MPP-Based Dimension Reduction Method for RBDO Problems with Correlated Input Variables

Abstract

In reliability-based design optimization (RBDO) problems with correlated input variables, a joint cumulative distribution function (CDF) needs to be obtained to transform, using the Rosenblatt transformation, the correlated input variables into independent standard Gaussian variables for the reliability analysis. However, a true joint CDF requires infinite number of data to be obtained, so in this paper, a copula is used to model the joint CDF using marginal CDFs and correlation parameters obtained from samples, which are available in practical applications. Using the joint CDF modeled by the copula, the transformation can be carried out based on the first order reliability method (FORM), which has been commonly used in reliability analysis. However, the FORM may yield different reliability analysis results with some errors for different transformation ordering of input variables due to the nonlinearities of differently transformed constraint functions. For this, the most probable point (MPP) based dimension reduction method (DRM), which more accurately and efficiently calculates the probability of failure than the FORM and the second order reliability method (SORM), respectively, is proposed to use to reduce the effect of transformation ordering in the inverse reliability analysis, and thus RBDO. To study the effect of transformation ordering on RBDO results, several numerical examples are tested using two different reliability methods, the FORM and DRM.