## 3 Results
### Analysis Stage  
Figure 7a shows the best network topology obtained through the normal profile; Figure 7b describes the best topology through the desirable profile, and Figure 7c describes the best network topology using the maximized desirable profile. The three network profiles were obtained through statistical analysis in the JMP software to identify the optimal values in each of the proposed profiles. After performing the analysis of the S/N ratio, the values in which the levels for each of the variables involved were nearest to the average and S/N ratio red lines on the X axis were chosen, which are described in Table 7.  
For the choice of the best network profile obtained, three training sessions were carried out for each of the three profiles in order to contrast them based on the size of the training and test data and their generalization capacity, estimating the percentage of correct answers in the prediction of the data, obtaining the results shown in Table 8.  
The best topology corresponds to the maximized desirable profile, with the percentage of obtained hits being \(87.71\%\) with a margin of error of less than \(5\%\) in the tests. Once the best topology was chosen, the statistical tests of correlation and chi-square were performed, showing the best and worst prediction of the network, as shown in Figures 8 and 9, respectively. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Trial No.** & **G1** & **G2** & **G3** & **G4** & **Average** & **S/N** \\ \hline
1 & 0.0825789 & 0.08150994 & 0.08200742 & 0.08102935 & 0.0817814 & \(-41.797957\) \\ \hline
2 & 0.0651544 & 0.06734919 & 0.06683558 & 0.0666657 & 0.0665012 & \(-36.960574\) \\ \hline
3 & 0.0568985 & 0.05618239 & 0.05984281 & 0.05778079 & 0.0576761 & \(-31.219083\) \\ \hline
4 & 0.074502 & 0.06984874 & 0.07645081 & 0.07592863 & 0.0741825 & \(-27.856466\) \\ \hline
5 & 0.0618532 & 0.06118982 & 0.06071765 & 0.05706847 & 0.0602073 & \(-28.973660\) \\ \hline
6 & 0.0525082 & 0.05237245 & 0.05415778 & 0.05406061 & 0.0532747 & \(-34.832469\) \\ \hline
7 & 0.070358 & 0.06704642 & 0.06866684 & 0.07036554 & 0.0691092 & \(-32.761969\) \\ \hline
8 & 0.0549823 & 0.04965534 & 0.05378926 & 0.05494074 & 0.0533419 & \(-26.523630\) \\ \hline
9 & 0.0465695 & 0.04604935 & 0.04942250 & 0.05026433 & 0.0480764 & \(-27.302767\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Responses measured during the implementation of the crossed OA. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Profile** & **A** & **B** & **C** & **D** \\ \hline Normal & 80 & 30 & 0.01 & 0.1 \\ \hline Desirable & 80 & 30 & 0.01 & 0.1 \\ \hline Maximized & 100 & 30 & 0.2 & 0.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Best design values with normal desirable and maximized profiles. Figure 7: S/N analysis for the determination of the optimal parameters of the network: (**a**) normal profile; (**b**) desirability profile; (**c**) maximized desirability profile. Figure 8: Trajectory of the manipulator with the best prediction and correlation test: (**a**) best predicted values; (**b**) correlation test. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Training** & **Profile** & **Density** & **Training time** & **\% of Hits** \\  & & & **(m)** & **\(\chi^{2}\)**\(<\)5\%** \\ \hline
1 & Normal & 70:30 & 13.2649 & 85.72 \\ \hline
2 & Normal & 80:20 & 16.1627 & 85.83 \\ \hline
3 & Normal & 90:10 & 18.3473 & 86.40 \\ \hline
4 & Desirable & 70:30 & 13.4989 & 87.39 \\ \hline
5 & Desirable & 80:20 & 16.1765 & 85.32 \\ \hline
6 & Desirable & 90:10 & 18.5385 & 85.50 \\ \hline
7 & Maximized & 70:30 & 16.3393 & 87.71 \\ \hline
8 & Maximized & 80:20 & 17.7275 & 86.30 \\ \hline
9 & Maximized & 90:10 & 19.5463 & 86.86 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Comparison of density and percentage of hits in the three best profiles. To determine if the predicted data are statistically reliable, the cross-validation method was used by splitting the training and testing datasets.