A new global sensitivity measure based on derivative-integral and variance decomposition and its application in structural crashworthiness

For the traditional variance-based global sensitivity analysis, the total effect of individual variable commonly involves the interactions with other variables. To further decompose the interactive effects, this paper proposes a new global sensitivity measure based on derivative-integral and variance decomposition. Firstly, the first-order sensitivity index only relating to individual variable and the high-order sensitivity indices involving with other interactive variables are analyzed through analysis of variance (ANOVA) representation. Then, the partial derivatives of high-order interaction terms of ANOVA representation with respect to individual variable and the integrals of the squares of partial derivative functions are calculated in the whole variable space. Consequently, to measure the contribution of individual variable to each high-order interaction term, the ratio of the square root of each integral to their sum is defined as the sensitivity weight factor. A high-order sensitivity index can be further decomposed into a series of sensitivity sub-indices by using the defined sensitivity weight factors. Accordingly, a new global sensitivity measure for individual variable is proposed by combining the first-order sensitivity index with the decomposed sensitivity sub-indices. Finally, three numerical examples and an engineering application are investigated to demonstrate the reasonability and superiority of the proposed sensitivity measure.