# On the Use of Neuro-Swarm System to Forecast the Pile Settlement
## 4 Results and Discussion  
During ANN model development, it was found that a model with three hidden neurons provides the best performance prediction for estimation of pile settlement. The R\({}^{2}\) values of 0.809 and 0.816 for \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{3}{*}{\
\begin{tabular}{c} **Model** \\ **No.** \\ \end{tabular} } & \multirow{3}{*}{
\begin{tabular}{c} **Inertia** \\ **Weight** \\ \end{tabular} } & \multicolumn{3}{c}{**Neuro-Swarm Results**} & \multicolumn{3}{c}{**Ranking**} & \multicolumn{3}{c}{**Total**} \\ \cline{3-10}  & & & \multicolumn{3}{c}{**Training**} & \multicolumn{3}{c}{**Testing**} & \multicolumn{3}{c}{**Training**} \\ \cline{3-10}  & & **R\({}^{2}\)** & **RMSE** & **R\({}^{2}\)** & **RMSE** & **R\({}^{2}\)** & **RMSE** & **R\({}^{2}\)** & **RMSE** & \\ \hline
1 & 0.25 & 0.836 & 0.093 & 0.867 & 0.092 & 2 & 1 & 3 & 3 & 9 \\
2 & 0.5 & 0.848 & 0.088 & 0.805 & 0.114 & 3 & 3 & 1 & 1 & 8 \\
3 & 0.75 & 0.851 & 0.087 & 0.856 & 0.103 & 4 & 4 & 2 & 2 & 12 \\
4 & 1 & 0.851 & 0.089 & 0.892 & 0.083 & 4 & 2 & 4 & 4 & 14 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Neuro-swarm models with different inertia weights. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{3}{*}{\begin{tabular}{c} **Model** \\ **No.** \\ \end{tabular} } & \multirow{3}{*}{\
\begin{tabular}{c} **C\({}_{1}\)** \\ \end{tabular} } & \multirow{3}{*}{
\begin{tabular}{c} **C\({}_{2}\)** \\ \end{tabular} } & \multicolumn{3}{c}{**Neuro-Swarm Results**} & \multicolumn{3}{c}{**Ranking**} & \multicolumn{3}{c}{**Total**} \\ \cline{3-10}  & & & \multicolumn{3}{c}{**Training**} & \multicolumn{3}{c}{**Testing**} & \multicolumn{3}{c}{**Training**} & \multicolumn{3}{c}{**Testing**} \\ \cline{3-10}  & & & **R\({}^{2}\)** & **RMSE** & **R\({}^{2}\)** & **RMSE** & **R\({}^{2}\)** & **RMSE** & **R\({}^{2}\)** & **RMSE** & \\ \hline
1 & 0.8 & 3.2 & 0.812 & 0.092 & 0.920 & 0.079 & 2 & 6 & 7 & 7 & 22 \\
2 & 1.333 & 2.667 & 0.849 & 0.092 & 0.741 & 0.114 & 4 & 6 & 3 & 2 & 15 \\
3 & 1.714 & 2.286 & 0.854 & 0.092 & 0.844 & 0.083 & 5 & 6 & 6 & 6 & 23 \\
4 & 3.2 & 0.8 & 0.785 & 0.109 & 0.830 & 0.098 & 1 & 4 & 5 & 3 & 13 \\
5 & 2.667 & 1.333 & 0.813 & 0.104 & 0.825 & 0.087 & 3 & 5 & 4 & 5 & 17 \\
6 & 2.286 & 1.714 & 0.858 & 0.089 & 0.671 & 0.133 & 6 & 7 & 2 & 1 & 16 \\
7 & 2 & 2 & 0.873 & 0.089 & 0.670 & 0.090 & 7 & 7 & 1 & 4 & 19 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Neuro-swarm models with different coefficient of velocity equations. train and test stages were achieved respectively for the best ANN model. Then, in order to propose higher performance capacity in predicting pile settlement, the effects of the most important PSO parameters on the neuro-swarm system have been investigated. It was observed that by determining of each effective PSO parameter, the prediction performance of neuro-swarm system improves based on system error and R\({}^{2}\). Finally, based on the obtained values of the most significant PSO parameters, five neuro-swarm models have been built to predict pile settlement. To select the best predictive neuro-swarm model, five performance indices including variance account for (VAF), R\({}^{2}\), mean absolute error (MAE), RMSE and the _a20-index_ have been used and applied. These performance indices have been widely utilized to assess model performance in the previous related works [23; 71; 72; 73; 74; 75; 76; 77; 78; 79; 80; 81]. The computation formulas of VAF, MAE and _a20-index_ are presented as follows:  
\[VAF=[1\ -\ \frac{var\ (x_{times}-x_{ipred})}{var\ (x_{times})}\ ]\times 100 \tag{5}\]  
\[MAE=\ \frac{1}{N}\sum_{i=1}^{N}\abs{x_{ipred}-x_{times}} \tag{6}\]  
\[a20-index=\frac{m20}{N} \tag{7}\]  
where, \(x_{times}\) and \(x_{ipred}\) are the measured and predicted values, respectively. \(N\) is the total No. of datasets, and _m20_ is the No. of samples with values of rate measured/predicted value (range between 0.8-1.2).