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摘要: 连续隐半Markov模型(Continuous hidden semiMarkov model, CHSMM)是隐Markov模型(Hidden Markov model ,HMM)的一种扩展形式,可用于时间序列过程的动态建模。通过加入状态分布参数并对多组观测值进行连续化,可加强模型对新观测值的处理能力以及对状态驻留时间的建模能力。利用该方法建立了轴承性能退化的评估模型。首先,分析振动信号并提取频带能量作为退化特征;然后将正常状态下的特征样本作为模型的观测值对CHSMM进行训练;最后将待测的特征样本输入模型,得到待测样本相对于所建立正常模型的输出概率,作为轴承性能退化状态的标志。轴承疲劳寿命试验结果表明:所提的评估模型能较好地刻画轴承性能退化的过程,并能在早期对轴承的性能退化做出预警。关键词: 故障预测;轴承;连续隐半马尔科夫模型;频带能量;性能退化评估
中图分类号: TH165+.3;TP206.3文献标识码: A文章编号: 10044523(2014)04061308
1概述
设备的性能退化评估是基于状态的维护(CBM)策略制定的前提,也是降低生产损失的有效措施。目前设备性能退化评估方法大致可分为:基于力学模型、基于概率统计和基于信息新技术的方法等[1,2]。其中基于概率统计的方法更能反映机械性能的一般规律和整体特性,但往往需要大量的历史样本和全寿命周期的先验知识建模,这一特点成为制约其发展的主要因素。Baum等于20世纪70年代建立的隐Markov模型(HMM)[3,4],着意于从概率的角度刻画动态系统的内在状态与外在表象之间的关系,用不完全统计的方式克服了传统统计理论对样本需求大的缺点。
J D Ferguson在20世纪80年代将HMM的状态驻留时间显式化,形成隐半Markov模型(HSMM),显著提高了模型对状态驻留时间的建模能力[5]。Yu等在前人研究的基础上,推导了离散化单组观测值HSMM的参数重估、输出概率计算及最优状态识别的快速算法[6]。Heiga ZEN则推导了状态驻留时间参数为高斯分布的单组观测值连续HSMM参数重估方法[7]。
HMM及其扩展形式—HSMM早期应用于语音识别领域,成为经典的语音识别技术之一。20世纪90年代以后有学者将HMM应用于故障诊断、预测及性能退化,取得了一定的成果。如冯长建探讨了HMM在旋转机械的故障诊断中的应用[8],Ocak和Purushotham等将HMM应用于轴承故障诊断[9,10]。滕红智、肖文斌、朱义等分别将连续隐Markov模型(CHMM)应用于不同对象的状态识别和性能退化评估中[11~13]。近年来,Dong利用HSMM对液压泵进行了故障诊断和寿命预测,经对比证明了HSMM比HMM具有更优的模式识别能力[14]。胡海峰等将Yu的算法扩展到多组观测值[15],提高了模型的稳定性,应用于故障诊断和寿命预测取得较好效果。曾庆虎等将HSMM应用于轴承正常及滚动体不同故障程度的识别[16]。Dong在文中指出使用连续型观测值可提高信息利用率,但未给出连续化参数c,u和U的初始化和重估算法。结合上述学者的研究成果,考虑到将状态驻留时间预设成高斯分布可能失真,以Yu的算法为参考主体,本文给出多组观测值的连续隐半马尔科夫模型(CHSMM)的参数初始化和重估算法,建立了基于CHSMM的轴承性能退化评估模型。步骤如下:首先,将正常轴承振动信号的频带能量比作为模型的观测值,并使用Kmeans聚类方法对模型进行初始化;然后使用CHSMM的前向后向算法对模型的参数进行重估;最后将监测样本振动信号的频带能量输入上述模型,得到输出概率,这一概率反映了其与正常信号的相似度,将各组概率进行记录,即可做出设备性能退化曲线。具体流程如图1所示。
图1机械设备性能退化评估流程图
Fig.1Flowchart of the machine performance degradation assessment第4期李巍华,等:连续隐半马尔科夫模型在轴承性能退化评估中的应用振 动 工 程 学 报第27卷2退化状态特征提取
通过对轴承疲劳寿命实验的振动信号分析发现,对于特定退化阶段的轴承,即便是较为稳定的实验工况,由于实验中的噪声和微小的转速波动不可避免,特征频率处的幅值有时会产生较大的波动,但振动信号的频谱相对于转频的分布却较为稳定。同时不同退化阶段在频谱的分布上也会呈现出不同的态势。因此,将频带能量作为表征轴承退化状态的特征。即:对振动信号做FFT变换后,将频谱平均分为T个频带,则频带能量即为Ei=∑biaiA2j, 1≤i≤T (1)式中ai,bi分别为第i个频段的上下限,Aj为第i个频段内的第j个频谱幅值。
3基于CHSMM的性能退化评估模型用连续隐半马尔可夫模型将轴承振动信号的频带能量的变化看作一个动态变化的过程,并通过一系列的参数来描述这个过程。
3.1模型参数
本文利用CHSMM对轴承的退化性能进行评估,通过轴承疲劳寿命实验对方法进行验证,结果表明:
1) 所给出的CHSMM方法只需对轴承正常运行的样本进行建模,无需全寿命周期的先验知识,可应用于实际中设备性能退化的评估。
2) 监测样本对于模型的输出概率能较好地刻画轴承的退化过程,建立的退化评估模型具有较好的稳定性和快速的学习能力。
3) 该模型对轴承运行状态的变化敏感,能较好地发现早期故障及其加深过程,有助于根据对设备状态的认识,制定相应的维修策略。
参考文献:
[1]张小丽,陈雪峰,李兵,等. 机械重大装备寿命预测综述[J].机械工程学报,2011,47(11):100—116.
ZHANG Xiaoli, CHEN Xuefeng, LI Bing, et al. Review of life prediction for mechanical major equipment[J]. Chinese Journal of Mechanical Engineering, 2011, 47(11):100—116. [2]郭磊,陈进. 设备性能退化评估与预测研究综述[A].第11届全国设备故障诊断学术会议论文集[C]. 西宁,2008:139—142.
[3]Baum L E, Petrie T, Soules G, et al. A maximization technique occurring in the statistical analysis of probabilistic functions of Markov chains[J].The Annals of Mathematical Statistics, 1970, 1(41):164—171.
[4]Baum L E. An inequality and associated maximization technique in statistical estimation for probabilistic functions of Markov processes[J].Journal of Inequalities in Pure and Applied Mathematics, 1972,(3):1—8.
[5]Ferguson J D. Variable duration models for speech[J]. Symp. Application of Hidden Markov Models to Text and Speech, 1980,(10) : 143—179.
[6]Yu ShunZheng,Kobayashi H. An efficient forwardbackward algorithm for an explicitduration hidden Markov model[J]. IEEE Signal Processing Letters,2003,10 (1):11—14.
[7]ZEN Heiga, TOKUDA Keiichi, MASUKO Takashi, et al. A hidden semimarkov modelbased speech synthesis system[J].IEICE Transactions on Information and Systems,2007, E90D(5):825—834.
[8]冯长建. HMM动态模式识别理论、方法以及在旋转机械故障诊断中的应用[D].杭州:浙江大学,2002.
Feng Changjian. HMM dynamical pattern recognition theories, methods and applications in faults diagnosis of rotating machine[D].Hangzhou: Zhejiang University, 2002.
[9]Ocak H, Loparo K A, Discenzo F M. Online tracking of bearing wear using wavelet packet decomposition and probabilistic modeling: A method for bearing prognostics[J].Journal of Sound and Vibration, 2007, 302(4/5): 951—961
[10]Purushotham V,Narayanan S,Prasad SAN,et al. Multifault diagnosis of rolling bearing elements using wavelet analysis and hidden Markov model based fault recognition[J].NDT and E International,2005, 38(8): 654—664.
[11]滕红智,赵建民,贾希胜,等. 基于CHMM的齿轮箱状态识别研究[J].振动与冲击,2012,31(5):92—96,127.
TENG Hongzhi, ZHAO Jianmin, JIA Xisheng, et al. Gearbox state recognition based on continuous hidden markov model[J].Journal of Vibration and Shock, 2012,31(5):92—96,127.
[12]肖文斌,陈进,周宇,等. 小波包变换和隐马尔可夫模型在轴承性能退化评估中的应用[J].振动与冲击, 2011,30(8):32—35.
XIAO Wenbin, CHEN Jin,ZHOU Yu, et al. Wavelet packet transform and hidden Markov model based bearing performance degradation assessment[J].Journal of Vibration and Shock , 2011,30(8):32—35.
[13]朱义. 基于CHMM的设备性能退化评估方法研究[D].上海:上海交通大学,2009.
Zhu Yi. Research on CHMM based equipment performance degradation assessment[D].Shanghai: Shanghai Jiao Tong University,2009.
[14]Ming Dong,David He. A segmental hidden semiMarkov model (HSMM)based diagnostics and prognostics framework and methodology [J].Mechanical Systems and Signal Processing, 2007,21:2 248—2 266 [15]胡海峰,安茂春,秦国军,等. 基于隐半Markov模型的故障诊断和故障预测方法研究[J].兵工学报,2009,30(1):69—75.
HU Haifeng , AN Maochun, QIN Guojun, et al. Study on fault diagnosis and prognosis methods based on hidden semi Markov model[J]. Acta Armamentarii,2009,30(1):69—75.
[16]曾庆虎,邱静,刘冠军,等.小波相关特征尺度熵和隐半马尔可夫模型在设备退化状态识别中的应用[J].机械工程学报,2008,44(11):236—241,247.
ZENG Qinghu, QIU Jing, LIU Guanjun, et al. Application of wavelet correlation feature scale entropy and hidden semimarkov models to equipment degradation state recognition[J].Chinese Journal of Mechanical Engineering,2008,44(11):236—241,247.
[17]韩纪庆,张磊,郑轶然. 语音信号处理[M].北京:清华大学出版社,2002.
[18]Qiu H,Lee J,Lin J,et al.Wavelet filterbased weak signature detection method and its application on rolling element bearing prognostics[J].Journal of Sound and Vibration,2006, 289(4/5):1 066—1 090.
Application of continuous hidden semiMarkov model in
bearing performance degradation assessment
LI Weihua1,2, LI Jing1, ZHANG Shaohui1
(1.School of Mechanical and Automotive Engineering, South China University of Technique, Guangzhou 510640, China;
2.State Key Laboratory for Manufacturing Systems Engineering, Xi′an 710054, China)
Abstract: Continuous hidden semiMarkov model (CHSMM) is an extension of hidden Markov model (HMM), and it can be used to model time series process dynamically. It is capable of processing a new observation and modeling the time duration of hidden states by using a continuous observations density function and estimating the state duration parameters. In this paper, a model based on the CHSMM was constructed to assess the bearing performance degradation. First, the frequency band energy was extracted as the degradation indicators from the vibration signal. Second, the CHSMM was trained by the feature samples under normal conditions. Then, the test samples were input into this health assessment model, and their output probability was obtained. The difference between this probability and that of normal samples could be regarded as an index of degradation. Experiment results on the bearing performance degradation test indicated that, the proposed model can depict the degradation process effectively, and predict the occurrence of some incipient faults.Key words:fault prognosis; bearing; CHSMM;frequency band energy; performance degradation assessment作者简介: 李巍华(1973—),男,教授。电话: (020)87110061; Email: whlee@scut.edu.cn
中图分类号: TH165+.3;TP206.3文献标识码: A文章编号: 10044523(2014)04061308
1概述
设备的性能退化评估是基于状态的维护(CBM)策略制定的前提,也是降低生产损失的有效措施。目前设备性能退化评估方法大致可分为:基于力学模型、基于概率统计和基于信息新技术的方法等[1,2]。其中基于概率统计的方法更能反映机械性能的一般规律和整体特性,但往往需要大量的历史样本和全寿命周期的先验知识建模,这一特点成为制约其发展的主要因素。Baum等于20世纪70年代建立的隐Markov模型(HMM)[3,4],着意于从概率的角度刻画动态系统的内在状态与外在表象之间的关系,用不完全统计的方式克服了传统统计理论对样本需求大的缺点。
J D Ferguson在20世纪80年代将HMM的状态驻留时间显式化,形成隐半Markov模型(HSMM),显著提高了模型对状态驻留时间的建模能力[5]。Yu等在前人研究的基础上,推导了离散化单组观测值HSMM的参数重估、输出概率计算及最优状态识别的快速算法[6]。Heiga ZEN则推导了状态驻留时间参数为高斯分布的单组观测值连续HSMM参数重估方法[7]。
HMM及其扩展形式—HSMM早期应用于语音识别领域,成为经典的语音识别技术之一。20世纪90年代以后有学者将HMM应用于故障诊断、预测及性能退化,取得了一定的成果。如冯长建探讨了HMM在旋转机械的故障诊断中的应用[8],Ocak和Purushotham等将HMM应用于轴承故障诊断[9,10]。滕红智、肖文斌、朱义等分别将连续隐Markov模型(CHMM)应用于不同对象的状态识别和性能退化评估中[11~13]。近年来,Dong利用HSMM对液压泵进行了故障诊断和寿命预测,经对比证明了HSMM比HMM具有更优的模式识别能力[14]。胡海峰等将Yu的算法扩展到多组观测值[15],提高了模型的稳定性,应用于故障诊断和寿命预测取得较好效果。曾庆虎等将HSMM应用于轴承正常及滚动体不同故障程度的识别[16]。Dong在文中指出使用连续型观测值可提高信息利用率,但未给出连续化参数c,u和U的初始化和重估算法。结合上述学者的研究成果,考虑到将状态驻留时间预设成高斯分布可能失真,以Yu的算法为参考主体,本文给出多组观测值的连续隐半马尔科夫模型(CHSMM)的参数初始化和重估算法,建立了基于CHSMM的轴承性能退化评估模型。步骤如下:首先,将正常轴承振动信号的频带能量比作为模型的观测值,并使用Kmeans聚类方法对模型进行初始化;然后使用CHSMM的前向后向算法对模型的参数进行重估;最后将监测样本振动信号的频带能量输入上述模型,得到输出概率,这一概率反映了其与正常信号的相似度,将各组概率进行记录,即可做出设备性能退化曲线。具体流程如图1所示。
图1机械设备性能退化评估流程图
Fig.1Flowchart of the machine performance degradation assessment第4期李巍华,等:连续隐半马尔科夫模型在轴承性能退化评估中的应用振 动 工 程 学 报第27卷2退化状态特征提取
通过对轴承疲劳寿命实验的振动信号分析发现,对于特定退化阶段的轴承,即便是较为稳定的实验工况,由于实验中的噪声和微小的转速波动不可避免,特征频率处的幅值有时会产生较大的波动,但振动信号的频谱相对于转频的分布却较为稳定。同时不同退化阶段在频谱的分布上也会呈现出不同的态势。因此,将频带能量作为表征轴承退化状态的特征。即:对振动信号做FFT变换后,将频谱平均分为T个频带,则频带能量即为Ei=∑biaiA2j, 1≤i≤T (1)式中ai,bi分别为第i个频段的上下限,Aj为第i个频段内的第j个频谱幅值。
3基于CHSMM的性能退化评估模型用连续隐半马尔可夫模型将轴承振动信号的频带能量的变化看作一个动态变化的过程,并通过一系列的参数来描述这个过程。
3.1模型参数
本文利用CHSMM对轴承的退化性能进行评估,通过轴承疲劳寿命实验对方法进行验证,结果表明:
1) 所给出的CHSMM方法只需对轴承正常运行的样本进行建模,无需全寿命周期的先验知识,可应用于实际中设备性能退化的评估。
2) 监测样本对于模型的输出概率能较好地刻画轴承的退化过程,建立的退化评估模型具有较好的稳定性和快速的学习能力。
3) 该模型对轴承运行状态的变化敏感,能较好地发现早期故障及其加深过程,有助于根据对设备状态的认识,制定相应的维修策略。
参考文献:
[1]张小丽,陈雪峰,李兵,等. 机械重大装备寿命预测综述[J].机械工程学报,2011,47(11):100—116.
ZHANG Xiaoli, CHEN Xuefeng, LI Bing, et al. Review of life prediction for mechanical major equipment[J]. Chinese Journal of Mechanical Engineering, 2011, 47(11):100—116. [2]郭磊,陈进. 设备性能退化评估与预测研究综述[A].第11届全国设备故障诊断学术会议论文集[C]. 西宁,2008:139—142.
[3]Baum L E, Petrie T, Soules G, et al. A maximization technique occurring in the statistical analysis of probabilistic functions of Markov chains[J].The Annals of Mathematical Statistics, 1970, 1(41):164—171.
[4]Baum L E. An inequality and associated maximization technique in statistical estimation for probabilistic functions of Markov processes[J].Journal of Inequalities in Pure and Applied Mathematics, 1972,(3):1—8.
[5]Ferguson J D. Variable duration models for speech[J]. Symp. Application of Hidden Markov Models to Text and Speech, 1980,(10) : 143—179.
[6]Yu ShunZheng,Kobayashi H. An efficient forwardbackward algorithm for an explicitduration hidden Markov model[J]. IEEE Signal Processing Letters,2003,10 (1):11—14.
[7]ZEN Heiga, TOKUDA Keiichi, MASUKO Takashi, et al. A hidden semimarkov modelbased speech synthesis system[J].IEICE Transactions on Information and Systems,2007, E90D(5):825—834.
[8]冯长建. HMM动态模式识别理论、方法以及在旋转机械故障诊断中的应用[D].杭州:浙江大学,2002.
Feng Changjian. HMM dynamical pattern recognition theories, methods and applications in faults diagnosis of rotating machine[D].Hangzhou: Zhejiang University, 2002.
[9]Ocak H, Loparo K A, Discenzo F M. Online tracking of bearing wear using wavelet packet decomposition and probabilistic modeling: A method for bearing prognostics[J].Journal of Sound and Vibration, 2007, 302(4/5): 951—961
[10]Purushotham V,Narayanan S,Prasad SAN,et al. Multifault diagnosis of rolling bearing elements using wavelet analysis and hidden Markov model based fault recognition[J].NDT and E International,2005, 38(8): 654—664.
[11]滕红智,赵建民,贾希胜,等. 基于CHMM的齿轮箱状态识别研究[J].振动与冲击,2012,31(5):92—96,127.
TENG Hongzhi, ZHAO Jianmin, JIA Xisheng, et al. Gearbox state recognition based on continuous hidden markov model[J].Journal of Vibration and Shock, 2012,31(5):92—96,127.
[12]肖文斌,陈进,周宇,等. 小波包变换和隐马尔可夫模型在轴承性能退化评估中的应用[J].振动与冲击, 2011,30(8):32—35.
XIAO Wenbin, CHEN Jin,ZHOU Yu, et al. Wavelet packet transform and hidden Markov model based bearing performance degradation assessment[J].Journal of Vibration and Shock , 2011,30(8):32—35.
[13]朱义. 基于CHMM的设备性能退化评估方法研究[D].上海:上海交通大学,2009.
Zhu Yi. Research on CHMM based equipment performance degradation assessment[D].Shanghai: Shanghai Jiao Tong University,2009.
[14]Ming Dong,David He. A segmental hidden semiMarkov model (HSMM)based diagnostics and prognostics framework and methodology [J].Mechanical Systems and Signal Processing, 2007,21:2 248—2 266 [15]胡海峰,安茂春,秦国军,等. 基于隐半Markov模型的故障诊断和故障预测方法研究[J].兵工学报,2009,30(1):69—75.
HU Haifeng , AN Maochun, QIN Guojun, et al. Study on fault diagnosis and prognosis methods based on hidden semi Markov model[J]. Acta Armamentarii,2009,30(1):69—75.
[16]曾庆虎,邱静,刘冠军,等.小波相关特征尺度熵和隐半马尔可夫模型在设备退化状态识别中的应用[J].机械工程学报,2008,44(11):236—241,247.
ZENG Qinghu, QIU Jing, LIU Guanjun, et al. Application of wavelet correlation feature scale entropy and hidden semimarkov models to equipment degradation state recognition[J].Chinese Journal of Mechanical Engineering,2008,44(11):236—241,247.
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Application of continuous hidden semiMarkov model in
bearing performance degradation assessment
LI Weihua1,2, LI Jing1, ZHANG Shaohui1
(1.School of Mechanical and Automotive Engineering, South China University of Technique, Guangzhou 510640, China;
2.State Key Laboratory for Manufacturing Systems Engineering, Xi′an 710054, China)
Abstract: Continuous hidden semiMarkov model (CHSMM) is an extension of hidden Markov model (HMM), and it can be used to model time series process dynamically. It is capable of processing a new observation and modeling the time duration of hidden states by using a continuous observations density function and estimating the state duration parameters. In this paper, a model based on the CHSMM was constructed to assess the bearing performance degradation. First, the frequency band energy was extracted as the degradation indicators from the vibration signal. Second, the CHSMM was trained by the feature samples under normal conditions. Then, the test samples were input into this health assessment model, and their output probability was obtained. The difference between this probability and that of normal samples could be regarded as an index of degradation. Experiment results on the bearing performance degradation test indicated that, the proposed model can depict the degradation process effectively, and predict the occurrence of some incipient faults.Key words:fault prognosis; bearing; CHSMM;frequency band energy; performance degradation assessment作者简介: 李巍华(1973—),男,教授。电话: (020)87110061; Email: whlee@scut.edu.cn