复杂系统的选择性维修模型和求解算法

王海朋; 段富海; 马骏

doi:10.13700/j.bh.1001-5965.2019.0619

复杂系统的选择性维修模型和求解算法

doi: 10.13700/j.bh.1001-5965.2019.0619

大连理工大学机械工程学院, 大连 116024

基金项目:

航空科学基金 20150863003

详细信息

作者简介:
王海朋男, 博士研究生。主要研究方向:系统可靠性分析与维修策略

段富海男, 博士, 教授, 博士生导师。主要研究方向:复杂系统可靠性分析与多学科优化设计

通讯作者:
段富海, E-mail: duanfh@dlut.edu.cn

中图分类号: V241.07;E92
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- 文章访问数: 957
- HTML全文浏览量: 183
- PDF下载量: 106
- 被引次数: 22
出版历程
- 收稿日期: 2019-12-09
- 录用日期: 2020-02-14
- 网络出版日期: 2020-12-20

Selective maintenance model and its solving algorithm for complex system

School of Mechanical Engineering, Dalian University of Technology, Dalian 116024, China

Funds:

Aeronautical Science Foundation of China 20150863003

More Information

Corresponding author: DUAN Fuhai, E-mail: duanfh@dlut.edu.cn

摘要

摘要:
考虑不修、最小维修、换件维修和多中间维修水平，提出了一种基于粒子群优化（PSO）算法和多员维修的复杂系统选择性维修模型，将组件维修前状态、组件有效役龄和维修费用等因素引入不完全维修模型，更符合工程实际。提出了一种基于多员维修的系统组件维修分配算法，解决了如何将多维修任务分配给多维修人员，使得系统维修时间最小的问题，并将所提算法引入到PSO算法中，求解考虑多维修人员和不完全维修条件的复杂系统选择性维修模型。案例表明：所提模型和求解算法有效，能够为复杂系统提供切实有效的维修决策方案。
- 复杂系统 /
- 选择性维修 /
- 多维修人员 /
- 不完全维修 /
- 粒子群优化(PSO)算法
Abstract:
Considering no maintenance, minimal maintenance, replacement maintenance and multiple intermediate maintenance levels, a selective maintenance model for the complex system is proposed based on Particle Swarm Optimization (PSO) algorithm and multiple repairpersons. In the imperfect maintenance model, effective age, maintenance cost and pre-maintenance state of components are introduced, which is more in line with the engineering practice. A system components maintenance tasks assignment algorithm, to solve the problem of how to assign multiple maintenance tasks to multiple repairpersons in order to minimize the maintenance time, is also proposed. Furthermore, the proposed algorithm is introduced into the PSO algorithm to solve the selective maintenance model, which is given for complex system considering multiple repairpersons and imperfect maintenance. The results of case analysis show that the proposed model and the corresponding algorithm are effective, and can provide feasible maintenance decision-making schemes for complex system.
- complex system /
- selective maintenance /
- multiple repairpersons /
- imperfect maintenance /
- Particle Swarm Optimization (PSO) algorithm

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图 1 选择性维修模型技术路线

Figure 1. Selective maintenance model technology roadmap

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图 2 多维修人员维修任务分配图

Figure 2. Maintenance task assignment chart with multiple repairpersons

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图 3 混合不完全维修模型

Figure 3. Hybrid imperfect maintenance model

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图 4 串并联系统

Figure 4. Series parallel system

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图 5 SINS系统可靠性框图

Figure 5. System reliability block diagram of SINS

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图 6 SINS多维修人员维修任务分配图

Figure 6. Maintenance task assignment chart with multiple repairpersons of SINS

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图 7 维修资源变化对系统可靠性的敏感度分析

Figure 7. Sensitivity analysis of system reliability to maintenance resource variation

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表 1 组件E_ij维修水平赋值

Table 1. Maintenance level assignment for component E_ij

维修水平		赋值
故障组件	不修	1
	最小维修	2
	⋮	⋮
	不完全修复性维修	l_ij(k)
	⋮	⋮
	不完全修复性维修	L_ij(k)-1
	更换	L_ij(k)
正常组件	不修	1
	不完全预防性维修	2
	⋮	⋮
	不完全预防性维修	l_ij(k)
	⋮	⋮
	不完全预防性维修	L_ij(k)-1
	更换	L_ij(k)

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表 2 可变维修费用c^k_{ij, l_ij}与维修水平l_ij(k)的对应关系

Table 2. Corresponding relationship between variable maintenance cost c^k_{ij, l_ij} and maintenance level l_ij(k)

可变维修费用		赋值
故障组件	c_{ij, 1}^k=0	1
	c_{ij, 2}^k=c_ij^MR	2
	⋮	⋮
	c^k_{ij, l_ij}	l_ij(k)
	⋮	⋮
	c^k_{ij, L_ij}=c_ij^R	L_ij(k)
正常组件	c_{ij, 1}^k=0	1
	c_{ij, 2}^k	2
	⋮	⋮
	c^k_{ij, l_ij}	l_ij(k)
	⋮	⋮
	c^k_{ij, L_ij}=c_ij^R	L_ij(k)

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表 3 可变维修时间t^k_{ij, l_ij}与维修水平l_ij(k)的对应关系

Table 3. Corresponding relationship between variable maintenance time t^k_{ij, l_ij} and maintenance level l_ij(k)

可变维修时间		赋值
故障组件	t_{ij, 1}^k=0	1
	t_{ij, 2}^k=t_ij^MR	2
	⋮	⋮
	t^k_{ij, l_ij}	l_ij(k)
	⋮	⋮
	t^k_{ij, L_ij}=t_ij^R	L_ij(k)
正常组件	t_{ij, 1}^k=0	1
	t_{ij, 2}^k	2
	⋮	⋮
	t^k_{ij, l_ij}	l_ij(k)
	⋮	⋮
	t^k_{ij, L_ij}=t_ij^R	L_ij(k)

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表 4 系统参数及维修时间和费用^[5]

Table 4. System parameters, maintenance time and cost^[5]

子系统	组件	β_ij	α_ij	Y_ij(k)	A_ij(k)	T_ij^MR	T_ij^WR	Δt_ij^W	T_ij^FR	Δt_ij^F	C_ij^MR	C_ij^WR	Δc_ij^W	C_ij^FR	Δc_ij^F
子系统1	E₁₁	1.5	15	1	15	3	5	0.25	1	0.25	6	12	2.00	12	1.0
子系统1	E₁₂	1.5	15	1	20	3	5	0.25	1	0.25	5	12	1.75	12	1.0
子系统2	E₂₁	3.0	20	0	8	2	4	0.20	2	0.20	5	14	1.50	14	2.0
子系统2	E₂₂	3.0	20	1	15	2	4	0.20	2	0.20	6	15	1.60	15	1.5

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表 5 系统选择性维修决策优化方案

Table 5. System selective maintenance decision optimization scheme

q	组件	维修水平l_ij(k)	t_ij^E	t_sys	X_ij^E	B_ij^a	S^a	R
1	E₁₁	IM(5)	1.0	8.8	1	7.8	20.7	0.796 9
	E₁₂	WR(6)	5.0		1	0
	E₂₁	FR(7)	2.0		1	0
	E₂₂	IM(5)	0.8		1	12.9

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表 6 SINS系统参数及维修时间和费用^[15]

Table 6. SINS parameters, maintenance time and cost^[15]

组件	β_ij	α_ij	A_ij(k)/h	T_ij^MR/d	T_ij^WR/d	T_ij^FR/d	C_ij^MR/万元	C_ij^R/万元
E₁₁	2.5	25 000	2 000	4.5	14	10	0.4	1.2
E₁₂	2.5	25 000	3 800	4.5	14	10	0.4	1.2
E₂₁	1.8	9 000	3 000	3.5	9	7	0.5	1.6
E₂₂	1.8	9 000	5 000	3.5	9	7	0.5	1.6
E₃₁	3.5	11 750	1 500	4.0	15	12	1.2	4.6
E₃₂	3.5	11 750	2 000	4.0	15	12	1.2	4.6
E₃₃	3.5	11 750	2 000	4.0	15	12	1.2	4.6
E₃₄	3.5	11 750	3 800	4.0	15	12	1.2	4.6
E₄₁	2.2	11 000	1 500	3.5	10	8	0.2	0.6
E₄₂	2.2	11 000	2 500	3.5	10	8	0.2	0.6
E₄₃	2.2	11 000	3 000	3.5	10	8	0.2	0.6
E₄₄	2.2	11 000	4 000	3.5	10	8	0.2	0.6
E₄₅	2.2	11 000	3 500	3.5	10	8	0.2	0.6
E₄₆	2.2	11 000	1 500	3.5	10	8	0.2	0.6
E₅₁	1.9	8 700	3 000	3.5	13	10	0.6	3.0
E₅₂	1.9	8 700	2 000	3.5	13	10	0.6	3.0
E₆₁	3.5	12 000	2 000	4.0	10	8	5.0	20.0
E₆₂	3.5	12 000	3 500	4.0	10	8	5.0	20.0
E₇₁	2.1	24 000	2 000	3.0	8	6	1.0	5.0

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表 7 维修人员数量对SINS系统选择性维修决策的影响

Table 7. Influence of number of repairpersons on SINS selective maintenance decision

q	组件	维修水平l_ij(k)	t_ij^E	S^a	R
1	E₁₁	DN(1)	0	40796	0.9074
	E₁₂	DN(1)	0
	E₂₁	IM(4)	3.5
	E₂₂	WR(6)	9.0
	E₃₁	DN(1)	0
	E₃₂	DN(1)	0
	E₃₃	DN(1)	0
	E₃₄	DN(1)	0
	E₄₁	DN(1)	0
	E₄₂	DN(1)	0
	E₄₃	DN(1)	0
	E₄₄	DN(1)	0
	E₄₅	DN(1)	0
	E₄₆	DN(1)	0
	E₅₁	DN(1)	0
	E₅₂	FR(6)	10.0
	E₆₁	DN(1)	0
	E₆₂	DN(1)	0
	E₇₁	IM(2)	1.6
2	E₁₁	DN(1)	0	33068	0.9447
	E₁₂	DN(1)	0
	E₂₁	FR(6)	7.0
	E₂₂	WR(6)	9.0
	E₃₁	DN(1)	0
	E₃₂	DN(1)	0
	E₃₃	DN(1)	0
	E₃₄	DN(1)	0
	E₄₁	DN(1)	0
	E₄₂	DN(1)	0
	E₄₃	IM(4)	4.0
	E₄₄	DN(1)	0
	E₄₅	DN(1)	0
	E₄₆	DN(1)	0
	E₅₁	WR(6)	13.0
	E₅₂	FR(6)	10.0
	E₆₁	IM(2)	2.0
	E₆₂	DN(1)	0
	E₇₁	IM(4)	4.8
3	E₁₁	DN(1)	0	23104	0.9528
	E₁₂	DN(1)	0
	E₂₁	FR(6)	9.0
	E₂₂	WR(6)	9.0
	E₃₁	DN(1)	0
	E₃₂	DN(1)	0
	E₃₃	DN(1)	0
	E₃₄	DN(1)	0
	E₄₁	IM(3)	2.5
	E₄₂	IM(2)	2.0
	E₄₃	IM(3)	2.5
	E₄₄	IM(5)	8.0
	E₄₅	IM(2)	2.0
	E₄₆	IM(2)	2.0
	E₅₁	WR(6)	13.0
	E₅₂	FR(6)	13.0
	E₆₁	IM(2)	2.0
	E₆₂	IM(2)	2.0
	E₇₁	WR(6)	8.0

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参考文献(15)

[1]	史跃东, 徐一帆, 金家善.装备复杂系统多状态可靠性分析与评估技术[M].北京:科学出版社, 2017. SHI Y D, XU Y F, JIN J S.Multi-state reliability analysis and evaluation technology for complex equipment[M].Beijing:Science Press, 2017(in Chinese).
[2]	RICE W F, CASSADY C R, NACHLAS J A.Optimal maintenance plans under limited maintenance time[C]//Proceedings of the Seventh Industrial Engineering Research Conference, 1998: 1-3.
[3]	LIU Y, HUANG H Z.Optimal selective maintenance strategy for multi-state systems under imperfect maintenance[J].IEEE Transactions on Reliability, 2010, 59(2):356-367.
[4]	PANDEY M, ZUO M J, MOGHADDASS R.Selective maintenance for binary systems using age-based imperfect repair model[C]//Proceedings of 2012 International Conference on Quality, Reliability, Risk, Maintenance, and Safety Engineering.Piscataway: IEEE Press, 2012: 385-389.
[5]	PANDEY M, ZUO M J, MOGHADDASS R, et al.Selective maintenance for binary systems under imperfect repair[J].Reliability Engineering and System Safety, 2013, 113:42-51.
[6]	王少华, 张仕新, 李勇, 等.不完全维修条件下复杂系统的选择性维修决策方法研究[J].兵工学报, 2018, 39(6):1215-1224. WANG S H, ZHANG S X, LI Y, et al.Research on selective maintenance decision-making method of complex system considering imperfect maintenance[J].Acta Armamentarii, 2018, 39(6):1215-1224(in Chinese).
[7]	CAO W B, JIA X S, LIU Y, et al.Selective maintenance optimization for fuzzy multi-state systems[J].Journal of Intelligent & Fuzzy Systems, 2018, 34(1):105-121.
[8]	DJELLOUL I, KHATAB A, AGHEZZAF E H, et al.Optimal selective maintenance policy for series-parallel systems operating missions of random durations[C]//Proceeding of the 45th International Conference on Computers and Industrial Engineering, 2015: 1-8.
[9]	LIU Y, CHEN Y, JIANG T.On sequence planning for selective maintenance of multi-state systems under stochastic maintenance durations[J].European Journal of Operational Research, 2018, 268(1):113-127.
[10]	DAO C D, ZUO M J.Selective maintenance for multi-state series systems with s-dependent components[J].IEEE Transactions on Reliability, 2016, 65(2):525-539.
[11]	DIALLO C, KHATAB A, VENKATADRI U, et al.A joint selective maintenance and multiple repair-person assignment problem[C]//Proceedings of the 7th International Conference on Industrial Engineering and Systems Management, 2017: 317-322.
[12]	KHATAB A, DIALLO C, VENKATADRI U, et al.Optimization of the joint selective maintenance and repairperson assignment problem under imperfect maintenance[J].Computers & Industrial Engineering, 2018, 125:413-422.
[13]	DIALLO C, VENKATADRI U, AGHEZZAF E H, et al.Optimal joint selective imperfect maintenance and multiple repairpersons assignment strategy for complex multicomponent systems[J].International Journal of Production Research, 2019, 57(13):4098-4117.
[14]	贾希胜.以可靠性为中心的维修决策模型[M].北京:国防工业出版社, 2007. JIA X S.The decision models for reliability centered maintenance[M].Beijing:National Defence Industry Press, 2007(in Chinese).
[15]	JIANG X H, DUAN F H, TIAN H, et al.Optimization of reliability centered predictive maintenance scheme for inertial navigation system[J].Reliability Engineering and System Safety, 2015, 140:208-217.

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