Deep Learning-Based Rapid Flow Field Reconstruction Model with Limited Monitoring Point Information

The rapid reconstruction of the internal flow field within pressure vessel equipment based on features from limited detection points was of significant value for online monitoring and the construction of a digital twin. This paper proposed a surrogate model that combined Proper Orthogonal Decomposition (POD) with deep learning to capture the dynamic mapping relationship between sensor monitoring point information and the global flow field state during equipment operation, enabling rapid reconstruction of the temperature field and velocity field. Using POD, the order of the tested temperature field was reduced by 99.75%, and the order of the velocity field was reduced by 99.13%, effectively decreasing the dimensionality of the flow field. Our analysis revealed that the first modal coefficient of the temperature field snapshot data, after modal decomposition, had a higher energy proportion compared to that of the velocity field snapshot data, along with a more pronounced marginal effect. This indicates that more modes need to be retained for the velocity field to achieve a higher total energy proportion. By constructing a CSSA-BP model to represent the mapping relationship between the modal coefficients of the temperature and velocity fields and the data collected from the detection points, a comparison was made with the BP method in reconstructing the temperature field of a shell-and-tube heat exchanger. The CSSA-BP method yielded a maximum mean squared error (MSE) of 9.84 for the reconstructed temperature field, with a maximum mean absolute error (MAE) of 1.85. For the velocity field, the maximum MSE was 0.0135 and the maximum MAE was 0.0728. The global maximum errors for the reconstructed temperature field were 4.85%, 3.65%, and 4.29%, respectively. The global maximum errors for the reconstructed velocity field were 17.72%, 11.30%, and 16.79%, indicating that the model established in this study has high accuracy. Conventional CFD simulation methods require several hours, whereas the reconstruction model proposed here can rapidly reconstruct the flow field within 1 min after training is completed, significantly reducing reconstruction time. This work provides a new method for quickly obtaining the internal flow field state of pressure vessel equipment under limited detection points, offering a reference for online monitoring and the development of digital twins for pressure vessel equipment.