## 7 Results and Discussion  
In order to carry out experiments to find the optimal flotation parameters, a computer program written in C++ language was created. The experimental data consisted of two parts: the first one, which concerned the results of enrichment in the Denver flotation machine and the second one, which concerned the results obtained in the Jameson cell. Laboratory tests carried out with the use of the Denver flotation machine included 3240 cases. Tests concerning flotation enrichment of copper ore in the Jameson cell were limited to 540 cases. Above all, this was caused by technological differences between the flotation devices. Laboratory  
Figure 2: Mayer (left) and Halbich (right) curves for flotation of the dolomite copper ore type with particle size distribution of 0–25 \(\upmu\)m by means of an aqueous solution of ethyl sodium xanthate (E) and isobutyl sodium xanthate (Z) in doses of 100 and 150 g/Mg in the Jameson cell. tests were carried out for the feed with particle size of: 0-25, 25-45, 45-75 (\(\upmu\)m), because the size distribution of air bubbles in the flotation chamber favours the separation of finer particles, which was confirmed by the previous experimental work. Therefore, it would be practically impossible to enrich copper ore in which particles above 71 \(\upmu\)m would constitute the majority. Moreover, the transport restrictions resulted in the tests being carried out for only one type of lithological copper ore, namely dolomite ore. The choice was dictated by the fact that it is the predominant lithological type in the Polkowice-Sieroszowice mine from which the material for the research was obtained. The calculation process and data analysis were carried out in a similar way both for data obtained from the Denver flotation machine and for those obtained with the use of the Jameson cell. The limited number of experiments obtained using the Jameson cell resulted in a clear change in the accuracy of matching the model to empirical data. On their basis, the neural network determined a model for the flotation enrichment process of particular lithological types of Polish copper ore with selected process parameters. The model matching was assessed on the basis of the mean square error. In the process of network learning of the studied phenomenon, it was possible to compare the results of matching the model to empirical data. To illustrate the progress of change, the evaluation is summarised in Table 8.  
The evaluation of matching the model to the real conditions confirms the fact of increasing the accuracy with the number of repetitions in the learning process of the flotation phenomenon network, and at the same time, the time of obtaining the model is extended. Figure 3 shows two examples of 5 input parameters adopted for two tests conducted within 30 min. In order to illustrate the achieved accuracy of matching the model to the flotation parameters, the results obtained are presented in the diagrams in Table 9. It seems optimal to use 1000 repetitions, as the subsequent actions significantly increase the time of searching for a solution, while only slightly increasing the matching. In addition, with more repetitions, there is an increased risk of network overlearning which in these cases, needs to be further verified by dividing the data into a learning set and a verification set. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Number of Repetitions**} & \multicolumn{2}{c}{**Mean Square Error**} \\ \cline{2-3}  & **Denver Flotation Machine** & **Jameson Cell** \\ \hline
1 & 0.032700 & 0.15642 \\
50 & 0.013684 & 0.02103 \\
100 & 0.011555 & 0.00753 \\
200 & 0.010003 & 0.00419 \\
500 & 0.008739 & 0.00287 \\
1000 & 0.007937 & 0.00213 \\
2000 & 0.007457 & 0.00129 \\
3000 & 0.007222 & 0.00088 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The evaluation of matching the model generated by the neural network depending on the number of repetitions used for two flotation machines.