Time-Dependent Probability of Exceeding a Target Level of Recovery

The resilience of a system is generally defined in terms of its ability to withstand external perturbations, adapt, and rapidly recover. This paper introduces a probabilistic formulation to predict the recovery process of a system given past recovery data and to estimate the probability of reaching or exceeding a target value of functionality at any time. A Bayesian inference is used to capture the changes over time of model parameters as recovery data become available during the work progress. The proposed formulation is general and can be applied to continuous recovery processes such as those of economic or natural systems, as well as to discrete recovery processes typical of engineering systems. As an illustration of the proposed formulation, two examples are provided. The paper models the recovery of a reinforced concrete bridge following seismic damage, as well as the population relocation after the occurrence of a seismic event when no data on the duration of the recovery are available a priori.