Machine learning enhanced real-time aerodynamic forces prediction based
  on sparse pressure sensor inputs
Junming Duan Qian Wang Jan S. Hesthaven
Accurate prediction of aerodynamic forces in real-time is crucial for
autonomous navigation of unmanned aerial vehicles (UAVs). This paper presents a
data-driven aerodynamic force prediction model based on a small number of
pressure sensors located on the surface of UAV. The model is built on a linear
term that can make a reasonably accurate prediction and a nonlinear correction
for accuracy improvement. The linear term is based on a reduced basis
reconstruction of the surface pressure distribution, where the basis is
extracted from numerical simulation data and the basis coefficients are
determined by solving linear pressure reconstruction equations at a set of
sensor locations. Sensor placement is optimized using the discrete empirical
interpolation method (DEIM). Aerodynamic forces are computed by integrating the
reconstructed surface pressure distribution. The nonlinear term is an
artificial neural network (NN) that is trained to bridge the gap between the
ground truth and the DEIM prediction, especially in the scenario where the DEIM
model is constructed from simulation data with limited fidelity. A large
network is not necessary for accurate correction as the linear model already
captures the main dynamics of the surface pressure field, thus yielding an
efficient DEIM+NN aerodynamic force prediction model. The model is tested on
numerical and experimental dynamic stall data of a 2D NACA0015 airfoil, and
numerical simulation data of dynamic stall of a 3D drone. Numerical results
demonstrate that the machine learning enhanced model can make fast and accurate
predictions of aerodynamic forces using only a few pressure sensors, even for
the NACA0015 case in which the simulations do not agree well with the wind
tunnel experiments. Furthermore, the model is robust to noise.