Global Description of Flutter Dynamics via Koopman Theory
This work addresses the problem of global linear representation for nonlinear aeroelastic dynamics, particularly in flutter prediction, offering incremental improvements over existing Koopman-based methods.
The paper tackles the challenge of modeling aeroelastic systems with strong nonlinear dependencies by introducing the Extended Koopman Bilinear Form (EKBF) model, which effectively interpolates and extrapulates principal eigenvalues to capture flutter mechanisms and accurately predict flutter boundaries, even with noisy data.
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.