# Prediction Method for Mine Earthquake in Time Sequence Based on Clustering Analysis
## 4 Engineering Experiments
### Prediction of Mine Earthquake
#### 4.3.2 Prediction for Frequency of High-Energy Events  
For the microseism events in the cluster, the occurrence frequencies corresponding to different energy levels are counted every day. The energy levels are divided according to \(10^{2}\) J, \(10^{3}\) J, \(10^{4}\) J, \(10^{5}\) J... As with the location prediction, only high-energy events with energy above \(10^{4}\) J are selected as the prediction objects. The specific method is using the related frequency information of the previous three days, to predict the occurrence frequency of high-energy events in the next day. Therefore, the precursory pattern sequence features of the model are the daily occurrence frequency of microseism events with different energy levels in the previous three days, and the corresponding label is the occurrence frequency of high-energy mine earthquakes with different energy level in the next day. As shown in Figure 14, \(D=(d_{1},d_{2},d_{3},\ldots,d_{m})\) is the time series set of microseism energy  
Figure 13: Prediction of SVR with different kernel functions on X coordinate. (**a**) Linear kernel. (**b**) Sigmoid kernel. (**c**) Polynomial kernel. (**d**) RBF kernel.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Assessment**} & \multicolumn{4}{c}{**Kernel Functions**} \\ \cline{2-5}  & **Linear** & **Sigmoid** & **Polynomial** & **RBF** \\ \hline MSE & 0.0355 & 0.0403 & 0.0081 & 0.0076 \\ R\({}^{2}\) & 0.3642 & 0.2772 & 0.8517 & 0.8636 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Model performance with different kernel functions.  
information, where \(d_{i}\) is the energy frequency data within a day. When the sampling step is 3 and the moving step is 1, the precursory pattern sequence set \(S=(s_{1},s_{2},s_{3},\ldots,s_{v})\) can be obtained, where \(s_{i}\) is a precursory pattern sequence, which contains the energy frequency information of the previous three days. The corresponding label set is \(L=(l_{1},l_{2},l_{3},\ldots,l_{v})\), where \(l_{i}\) is the label corresponding to \(s_{i}\) and contains the occurrence frequency of mine earthquakes with energy level above \(10^{4}\)J in the following day.  
The statistical result was \(m=31\). After \(D\) was processed as shown in the Figure 14, \(v=28\) was obtained, that is, the prediction model would have 28 samples and corresponding labels. The samples were divided into training set and test set according to the ratio of 7:3. The training set was used for the simulation training of the model, and the test set was used to test the effect of the training. Four kernel functions of SVR, Linear, Sigmoid, Polynomial and RBF, were selected for the experiment, and the grid search method was used to optimize the hyperparameters of model. The predicted values outputted from model and the true values were compared together to get Figure 15. In view of the equal position of different energy levels in energy frequency prediction, this case only presents the prediction of daily frequency of \(10^{4}\)J level mine earthquake due to space limitation. The MSE and \(R^{2}\) of the four prediction models with different kernel functions in the figure were calculated respectively, and the statistical results are shown in Table 6.  
Combined with Figure 15 and Table 6, it can be seen that the SVR model with RBF kernel function has the best prediction effect on the daily frequency of high-energy mine earthquakes with different energy levels.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Assessment**} & \multicolumn{4}{c}{**Kernel Functions**} \\ \cline{2-5}  & **Linear** & **Sigmoid** & **Polynomial** & **RBF** \\ \hline MSE & 1.8984 & 1.8063 & 0.6344 & 0.2251 \\ R\({}^{2}\) & \(-0.3962\) & \(-0.3301\) & 0.5328 & 0.8342 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Model performance with different kernel functions.  
Figure 14: The workflow of microseism energy data processing.