Reduction of Ordering Effect in Reliability-Based Design Optimizatioin Using Dimension Reduction Method

Abstract

In reliability-based design optimization problems with correlated input variables, a joint cumulative distribution function needs to be used to transform the correlated input variables into independent standard Gaussian variables for the inverse reliability analysis. To obtain a true joint cumulative distribution function, a very large number of data (if not infinite) needs to be used, which is impractical in industry applications. In this paper, a copula is proposed to model the joint cumulative distribution function using marginal cumulative distribution functions and correlation parameters obtained from samples. Using the joint cumulative distribution function modeled by the copula, the transformation and the first-order reliability method can be carried out. However, the first-order reliability method may yield different reliability analysis results for different transformation ordering of input variables. Thus, the most probable-point-based dimension reduction method, which is more accurate than the first-order reliability method and more efficient than the second-order reliability method, is proposed for the inverse reliability analysis to reduce the effect of transformation ordering.