## 3 Results and Discussion  
All the training phases explained previously were carried out using the 70% of the data, while the rest were set aside to verify the generalization capability of the system. This means testing to see if, once the particular GNF system has been trained, it is able to provide satisfactory outputs to unknown inputs (unused data for the training procedure). By analyzing the results, it is possible to conclude that an appropriate level of generalization has been obtained.  
The results of the GNF phase and the unsupervised phase are shown below for the two trained systems. Once the complete training process is concluded for each GNF, the one with the least error function is selected.  
Figure 6 shows the result of the genetic algorithm phase when the HPP pressure is being processed. Note that after 20 generations, the best fitness value results are very similar to the mean, and after 50 generations, the average value between individuals is zero. This result indicates that the system has been properly trained. Particular results are shown in Table 3. The right columns present some results provided by GNF after an unsupervised phase, and they are compared with the real HPP values. As we can see, the outputs given by the trained system are quite similar to the expected values, as evidenced by the mean quadratic error of 0.047109 for the generalization. It is important to highlight that these results correspond to outputs generated when unknown inputs are provided, that is, values that have not been used for the training phases.  
Regarding feed flow rate, when this output is processed, a good generalization is also achieved. The evolution of the fitness value and the average distances between individuals after the Genetic phase are given in Figure 7, which shows that it is not as good as GNF for HPP pressure, although the result could be acceptable, since it improves in the next phase. After the unsupervised phase, the absolute training error is 0.018749 and the absolute generalization error is 0.022766. This is shown in the left columns of the Table, where some of the feed flow rate values provided by the GNF are presented and compared with the expected values. An analysis of these graphs and a comparison of the values obtained with the real ones allows us to confirm the success of the training process.  
Figure 5: Diagram of inputs and outputs to Genetic Neuro-Fuzzy.  
Figure 6: Average distances between individuals for HPP pressure as performance and evolution of the fitness value.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Genetic Neuro-Fuzzy** & \multirow{2}{*}{**Real Feed Flow Rate (m3/h)**} & **Genetic Neuro-Fuzzy** & \multirow{2}{*}{**Real HPP (Bar)**} \\
**Output (m3/h)** & & **Output (Bar)** & \\ \hline
8.7748 & 8.76 & 56.584 & 56.2 \\
8.1005 & 8.11 & 53.7296 & 53.6 \\
9.7989 & 9.83 & 53.7027 & 54 \\
8.1168 & 8.13 & 53.733 & 53.8 \\
8.1023 & 8.10 & 56.0792 & 56.1 \\
9.1191 & 9.13 & 53.74 & 53.5 \\
9.1303 & 9.11 & 53.7342 & 53.7 \\
9.4670 & 9.46 & 54.7407 & 54.6 \\
8.7748 & 8.81 & 53.7927 & 53.8 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of results between outputs provided by GNF system and the real ones for HPP pressure (Bar) and Feed Flow rate (m3/h).  
Figure 7: Trend in fitness value and average distances between individuals for feed flow rate as output.