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

TLDR

Resilience refers to a system’s capacity to withstand stressors, adapt, and recover quickly, yet quantifying resilience from recovery curves and building a rigorous mathematical model remain major challenges. The study proposes a mathematical framework that quantifies resilience via partial descriptors called resilience metrics and introduces a reliability‑based definition of damage levels for probabilistic analysis. A stochastic formulation models the influence of recovery actions and disruptive shocks on system state, and is illustrated by applying it to a fiber‑reinforced polymer‑repaired reinforced concrete bridge. The resilience metrics are simple, clearly interpretable, and general enough to characterize resilience for any recovery curve.

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.