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

arXiv: https://arxiv.org/abs/1910.00838 · HTML: https://mlsanity.com/paper/1910.00838/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Oct 2019.

## Built on by (most cited first, 1 of 1)

- [Second-order AAA algorithms for structured data-driven modeling](https://mlsanity.com/paper/2506.02241/) (2025)

## Abstract (arXiv)

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.