Fuzzy multi-outputs global sensitivity analysis based on LSSVRM

Abstract

This paper presents a global sensitivity analysis method based on fuzzy credibility theory to identify the impact of input variables on the output performance, and the difference between unconditional and conditional uncertainty distributions of the output is quantified by the Euclidean distance of statistical characteristics (expected value and standard deviation). Within the overall range, the global sensitivity indexes of input variables are defined by the best non-fuzzy performance value and then normalized. In addition, a double-loop fuzzy simulation is used to estimate the statistical characteristics. Since the actual process usually involves many output performances, this article utilizes the two reference points in the technique for order preference by similarity to an ideal solution (TOPSIS) to extend the single-output global sensitivity to multi-outputs global sensitivity, and uses the adaptive least squares support vector regression machine (LSSVRM) as a substitute model to determine the comprehensive priority of input variables. To prove the rationality of the fuzzy global sensitivity index and the accuracy of the hybrid algorithm, linear and nonlinear examples are used in the analysis. This paper provides a useful tool for complex industrial processes, especially time-consuming research objects, to find key input variables and reduce the difficulty of research problems.