An efficient variance-based global sensitivity analysis method based on multiplicative dimensional reduction method and Taylor series expansion

Abstract

In this study, the detailed derivation of unconditional and conditional statistical moments for calculating two variance-based global sensitivity indices is presented based on the multiplicative dimensional reduction method. Furthermore, an efficient calculation method for the statistical moment of performance function is proposed using Taylor series expansion, transforming it into a calculation of the statistical moment of random variable. Additionally, a recursive formula for the raw moment of normally distributed random variables is derived and a calculation formula for non-normally distributed random variables’ raw moment is provided. Finally, by combining the multiplicative dimensional reduction method with Taylor series expansion, two more effective methods are proposed for variance-based global sensitivity index. Compared with the reference method, the two proposed methods increase efficiency by 66.66% and 33.33%, respectively. The accuracy and efficiency of this approach are verified by a low-dimensional roof truss and a high-dimensional ten-bar truss structure in conjunction with finite element software. Moreover, its engineering application value is demonstrated by applying it to a high-dimensional complex hydraulic piping system containing 28 input variables.