## 2 Methods and Steps
### Explosion Surface Fitting Based on Data Fusion Method
#### 2.3.2 Data Fusion Algorithm Process
After processing with the data fusion method, the accuracy \(\sigma^{2}\) relation of each heaped-up bulk profile at position P can be expressed as follows:  
\[\begin{array}{l}\sigma^{2}=E\Big{[}\big{(}h_{2p}-H_{2p}\big{)}^{2}\Big{]}\\ =E\Bigg{[}\Bigg{(}\sum\limits_{i=1}^{m}\omega_{i}h_{2p}-\sum\limits_{i=1}^{m} \omega_{i}h_{ip}\Bigg{)  
Calculation of the optimal weight value of data fusion  
Considering that the true value of each elevation point on the profile curve of the 3D model of the heaped-up bulk is unknown, the measured value after averaging all profiles at any point \(P\) is taken as the reference value in the research process. Then, the deviation between the measured value and the reference value is regarded as the deviation from the real value; thus, the variance of the deviation of the measured value at point \(P\) and the optimal weight value are obtained. The relationship between the measured mean value at point \(P\) can be expressed as follows:  
\[h_{i}(P)=\frac{1}{m}\sum\limits_{i=1}^{m}h_{i}(P) \tag{13}\]  
Then, the deviation relation between the measured elevation values and reference values of all of the 3D model profiles of the heaped-up bulk at point \(P\) can be expressed as per the following:  
\[\Delta h_{i}(P)=h_{i}(P)-\overline{h}_{i}(P) \tag{14}\]  
The mean value relation of the elevation deviation of all of the 3D model profiles of heaped-up bulk at different measuring places can be expressed as follows:  
\[\Delta h_{i}(P)=\frac{1}{n}\sum\limits_{p=1}^{n}\Delta h_{i}(P) \tag{15}\]  
The accuracy of the blasting curve corresponding to all 3D model sections of the heaped-up bulk--that is, the standard deviation relation of the deviation--can be expressed as per the following:  
\[\sigma_{h}(i)=\sqrt{\frac{\sum\limits_{p=1}^{n}\left(\Delta h_{i}(P)-\Delta h \right)^{2}}{n-1}} \tag{16}\]  
The optimal weight value relation of the profile measurement values of all of the 3D models of the heaped-up bulk can be expressed as follows:  
\[\omega_{i}=\frac{1}{\sigma_{h}^{2}(i)\sum\limits_{i=1}^{m}\frac{1}{\sigma_{h }^{2}(i)}} \tag{17}\]  
After the integration of the above relations, the elevation fusion value of all of the 3D model profiles of heaped-up bulk at each position can be expressed as follows:  
\[H_{ZP}=\sum\limits_{i=1}^{m}\omega_{i}\times h_{i}(P) \tag{18}\]  
In view of this, the 3D shape simulation curve of the heaped-up bulk model can be calculated from the elevation fusion value \(H_{ZP}\). Finally, the height fusion value obtained through the data fusion is shown in \[\sum_{i=1}^{m}\omega_{i}=1 \tag{6}\]0  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Position** & **No 1** & **No 2** & **No 3** & **No 4** & **No 5** & **No 6** & **No 7** &... \\ \hline
0 & 1094.0 & 1093.9 & 1096.2 & 1106.6 & 1095.3 & 1095.0 & 1096.4 &... \\
10 & 1094.5 & 1093.5 & 1086.6 & 1106.3 & 1095.3 & 1094.7 & 1095.8 &... \\
20 & 1095.1 & 1093.4 & 1086.5 & 1106.6 & 1094.6 & 1094.2 & 1095.2 &... \\
30 & 1095.0 & 1094.1 & 1087.3 & 1107.8 & 1097.1 & 1096.1 & 1094.8 &... \\... &... &... &... &... &... &... &... &... &... \\
180 & 1047.7 & 1047.3 & 1049.5 & 1064.1 & 1061.9 & 1062.5 & 1062.4 &... \\
190 & 1047.8 & 1047.5 & 1050.6 & 1063.4 & 1063.5 & 1062.3 & 1064.2 &... \\
200 & 1047.4 & 1047.8 & 1051.4 & 1063.1 & 1059.4 &