论文标题
基于条件的不完美维护模型的分段确定性马尔可夫流程
Piecewise deterministic Markov process for condition-based imperfect maintenance models
论文作者
论文摘要
在本文中，构建了基于基于条件的不完美维护模型，基于分段确定马尔可夫流程（PDMP）。系统的降解包括两种类型：自然降解和随机冲击。自然降解是确定性的，可以是非线性的。由随机冲击造成的损害增加遵循一定的分布，其参数与降解状态有关。维护方法包括纠正性维护和不完美的维护。不完美的维护会根据随机比例降低系统的降解度。维护动作被延迟，并且在等待维护时，系统将遭受自然降解和随机冲击。在每次检查时间，决策者需要在计划不进行维护，不完美的维护和完美维护的情况下做出选择，以最大程度地减少系统的总折扣成本。 PDMP的脉冲最佳控制理论用于确定最佳维护策略。提出了有关涉及组件涂料维护问题的数值研究。讨论了与最佳阈值策略的关系。提出了对折现因子，观察间隔和维护成本对折现成本和最佳行动的影响的敏感性分析。
In this paper, a condition-based imperfect maintenance model based on piecewise deterministic Markov process (PDMP) is constructed. The degradation of the system includes two types: natural degradation and random shocks. The natural degradation is deterministic and can be nonlinear. The damage increment caused by a random shock follows a certain distribution, and its parameters are related to the degradation state. Maintenance methods include corrective maintenance and imperfect maintenance. Imperfect maintenance reduces the degradation degree of the system according to a random proportion. The maintenance action is delayed, and the system will suffer natural degradations and random shocks while waiting for maintenance. At each inspection time, the decision-maker needs to make a choice among planning no maintenance, imperfect maintenance and perfect maintenance, so as to minimize the total discounted cost of the system. The impulse optimal control theory of PDMP is used to determine the optimal maintenance strategy. A numerical study dealing with component coating maintenance problem is presented. Relationship with optimal threshold strategy is discussed. Sensitivity analyses on the influences of discount factor, observation interval and maintenance cost to the discounted cost and optimal actions are presented.
