Combining line sampling and saddlepoint approximation for reliability sensitivity analysis

Reliability and sensitivity analysis by line sampling for independent normal variables is extended for the reliability sensitivity analysis involving correlated variables. The line sampling combining saddlepoint approximation reliability sensitivity analysis method, named as saddlepoint approximation based line sampling method, is presented. It is suitable for structural system with a single failure mode and multiple failure modes involving correlated variables. Firstly, the correlated variables should be transformed into independent ones by using of the Copula theory. And then in the independent variables space, the extended line sampling can be implemented to obtain the reliability and sensitivity estimations. Finally, using the distribution parameters relationship among the correlated variables and the independent ones, the reliability sensitivity in the space of the correlated variables can be obtained by the chain rule of derivative. The results of the examples show that the presented method can efficiently obtain the approximate solution with high precision for structural system involving correlated variables.