Experimental flapping wing optimization and uncertainty quantification using limited samples

Flapping wing micro air vehicles are capable of hover and forward flight with high maneuverability. However, flapping wing flight is difficult to simulate accurately because it is a more complex phenomenon than fixed wing or rotorcraft flight. Consequently, the optimization of flapping wing behavior based on simulation is limited and, therefore, we have elected to optimize a wing experimentally. Specifically, we use experimental data to optimize the flapping wing structure for maximum thrust production in hover mode. We point out the similarities or otherwise between experimental optimization and the more common simulation-based optimization. Experimental optimization is hampered by noisy data, which is due to manufacturing variability and testing/measurement uncertainty in this study. These uncertainties must be reduced to an acceptable level and this requires their quantification. Therefore, improvements in manufacturing and testing procedures were implemented to reduce the noise. Another challenge is to limit the number of experiments for reducing time and cost. This is realized by using surrogates, or meta-models, to approximate the response (in this case, thrust) of the wing. In order to take into account the uncertainty, or noise, in the response, we use a Gaussian Process surrogate with noise and a 2nd order polynomial response surface. We apply a surrogate-based optimization algorithm called Efficient Global Optimization with different sampling criteria and multiple surrogates. This enables us to select multiple points per optimization cycle, which is especially useful in this case as it is more time efficient to manufacture multiple wings at once and this also serves as insurance against failed designs.