Societal risk and resilience analysis: A multi-scale approach to model the dynamics of infrastructure-social systems

The prosperity of modern societies and public well-being increasingly depend on critical infrastructure to enable the continuous flow of essential resources and services to communities. Infrastructure loss of functionality in the aftermath of hazards can disrupt regular residential and commercial activities, hinder emergency responses, and adversely impact the ability of communities to recover. The severity of consequences and the recovery progression can significantly vary among communities, depending upon the socio-economic characteristics and infrastructure functionality. The scarcity of resources and the ever-growing demand on infrastructure call for resilient infrastructure which are more reliable in the face of hazards and remain in service for longer period of time. However, the consequences of past disasters around the world have raised concerns about the vulnerability of existing infrastructure and highlighted the significance of risk mitigation and management. To leverage limited resources, the decision about risk mitigation and management should be informed by a comprehensive risk analysis. To do so, there is a need for 1) a theoretical framework that enables conceptualizing the connections among diverse consequences and distinguishing which ones are important and relevant to risk mitigation; 2) mathematical tools to translate the performance of infrastructure to the broad societal impact and the dynamics of society over time; and 3) a scalable and adaptable mathematical approach that can model the performance of infrastructure at different scales of space and time, subject to different hazards. For the reliability and serviceability analysis of infrastructure, the dissertation develops general probabilistic and stochastic models. The reliability analysis aims to estimate the probability that an extreme response of a system subject to a given hazard (i.e., its demand) meets or exceeds the respective capacity. Specifically, probabilistic predictive capacity and seismic demand models are developed for the reliability analysis of typical reinforced concrete bridges, retrofitted with fiber reinforced polymer composites. The formulation of the probabilistic predictive models builds upon the governing laws of physics/mechanics and exploits the information from computer simulations, laboratory tests, and field data. A Bayesian hierarchical inference is employed to account for the effects of statistical dependence of the training data on the estimate of model parameters and, thus, on the reliability estimate. Alternatively, when there is a need for a detailed analysis of a specific dynamical system subject to a stochastic excitation, the methods of random vibration analysis can be employed. The random vibration analysis aims to model the time evolution of the complete probabilistic response. The information from the complete probabilistic response can be used to estimate the probability of failure due to excessive accumulated damage and response instability, in addition to the reliability estimate. Furthermore, the random vibration analysis provides information about the serviceability of dynamical systems, such as the cumulative excursion duration and out-crossing rates. The dissertation developed a novel approach for the random vibration analysis of general nonlinear dynamical system, called a Dirichlet Process Mixture Model. The proposed approach uses the observational data from a limited number of simulations and the information available a priori to simplify and solve the nonlinear stochastic differential equations that govern the response of nonlinear dynamical systems. The reliability and random vibration analyses aim to estimate the physical damage to infrastructure and, thus, to determine the scope of the recovery due to a given hazard. The dissertation then develops a mathematical approach for the recovery modeling and resilience analysis of damaged infrastructure. The recovery of infrastructure components is modeled as a stochastic jump process that closely replicates the actual work progress. Analogous to the statistical moments of a random variable, resilience metrics are defined as the partial descriptors of the (predicted) recovery curve. The deterioration of infrastructure due to regular use and the occurrence of extreme events adversely impacts their reliability and resilience. A stochastic life-cycle formulation is developed that captures the effects of deterioration and recovery strategy on the reliability and resilience of infrastructure. The physical recovery of individual components are then integrated into a detailed schedule for the recovery of interdependent infrastructure. For a developed recovery schedule, network flow analyses are performed to model the recovery of disrupted services. The proposed approach is illustrated through a large-scale problem for the post-disaster recovery modeling of infrastructure in Shelby County, Tennessee. Successful risk mitigation and management cannot be limited to engineering considerations. A novel approach is proposed for the societal risk and resilience analysis, called a Reliability-based Capability Approach. The proposed RCA is a mathematical approach to translate the impact on infrastructure to the impact on the well-being of individuals, accounting for the available knowledge about the socio-economic characteristics and social vulnerability factors. The capability approach is the theoretical framework to conceptualize the connection among diverse consequences. The proposed approach develops a set of probabilistic models to predict the broad societal impact of hazards in terms of changes in dimensions of individuals’ well-being, called capabilities. The probabilistic models are used in a system reliability analysis to estimate the probability that the state of individuals’ well-being is above or below a desired level. To model societal recovery, the proposed approach integrates the recovery modeling of infrastructure and socio-economic characteristics into a time-dependent reliability analysis. To facilitate the probabilistic modeling, the time-dependent reliability analysis is implemented with a Dynamic Bayesian Network. Finally, the quantified risk and resilience are evaluated to provide insights about the severity levels of hazards. The proposed approach is explained through a real case study example to quantify the cascading impact of infrastructure disruptions