Determination of Markov Transition Probabilities to be Used in Bridge Management from Mechanistic-Empirical Models

# Determination of Markov Transition Probabilities to be Used in Bridge Management from Mechanistic-Empirical Models

- Lethanh, N., Hackl, J., and Adey, B. T. (2017). Determination of Markov
Transition Probabilities to be Used in Bridge Management from
Mechanistic-Empirical Models.
*Journal of Bridge Engineering*, 22(10). doi: 10.1061/(ASCE)BE.1943-5592.0001101

## Abstract

Many bridge management systems use Markov models to predict the future deterioration of structural elements. This information is subsequently used in the determination of optimal intervention strategies and intervention programs. The input for these Markov models often consists of the condition states of the elements and how they have changed over time. This input is used to estimate the probabilities of transition of an object from each possible condition state to each other possible condition state in one time period. A complication in using Markov models is that there are situations in which there is an inadequate amount of data to estimate the transition probabilities using traditional methods (e.g., due to the lack of recording past information so that it can be easily retrieved, or because it has been collected in an inconsistent or biased manner). In this paper, a methodology to estimate the transition probabilities is presented that uses proportional data obtained by mechanistic-empirical models of the deterioration process. A restricted least-squares optimization model is used to estimate the transition probabilities. The methodology is demonstrated by using it to estimate the transition probabilities for a reinforced concrete (RC) bridge element exposed to chloride-induced corrosion. The proportional data are generated by modeling the corrosion process using mechanistic-empirical models and Monte Carlo simulations.