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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。
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关键词:
- 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.
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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
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
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
表 1 组件Eij维修水平赋值
Table 1. Maintenance level assignment for component Eij
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 lij(k) ⋮ ⋮ 不完全修复性维修 Lij(k)-1 更换 Lij(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 lij(k) ⋮ ⋮ 不完全预防性维修 Lij(k)-1 更换 Lij(k) 
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表 2 可变维修费用ckij, lij与维修水平lij(k)的对应关系
Table 2. Corresponding relationship between variable maintenance cost ckij, lij and maintenance level lij(k)
可变维修费用 赋值 故障组件 cij, 1k=0 1 cij, 2k=cijMR 2 ⋮ ⋮ ckij, lij lij(k) ⋮ ⋮ ckij, Lij=cijR Lij(k) 正常组件 cij, 1k=0 1 cij, 2k 2 ⋮ ⋮ ckij, lij lij(k) ⋮ ⋮ ckij, Lij=cijR Lij(k)
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表 3 可变维修时间tkij, lij与维修水平lij(k)的对应关系
Table 3. Corresponding relationship between variable maintenance time tkij, lij and maintenance level lij(k)
可变维修时间 赋值 故障组件 tij, 1k=0 1 tij, 2k=tijMR 2 ⋮ ⋮ tkij, lij lij(k) ⋮ ⋮ tkij, Lij=tijR Lij(k) 正常组件 tij, 1k=0 1 tij, 2k 2 ⋮ ⋮ tkij, lij lij(k) ⋮ ⋮ tkij, Lij=tijR Lij(k)
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子系统 组件 βij αij Yij(k) Aij(k) TijMR TijWR ΔtijW TijFR ΔtijF CijMR CijWR ΔcijW CijFR ΔcijF 子系统1 E11 1.5 15 1 15 3 5 0.25 1 0.25 6 12 2.00 12 1.0 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 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lij(k) tijE tsys XijE Bija Sa 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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组件 βij αij Aij(k)/h TijMR/d TijWR/d TijFR/d CijMR/万元 CijR/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lij(k) tijE Sa 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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