# On the Use of Neuro-Swarm System to Forecast the Pile Settlement
## 3 Model Development
### Neuro-Swarm Design
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \multirow{2}{*}{**Model No.**} & \multirow{2}{*}{**SS**} & \multicolumn{4}{c}{**Neuro-Swarm Results**} & \multicolumn{4}{c}{**Ranking**} & \multirow{2}{*}{**Total Rank**} \\ \cline{3-3} \cline{5-12}  & & \multicolumn{2}{c}{**Training**} & \multicolumn{2}{c}{**Testing**} & & \multicolumn{2}{c}{**Training**} & & \multicolumn{2}{c}{**Testing**} & \\  & & \(\mathbf{R^{2}}\) & **RMSE** & \(\mathbf{R^{2}}\) & **RMSE** & \(\mathbf{R^{2}}\) & **RMSE** & \(\mathbf{R^{2}}\) & **RMSE** & **RMSE** & \\ \hline
1 & 25 & 0.749 & 0.104 & 0.909 & 0.098 & 3 & 6 & 10 & 5 & 24 \\
2 & 50 & 0.772 & 0.101 & 0.885 & 0.107 & 4 & 8 & 9 & 3 & 24 \\
3 & 75 & 0.828 & 0.102 & 0.785 & 0.087 & 9 & 7 & 3 & 8 & 27 \\
4 & 100 & 0.805 & 0.101 & 0.819 & 0.109 & 6 & 8 & 6 & 2 & 22 \\
5 & 150 & 0.818 & 0.095 & 0.781 & 0.123 & 7 & 10 & 2 & 1 & 20 \\
6 & 200 & 0.827 & 0.010 & 0.771 & 0.103 & 8 & 9 & 1 & 4 & 22 \\
7 & 250 & 0.827 & 0.102 & 0.811 & 0.076 & 8 & 7 & 5 & 10 & 30 \\
8 & 300 & 0.796 & 0.106 & 0.881 & 0.081 & 5 & 5 & 8 & 9 & 27 \\
9 & 350 & 0.844 & 0.095 & 0.792 & 0.096 & 10 & 10 & 4 & 6 & 30 \\
10 & 400 & 0.828 & 0.095 & 0.860 & 0.089 & 9 & 10 & 7 & 7 & 33 \\ \hline \end{tabular}
\end{table} 
Table 2: Results of neuro-swarm models with different SS values. Figure 4: Parametric study to determine max iteration. of these combinations based on R\({}^{2}\) and RMSE. According to this table and also application of simple ranking by [PERSON] et al. [69], model number 3 with the combination of \(C_{1}=1.714\) and \(C_{2}=2.286\) outperforms the other implemented models. These \(C_{1}\) and \(C_{2}\) values will be used for the rest of neuro-swarm models. It is worth noting that in these models, SS = 400 and max iteration of 400 obtained from the previous stages, were used. Selection of the appreciate value for inertia weight is the next modeling stage. This has been done by using the different values of \(w\) i.e., 0.25, 0.5, 0.75 and 1 to see their prediction performance in estimating pile settlement. In conducting this parametric study, the obtained values from the previous stages have been considered and utilized. Table 4 shows results of 4 neuro-swarm models with \(w=0.25\), \(w=0.5\), \(w=0.75\) and \(w=1\) based on their performance prediction together with rankings and total rankings of each model. As a result, the highest prediction performance can be achieved when inertia weight set as 1 (model number 4). Hence, \(w=1\) was chosen as the best inertia weight in modeling of neuro-swarm intelligence system. As the last modeling stage of neuro-swarm system, there is a need to divide the database into 5 different trains and tests sections to see their effects on system's results. The process has been suggested in the previous studies as well [19; 70]. Five neuro-swarm models have been constructed to forecast settlement of the pile according to the architecture of ANN (\(5\times 3\times 1\)), SS = 400, max iteration = 400, \(C_{1}=1.714\) and \(C_{2}=2.286\) and \(w=1\). Five time running is due to the fact that the system could use the randomly selected datasets, train them and test them to see their effects on the neuro-swarm model performance. The performance predictions of these hybrid models to forecast the pile settlement will be assessed in details later.