Information Reuse for Importance Sampling in Reliability-Based Design Optimization

This paper introduces a new approach for importance-sampling-based reliability-based design optimization (RBDO) that reuses information from past optimization iterations to reduce computational effort. RBDO is a two-loop process-an uncertainty quantification loop embedded within an optimization loop-that can be computationally prohibitive due to the numerous evaluations of expensive high-fidelity models to estimate the probability of failure in each optimization iteration. In this work, we use the existing information from past optimization iterations to create efficient biasing densities for importance sampling estimates of probability of failure. The method involves two levels of information reuse: (1) reusing the current batch of samples to construct an a posteriori biasing density with optimal parameters, and (2) reusing the a posteriori biasing densities of the designs visited in past optimization iterations to construct the biasing density for the current design. We demonstrate for the RBDO of a benchmark speed reducer problem and a combustion engine problem that the proposed method leads to computational savings in the range of 51% to 76%, compared to building biasing densities with no reuse in each iteration.