## 2 Data Source
### Data Augmentation  
Data from various sources may present inconsistencies, noise, incompleteness, or inadequate quantity, which can lead to challenges in data analysis. This study's small-scale database signifies that the fragmented data may be considered incomplete. The acquisition of blasting data is time-consuming and expensive, which has led to primarily limited-scale datasets. Inadequate data diminish the validity of insights that are obtained and decrease the accuracy of models in the training process. A substantial quantity of data is essential to accurate predictions and analyses, as well as for preventing overfitting and ensuring robust models. For tree-based algorithms, the prediction accuracy depends not only on hyperparameter optimization but also on the quantity of training data. Larger training datasets enable ML algorithms to better capture patterns and relationships, increasing their likelihood of making accurate predictions on unseen data. Moreover, acquiring blasting data is both time-consuming and costly [52]. Consequently, data augmentation offers a practical and recommended approach to generating large-scale datasets and thereby enhances the performance and generalizability of ML models. Data augmentation methods vary depending on the type and dimensionality of the data. For instance, techniques such as rotating, cropping, and filtering are commonly used for image data, while jittering, slicing, and permutation are employed for curve data [59; 60]. Among these, only filtering and jittering are noise-based methods. Noise-based methods are widely adopted for data augmentation because they are versatile and applicable across different data types [61]. This study implemented noise-based data \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Data Source** & **Blast Samples** & **Input Parameters** & **Output Parameters** \\ \hline \multirow{3}{*}{[55]} & \multirow{3}{*}{76} & D, H, J, S, B, ST, L, Wd, S.B, T.B, & \multirow{3}{*}{X\({}_{50}\) (m)} \\  & & H.B, J.B, B.D, L.W, NH, Qe, De, & \\  & & PF, UCS & \\ \multirow{3}{*}{[57]} & \multirow{3}{*}{103} & SB, HB, BD, TB, Pf(kg/m\({}^{3}\)), & \multirow{3}{*}{X\({}_{50}\) (m)} \\  & & XB(m), E & \\ \multirow{3}{*}{[58]} & \multirow{3}{*}{8} & SB, HB, BD, TB, Pf(kg/m\({}^{3}\)), & \multirow{3}{*}{X\({}_{50}\) (m)} \\  & & XB(m), E & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Data collected from the published literature. augmentation by adding noise that was equivalent to 3% of the parameter values and that followed a normal distribution. This level of noise is designed to mimic uncontrollable human errors typically associated with the measurement and collection of in situ blasting data [52]. Additionally, the 3% noise does not present significant differences between the original and the augmented dataset. The dataset is organized as a 187 \(\times\) 8 matrix that contains 187 blasting samples represented as rows, with seven input parameters and one output parameter represented as columns. To expand the dataset, each data point was used to generate 20 additional points through noise-based augmentation. The newly generated data points follow a normal distribution, with the mean set being equal to the original value and the standard deviation being adjusted so that 99.7% of the generated points fall within three standard deviations of the mean. This process was applied to every value in the matrix, which resulted in a significantly larger dataset of 3740 data groups, with each retaining the same seven input and one output parameter structure. A statistical summary of the augmented large-scale dataset is provided in Table 3.  
Figure 1 presents a correlation heatmap of the features in the dataset. The correlation was computed using the mutual information (MI) regression technique, a measure of the shared information shared between two variables. MI regression quantifies how much knowing one variable reduces the uncertainty of another variable.