Neural-network-based optimization of the wing kinematics and geometry of a hovering flapping flight

We optimize the wing kinematics and geometry for minimum power consumption during a hovering flight in a similar condition to that of the fruit fly. A neural network is constructed to predict the aerodynamic characteristics of a flapping wing from its kinematic and geometric information. For training and testing of the neural network, data are obtained from unsteady three-dimensional numerical simulations of a total of 900 sets of randomly generated wing kinematics and geometries. Given the input data of a time sequence of the wing kinematics and geometry, the trained neural network provides the aerodynamic force and torque coefficients in time. Its prediction performance is compared with the existing quasi-steady blade element model and is found to be more accurate not only for parameterized wing kinematics and geometry but also for a fruit fly wing motion. Using this neural network, we optimize the wing kinematics and geometry without and with elastic energy storage, respectively. As a result, the optimal wing planform shapes obtained are found to be similar to that of the fruit fly wing, and the optimal wing kinematics involves a large deviation motion with the peak-to-peak amplitude of 27.2° as similarly observed from the fruit fly wing. Also, the optimal wing kinematics obtained with and without elastic energy storage is very similar to the asymmetric upstroke and downstroke motions of the fruit fly wing, respectively. Finally, with the constraint of no deviation motion, the optimal wing kinematics without deviation motion consumes more power than that with deviation motion.