单调关联系统的矩阵化分析方法

A Matrix Method for Coherent System Analysis

概率安全分析是对复杂系统进行系统可靠性分析的有效方法,它的一个重要方面就是单调关联系统分析。单调关联系统分析的实质可归结为布尔表达式的演绎。矩阵运算在计算机上是易于实现的,因此,给出了析范矩阵的定义和运算规则,将布尔运算矩阵化,在此基础上又提出了扩展析范矩阵的概念和展开规则,并利用表达式的分析树,给出了单调关联系统的矩阵化分析方法。该方法已编程实现,被证明是快速、有效的,不仅适用于单调关联系统的静态分析,也适用于单调关联系统的动态实时仿真分析。

Probabilistic Security Assessment (PSA) is an efficient method for complex system analysis. The coherent system analysis is a key issue in PSA and is boolean expression deduction substantially. Matrix calculation can be realized easily in computer. This paper gives the definition of disjunctive normal formal matrix and its formulae, and boolean operation is changed to matrix form. Based on that, the concept of extended disjunctive normal formal matrix is presented. Then it presents the matrixing method using analysis tree for coherent system analysis. The method is put into practice by programming and shows good results. This method can be applied not only to coherent system static analysis, but also to coherent system dynamic real time simulation analysis.