Optimization of Bridge Maintenance Management Using Markovian Models

This paper presents a systematic approach for bridge maintenance management that combines a stochastic Markovian performance prediction model with a multi-objective optimization procedure to determine the optimal allocation of funds and prioritization of bridges for maintenance, repair and replacement (MR&R). The prioritization of the bridges is based on the satisfaction of several conflicting objectives simultaneously, including minimum bridge condition ratings, minimum MR&R costs, and maximum average daily traffic. The Markov chain model is a key component of this bridge management system, as it forecasts the future condition of the bridge network, thus enabling a reliable allocation of required MR&R funds. Highway bridges deteriorate with time as a result of aggressive environmental factors, increased traffic load, inadequate design, and lack of maintenance. The stochastic modeling of the bridge performance via a discrete Markov chain model captures the time-dependence, uncertainty and variability associated with condition ratings, resulting from deterioration and maintenance. The Markovian transition probability matrix can be estimated from the condition ratings data collected during the required biannual bridge inspections. The bridge maintenance management problem is formulated as a stochastic multi-objective optimization problem, where several conflicting objectives are simultaneously satisfied. The most relevant objectives include the minimization of the MR&R costs and maximization of the bridge network reliability or condition rating. Compromise programming, and specifically the minimum Euclidean distance criterion is used to determine the optimal ranking of the deteriorated bridges in terms of their priority for rehabilitation and replacement. This optimal ranking achieves a satisfactory tradeoff between the competing or conflicting objectives.