考虑非完美维修的多部件系统劣化状态空间划分建模
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摘要
为了进一步深入研究考虑非完美维修效果的建模方法,利用劣化状态空间划分思想对考虑非完美维修的多部件系统视情机会维修策略进行了统一建模。针对多部件系统,考虑非完美维修效果,制定了基于周期检测的视情机会维修策略,建立了联合劣化状态空间划分模型,给出了所有维修需求组合及其概率计算通式,推导了联合稳态概率密度函数。通过数值实验验证了上述模型及联合稳态概率密度函数求解的正确性,同时定性分析了该建模方法对研究相同多部件系统维修优化建模的有效性,为后续的维修优化研究奠定了基础。
To further research the modeling method with imperfect maintenance effect,by using the deterioration state space partitioning method,the condition-based opportunistic maintenance for multi-units system with imperfect maintenance actions was modeled,and the condition-based opportunistic maintenance strategy based on periodic detection was formulated.The joint deterioration state space partitioning model was built,and all possible maintenance combinations of multi-unit systems with imperfect maintenance actions at each maintenance decision point and their corresponding probabilities were deduced.The stationary probabilistic density and its numerical solution were developed.The correctness of the proposed deterioration state space partitioning method was verified with numerical experiments.Eventually,the effectiveness of the proposed method for follow-up repair optimization was also verified.
To further research the modeling method with imperfect maintenance effect,by using the deterioration state space partitioning method,the condition-based opportunistic maintenance for multi-units system with imperfect maintenance actions was modeled,and the condition-based opportunistic maintenance strategy based on periodic detection was formulated.The joint deterioration state space partitioning model was built,and all possible maintenance combinations of multi-unit systems with imperfect maintenance actions at each maintenance decision point and their corresponding probabilities were deduced.The stationary probabilistic density and its numerical solution were developed.The correctness of the proposed deterioration state space partitioning method was verified with numerical experiments.Eventually,the effectiveness of the proposed method for follow-up repair optimization was also verified.
引文
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[14] ZHANG Chen,GUO Wei,GUO Sheng,et al.Opportunistic maintenance for wind turbines considering imperfect,reliability-based maintenance[J].Renewable Energy,2017,103:606-612.
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[16] LIU Bin,XIE Min,XU Zhengguo,et al.An imperfect maintenance policy for mission-oriented systems subject to degradation and external shocks[J].Computers&Industrial Engineering,2016,102:21-32.
[17] ZHANG Xiaohong,ZENG Jianchao.State space partition based optimization of the opportunistic preventive maintenance of two-unit systems[J].Systems Engineering—Theory&Practice,2015,35(6):1547-1560(in Chinese).[张晓红,曾建潮.基于状态空间分割的两部件系统机会维修优化[J].系统工程理论与实践,2015,35(6):1547-1560.]
[18] WANG Shaohua,ZHANG Yaohui,XU Longyang,et al.Optimal condition-based maintenance decision-making method of multi-component system based on simulation[J].Acta Armamentarii,2017,38(3):568-575(in Chinese).[王少华,张耀辉,徐隆洋,等.基于仿真的多部件系统状态维修决策优化方法[J].兵工学报,2017,38(3):568-575.]
[19] BOUVARD K,ARTUS S,BRENGUER C,et al.Condition-based dynamic maintenance operations planning&grouping.application to commercial heavy vehicles[J].Reliability Engineering&System Safety,2011,96(6):601-610.
[20] LI Zhidong,ZHANG Tao.Inspection and maintenance optimization of multi-State series repairable system[J].Computer Simulation,2017,34(3):385-390(in Chinese).[李志栋,张涛.多状态串联维修系统的检测及维修优化[J].计算机仿真,2017,34(3):385-390.]
[21] VAN P D,BRENGUER C.Condition-based maintenance with imperfect preventive repairs for a deteriorating production system[J].Quality&Reliability Engineering International,2012,28(6):624-633.
[22] DO P,VOISIN A,LEVRAT E,et al.A proactive conditionbased maintenance strategy with both perfect and imperfect maintenance actions[J].Reliability Engineering&System Safety,2014,133(11):22-32.
[23] GAN Jie,ZHENG Jianchao,ZHANG Xiaohong.Maintenance decision model with performance reliability constraint[J].Computer Integrated Manufacturing Systems,2016,22(4):1079-1087(in Chinese).[甘婕,曾建潮,张晓红.考虑性能可靠度约束的维修决策模型[J].计算机集成制造系统,2016,22(4):1079-1087.]
[24] ZHANG Xiaohong,ZENG Jianchao.Joint optimization of condition-based opportunistic maintenance and spare parts provisioning policy in multiunit systems[J].European Journal of Operational Research,2017,262(2):479-498.
[25] NOORTWIJK J M V.A survey of the application of gamma processes in maintenance[J].Reliability Engineering&System Safety,2009,94(1):2-21.
[26] TAN Lin,CHENG Zhijun,GUO Bo,et al.Condition-based maintenance policy for gamma deteriorating systems[J].Journal of Systems Engineering and Electronics,2010,21(1):57-61.
[27] TAN Lin,GUO Chiming,CHENG Zhijun,et al.Optimal maintenance decisions for gamma deteriorating systems[J].Journal of Systems Engineering and Electronics,2011,22(5):788-793.
[28] LI Ling,CHENG Guoqing,LIU Bingxiang.Accelerated deteriorating system model based on Gamma process and its optimal condition-based maintenance policy[J].Computer Integrated Manufacturing Systems,2013,19(11):2922-2927(in Chinese).[李玲,成国庆,柳炳祥.基于Gamma过程的加速劣化系统模型及其最优视情维修策略[J].计算机集成制造系统,2013,19(11):2922-2927.]
[2] ZHANG Xiaohong.Optimal maintenance descision and joint optimal decision of maintenance and spare parts inventory for multi-unit systems[D].Taiyuan:Taiyuan University of Science and Technology,2015(in Chinese).[张晓红.多部件系统维修决策及维修与备件库存联合决策研究[D].太原:太原科技大学,2015.]
[3] ZHANG Xiaohong,ZENG Jianchao.Deterioration state space partitioning method for opportunistic maintenance modelling of identical multi-unit systems[J].International Journal of Production Research,2015,53(7):2100-2118.
[4] ZHANG Xiaohong,ZENG Jianchao.A general modeling method for opportunistic maintenance modeling of multi-unit systems[J].Reliability Engineering&System Safety,2015,140:176-190.
[5] BADA F G,BERRADE M D.Optimum maintenance policy of a periodically inspected system under imperfect repair[J].Advances in Operations Research,2009.DOI:10.1155/2009/691203.
[6] PANDEY M,ZUO M J,MOGHADDASS R.Selective maintenance modeling for a multistate system with multistate components under imperfect maintenance[J].IIE Transactions,2013,45(11):1221-1234.
[7] TOLEDO M L G D,FREITAS M A,COLOSIMO E A,et al.ARA and ARI imperfect repair models:estimation,goodnessof-fit and reliability prediction[J].Reliability Engineering&System Safety,2015,140:107-115.
[8] MELCHOR-HERNNDEZ C L,RIVAS-DVALOS F,MAXIMOV S,et al.A model for optimizing maintenance policy for power equipment[J].International Journal of Electrical Power&Energy Systems,2015,68:304-312.
[9] TONG Peng,LIU Zixian,MEN Feng,et al.Two-dimensional extended warranties strategy of automotive product based on usage rate[J].Computer Integrated Manufacturing Systems,2014,20(5):1149-1159(in Chinese).[仝鹏,刘子先,门峰,等.基于产品使用率的二维延伸性汽车产品保证策略[J].计算机集成制造系统,2014,20(5):1149-1159.]
[10] CHAN P K W,DOWNS T.Two criteria for preventive maintenance[J].IEEE Transactions on Reliability,2009,R-27(4):272-273.
[11] CHAUDHURI D,SAHU K C.Preventive maintenance interval for optimal reliability of deteriorating system[J].IEEE Transactions on Reliability,2009,R-26(5):371-372.
[12] PHAM H,WANG Hongzhou.Imperfect maintenance[J].European Journal of Operational Research,1996,94(3):425-438.
[13] LI Changyou,ZHANG Yimin,XU Minqiang.Reliabilitybased maintenance optimization under imperfect predictive maintenance[J].Chinese Journal of Mechanical Engineering,2012,25(1):160-165.
[14] ZHANG Chen,GUO Wei,GUO Sheng,et al.Opportunistic maintenance for wind turbines considering imperfect,reliability-based maintenance[J].Renewable Energy,2017,103:606-612.
[15] NODEM F I D,KENNE J P,GHARBI A.Hierarchical decision making in production and repair/replacement planning with imperfect repairs under uncertainties[J].European Journal of Operational Research,2009,198(1):173-189.
[16] LIU Bin,XIE Min,XU Zhengguo,et al.An imperfect maintenance policy for mission-oriented systems subject to degradation and external shocks[J].Computers&Industrial Engineering,2016,102:21-32.
[17] ZHANG Xiaohong,ZENG Jianchao.State space partition based optimization of the opportunistic preventive maintenance of two-unit systems[J].Systems Engineering—Theory&Practice,2015,35(6):1547-1560(in Chinese).[张晓红,曾建潮.基于状态空间分割的两部件系统机会维修优化[J].系统工程理论与实践,2015,35(6):1547-1560.]
[18] WANG Shaohua,ZHANG Yaohui,XU Longyang,et al.Optimal condition-based maintenance decision-making method of multi-component system based on simulation[J].Acta Armamentarii,2017,38(3):568-575(in Chinese).[王少华,张耀辉,徐隆洋,等.基于仿真的多部件系统状态维修决策优化方法[J].兵工学报,2017,38(3):568-575.]
[19] BOUVARD K,ARTUS S,BRENGUER C,et al.Condition-based dynamic maintenance operations planning&grouping.application to commercial heavy vehicles[J].Reliability Engineering&System Safety,2011,96(6):601-610.
[20] LI Zhidong,ZHANG Tao.Inspection and maintenance optimization of multi-State series repairable system[J].Computer Simulation,2017,34(3):385-390(in Chinese).[李志栋,张涛.多状态串联维修系统的检测及维修优化[J].计算机仿真,2017,34(3):385-390.]
[21] VAN P D,BRENGUER C.Condition-based maintenance with imperfect preventive repairs for a deteriorating production system[J].Quality&Reliability Engineering International,2012,28(6):624-633.
[22] DO P,VOISIN A,LEVRAT E,et al.A proactive conditionbased maintenance strategy with both perfect and imperfect maintenance actions[J].Reliability Engineering&System Safety,2014,133(11):22-32.
[23] GAN Jie,ZHENG Jianchao,ZHANG Xiaohong.Maintenance decision model with performance reliability constraint[J].Computer Integrated Manufacturing Systems,2016,22(4):1079-1087(in Chinese).[甘婕,曾建潮,张晓红.考虑性能可靠度约束的维修决策模型[J].计算机集成制造系统,2016,22(4):1079-1087.]
[24] ZHANG Xiaohong,ZENG Jianchao.Joint optimization of condition-based opportunistic maintenance and spare parts provisioning policy in multiunit systems[J].European Journal of Operational Research,2017,262(2):479-498.
[25] NOORTWIJK J M V.A survey of the application of gamma processes in maintenance[J].Reliability Engineering&System Safety,2009,94(1):2-21.
[26] TAN Lin,CHENG Zhijun,GUO Bo,et al.Condition-based maintenance policy for gamma deteriorating systems[J].Journal of Systems Engineering and Electronics,2010,21(1):57-61.
[27] TAN Lin,GUO Chiming,CHENG Zhijun,et al.Optimal maintenance decisions for gamma deteriorating systems[J].Journal of Systems Engineering and Electronics,2011,22(5):788-793.
[28] LI Ling,CHENG Guoqing,LIU Bingxiang.Accelerated deteriorating system model based on Gamma process and its optimal condition-based maintenance policy[J].Computer Integrated Manufacturing Systems,2013,19(11):2922-2927(in Chinese).[李玲,成国庆,柳炳祥.基于Gamma过程的加速劣化系统模型及其最优视情维修策略[J].计算机集成制造系统,2013,19(11):2922-2927.]