Aerodynamic Shape Optimization Design Based On Kriging Surrogate Model

Based on Kriging surrogate model, an efficient and stable dynamic shape optimization method is developed. Firstly, the CFD method which is used to calculate the aerodynamic characteristics is introduced, including governing equations, spatial discretization, temporal discretization and so on. Then the Genetic Algorithms is studied. In allusion to the prematurity phenomenon that the Simple Genetic Algorithms may have, an Adaptive Genetic Algorithms which combines with adaptive crossover numbers, adaptive crossover and mutation rate and has survival stress and suitable perturbation is adopted. Afterwards, the theory of Kriging surrogate model is discussed detailedly, including experimental design method, construction of Kriging surrogate model, dynamic Kriging surrogate model, stopping criterion for iteration, et al. Considering the disadvantage of the traditional dynamic Kriging surrogate model that the hyper parameters of Kriging surrogate model need to be updated during every iteration which leads to computational inefficiency when the number of sample points or design variables is large, an improved dynamic Kriging surrogate model with M-MUMS strategy used to update the hyper parameters is adopted. It can update the hyper parameters of Kriging surrogate model only when they produce a poor approximation. Besides, the methods for parametrization of aerodynamic shape and dynamic grid are presented. And the FFD parametric method and linear elasticity dynamic grid approach for the unstructed grid composed of tetrahedron cells are expounded in detail. Meanwhile, the methods for solving large sparse linear systems that the dynamic grid approach involves are discussed briefly. Finally, the developed approach is used to optimize a transonic wing and a supersonic lifting body with the target of minmizing the drag coefficient. The results show that the drag coefficient of optimized wing and lifting body are decreased by 11.21% and 10.26%, respectively, while the lift coefficient and volume that used as the constraint conditions remain the same generally. Besides, compared with the results of optimization based on the traditional dynamic Kriging surrogate model, the developed method is accurate and computationally efficient.