Resilience analysis: A mathematical formulation to model resilience of engineering systems

Abstract

The resilience of a system is related to its ability to withstand stressors, adapt, and rapidly recover from disruptions. Two significant challenges of resilience analysis are to (1) quantify the resilience associated with a given recovery curve; and (2) develop a rigorous mathematical model of the recovery process. To quantify resilience, a mathematical approach is proposed that systematically describes the recovery curve in terms of partial descriptors, called resilience metrics. The proposed resilience metrics have simple and clear interpretations, and their definitions are general so that they can characterize the resilience associated with any recovery curve. This paper also introduces a reliability-based definition of damage levels which is well-suited for probabilistic resilience analysis. For the recovery modeling, a stochastic formulation is proposed that models the impact of recovery activities and potential disrupting shocks, which could happen during the recovery, on the system state. For illustration, the proposed formulation is used for the resilience analysis of a reinforced concrete (RC) bridge repaired with fiber-reinforced polymer.