面向气动数据融合的D-最优试验设计方法研究

周小怡; 孔轶男; 韩仁坤; 钱炜琪; 陈刚

doi:10.7527/S1000-6893.2026.33562

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DOI: https://doi.org/10.7527/S1000-6893.2026.33562

面向气动数据融合的D-最优试验设计方法研究

周小怡 ,
孔轶男 ,
韩仁坤 ,
钱炜琪 ,
陈刚

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1. 西安交通大学
2. 中国空气动力研究与发展中心计算空气动力学研究所
3. 西安交通大学，航天航空学院，机械结构强度与振动国家重点实验室，陕西省先进飞行器服役环境与控制重点实验室
4. 中国空气动力研究与发展中心计算空气动力研究所
5. 西安交通大学;西安交通大学机械结构强度与振动国家重点实验室

收稿日期: 2026-03-11

修回日期: 2026-07-28

网络出版日期: 2026-07-30

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Research on D-optimal Design Method for Aerodynamic Data Fusion

ZHOU Xiao-Yi ,
KONG Yi-Nan ,
HAN Ren-Kun ,
QIAN Wei-Qi ,
CHEN Gang

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Received date: 2026-03-11

Revised date: 2026-07-28

Online published: 2026-07-30

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摘要

针对高速飞行器气动设计中高精度数据获取成本昂贵以及传统代理模型在大攻角与高马赫数等强非线性区域预测精度不足的问题，本文提出一种耦合D-最优试验设计准则与深度迁移学习的多精度气动数据融合建模框架。该方法首先利用低成本的欧拉方程仿真计算构建覆盖全飞行包线的低精度数据集，旨在快速捕捉气动力随工况变化的全局物理趋势。在此基础上，引入D-最优准则，通过最大化信息矩阵的行列式从候选样本库中主动筛选出对模型参数估计贡献最大的关键工况点，并开展基于RANS方程的高精度数值模拟。在模型架构方面，本文建立基于预训练微调机制的深度神经网络，利用海量低精度数据训练特征提取层以构建通用的流场特征空间。随后采用参数冻结策略，利用极少量的高精度样本仅对输出层权重进行微调，从而实现从低精度趋势向高精度量值的精准映射。以典型三维旋成体飞行器为研究对象，在马赫数1.5~6 、攻角-2°~20°的宽包线范围内进行了算例验证。研究结果表明，采用D-最优采样策略微调后的模型在测试集均方根误差上较拉丁超立方抽样平均降低约6.41%，能够更有效地捕捉强激波干扰区的非线性特征。相比于克里金直接建模方法，融合模型对阻力系数的预测均方误差降低了78.1%，且在全工况范围内展现出优异的拟合稳健性。在保证同等预测精度的前提下，该方案较纯高精度计算方案节约了约13.33%的总时间成本。本研究证明了所提框架在处理高维、小样本气动建模问题中的有效性，为复杂飞行器的高效气动评估与设计优化提供了技术支撑。

关键词： 高速飞行器; D-最优试验设计; 迁移融合; 数据融合; 预训练微调

本文引用格式

周小怡 , 孔轶男 , 韩仁坤 , 钱炜琪 , 陈刚 . 面向气动数据融合的D-最优试验设计方法研究[J]. 航空学报, 0 : 1 -0 . DOI: 10.7527/S1000-6893.2026.33562

Abstract

To address the high costs of obtaining high-fidelity data in aerodynamic design and the insufficient prediction accuracy of traditional surrogate models in strong nonlinear regions such as high angles of attack and transonic speeds, this paper proposes a multi-fidelity aerodynamic data fusion modeling framework coupling the D-optimal experimental design criterion with deep transfer learning. The method first constructs a low-fidelity dataset covering the entire flight envelope using low-cost Euler simulations to rapidly capture the global physical trends of aerodynamic forces. Based on this, the D-optimal criterion is introduced to actively select key operating points that contribute most to model parameter estimation by maximizing the determinant of the information matrix, followed by high-fidelity numerical simulations based on the Reynolds-Averaged Navier-Stokes equations.Regarding the model architecture, a deep neural network based on pre-training and fine-tuning mechanisms is established, utilizing a large volume of low-fidelity data to train feature extraction layers for building a general flow field feature space. A parameter freezing strategy is then employed, using a minimal number of high-fidelity samples to fine-tune only the output layer weights, thereby achieving precise mapping from low-fidelity trends to high-fidelity values. Taking a typical three-dimensional missile as the research object, validation was conducted within a broad envelope ranging from Mach 1.5 to 6 and angles of attack from minus 2 degrees to 20 degrees.The research results indicate that the model fine-tuned using the D-optimal sampling strategy reduces the root mean square error on the test set by approximately 6.41 percent compared to Latin Hypercube Sampling, demonstrating a superior ability to capture nonlinear features in strong shock interference zones. Compared to direct Kriging modeling, the fusion model reduces the mean square error for drag coefficient prediction by 78.1 percent and exhibits excellent fitting robustness across the entire range of operating conditions. Under the premise of maintaining equivalent prediction accuracy, this scheme saves approximately 13.33 percent of the total time cost compared to pure high-fidelity computation. This study proves the effectiveness of the proposed framework in handling high-dimensional and small-sample aerodynamic modeling problems, providing technical support for the efficient aerodynamic assessment and design optimization of complex aircraft.

Key words： High-speed Aerial Vehicle; D-optimal Design; Transfer Fusion; Data Fusion; Pre-training and Fine-tuning

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