Data-driven modeling method of cooling tower systems: Holistic, dynamic, and explainable

Cooling towers are of great significance for the sustainability of the entire energy system. This study developed a holistic, dynamic, and explainable modeling method for cooling tower systems. A simplified holistic modeling framework of cooling tower systems was constructed using physics-guided feature selection. Within this framework, three steady-state models were first developed as baseline references, against which three time-series algorithms were employed to develop the dynamic model of cooling tower systems. All model hyperparameters were optimized by five-fold cross-validation, and the best timesteps for the three dynamic models were identified. The accuracy, training speed, and dynamic response capability of models were compared. The optimal model was explained by the SHAP method. Results show that the optimal timestep for dynamic models is 10 min. Among steady-state models, eXtreme Gradient Boosting (XGBoost) achieved competitive accuracy with the shortest training time of 2.8s, outperforming others in mean relative error. For dynamic models, the Gated Recurrent Unit model achieved the highest accuracy, reducing the maximum absolute error from 1.48 °C (XGBoost) to 0.34 °C and the maximum relative error from 4.59% to 1.15%. These reductions in error were particularly significant under dynamic conditions. The explanation analysis shows that an increasing number and frequency of cooling towers in operation, and a decrease in inlet water temperature and wet-bulb temperature, typically lower the predicted outlet temperature of the cooling tower system, consistent with thermodynamic principles. The study provides data-driven model support for the intelligent operation and maintenance of cooling towers.