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.

Modeling the resilience of critical infrastructure: the role of network dependencies

“…They not only contribute – through cascading effects – to widespread failure propagation, but also to the smoothness or difficulty of the entire recovery process. The recovery rate of system components depends upon several factors that are often difficult to understand, model, and predict, as for example the recovery strategy and the amount, rate and prioritization of resource mobilization (Bruneau et al, 2003; Franchin & Cavalieri, 2015; Jia et al, 2016; Sharma et al, 2016). It may be impractical and unnecessary to model every infrastructure system within a community fully capturing every physical and societal factors during the recovery.…”

“…Examples of restoration functions can be found in the literature either postulated (e.g. Ayyub, 2014; Bocchini et al, 2012; Cimellaro et al, 2010; Titi et al, 2015) or derived based on more fundamental recovery activities (Sharma et al, 2016). The state of system damage, functionality, and operational values is updated and used for the next time step, taking into account interand intra-system dependencies.…”

“…The concept of resilience is often measured using dimensions of vulnerability, severity of consequences, and time to recover from failures (Bruneau et al, 2003; Sharma et al, 2016). Extensive work has been conducted on the modeling of individual networks (e.g.…”

Stochastic procedure for the simulation of synthetic main shock‐aftershock ground motion sequences

“…They showed that seismic degradation significantly increases structures' vulnerability. Recent progress in life cycle analysis and resilience analysis confirm these results . Zhai et al investigated the input energy spectra of main shock‐aftershock (MS‐AS) sequences for inelastic single‐degree‐of‐freedom (SDOF) systems and concluded that the effects of aftershocks on the input energy are significant in almost the whole period region.…”

“…Recent progress in life cycle analysis and resilience analysis confirm these results. [14][15][16][17][18] Zhai et al 19 investigated the input energy spectra of main shock-aftershock (MS-AS) sequences for inelastic single-degree-of-freedom (SDOF) systems and concluded that the effects of aftershocks on the input energy are significant in almost the whole period region. Therefore, over time, structures can be progressively damaged by aftershocks, which leads to a higher probability of structural failure than when considering the main shock only.…”