Reliability analysis and importance measure analysis of basic variables based on Copula under incomplete probability information

For engineering reliability problem under incomplete probability information, Copula theory is employed to approximate joint distribution function and joint probability density function of basic variables, on which an adaptive truncated sampling method is established to analyze the reliability and the importance measure about effect of the basic variables on failure probability. In the established model, the Spearman's correlation coefficient based model is used to describe the correlation part in the Copula function, and it is not restricted by marginal distribution function of the basic variable, and it's more practical than traditional Pearson correlation coefficient. The adaptive truncated sampling on the Copula approximation can compute the failure probability by use of the information from process of adaptively searching design point, as a result, the efficiency and the robustness of the reliability method are both enhanced. After the model concepts and the implementation are given, several examples are presented to demonstrate the rationality of the model and the feasibility of the solutions.