The prediction of residual life (RL) is the key of the predictive maintenance for engineering equipment. Accurate and real-time prediction can provide more effective decision support to the subsequent maintenance schedule and avoid the failure effectively. In engineering practice, the performance index reflecting the degradation process of the equipment is generally not observed directly. To tackle the residual life problem under hidden degradation, a prediction method based on semi-stochastic and expectation maximization (EM) algorithm is proposed in this paper. First, the residual life is taken as the hidden state and the prediction model is constructed by building the stochastic relationship between the residual life and monitoring data. Secondly, based on the monitoring data up to the current time, a collaborative method by the extended Kalman filter (EKF) and expectation maximization algorithm is presented to achieve a real-time estimation and updating of the residual life distribution and unknown model parameters. Finally, the proposed method is validated by the application to the inertial measurement unit (IMU) and the results indicate that the method can improve the accuracy and reduce the uncertainty of the estimated residual life.
冯磊, 王宏力, 司小胜, 杨晓君, 王标标. 基于半随机滤波-期望最大化算法的剩余寿命在线预测[J]. 航空学报, 2015, 36(2): 555-563.
FENG Lei, WANG Hongli, SI Xiaosheng, YANG Xiaojun, WANG Biaobiao. Real-time residual life prediction based on semi-stochastic filter and expectation maximization algorithm. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2015, 36(2): 555-563.
 Si X S, Wang W B, Hu C H, et al. Remaining useful life estimation—a review on the statistical data driven approaches[J]. Europen Journal of Operational Research, 2011, 213(1): 1-14. Zio E, Peloni G. Praticle filtering prognostic estimation of the remaining useful life of nonlinear components[J]. Reliability Engineering and System Safety, 2011, 96(3): 403-409. Ghasemi A, Yacout S, Ouali M S. Evaluating the reliability function and the mean residual life for equipment with unobservable states[J]. IEEE Transactions on Reliability, 2010, 59(1): 45-54. Peng Y, Dong M. A prognosis method using age-dependent hidden semi-Markov model for equipment health prediction[J]. Mechanical Systems and Signal Processing, 2011, 25(1): 237-252. Wang W B, Christer A H. Towards a general condition based maintenance model for a stochastic dynamic system[J]. Journal of the Operational Research Society, 2000, 51(2): 145-155. Wang W B. A prognosis model for wear prediction based on oil-based monitoring[J]. Journal of the Operational Research Society, 2006, 58(7): 887-893. Wang W B, Zhang W. An asset residual life prediction model based on expert judgments[J]. Europen Journal of Operational Research, 2008, 188(2): 496-505. Wang W B, Hussin B. Plant residual time modelling based on observed variables in oil samples[J]. Journal of the Operational Research Society, 2009, 60(6): 789-796. Carr M, Wang W B. Modeling failure modes for residual life prediction using stochastic filtering theory[J]. IEEE Transactions on Reliability, 2010, 59(2): 346-355. Carr M, Wang W B. An approximate algorithm for prognostic modeling using condition monitoring information[J]. Europen Journal of Operational Research, 2011, 211(1): 90-96. Wang W B. A model to predict the residual life of rolling element bearings given monitored condition information to date[J]. IMA Journal of Management Mathematics, 2002, 13(1): 3-16. Wang Z X. Optimal state estimation and system identification[M]. Xi'an: Northwestern Polytechnical University Press, 2004: 137-141 (in Chinese). 王志贤. 最优状态估计与系统辨识[M]. 西安: 西北工业大学出版社, 2004: 137-141. Zhou Z J, Hu C H, Yang J B, et al. Online updating belief-rule-based systems using the RIMER approach[J]. IEEE Transactions on Systems, Man and Cybernetics—Part A: Systems and Humans, 2011, 41(6): 1225-1243. Hu L, Zhou J X, Shi Z G, et al. An EM-based approach for compressed sensing using dynamic dictionaries[J]. Journal of Electronics & Information Technology, 2012, 34(11): 2554-2560 (in Chinese). 胡磊, 周剑雄, 石志广, 等. 利用期望-最大化算法实现基于动态词典的压缩感知[J]. 电子与信息学报, 2012, 34(11): 2554-2560. Borkar V, Ghosh M, Rangarajan G. Application of nonlinear filtering to credit risk[J]. Operations Research Letters, 2010, 38(6): 527-532. Hu C H, Ma Q L, Zheng J F. The control technique of missile testing and launching[M]. Beijing: National Defence Industry Press, 2010: 62-74 (in Chinese). 胡昌华, 马清亮, 郑建飞. 导弹测试与发射控制技术[M]. 北京: 国防工业出版社, 2010: 62-74. Si X S, Wang W B, Hu C H, et al. Remaining useful life estimation based on a nonlinear diffusion degradation process[J]. IEEE Transactions on Reliability, 2012, 61(1): 50-67. Hu C H, Si X S. Real-time parameters estimation of belief rule base health condition for inertial platform[J]. 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[J]. 航空学报, 2010, 31(7): 1454-1465. Akaike H. A new lool at the statistical model identification[J]. IEEE Transactions on Automatic Control, 1974, 19(6): 716-722. Zhang B C, Han X X, Zhou Z J, et al. Construction of a new BRB based for time series forecasting[J]. Applied Soft Computing, 2013, 13(12): 4548-4556. Feng L, Wang H L, Si X S, et al. A state space based prognostic model for hidden and age-dependent nonlinear degradation process[J]. IEEE Transactions on Automation Science and Engineering, 2013, 10(4): 1072-1086.