Resilience to Extreme Events: A Bayesian Nonparametric Approach

Abstract

Decision making about the management of infrastructure systems is based on models of cost, degradation, effectiveness of maintenance actions. These models can be informed by data collected in the past, and progressively updated as more data becomes available. While parametric models are suitable when an appropriate statistical form is assumed, non-parametric models provide a flexible alternative, which does not impose a specific pre-selected form. This paper investigates the use of non-parametric modeling in the emergency management of infrastructure systems after extreme events. We consider a Markov management process, and we introduce a nonparametric approach called infinite Markov decision process (iMDP), to perform adaptive control. The approach is made up by two parts. In the learning phase, we use a Bayesian iterative approach to update the model uncertainty, and a sampling approach to represent that posterior distribution. In the planning part, we adopt a myopic optimization scheme based on dynamic programming. The approach has the potential of enhancing system resilience, by the interaction between adaptive learning and planning under uncertainty. We apply the method to a small-scale numerical benchmark, and discuss its performance in that setting. This paper illustrates a preliminary investigation, and the performance analysis in more complex settings, or under alternative conditions, requires additional work.