New spearman correlation based sensitivity index and its unscented transformation Solutions

For consideration of the wide applications of concordance and order information in global sensitivity analysis (SA), a new sensitivity index based on the spearman correlation coefficient (S-CC) is presented in this article. S-CC can reflect the linear order correlation between variables; thus the proposed sensitivity index can be used to measure the influence of input on the linear order of output. Then the main task becomes efficiently estimating the defined index. Here the authors introduce the basic unscented transformation (UT) to compute the index with high efficiency, and high order unscented transformation (HOUT) is also employed to further improve the computational accuracy. Several examples, including the commonly used Ishigami test function and other engineering examples, are used to demonstrate the validity of the proposed sensitivity index and the efficiency of the proposed UT-based methods.