用数学新方法分析飞机颤振，能准确预测临界条件且抗噪声干扰。
Global Description of Flutter Dynamics via Koopman Theory
- 基于扩展的科普曼双线性模型，实现非线性颤振系统的全局线性建模。
- 在含噪数据下仍能准确外推主特征值，捕捉颤振机理并定位失稳边界。
- 适合航空航天领域研究复杂非线性动力学的科研人员参考。
本文提出一种基于科普曼理论的气动弹性系统新参数化方法，采用科普曼双线性形式（KBF）模型。为克服传统KBF模型线性依赖参数的局限性，引入扩展型科普曼双线性形式（EKBF）模型，可在保持全局线性表征的同时，更精准地刻画对颤振参数等强非线性依赖关系。通过二维学术案例与面板颤振问题两个实例验证，结果表明：EKBF能有效插值和外推主特征值，准确捕捉颤振机制，并在数据含噪情况下仍可精确预测颤振边界。此外，由EKBF识别出的参数化同宿面与同相面，为理解非线性颤振系统提供了深层洞察。
原文摘要 · Abstract (English)
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.
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