Sensitivity Analysis of Tabular Represented Functions Based on Analysis of Finite Fluctuations

Sensitivity Analysis of mathematical models involves a large number of approaches, among which there are local methods (studying the influence of a factor on the response in the case of its isolated variation) and global methods (involving the study of simultaneous fluctuations in groups of factors). Previously, it was proposed an analytical method for analyzing the sensitivity by factors of mathematical models based on Analysis of Finite Fluctuations. In this case, the well-known Lagrange mean value theorem is used to study fluctuations of function response. However, in some situations the process of finding partial derivatives can be a computationally laborintensive task, and in some cases the function is given tabularly. In this case, it is possible to use numerical differentiation with further restoration of the analytical representation of the function. For this purpose it is suggested to use approximation of partial derivatives and to apply linear regression models with interaction effects as a remodeling class. This assumption is natural, as it models the presence of a linear relationship between the model factors. The paper presents a numerical example - the analysis of the Isigami function, performed in two ways: analytical method and using approximations to recover partial derivatives. The results obtained show the high quality of the obtained sensitivity estimates.