高超声速气动热是典型的多物理因素耦合的强非线性问题，受到激波、粘性、热化学反应、非定常效应等众多复杂因素的影响，这样的特性对传统的理论方法和仿真技术提出了巨大的挑战。数据驱动的研究方法向来是分析研究此类问题的重要途径。真实流动环境中采集的风洞实验数据在分析气动热问题中具有无可替代的价值，机器学习作为代表性的数据驱动研究方法，则是目前极具潜力的数据分析手段。依托实验数据，一方面可以建立快速可靠的气动热估算方法，这对高超声速飞行器的设计，尤其是初期设计阶段，具有重要的指导意义；另一方面，也是探索目前理论方法不足以准确描述和数值模拟无法准确复现的物理现象的重要手段。如今，人工智能技术的发展为开展数据驱动的研究提供了强有力的支撑，而其中的机器学习方法或将是推动气动热实验数据研究的关键。
传统的机器学习方法通常构建足够复杂的模型，这要依赖规模庞大的数据充分表达问题隐含的特征或是根据明确的规则来建立自主学习策略。实验技术的限制与高昂的成本导致获取大量的气动热实验数据十分困难，而气动热问题的数学物理模型描述尚不足以构建自主学习的策略。本文针对气动热实验数据的特点，开展了建立专业化机器学习方法的研究，重点考察了建模气动热实验数据时的特征工程、模型及训练方法等问题。在此基础上，提出了具有全局优化特性的气动热实验数据机器学习方法。本文的主要内容组织如下：
首先，给出一种以数值模拟求解无粘流动控制方程的实验数据特征工程方法。该方法基于气动热问题的物理背景与应用中广泛采用的工程方法。热流，作为度量气动热的核心指标，根据其定义，是具有明显局部特征的物理量。通过数值模拟，可以实现将实验来流条件这样全局统一的参数映射到测点局部。利用无粘流动仿真的结果，可以提取壁面处的流场信息，这些参数近似描述了真实流动中边界层外缘的流动状态。在此基础上，以这些特征参数作为机器学习模型的输入特征，实现了用于训练机器学习模型的气动热实验特征数据集的构建。利用传统的机器学习方法——多层神经网络，对该数据集进行初步的建模研究。结果表明，机器学习方法可以有效地建立特征工程方法提取的参数与实验测量的热流值之间的数据关联模型。并且，根据对模型性能指标的评估，确定了合适的数据归一化方法。
更进一步，本文提出了整合建模特征选择、模型复杂度优化和高效模型训练于一体的多层学习方法。在模型参数训练环节，本文提出了针对气动热实验数据建模设计的高效单隐层神经网络模型训练方法——全局优化算法改进的极限学习机方法，并使用理论数据验证了这一模型训练方法的可靠性。接下来，本文设计了组合使用极限学习机与其改进方法的模型复杂度优化策略。在复杂度优化方面，提出了临界复杂度的概念，其含义为建模气动热实验数据集时容许的单隐层神经网络模型最高的复杂度。这一参数的确定，通过评估极限学习机方法的结果实现。在模型特征参数优化方面，采取了基于临界复杂度的枚举策略，并通过全局优化算法改进的极限学习机方法实现。本文将多层学习方法用于建模气动热实验数据集，结果表明，该方法实现了有效的模型优化训练，其建立的数据关联模型能够可靠地描述气动热分布规律。
 

Aerodynamic heating is a complicated physical phenomenon that many factors affect it nonlinearly. The wind tunnel experimental data collected from real-world hypersonic flow is irreplaceable in the study of aerodynamic heating. Machine learning is regarded as the most promising approach to data modeling. As a critical problem in hypersonic flow, aerodynamic heating is influenced by shock-waves, viscosity, thermal-chemical reactions and so on, and those factors challenge both theoretical analysis and numerical simulation severely. Data-driven has always been an effective path to handle those problems. Modeling experimental data to predict aerodynamic heating rapidly and reliably plays an important role in hypersonic aircraft design, especially at the preliminary stage. Besides, it can also be applied to detect the physical mechanism when theoretical models or numerical simulations are not exact enough. Nowadays, the development of artificial intelligence provides a powerful data-driven technique, which is promising in the research on aerodynamic heating.
In traditional machine learning, the commonly used strategy is constructing a complex model trained by gathering a large scale of data to cover latent features sufficiently or embedding some principle to enable unsupervised learning. However, for aerodynamic heating, it is very expensive, if not impossible, to collect experimental data due to the cost and restrictions of hypersonic ground testing. Therefore, the prediction of aerodynamic heating usually relies on a small sample dataset of experimental data. In addition, mathematical models of aerodynamic heating do not support to construct unsupervised learning methods. Therefore, in this work, a dedicated machine learning method suitable for small sample data is established to study aerodynamic heating.
First, an experimental data feature engineering method is proposed based on solving governing equations of inviscid flow, in consideration of the physical background of aerodynamic heating and engineering methods for real-world applications. Heat flux is the key quantified parameter of aerodynamic heating and a characteristically locally physical quantity based on its definition. According to the results of simulations, flowfield information at measure points could be extracted from inflow conditions of the wind tunnel test, and the flowfield near the wall approximates that at the outer boundary layer in the real flight. That information has been used as input features of the Multi-hidden-Layer Feedforward Neural Networks (MLFN) model and this MLFN model has been trained for modeling data of aerodynamic heating. The study shows that the machine learning method has the ability to capture the relation between flowfield features and heat flux, and the best option of normalization has been determined from evaluating these results, as well.
Furthermore, the strategy with feature combination selection, model complexity optimization, and model parameters optimization has been proposed. The integrated method is named Multi-Level Learning (MLL) in this work. Two techniques, Extreme Learning Machine (ELM) and Global Optimization (GO), have been applied to improve the performance of Single-hidden-Layer Feedforward Neural Networks (SLFN) on small sample data. The specifically designed methods focus on modeling the small sample, which consists of basic modules in MLL. The target of model complexity optimization is defined as critical complexity, which means the maximum tolerated complexity of the SLFN model used in modeling the aerodynamic heating dataset. The critical complexity is determined by evaluating a series of results from ELM. Then GO-powered ELM is used to get the best one in different feature combinations at the critical complexity based on enumeration strategy. MLL has also been applied to modeling the aerodynamic heating dataset constructed by feature engineering. The studies show that the data correlation model learned by MLL is capable of producing cogent for aerodynamic heating predictions.