基于深度学习的超临界翼型设计

近年来，深度学习在航空领域得到广泛应用。传统代理模型方法仅能利用少量气动性能参数，而深度学习可以充分利用大量原始流场数据，从而预测出流场的特征，弥补传统方法的不足。本文将深度学习方法与飞行器设计方法相结合，实现对超临界翼型的性能预测和反向设计。此外，宽体客机的机翼设计对抖振边界和阻力发散边界提出了更高的要求，本文以这两种性能约束作为参考指标。翼型的压力分布可以反映流场和性能特征，为进一步基于抖振和阻力发散特性的性能预测及反向设计提供支持，因此，本文引入压力分布作为流场和性能的物理描述。

本文探究了翼型设计中采样策略对深度学习模型预测效果的影响。首先从几何形状均匀分布与抖振和阻力发散性能均匀分布两个角度出发，设计了两种采样方法，分别建立了训练集，并在两训练集的交集中建立了测试集。针对两种不同的样本集，分别采用多层感知机模型和VGG16卷积神经网络模型实现了翼型的双向设计。结果显示，采样策略仅能保证目标空间的均匀性，而性能均匀采样在预测性能空间边界特征方面优于几何均匀采样。

正向设计时，基于多层感知机模型预测给定翼型和迎角的压力分布。采用NURBS方法描述翼型，并采用离散格式表示压力分布。结果表明，两个训练集得到的模型都能取得较高的预测精度。其中，几何均匀集训练的模型在预测压力分布时具有更高的精度，性能均匀集训练的模型仅能预测压力分布的变化趋势。这说明几何均匀集训练的模型能够更好地捕捉翼型几何形状对压力分布的影响。

反向设计时，基于VGG16卷积神经网络预测给定迎角和压力分布的相应翼型。采用与正向设计中相同的NURBS方法表示翼型，并通过符号距离函数（SDF）将压力分布处理为图片。结果表明，性能均匀集训练的模型在预测几何时具有更高的精度。这说明性能均匀集训练的模型能够更好地还原压力分布对应的翼型几何形状。

综上所述，不同均匀采样策略建立的数据集均具有良好的泛化性，而输入空间的均匀性更有利于提高模型的预测精度。本文展示了深度学习在翼型设计优化领域的有效性和优势，有助于指导翼型设计。

In recent years, deep learning has been widely used in the field of aviation. Deep learning can utilize much more original flow field data than traditional surrogate model methods do. When predicting the characteristics of the flow field, deep learning can compensate for the shortcomings of traditional methods. In this paper, the deep learning method is combined with the aircraft design method to realize the performance prediction and reverse design of the supercritical airfoil. In addition, the wing design of wide-body passenger aircraft requires buffeting boundary and drag divergence boundary with high quality. This paper takes these two performance constraints into consideration in airfoil design. By contrast, the pressure distribution of the airfoil reflects the flow field and performance characteristics, supporting performance prediction and reverse design based on the buffeting and drag divergence characteristics. Therefore, the pressure distribution is used to describe the flow field.

This paper explores the influence of sampling strategies in airfoil design on the prediction performance of deep learning models. Firstly, two sampling methods are designed base on the uniform distribution of geometry and the performance of uniform distribution of buffeting and drag divergence. The training set is established for above two methods, respectively. The test set is established in the intersection of the two sample sets. For two different sample sets, the multi-layer perceptron model and the VGG16 convolutional neural network model are built to realize the bidirectional design of the airfoil. The results show that the sampling strategy can only guarantee the uniformity of the target space. In addition, the performance uniform sampling is better than the geometric uniform sampling in predicting the boundary characteristics of the performance space.

In forward design, the pressure distribution for a given airfoil and angle of attack is predicted based on a multi-layer perceptron model. The airfoil is described by NURBS method, and the pressure distribution is represented by a discrete format. The results show that the models obtained from the two training sets can achieve high prediction accuracy. In addition, the model trained by the geometric uniform set has higher accuracy in predicting the pressure distribution, while the model trained by the performance uniform set can only predict the change trend of the pressure distribution. Therefore, the model trained by the geometrically uniform set can better reflect the influence of the airfoil geometry on the pressure distribution.

In reverse design, the airfoil is predicted for given angle of attack and pressure distribution based on the VGG16 convolutional neural network. The airfoil is represented using the same NURBS method as in the forward design, and the pressure distribution is processed as a picture by signed distance function (SDF). The results show that the model trained on the uniform set of performance has higher accuracy in predicting geometry, better restoring the airfoil geometry corresponding to the pressure distribution.

In summary, the data sets established by different uniform sampling strategies have good generalization, and the uniformity of the input space is more conducive to improving the prediction accuracy of the model. This paper demonstrates the effectiveness and advantages of deep learning in the field of airfoil design optimization to help guide airfoil design.

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