Mathematical Remodeling: Hierarchical Sensitivity Analysis Approach Based on Analysis of Finite Fluctuations

Abstract

To make the process of evaluating complicated hierarchical systems more tractable, it is beneficial to represent them through models derived from a unified class of frameworks that are conducive to subsequent analytical endeavors. This method of interchanging the original model with ones from predetermined categories possessing desirable characteristics is referred to as Mathematical Remodeling. Among remodeling classes there can be mentioned Neural Networks as structures being universal approximators and which are acceptable to be analyzed. The question related to the importance of model inputs (Sensitivity Analysis) has a great practical meaning, for example, this information can be used for model reduction, control of the system, etc. There are a wide variety of methods of Sensitivity Analysis, which can be classified both by the mathematical approaches used and by the types of models to which they are relevant. However, there are almost no unified approaches to assessing sensitivity in the case of hierarchical systems. The paper introduces the approach to estimate sensitivity measures for hierarchical system obtained by applying remodeling concept. The proposed method is based on Analysis of Finite Fluctuations built on the Lagrange mean value theorem. The proposed approach provides both end-to-end analysis (investigation of the influence of inputs of sub-systems on the output of the main system) and analysis of the components of the hierarchical system. The paper also contains a numerical example which demonstrates the ability of the proposed approach to deliver sensitivity measures of hierarchical system.