Robust optimization based on a polynomial expansion of chaos constructed with integration point rules

Abstract

Robust optimization is a probabilistic approach to engineering design under uncertainty. The main idea is to select designs insensitive to changes in given parameters. Robust optimization using numerical simulations for black-box problems has received increasing interest. However, when the simulation programmes are computationally expensive, robust optimization is difficult to implement due to the intensive computational demand of uncertainty propagation. Based on polynomial chaos expansion (PCE), an efficient robust optimization method is presented. The PCE is constructed with points of monomial cubature rules (MCRs) to approximate the original model. As the number of points of MCRs is small and all of the points are sampled, the robust optimization procedure is computationally efficient and stable. Two engineering design problems are employed to demonstrate the availability of the proposed method.