Genetic Algorithm Based Optimization of Wing Rotation in Hover

Abstract

The pitching kinematics of an experimental hovering flapping wing setup are optimized by means of a genetic algorithm. The pitching kinematics of the setup are parameterized with seven degrees of freedom to allow for complex non-linear and non-harmonic pitching motions. Two optimization objectives are considered. The first objective is maximum stroke average efficiency, and the second objective is maximum stroke average lift. The solutions for both optimization scenarios converge within less than 30 generations based on the evaluation of their fitness. The pitching kinematics of the best individual of the initial and final population closely resemble each other for both optimization scenarios, but the optimal kinematics differ substantially between the two scenarios. The most efficient pitching motion is smoother and closer to a sinusoidal pitching motion, whereas the highest lift-generating pitching motion has sharper edges and is closer to a trapezoidal motion. In both solutions, the rotation or pitching motion is advanced with respect to the sinusoidal stroke motion. Velocity field measurements at selected phases during the flapping motions highlight why the obtained solutions are optimal for the two different optimization objectives. The most efficient pitching motion is characterized by a nearly constant and relatively low effective angle of attack at the start of the half stroke, which supports the formation of a leading edge vortex close to the airfoil surface, which remains bound for most of the half stroke. The highest lift-generating pitching motion has a larger effective angle of attack, which leads to the generation of a stronger leading edge vortex and higher lift coefficient than in the efficiency optimized scenario.

Phenomenology and scaling of optimal flapping wing kinematics

“…The experimental parameters for the model wing are summarised in table 1 and are the same as those applied in a previous study where we conducted single objective optimisations [29].…”

“…Experimental optimisations with dynamically scaled wings and force measurements combine accurate measurements with comparatively low experimental times [29][30][31]. Automated data transfer and processing between the experimental system and the optimisation framework is required and the mechanism needs to have a robust control scheme and mechanical design to conduct a large number of iterations without human supervision.…”

Aeroelastic characterisation of a bio-inspired flapping membrane wing

“…The aerodynamic performance of the new adaptive membrane wing is evaluated in terms of the stroke-average lift coefficient C L and its hovering efficiency η [54,62]:…”

On the parametrisation of motion kinematics for experimental aerodynamic optimisation

“…The kinematics for the different optimisation studies are evaluated with a robotic flapping wing mechanism immersed in an octagonal water tank (see also [9,8]).…”

“…Here, we will present three different approaches to define and parameterise kinematics for optimisation studies. The different approaches will be presented, compared, and evaluated for the example of the experimental optimisation of the pitching kinematics of a flapping wing, building upon the work presented in Gehrke et al [9] and Gehrke and Mulleners [8]. An optimisation is performed for each kinematic function with 6, 12 and 18 parameters, leading to more than 30 000 individual experiments in total.…”