The fusion method based on small-sample aerodynamic thermal and force data

At present, high-fidelity data are expensive to acquire. When fusing limited high-fidelity data, the small-sample size introduces problems such as missing information and sample bias, which leads to overfitting of the results and accuracy degradation. In this paper, we propose a small-sample aerodynamic data fusion method based on deep neural networks. The method applies semi-supervised learning for model construction using multi-fidelity aerodynamic thermal and force data. The initial model is trained with both labeled and unlabeled data by an improved flexible loss function. Using unlabeled data as a soft constraint combined with semi-supervised learning enables the model to perform better with small-sample data. This article investigates the ONERA (National Office for Aerospace Studies and Research) M6 wing surface pressure distributions at different airfoil spread coordinates and verifies the applicability of the proposed method by reducing the proportion of high-fidelity data in the training and test datasets. The proposed method is then applied to the prediction of aerothermal data on the surface of a blunt bicone. The results show that, using a small-sample high-fidelity dataset, the proposed method can predict the surface pressure distribution and surface aerodynamic heat distribution of the aircraft relatively well. As the volume of high-fidelity data decreases, the proposed method outperforms other methods.