The Transform Method on self-adaptive radial-based importance sampling for reliability sensitivity analysis with corralated normal variables

For the reliability sensitivity estimation with correlated normal variables, the Transform Method (TM) based on Monte Carlo simulation has been established firstly through transforming the correlated normal variables into independent ones, and then, the variances have been analyzed in detail. Following, the TM is combined with a self-adaptive radial-based importance sampling (ARBIS) method for the reliability sensitivity analysis with correlated normal variables. Using the information provided by the required samples, the optimal radii of the ARBIS method can be determined by gradual iteration, which enables the robustness and the accuracy of ARBIS method to be improved greatly. Since the universality and the robustness of the Monte Carlo simulation and the high efficiency of the radial-based importance sampling are merged into the ARBIS-based TM, the established method is strongly applicable to highly non-linear implicit limit state equation, systems with multiple failure modes in series, in parallel or in mixed states, and the multiple Most Possible Points (MPP). The examples given in the paper show these advantages finally.