Lift maximization with uncertainties for the optimization of high lift devices using Multi-Criterion Evolutionary Algorithms

In this paper, the aerodynamic shape optimization problems with uncertain operating conditions has been addressed. After a review of robust control theory and the possible approaches to take into account uncertainties, the use of Taguchi robust design methods in order to overcome single point design problems in aerodynamics is proposed. Under the Taguchi concept, a design with uncertainties is converted into an optimization problem with two objectives which are the mean performance and its variance, so that the solutions are as less sensitive to the uncertainty of the input parameters as possible. Furthermore, the multi-criterion evolutionary algorithms (MCEAs) are used to capture a set of compromised solutions (Pareto front) between these two objectives. The flow field is analyzed by Navier-Stokes computation using an unstructured mesh. The proposed approach drives to the solution of a multi-objective optimization problem that is solved using a modification of a non-dominated sorting genetic algorithm (NSGA). In order to reduce the number of expensive evaluations of the fitness function a response surface modeling (RSM) is employed to estimate the fitness value using the polynomial approximation model. During the solution of the optimization problem a semi-torsional spring analogy is used for the adaption of the computational mesh to all the obtained geometrical configurations. The proposed approach is applied to the robust optimization of the 2D high lift devices of a business aircraft by maximizing the mean and minimizing the variance of the lift coefficients with uncertain free-stream angle of attack at landing and takeoff flight conditions, respectively.