基于自适应代理模型的翼型气动隐身多目标优化*

针对翼型气动隐身多目标优化设计存在的计算量大与权重难以选取的问题，提出基于自适应径向基函数代理模型与物理规划的高效多目标优化策略(Multi-objective optimization strategy using adaptive radial basis function and physical programming， ARBF-PP)。利用物理规划法通过非线性加权的方式将多目标优化问题转化为直接反映设计偏好的单目标优化问题，然后分别对综合偏好函数和约束条件构造径向基函数代理模型，采用增广Lagrange乘子法处理约束，并用遗传算法(Genetic algorithm， GA)进行求解。优化迭代过程中，在当前可能最优解附近增加样本点，更新代理模型，提高代理模型在最优解附近的近似精度，引导搜索过程快速收敛。使用数值多目标优化算例与翼型气动隐身多目标优化实例验证了本文所提出优化策略的有效性。翼型气动隐身多目标优化结果表明：相比于初始翼型，优化翼型的升阻比提高了34.28%，重点方位角的雷达散射截面(Radar cross section， RCS)均值减小了24.19%。此外，在相同样本规模的情况下，本文方法所得最优翼型的气动隐身性能比静态径向基函数代理模型方法的优化结果分别提高了11%与25.6%;与遗传算法相比，本文方法所需的分析模型调用次数(Number of evaluation function， Nfe)降低了93.5%。

Aerodynamic and Stealthy Performance Optimization of Airfoil Based on Adaptive Surrogate Model

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％.