Data-Driven Balanced Truncation for Second-Order Systems with Generalized Proportional Damping

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 we propose a computational procedure for inferring the damping coefficients from data by minimizing a least-squares error over the coefficients. Several numerical examples demonstrate the effectiveness of the proposed method. Reproducibility of computational results. This paper has been awarded the “SIAM Reproducibility Badge: Code and data available” as a recognition that the authors have followed reproducibility principles valued by SISC and the scientific computing community. Code and data that allow readers to reproduce the results in this paper are available at https://zenodo.org/records/18148591 . [Formula: see text]