Incorporating Uncertainty into the Resilience Analysis of Interdependent Critical Infrastructure: A System-Level Robustness Analysis

Critical Infrastructure (CI) are increasingly exposed to multi-hazard events that produce spatially correlated and multi-node failures, challenging traditional approaches to resilience assessment. This paper presents a system-level robustness analysis of interdependent critical infrastructures under uncertainty, using the Stochastic Dynamic Functional Model of Critical Infrastructure Interdependencies (S-DMCI-e). The framework integrates stochastic simulation, dynamic functional modelling, and network-based robustness metrics to evaluate the temporal evolution of system performance under complex disruption scenarios. The analysis is built upon Robustness Network Analysis (RNA), which assesses both structural and functional resilience under multi-node failures. The approach is applied to a multi-layer transportation network in the Milan Metropolitan Area, with a focus on the 2014 Seveso River flooding as a representative widespread (compound) hazard impacting numerous nodes simultaneously. Results reveal non-linear system responses, including tipping points and anomalous increases in global efficiency caused by network contraction following node failures. These "efficiency spikes" are shown to be counterintuitive indicators of local performance improvement and may instead serve as early-warning signals of systemic stress. The results show that resilience cannot be inferred from static or deterministic metrics alone and must be understood as a dynamic and probabilistic property of interdependent systems. The proposed approach supports stress testing, early-warning interpretation and robustness-oriented planning for urban infrastructures exposed to multi-hazard risks.

Keywords: Critical Infrastructure Resilience, Robustness Network Analysis, Stochastic simulation, Multi-Hazard