Data-Driven Identification of Rayleigh-Damped Second-Order Systems

TL;DR

This paper introduces a data-driven method to identify Rayleigh-damped second-order systems from frequency response data, extending the Loewner framework and validated through numerical benchmarks.

Contribution

It extends the Loewner framework to efficiently identify Rayleigh-damped second-order systems from frequency response data.

Findings

The method accurately identifies systems in numerical benchmarks.

The approach is computationally efficient.

It effectively handles systems with Rayleigh damping.

Abstract

In this paper, we present a data-driven approach to identify second-order systems, having internal Rayleigh damping. This means that the damping matrix is given as a linear combination of the mass and stiffness matrices. These systems typically appear when performing various engineering studies, e.g., vibrational and structural analysis. In an experimental setup, the frequency response of a system can be measured via various approaches, for instance, by measuring the vibrations using an accelerometer. As a consequence, given frequency samples, the identification of the underlying system relies on rational approximation. To that aim, we propose an identification of the corresponding second-order system, extending the Loewner framework for this class of systems. The efficiency of the proposed method is demonstrated by means of various numerical benchmarks.