A new method for reliability sensitivity analysis with correlative normal variables

Based on line sampling for reliability sensitivity in case of independent normal variables, a new reliability sensitivity analysis method is presented for the structure with correlative normal variables. In this method, the correlative normal variables are firstly transformed into independent normal variables equivalently. Then, the line sampling algorithm is employed to complete the reliability sensitivity of failure probability with respect to all distribution parameters in the space of equivalent independent variables. At last, by use of the distribution parameters relationship between the correlative normal variables and the independent normal variables, the reliability sensitivity of the failure probability with respect to all distribution parameters in the space of the correlative normal variables can be obtained by derivative formula of compound function. In order to investigate convergence and precision of the method, the variance and the variation coefficient of the reliability sensitivity estimation are derived. The results of the examples show that the presented method is accurate for the reliability sensitivity analysis of the linear limit states function with one sampling, and it can efficiently obtain the approximate solution with high precision for the non-linear limit function. The dependence of the variables can change the positive and negative sign of the reliability sensitivity of the failure probability with respect to the standard derivation of the variable, which is demonstrated by an example and is important for reliability design.