英文摘要 | 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.
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