Yuhang Li

The accurate reconstruction of the internal temperature field in rotary kilns is critical for optimizing the clinker calcination process and ensuring energy efficiency. In this study, a rapid and high-fidelity surrogate modeling framework is proposed, utilizing snapshot ensembles generated by full-order Computational Fluid Dynamics (CFD) simulations to reconstruct the temperature field of the axial center section. The framework incorporates a symmetric Autoencoder (AE) coupled with a TabPFN network as its core components. Capitalizing on the kiln’s strong axial symmetry, this reduction–regression system efficiently maps the high-dimensional nonlinear thermodynamic topology of the central section into a compact low-dimensional latent manifold via AE, while utilizing TabPFN to establish a robust mapping between operating boundary conditions and these latent features. By leveraging the In-Context Learning (ICL) mechanism for prior-data fitting, TabPFN effectively overcomes the data scarcity inherent in high-cost CFD sampling. Predictive results demonstrate that the model achieves a coefficient of determination (R²) of 0.897 for latent feature regression, outperforming traditional algorithms by 6.53%. In terms of field reconstruction on the test set, the model yields an average temperature error of 15.31 K. Notably, 93.83% of the nodal errors are confined within a narrow range of 0–50 K, and the reconstructed distributions exhibit high consistency with the CFD benchmarks. Furthermore, compared to the hours required for full-scale simulations, the inference time is reduced to 0.45 s, representing a speedup of four orders of magnitude. Consequently, the predictive system demonstrates excellent accuracy and efficiency, serving as an effective substitute for traditional models to realize online monitoring and intelligent optimization.

The temperature at the rotary kiln inlet is a core process parameter in cement clinker calcination. Its accurate prediction is crucial for ensuring production stability, optimizing energy consumption, and improving product quality. However, this temperature series exhibits complex dynamic characteristics such as multivariate strong coupling, nonlinearity, and long time delays, posing significant challenges for precise modeling. To address this, this paper proposes a novel residual TCN-GRU-SelfAttention time series prediction model. The model begins by preprocessing and standardizing industrial data to construct high-quality input features. On this basis, dilated convolutions in the Temporal Convolutional Network (TCN) are employed to effectively extract local multi-scale features, with residual connections incorporated to ensure training stability. The Gated Recurrent Unit (GRU) is utilized to capture long-term dependencies in the temperature series. Finally, a Self-Attention mechanism is introduced to dynamically evaluate and weight the importance of features at different time steps, thereby focusing on key information. Experiments based on real rotary kiln operation datasets show that, compared to baseline models such as TCN, GRU, and TCN-GRU, the proposed model achieves significant improvements in key metrics: the coefficient of determination (R²) reaches 0.88, an increase of 4.8%, while the root mean square error (RMSE) is reduced by 31.4%. The results demonstrate that the proposed model exhibits good adaptability and robustness to the complex dynamic conditions of rotary kilns, providing high-precision predictive support for fine-grained kiln control and process decision-making.