Sparse Sensing for Nonlinear Data-Driven Modeling of Fluid–Structure Interactions

Reconstruction of unsteady fluid–structure interaction flows from sparse measurements taken at the interface can facilitate data-driven modeling or real-time control; however, current methods often lead to nonoptimal sparse measurement placement and hinder insights into underlying physics and mechanisms. This paper proposes an embedded methodology whereby a concrete autoencoder is used to simultaneously optimize the sparse measurement placement and the flow reconstruction process. The concrete autoencoder uses a concrete selector layer as an encoder such that a low-dimensional state is indicated by concrete sparse measurements rather than abstract latent variables. The decoder can then be set up with any reasonable neural network depending on the problem of the fluid–structural interaction problem to be solved. The proposed method is applied to the sparse sensing and reconstruction of unsteady pressure distributions for an airfoil and a swept wing. In addition, the data-driven aerodynamic models based on sparse measurements are coupled with the structural models to efficiently predict the problem of transonic aeroelasticity. The numerical results demonstrate that the proposed method outperforms the conventional sparse sensing based on proper orthogonal decomposition.