# Energy Optimisation of Industrial Limestone Grinding Using ANN
## 11 Conclusions  
This study demonstrated the development and validation of advanced data-driven models for predicting and optimising the energy performance of industrial limestone grinding. By combining ANN and a hybrid ensemble model incorporating MLP and XGBoost, we successfully established a predictive framework that performs reasonably well. The proposed ensemble model exhibited superior predictive accuracy compared to standalone ANN, as confirmed by lower MAE, MSE, and RMSE values across multiple datasets and higher R\({}^{2}\) coefficients, particularly for the W energy indicator. These improvements stem from the ensemble's ability to jointly capture smooth nonlinear interactions and piecewise linearities characteristic of the grinding process. Importantly, despite the enhanced predictive capability, the optimisation results obtained using the ensemble-based surrogate models are comparable to those generated by the standalone ANN. Both Bayesian and genetic optimization approaches, when applied to the ensemble models, identified operational settings that deliver similar energy savings, confirming the consistency and reliability of the optimised solutions. The ensemble model, therefore, provides a more accurate yet equally practical tool for real-world energy optimisation tasks. \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Dataset** & **Filtered Process Data (2022)** & **Industrial Experiment Data** \\ \hline
**Indicator** & **S (kWh/Mg)** & **W (kWh/Mg)** & **S (kWh/Mg)** & **W (kWh/Mg)** \\ \hline Minimum & & & & \\ before optimization & 11.7 & N/A & 15.40 & 2.30 \\ \hline Minimum & & & & \\ after optimisation & 10.78 & 0.98 & 9.88 & 1.19 \\ \hline Energy savings & 8\% & N/A & 35\% & 48\% \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Comparison of optimization results for different datasets. The findings of this research validate the robustness and industrial relevance of AI-enhanced surrogate modelling in mineral grinding processes. The proposed methodology offers a data-supported basis for optimising energy consumption while maintaining operational flexibility and process stability. Future work will focus on integrating these models into real-time control architectures and extending the approach to other communution technologies. Limitations: Although the training log contained nearly 14,000 steady-state records, only nine factorial test runs were available to probe the extreme corners of the operating envelope. All data originated from a single limestone line in one plant, lithological changes or a different mill design could therefore shift the response surface and reduce model accuracy. In addition, the validation presented here is strictly _open-loop_: the recommended set points were compared with historical measurements offline, so potential feedback effects such as recycle loads or product-quality drift were not captured. Future work: To move from offline feasibility to full industrial deployment, we plan to (i) embed the ensemble surrogate and Bayesian optimiser in the plant's SCADA system with automated set-point, write-back, and rule-based failsafes; (ii) run a multi-month closed-loop trial to quantify long-term savings under variable ore hardness and ambient conditions; (iii) transfer the workflow to other communution technologies such as ball mills and HPGRs; and (iv) investigate hybrid physics-informed networks that could reduce the amount of plant data required for re-training. Parallel studies will examine the economic impact of energy savings on the cost-per-tonne of product and the associated reduction in CO\({}_{2}\) emissions. By addressing these points, we aim to establish a broadly applicable, field-proven toolkit for energy-aware optimisation across the mineral-processing sector. Conceptualization, D.K. ([PERSON]); Methodology, P.B. and P.K. ; Software, P.B. and P.K. ; Validation, P.B. and P.K. ; Formal analysis, K.L. ; Data curation, D.K. ([PERSON]); Writing--original draft, D.K. ([PERSON]), P.B., P.K. and D.K. ([PERSON]); Writing--review & editing, P.B., P.K. and K.L.