Subset simulation for non-Gaussian dependent random variables given incomplete probability information

Abstract

Reliability analysis under incomplete probability information is a challenging task. This paper focuses on the extension of the subset simulation (SS), an efficient reliability approach, to the modeling of any dependent random variables under incomplete probability information. The Nataf transformation is commonly adopted to generate correlated random variables given marginal distributions and correlations; however, it inherently assumes a Gaussian dependence structure. In contrast, the Rosenblatt transformation can be used to generate correlated random variables with any dependence structure; however, the joint probability information must be known. To remove the limitation, the vine copula approach, which is highly flexible in dependence modeling, is used to reconstruct the joint probability information from the prescribed marginal distributions and correlations. The copula parameters in the vine structure are retrieved using an efficient approximation method. Three copula cases including the Gaussian and non-Gaussian dependence structures are investigated by applying the proposed method to a numerical example. The failure probabilities and the effects of the uncertain parameters correspond to different cases are compared, which aims to provide insights into the impact of the dependence structure on the SS results when only the incomplete probability information is given.