基于聚合随机过程的元件相依多状态系统可靠性研究

The Multi-State System can represent the characteristic of multi-state of complex systems and reflect the relations between systems and their components, being an emerging topic in reliability theory and engineering. How to compress the state space which increases greatly with the increasing of component's number reasonably and how to describe operational dependencies exist widely among components accurately are significant issue in reliability management of Multi-State Systems. .Based on present engineering practice, the following work will be studied: .(1) Three new Multi-State Systems with interacting components, redundant dependence, spatial dependence and environmental dependence, will be structured on the basis of the theory of multiple ion channels. Dependence functions will be introduced to quantify the dependency among components. .(2) The multivariate semi-Markov processes will be constructed using the method of state aggregation to alleviate the problem of "dimension damnation" and describe the operation processes of Multi-State Systems accurately. .(3)Reliability assessment of these systems will be provided via aggregated stochastic processes which mainly concern the ion channel theory, and the sensitivity analysis of dependence affection will also be made..The expected outcomes of the research will have extremely important value for the theory of Multi-State Systems with interacting components, provide guidelines for reliability analysis and optimal design of large complex systems, and promote the development and application of aggregated stochastic processes.

多状态系统既能表征复杂系统多状态的特点，也能反映系统与元件之间的关系，是可靠性理论与工程的研究热点。合理压缩随元件个数增加而急剧增长的状态空间、精确描述元件之间普遍存在的相依性是多状态系统可靠性管理研究中亟待解决的重点问题。.本项目拟结合可靠性工程背景展开以下研究: (1)借鉴多离子通道理论，引入相依函数定量表示元件间的相依关系，建立元件冗余相依、元件空间相依、元件环境相依三类多状态系统可靠性模型；(2)利用状态聚合法，构建多变量半马尔可夫过程，以缓解"状态空间爆炸"问题，精确描述系统的运行过程； (3)运用以离子通道理论为主的聚合随机过程理论对所建模型进行可靠性评估，并开展相依影响敏感性分析。.预期研究成果对元件相依多状态系统理论的发展具有重要理论价值，为大型复杂系统的可靠性分析和优化设计提供理论依据，可促进聚合随机过程理论的发展和应用。

如何定量描述元件之间普遍存在的相依性，如何合理压缩随元件个数增加而急剧增长的状态空间、是多状态系统可靠性管理研究中亟待解决的重点问题。.本项目结合可靠性工程背景开展了以下研究:(1)引入相依函数定量表示载荷共享系统元件间的相依关系，建立了元件冗余相依马尔可夫和半马尔可夫多状态系统模型；(2)考虑元件空间结构对相依性的影响，构建空间相依线型和圆型多状态系统模型；(3)引入有两个不同核函数的半马尔可夫过程描述系统在不同环境下的运行，构建交替环境下的半马尔可夫多状态系统模型；（4）通过状态聚合，缩减系统状态数目，运用聚合随机过程理论对所建模型进行可靠性评估，并开展相依影响敏感性分析。.研究成果对元件相依多状态系统理论的发展有理论价值，为大型复杂系统的可靠性分析和优化设计提供理论依据，也可促进聚合随机过程理论的发展和应用。