An Improved Sobol Sensitivity Analysis Method

Abstract

The Sobol method is a variance-based global sensitivity analysis method that evaluates single-input and multiple-input interaction effects by calculating the contribution of a single input to the output variance and the contribution of multiple inputs to the output variance. The Sobol method requires each input to obey a uniform distribution of U [0,1], but it is difficult to meet the requirements in practice. Taking the sum function as an example, this paper analyzes the inapplicability of the existing Sobol method when the input does not obey the uniform distribution U [0,1]. To solve the inapplicability of the Sobol method and broaden the application scope, an improved Sobol sensitivity analysis method is proposed. First, the effect of the joint probability density function not 1 on sensitivity calculation is studied; second, the input parameters are changed to uniform distribution U [0,1] through variable substitution; finally, a complete algorithm model is presented and logical sensitivity analysis results are obtained. Application verification shows that the improved Sobol method is more scientific, applicable and practical.