Reconstruction of missing flow field from imperfect turbulent flows by machine learning

Obtaining reliable flow data is essential for the fluid mechanics analysis and control, and various measurement techniques have been proposed to achieve this goal. However, imperfect data can occur in experimental scenarios, particularly in the particle image velocimetry technique, resulting in insufficient flow data for accurate analysis. To address this issue, a novel machine learning-based multi-scale autoencoder (MS-AE) framework is proposed to reconstruct missing flow fields from imperfect turbulent flows. The framework includes two missing flow reconstruction strategies: complementary flow reconstruction and non-complementary flow reconstruction. The former requires two independent measurements of complementary paired flow fields, posing challenges for real-world implementation, whereas the latter requires only a single measurement, offering greater flexibility. A benchmark case study of channel flow with ordinary missing configuration is used to assess the performance of the MS-AE framework. The results demonstrate that the MS-AE framework outperforms the traditional fused proper orthogonal decomposition method in reconstructing missing turbulent flow, irrespective of the availability of complementary paired faulty flow fields. Furthermore, the robustness of the proposed MS-AE approach is assessed by exploring its sensitivity to various factors, such as latent size, overlap proportion, reconstruction efficiency, and suitability for multiscale turbulent flow structures. The new method has the potential to contribute to more effective flow control in the future, thanks to its characteristic that eliminates the requirement for complementary flow fields.