Time-inhomogenous Markov chains in the bridge management

Abstract

Available Bridge Management Systems vary in detail, but generally they comprise a deterioration model to predict condition development and a preservation optimization model to determine the optimum preservation policy. Time-homogenous Markov chains are commonly used to model condition development in the Bridge Management Systems. The popularity of Markov Chains in the Bridge Management is based on the ability to obtain preservation policies for each element using the Markov Decision Process. It was observed, compared with historical data, that stationary transition probabilities of Markov chains models have fairly rapid initial deterioration. Therefore, the dependency of transition probability on sojourn time in the best/initial condition state has been already modeled in literature with the Weibull survival function. However, the adoption of time-inhomogeneous Markov chains is hampered by mathematical complexity in determining the optimum preservation policy. Procedures for determination of optimum preservation policy time-inhomogeneous Markov chains are reviewed in this paper and recommendation for practical applications are given.