# Energy Optimisation of Industrial Limestone Grinding Using ANN
## 7 Optimisation of the Grinding Process Using Artificial Neural Networks
### Design of a Hybrid Ensemble for Evaluation Indicators
#### 7.2.5 Evaluation of the Predictive Model for Indicators  
To evaluate the generalization capability of the neural network models, training and testing were conducted using four different datasets derived from the limestone grinding and classification system. These datasets, collected during various operational periods and experimental campaigns, were extracted from the SCADA system and preprocessed to retain 26 relevant process variables--primarily those that are controllable. An overview of the datasets used is provided below:  
1. July-December 2022--Consists of 7440 samples and 26 variables, representing routine operational data from the second half of 2022. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Symbol** & **Model Description** & **Key Hyper-Parameters** \\ \hline \multirow{8}{*}{XGB} & Gradient-boosted decision trees (XGBoost) & \multirow{2}{*}{800 trees; learning\_rate = 0.03;} \\  & ensembles partition the space along & max\_depth = 7; \\ \cline{1-1}  & axis-aligned splits, excelling at piece-wise & subsample=colsample\_bytree = 0.9; \\ \cline{1-1}  & linear regimes and capturing monotone & \(\alpha=0.3\), \(\lambda=1.0\); early stopping after \\ \cline{1-1}  & effects such as the quasi-linear growth of & 50 rounds. \\ \cline{1-1}  & fan power with volumetric flow. & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: _Cont._* Industrial Experiments 2023--Contains 2226 samples and 26 variables. This dataset was recorded during targeted industrial experiments conducted in 2023 to explore new process configurations. * June-August 2023--Includes 4294 samples and 26 variables, capturing standard plant operations during the summer months of 2023. * Combined Dataset--An aggregated dataset comprising all of the above, totalling 13,960 samples. It was constructed to develop a model capable of capturing more general patterns across varied operating conditions. Each dataset was used independently to train a separate instance of the model. In total, four training procedures were performed--three on the individual datasets (A-C) and one on the  
After the training process, each model was tested on the individual datasets used during the training phase. The model, which is a function of four variables (the controlled parameters), was represented using four plots that show the evaluation indicator as a function of the controlled parameters. For each comparison between the actual and predicted values, the distribution of these values was presented, providing a more detailed insight into the performance quality of the models (Figures 10-12). Based on the comparison between actual (blue) and predicted (orange) S-index values for dataset A (Figure 10), several patterns emerge. First, the model consistently \"compresses\" its prediction range: While the true S varies from about 13 to 24 kWh/Mg, the forecasts lie mainly between 15 and 20 kWh/Mg, indicating an underestimation of the highest values and an overestimation of the lowest. Second, different process features reveal distinct error patterns: At very low and very high mill-screw speeds, the model fails to capture the steep rise or fall in energy use; for temperatures after milling, the slope of the predicted trend is noticeably shallower than in the real data; with airflow, predictions form a narrow \"corridor\" while the true values spread out at extreme flows; for pressure drop, the model hits the central region accurately but underestimates S at high drops and overestimates it at low drops. Moreover, the scatter of residuals varies by feature: For temperature, the error band remains relatively uniform, whereas for pressure drop, it widens at the axis extremes. In practice, this means the model predicts the distribution center well but loses reliability near the parameter boundaries.