Reliability-based Design Optimization by a Univariate Decomposition Method

Abstract

This article presents a new univariate decomposition method for design sensitivity analysis and reliability-based design optimization of mechanical systems subject to uncertain performance functions in constraints. The method involves a novel univariate approximation of a general multivariate function in the rotated Gaussian space for reliability analysis, analytical sensitivity of failure probability with respect to design variables, and standard gradient-based optimization algorithms. In both reliability and sensitivity analyses, the proposed effort has been reduced to performing multiple onedimensional integrations. The evaluation of these one-dimensional integrations requires calculating only conditional responses at selected deterministic input determined by sample points and Gauss-Hermite integration points. Numerical results indicate that the proposed method provides accurate and computationally efficient estimates of the sensitivity of failure probability, leading to accurate design optimization of uncertain mechanical systems.