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    动态故障树的不交化定量分析方法

    A Method of Disjoint Quantitative Analysis for Dynamic Fault Tree

    • 摘要: 动态故障树被广泛应用于动态系统的可靠性分析中,其中割序描述了系统的失效模式,割序集的不交化可以简化顶点失效概率的求解,目前还没有有效的适用于动态故障树的不交化定量分析方法.提出了一种不交化定量分析方法:在割序的基础上融入时序逻辑提出扩展割序的概念,其与以往类似概念相比增强了表达能力;根据基事集和时限集分解最小扩展割序集,将其转换成不交化扩展割序集;再将不交化扩展割序转换成标准扩展割序,然后对其各割项进行冲突检测、时限集精简、基事集拓扑排序,以对标准扩展割序进行量化计算;并对该方法所涉及到的算法进行了详细的证明和时间复杂性分析.最后将其应用到一个案例中,并同基于inclusion-exclusion规则的MCS方法进行了对比,实验结果显示该方法的时间开销明显降低.该方法可以获得动态故障树的不交化扩展割序集,降低求解时间开销.

       

      Abstract: Dynamic fault tree is widely used in the reliability analysis of dynamic system, where the cut sequence describes the failure mode of the system. Though the disjoint of cut sequence set can simplify the solving of top event failure probability, there is no available method of disjoint quantitative analysis that applies to the dynamic fault tree for the moment. A method of disjoint quantitative analysis is proposed. The conception of extended cut sequence is brought forward, which incorporates with the temporal logic based on cut sequence and has more representative capabilities than other similar conceptions. The extended cut sequence set is splited into the disjoint extended cut sequence set according to the basic event set and the temporal constraint set. The disjoint extended cut sequence is then transformed into the standard extended cut sequence. Conflict detection, reduction of temporal restriction set and topological sort of basic event set for each cut item, are carried out to quantitatively analyze each standard extended cut sequence. The involved algorithms and their complexities are particularly proved and analyzed. Finally this method is applied to a case and compared to the MCS method based on the rule of inclusion-exclusion. The result shows that the time cost of this method is greatly decreased. This method can obtain the disjoint extended cut sequence set of dynamic fault tree,and decrease the time cost of the solving.

       

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