## 2 Methods and Steps
### Sensitivity Analysis Method for the Influencing Factors of the Haeped-Up Bulk Characteristics
#### 2.4.2. Gray Correlation Degree and Its Calculation Method  
The mean value image is obtained by means of variable averaging  
Considering the different units of cast blasting factor variables and characteristic variables, in order to ensure the accuracy and convenience of the correlation degree calculation, it is necessary to average the variables before the correlation degree calculation to obtain the corresponding mean image so as to achieve the purpose of unit unity. Then, based on the averaging operator \(D_{1}\), the mean image of the variable sequence can be obtained as follows:  
\[\left\{ \begin{array}{l}X_{i}^{1}=X_{i}D_{1}=\left[x_{i}^{1}(1),x_{i}^{1}(2),x _{i}^{1}(3),\cdots,x_{i}^{1}(k),\cdots,x_{i}^{1}(s)\right]\\ Y_{i}^{1}=Y_{i}D_{1}=\left[y_{i}^{1}(1),y_{i}^{1}(2),y_{i}^{1}(3),\cdots,y_{i} ^{1}(k),\cdots,y_{i}^{1}(s)\right]\end{array} \right. \tag{20}\]  
Among these, we have the following:  
\[\left\{ \begin{array}{l}x_{i}^{1}(k)=x_{i}(k)/x,x=\frac{1}{n}\sum\limits_{k= 1}^{n}x_{i}(k)\\ y_{i}^{1}(k)=y_{i}(k)/y,y=\frac{1}{n}\sum\limits_{k=1}^{n}y_{i}(k)\end{array} \right. \tag{21}\]  
According to the above calculation process, after calculating the variable samples of the cast blasting system, the corresponding mean values that were obtained are shown in Table 4 below. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline
**No** & \(x_{1}\) & \(x_{2}\) & \(x_{3}\) & \(x_{4}\) & \(x_{5}\) & \(x_{6}\) & \(x_{7}\) & \(x_{8}\) & \(x_{9}\) & \(y_{1}\) & \(y_{2}\) & \(y_{3}\) \\ \hline
1 & 0.861 & 1.000 & 0.953 & 1.000 & 0.978 & 1.006 & 1.026 & 1.028 & 1.000 & 0.990 & 0.915 & 0.904 \\
2 & 0.869 & 1.000 & 0.994 & 1.000 & 1.022 & 1.015 & 0.969 & 0.986 & 1.000 & 1.006 & 0.969 & 0.915 \\
3 & 0.876 & 1.000 & 1.008 & 1.000 & 1.022 & 1.023 & 0.983 & 1.056 & 1.000 & 0.990 & 0.955 & 0.930 \\
4 & 0.883 & 1.000 & 0.967 & 1.000 & 0.993 & 0.981 & 1.012 & 0.944 & 1.000 & 0.998 & 0.940 & 0.918 \\
5 & 0.890 & 1.000 & 0.953 & 1.000 & 0.978 & 1.023 & 0.983 & 1.000 & 1.000 & 0.990 & 0.986 & 0.934 \\
6 & 0.890 & 1.000 & 0.925 & 1.000 & 1.022 & 0.981 & 1.040 & 0.958 & 1.000 & 0.974 & 0.943 & 0.922 \\
7 & 0.900 & 1.000 & 1.008 & 1.000 & 1.036 & 0.990 & 1.026 & 1.000 & 1.000 & 1.014 & 0.986 & 0.974 \\
8 & 0.909 & 1.000 & 1.008 & 1.000 & 0.993 & 0.990 & 0.983 & 1.014 & 1.000 & 0.998 & 0.963 & 0.999 \\
9 & 0.916 & 1.000 & 0.925 & 1.000 & 0.935 & 1.023 & 0.955 & 1.042 & 1.000 & 1.006 & 0.932 & 0.963 \\... &... &... &... &... &... &... &... &... &... &... &... &... \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Partial mean image of the cast blasting system. Figure 5: Schematic diagram of the parameters of the cast blasting step. * Construction of the absolute correlation matrix \[y_{i}^{0}(k)=y_{i}^{1}(k)-y_{i}^{1}(1)\] (22) Among these, we have the following: \[\left\{ \begin{array}{l}\left|XS_{i}\right|=\left|\sum\limits_{k=2}^{n-1}x_{i}^ {0}(k)+\frac{1}{2}x_{i}^{0}(s)\right|\\ \left|YS_{j}\right|=\left|\sum\limits_{k=2}^{n-1}y_{j}^{0}(k)+\frac{1}{2}y_{j}^ {0}(s)\right|\end{array} \right.\] (23) \[\left|XS_{i}-YS_{j}\right|=\left|\sum\limits_{k=2}^{n-1}x_{i}^{0}(k)-y_{j}^{0} (k)\right|+\frac{1}{2}\left[x_{i}^{0}(s)-y_{j}^{0}(s)\right]\] (24)  
By calculating the gray absolute correlation degree of the related variables of the cast blasting above, the corresponding absolute correlation matrix can be obtained at last:  
\[A=\left(\varepsilon_{ij}\right)= \begin{bmatrix}\varepsilon_{11}&\varepsilon_{12 }&\cdots&\varepsilon_{1m}\\ \varepsilon_{21}&\varepsilon_{22}&\cdots&\varepsilon_{2m}\\ \cdots&\cdots&\cdots&\cdots\\ \varepsilon_{n1}&\varepsilon_{n2}&\cdots&\varepsilon_{nm}\end{bmatrix}  \tag{25}\]  
According to the sample mean image of the cast blasting system and the calculation method of the gray absolute correlation degree, the corresponding absolute correlation matrix is obtained, as shown in Table 5.  
By calculating the absolute correlation matrix of the sample variables of the cast blasting system, the sensitivity of the blasting parameter index, which affects the cast blasting effect, was obtained.