多部件系统视情维修决策技术研究
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摘要
维修问题是影响工业、军事、航空等领域发展的一个关键因素,与工业生产率、产品质量、工业设备或军事装备的可靠性水平、资源消耗、可持续发展等问题息息相关。制定合理有效的维修控制策略对提高维修效率至关重要,因此设备的维修决策分析一直是研究者们关注的热点之一。
在实际工作中,设备大都是多功能集成系统,其机电液一体、大功率多功能化的特点造成了组成部件间较强的相互关系。为了使维修决策模型更符合实际情况的需要,开展考虑部件间相互关系的多部件系统视情维修决策研究具有十分重要的意义。本文围绕考虑经济相关性的多部件串联系统视情维修决策中的重点问题展开研究,主要工作包括:
第一、针对基于连续状态劣化模型的多部件系统视情维修决策问题,提出了一种事后维修与视情维修相结合的机会策略,在部件维修策略优化分析的基础上建立了机会策略下系统的维修优化模型。根据连续状态劣化模型的特点,提出了一种迭代求解方法。运用该方法,能够确定系统的检测周期,并为部件设定对应的机会维修阈值,将视情维修与事后维修在系统层次组合起来,达到系统整体优化的目的。
第二、连续状态劣化模型的特性造成相应决策模型分析的困难,为了解决更为复杂情况下的多部件系统视情维修决策问题,引入离散状态模型描述部件劣化过程。考虑到部件策略优化分析是系统维修决策的基础,首先针对序贯检测条件下的部件视情维修决策问题,提出了一类基于半马氏决策过程的检测与维修优化模型。同时分别针对其中两类假设条件讨论了对应的分析和求解方法。针对模型中劣化阶段停留时间满足一般分布的情况,提出了一类基于位相型(PH)分布拟合的近似处理方法,将物理意义上的状态进行概率扩展,简化了维修决策的求解过程,并给出了对应的改进迭代算法,同时从理论上证明了该算法的收敛性。
第三、在部件优化分析的基础上,针对基于离散状态劣化模型的多部件系统视情维修决策中的两类典型问题,提出了相应的机会维修策略和优化分析方法:
(1)针对串联系统由分别采用视情维修和事后维修的两类部件组成的情况,提出了一类事后维修与视情维修相结合的机会策略,建立了相应的多部件系统维修优化模型,并根据离散状态劣化模型的特点,提出了一类基于序贯决策的求解方法。该模型能够较好地解决采用不同检测方式时,系统中视情维修与事后维修的组合优化问题。
(2)针对串联系统由多个采用视情维修的劣化部件组成的情况,建立了一个基于机会策略的系统多维决策模型。该模型综合考虑了系统中不同部件的检测与维修策略两方面的优化组合。为了解决多维决策分析中的状态空间组合爆炸问题,提出了一种降维简化求解方法,将多维决策过程转化为多个一维过程进行求解。
示例表明,当部件间存在较强的经济相关性时,上述机会策略在降低系统运行费用上具有较好的效果。
多部件系统视情维修决策分析涉及的模型和分析方法十分复杂,还存在诸多尚未解决的问题,模型在实际工作中的应用也还需要付出较多努力。本文的研究成果是在多部件系统视情维修决策技术方面做了一些有益的理论探讨,能够为今后的相关研究提供一定的借鉴和参考。
Maintenance is a key factor to influence the development of industry, military and aviation fields, which is closely bound up with the productivity, quality, reliability and resources expenses of equipments. The growing importance of maintenance has generated an increasing interest in the development and implementation of optimal maintenance strategies for improving system reliability, preventing the occurrence of system failures and reducing maintenance costs of deteriorating system. Therefore, in the past decades, maintenance and replacement decision analysis becomes one of hot topics discussed by many scholars and practitioners.
In practice, the equipments are mostly integrated systems which consist of several functional parts such as mechanical units, electronic units and hydraulic units. The integration characteristic brings on the interaction between units namely economic, structural and/or stochastic dependencies. Then the optimal decision on one unit is not necessarily optimal for the whole system. In order to improve the practicability of maintenance models, the new policy and analytical approach should be studied to solve the optimization problem of multi-unit system. This paper focuses on condition-based maintenance for multi-unit systems in the context of economical dependences. The major contributions of this dissertation include:
Firstly, to investigate the problem of optimization for the maintenance of multi-unit system based on the continuous-state deterioration model, a kind of new opportunistic policy is proposed to combine the corrective and on-condition maintenance. Then the maintenance model based on this policy is built and the iteration method to get the solution is analyzed according to the characteristic of deterioration model. This method can solve the problem of determining the optimal inspection interval of system and the opportunistic threshold of deteriorating unit, which combines the condition-based maintenance and corrective maintenance to achieve the optimization of the whole system.
Secondly, since the continuous-state deterioration model result in the complex decision model and most of them has to resort to simulation tools, the discrete-state deterioration model is introduced to analyze the maintenance decision under the more complex conditions. The optimal model of inspection and maintenance for the deteriorating unit is presented with the semi-Markov decision process to solve the problem of joint optimization of sequential inspection schedule and preventive maintenance threshold. When the sojourn time of deteriorating state, inspection interval and maintenance time are the stochastic variables which follow the general distribution, the phase-type approach is proposed to preserve the analytical tractability of the transition probability matrix. To solve the problem that the PH distribution changes the state space of system, the value iteration algorithm for the semi-Markov decision process is improved to get the optimal inspection and maintenance policy. The algorithm is proved to be convergent theoretically and implemented for numerical calculation.
Thirdly, two kind problems of multi-unit system maintenance based on the discrete-state deterioration model are analyzed:
To achieve the optimization aim of series system consist of two types of units with different failure mode, an opportunistic policy is presented to combine the corrective and condition-based maintenance. The optimal model based on this policy is built and an iteration algorithm based on sequential decision is proposed according to the characteristic of discrete-state deterioration model. This policy and model can solve the problem of combing the corrective and condition-based maintenance in the system level when the different inspection style is taken.
To analyze the optimal maintenance policy of multi-unit system consist of different deteriorating units which all take the condition-based maintenance, the multidimensional decision model based on the opportunistic policy is presented. This model realizes the combination of the inspection interval and preventive maintenance threshold of different units to reach the optimal aim of the whole system. To solve the problem of state space overextended in the multidimensional decision process, a heuristic approach is given to decompose of the multi-unit problem into several single-unit Markov decision problems.
The examples demonstrate: when the economical dependence between the units of system is stronger, the opportunistic policy given in this paper is more effective in the decreasing the long-run cost rate of system.
The maintenance models and analytical methods to deal with the problem of multi-unit system maintenance decision are complicated and require new technologies and methodologies. There is more work to do to make it practical. The research work of this dissertation only focus on the small parts of the multi-unit system maintenance and can provide some reference for the future work.
在实际工作中,设备大都是多功能集成系统,其机电液一体、大功率多功能化的特点造成了组成部件间较强的相互关系。为了使维修决策模型更符合实际情况的需要,开展考虑部件间相互关系的多部件系统视情维修决策研究具有十分重要的意义。本文围绕考虑经济相关性的多部件串联系统视情维修决策中的重点问题展开研究,主要工作包括:
第一、针对基于连续状态劣化模型的多部件系统视情维修决策问题,提出了一种事后维修与视情维修相结合的机会策略,在部件维修策略优化分析的基础上建立了机会策略下系统的维修优化模型。根据连续状态劣化模型的特点,提出了一种迭代求解方法。运用该方法,能够确定系统的检测周期,并为部件设定对应的机会维修阈值,将视情维修与事后维修在系统层次组合起来,达到系统整体优化的目的。
第二、连续状态劣化模型的特性造成相应决策模型分析的困难,为了解决更为复杂情况下的多部件系统视情维修决策问题,引入离散状态模型描述部件劣化过程。考虑到部件策略优化分析是系统维修决策的基础,首先针对序贯检测条件下的部件视情维修决策问题,提出了一类基于半马氏决策过程的检测与维修优化模型。同时分别针对其中两类假设条件讨论了对应的分析和求解方法。针对模型中劣化阶段停留时间满足一般分布的情况,提出了一类基于位相型(PH)分布拟合的近似处理方法,将物理意义上的状态进行概率扩展,简化了维修决策的求解过程,并给出了对应的改进迭代算法,同时从理论上证明了该算法的收敛性。
第三、在部件优化分析的基础上,针对基于离散状态劣化模型的多部件系统视情维修决策中的两类典型问题,提出了相应的机会维修策略和优化分析方法:
(1)针对串联系统由分别采用视情维修和事后维修的两类部件组成的情况,提出了一类事后维修与视情维修相结合的机会策略,建立了相应的多部件系统维修优化模型,并根据离散状态劣化模型的特点,提出了一类基于序贯决策的求解方法。该模型能够较好地解决采用不同检测方式时,系统中视情维修与事后维修的组合优化问题。
(2)针对串联系统由多个采用视情维修的劣化部件组成的情况,建立了一个基于机会策略的系统多维决策模型。该模型综合考虑了系统中不同部件的检测与维修策略两方面的优化组合。为了解决多维决策分析中的状态空间组合爆炸问题,提出了一种降维简化求解方法,将多维决策过程转化为多个一维过程进行求解。
示例表明,当部件间存在较强的经济相关性时,上述机会策略在降低系统运行费用上具有较好的效果。
多部件系统视情维修决策分析涉及的模型和分析方法十分复杂,还存在诸多尚未解决的问题,模型在实际工作中的应用也还需要付出较多努力。本文的研究成果是在多部件系统视情维修决策技术方面做了一些有益的理论探讨,能够为今后的相关研究提供一定的借鉴和参考。
Maintenance is a key factor to influence the development of industry, military and aviation fields, which is closely bound up with the productivity, quality, reliability and resources expenses of equipments. The growing importance of maintenance has generated an increasing interest in the development and implementation of optimal maintenance strategies for improving system reliability, preventing the occurrence of system failures and reducing maintenance costs of deteriorating system. Therefore, in the past decades, maintenance and replacement decision analysis becomes one of hot topics discussed by many scholars and practitioners.
In practice, the equipments are mostly integrated systems which consist of several functional parts such as mechanical units, electronic units and hydraulic units. The integration characteristic brings on the interaction between units namely economic, structural and/or stochastic dependencies. Then the optimal decision on one unit is not necessarily optimal for the whole system. In order to improve the practicability of maintenance models, the new policy and analytical approach should be studied to solve the optimization problem of multi-unit system. This paper focuses on condition-based maintenance for multi-unit systems in the context of economical dependences. The major contributions of this dissertation include:
Firstly, to investigate the problem of optimization for the maintenance of multi-unit system based on the continuous-state deterioration model, a kind of new opportunistic policy is proposed to combine the corrective and on-condition maintenance. Then the maintenance model based on this policy is built and the iteration method to get the solution is analyzed according to the characteristic of deterioration model. This method can solve the problem of determining the optimal inspection interval of system and the opportunistic threshold of deteriorating unit, which combines the condition-based maintenance and corrective maintenance to achieve the optimization of the whole system.
Secondly, since the continuous-state deterioration model result in the complex decision model and most of them has to resort to simulation tools, the discrete-state deterioration model is introduced to analyze the maintenance decision under the more complex conditions. The optimal model of inspection and maintenance for the deteriorating unit is presented with the semi-Markov decision process to solve the problem of joint optimization of sequential inspection schedule and preventive maintenance threshold. When the sojourn time of deteriorating state, inspection interval and maintenance time are the stochastic variables which follow the general distribution, the phase-type approach is proposed to preserve the analytical tractability of the transition probability matrix. To solve the problem that the PH distribution changes the state space of system, the value iteration algorithm for the semi-Markov decision process is improved to get the optimal inspection and maintenance policy. The algorithm is proved to be convergent theoretically and implemented for numerical calculation.
Thirdly, two kind problems of multi-unit system maintenance based on the discrete-state deterioration model are analyzed:
To achieve the optimization aim of series system consist of two types of units with different failure mode, an opportunistic policy is presented to combine the corrective and condition-based maintenance. The optimal model based on this policy is built and an iteration algorithm based on sequential decision is proposed according to the characteristic of discrete-state deterioration model. This policy and model can solve the problem of combing the corrective and condition-based maintenance in the system level when the different inspection style is taken.
To analyze the optimal maintenance policy of multi-unit system consist of different deteriorating units which all take the condition-based maintenance, the multidimensional decision model based on the opportunistic policy is presented. This model realizes the combination of the inspection interval and preventive maintenance threshold of different units to reach the optimal aim of the whole system. To solve the problem of state space overextended in the multidimensional decision process, a heuristic approach is given to decompose of the multi-unit problem into several single-unit Markov decision problems.
The examples demonstrate: when the economical dependence between the units of system is stronger, the opportunistic policy given in this paper is more effective in the decreasing the long-run cost rate of system.
The maintenance models and analytical methods to deal with the problem of multi-unit system maintenance decision are complicated and require new technologies and methodologies. There is more work to do to make it practical. The research work of this dissertation only focus on the small parts of the multi-unit system maintenance and can provide some reference for the future work.
引文
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