## 3 Results and Discussions  
The data in this study were split into two sections: a training dataset and a testing dataset. The majority of the datasets (about 118 blasting events) are utilized for training, and the remaining (28 observations) are used for testing. The training dataset is utilized to create the aforementioned models, as shown in Figure 15. The testing dataset is used to evaluate the performance of the built models. Two statistical metrics, MAPE and RMSE were used in this research to evaluate the performance of XG Boost, KNN, and Random Forest constructed the models shown in Figure 15. The most often-used measure for determining the accuracy is the Mean Absolute Percentage Error. This falls within the category of scale-independent percentage errors, which may be used to compare series on different scales. Likewise, MSE is used to measure the degree of inaccuracy in the statistical models. The average squared difference between observed and expected values is calculated. The MSE equals zero when a model has no errors and the value rises as the model inaccuracy rises. Figure 15: Model execution and best model selection. The following equations were used to calculate MAPE and MSE in this study. \[\text{MSE}=\frac{1}{\text{n}}\sum_{i=1}^{\text{n}}\left(y_{i}-Y_{i}\right)^{2} \tag{7}\]  
Here, n represents a number of data points; \(y_{i}\) denotes observed values and \(Y_{i}\) are the predicted values. Hence, MSE is the average squared difference between the actual and predicted value. \[\text{MAPE}=\frac{100\%}{\text{n}}\sum_{t=1}^{\text{n}}\left|\ \frac{A_{t}-F_{t}}{A_{t}}\ \right| \tag{8}\]  
where \(A_{t}\) denotes the current value and \(Ft\) denotes the predicted value. The difference between them is divided by the actual value of \(A_{t}\). This ratio's absolute value is added for each projected point in time and divided by the number of fitted points (n). \[\text{R}^{2}\ =1-\frac{\sum\text{i}\left(\text{y}_{i}-\hat{\text{y}_{1}} \right)^{2}}{\sum\text{i}\left(\text{y}_{i}-\bar{\text{y}}\right)^{2}} \tag{9}\]  
A number of data here represented by n, yi & \(\hat{\text{y}_{i}}\) denote the actual and forecasted vales and \(\bar{\text{y}}\) denotes the mean. Metrics such as MAPE, RMSE, and R\({}^{2}\) were computed on both training and testing datasets to evaluate the performance and accuracy of the model to decide the final algorithm and to develop a formula to predict fragmentation and ground vibration. The values are presented in Table 3.  
According to Table 3 and Figure 16, XG Boost algorithms perform well in both fragmentation and peak particle velocity based on metric values of MAPE, RMSE, and R\({}^{2}\) in both 80% training and 20% testing data. Fragmentation and peak particle velocity were measured in the field, and the XG Boost, Random Forest, and KNN models predicted values using the testing data shown in Figure 17. The predicted values of the XG Boost model were very close to the measured values of both fragmentation and peak particle velocity. In this study, the XG Boost regression method was finalized and utilized to forecast the simultaneous formula for fragmentation and PPV. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **Metric** \\ **Type** \\ \end{tabular} } & \multicolumn{3}{c}{**XG Boost Regression**} & \multicolumn{2}{c}{**Random Forest**} & \multicolumn{2}{c}{**KN Nearest**} \\ \cline{2-7}  & \multicolumn{4}{c}{**Fragmentation**} \\ \cline{2-7}  & **Training** & **Testing** & **Training** & **Testing** & **Training** & **Testing** \\ \hline MAPE & 24 & 22.5 & 21.2 & 20.1 & 19.2 & 18.1 \\ \hline RMSE & 0.0854 & 3.873 & 0.0021 & 4.221 & 0.0031 & 5.321 \\ \hline R\({}^{2}\) & 0.953 & 0.9125 & 0.89 & 0.67 & 0.9 & 0.87 \\ \hline \multicolumn{7}{c}{**Peak Particle Velocity**} \\ \hline MAPE & 19 & 18.4 & 17.5 & 15.8 & 16.9 & 14.32 \\ \hline RMSE & 0.0056 & 2.8890 & 0.0041 & 3.78 & 0.0886 & 4.88 \\ \hline R\({}^{2}\) & 0.96 & 0.932 & 0.79 & 0.65 & 0.83 & 0.72 \\ \hline \hline \end{tabular}
\end{table}