Probability Propagation Method for Reliability Assessment of Acyclic Directed Networks

Abstract

Many civil infrastructure systems that deliver resources from source points to sinks, e.g., power distribution and gas pipeline networks, can be described as acyclic directed networks comprising nodes and links. Reliability assessment of these systems can be challenging, particularly for systems of increasing size and complexity and if the probabilities of rare events are of interest. This paper proposes a new analytical probability propagation method for reliability assessment of acyclic directed networks called the directed probability propagation method (dPrPm). Through a link-adding sequence to propagate a message consisting of the marginal and pairwise node reliabilities from source nodes to sink nodes, the method results in the upper and lower bounds of all sink node reliabilities. Reliability of a sink node is measured by the probability of reaching that node from a source node. Compared with previous methods, dPrPm addresses the case of multiple-sink networks, results in guaranteed reliability bounds, and analyzes acyclic directed networks as relevant for infrastructure systems. Proofs are provided guaranteeing the accuracy of dPrPm, and computation time is significantly reduced from typical exponential increases with system size to a polynomial increase. To assess performance, the proposed method was applied to three test applications: a directed grid network, a power distribution network, and a more complex gas pipeline network under seismic hazard. Results were compared with the exact solution and Monte Carlo simulations to evaluate accuracy and computational cost. Results showed that dPrPm performs equally well in terms of accuracy across network reliabilities and achieved order-of-magnitude increases in computational efficiency to obtain exact bounds on reliability assessments at all system sink nodes.