An efficient variance-based global sensitivity index based on C-DRM and Taylor expansion

Sensitivity analysis plays an important role in quantifying the impact of input uncertainty on model response uncertainty. Through sensitivity analysis, we can grasp the crucial parameters and gain a deeper understanding of the model behavior. In this paper, an effective analytical solution for solving the variance-based global sensitivity index is proposed. Firstly, the original performance function is approximated as the sum of a series of univariate functions using the conventional dimensional reduction method (C-DRM). Then, the Taylor series expansion is used to expand the univariate function as unary linear function and unary quadratic functions. Finally, the analytical solutions of the variance-based global sensitivity index based on unary linear function and unary quadratic functions are derived respectively. The computational cost of the proposed method is completely concentrated on the calculation of the partial derivative information of the performance function with respect to each variable. As long as the partial derivative information is obtained, the variance-based global sensitivity index can be obtained directly by the proposed method without any additional computational cost. For simple explicit performance functions, the derivative information can be directly derived analytically. For complex explicit or implicit performance functions, the derivative information can be estimated by some simple numerical difference methods. Five examples are studied to investigate the accuracy and efficiency of the proposed method.