A hybrid physical information deep learning framework for energy consumption forecasting of forging heating furnace

The forging heat furnace (FHF) significantly improves the mechanical and forming properties of billets through precise temperature and time control. However, with an energy density of approximately 880 kW h/t of processed billets, the FHF represents a highly energy-intensive process that poses a major constraint on energy-efficiency optimization within the forging industry. Accurate energy consumption forecasting provides theoretical support for FHF energy-efficiency optimization and process parameter regulation. A physics-informed neural network (PINN) was proposed in this study to improve the accuracy and physical interpretability of FHF energy consumption forecasting. First, the energy transfer characteristics of the four-phase FHF were systematically analyzed. A heat transfer model of the furnace wall and a multi-process coupled energy consumption model were established based on thermodynamic laws, and the key physical intermediate variables affecting energy consumption were determined. Subsequently, the physical intermediate variables were combined with real-time operating data to construct an energy-sensitive multi-source feature fusion space. Finally, a PINN integrating thermodynamic mechanisms and data-driven methods was proposed based on the Convolutional Neural Network, Bidirectional Long Short-Term Memory, and Attention Mechanism architecture (PINN-CBA). The PINN-CBA model embedded thermodynamic intermediate variables into the loss function to achieve mechanism-data fusion. In the ablation experiments, the model significantly outperformed the six benchmark models, with root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R2) of 1.28 %, 0.73 %, and 97.10 %, respectively. The physical consistency analysis showed that the forecasting results of the PINN-CBA model were consistent with physical explanations, effectively breaking through the interpretability limitations of traditional black-box models.