Heating load profiles analysis and probabilistic prediction for a public building: A data-driven deep learning approach

Accurate prediction of heating load is essential for optimizing energy system efficiency and enabling intelligent control. Real-world data often involves aleatoric uncertainty from irregular operations and sensor noise, while epistemic uncertainty arises from limited model capacity. This study applies K-means clustering with engineered features to hourly load data, identifying five representative daily profiles: intraday-on/off, all-day-off, and three levels of all-day-on. A correlation coefficient of –0.41 indicates a moderate negative relationship with ambient temperature, while the hourly autocorrelation drops below 0.5 during working hours due to manually driven switching of operation modes. This data-driven clustering informs tailored modeling strategies and reveals structural variability, indicating cluster-specific aleatoric uncertainty. To quantify both data and model uncertainty, we develop a probabilistic weight-ensemble LSTM with adaptive parameter projection, trained under negative log-likelihood loss and equipped with Monte Carlo dropout for Bayesian approximation. It achieves a test mean absolute error (MAE) of 47.72 kW and root mean square error (RMSE) of 81.22 kW, substantially outperforming individual models and naive ensembles by dynamically emphasizing more reliable sub-models. During active periods, its prediction intervals achieve a well-calibrated 72% coverage, reliably capturing uncertainty. The modeled uncertainties are interpreted in relation to the data characteristics and the underlying model mechanisms. The proposed framework innovatively bridges clustering-based load profile analysis and model design, enhancing interpretability through structured insights. This data-driven approach further provides a robust foundation for reliable load forecasting and safe model predictive control.