基于顺序二元决策图的可修动态故障树快速计算方法研究

Sequential failure behaviors pervasively exist in modern industrial systems. Dynamic Fault Tree (DFT) is a common tool for reliability modeling of such systems. The current calculation methods for repairable DFT cannot meet the practical requirements due to low computing efficiency. The sequential binary decision diagram (SBDD) is expected to be one of the efficient methods for solving repairable DFT due to advantages of its disjoint paths. However, the conversion of DFT to SBDD and the probability calculation of sequential failure events (SFE) in the post-conversion models are the main bottlenecks restricting the implementation of this technology. This project intends to explore the state change laws of relevant variables by exploring the set relationships of repairable events (SFE and basic events), so as to expand the Shannon decomposition theorem to deal with non-independent variables and establish the transformation algorithm of repairable DFT to SBDD. Then, the occurrence prerequisite of the repairable SFE and its failure time boundary constraint characteristics are studied. The generalized stress-strength interference model of mechanical reliability is introduced to establish the mathematic model for solving the occurrence probability of repairable SFE. This project will provide theoretical and methodological support for the fast calculation of repairable DFT, and has strong scientific significance. The proposed method is helpful to solve the reliability assessment problem of large-scale dynamic systems, and has certain engineering application prospects.

现代工业系统普遍存在时序失效行为，动态故障树（DFT）是对此类系统进行可靠性建模的常用工具。可修DFT的现有计算方法因求解效率低而无法满足实践需求。顺序二元决策图（SBDD）由于其路径不交化优点有望成为求解可修DFT的高效方法之一。但是可修DFT向SBDD的转化以及转化后模型中时序失效序列事件（SFE）的概率计算是制约该技术的主要瓶颈。本项目拟以探究可修事件（SFE和基本事件）的集合关系为切入点，研究相关性事件的状态变化规律，以此拓展香农分解定理，使之能够对非独立变量进行不交化处理，进而建立可修DFT向SBDD的转化算法；然后，研究可修SFE发生的条件以及失效时间边界约束特征，参考机械可靠性的广义应力-强度干涉模型，建立可修SFE发生概率的求解模型。本项目将为可修DFT的快速计算提供理论和方法指导，具有较强的科学意义，所提方法有利于解决大型动态系统的可靠性评估问题，具有一定的工程应用前景。

现代工业系统普遍存在时序失效行为，动态故障树（DFT）是对此类系统进行可靠性建模和分析的常用工具之一。可修DFT的现有计算方法因求解效率低而无法满足实践需求。本项目围绕解决可修DFT求解速度慢的技术难题，从DFT的结构特性和失效特性出发，并结合先进的可靠性理论和方法，建立了DFT精确的概率模型，研究并发展了一系列DFT快速分析方法，显著提升了DFT的建模精度和求解效率，实现复杂系统可靠性的精确且高效分析。. 本项目已经完成如下研究内容：1）可修DFT的失效机理以及快速数值模拟，建立了系统MTBF、MTTR、设备失效关键重要度指标IFC统计量表达式；2）含可修DFT的两阶段任务系统可靠性建模和计算，构建了一种基于Markov的一体化数学模型和计算方法；3）DFT向顺序二元决策图（Sequential Binary Decision Diagram, SBDD）的转化方法，发展一种DFT向SBDD转化的强化连接规则，并在连接的过程中发展了一种启发式的连接机制；4）基于生存标签理论的DFT快速分析方法，发展了基于系统生存标签的DFT解析求解模型和数值模拟方法；5）考虑启动时间和启动失效的核电厂冷冗余系统可靠性数值模拟，建立耦合设备启动时间和启动失效的冷冗余系统可靠性数学模型，发展了一套考虑启动时间和启动失效的核电厂冷冗余系统可靠性数值模拟方法；6）DFT在核能系统可靠性和事故风险评价中的应用研究。. 本项目共发表学术论文10篇，其中高水平论文5篇。申请国家专利1项，软件著作权1项，培养博士生2名、硕士生1名。成果已经在中广核工程有限公司等单位获得初步应用。