Interpolatory model reduction of dynamical systems with root mean squared error

TL;DR

This paper introduces new model reduction techniques that directly target the root mean squared error in large-scale dynamical systems, improving computational efficiency in applications like structural dynamics.

Contribution

It proposes novel methods for directly approximating the root mean squared error using quadratic-output models, reducing reliance on large linear output systems.

Findings

Effective surrogate models for RMS error in vibrational systems

Reduced computational cost compared to classical methods

Validated on a plate vibration model with tuned absorbers

Abstract

The root mean squared error is an important measure used in a variety of applications such as structural dynamics and acoustics to model averaged deviations from standard behavior. For large-scale systems, simulations of this quantity quickly become computationally prohibitive. Classical model order reduction techniques attempt to resolve this issue via the construction of surrogate models that emulate the root mean squared error measure using an intermediate linear system. However, this approach requires a potentially large number of linear outputs, which can be disadvantageous in the design of reduced-order models. In this work, we consider directly the root mean squared error as the quantity of interest using the concept of quadratic-output models and propose several new model reduction techniques for the construction of appropriate surrogates. We test the proposed methods on a model for the vibrational response of a plate with tuned vibration absorbers.