# Prediction Method for Mine Earthquake in Time Sequence Based on Clustering Analysis
## 4 Engineering Experiments
### Clustering of Microseism Events  
The ST-DBSCAN algorithm is used to cluster microseism events in the target working face. According to the empirical formula (3), \(\mathit{Minpts}=\mathit{lnN}\approx\mathit{9}\) can be calculated. The spatial radius \(\mathit{Eps}\) and time window \(\Delta T\) of the cluster are obtained from the K-Dist graph [32], where K takes the value of \(\mathit{Minpts}\), which is 9 at this time. The specific steps are to calculate the spatial distance and temporal distance between each sample point and the ninth closest point, and draw the corresponding 9-Dist graph in descending order, the distance value corresponding to the inflection point is the effective radius of dividing the noise point and the non-noise point. The 9-Dist graph is shown in the following Figure 8.  
Figure 6: Distribution of microseisms on working face. Figure 7: Distribution of microseisms in three-dimensional space. By observing Figure 8, the vertical axis coordinate values corresponding to the two inflection points are 80 and 20, respectively. However, considering the influence of human factors, there may be subjective errors in the vertical axis coordinate values. In order to find the parameters with the best clustering results, different distance values corresponding to inflection points were selected to carry out the parameter combination clustering tests. \(Eps\) was taken as [70 80 90], and \(\Delta T\) was taken as [15 20 25]. In Table 2, nine parameter combinations can be obtained based on the different values of \(Eps\) and \(\Delta T\), numbered ID1 to ID9. respectively. In order to measure the effect of clustering, the Silhouette Coefficient (SC) is selected as the clustering effectiveness assessment index [33]. Generally speaking, the higher the average SC of the samples in the clusters, the better the clustering quality. For any point \(i\) in the cluster, the SC is calculated as follows:  
\[SC(i)=\frac{b(i)-a(i)}{\max\{a(i),b(i)\}} \tag{18}\]  
where \(a(i)\) is the degree of dissimilarity within the cluster, representing the average value of the degree of dissimilarity from point \(i\) to other points in the same cluster, reflecting the degree of cohesion; \(b(i)\) is the degree of dissimilarity between clusters, representing the minimum value of the average degree of dissimilarity from point \(i\) to other clusters, reflecting the degree of separation. It can be seen that the value of SC is between \([-1,1]\), and the closer it is to 1, the better cohesion and separation degree are. The average of the SC of all points is the comprehensive SC of the clustering result. The clustering algorithm program is run on the nine parameter combinations in Table 2, and the output results are the specific cluster sets and noise points that are not classified into any clusters. Different parameter combinations of \(Eps\) and \(\Delta T\) will get different clustering results. Their SC are calculated respectively and the noise rate is counted. The results are shown in Table 3 and Figure 9. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{_Eps_ **(m)**} & \multicolumn{3}{c}{**\(\Delta T\) (h)**} \\ \cline{2-4}  & **15** & **20** & **25** \\ \hline
70 & ID1 & ID4 & ID7 \\
80 & ID2 & ID5 & ID8 \\
90 & ID3 & ID6 & ID9 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameter combinations of \(Eps\) and \(\Delta T\). Figure 8: 9-Dist graph. (**a**) Spatial distance. (**b**) Temporal distance. It can be easily seen from Figure 9 that the SC of ID5 is high and the noise rate is low. Therefore, when \(Eps\) is set to 80 and \(\Delta T\) is set to 20, the clustering result is the best. Different colors are used to represent different clusters, and the clustering result of this parameter combination is presented in three-dimensional space, as shown in Figure 10.  
At this time, the noise rate is 12.2%, and 47 microseism clusters are obtained, and the largest cluster contains 1077 events.