多元退化系统维修与备件订购策略优化模型

doi:10.16183/j.cnki.jsjtu.2019.221

上海交通大学学报 ›› 2021, Vol. 55 ›› Issue (7): 858-867.doi: 10.16183/j.cnki.jsjtu.2019.221

所属专题：《上海交通大学学报》2021年12期专题汇总专辑；《上海交通大学学报》2021年“工业工程与管理”专题

多元退化系统维修与备件订购策略优化模型

杨志远¹, 赵建民¹, 程中华¹(), 郭驰名¹, 李俐莹²

1.陆军工程大学石家庄校区装备指挥与管理系,石家庄 050003
2.河北科技大学信息科学与工程学院, 石家庄 050000

收稿日期:2019-07-29 出版日期:2021-07-28 发布日期:2021-07-30
通讯作者: 程中华 E-mail:13143648622@163.com
作者简介:杨志远(1990-),男,河北省石家庄市人,博士生,主要研究方向为装备维修保障理论与技术
基金资助:
国家自然科学基金资助项目(71871220);国家自然科学基金资助项目(71871219)

Optimization Model of Maintenance and Spare Parts Ordering Policy in Multivariate Degradation System

YANG Zhiyuan¹, ZHAO Jianmin¹, CHENG Zhonghua¹(), GUO Chiming¹, LI Liying²

1. Department of Equipment Command and Management, Shijiazhuang Campus of Army Engineering University, Shijiazhuang 050003, China
2. School of Information Science and Engineering, Hebei University of Science and Technology, Shijiazhuang 050000, China

Received:2019-07-29 Online:2021-07-28 Published:2021-07-30
Contact: CHENG Zhonghua E-mail:13143648622@163.com

摘要/Abstract

摘要：

针对具有多个相关退化过程系统的状态维修及备件订购决策问题,在连续监测条件下,建立系统维修与备件订购决策优化模型.首先,采用Gamma过程和Copula函数建立系统多元退化模型,然后提出基于控制限策略的系统维修与备件订购策略.在此基础上,考虑系统退化量对维修费用的影响,获得系统长期运行条件下的期望维修费用率解析表达式.同时为简化模型计算,提出系统期望维修费用率近似表达式.利用人工蜂群算法在费用准则下获得系统最优预防性更换阈值和备件订购阈值.案例分析结果说明了在维修决策中考虑退化相关的必要性.与已有策略相比,综合优化预防性更换和备件订购阈值能够有效降低系统维修费用.

关键词: 维修决策, 备件订购, 多元退化过程, 退化相关性, 状态监测

Abstract:

Aimed at the decision-making problem of condition-based maintenance and spare parts ordering for systems with multiple dependent degradation processes, an optimization model of system maintenance and spare parts ordering policy is developed under the condition of continuously monitoring. First, the Gamma process and Copula function are used to develop the system multivariate degradation model. Then, the system maintenance and spare parts ordering policy based on the control limit strategy is proposed. Considering the influence of system degradation on maintenance cost, the analytical expression of the expected maintenance cost rate under long-term operation conditions is obtained. At the same time, an approximate expression of the expected maintenance cost rate is proposed to simplify the model calculation. The optimal preventive replacement threshold and spare parts ordering threshold of the system are obtained by using the artificial bee colony algorithm under the cost criterion. The case analysis shows that it is necessary to consider degradation in maintenance decision-making. Compared with the existing policy, the comprehensive optimization of preventive replacement and spare parts ordering thresholds can effectively reduce the maintenance cost of the system.

Key words: maintenance decision, spare parts ordering, multivariate degradation process, dependent degradation, condition monitoring

中图分类号:

TB114

杨志远, 赵建民, 程中华, 郭驰名, 李俐莹. 多元退化系统维修与备件订购策略优化模型[J]. 上海交通大学学报, 2021, 55(7): 858-867.

YANG Zhiyuan, ZHAO Jianmin, CHENG Zhonghua, GUO Chiming, LI Liying. Optimization Model of Maintenance and Spare Parts Ordering Policy in Multivariate Degradation System[J]. Journal of Shanghai Jiao Tong University, 2021, 55(7): 858-867.

图/表 12

图1

图2

表1

系统退化过程及故障阈值参数

退化过程	案例1			案例2
退化过程	α_i	β_i	$Q L i$	α_i	β_i	$Q L i$
i=1	1	2	10	1	2	10
i=2	1	2	10	9/4	2/3	8

表1

表2

表3

解析结果与仿真结果对比

案例	( $Q A 1$ , $Q A 2$ , $Q M 1$ , $Q M 2$ )	解析结果	MC仿真结果	MC仿真95% 置信区间
1	(2,2,5,3)	11.25	11.18	[10.75,11.62]
	(4,3,6,5)	10.07	10.02	[9.64,10.40]
	(3,3,8,8)	10.34	10.27	[9.76,10.77]
2	(2,2,3,3)	10.66	10.61	[9.88,11.34]
	(3,2.5,5,5)	9.69	9.67	[9.13,10.21]
	(3,3,7,6)	9.58	9.52	[9.04,10.01]

表3

图3

图4

图5

表4

图6

图7

表5

不同θ下的系统最优维修及备件订购策略

θ	案例1					案例2
θ	$Q A 1 *$	$Q A 2 *$	$Q M 1 *$	$Q M 2 *$	$γ ∞ *$	$Q A 1 *$	$Q A 2 *$	$Q M 1 *$	$Q M 2 *$	$γ ∞ *$
0	5.96	5.96	8.53	8.53	9.103	7.18	5.20	8.31	6.83	9.006
0.5	6.07	6.07	8.19	8.19	8.996	6.07	5.44	8.07	6.59	8.763
0.7	5.92	5.92	8.03	8.03	8.922	6.07	5.35	7.96	6.50	8.649
0.9	5.14	5.14	7.82	7.82	8.643	6.27	4.91	7.84	6.39	8.491

表5

参考文献 18

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参数	取值
C_I	1
C_O	3
C_S	5
C_LO	50
C_R	10
ρ	20

维修策略	案例1					案例2
维修策略	$Q_{{A}_{1}}^{*}$	$Q_{{A}_{2}}^{*}$	$Q_{{M}_{1}}^{*}$	$Q_{{M}_{2}}^{*}$	$γ_{∞}^{*}$	$Q_{{A}_{1}}^{*}$	$Q_{{A}_{2}}^{*}$	$Q_{{M}_{1}}^{*}$	$Q_{{M}_{2}}^{*}$	$γ_{∞}^{*}$
本文	5.92	5.92	8.03	8.03	8.922	6.07	5.35	7.96	6.50	8.649
文献[14]	—	—	6.06	6.06	9.586	—	—	6.94	4.80	9.192

多元退化系统维修与备件订购策略优化模型

Optimization Model of Maintenance and Spare Parts Ordering Policy in Multivariate Degradation System

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