利用贝叶斯网络(Bayesian network,BN)的不确定性推理和图形化表达的优势,提出一种基于BN的多状态系统可靠性建模与评估的新方法,确定BN的结点及系统各元件的多个状态,并给出各状态的概率,进而用概率分布表(Conditional probability distributing,CPD)描述元件各状态之间的关系来表达关联结点的状态,建立多状态系统BN模型。该模型表达直观,能够清晰地表示系统和元件的多种状态以及状态概率,并能够根据元件多种状态概率直接计算系统可靠度,对多状态系统可靠性进行定性分析和定量评估。实例分析表明了应用BN方法进行多状态系统可靠性评估的有效性。
The generating function approach is an important tool for performance assessment in multi-state systems. Aiming at strength reliability analysis of structural systems, generating function approach is introduced and developed. Static reliability models of statically determinate, indeterminate systems and fatigue reliability models are built by constructing special generating functions, which are used to describe probability distributions of strength (resistance), stress (load) and fatigue life, by defining composite operators of generating functions and performance structure functions thereof. When composition operators are executed, computational costs can be reduced by a big margin by means of collecting like terms. The results of theoretical analysis and numerical simulation show that the generating function approach can be widely used for probability modeling of large complex systems with hierarchical structures due to the unified form, compact expression, computer program realizability and high universality. Because the new method considers twin loads giving rise to component failure dependency, it can provide a theoretical reference and act as a powerful tool for static, dynamic reliability analysis in civil engineering structures and mechanical equipment systems with multi-mode damage coupling.
ZHOU JinYu1 & XIE LiYang2 1 Jiangsu Teacher’s University of Technology, Changzhou 213001, China
