Predicting the Condition Evolution of Controlled Infrastructure Components Modeled by Markov Processes

Abstract

When the operation and maintenance (O&M) of infrastructure components is modeled as a Markov Decision Process (MDP), the stochastic evolution following the optimal policy is completely described by a Markov transition matrix. This paper illustrates how to predict relevant features of the time evolution of these controlled components. We are interested in assessing if a critical state is reachable, in assessing the probability of reaching that state within a time period, of visiting that state before another, and in returning to that state. We present analytical methods to address these questions and discuss their computational complexity. Outcomes of these analyses can provide the decision makers with deeper understanding of the component evolution and suggest revising the control policy. We formulate the framework for MDPs and extend it to Partially Observable Markov Decision Processes (POMDPs).