This paper presents a novel parameterization 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. Currently, this study considers the supercritical case, where the system does not involve unstable limit cycles. 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 provide valuable insights into the nonlinear flutter system.
Song et al. (2026) studied this question.