Global Description of Flutter Dynamics via Koopman Theory

We introduce a data-driven method for flutter analysis and prediction based on Koopman theory. The Koopman formalism enables the representation of nonlinear dynamics in a higher-dimensional linear space through the lifting of coordinates. The resulting linear model is valid over a broad region, and in some cases, globally, within the state space, offering a powerful tool for extending classical linearized stability analysis to a global stability assessment for flutter. In this paper, we present a extended bilinear model parameterized by flutter parameter to capture nonlinear behavior of flutter dynamics. We then establish a rigorous connection between the eigenvalues and eigenvectors of the extended bilinear model and those of the nonlinear flutter dynamics, addressing both fixed-point (equilibrium) and limit-cycle (flutter) cases. Finally, the proposed methods are applied to a 2D academic example and a more realistic panel flutter problem, highlighting how pre-flutter data can be utilized to characterize the flutter mechanism and predict the flutter boundary in a model-free, data-driven manner.