A new global sensitivity measure based on the elementary effects method

Abstract

In the class of global sensitivity analysis methods, the elementary effects method focuses on identifying a few significant input parameters in a mathematical or engineering model including numerous input parameters with very few calculations. It was proved that the sensitivity index based on the elementary effects method is an appropriate proxy of the total sensitivity index based on the variance-based method. Nevertheless, it should be pointed out that two variance-based indices, i.e., the first-order and total sensitivity index, can denote the first-order and total effect of each input parameter to the model output respectively, while the elementary effects based sensitivity index can only reflect the total contribution of the input parameter to the model output, but cannot distinguish this effect resulting from each input parameter alone or the interactions between this input parameter and the others. Therefore, this paper proposes a first-order sensitivity index based on the elementary effects method by employing the high dimensional model representation. Next, the link between the first-order sensitivity index on the variance-based method and the proposed sensitivity index is explored. Subsequently, three computational algorithms, i.e., Monte Carlo simulation method, sparse grid method and dimensional reduction method, are developed to estimate the proposed sensitivity index.