关键词: 径向基函数, 物理规划, 增广Lagrange乘子法, 自适应代理模型, 翼型气动隐身优化

Abstract:

To solve the airfoil aerodynamical and stealthy optimization problems about large computational cost and weights are ususlly inappropriate, a multi-objective optimization strategy using adaptive radial basis function and physic programming(ARBF-PP) is proposed. Multi-objective optimization problem is transformed by physical programming method into single objective optimization problem that reflects design preference, then the radial basis function model is created to replace aggregate preference function and constraints. Augmented Lagrange multiplier method is used to solve the constraint problem, and use genetic algorithm(GA) to obtain current optimal solution. In the process of optimization, new sampling points are added and surrogate model is updated according to all the samples and their responses to improve the approximation accuracy around the optimal solution until the convergence of optimization. The multi-objective optimization strategy is validated by using numerical test and the problem of optimization of the aerodynamical and stealthy performance of airfoil to prove the efficiency of ARBF-PP. As the optimization results shown：Compared to the initial data, lift-to-drag ratio increases 34.28% and the average of radar cross section(RCS) in the key azimuth decreases 24.19%. Furthermore, compared to the traditional optimization method using static radial basis function surrogate model , when the amounts of samples are same, the lift-to-drag ratio increases 11% and the RCS decreases 25.6%; And compared to GA without surrogate model, the number of function evaluation(Nfe) decreases 93.5%.

Key words: adaptive surrogate model, augmented lagrange multiplier method, physical programming method, radial basis function, airfoil aerodynamic-stealthy optimization