Global Description of Flutter Dynamics via Koopman Theory

TL;DR

This paper introduces the Extended Koopman Bilinear Form (EKBF) model for aeroelastic systems, enabling global linear representation and better capturing nonlinear flutter dynamics, validated through case studies with noise robustness.

Contribution

The paper proposes the EKBF model, extending Koopman theory to provide a global linear parametrization of aeroelastic dynamics with improved nonlinear dependence modeling.

Findings

EKBF accurately interpolates and extrapolates eigenvalues.

EKBF captures flutter mechanisms and predicts flutter boundaries.

EKBF remains effective with noisy data.

Abstract

This paper presents a novel parametrization approach for aeroelastic systems utilizing Koopman theory, specifically leveraging the Koopman Bilinear Form (KBF) model. To address the limitations of linear parametric dependence in the KBF model, we introduce the Extended KBF (EKBF) model, which enables a global linear representation of aeroelastic dynamics while capturing stronger nonlinear dependence on, e.g., the flutter parameter. The effectiveness of the proposed methodology is demonstrated through two case studies: a 2D academic example and a panel flutter problem. Results show that EKBF effectively interpolates and extrapolates principal eigenvalues, capturing flutter mechanisms, and accurately predicting the flutter boundary even when the data is corrupted by noise. Furthermore, parameterized isostable and isochron identified by EKBF provides valuable insights into the nonlinear flutter system.