Approximate reliability-based optimization using a three-step approach based on subset simulation

A novel three-step approach is proposed to solve reliability-based optimization (RBO) problems. The new approach is based on a novel approach previously developed by the authors for estimating failure probability functions. The major advantage of the new approach is that it is applicable to RBO problems with high-dimensional uncertainties and with arbitrary system complexities. The basic idea is to transform the reliability constraint in the target RBO problem into nonprobabilistic one by first estimating the failure probability function and the confidence intervals using minimal amount of computation, in fact, using just a single subset simulation (SubSim) run for each reliability constraint. Samples of the failure probability function are then drawn from the confidence intervals. In the second step, candidate solutions of the RBO problems are found based on the samples, and in the third step, the final design solution is screened out of the candidates to ensure that the failure probability of the final design meets the target, which also only costs a single SubSim run. Four numerical examples are investigated to verify the proposed novel approach. The results show that the approach is capable of finding approximate solutions that are usually close to the actual solution of the target RBO problem.