基于网络缩简的K-剩余连通可靠度的蒙特卡洛方法

Monte Carlo Method for K-Residual Connectedness Reliability Based on Reliability Preserving Reductions

讨论了具有不可靠结点网络的可靠度估计问题,提出了具有不可靠结点K-终端网络的串并联缩简原则,并将该缩简原则应用于递归方差衰减(Recursive Variance Reduction,RVR)蒙特卡洛(Monte Carlo)方法中,得到一种无偏且高效的估计可靠度的方法.该方法是依据状态空间分解原理,将对原状态空间的抽样实验递归地转为对其子空间的实验,并且在对子空间抽样实验前进行网络缩简,使得有些子空间不用抽样,对应方差为0.最后,通过实验验证了算法的有效性.

Discusses the estimate of reliability of a network with unreliable nodes. Proposes the principle on which the reduction is available to the K-terminal networks with unreliable nodes in series/parallel. Applying the principle to the Monte Carlo method with RVR （recursive variance reduction）, an unbiased and efficient reliability estimating method is obtained, which depends on the decomposition of state space and reduces recursively the sampling test in original state space to that in subspace. Before the sampling test in subspace, reliability preserving reductions are performed so as to enable some sampling action not to be done in subspace with corresponding variance to be 0. The validity of the algorithm is verified by testing results.