Interpretable low-order representation of eigenmode deformation in parameterized dynamical systems

TL;DR

This paper introduces a method to derive an optimal orthogonal basis of eigen-deformation modes that effectively capture eigenmode variations across different parameter values in dynamical systems, aiding model reduction and physical understanding.

Contribution

It presents a novel approach to obtain eigen-deformation modes that are valid across parameter ranges, improving interpretability and reduction of parameterized dynamical systems.

Findings

EDMs effectively capture eigenmode variations across parameters

EDMs improve parameterized model reduction

EDMs provide physical insights into parameter effects

Abstract

Modal analysis has long been consolidated as a basic tool to interpret dynamics and build low-order models of mechanical, thermal, and fluid systems. Eigenmodes arising from the spectral decomposition of the underlying linearized dynamics represent spatial patterns in vibration, temperature, or velocity fields associated with simple time dynamics. However, for systems that depend on one or more parameters, eigenmodes obtained for one set of parameter values are not necessarily dynamically relevant in other regions of parameter space. In this work, we formulate a method to obtain an optimal orthogonal basis of eigen-deformation modes (EDMs) that capture eigenmode variations across a range of parameter values. Through numerical examples of common parameterized dynamical systems in engineering, we show that EDMs are useful for parameterized model reduction and to provide physical insight into the effects of parameter changes on the underlying dynamics.