. Signal processing of vibrations for condition monitoring of an induction motor [C]. First international symposium on control, communications and signal processing,2004,499-502.
[11]B.Gu, Z.Y.Wang, B.Y.Jing, Fault detection and diagnosis in chillers using artificial neural networks[C]. Proceedings of the 2003 International Conference on Cryogenics and Refrigeration,2003.
[12]L.Atlas, M.Ostendorf, G.D.Bernard, Hidden Markov models for monitoring machining tool-wear [C], Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing ICASSP,2000.
[13]Djurdjanovic D, Ni J, Lee J. Time-frequency based sensor fusion in the assessment and monitoring of machine performance degradation [C]. Proceeding of ASME IMEC&E 2002, New Orleans, LA. Paper number IMECE,2002.
[14]Zhang Lei. PCA-CMAC based machine performance degradation assessment [J]. Journal of Southeast University (English Edition),2005,21(3):299-303.
[15]Casoetto N, Djurdjanovic D, Mayor, D, Lee, J and Ni, J, Multi-sensor Process Performance Assessment Through the Use of Autoregressive Modeling and Feature Maps [J]. Journal of Manufacturing Systems,2003,22(1):64-72.
[16]Yuan S, Ge M, Qiu H, Lee J, Xu Y. Intelligent diagnosis in electromechanical operations systems [C]. Proceedings of 2004 IEEE international conference on robotics and automation, New Orleans,2004:2267-2272.
[17]Yan Jihong, Lee Jay, Degradation assessment and fault modes classification using logistic regression [J]. Journal of Manufacturing Science and Engineering, Transactions of the ASME, 2005,127(4):912-914.
[18]Vachtsevanos G, Wang P, Fault prognosis using dynamic wavelet neural networks [C]. AUTOTESTCON (Proceedings),2001:857-870.
[19]胡桥,张周锁,何正嘉.机械设备运行状态智能评估研究[J].振动工程学报,2004,17：313-316.
[20]董国金等.Elman神经网络在起重机安全状态评估中的应用[J].装备制造技术,2007,4：64-66.
[21]周炎涛等.RBF神经网络在电气设备状态评估中的应用[J],航空计算技术,2005,35(3)：1-4.
[22]朱义,陈进.基于HMM的设备性能退化评估方法的研究[J],振动与冲击,200827(8)：110-112.
[23]曾庆虎等.基于KPCA-HSMM设备退化状态识别与故障预测方法研究[J],仪器仪表学报,2009,30(7)：1341-1346.
[24]刘雨等.基于SVDD与信息融合技术的设备性能退化评估[J].振动与冲击,2009,28(9)：21-24.
[25]潘玉娜,陈进.基于二代小波包-支持向量数据描述的轴承性能退化评估研究[J].振动与冲击,2008,27(8)：299-301.
[26]刘伯运,欧阳光耀,常汉宝.基于神经网络和D_S证据理论的柴油机状态评估[J].车用发动机,2005,5：14-17.
[27]雷亚国等.基于特征评估和神经网络的机械故障诊断模型[J].西安交通大学学报,2006,40(5)：558-562.
[28]杨光正,吴眠,张晓莉.模式识别[M].合肥：中国科学技术大学出版社,2001.
[29]边肇棋,张学工等.模式识别(第二版)[M].北京：清华大学出版社,1999.
[30]R.O.Duda, P.E.Hart, D.G.Stor. Pattern Classification, second edition [M]. Wiley, New York, 2001.
[31]王奉涛,马孝江,邹岩琨.智能故障诊断技术综述[J].机床与液压,2003,4：6-8.
[32]Xu Y, Ge M. Hidden Markov model-based process monitoring system [J]. Journal of intelligent manufacturing,2004,15:337-350.
[33]Ye D. New method for faults diagnosis of rotating machinery based on 2-dimensional Hidden Markov Model [J]. Proceedings of the international symposium on precision mechanical measurement, Hefei, China,2002,4:391-395.
[34]Sppoerre J K. Application of the cascade correlation algorithm to bearing fault classification problems [J]. Computers in industry,1997,32:295-304.
[35]Wang C. C, Tao G. P. J. Rotating machine fault detection based on HOS and artificial neural networks [J]. Journal of Intelligent Manufacturing.2002,13,283-293.
[36]Tallam et al. Self-commissioning training algorithms for neural networks with applications to electric machine fault diagnosis [J]. IEEE transactions on Power Electronics. 2002,17:1089-1095.
[37]Sohn H, Worden K, Farrar C. R. Statistical damage classification under changing environment and operational conditions [J]. Journal of Intelligent Material Systems and Structures. 2002,13:561-574.
[38]Yang B. S, Han T. Kim Y. S. Integration of ART-Kohonen neural network and case-based reasoning for intelligent fault diagnosis [J]. Expert Systems with applications,2004, 26:387-395.
[39]Sampath S. Ogaji S. Singh R. Engine fault diagnostics:An optimization procedure [J]. Applied Energy,2002,73:47-70.
[40]Yang B. S, Jeong S. K, Oh Y. M. Case-based reasoning system with petri nets for induction motor fault diagnosis [J]. Expert Systems with applications,2004,27:301-311.
[41]唐贵基,田丽洁,田学航.人工神经网络在混合智能故障诊断技术中的应用研究[J].汽轮机技术,2005,47(5)：378-380.
[42]王志鹏,马孝江.基于RBF网络的旋转机械故障诊断方法[J].大连理工大学学报,2001,41(6)：696-699.
[43]刘占生等.基于遗传算法的旋转机械故障诊断方法融合[J].机械工程学报,2007,43(10)：227-233.
[44]张龙等.基于时变自回归模型与支持向量机的旋转机械故障诊断方法[J].中国电机工程学报,2007,27(9)：99-103.
[45]李志农,丁启全,吴昭同.旋转机械升降速过程的双谱-FHMM识别方法[J].振动工程学报,2003,(6)：172-174.
[46]苗强.基于隐马尔可夫模型的故障诊断系统研究[J].航空学报,2005,9：212-214.
[47]刘天雄,华宏星,李中付,陈兆能.基于分行集合状态检测方法的应用研究[J].机械工程学报,2001,5：234-237.
[48]肖涵,李友荣,吕勇.基于四分位偏差分型维与高斯混合模型的故障识别算法研究[J].振动工程学报.2008,21(1)：79-83.
[49]何正嘉.机械设备非平稳信号的故障诊断原理及应用[J].高等教育出版社,2001,11：169-171.
[50]彭斌,刘振全.基于改进小波神经网络的旋转机械故障诊断[J].振动、测试与诊断,2007,27,(1)：32-35.
[51]岳玉梅,毛雅丽,王家庆.高速旋转机械故障智能诊断系统的研究[J].沈阳建筑大学学报(自然科学版),2005,21(6)：770-773
[52]程佩青.数字信号处理(第二版)[M].北京：清华大学出版社,2001.
[53]胡广书.数字信号处理理论,算法与应用[M].清华大学出版社.2003
[54]彭玉华.小波变换与工程应用[M].北京：科学出版社,1999.
[55]张梅军.机械状态检测与故障诊断[M].北京：国防工业出版社,2008.
[56]孙传奇.基于小波包变换的谐波电能计量技术研究.湖南大学硕士学位论文[D].2006.
[57]W.J.Staszewski and GR.Tomlinson. Application of the wavelet transforms to fault detection in a spur gear [J]. Mechanical Systems and Signal Processing,1994,8(3):289-307.
[58]Philippe Ravier and Pierre Olivier Amblard. Wavelet Packets and de-noising based on higher-order-statistics for transient detection [J]. Signal Processing,2001,81:1909-1926.
[59]Yen, Lin. Wavelet packet feature extraction for vibration monitoring. Industrial Electronics [C], IEEE Transactions,2000,47(3),650-667.
[60]John Neter著,张勇,王国明,赵秀珍译.应用线性回归模型[M].北京：中国统计出版社,1988.
[61]王济川,郭志刚.Logistic回归模型——方法与应用[M].北京：高等教育出版社,2001.
[62]刘宝龙,樊晶光,陈胜.Logistic回归模型在尘肺发病预测与控制中的应用研究[J].中国安全科学学报,2001,11(1)：40-43.
[63]Hosmer, D. W, Lemeshow, S. Applied Logistic Regression [M](Wiley),1989.
[64]Spezzaferro, K. E. Applying logistic regression to maintenance data to establish inspection intervals. Proceedings of Annual Reliability and Maintainability Symposium,1996:296-300.
[65]Rego L. C, Menezes Campello de Souza. Improved estimation of left ventricular hypertrophy. IEEE Engineering in Medicine and Biology Magazine [J],2002,21(1):66-73.
[66]J.Yan, Muammmer.K, J.Lee. A prognostic algorithm for machine performance assessment and its application [J]. Production, Planning& Control,2004,15(8):796-801.
[67]崔桂香,丁晓明.基于GMM的说话人识别系统研究[J].北京电子科技学院学报,2004,12(4).
[68]Celeux, Gand Govaret. A classification EM algorithm for clustering and two stochastic versions [J]. Computational Statistics and Data Analysis,1992,14:315-332.
[69]S.W.Choi, J.H.Park, I.B.Lee. Process monitoring using a Gaussian mixture model via principal component analysis and discriminant analysis[J], Computers& Chemical Engineering,2004,28 (8):1377-1387.
[70]K.Krishnan Nair, Anne S. Kiremidjian. Time series based structural damage detection algorithm using Gaussian mixture model [J]. Journal of Dynamic Systems, Measurement and Control,2007,129(5):285-293.
[71]G. Schwarz. Estimating the dimension of a model [J]. The Annals of Statistics,1978, 6(2):461-464.
[72]G.J.Mclachlan (Ed.), Discriminant Analysis and Statistical Pattern Recognition [M]. Wiley, New York,1992.