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浙江大学学报(工学版)  2020, Vol. 54 Issue (7): 1298-1307    DOI: 10.3785/j.issn.1008-973X.2020.07.007
自动化技术、计算机技术     
基于延迟时间模型的不完全检修计划优化模型
刘葛辉(),陈绍宽*(),金华,刘爽,彭宏勤
北京交通大学 交通运输部综合交通运输大数据应用技术交通运输行业重点实验室,北京 100044
Optimum imperfect inspection and maintenance scheduling model considering delay time theory
Ge-hui LIU(),Shao-kuan CHEN*(),Hua JIN,Shuang LIU,Hong-qin PENG
MOT Key Laboratory of Transport Industry of Big Data Application Technologies for Comprehensive Transport, Beijing Jiaotong University, Beijing 100044, China
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摘要:

针对现有基于检测的状态维修方法仅适用于短期维修计划,且通常单一地考虑不完全维修或不完全检测的问题,构建适合设备维修现场特征的长期维修计划优化模型,考虑检测与维修活动均不完全情况下的退化过程. 利用延迟时间模型描述退化过程,围绕双重不确定的检修活动,构建基于递推关系的可靠度模型,该模型可以有效表示系统退化速度和故障发生概率. 以单位时间系统费用最小为决策目标,引入可靠度、可用度等约束,建立检修计划优化模型,求解得到最佳检测周期和更换周期. 案例研究表明,利用提出的模型能够有效优化系统检修计划,节省维修成本. 通过与固定周期和固定可靠度阈值的维修策略进行对比,说明检测精度对于检测模型的优化效果具有显著影响,当检测精度属于较高水平时,检修模型明显优于其他维修模型.

关键词: 延迟时间模型预防性检修不完全检修检测周期可靠度维修费用    
Abstract:

The existing condition-based maintenance methods based on inspection activities were only suitable for short-term schedules and involved only imperfect inspection or maintenance. A long-term optimization model was proposed based on on-site features of system maintenance scheduling by incorporating deterioration process with both imperfect maintenance and inspection activities. The delay time theory was introduced to describe deterioration process of system with double contingencies from imperfect maintenance and inspection. The proposed recursive reliability model can accurately evaluate the deterioration rate and failure rate of system. A maintenance scheduling optimization model was applied to minimize the average cost by searching appropriate inspection cycles and replacement strategy. The reliability and availability constraints were considered to meet the requirement of maintenance. Case studies show that the proposed model can attain optimal inspection strategy with minimum system cost. The accuracy of inspection was crucial for the scheduling optimization model compared with age-based and reliability-based maintenance models. The proposed model with a high accuracy of inspection reached the minimum cost compared to models without inspections.

Key words: delay time model    preventive maintenance    imperfect maintenance    inspection cycle    reliability    maintenance cost
收稿日期: 2019-07-02 出版日期: 2020-07-05
CLC:  TB 114  
基金资助: 国家自然科学基金资助项目(71571015,71621001)
通讯作者: 陈绍宽     E-mail: 16114221@bjtu.edu.cn;shkchen@bjtu.edu.cn
作者简介: 刘葛辉(1995—),男,博士生,从事系统可靠度分析和维修计划研究. orcid.org/0000-0003-1270-6011. E-mail: 16114221@bjtu.edu.cn
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刘葛辉
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引用本文:

刘葛辉,陈绍宽,金华,刘爽,彭宏勤. 基于延迟时间模型的不完全检修计划优化模型[J]. 浙江大学学报(工学版), 2020, 54(7): 1298-1307.

Ge-hui LIU,Shao-kuan CHEN,Hua JIN,Shuang LIU,Hong-qin PENG. Optimum imperfect inspection and maintenance scheduling model considering delay time theory. Journal of ZheJiang University (Engineering Science), 2020, 54(7): 1298-1307.

链接本文:

http://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2020.07.007        http://www.zjujournals.com/eng/CN/Y2020/V54/I7/1298

图 1  检测缺陷过程示意图
图 2  发生故障过程示意图
图 3  枚举优化算法流程图
系统序号 检修参数 退化参数 参数验证
a r m1 l1?1 m2 l2 统计量实际值 统计量参照值 通过检验
1 0.05 0.68 1 0.003 5.347 6 126.344 0 18.364 18.548
2 0.02 1.00 1 0.011 1.857 1 124.111 0 16.465 16.748
3 0.05 0.78 1 0.020 5.678 7 112.360 3 20.936 21.954
4 0.05 0.57 1 0.006 3.063 3 180.541 0 15.475 16.748
5 0.05 0.87 1 0.011 5.639 2 99.360 3 18.325 18.548
表 1  检修和退化参数估计结果
系统序号 ci/元 cp/元 cr/元 cc/元 ti/h tp/h tr/h tc/h Rmin
1 100 280 1 800 4 000 1.5 3.0 6.0 20.0 0.94
2 80 400 1 600 3 500 0.5 1.0 2.5 25.0 0.94
3 50 150 840 2 750 0.5 1.5 4.5 8.0 0.93
4 100 320 2 150 7 200 2.0 4.0 10.0 15.0 0.92
5 120 500 1 670 9 000 1.5 3.5 6.5 10.0 0.94
表 2  系统检修成本和可靠度参数
系统 Tmax/d $\bar C$/(元·d?1 T/d τ L/d A Ga/%
1 134 24.27 41 11 451 0.997 66 0.02
2 66 18.84 24 30 720 0.998 61 0
3 93 14.55 27 27 729 0.998 56 0
4 144 40.44 42 7 294 0.996 12 0.06
5 88 34.38 30 23 690 0.996 65 0.01
表 3  检修计划优化模型求解结果
图 4  枚举优化算法求解过程分析
系统 检修策略(P1) 对比策略1:固定周期维修(P2) 对比策略2:固定可靠度阈值维修(P3)
$\bar C$/(元·d?1 T/d L/d ${\bar C_1}$/(元·d?1 Gc/% T1/d L1/d ${\bar C_2}$/(元·d?1 Gc/% R2 L2/d
1 24.27 41 451 21.81 ?10.14 90 450 19.73 ?18.71 0.990 512
2 18.84 24 720 39.89 +111.67 42 126 33.95 +80.14 0.984 152
3 14.55 27 729 16.81 +15.59 61 366 15.04 +3.39 0.988 370
4 40.44 42 294 32.24 ?20.28 92 368 28.80 ?28.77 0.986 477
5 34.38 30 690 37.58 +9.31 65 260 34.39 +0.01 0.984 263
表 4  不同维修策略求解结果与比较
图 5  检出概率对目标函数和维修计划的影响
图 6  检出概率对不同维修策略的影响
图 7  理想情况下检测模型的目标值及其比较结果
图 8  预防性维修和故障期望随着检测次数的变化
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