Dimension Reduction Method-Based RBDO for Dependent Interval Variables

Abstract

Reliability-based design optimization (RBDO) under epistemic uncertainty (i.e., imprecise probabilistic information), especially in the presence of dependency of input variables, is a challenging problem. In this paper, we propose a dimension reduction-based RBDO framework considering dependent interval variables, which is pursued in a purely probabilistic manner. Most probable point (MPP) based dimension reduction method (DRM) is used for reliability evaluation due to its ability to circumvent the shortcomings of poor approximation by first order reliability method (FORM) and pronounced computational complexity by second order reliability method (SORM). For modeling correlation of input variables, copula is used instead of true joint cumulative density function (CDF). A flexible Johnson family of distributions is used to handle the stochastic but poorly known epistemic uncertainty. In order to handle the uncertainty in correlation measures, arisen due to interval data, expert suggested bounds of correlation measures have been recommended. For the overall RBDO problem, a decoupled approach to optimization is explored. Two numerical examples — one mathematical problem and one engineering problem — have been solved to properly explicate the proposed RBDO process. It is demonstrated that correlations in input variables have significant impact on the optimal design solutions.