应用Petri网的关联矩阵求最小割集的新方法

A New Method to Identify Minimal Cut Sets Using the Incidence Matrix of Petri Nets

在应用Petri网模型构建系统故障逻辑关系图的基础上,提出了一种应用Petri网的关联矩阵求最小割集的算法。具体方法是在关联矩阵中按行、列查找所表达的输入、输出关系,直到找到基本事件,并将对应事件按"与"、"或"关系展开,这样可以直接从关联矩阵中得出割集,再按照布尔吸收律、等幂率或素数法求出最小割集。应用关联矩阵法求有重复事件Petri网模型的最小割集简单明了。进行了基于Visual C++6.0的算法程序编制,并通过了检验。通过对某舰艇防空系统故障最小割集的求解说明了求解过程并证明了该算法的正确性。

A method using incidence matrix of Petri net to identify the minimal cut sets（MCS） was proposed. This method can find CS according to the relationship among inputs and outputs implied in the incidence matrix, finally using Boolean absorption law, idempotent law, or prime law to get MCS. This method also shows its advantage when dealing with models containing repeatable events. The Visual C＋＋ code was developed and several examples were performed to test it. A naval vessels aerial defense system was also analyzed to show the process of this method and finally its validity was proved.