A recurrent neural network for particle trajectory prediction in complex flow fields

Particle tracking velocimetry (PTV) is a flow velocity measurement technique with great potential to achieve high spatial resolution. It measures the velocity through the Lagrangian trajectories of tracer particles. When the tracer concentration is high, one of the most challenging steps lies in how to track the particles at different times correctly. Errors in particle matching not only interrupt the tracking process but also reduce the accuracy of the obtained velocity field. In the current study, recurrent neural network architectures, which are proficient in dealing with sequential data, are employed to address this issue. Various combinations of long short-term memory (LSTM) and gated recurrent unit (GRU) networks are proposed and compared. The networks are trained and tested using a dataset containing several typical turbulent flow fields, including flow around a cylinder, wake of a hydrofoil, channel flow, and thermal plumes. Three-dimensional trajectories are generated based on computational fluid dynamics simulation results, covering a wide range of particle densities in different complex flow fields. The long trajectories are segmented into short path snippets, with a total number of 150 000, while 80% is used for network training and 20% for validation. The networks are trained to predict the next frame particle positions based on the trajectories in the past 6–10 frames. Based on the parametric comparison, a double-layer LSTM-GRU network with 128 neurons for each has shown the best performance. The results indicate that the accurate prediction rate from the LSTM-GRU network has increased by over 15% compared with two traditional PTV algorithms, including the four-frame best estimation and the relaxation algorithm. In channel flow characterized by twisted particle trajectories, when the particle density is ∼0.03 ppp, the extraction rate of the LSTM-GRU algorithm exceeds 95%. Even in complex turbulent regions of a thermal plume flow field, where the performance of traditional algorithms drops significantly as the particle concentration increases, the extraction rate of the LSTM-GRU algorithm remains higher than 90%. Finally, the prediction algorithm is applied to practical experimental data of a buoyant jet. The results reveal that the proposed network can resolve satisfactory long trajectories with varying loop segmentation lengths between 6 and 10. The proposed LSTM-GRU network has been proven to be robust and computationally efficient, which has significant potential for large-scale particle tracking tasks in a wide range of experimental applications.