Dynamic mode decomposition-based reconstructions for fluid–structure interactions: An application to membrane wings

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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.