Emulator model-based analytical solution for reliability sensitivity analysis

Sensitivity analysis is frequently considered an essential component in engineering design. In the design process of engineered structures, the output is implicitly related with the input variables. The Kriging model, one of the most commonly used emulator models, is sometimes used for structure analysis. In order to efficiently estimate the sensitivities of failure probability or statistical moments of performance function with respect to distribution parameters of input variables, the analytical solutions are derived based on the Kriging model. Generally, the Kriging model can be expressed as a tensor product basis function, thus the multivariate integrals can be decomposed into the sum of univariate integrals, which makes it possible to solve the sensitivity of statistical moments with respect to distribution parameters of normal input variables by the properties of kernel functions. Next, the fourth-moment reliability sensitivity method is applied to compute the sensitivity of failure probability analytically. Numerical and engineering examples are introduced to demonstrate the accuracy and efficiency of the derived analytical solution of sensitivity of failure probability.