Data-driven balanced truncation for second-order systems with generalized proportional damping

TL;DR

This paper introduces a data-driven balanced truncation method for second-order systems that infers damping coefficients from data, producing structured reduced models with physical interpretability for control system design.

Contribution

It generalizes quadrature-based balanced truncation to second-order systems, enabling structure-preserving model reduction with data-driven damping coefficient inference.

Findings

Effective in numerical examples

Infers damping coefficients solely from data

Produces physically meaningful reduced models

Abstract

Structured reduced-order modeling is a central component in the computer-aided design of control systems in which cheap-to-evaluate low-dimensional models with physically meaningful internal structures are computed. In this work, we develop a new approach for the structured data-driven surrogate modeling of linear dynamical systems described by second-order time derivatives via balanced truncation model-order reduction. The proposed method is a data-driven reformulation of position-velocity balanced truncation for second-order systems and generalizes the quadrature-based balanced truncation for unstructured first-order systems to the second-order case. The computed surrogates encode a generalized proportional damping structure, and the damping coefficients are inferred solely from data by minimizing a least-squares error over the coefficients. Several numerical examples demonstrate the effectiveness of the proposed method.