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Critical infrastructure networks are becoming increasingly interdependent which adversely impacts their performance through the cascading effect of initial failures. Failing to account for these complex interactions could lead to an underestimation of the vulnerability of interdependent critical infrastructure (ICI). The goal of this research is to assess how important interdependent links are by evaluating the interdependency strength using a dynamic network flow redistribution model which accounts for the dynamic and uncertain aspects of interdependencies. Specifically, a vulnerability analysis is performed considering two scenarios, one with interdependent links and the other without interdependent links. The initial failure is set to be the same under both scenarios. Cascading failure is modeled through a flow redistribution until the entire system reaches a stable state in which cascading failure no longer occurs. The unmet demand of the networks at the stable state over the initial demand is defined as the vulnerability. The difference between the vulnerability of each network under these two scenarios is used as the metric to quantify interdependency strength. A case study of a real power-water-gas system subject to earthquake risk is conducted to illustrate the proposed method. Uncertainty is incorporated by considering failure probability using Monte Carlo simulation. By varying the location and magnitude of earthquake disruptions, we show that interdependency strength is determined not only by the topology and flow of ICIs but also the characteristics of the disruptions. This compound system-disruption effect on interdependency strength can inform the design, assessment, and restoration of ICIs. 

Abstract Modeling the resilience of interdependent critical infrastructure (ICI) requires a careful assessment of interdependencies as these systems are becoming increasingly interconnected. The interdependent connections across ICIs are often subject to uncertainty due to the lack of relevant data. Yet, this uncertainty has not been properly characterized. This paper develops an approach to model the resilience of ICIs founded in probabilistic graphical models. The uncertainty of interdependency links between ICIs is modeled using stochastic block models (SBMs). Specifically, the approach estimates the probability of links between individual systems considered as blocks in the SBM. The proposed model employs several attributes as predictors. Two recovery strategies based on static and dynamic component importance ranking are developed and compared. The proposed approach is illustrated with a case study of the interdependent water and power networks in Shelby County, TN. Results show that the probability of interdependency links varies depending on the predictors considered in the estimation. Accounting for the uncertainty in interdependency links allows for a dynamic recovery process. A recovery strategy based on dynamically updated component importance ranking accelerates recovery, thereby improving the resilience of ICIs.