A multi-step heating furnace temperature prediction method based on physics-informed residual learning and phase-aware conformal calibration

Precise temperature control in aluminum alloy heating furnaces is essential for achieving high processing quality and optimal energy efficiency. To address the challenges posed by nonlinear dynamics, time delays, and strong multi-variable coupling in temperature forecasting, this study proposes a unified multi-step temperature prediction framework for aluminum alloy heating furnaces, integrating energy consumption-driven residual modeling and phase-aware conformal calibration, adaptive prediction intervals are dynamically generated for each distinct processing stage, thereby enhancing both the accuracy and reliability of long-term forecasts. The model further incorporates energy consistency constraints and cost-sensitive weighting mechanisms to prioritize high-energy-consumption conditions and scenarios with significant prediction errors. Extensive experiments on real-world industrial datasets from multiple furnaces and production batches demonstrate that the proposed method consistently outperforms state-of-the-art baseline models across prediction horizons of 1, 3, 5, and 10 minutes. At the 5-minute prediction step, the mean absolute error (MAE) is reduced by 17.26% and the root mean square error (RMSE) by 34.08%; simultaneously, the 90% prediction interval achieves a coverage probability (PICP) of 88.65% with a significantly narrower average width (MPIW). Potential annual energy savings are quantitatively estimated using excess duration (EDur) analysis, while leave-one-batch-out validation protocols confirms the model’s robust generalization capability. The proposed method has achieved excellent performance in both point prediction and probability prediction, and supports improved batch consistency and lower energy use through a reusable algorithmic and engineering framework.