Four data-driven low-order modeling approaches, Dynamic mode decomposition (DMD) and three other variations (optimal mode decomposition, total-least-squares DMD and high-order DMD), are used to capture the spatio-temporal evolution of fluid–structure interactions. These methods are applied to experimental data obtained in a flow over a flexible membrane wing and its elastic deformation. Spectral coherence indicates there exists an interaction between the flow and structural deformation at a single frequency for this problem (depending on the angle of attack and/or the presence of a ground). It is therefore an ideal dataset to assess the performance of the four different methods in terms of the relevant modes/frequencies and reconstruction of flow and structural deformation. We show that the four methods detect the same dominant frequency (within Fourier resolution) and qualitatively the same associated mode. However, the modes appear to be heavily damped or amplified preventing a successful flow and structure reconstruction (except when using high-order DMD). This problem persists even if the damping coefficients are set to 0 due to imprecision in the estimation of the dominant frequency. The reconstruction is assessed by means of the average correlation between the real and reconstructed fields corresponding to 0.42 and 0.85 for the fluid and membrane deformation respectively when using high-order DMD (and virtually 0 for the other three methods). Based on the analysis, we conclude that high-order DMD, particularly for when fluid and structural data are modeled simultaneously, is the most suitable method to generate linear low-order models for fluid–structure interaction problems. Further, we show that this modeling is not dependent on the relative energies of fluid and membrane deformation.

四种数据驱动的低阶建模方法，动态模式分解（DMD）和其他三种变化（最优模式分解，总最小二乘DMD和高阶DMD）用于捕获流体的时空演化。结构相互作用。这些方法适用于在柔性膜翼上方流动及其弹性变形中获得的实验数据。频谱相干性表明，对于该问题（取决于迎角和/或地面的存在），流动和结构变形之间存在单一频率的相互作用。因此，它是理想的数据集，可以根据相关的模式/频率以及流动和结构变形的重构来评估四种不同方法的性能。我们表明，这四种方法检测相同的主频（在傅立叶分辨率内）和定性相同的关联模式。但是，这些模式似乎被严重阻尼或放大，从而阻碍了成功的流动和结构重建（使用高阶DMD时除外）。即使由于主频率的估计中的不精确性而将阻尼系数设置为0，该问题仍然存在。通过使用高阶DMD时分别对应于流体和膜变形的0.42和0.85的实场和重构场之间的平均相关性来评估重构，对于其他三种方法，则为0。根据分析，我们得出结论，高阶DMD尤其适用于同时对流体和结构数据进行建模的情况，是针对流体-结构相互作用问题生成线性低阶模型的最合适方法。此外，我们表明该模型不依赖于流体和膜变形的相对能量。