He Lei, Qian Weiqi, Zhao Tun, Wang Qing
Computational Aerodynamics Research Institute, China Aerodynamics Research and Development Center, Mianyang 621000, China.
Entropy (Basel). 2020 Sep 12;22(9):1022. doi: 10.3390/e22091022.
To generate more high-quality aerodynamic data using the information provided by different fidelity data, where low-fidelity aerodynamic data provides the trend information and high-fidelity aerodynamic data provides value information, we applied a deep neural network (DNN) algorithm to fuse the information of multi-fidelity aerodynamic data. We discuss the relationships between the low-fidelity and high-fidelity data, and then we describe the proposed architecture for an aerodynamic data fusion model. The architecture consists of three fully-connected neural networks that are employed to approximate low-fidelity data, and the linear part and nonlinear part of correlation for the low- and high-fidelity data, respectively. To test the proposed multi-fidelity aerodynamic data fusion method, we calculated Euler and Navier-Stokes simulations for a typical airfoil at various Mach numbers and angles of attack to obtain the aerodynamic coefficients as low- and high-fidelity data. A fusion model of the longitudinal coefficients of lift CL and drag CD was constructed with the proposed method. For comparisons, variable complexity modeling and cokriging models were also built. The accuracy spread between the predicted value and true value was discussed for both the training and test data of the three different methods. We calculated the root mean square error and average relative deviation to demonstrate the performance of the three different methods. The fusion result of the proposed method was satisfactory on the test case, and showed a better performance compared with the other two traditional methods presented. The results provide evidence that the method proposed in this paper can be useful in dealing with the multi-fidelity aerodynamic data fusion problem.
为了利用不同保真度数据提供的信息生成更多高质量的空气动力学数据，其中低保真空气动力学数据提供趋势信息，高保真空气动力学数据提供数值信息，我们应用了深度神经网络（DNN）算法来融合多保真度空气动力学数据的信息。我们讨论了低保真和高保真数据之间的关系，然后描述了所提出的空气动力学数据融合模型的架构。该架构由三个全连接神经网络组成，分别用于逼近低保真数据以及低、高保真数据相关性的线性部分和非线性部分。为了测试所提出的多保真度空气动力学数据融合方法，我们针对典型翼型在不同马赫数和攻角下进行了欧拉和纳维 - 斯托克斯模拟，以获得作为低、高保真数据的空气动力学系数。采用所提出的方法构建了升力系数CL和阻力系数CD的纵向系数融合模型。为了进行比较，还构建了可变复杂度建模和协同克里金模型。针对三种不同方法的训练数据和测试数据，讨论了预测值与真实值之间的精度差异。我们计算了均方根误差和平均相对偏差来展示三种不同方法的性能。所提出方法在测试案例上的融合结果令人满意，并且与所呈现的其他两种传统方法相比表现更好。结果表明本文提出的方法可用于处理多保真度空气动力学数据融合问题。
