Reliability-Based Optimization for Maintenance Management in Bridge Networks
This dissertation addresses the problem of optimizing maintenance, repair and reconstruction decisions for bridge networks. Incorporating network topologies into bridge management problems is computationally difficult. Because of the interdependencies among networked bridges, they have to be analyzed together. Simulation-based numerical optimization techniques adopted in past research are limited to networks of moderate sizes.
In this dissertation, novel approaches are developed to determine the maintenance policies that best balance network performance and agency cost. For two different types of networks, two performance metrics are adopted, and the research is divided into two parts accordingly.
The first part focuses on moderate-size networks with limited redundancy. The network performance is quantified by a graph-theoretic indicator of network connectivity, since connectivity is the fundamental service function of a network. The objective is to ensure an adequate level of network connectivity at the lowest possible life-cycle maintenance cost. A novel two-stage approach is developed, which makes it possible to solve the problem by using standard optimization tools (with guaranteed convergence to optimality), as opposed to the heuristic algorithms used in related literature.
The second part studies large and redundant networks, and the network performance is quantified by the total user costs due to potential bridge failures. The objective is to minimize the total user costs, specifically, the extra travel distance over a planning horizon and under a budget constraint. It is conjectured and then verified that the expected increase in vehicle-miles travelled due to failures can be approximated by the sum of expected increases due to individual failures. This allows the network-level problem to be decomposed into single-bridge problems and tackled efficiently. The computational effort increases linearly with the number of bridges.