Enhancing hydrofoil velocity estimation through residual learning

Abstract

Recovering flow states from limited observations provides supports for flow control and super-resolution. Advances in deep learning have made it possible to construct precise state estimators. In this work, a deep learning estimator with an initialization branch and a residual branch is proposed to predict velocity fields from sparse pressure on the hydrofoil surface. In detail, on the one hand, the pre-trained proper orthogonal decomposition-based model as an initialization branch is employed to generate initial predictions. On the other hand, the U-shaped neural network-based model as the residual branch is trained to learn the residual between the initial predictions and the ground truth. Compared to previous models, the proposed model not only enhances prediction accuracy but also improves the interpretability of the model. Furthermore, the incorporation of the initialization branch has little influence on training and inference speed. Test results illustrate that residual learning provides additional model capacity for improving the prediction of transverse velocity fields and flow details. Moreover, even in the presence of intense velocity fluctuations near the trailing edge, predictions from the improved model are more consistent with ground truth. Visualization of feature maps underscores a significant advantage of the improved model over the baseline model in terms of structural features and increased distinctiveness among features, thereby facilitating interpretability enhancements.