Global sensitivity evolution equation of the Fréchet-derivative-based global sensitivity analysis

For stochastic dynamical systems with multiple uncertain parameters, it is often of interest to detect which parameters are dominant, in which the global sensitivity analysis may be one of the common means. To measure the global sensitivity in both qualitative and quantitative terms, it is of significant importance to adopt a global sensitivity index with sufficient quantification information. The Fréchet-derivative-based global sensitivity index (Fre-GSI) proposed by Chen et al. (2020) is appropriate to this goal. The present paper aims to provide new aspects of the Fre-GSI, including: (1) The numerical solution of the Fre-GSI given by Chen et al. (2020) is investigated in both analytical and numerical aspects; (2) A novel global sensitivity evolution equation is derived from the generalized density evolution equation, thus the Fre-GSI can be estimated by directly solving the global sensitivity evolution equation, rather than repeatedly solving the generalized density evolution equation as suggested in Chen et al. (2020). Numerical examples are studied to illustrate the efficiency and accuracy of the proposed approach. Some problems to be further studied are also outlined.