## 5 Experiment
### Clustering Comparison Experiment  
This experiment was conducted on a computer with 11 th Gen Intel(R) Core(TM) i7-11700K 3.60 GHz, RAM: 32.0 GB, and graphics card NVIDIA GeForce RTX3050, using python 3.9 and tensorflow-gpu 2.6.0. The data was input into the MDCAE model for training, and then the similarity measurement matrices were extracted using the CSBD-Vol, CSBD, SBD-Vol, and SBD algorithms, respectively, and k-medoids clustering was performed. The results are shown in detail in Table 4.  
\begin{table}
\begin{tabular}{c c c} \hline
**Model** & **Reach Optimal Number of Iterations** & **Achieve Optimal MSE** \\ \hline MDCAE & 1399 & \(6.4803\times 10^{-5}\) \\ MCAE & 958 & \(9.4358\times 10^{-5}\) \\ DCAE & 1042 & \(8.6346\times 10^{-5}\) \\ CAE & 1794 & \(1.6542\times 10^{-4}\) \\ \hline \end{tabular}
\end{table}
Table 2: Comparison of reconstruction performance of different experimental models.  
\begin{table}
\begin{tabular}{c c c} \hline
**Model** & **Reach Optimal Number of Iterations** & **Achieve Optimal MSE** \\ \hline MDCAE & 1399 & \(6.4803\times 10^{-5}\) \\ ExtraMAE & 516 & 0.0074 \\ LSTM-SAE & 357 & \(6.5176\times 10^{-4}\) \\ Time-VAE & 1522 & \(6.5043\times 10^{-5}\) \\ \hline \end{tabular}
\end{table}
Table 3: Comparison of reconstruction performance between the candidate model and the the proposed model.  
From the results presented in Table 4, it can be seen that the running time cost of the SBD algorithm without adding the constrained time window is higher than that of adding the constrained time window. Moreover, the tail oscillation effect of the time series without adding the constrained time window is extremely sensitive, resulting in a higher classification error rate. Therefore, it can be concluded that for time series clustering, adding a constrained time window is necessary. The volatility proposed in this paper has greatly improved the accuracy and robustness of the algorithm. The CSBD-Vol algorithm, which incorporates volatility and adds a constrained time window, performs excellently in multiple indicators such as the Silhouette Coefficient, the Rand Index, the Adjusted Rand Index, and the standardized mutual information. The final clustering RI reaches more than 87%. This indicates that each component of the algorithm model is indispensable, and they complement each other and play a key role. Figures 7 and 8 present the clustering effects under the four calculation methods of CSBD-Vol, CSBD, SBD-Vol, and SBD, respectively.  
According to the results shown in Figures 7 and 8, the clustering effect of the CSBD algorithm fused with volatility is significantly better than the original SBD and other algorithms, especially showing significant advantages in the discrimination between micro-seismic events and other events such as blasting and noise. Therefore, it can be concluded  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Model** & **Time per Iteration** & **SC** & **RI** & **ARI** & **NMI** \\ \hline CSBD-Vol & 1.44 s & 0.80 & 0.87 & 0.72 & 0.71 \\ CSBD & 1.58 s & \(-\)0.02 & 0.56 & 0.02 & 0.02 \\ SBD-Vol & 1.93 s & 0.69 & 0.82 & 0.60 & 0.61 \\ SBD & 1.985 s & \(-\)0.03 & 0.57 & 0.05 & 0.06 \\ \hline \end{tabular}
\end{table}
Table 4: Clustering results of different similarity measurement methods.  
Figure 7: T-SNE visualization of clustering results using CSBD-Vol, CSBD, SBD-Vol, and SBD.  
that the CSBD-Vol algorithm proposed in this paper provides a new, more accurate and efficient method for capturing abnormal events in the microseismic system.