基于两层POD和BPNN的翼型反设计方法

翼型优化过程需要大量的 CFD 分析，计算量大、耗时长。本文发展基于本征正交分解（POD）和反向传播神经网络（BPNN）的翼型反设计方法，该方法的优化过程如下：首先，通过 Hicks-Henne 参数化，在设计空间中构造翼型外形的样本库，并利用 Xfoil/Fluent 对样本翼型的流场进行求解；然后，对翼面压力系数和几何外形分别建立 POD 模型，即两层 POD 模型，并得到对应的基模态系数；最后，使用 BPNN 建立从压力系数的基模态系数到几何外形的基模态系数的映射，实现在给定压力系数下对几何外形的快速预测。通过算例分析，结果表明：在亚/跨声速状态，基于 200 个样本训练所得的两层 POD+BPNN 模型可以实现对具有目标压力系数分布的翼型的预测，其精度满足翼型反设计要求。

Airfoil inverse design method based on two-layer POD and BPNN

It is computationally intensive and time-consuming to perform a large number of CFD simulations in the process of airfoil optimization. This paper develops an airfoil inverse design method using the proper orthogonal decomposition (POD) and back propagation based neural network (BPNN). The optimization process of this method is as follows: First a sample set of airfoil shapes in the design space are generated through Hicks-Henne parameterization, and the flow fields of the sample airfoils are solved by Xfoil and Fluent. Then two POD models of the airfoil pressure coefficients and the geometric shapes are respectively built, and the corresponding base modal coefficients are obtained. Finally, the BPNN is used to map the base modal coefficients of the pressure coefficients to the base modal coefficients of the geometric shapes, in order to achieve rapid prediction of the specified geometric shape under a given pressure coefficient distribution. The results of the test example at subsonic and transonic shows: a two-layer POD+BPNN model based on 200 samples can realize the prediction of the airfoil with target pressure coefficient distribution, and meet the precision requirement of airfoil inverse design.