Interpretable dynamic modeling of coal-fired boiler–turbine systems: a physics-aligned deep learning approach

Dynamic modeling of coal-fired boiler–turbine systems is crucial for flexible and safe operation under high renewable energy penetration. However, strong nonlinearity, multivariable coupling, and variable-specific multi-scale dynamic responses pose significant challenges to accurate prediction. Although data-driven models can achieve high prediction accuracy, their limited transparency restricts their engineering applicability. To address these issues, this study proposes a physics-aligned deep learning framework, termed Multi-dimensional Dynamic Attention Network (MDANet), for boiler–turbine dynamic modeling. In MDANet, adaptive receptive-field temporal feature extraction is designed to characterize variable-specific temporal dynamics, adaptive feature re-weighting is introduced to adjust the relevance of different variables under changing operating conditions, and a temporal context-aware multi-gate mixture-of-experts structure is employed to represent coupled multi-output prediction tasks. The proposed model is validated using DCS data from a 600 MW coal-fired boiler–turbine unit. Comparative experiments, ablation studies, and out-of-sample robustness analysis demonstrate that MDANet achieves accurate and stable prediction performance for unit load, main steam pressure, and main steam temperature. Furthermore, attention-based visualization and quantitative interpretability analysis show that the learned model-internal relevance patterns are consistent with the expected dynamic behavior of the boiler–turbine system. The results indicate that MDANet provides an effective and transparent data-driven modeling approach for the considered boiler–turbine dynamic prediction task.