基于状态的n中取k多重相依系统维修策略优化

doi:10.3901/JME.260751

摘要/Abstract

摘要： n中取k系统单元间普遍存在退化相依性、失效相依性与经济相依性，难以基于单元间相互独立或仅单一类型相依性假定有效制定其维修策略。因此，考虑n中取k系统的多重相依性特征，开展了基于状态的系统维修策略优化方法研究。首先，以Wiener过程刻画单元退化过程，利用因子分析与负载平均分配机制，构建考虑退化相依性和失效相依性的n中取k系统退化模型，并推导任意初始退化水平下的系统可靠性函数；接着，考虑设置费用分担引起的单元间经济相依性，提出以最小化长期维修费用率为目标的n中取k系统预防性维修与机会性维修策略联合优化模型；最后，分别通过半再生过程求解系统退化状态稳态概率与遗传算法求解维修策略联合优化模型，给出最优预防性维修阈值、机会性维修阈值与检测周期，实现退化相依性、失效相依性与经济相依性下n中取k系统维修策略制定。通过数值案例分析，验证了所提维修策略优化方法可有效支撑复杂工程系统运维管理。

关键词: 维修策略优化, n中取k系统, 退化相依性, 失效相依性, 经济相依性

Abstract: In k-out-of-n systems, degradation dependency, failure dependency, and economic dependency are commonly present among units, and it is difficult to effectively formulate maintenance strategies based on the assumption of unit independence or a single type of dependency. Therefore, considering the multiple dependencies in k-out-of-n systems, research on condition-based system maintenance strategy optimization is conducted. Initially, the Wiener process is employed to model the degradation performance of individual units, and a k-out-of-n system degradation model that incorporates both degradation and failure dependencies is proposed through factor analysis and a load-averaging allocation mechanism, based on which the system reliability function with arbitrary initial degradation levels is derived. Subsequently, to address the economic dependency arising from shared setup costs among units, a joint optimization model for preventive maintenance and opportunistic maintenance is established with the objective of minimizing long-term maintenance cost rates. Finally, the steady-state probability of system degradation is calculated using semi-regenerative processes, and the joint optimization model is solved by a genetic algorithm. Consequently, optimal thresholds for preventive maintenance and opportunistic maintenance as well as inspection intervals are identified to realize the formulation of maintenance strategies for k-out-of-n systems with degradation dependency, failure dependency, and economic dependency. The numerical study demonstrates that the proposed maintenance optimization method can effectively support the operation and maintenance management of complex engineering systems.

Key words: maintenance optimization, k-out-of-n system, degradation dependency, failure dependency, economic dependency

中图分类号:

TB114

孔雪峰, 赵志伟, 潘骏, 陈文华. 基于状态的n中取k多重相依系统维修策略优化[J]. 机械工程学报, 2026, 62(14): 376-390.

KONG Xuefeng, ZHAO Zhiwei, PAN Jun, CHEN Wenhua. Condition-based Maintenance Optimization for k-out-of-n System with Multi-dependency[J]. Journal of Mechanical Engineering, 2026, 62(14): 376-390.

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http://www.cjmenet.com.cn/CN/Y2026/V62/I14/376

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