Invariant spectral foliations with applications to model order reduction and synthesis

TL;DR

This paper presents a novel nonlinear decomposition technique called Invariant Spectral Foliations (ISF) for model order reduction and system analysis, applicable directly to vibration data without prior model identification.

Contribution

It introduces ISF as a unique, smooth invariant foliation for nonlinear systems, enabling reduced order modeling and data-driven analysis.

Findings

ISF effectively decomposes nonlinear dynamics into low order components.

The method accurately reconstructs full dynamics from reduced models.

Application to vibration data demonstrates practical utility.

Abstract

The paper introduces a technique that decomposes the dynamics of a nonlinear system about an equilibrium into low order components, which then can be used to reconstruct the full dynamics. This is a nonlinear analogue of linear modal analysis. The dynamics is decomposed using Invariant Spectral Foliations (ISF), which is defined as the smoothest invariant foliation about an equilibrium and hence unique under general conditions. The conjugate dynamics of an ISF can be used as a reduced order model. An ISF can be fitted to vibration data without carrying out a model identification first. The theory is illustrated on a analytic example and on free-vibration data of a clamped-clamped beam