Reliability-Based Structural Design with Markov Decision Processes

Abstract

An optimal structural design is defined as the synthesis of a structural initial design and its maintenance/management policy over a design lifetime. Using a Markov decision process (MDP) model and structural reliability theory, a designer at the initial design stage is able to incorporate a reliability-based model of the lifetime process of the structure. The advantage of MDP is that it systematically characterizes the entire process, including decisions, costs, and system performance. It also provides a solution of this dynamic problem through a static method, thus retaining computational tractability. A long-term maintenance policy under the criterion of minimum expected lifetime cost can be found with respect to the chosen initial design, and used to select an optimum initial design to minimize cost and maintain acceptable reliability. For an existing structure, the approach gives a decision maker a future maintenance policy leading to identification of the minimum discounted expected future cost of the structure, based on its present condition, and maintains acceptable reliability.