Parametric optimization for morphing structures design: application to morphing wings adapting to changing flight conditions

Morphing structures can allow significant improvements in performance by optimally changing shape across varying conditions. A critical barrier to the design of morphing structures is the challenge of determining how optimal shape changes as a function of the many operating conditions that affect optimality. Traditional engineering optimization techniques are able to determine an optimal shape only for one condition or an aggregation over operating conditions (i.e., optimizing average performance). Parametric optimization is an alternative approach that can solve a family of related optimization problems simultaneously. Herein the authors analyze the design of a structurally consistent camber morphing wing for light aircraft applications using parametric optimization techniques. The approach combines rigorous consideration of structural constraints via Class/Shape Transformation (CST) equations and use of a C1-continuous analytical representation of wing outer mold line geometry with the Predictive Parametric Pareto Genetic Algorithm (P3GA), an algorithm for nonlinear multi-parametric optimization. The system is tuned to maximize lift-to-drag ratio, a key metric for aircraft flight range. Kriging-based interpolation is applied to P3GA output to obtain an optimal solution map determining optimal shape variable values as a function of flight conditions (airspeed, angle of attack, and altitude). Solutions obtained from iterated use of traditional optimization techniques are utilized to benchmark the more novel and efficient parametric optimization accuracy. Results show that parametric optimization is useful for optimizing morphing structures across a range of operating conditions.