Interval Simulation of Narmax Models Based on Computer Arithmetic

TL;DR

This paper introduces an interval arithmetic simulation algorithm for NARMAX models to control computational errors, demonstrating improved accuracy over existing tools like Intlab through numerical experiments.

Contribution

The paper presents a novel interval arithmetic algorithm for NARMAX models that reduces error propagation and outperforms existing Matlab tools.

Findings

Our method produces narrower intervals than Intlab.

Numerical experiments confirm improved accuracy.

Interval simulation effectively controls error growth.

Abstract

System identification is an important area of science, which aims to describe the characteristics of the system, representing them by mathematical models. Since many of these models can be seen as recursive functions, it is extremely important to control the errors in these functions, because small errors introduced in each computational step can grow exponentially due to the sensitivity to initial conditions present in this type of functions. One of the ways to control rounding and truncation errors is through interval arithmetic, since it is not possible to represent all numbers in the computer because of the finite representation in them. Thus, in arithmetic interval a number is represented by an interval in which the true number is within that interval. In this manuscript we developed an algorithm that performs the operations of interval arithmetic using basic functions. We have compared compared our results with the Matlab-toolbox Intlab. Numerical experiments have shown that our method is superior producing narrower intervals.