Reconstruction of Gappy Data for Experiments of Flow past a Circular Cylinder based on the Deep Learning Method
Authors: ZHANG Fan  , ZHANG Heng  , LI Zhuoyue  , WEN Jun  , HU Haibao  ,   1 School of Marine Science and Technology, Northwestern Polytechnical University, Xi' an 710072, China;,   2 Research and Development Institute of Northwestern Polytechnical University in Shenzhen, Shenzhen 518063, China
Published: February 2025

The prerequisite for accurate prediction and effective control of flow phenomena fundamentally lies in the understanding of flow dynamics, and experimental studies provide essential data to support this process. Particle image velocimetry (PIV), as one of the important methods for flow field measurement, plays a critical role in experimental investigations such as flow past a circular cylinder. PIV is a non-contact laser-optical measurement technique; however, it often faces challenges in obtaining complete and accurate flow field data when the optical path is obstructed. Particularly in PIV experiments involving flow past a circular cylinder, the presence of the cylinder itself and the supporting structure can significantly obscure the optical path, making it highly challenging to acquire complete PIV data. To address this issue, we propose a deep learning-based flow field data reconstruction method, which employs a deep learning framework centered on convolutional neural networks (CNNs). The method aims to solve the reconstruction problem of gappy regions in flow field data by establishing a mapping relationship between flow fields with gappy regions and complete flow fields. First, the influence of gappy regions with different characteristics on the reconstruction accuracy of numerically simulated flow fields is investigated. The reconstructed flow fields are carefully compared and analyzed against ground truth data across multiple dimensions, including instantaneous flow fields and velocity time statistics. The results indicate that the maximum $L_2$ error between the reconstructed flow field and the ground truth remains at approximately 0.02. Furthermore, it is observed that as the size of the gappy region along the flow direction increases, the difficulty of flow field reconstruction increases significantly. In contrast, changes in the size of the gappy region perpendicular to the flow direction have minimal impact on the accuracy of flow field reconstruction. Additionally, the robustness of the proposed deep neural network to noise is systematically evaluated. While clean numerical simulation data are used for training, test data are generated by artificially introducing varying levels of Gaussian noise to assess the network's performance under noisy conditions. The results demonstrate that the error between the reconstructed data and the ground truth increases exponentially as the noise level rises. Finally, the proposed deep neural network model is applied to real PIV experimental data, with the training data remaining clean and numerically simulated. Both instantaneous flow fields and time-averaged statistics are analyzed and compared. The results reveal that the network model successfully reconstructs velocity information in the missing regions and effectively corrects data errors caused by measurement inaccuracies in the backflow zones. The reconstructed experimental results show closer statistical agreement with numerical simulation data, demonstrating that the model proposed in this paper, when trained solely on numerical simulation data, is capable of reconstructing missing physical information in PIV experiments. This approach provides a novel methodology for addressing data reconstruction challenges in PIV experiments.