Structured vector fitting framework for mechanical systems

TL;DR

This paper introduces a structure-preserving data-driven vector fitting method tailored for modally damped mechanical systems, ensuring the learned models retain physical properties and are computed efficiently from data.

Contribution

The paper presents two novel structured extensions of the vector fitting algorithm specifically designed for modally damped mechanical systems, guaranteeing physically meaningful models.

Findings

Algorithms successfully recover system structures from data.

Validated on two benchmark models with promising results.

Ensures models adhere to physical damping properties.

Abstract

In this paper, we develop a structure-preserving formulation of the data-driven vector fitting algorithm for the case of modally damped mechanical systems. Using the structured pole-residue form of the transfer function of modally damped second-order systems, we propose two possible structured extensions of the barycentric formula of system transfer functions. Integrating these new forms within the classical vector fitting algorithm leads to the formulation of two new algorithms that allow the computation of modally damped mechanical systems from data in a least squares fashion. Thus, the learned model is guaranteed to have the desired structure. We test the proposed algorithms on two benchmark models.