# Investigating Data-driven systems as digital twins: Numerical behavior of Ho-Kalman method for order estimation

## TL;DR

This paper investigates the numerical behavior of the Ho-Kalman method for system order estimation, emphasizing its role in creating digital twins through system identification in the time domain.

## Contribution

It provides an analysis of the Ho-Kalman method's effectiveness for order estimation using numerical examples, highlighting its potential in digital twin development.

## Key findings

- Ho-Kalman method effectively estimates system order from time-domain responses
- Numerical examples demonstrate the method's accuracy and limitations
- Discussion on future outlook for digital twin applications

## Abstract

System identification has been a major advancement in the evolution of engineering. As it is by default the first step towards a significant set of adaptive control techniques, it is imperative for engineers to apply it in order to practice control. Given that system identification could be useful in creating a digital twin, this work focuses on the initial stage of the procedure by discussing simplistic system order identification. Through specific numerical examples, this study constitutes an investigation on the most \natural" method for estimating the order from responses in a convenient and seamless way in time-domain. The method itself, originally proposed by Ho and Kalman and utilizing linear algebra, is an intuitive tool retrieving information out of the data themselves. Finally, with the help of the limitations of the methods, the potential future outlook is discussed, under the prism of forming a digital twin.