Dual Graph-Based Bayesian Network Modeling With Rao-Blackwellization for Seismic Reliability and Complexity Quantification of Network Connectivity

Abstract

Modern societies depend on various lifeline networks such as transportation, electricity, and gas distribution systems, which are vulnerable to seismic events. Although numerous analytical and simulation-based methods have been developed for efficient seismic system reliability analysis (SRA), dealing with high-dimensional events arising from large-scale infrastructure networks remains challenging. To address this challenge, this paper proposes a system reliability method that efficiently computes the connectivity of directed graphs. The method employs the dual graph representation of a target system to automate the construction of a Bayesian network (BN). This enables the application of the junction tree algorithm, a well-established BN inference method, to perform reliability analysis and quantify complexity based on a network topology. The paper further tackles SRA challenges associated with fully correlated seismic uncertainties, which typically lead to a significant increase in computational complexity. To this end, we propose to combine a cross entropy-based adaptive importance sampling technique with Rao-Blackwellization. Thereby, sampling methods and exact analytical inference can be effectively combined to improve computational efficiency for seismic SRA of lifeline networks. The proposed methods are demonstrated through three numerical examples.