Real-­time parametric estimation of periodic wake-­foil interactions using bioinspired pressure sensing and machine learning

Periodic wake-­foil interactions occur in the collective swimming of bio­inspired robots. Wake interaction pattern estimation (and control) is crucial to thrust enhancement and propulsive efficiency optimization. In this paper, we study the wake interaction pattern estimation of two flapping foils in tandem configurations. The experiments are conducted at a Reynolds number of 1.41×10^4 in a water channel. A modified wake-­foil phase parameter Φ, which unifies the influences of inter­foil distance Lx, motion phase difference ∆φ and wake convection velocity Uv, is introduced to describe the wake interaction patterns parametrically. We use a differential pressure sensor on the downstream foil to capture wake interaction characteristics. Data sets at different tandem configurations are collected. The wake-­foil phase Φ is used to label the pressure signals. A one ­dimensional convolutional neural networks (1D-CNN) model is used to learn an end­to­end mapping between the raw pressure measurements and the wake-­foil phase Φ. The trained 1D-­CNN model shows accurate estimations (average error 3.5%) on random wake interaction patterns and is fast enough (within 40 ms). Then the trained 1D ­CNN model is applied to online thrust enhancement control of a downstream foil swimming in a periodic wake. Synchronous force monitoring and flow visualization demonstrate the effectiveness of the 1D-­CNN model. The limitations of the model are discussed. The proposed approach can be applied to the online estimation and control of wake interactions in the collective swimming and flying of biomimetic robots.