网络可靠性评估的演化过程重要度抽样模拟方法

Evolution process based importance sampling model for network reliability evaluation

针对具有高可靠度网络的连通失效概率计算问题,提出了一种重要度抽样Monte Carlo模拟方法.首先提出了考虑节点和边单元失效网络连通状态判别的演化过程算法,算法根据网络节点和边单元的可靠度,将每次模拟抽样产生的随机数转化为单元的修复时间;按照单元修复时间次序构建网络连通拓扑结构,并视为向网络连通状态转变的演化过程.然后基于重要度抽样Mont,e Carlo模拟求解高可靠度网络的2\K\All端连通失效概率,其中重要度抽样函数的计算采用基于演化过程和交叉熵模型的多准则迭代方法.高可靠度网络算例的计算结果表明,预抽样求解重要度抽样函数时,多准则迭代方法所需的预抽样次数约为其他迭代方法的1/40.因此,本文方法具有较高的计算效率.

This paper describes an importance sampling Monte Carlo （MC） simulation model for the failure probability calculation of networks with high reliability. First, an evolution process algorithm for network connectivity judgment with imperfect nodes and arcs is proposed. Random numbers generated in each simulation were transformed into repair time of network elements （arcs and nodes） according to the elements＇ reliability. The network connectivity topology is constructed by the order of repair times, which is treated as the evolution process of network connectivity. Next, network failure probabilities of 2／K／All terminal problems are calculated by importance sampling Monte Carlo （ISMC） simulation. The importance sampling function of ISMC is evaluated by a multi-criteria iterative method based on the evolution process algorithm and cross entropy model. Finally, the proposed model is illustrated and tested by benchmark networks. Testing results of network with high reliability show that the number of iterations required by the multi-criteria iterative method is about one fortieth of that number of exist method when solving the importance sampling function. Therefore, the proposed model is efficient for networks models with high reliability.