A Bayesian Approach for Inferring the Topology of a System of Interdependent Infrastructure Networks: A Case Study of the U.K. Interdependent Power-Gas System

Abstract

Understanding the behavior of complex systems is essential to plan for future disasters that impact complex systems including infrastructure, social, and environmental systems. The complexity of the behavior of these systems is often the result of uncertain and dynamic interactions that are difficult to capture with traditional simulation and computational methods. These interactions are characterized by system interdependencies between multiple networks, and modeling them is essential to evaluate vulnerability and plan for resilience of these systems. Such information allows operators to understand the behavior of complex systems of interdependent networks under disruption (e.g., anticipating cascading effects) and better assess their performance. However, this information is not available for all types of systems and networks. To address this issue, we propose a Bayesian approach to infer interdependencies between networks based on cascading failure data. While this study focuses on systems of infrastructure networks, the method is generalized and can be applied across other types of networks (e.g., social and environmental).

Our proposed approach utilizes a hierarchical stochastic block model to generate the initial networks along with their corresponding prior probability and employs the susceptible-infectious epidemic spreading model to calculate the likelihood of the observed cascading failure sequence. We use Metropolis-Hastings algorithm with the proposal designed specifically for interdependent infrastructure networks, the infrastructure-dependent proposal, to obtain the posterior distribution of network topology. A heatmap of the adjacency matrix is used to validate our approach by evaluating the topological similarity between the reconstructed networks and the real network.

A case study on inferring the topology of a synthetic system of the U.K. interdependent power-gas system is conducted to demonstrate the effectiveness of our approach in reconstructing the topology of interdependent infrastructure networks. This paper devises a probabilistic estimation of network topology based on the cascading failure of interdependent infrastructure networks, which can inform the design, risk assessment, and restoration of interdependent infrastructure networks.