# On the Use of Neuro-Swarm System to Forecast the Pile Settlement
## 4 Results and Discussion
The values of 1, 100%, 0 and 0 are required for performance indices of \(R^{2}\), _VAF_, _RMSE_ and _MAE_, respectively, when a perfect predictive model is of interest. It is important to mention that the _a20-index_ with value of one should be obtained for a perfect predictive model. Table 5 represents the prediction performance of 5 neuro-swarm models in estimating settlement of pile. Great performances of the training datasets imply the fruitfulness of the learning process. Moreover, more accurate testing datasets results reveal the well-generalized nature of the proposed models. It should be noted that the authors split data into the training (80%) and testing (20%) datasets in this study. This combination has been suggested and used by many scholars (e.g., [65; 82; 83]). Since the best neuro-swarm model in Table 5 was barely recognizable because the results of 5 models are very close to each other, the ranking system proposed by [PERSON] et al. [69] has been used to recognize the best model similar to the model development stages. In this table, the total rank refers to the ranking values obtained by each datasets (i.e., training and testing), while, the final rank is a summation value of total rank for the specific datasets (train and test). Therefore, the final rank values should be used for comparison purposes of the neuro-swarm models. The best results in predicting pile settlement are related to model number 4 with final rank of 32 and total rank values of 13 and 19, respectively for train and test. Results of (0.851, 0.079, 85.056%, 0.071 and 0.649) and (0.892, 0.099, 84.738%, 0.087 and 0.474) were obtained for the performance indices of R\({}^{2}\), RMSE, VAF, MAE and _a20-index_, respectively. Generally, these results reveal that the neuro-swarm model is capable enough to predict pile settlement. Figures 5 and 6 depict the predicted pile settlement values along with their actual values for train and test sections of the best neuro-swarm model, respectively. These two figures show the ability of the neuro-swarm model in solving pile settlement with low level of system error. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**R2**} & \multicolumn{3}{c}{**RMSE**} & \multicolumn{3}{c}{**VAF**} & \multicolumn{3}{c}{**MAE**} & \multicolumn{3}{c}{_a20-index_} & \multicolumn{1}{c}{**Total**} & \multicolumn{1}{c}{**Final**} \\ \cline{2-13}
**Model** & **Dataset** & **Value** & **Rank** & **Value** & **Rank** & **Value** & **Rank** & **Value** & **Rank** & **Value** & **Rank** & **Value** & **Rank** & **Rank** \\ \hline \multirow{2}{*}{\(1\)} & Training & 0.884 & 5 & 0.082 & 4 & 88.306 & 5 & 0.066 & 5 & 0.675 & 4 & 23 & \\  & Testing & 0.623 & 1 & 0.156 & 1 & 53.748 & 1 & 0.130 & 1 & 0.421 & 2 & 6 & 29 \\ \hline \multirow{2}{*}{\(2\)} & Training & 0.854 & 2 & 0.093 & 2 & 85.206 & 2 & 0.078 & 1 & 0.610 & 2 & 9 & 31 \\  & Testing & 0.844 & 4 & 0.087 & 5 & 83.581 & 4 & 0.072 & 5 & 0.526 & 4 & 22 & 31 \\ \hline \multirow{2}{*}{\(3\)} & Training & 0.869 & 4 & 0.085 & 3 & 86.877 & 4 & 0.069 & 4 & 0.688 & 5 & 20 & \\  & Testing & 0.775 & 2 & 0.114 & 2 & 77.526 & 2 & 0.092 & 2 & 0.474 & 3 & 11 & 31 \\ \hline \multirow{2}{*}{\(4\)} & Training & 0.851 & 1 & 0.079 & 5 & 85.056 & 1 & 0.071 & 3 & 0.649 & 3 & 13 & 32 \\  & Testing & 0.892 & 5 & 0.099 & 3 & 84.738 & 5 & 0.087 & 3 & 0.474 & 3 & 19 & 32 \\ \hline \multirow{2}{*}{\(5\)} & Training & 0.856 & 3 & 0.093 & 2 & 85.532 & 3 & 0.074 & 2 & 0.558 & 1 & 11 & \\  & Testing & 0.821 & 3 & 0.098 & 4 & 81.929 & 3 & 0.078 & 4 & 0.684 & 5 & 19 & 30 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Obtained results of performance indices for 5 neuro-swarm hybrid models. It is important to say that the same database has been applied by [PERSON] et al. [3] to introduce GEP model for pile settlement estimation. In that study, they successfully indicated that GEP model is able to deliver higher capacity in comparison with the MLR model. The results of GEP model based on R\({}^{2}\) were 0.872 and 0.861, respectively for train and test stages.