Novel framework for reconstructing the velocity field of pump-jet propulsor by super-resolution and Bayesian method

This study designs a deep learning framework to obtain high-precision velocity fields of a pump-jet propulsor (PJP) from low-resolution (LR) velocity fields using super-resolution (SR) methods. In actual engineering or experiments, the velocity fields obtained via particle image velocimetry have low spatial resolution, which is limited by equipment and technology. This study investigates the performance of convolutional neural network (CNN) and hybrid downsampled skip-connection/multi-scale (DSC/MS) models in reconstructing the LR velocity fields of PJP. Moreover, the variational Bayesian (VB) idea is considered in two SR methods to design VB-DSC/MS and VB-CNN neural networks, which exhibit superior performance on small datasets and can analyze the uncertainty distribution. The optimal weight and bias distributions for four different SR methods are determined, which efficiently and accurately afford the SR velocity fields from the LR velocity fields of the wake and stator domain fields. Furthermore, the reconstruction ability of the SR method under different scaling factors is analyzed. The results show that the VB-DSC/MS method has higher accuracy and generalization ability than the other three SR methods in terms of reconstructing the velocity field gradient and velocity profile of PJP. It can enhance the LR velocity field by 256 times, which is difficult for CNN-related SR methods to improve the LR velocity field by a higher factor. Among the methods considered, the VB-DSC/MS method has the smallest uncertainty distribution under different scaling factors and different rotational speeds.