Robust design optimization by polynomial dimensional decomposition

This paper introduces four new methods for robust design optimization (RDO) of complex engineering systems. The methods involve polynomial dimensional decomposition (PDD) of a high‐dimensional stochastic response for statistical moment analysis, a novel integration of PDD and score functions for calculating the second‐moment sensitivities with respect to the design variables, and standard gradient‐based optimization algorithms. New closed‐form formulae are presented for the design sensitivities that are simultaneously determined along with the moments. The methods depend on how statistical moment and sensitivity analyses are dovetailed with an optimization algorithm, encompassing direct, single‐step, sequential, and multi‐point single‐step design processes. Numerical results indicate that the proposed methods provide accurate and computationally efficient optimal solutions of RDO problems, including an industrial‐scale lever arm design.