Frequency-Based Reduced Models from Purely Time-Domain Data via Data Informativity

TL;DR

This paper introduces a robust method to derive frequency-based reduced models from purely time-domain data, eliminating the need for complex frequency response measurements and improving system identification accuracy.

Contribution

It extends the data informativity framework for moment matching, enhancing conditioning, providing an error indicator, and removing the assumption of known system order.

Findings

Effective frequency data recovery from time-domain trajectories.

Improved conditioning of linear systems in the model reduction process.

Successful application to large-scale dynamical systems.

Abstract

Frequency-based methods have been successfully employed in creating high fidelity data-driven reduced order models (DDROMs) for linear dynamical systems. These methods require access to values (and sometimes derivatives) of the frequency-response function (transfer function) in the complex plane. These frequency domain values can at times be costly or difficult to obtain (especially if the method of choice requires resampling); instead one may have access to only time-domain input-output data. The data informativity approach to moment matching provides a powerful new framework for recovering the required frequency data from a single time-domain trajectory. In this work, we analyze and extend upon this framework, resulting in vastly improved conditioning of the associated linear systems, an error indicator, and removal of an assumption that the system order is known. This analysis leads to a robust algorithm for recovering frequency information from time-domain data, suitable for large scale systems. We demonstrate the effectiveness of our algorithm by forming frequency based DDROMs from time-domain data of several dynamical systems.