## 3 Artificial Intelligence Prediction
### Algorithm Results and Discussion
#### 3.3.2 Deflection Prediction  
Firstly, the best number of populations needs to be found by considering a constant number of repetitions equal to 45. In Table 13, the population of 250 is identified as the best result in the test phase. After finding the best population, the calculations to find the optimal number of repetitions are carried out. According to Table 14, the optimal number of repetitions in the test phase is 45. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Population**} & \multicolumn{8}{c}{**Network Result**} \\ \cline{2-11}  & \multicolumn{4}{c}{**Training Phase**} & \multicolumn{8}{c}{**Testing Phase**} \\ \cline{2-11}  & **r** & **NSE** & **RMSE** & **MAE** & **WI** & **r** & **NSE** & **RMSE** & **MAE** & **WI** \\ \hline
150 & 0.948 & 0.886 & 5.434 & 3.186 & 0.972 & 0.933 & 0.852 & 6.200 & 3.567 & 0.964 \\ \hline
250 & 0.942 & 0.874 & 5.706 & 3.409 & 0.970 & 0.943 & 0.878 & 5.702 & 1.457 & 0.970 \\ \hline
350 & 0.944 & 0.879 & 5.594 & 3.354 & 0.971 & 0.936 & 0.856 & 6.093 & 3.623 & 0.966 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: The calculated accuracy criteria for the performance of the implemented models (iteration = 45). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Feature**} & \multicolumn{8}{c}{**Number of Inputs**} \\ \cline{2-7}  & **1** & **2** & **3** & **4** & **5** & **6** \\ \hline Length & & & & & & X \\ \hline Bolt & & & & & & X \\ \hline Thickness & & X & X & X & X & X \\ \hline Deflection & & & & X & X & X \\ \hline Ult moment & X & X & X & X & X & X \\ \hline Ult load & & & & X & X & X \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Most effective inputs based on feature selection. Following finding the best parameters for the neural network, the optimal input combination is found through the feature selection technique. As mentioned earlier, this technique does not require testing all possible combinations, and it is sufficient to test them only once for each set of k members. For example, if the best combination of inputs with four members is required to be determined, the network needs to be run only once and the value of nf needs to be set to six. Additionally, the network of six inputs that has the most impact on the answer should be selected. In Table 15 and Figure 31, the best value of k is specified. As shown in Table 16, the results are almost the same for four or more inputs. As it is clear, the ultimate moment has the smallest effect and the effect of the other parameters is almost the same. In Figures 31-33, the diagrams related to the six compounds are presented. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Feature**} & \multicolumn{6}{c}{**Number of Inputs**} \\ \cline{2-9}  & **1** & **2** & **3** & **4** & **5** & **6** \\ \hline Length & & & X & X & X & X \\ \hline Bolt & & & X & X & X & X \\ \hline Thickness & & & & X & X & X \\ \hline (M/ZY.Fy) & & & X & X & X & X \\ \hline Ult moment & & X & & & & X \\ \hline Ult load & X & X & & & X & X \\ \hline \hline \end{tabular}
\end{table} 
Table 16: Most effective inputs based on feature selection. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Iteration**} & \multicolumn{6}{c}{**Network Result**} \\ \cline{2-11}  & \multicolumn{6}{c}{**Training Phase**} & \multicolumn{6}{c}{**Testing Phase**} \\ \cline{2-11}  & **r** & **NSE** & **RMSE** & **MAE** & **WI** & **r** & **NSE** & **RMSE** & **MAE** & **WI** \\ \hline
45 & 0.942 & 0.874 & 5.706 & 3.409 & 0.970 & 0.943 & 0.878 & 5.702 & 1.457 & 0.970 \\ \hline
75 & 0.948 & 0.886 & 5.415 & 3.235 & 0.972 & 0.932 & 0.848 & 6.297 & 3.583 & 0.964 \\ \hline
100 & 0.947 & 0.884 & 5.49 Figure 31: MLP–PSO–FS regression charts (iteration = 100): (**a**) P150, (**b**) P250, (**c**) P350. Figure 32: MLP–PSO–FS regression charts (iteration = 75): (**a**) P150, (**b**) P250, (**c**) P350. Figures 31-33 demonstrate the results of the MLP-PSO-FS models in the prediction of the deflection.