A Rosenblatt Transformation Method Based on Copula Function for Solving Structural Reliability

Abstract

Rosenblatt transformation is a general method for transforming a group of non-normal random variables into a group of equivalent independent normal random variables. However, this method is not suitable for the problem of unknown joint distribution function. In view of the above problems, the joint distribution function is constructed by the Copula function in this paper, and the transformation problem of correlation non-normal variables to independent normal variables is solved. Firstly, the Copula function is used to construct the joint distribution function of correlation variables. It includes the solution of Copula function correlation parameters and the selection of correlation structure types between variables. Secondly, the Copula function is introduced into Rosenblatt transformation to obtain the conditional distribution function of variables,. The correlation variables can be transformed into independent variables. Finally, the structural reliability problem with correlation random variables is analyzed. The feasibility of the proposed method is verified by the specific examples.