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.

对于具有多个不确定参数的随机动力系统，人们常常感兴趣的是检测哪些参数占主导地位，其中全局敏感性分析可能是常用手段之一。为了从定性和定量两个方面衡量全局敏感性，采用具有足够量化信息的全局敏感性指数具有重要意义。Chen 等人提出的基于 Fréchet 导数的全局敏感度指数（Fre-GSI）。（2020）适合这一目标。本文旨在提供Fre-GSI的新方面，包括：（1）Chen等人给出的Fre-GSI的数值解。（2020）在分析和数值方面进行了研究；(2)从广义密度演化方程推导了一种新颖的全局灵敏度演化方程，因此可以通过直接求解全局灵敏度演化方程来估计Fre-GSI，而不是像Chen等人提出的那样重复求解广义密度演化方程。（2020）。研究了数值例子来说明所提出方法的效率和准确性。还概述了一些有待进一步研究的问题。