Degradation Data-Driven Remaining Useful Life Estimation Approach under Collaboration between Bayesian Updating and EM Algorithm
SI Xiao-Sheng1,3,HU Chang-Hua1,LI Juan2,CHEN Mao-Yin3
1. Department of Automation,Xian Institute of High-Technology,Xian 710025 2.College of Electromechanical Engineering,Qingdao Agricultural University,Qingdao 266109 3.Department of Automation,Tsinghua University,Beijing 100084
Abstract：Remaining useful life (RUL) estimation is one of the key issues in condition-based maintenance and prognostics and health management. To achieve degradation modeling and RUL estimation for the individual equipment in service,a degradation data-driven RUL estimation approach under the collaboration between Bayesian updating and expectation maximization (EM) algorithm is presented. Firstly,an exponential-like degradation model is utilized to describe the equipment degradation process and the stochastic parameters in the model are updated by Bayesian approach. Based on the Bayesian updating results,the probability distribution of the RUL is derived and the point estimation of the RUL is obtained accordingly. Secondly,based on the monitored degradation data to date,a parameter estimation approach for other non-stochastic parameters in the established degradation model is proved. Furthermore,it is proved that the obtained estimation in each iteration is unique and optimal. Finally,a numerical example and a practical case study are provided to show that the presented approach effectively models degradation process for the individual equipment,achieves RUL estimation,estimates the model parameters and generates better results than a previously reported approach in the literature.
司小胜，胡昌华，李娟，陈茂银. Bayesian更新与EM算法协作下退化数据驱动的剩余寿命估计方法[J]. 模式识别与人工智能, 2013, 26(4): 357-365.
SI Xiao-Sheng,HU Chang-Hua,LI Juan,CHEN Mao-Yin. Degradation Data-Driven Remaining Useful Life Estimation Approach under Collaboration between Bayesian Updating and EM Algorithm. , 2013, 26(4): 357-365.
[1] Pecht M G. Prognostics and Health Management of Electronics. New York,USA: John Wiley Sons,2008 [2] Zeng Shengkui,Pecht M G,Wu Ji. Status and Perspectives of Prognostics and Health Management Technologies. Acta Aeronautica Et Astronautica Sinica,2005,26(5): 626-631 (in Chinese) (曾声奎,Pecht M G,吴 际.故障预测与健康管理(PHM)技术的现状与发展.航空学报,2005,26(5): 626-631) [3] Hu Changhua,Si Xiaosheng. Real-Time Parameters Estimation of Inertial Platforms Health Condition Based on Belief Rule Base. Acta Aeronautica Et Astronautica Sinica,2010,31(7): 1454-1465 (in Chinese) (胡昌华,司小胜.基于信度规则库的惯性平台健康状态参数在线估计.航空学报,2010,31(7): 1454-1465) [4] Si Xiaosheng,Wang Wenbin,Hu Changhua,et al. Remaining Useful Life Estimation-A Review on the Statistical Data Driven Approaches. European Journal of Operational Research,2011,213(1): 1-14 [5] Meeker W Q,Escobar L A. Statistical Methods for Reliability Data. New York,USA: John Wiley Sons,1998 [6] Chen Liang,Hu Changhua. Review of Reliability Analysis Method Based on Degradation Modeling. Control and Decision,2009,24(9): 1281-1287 (in Chinese) (陈 亮,胡昌华.基于退化建模的可靠性分析研究现状.控制与决策,2009,24(9): 1281-1287) [7] Peng C Y,Tseng S T. Mis-Specification Analysis of Linear Degradation Models. IEEE Trans on Reliability,2009,58(3): 444-455 [8] Joseph V R,Yu I T. Reliability Improvement Experiments with Degradation Data. IEEE Trans on Reliability,2006,55(1): 149-157 [9] Park J I,Bae S J. Direct Prediction Methods on Lifetime Distribution of Organic Light-Emitting Diodes from Accelerated Degradation Test. IEEE Trans on Reliability,2010,59(1): 74-90 [10] Gertsbackh I B,Kordonskiy K B. Models of Failure. New York,USA: Springer-Verlag,1969 [11] Nelson W. Accelerated Testing: Statistical Models,Test Plans and Data Analyses. New York,USA: John Wiley Sons,1990 [12] Lu C J,Meeker W Q. Using Degradation Measures to Estimate a Time-to-Failure Distribution. Technometrics,1993,35(2): 161-174 [13] Gebraeel N Z,Lawley M A,Li R,et al. Residual-Life Distributions from Component Degradation Signals: A Bayesian Approach. IIE Transactions,2005,37(6): 543-557 [14] Elwany A,Gebraeel N Z,Maillart L. Structured Replacement Policies for Components Systems with Complex Degradation Processes and Dedicated Sensors. Operations Research,2011,59(3): 684-695 [15] Gebraeel N Z,Elwany A,Pan J. Residual Life Predictions in the Absence of Prior Degradation Knowledge. IEEE Trans on Reliability,2009,58(1): 106-117 [16] Dempster A P,Laird N M,Rubin D B. Maximum Likelihood from Incomplete Data via the EM Algorithm. Journal of the Royal Statistical Society: Series B,1977,39(1): 1-38 [17] Si Xiaosheng,Wang Wenbin,Hu Changhua,et al. Remaining Useful Life Estimation Based on a Nonlinear Diffusion Degradation Process. IEEE Trans on Reliability,2012,61(1): 50-67 [18] Park C,Padgett W J. Stochastic Degradation Models with Several Accelerating Variables. IEEE Trans on Reliability,2006,55(2): 379-390 [19] Tseng S T,Tang J,Ku L H. Determination of Optimal Burn-in Parameters and Residual Life for Highly Reliable Products. Naval Research Logistics,2003,50(1): 1-14 [20] Wu C F J. On the Convergence Property of the EM Algorithm. The Annals of Statistics,1983,11(1): 95-103 [21] Pecht M,Jaai R. A Prognostics and Health Management Roadmap for Information and Electrics-Rich System. Microelectronics Reliability,2010,50(3): 317-323
2013, Vol. 26 
