7th World Congresses of Structural and Multidisciplinary Optimization

1. Abstract For the performance measure approach (PMA) of RBDO, a transformation between the input random variables and the standard normal random variables is required to carry out the inverse reliability analysis. Since the transformation uses the joint cumulative density function (CDF) of input variables, the joint CDF should be known before carrying out RBDO. In many industrial RBDO problems, even though the input random variables are correlated, they are often assumed to be independent because only marginal distribution and covariance are practically obtained and the joint CDF is very difficult to obtain. With the assumption of independent input variables, it is easy to construct the joint CDF, and Rosenblatt transformation, which transforms the conditional CDF of input variables into the standard normal distribution, has been used for RBDO. However, when input variables are correlated, Rosenblatt transformation cannot be directly used because it is hard to obtain the joint CDF of correlated variables. On the other hand, Nataf transformation can be used for correlated input variables because it only requires marginal distribution and covariance. However, since Nataf transformation uses Gaussian copula, which joins multivariate normal and marginal distributions, it cannot be used for input variables with non-Gaussian joint distribution. In this paper, a new transformation that uses a non-Gaussian copula, such as Clayton copula, as the joint CDF of correlated input variables, which is then followed by Rosenblatt transformation, is proposed for non-Gaussian correlated variables. In addition, it is shown that the correlation coefficient between input variables significantly affect RBDO results and different transformations such as Nataf transformation using Gaussian copula and the new transformation using non-Gaussian copula (Clayton copula) provide different RBDO results.