Sensitivity Analysis of Interdependency Parameters Using Probabilistic System Models

Comprehensive models of infrastructure networks feature many parameters characterizing the complex interdependencies that exist between systems. Most of these parameters are uncertain. Conducting sensitivity analyses is one way to characterize uncertainty in estimations of system-level performance based on component and interdependency parameters. Doing so provides an assessment of the importance of varying parameters and informs how to achieve targeted system outcomes through componentand system-level changes. To do this over interdependent infrastructure networks, we conduct inference over probabilistic Bayesian network-based models of these systems. We have developed a framework along with accompanying algorithms to conduct computationally tractable exact inference over the network model. Through a series of these analyses, we are able to analyze the impacts of changes in parameters on estimations of system-level performance. We apply the framework to a water distribution system including its dependencies with power and transportation networks. The results of the analyses show the effect of varying system parameters on probabilities of providing service across the network. We investigate the impacts on system performance of adding redundant power supplies, changing link configurations, and increased or reduced probabilities of component failures. The use of the sensitivity analysis results to support performance-based design based on system-level reliability measures is discussed. Infrastructure systems are increasingly connected, with interdependencies between them often governing their performance and leading to increased vulnerabilities to cascading failures (Buldyrev et al. 2010). Previously, we defined three generalized, comprehensive infrastructure interdependency types (Johansen and Tien 2017), advancing upon previous work in interdependency analysis (e.g., Rinaldi et al. 2001) to include parameters affecting the recovery and resilience of infrastructure networks. Comprehensive models of infrastructure networks feature many parameters characterizing the complex interdependencies that exist between systems. Most of these parameters are uncertain. Conducting sensitivity analyses is one way to characterize uncertainty in estimations of system-level performance based on component and interdependency parameters. Doing so provides an assessment of the importance of varying parameters and informs how to achieve targeted system outcomes through componentand system-level changes. Prioritizing varying changes supports effective decisions to increase resilience of interdependent systems (Johansen et al. 2016, Ouyang 2016). In this paper, we conduct these analyses for interdependent infrastructure networks by performing inference over probabilistic Bayesian network-based models of these systems. We utilize a previously proposed framework for probabilistic vulnerability of interdependent 13 International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP13 Seoul, South Korea, May 26-30, 2019 2 infrastructure systems and its accompanying algorithms to conduct computationally tractable exact inference over the network model (Applegate and Tien 2019). Through a series of these analyses, we are able to analyze the impacts of changes in parameters on estimations of system-level performance. We apply the framework to a water distribution system including its dependencies with electrical power and transportation networks to illustrate the approach. We investigate the impacts on system performance of adding redundant power supplies, changing link configurations, and increased or reduced probabilities of component failures. The results of the analyses show the effect of varying system parameters on probabilities of providing service across the network. We conclude with a discussion of the use of the sensitivity analysis results to support performance-based design based on system-level reliability measures. 1. PROBABILISTIC SYSTEM MODEL AND APPLICATION To model the infrastructure network, we represent each component in the network as a node and the connections between them as links. With the connectivity and dependency relationships defined, we build the Bayesian network model of the interdependent system. The Bayesian network is a probabilistic graphical model that enables us to capture the uncertainties in the infrastructure system parameters, including uncertainties in the hazards a system is exposed to, individual component performance under hazards, and propagation to system-level responses. We define and capture three interdependency types: service provision interdependencies, where the functioning of one component depends on a service provided by a component in another system; geographic interdependencies, where components are more likely to fail together under a hazard due to geographic proximity or physical similarity; and access for repair interdependencies, where the ability of a failed component to be repaired depends on physical or cyber access provided by a component in another system. The application network of interest is the City of Atlanta water distribution system located in the state of Georgia, USA, including its dependencies with power and transportation networks. Figure 1 shows the distribution system, where smaller solid circles indicate endpoint distribution nodes and larger empty circles indicate water supply nodes. As the water supply components require electrical power to operate the treatment plants and pumping stations located at these nodes, the power supply components are also located at these nodes. Figure 1: Water distribution system and power supply dependencies for application A representation of the probabilistic Bayesian network model that is built for this system is shown in Figure 2. Hazards are included to capture the geographic interdependencies. The reliance of water supply components on power supply components to function captures the service provision interdependencies. In Figure 2, MLS indicates the minimum link sets for the system. These provide the minimum paths required to be functioning to transport the infrastructure Application To demonstrate the proposed framework and our approach, we applied it to the interdependent water and power distribution networks in Atlanta, Georgia. We modeled the system and performed inference on the network using the model. We validated the methodology by comparing the results from inference using the constructed model to a real-world scenario in which a power outage led to cascading failures in the water system.