Deep learning and data assimilation approaches to sensor reduction in estimation of disturbed separated flows

Abstract

Unsteady loads created by environmental perturbations - namely gusts - can strongly affect small and light-weighted aerial vehicles. To control vehicle's behavior in this perturbed environment, a robust, cheap and accurate estimator of the surrounding flow field and aerodynamic load is essential. Low-order inviscid vortex models constitute an attractive solution to this problem. For aerodynamic applications, the role of viscosity is primarily to inject vorticity into the flow. Intrinsically, this mechanism can't be captured by an inviscid model and need to be modeled. In modern inviscid models, the vorticity shedding criterion is set by the critical leading edge suction parameter (LESP) (Ramesh et al., Theor. Comput. Fluid Dyn., 2013). Without satisfying closure model, the critical LESP has been estimated from data assimilation (Darakananda et al., Phys. Rev. Fluids, 2018) and deep learning (Hou et al., AIAA J., 2019). Refining these works, we explore the influence of the spatial distribution of sensors through these two questions: what is the optimal placement of the pressure sensors? How many sensors are required to accurately estimate the LESP? For the deep learning model, a weight vector is determined which measures the influence of each pressure sensor on the final estimate. This weight vector is regularized by the L1 norm to promote sparsity. The number of sensors used is skrunk from 126 to 3 without significant loss of accuracy. Our deep learning framework is interpreted as the learning of a Koopman invariant subspace for the LESP and angle of attack. In the ensemble Kalman filter framework, an iterative algorithm based on the representers identifies the most impactful sensors. We reduce the number of sensors from 50 to 30.