# Supervised Machine Learning Techniques to the Prediction of Tunnel Boring Machine Penetration Rate
## 4 Results and Discussion
### Result of Selected Models  
As mentioned in the previous section, KNN has been selected as the best predictive model of TBM PR. Figures 6 and 7 show the suggested structure of the KNN predictive model in predicting PR of TBM. In the development of the k-NN model, the objective of performing the model was to establish the balance between speed and accuracy. Therefore, the model automatically selected the best number of neighbors, within a small range. In the present study, we used k number between the values 3-5 by implementing a trial-and-error method of the system. Figure 6 presents the predictor space chart of the KNN model. In this figure, the predictor space gave excellent results, using the three input variables of UCS, RQD, and BTS as predictors for predicting the PR. The predictor space chart is an interactive graph of the predictor space and is directly printed out from the software. Any dot can temporarily become a focal record if selected. \"Focal records\" are simply points selected in the predictor space chart. If a focal record variable is specified, the points representing the focal records will initially be selected and becomes red. Figure 7 shows the relationship between the predictors and K selection. In the horizontal axis of the chart, the numbers of the nearest neighbor are presented. Sums of square errors are shown in the vertical axis. As shown by the figure, the errors for k = 3, 4, and 5 were determined as 7.41, 7.39, and 7.85, respectively. The results reveal that k = 4 is the best value of the nearest neighbor numbers for the developed k-NN model. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Method** & **Stage** & **R\({}^{2}\)** & **RMSE** & **VAF** & **MAE** & **a\({}^{20}\)-Index** & **R\({}^{2}\) Rank** & **RMSE** & **VAF** & **MAE** & **a\({}^{20}\)-Index** & **Total** \\  & & & & & & & & & & & & & \\ \hline \multirow{2}{*}{NN} & TS & 0.924 & 0.180 & 91.735 & 0.137 & 0.944 & 5 & 5 & 5 & 5 & 4 & 24 \\  & TR & 0.916 & 0.173 & 91.602 & 0.136 & 0.967 & 1 & 2 & 1 & 1 & 2 & 7 \\ \hline \multirow{2}{*}{SVM} & TS & 0.914 & 0.183 & 91.393 & 0.139 & 0.981 & 4 & 4 & 4 & 4 & 5 & 21 \\  & TR & 0.942 & 0.144 & 94.207 & 0.114 & 0.987 & 3 & 4 & 3 & 2 & 4 & 16 \\ \hline \multirow{2}{*}{KNN} & TS & 0.907 & 0.204 & 89.574 & 0.157 & 0.944 & 3 & 3 & 3 & 3 & 4 & 16 \\  & TR & 0.962 & 0.116 & 96.226 & 0.081 & 0.993 & 5 & 5 & 5 & 5 & 5 & 25 \\ \hline \multirow{2}{*}{CART} & TS & 0.897 & 0.216 & 88.020 & 0.164 & 0.944 & 2 & 2 & 2 & 2 & 4 & 12 \\  & TR & 0.944 & 0.144 & 94.265 & 0.104 & 0.993 & 4 & 4 & 4 & 4 & 4 & 5 & 21 \\ \hline \multirow{2}{*}{CHAID} & TS & 0.850 & 0.252 & 83.838 & 0.179 & 0.944 & 1 & 1 & 1 & 1 & 4 & 8 \\  & TR & 0.934 & 0.153 & 93.389 & 0.110 & 0.980 & 2 & 3 & 2 & 3 & 3 & 13 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The obtained results of performance indices for all predictive models in estimating TBM PR. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **NN** & **SVM** & **KNN** & **CART** & **CHAID** \\ \hline Grand total & 31 & 37 & 41 & 33 & 21 \\ rank & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Total performance ratings. Predicted PR values by KNN, along with their actual values for training and testing datasets, are displayed in Figure 8. The R\({}^{2}\) between predicted and actual PR in training and testing dataset were 0.962 and 0.907, respectively. Besides, an RMSE of (0.204 and 0.116), a VAF of (89.574% and 96.226%) and an MAE of (0.157 and 0.081) were obtained for testing and training datasets of the best predictive model of this study, respectively. These results show that KNN, as a newly developed model in the field of TBM performance, can provide higher prediction performance compared to other predictive models. It is worth mentioning that CHAID (as a tree-based model) was also implemented for the first time in this field with the obtained R\({}^{2}\) values of 0.850 and 0.934, for testing and training datasets, respectively, which showed an enhanced performance of this model in solving TBM performance.