基于聚合随机过程的多状态可修系统弹性建模与分析

As a new requirement of reliability and maintainability for complex engineering systems, resilience has been received more and more attentions in recent years. Existing research on engineering resilience mainly focuses on concrete systems, e.g., infrastructure systems, network systems. The resilience of multi-state repairable system, which is an important abstract system model in reliability theory, however, is seldom discussed in literatures. The project focuses on the resilience of multi-state system and the theory of aggregated stochastic processes is exploited to investigate two scientific problems, i.e., how to describe the resilience behavior of a system and what the major mechanism of system resilience is. The contents in this project are organized as follows. First, generic resilience metrics are defined and generic resilience models are developed for resilience analysis of a general multi-state repairable system. In order to clarify its resilience mechanism, methods to identify influencing factors to resilience are also developed for generic multi-state repairable system, based on which resilience enhancement measures can be determined. Second, two specific systems are taken into considerations, i.e., the load-capacity model and the recovery-time-neglected model. Using the developed generic approaches and considering the system-specific characteristics of the two systems, the resilience analysis and improvement methods are developed for the two systems. Two actual case studies are conducted to demonstrate the developed methods. The results of this project are anticipated to enrich the resilience theory of the complex engineering system, and support the application of resilience in engineering practices.

近年来，弹性逐渐成为复杂工程系统可靠性与维修性方面的一项新要求。从研究对象上看，现有的弹性研究主要集中在关键基础设施、网络等具体系统上，对于多状态可修系统这一可靠性理论中重要的抽象系统模型则较少涉及。本项目以多状态可修系统为研究对象，运用聚合随机过程理论，针对“刻画复杂工程系统的弹性行为”与“阐明复杂工程系统的弹性机理”两个科学问题开展研究：首先，针对多状态可修系统的共性特点，给出多状态可修系统弹性指标定义，并基于聚合随机过程研究给出其弹性建模分析与弹性影响因素分析的通用方法；第二，分别以基于负载-容量模型与恢复时间可忽略的两类具体可修系统为对象，应用前述建立的通用方法，结合系统特点，研究给出适用于这两类具体系统的弹性行为描述与弹性机理研究方法，并分别展开典型案例上开展应用研究。本项目的研究成果能够充实复杂工程系统的弹性理论，为保证实际工程中复杂工程系统弹性要求的顺利实现提供方法支撑。

本项目围绕“刻画复杂多状态可修系统的弹性行为”与“阐明复杂多状态可修系统的弹性机理”两个问题开展研究，运用聚合随机过程这一数学工具，系统地构建了复杂多状态可修系统弹性表征、建模及分析的理论体系，取得了一系列原创成果。首先，基于复杂多状态可修系统在扰动事件影响下的预期损失，从抵抗力弹性、吸收力弹性、恢复力弹性以及总体弹性四个方面定义了弹性指标；实现了对复杂多状态可修系统弹性的全面量化；其次，针对多状态可修系统行为复杂的特点，基于聚合随机过程理论，对以故障历史相关性、故障可忽略性为代表的多状态可修系统典型复杂行为进行了建模与分析，为后续开展弹性量化奠定了基础；第三，分别基于马尔可夫奖励过程与半马尔可夫奖励过程两种模型，构建了复杂多状态可修系统弹性的建模与分析框架，为复杂多状态可修系统的弹性建模提供了一种解决途径，为进一步研究揭示复杂多状态可修系统弹性的产生机理与控制方法奠定了坚实的基础。以上研究成果为复杂多状态可修系统的弹性量化与分析探索了一条新的解决途径，具有较为广阔的理论价值和应用前景。在本项目的资助下，项目组在Reliability Engineering and System Safety, IEEE Transaction on Reliability 等可靠性领域顶级期刊与学术会议上共发表论文5篇，出版专著1部，受邀参加ESREL, MMR, ICSRS等领域内顶级会议并做分组报告3次. 课题负责人受项目资助对巴黎萨克雷大学进行了短期访问，与领域内知名学者Enrico Zio 教授建立了良好的合作关系。