基于实验数据的倒置旗帜规则与混沌动力学建模
Data-driven modeling of the regular and chaotic dynamics of an inverted flag from experiments
AI总结：
本研究利用水洞实验视频，通过吸引谱子流形（SSM）降阶模型，成功构建了倒置旗帜在均匀流中拍动动力学的二维及四维模型，准确再现了规则与混沌状态下的动力学行为，并证实了先前发现的不稳定不动点。
摘要：
我们利用水洞实验的视频素材，构建了一个二维降阶模型，用于描述均匀流中倒置旗帜的拍动动力学。该模型是通过吸引谱子流形（SSM）上的约化动力学获得的，该子流形源自旗帜不稳定不动点的两个最慢模态。除了从观测中预期的不稳定不动点和极限环之外，我们的SSM降阶模型还证实了旗帜存在两个不稳定不动点，这一发现与先前研究相符。重要的是，该模型仅利用少量一般轨迹即可正确重构动力学，无需系统的其他信息。在混沌拍动状态下，我们构建了一个四维SSM降阶模型，该模型能够捕捉系统的混沌吸引子。
英文摘要：
We use video footage of a water tunnel experiment to construct a two-dimensional reduced-order model of the flapping dynamics of an inverted flag in uniform flow. The model is obtained as the reduced dynamics on an attracting spectral submanifold (SSM) that emanates from the two slowest modes of the unstable fixed point of the flag. Beyond an unstable fixed point and a limit cycle expected from observations, our SSM-reduced model also confirms the existence of two unstable fixed points for the flag, which were found by previous studies. Importantly, the model correctly reconstructs the dynamics from a small number of general trajectories and no further information on the system. In the chaotic flapping regime, we construct a 4D SSM-reduced model that captures the system's chaotic attractor.
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