Analytical probability propagation method for reliability analysis of general complex networks

Abstract

Reliability analysis of complex networks is often limited by large and exponentially increasing computational requirements with system size. In this paper, a new approximated analytical method the authors call the probability propagation method (PrPm) is proposed to calculate the reliability of general complex networks. The proposed method originates from the idea of belief propagation for inference in network graphs to pass a joint probability distribution between nodes in the network. At each step, the distribution is updated and passed as the message to its direct neighbors. After the message passes to the terminal node, an approximation of the network reliability is found. In this paper, the derived updating rules for message passing are provided, as well as a precise formulation of the error compared to the exact solution. The method is applied to three test applications: an example from a previous study on network reliability, a power distribution network, and a general grid network. Results from these applications show high accuracy for the proposed method compared to exact solutions where possible for comparison. In addition, the authors show orders of magnitude increases in computational efficiency of PrPm compared to existing approaches. This includes reducing the computational cost for analyses from an exponential increase in computation time with the size of the system to a quartic increase. The proposed PrPm enables accurate and computationally tractable reliability assessments of larger, complex networks.