基于多阶段-多阈值的设备退化建模与维护决策优化

Equipment degradation modeling and maintenance decision optimization based on multi-phase and multi-threshold

在现有考虑非完美性维护的设备随机退化建模研究中,通常仅考虑了单一加工环境及单一预防性维护阈值下的设备维护决策优化问题,缺乏对多阶段退化及多阈值维护策略的研究.鉴于此,本文首先利用生产与退化的关系构建了变速生产环境下Wiener漂移系数与实际加工速度的关系,并在考虑随机冲击影响的情况下设计了具有随机漂移系数的Wiener退化过程.然后以设备维护间隔为基础,将设备全生命周期平均地分割成多个独立的加工阶段,且每个加工阶段具有可供选择的加工速度、预防性维护阈值和预防性更换阈值.紧接着在首达时间的定义下推导了设备剩余寿命、不同维护活动发生的概率及其维护间隔等变量,提出了基于平均剩余寿命和经验检查间隔的混合检查策略及“多阶段-多阈值”的视情维护决策模型.最后通过大量的仿真实验发现:1)本文所提混合检查策略显著优于文献检查策略,且“多阶段-多阈值”维护模型与三种经典维护模型在平均ACR(average cost rate)指标上的偏差分别为−275.85%,−20.96%和−533.58%,这也进一步论证了本文所提维护模型的有效性和优越性;2)通过对预防性维护成本、检查成本、最小检查间隔和分割阶段总数进行敏感性分析发现,分割阶段总数对维护决策模型具有显著性影响且影响程度最大.

In the study of stochastic degradation modeling of equipment that considers imperfect maintenance,the existing optimization problems of equipment maintenance decision usually only consider a single processing environment and a single preventive maintenance threshold,and there is a lack of research on multi-phase degradation and multi-threshold maintenance strategies.Under these contexts,this paper firstly utilizes the relationship between production and degradation to construct a relationship between the Wiener drift coefficient and the processing speed in a variable-speed production environment,and designs a Wiener degradation process with random drift coefficient and random shock effect.Next,on the basis of discrete maintenance intervals,the whole life cycle of equipment is evenly divided into several independent processing phases,and each processing phase has the selectable processing speed,preventive maintenance threshold and preventive replacement threshold.After that,some variables such as the remaining useful life of equipment,the probability of occurrence of different maintenance activities and their maintenance intervals are derived under the definition of the first passage time,and a hybrid inspection policy based on the mean remaining life and the empirical inspection intervals as well as a“multi-phase-multi-threshold”model for condition-based maintenance decision are proposed.Finally,through numerous simulation experiments,we can find that:1)The proposed hybrid inspection policy is significantly better than the literature inspection policies,and the deviations between“multi-phase-multi-threshold”maintenance model and three classical maintenance models in the average ACR(average cost rate)metric are separately−275.85%,−20.96%and−533.58%,which further demonstrates the effectiveness and superiority of proposed maintenance model;and 2)Through the sensitivity analysis of preventive maintenance cost,inspection cost,minimum inspection interval and total number of processing phases,the results show that the total number of processing phases has a significant effect on the maintenance decision model and it has the largest effect.