## 5 Ultimate Load Prediction  
In order to find the best scenario of populations and iterations by considering an endless number of repetitions, and following the adjusting process, according to the feature-selection results, bolt spacing plays the most critical role in predicting the ultimate load. Table 11 shows the order of each input and their effect based on the combination participation. After the mentioned process, the model with 150 iterations and 250 populations was selected, and the results of the prediction were indicated in Table 12. As mentioned earlier, this technique does not require testing all possible combinations, and it is sufficient to test only once for each set of k members. For example, if we want to determine the best combination of inputs with four members, we run the network only once and set the value of nf to five, and the network of six inputs that has the most impact on the answer is selected. As shown in Table 12, the results are almost identical for four inputs, while the five inputs show a noticeable accuracy compared to other combinations. In Table 11, the composition of parameters in the order of feature-selection decision is indicated in which the bolt spacing is shown in most of the input groups, while the shape factor has the lowest participation. Figure 27 indicates the result of the MPF models in the prediction of the ultimate load. Predicting the load faced more challenges compared to displacement prediction. Figure 27 illustrates the training and testing phase of the MPF model with 150 times of iteration. Upper regressions present the training phase, and the lower ones show the test phase, and considering Figure 27a-e, the difference between the qualities of the prediction is obvious. The best achieved result is related to the model with 5 inputs along 150 iterations and 250 populations including R\({}^{2}\) = 0.907, r = 0.8, NS = 0.435, MAE = 1.203, RMSE = 1.678 and WI = 0.882 in the testing phase, and the same values were obtained in the training phase with acceptable variation. RMSE and MAE are both more than 1 with 0.28% tolerance, which indicates the same behaviour of the predicted data around the standard deviation. Except for the NS value, other evaluation criteria have proven the reliability of prediction and the neural network. According to Figure 27 and Table 12, employing the MPF network is conservative for upright ultimate axial load capacity prediction. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & \multicolumn{6}{c}{**Train**} \\ \hline  & & \multicolumn{6}{c}{**The MPF Network**} \\ \hline
**Iteration** & **Population** & **nf** & R\({}^{2}\) & **r** & **NS** & **RMSE** & **MAE** & **WI** \\ \hline
45 & 250 & 1 & 0.885 & 0.941 & 0.870 & 0.035 & 0.026 & 0.969 \\ \hline
45 & 250 & 2 & 0.971 & 0.985 & 0.970 & 0.018 & 0.003 & 0.993 \\ \hline
45 & 250 & 3 & 0.825 & 0.996 & 0.992 & 7.244 & 5.270 & 0.998 \\ \hline
45 & 250 & 4 & 0.999 & 1.000 & 1.000 & 0.001 & 0.000 & 1.000 \\ \hline
45 & 250 & 5 * & 1.000 & 1.000 & 1.000 & 0.000 & 0.000 & 1.000 \\ \hline  & & \multicolumn{6}{c}{**Test**} \\ \hline  & & \multicolumn{6}{c}{**The MPF Network**} \\ \hline
**Iteration** & **Population** & **nf** & **R\({}^{2}\)** & **r** & **NS** & **RMSE** & **MAE** & **WI** \\ \hline
45 & 250 & 1 & 0.992 & 0.935 & 0.854 & 0.038 & 0.028 & 0.965 \\ \hline
45 & 250 & 2 & 0.997 & 0.978 & 0.955 & 0.022 & 0.004 & 0.989 \\ \hline
45 & 250 & 3 & 0.921 & 0.907 & 0.798 & 7.199 & 5.246 & 0.951 \\ \hline
45 & 250 Figure 27: Regression of the training (above charts) and testing (below charts) phase results with measured values of normalised load for (**a**) one input, (**b**) two inputs, (**c**) three inputs, (**d**) four inputs, (**e**) five inputs. Figure 29: The MPF (five inputs) error histograms for ultimate load prediction: (**above**) training phase and (**below**) testing phase.