# Energy Optimisation of Industrial Limestone Grinding Using ANN
## 10 Results  
This analysis focused on two key aspects regarding the use of neural networks for optimising mill operations:  
* Estimation of energy indicators \(S\) and \(W\) for unobserved operating parameters. * Optimisation of the operating point considering only controlled signals. In the first case, neural networks were used to identify the model's hyperplane, which allowed for determining the quality indicators even when some signals were unobservable. This means that the developed neural network model can estimate the values of \(S\) and \(W\) even in the event of sensor failure. On the other hand, when all signals are available, the mechanism can predict the indicator values for different parameter settings without \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Variable** & **Unit** & **Value D** & **Value Ensemble** \\ \hline Mill screw conveyor motor speed & rpm & 51.2 & 50.5 \\ \hline Temperature after the mill & \({}^{\circ}\)C & 68.7 & 72.1 \\ \hline Airflow before the fan & m\({}^{3}\)/h & 190,000 & 188,000 \\ \hline Pressure difference across the mill & mbar & 25.73 & 23.9 \\ \hline \(S\) & kWh/Mg & 11.65 & 10.95 \\ \hline \(W\) & kWh/Mg & 1.85 & 0.72 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Genetic algorithm optimisation results for the combined dataset. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Variable** & **Unit** & **Value B** & **Value Ensemble** \\ \hline Mill screw conveyor motor speed & rpm & 51.20 & 50.1 \\ \hline Temperature after the mill & \({}^{\circ}\)C & 69.40 & 72.3 \\ \hline Airflow before the fan & m\({}^{3}\)/h & 190,000 & 181,520 \\ \hline Pressure difference across the mill & mbar & 26.52 & 27.9 \\ \hline \(S\) & kWh/Mg & 9.99 & 10.45 \\ \hline \(W\) & kWh/Mg & 2.15 & 1.32 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Genetic algorithm optimisation results for the Industrial Experiment 2023 data. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Variable** & **Unit** & **Value C** & **Value Ensemble** \\ \hline Mill screw conveyor motor speed & rpm & 51.2 & 40.3 \\ \hline Temperature after the mill & \({}^{\circ}\)C & 80.9 & 73.5 \\ \hline Airflow before the fan & m\({}^{3}\)/h & 160,000 & 169,500 \\ \hline Pressure difference across the mill & mbar & 22.7 & 19.8 \\ \hline \(S\) & kWh/Mg & 6.92 & 12.75 \\ \hline \(W\) & kWh/Mg & 1.63 & 1.47 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Genetic algorithm optimisation results for the C data. requiring additional experimentation. The practical application of this methodology can serve comparative purposes, avoiding costly experiments. The system operator can obtain a set of indicator values for the current operating state. By adjusting individual parameters and processing them through the proposed neural network, the operator can determine whether the indicators improve. In this way, an optimal set of parameters can be determined and implemented in the actual system. The second part of the analysis employed two different approaches to optimising black-box functions, aiming to optimize the mill's operating parameters for four different cases (datasets A-D). Both Bayesian optimisation and genetic algorithms successfully identified operating settings that minimize energy indicators \(S\) and \(W\). The results demonstrate that Bayesian optimisation achieved slightly better energy savings in several cases, although genetic algorithms also found comparable settings. Importantly, the ensemble model developed in this study exhibited significantly better fit quality compared to standalone artificial neural networks, as confirmed by lower error metrics (MAE, MSE, and RMSE) and higher \(R^{2}\) values across multiple datasets. Despite the improved predictive accuracy of the ensemble model, the optimisation results obtained using this model were comparable to those achieved with the standalone ANN models.