A global sensitivity analysis method based on ANOVA with convex set model and its state-dependent parameter solution

Abstract

Convex set model is most widely applied around nonprobabilistic uncertainty description. This paper combines the convex model with global sensitivity analysis theory of variance, and then proposes an index based on convex set model and variance-based global sensitivity analysis method to illustrate the effect of the nonprobability variables on the dangerous degree. The proposed index consists of two parts, including the main and total indices. The main index can quantitatively reflect the effect of uncertainties of input variables on the variance of output response, and the total index reflects the influence of interaction with other variables in addition to the individual influence of input variables. Furthermore, an efficient state-dependent parameter solution for solving the variance-based global sensitivity analysis of nonprobabilistic convex uncertainty is given in this paper. The state-dependent parameter solution not only greatly improves the efficiency but also guarantees the computational accuracy, and the times of performance functions evaluation decrease from ${10}^6$ in single-loop Monte Carlo solution to 2048 in the state-dependent parameter method. Finally, three numerical examples and a finite element example are used to verify the feasibility and rationality of the proposed method.