发展了一种基于多可信度代理模型的翼型、机翼多目标优化方法，并应用于某翼型和机翼的多目标气动优化设计。采用主成分分析方法对基于CST参数化方法得到的参数进行降维，进一步减少设计变量。对不同精度翼型、机翼网格分别进行数值模拟，求解其气动参数，建立了翼型、机翼在特定工况的多可信度数据库。以翼型、机翼几何参数和高、低可信度气动参数为训练样本，基于深度置信网络DBN建立了代理模型，并采用包括输入增强、迁移学习、加法标度与集成训练等多种策略建立了翼型多可信度代理模型，用以预测气动参数。经过预测精度对比，选取其中精度最高的基于加法标度与集成训练的多可信度代理模型用于翼型气动参数预测，并将该方法扩展到三维机翼，建立了机翼多可信度代理模型，用于机翼气动参数预测。采用基于α-stable分布函数的改进的多目标粒子群优化算法，提高标准多目标粒子群算法的收敛速度和全局搜索能力。将上述多可信度代理模型嵌入改进的多目标粒子群优化算法，开展了某翼型和机翼的多目标气动优化设计。优化结果表明，优化翼型和机翼的升力系数较原始翼型、机翼均获得有效提升，阻力系数基本未增加。
A multi-objective optimization method for airfoils and wings, based on multi-fidelity surrogate models, is developed and applied to the multi-objective aerodynamic optimization design of a specific airfoil and wing. Principal Component Analysis (PCA) is used to reduce the dimensionality of the parameters from the CST parameterization method, thereby refining the design variables. Numerical simulations are conducted separately on airfoil and wing grids with different precisions to compute aerodynamic parameters, and a multi-fidelity database for the airfoil and wing under specific operating conditions is established. Geometric parameters of the airfoil and wing, as well as high- and low-fidelity aerodynamic parameters, are used as training samples to construct Deep Belief Network (DBN)-based surrogate models. Furthermore, airfoil multi-fidelity surrogate models are established using various strategies, including input augmentation, transfer learning, additive scaling, and ensemble training, to predict aerodynamic parameters. A comparison of prediction accuracy shows that the multi-fidelity surrogate model based on additive scaling and ensemble training achieves the highest accuracy and is selected for airfoil aerodynamic parameter prediction. Subsequently, this method is extended to the three-dimensional wing, where a wing multi-fidelity surrogate model is established for wing aerodynamic parameter prediction. An improved Multi-Objective Particle Swarm Optimization (MOPSO) algorithm based on the α-stable distribution function is used to enhance the convergence speed and global search capability of the standard MOPSO algorithm. The aforementioned multi-fidelity surrogate models are embedded into the improved MOPSO algorithm to conduct the multi-objective aerodynamic optimization design of the specific airfoil and wing. The optimization results reveal that the lift coefficients of the optimized airfoil and wing are effectively improved compared to the original airfoil and wing, while the drag coefficients remain substantially unchanged.
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