Abstract: To study the maintenance strategy of slow degradation system under the condition of incomplete sampling and individual differences,a linear mixed effect model was employed to model the slow degradation system with individual differences,and autoregressive method was used to adjust the correlation of time series in the model residuals,which had improved the accuracy of model.On this basis,a reasonable state space and maintenance decision space were constructed to solve the state transition probability of degradation process,and the optimal maintenance strategy was solved by using policy iteration algorithm to minimize the long-term estimated cost per unit time.The maintenance strategy based on semi-Markov decision process was demonstrated by a practical case of laser degradation.Compared with the classical maintenance strategy based on service life and periodic inspection,the results showed that the proposed method could describe the degradation process more accurately and help to formulate maintenance strategy considering both cost and reliability.

Key words: semi-Markov decision process, slow degradation system, linear mixed-effects model, policy iteration algorithm

摘要： 为了在采样不完全、个体差异明显的条件下对缓慢退化系统的维修策略进行研究,针对具有个体差异的缓慢退化系统,选择线性混合效应模型进行退化建模,并利用自回归方法对模型残差中的时间序列相关性进行调节,提高了模型的准确性。在此基础上构造合理的状态空间和维修决策空间,求解退化过程的状态转移概率,并使用策略迭代算法求解最小化单位时间长期预计成本的最优化维修策略。以激光退化实际案例求解了基于半Markov决策过程的维修策略,并与经典的基于役龄的维修策略和周期检查的维修策略进行比较,证明了所提方法能够更加精确地刻画系统的退化过程,并可帮助制定兼顾成本与可靠性的维修策略。

关键词: 半Markov决策过程, 缓慢退化系统, 线性混合效应模型, 策略迭代算法