New Decoupled Framework For Reliability-Based Design Optimization

Abstract

Traditionally, reliability-based design optimization (RBDO) has been formulated as a nested optimization problem. The inner loop, generally, involves the solution to optimization problems for computing the probabilities of failure of the critical failure modes, and the outer loop performs optimization by varying the decision variables. Such formulations are by nature computationally intensive, requiring numerous function and constraint evaluations. To alleviate this problem, researchers have developed iterative decoupled RBDO approaches. These methods perform deterministic optimization and reliability assessment in a sequential manner until a consistent reliability-based design is obtained. The sequential methods are attractive because a consistent reliable design can be obtained at considerably lower computational cost. However, the designs obtained by using these decoupled approaches cannot guarantee production of the true solution. A new decoupled method for RBDO is developed in this investigation. Postoptimal sensitivities of the most probable point (MPP) of failure with respect to the decision variables are introduced to update the MPPs during the deterministic optimization phase of the proposed approach. A damped Broyden‐Fletcher‐Goldfarb‐Shanno method is used to significantly reduce the cost of obtaining these sensitivities. It is the use of postoptimal sensitivities that differentiates this new decoupled RBDO approach from previous efforts.