# Predicting the Mine Friction Coefficient Using the GSCV-RF Hybrid Approach
## 3 Example Analysis
### GSCV-RF Model Predictions
#### 3.5.2 Model Training and Prediction  
The parameters shown in Table 6 were used as the input parameters, and training models for the passive and active support training sets were employed. Figures 10 and 11 depict the \(\alpha\) of the corresponding test set prediction result after the training.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**No.** & **Parameter Name** & \
\begin{tabular}{c} **Optimum Value** \\ **(Passive Support)** \\ \end{tabular} &
\begin{tabular}{c} **Optimum Value** \\ **(Active Support)** \\ \end{tabular} \\ \hline
1 & _n_estimators_ & 67 & 110 \\
2 & _max\_features_ & 0.9 & 1.0 \\
3 & _max\_depth_ & 9 & 3 \\ \hline \hline \end{tabular}
\end{table}
Table 6: GSCV-RF Model Parameter Optimization Results.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**No.** & **Parameter Name** & **Parameter Range** & **Step Length** \\ \hline
1 & _n\_estimators_ & [10, 150] & 1 \\
2 & _max\_features_ & [0.1, 1.0] & 0.1 \\
3 & _max\_depth_ & [3; 50] & 1 \\ \hline \hline \end{tabular}
\end{table}
Table 5: GSCV-RF Model Parameter Optimization Settings.  
Figure 9: The active support RF model prediction results. (**a**) Correlation evaluation of the measured and predicted values of \(\alpha\); (**b**) curves of the measured and predicted values of the samples; (**c**) sample prediction error curve; (**d**) sample error frequency distribution.  
As demonstrated in Figures 10a and 11a, the majority of samples were positioned near y = x. Hence, we know that the actual measurement value of the passive and active support training sets and test sets was more closely comparable to the predicted value. In the passive support training sets, the values of _MAE_, _RMSE_ and \(R^{2}\) were 0.0018, 0.0025 and 0.9965, respectively, and in the passive support test sets, the values were 0.0112, 0.01597 and 0.8845, respectively. In the active support training sets, the values were 0.0014, 0.0019 and 0.9641, respectively, and in the active support test sets, the values were 0.0024, 0.0028 and 0.9294, respectively. All the values of the _MAE_ and _RMSE_ of datasets were less than 0.05, and the value of \(R^{2}\) was more than 0.85.  
As observed in Figure 10b,c and Figure 11b,c, the sample numbers of the passive support test sets were 1, 2, 6, 11, 14, 15, 18, 21 and 24. The deviation of the prediction from the field-measured value was slightly large, accounting for 37.5% of all the sample numbers. The sample numbers of the active support training sets were 1, 8, 11, 14, 22, 23, 26, 29 and 30. The deviation of the prediction from the field-measured value was slightly large, accounting for 30% of all the sample numbers. The sample numbers of the active support test sets were 1, 2, 5 and 6. The deviation of the prediction from the field-measured value was slightly large, which was 66% of all the sample numbers. In addition, the prediction values of the remaining samples were close to the actual value.  
In Figures 10d and 11d, the frequency distribution of the samples' relative error is depicted. Thus, we can conclude that the majority of the samples' relative error was closer to 0.  
As stated previously, the GSCV-RF model can achieve superior prediction results for both passive and active support datasets. Additionally, the trained GSCV-RF model was used for the test set prediction, and the prediction result of the active support test sets was superior to that of the passive support test sets.  
Figure 10: The passive support GSCV-RF model prediction results. (**a**) Correlation evaluation of the measured and predicted values of \(\alpha\); (**b**) curves of the measured and predicted values of the samples; (**c**) sample prediction error curve; (**d**) sample error frequency distribution.