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

Abstract

Resilience of engineering systems is related to their ability of absorbing both gradual and abrupt changes under exposure conditions and rapidly recover from disruptions. In this thesis, we develop a general stochastic formulation to model the recovery process and quantify system's resilience. In particular, we develop models for time-dependent capacity of a system and the imposed demand, under joint effects of recovery and shock deterioration processes. Using the developed models, a recovery curve is formulated in terms of system's reliability, functionality and work progress. Furthermore, we propose a novel approach for resilience analysis by defining measures to capture characteristics of recovery curves. The proposed approach makes a distinction in resilience of systems with different recovery patterns. A numerical example is provided to illustrate the application of the model.