Identification of Dynamic Systems with Interval Arithmetic

TL;DR

This paper presents a method for identifying electrical system models using interval arithmetic to manage numerical errors, demonstrated on three systems with verified model quality.

Contribution

It introduces an approach combining interval arithmetic with least squares estimation for system identification, enhancing error management in model accuracy.

Findings

Interval arithmetic effectively captures numerical errors.

Models' intervals encompass actual system data.

Method verified on three different electrical systems.

Abstract

This paper aims to identify three electrical systems: a series RLC circuit, a motor/generator coupled system, and the Duffing-Ueda oscillator. In order to obtain the system's models was used the error reduction ratio and the Akaike information criterion. Our approach to handle the numerical errors was the interval arithmetic by means of the resolution of the least squares estimation. The routines was implemented in Intlab, a Matlab toolbox devoted to arithmetic interval. Finally, the interval RMSE was calculated to verify the quality of the obtained models. The applied methodology was satisfactory, since the obtained intervals encompass the system's data and allow to demonstrate how the numerical errors affect the answers.