Towards reliability evaluation involving correlated multivariates under incomplete probability information: A reconstructed joint probability distribution for isoprobabilistic transformation

Abstract

Reliability evaluation under incomplete probability information (prescribed marginal distributions and correlation coefficients) is a challenging task. The widely used Nataf transformation inherently assumes a normal copula for dependence modeling, which can be inappropriate in some cases. This paper aims to provide a more general isoprobabilistic transformation method for reliability evaluations under incomplete probability information. To this end, the joint probability distribution is represented using the pair-copula decomposition approach, which is highly flexible in dependence modeling. The desired pair-copula parameters are retrieved from the incomplete probability information by a simulation-based method. Finally, based on the reconstructed joint probability distribution, the Rosenblatt’s transformation is adopted for the subsequent reliability evaluation. The proposed method is illustrated in a tunnel excavation reliability problem. Several dependence structures characterized by different pair-copulas are investigated to provide insights into the effect of copula selection on reliability results.