## 4 Displacement Prediction  
Following the prediction process, available inputs were tested with five different scenarios to predict the displacement of the upright frames under the axial compressive load. Table 9 presents the five combinations of the MPF and the quality of input selection. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Phase**} & \multicolumn{8}{c}{**Network Result**} \\ \cline{2-7}  & **R2** & **R** & **NS** & **RMSE** & **MAE** & **WI** \\ \hline Test & 0.999 & 1.000 & 1.000 & 0.001 & 0.000 & 1.000 \\ \hline Train & 1.000 & 1.000 & 1.000 & 0.000 & 0.000 & 1.000 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Best obtained results for normalised load estimation. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**FIS Clusters**} & \multirow{2}{*}{**Population Size**} & \multirow{2}{*}{**Iterations**} & \multirow{2}{*}{**Inertia Weight**} & \multirow{2}{*}{**Damping Ratio**} & \multicolumn{2}{c}{**Learning Coefficient**} \\ \cline{5-6}  & & & & & **Personal** & **Global** \\ \hline
10 & 150–350 & 45–100 & 1 & 0.98 & 2 & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Parameter characteristics used for PSO in this study. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**FIS Clusters**} & \multirow{2}{*}{**Population Size**} & \multirow{2}{*}{**Iterations**} & \multirow{2}{*}{**Inertia Weight**} & \multirow{2}{*}{**Damping Ratio**} & \multicolumn{2}{c}{**Learning Coefficient**} \\ \cline{5-6}  & & & & & **Personal** & **Global** \\ \hline
10 & 150–350 & 45–100 & 1 & 0.98 & 2 & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Parameter characteristics used for MLP and FE. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Phase**} & \multicolumn{8}{c}{**Network Result**} \\ \cline{2-7}  & **R2** & **R** & **NS** & **RMSE** & **MAE** & **WI** \\ \hline Test & 0.999 & 1.000 & 1.000 & 0.001 & 0.000 & 1.000 \\ \hline Train & 1.000 & 1.000 & 1.000 & 0.000 & 0.000 & 1.000 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Best achieved results for displacement estimation. According to this table, the load itself was the most significant input on the displacement prediction, and the thickness stands in second place. In order to avoid ambiguity, Table 10 shows the best-predicted results using the MPF network by tabulating the value of evaluation criteria for 45 and 250 as iteration and population, respectively. Table 9 reveals the quality of presence for each input parameter, where the axial load has the most participation among other parameters, while the shape factor has the lowest participation. Table 10 also indicates that the fifth combination of inputs leads to the best prediction in the test phase. Moreover, the fifth combination presented the most accurate results in the training phase. On the other hand, since the test results are more substantial scale for accuracy, the fifth combination showed the best estimation of upright displacement by the MPF network. Figure 24 illustrates the predicted and measured displacement by the MPF model in scatter diagrams. Figure 24a shows the training and testing phase of the model with a single input whose performance parameters are shown in Table 10. Figure 24b depicts the testing and training phase of the model with two inputs. According to this procedure, it is obvious that MPF networks have an acceptable performance where the number of inputs increased to five inputs. Figure 24d,e represent the best-achieved predictions amongst other models. In addition, there is a slight difference between these two models in the prediction capability mentioned in Table 10. As can be seen, some improvements in the performance of the MLP were obtained in this phase using the PSO algorithm such that the r and R\({}^{2}\) values have increased and the RMSE value has decreased.