Design Optimization of a Bendable UAV Wing Under Uncertainty

Abstract

Load stiffening ability in the flight load direction and complaint nature in the opposite direction are important structural behaviors of the bendable unmanned air vehicle (UAV) wing, developed at the University of Florida. The complaint nature of the wing enables UAV storage inside smaller packing volumes. The present paper discusses deterministic and probabilistic design optimization of a bendable wing having 24 inch span and 7 inch root chord. In deterministic optimization, the wing shape definition parameters and the layup scheme used to manufacture the wing are treated as design variables. Aerodynamic and structural performances of the wing are studied to determine wing aerodynamic efficiency and a maximum flying velocity that the wing can withstand without buckling or failing under flight loads. The Tsai-Wu criterion is used to check failure of the wing due to rolling stresses to determine minimum safe storage diameter. Multidisciplinary (aerodynamics and structural) shape and layup optimization is performed using an elitist non-dominated sorting genetic algorithm: NSGA-II. Simultaneous maximization of wing aerodynamic efficiency and maximum flying velocity a wing can withstand without in-flight buckling are used as two design objectives. The design points on the deterministic Pareto optimal front achieved are compared with a baseline design to observe some designs with improved performance. A mixed approach is tried during probabilistic optimization. The design variable and random parameter uncertainties are included explicitly and a modeling uncertainty is included through a factor (similar to factor of safety). We found that when uncertainties in modeling, design variables and random parameters are taken into account, deterministic optimization designs show high probability of failure. In the probabilistic design optimization a single constraint of satisfying target probability of failure is used. To reduce computational cost, we use surrogate models for objectives and constraints. After several surrogates were evaluated for each of the objectives and the constraints, the best surrogates based on cross validation or RMSE were selected for the probabilistic optimization work. Finally, the effect of the target probability of failure on the Pareto front was studied. It was observed that as the target probability of failure becomes stringent, all of the Pareto front designs use almost the same leading edge curvature indicating the original storage diameter constraint drives the designs when higher reliability is desired. By relaxing the target probability of failure, stiffer wings can be obtained. Some designs with acceptable probability of failure are identified which have higher aerodynamic efficiency than a baseline wing having higher probability of failure.