PID-Optimized Deep Learning for Adaptive Time–Frequency Forecasting in Dynamic Systems: Coal Calorific Value Prediction

Accurate real-time prediction in dynamic industrial systems is crucial for optimization and efficiency. This article introduces a novel intelligent monitoring framework leveraging proportional-integral-derivative (PID)-optimized deep learning for adaptive time-frequency forecasting to address the challenges posed by nonstationary industrial data. The proposed method uniquely integrates a channel-independent separable dynamic filter (CSDF) that adapts to real-time multivariate process variables, minimizing cross-channel interference. Furthermore, a closed-loop PID optimization strategy enhances the convergence and prediction accuracy of the deep learning model. The effectiveness of this framework is demonstrated through a case study in the prediction of cleaned coal calorific value, a vital parameter for optimizing coal preparation processes and improving energy efficiency. Industrial experiments in this application show that the proposed method achieves a significant 5.36% increase in forecast hit rate (FHR) compared to existing techniques, highlighting its potential for advanced monitoring and control in dynamic systems.