High order properties of kernel functions and their application in sensitivity analysis

Sensitivity analysis can reflect how the distribution parameters of basic variables affect the failure probability and the distribution function of the structure or system output, and the kernel functions play a significant role in getting the sensitivities. So in order to obtain more accurate analytical results of the sensitivities, the high order properties of the kernel functions for the normal variables are derived. Based on the properties of the kernel functions and the relationship between the failure probability and the distribution function, and by taking a quadratic polynomial without cross-terms as an example of a performance function, the analytical sensitivity solutions of the failure probability and the distribution function are derived when considering the first forth-order moments. Comparing the numerical simulation results with the analytical results, it demonstrates that the forth-order moment method is more precise than the second-order method in sensitivity analysis, and that the derived analytical sensitivity expressions are correct, besides, it well shows good application of the proposed method.