# Open-Pit Bench Blasting Fragmentation Prediction Based on Stacking Integrated Strategy
## 3 Database  
### Data Description  
The database used in this study was established by [PERSON] et al. [4] based on the collection and evaluation of several blasting tests in different mines and rock formations around the world, all of which involved open-pit bench blasting. This database contains a total of 97 samples of blasting data covering various open-pit mines in the world, and takes into account five blasting design parameters, including burden (\(B\)), spacing (\(S\)), bench height (\(H\)), stemming (\(T\)), and hole diameter (\(D\)). The inputs for the blast design parameters are in the form of ratios to avoid the influence of different parameter units on predictions. Additionally, the explosive parameters, structural parameters, and physical and mechanical properties of the rock were used as input parameters. Specifically, this study used bench height to drilled burden (\(H\)/\(B\)), spacing to burden (\(S\)/\(B\)), burden to hole diameter (\(B\)/\(D\)), stemming to burden (\(T\)/\(B\)), powder factor (\(Pf\)), in situ block size (\(X_{B}\)), and modulus of elasticity (\(E\)) as input variables, with mean fragment size (\(X_{50}\)) as the output variable.  
In order to better characterize the data used, Figure 4 shows the detailed distribution of the seven input parameters through a combination of bar charts and violin plots, with the mean and median of the data indicated by solid and hollow dots in the half violin plots. It can be observed that the sample point distribution of most input parameters is relatively concentrated, particularly for input parameter \(E\), which is mostly concentrated in the 0-20 and 40-70 intervals. Table 1 details the four statistical characteristics of all input parameters, including minimum, maximum, mean, and standard deviation. Figure 5 illustrates the degree of correlation between the input parameters using a heat map. It can be observed that there is a certain correlation between the input parameters, which makes them reasonable as input variables for the model. The dataset was randomly divided into two groups: 80% was used as the training set to construct the prediction model, and the remaining 20% was used as the testing set to evaluate the model's performance. To reduce bias among the input variables and enhance the model's accuracy, the data were normalized using the StandardScaler function before prediction. The standardization formula is as follows:  
\[x^{\star}=\frac{x-\mu}{\sigma} \tag{3}\]  
where \(\mu\) is the mean of the data set, \(\sigma\) is the standard deviation of the dataset, and \(x\) and \(x^{\star}\) are the data values before and after standardization, respectively.  
Figure 4: \(Cont\).  
Figure 4: Distribution of input parameters: (**a**) spacing to burden; (**b**) bench height to drilled; burden; (**c**) burden to hole diameter; (**d**) stemming to burden; (**e**) powder factor; (**f**) insitu block size; (**g**) modulus of slasticity.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameters** & **Minimum** & **Maximum** & **Mean** & **Standard Deviation** \\ \hline S/B & 1.00 & 1.75 & 1.20 & 0.109 \\ H/B & 1.33 & 6.82 & 3.44 & 1.64 \\ B/D & 17.98 & 39.47 & 27.21 & 4.77 \\ T/B & 0.50 & 4.67 & 1.27 & 0.688 \\ Pf(kg/m\({}^{3}\)) & 0.22 & 1.26 & 0.53 & 0.238 \\ XB(m) & 0.02 & 2.35 & 1.17 & 0.479 \\ E(GPa) & 9.57 & 60.00 & 30.74 & 17.72 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Statistical characterization of model input parameters.