## 4 Wavelet Energy Evolution Characteristics
### Characteristics of the Wavelet Energy Evolution  
During the entire rockburst test, the wavelet energy evolution characteristics of the TL3 specimen's AE signals were analyzed. Firstly, all the effective acoustic emission signals were extracted, and the full-time waveform was plotted, which is shown in Figure 11. Then, the acoustic emission signals were subjected to a five-layer wavelet decomposed and reconstructed to obtain six frequency band sub-signals. Finally, the wavelet energy and its energy distribution coefficients of different frequency band reconstructed signals were calculated, and the energy distribution coefficient evolution process of each frequency band was plotted. As shown in Figure 12, the moving average, marked by the red line, is to eliminate the randomness of the data and obtain a relatively smooth trend line. \begin{table}
\begin{tabular}{c c c c c c c} \hline  & **CD\({}_{1}\)** & **CD\({}_{2}\)** & **CD\({}_{3}\)** & **CD\({}_{4}\)** & **CD\({}_{5}\)** & **CA\({}_{5}\)** \\ \hline E & 0.1983 & 0.2812 & 0.1352 & 0.0830 & 0.0046 & 0.0025 \\ K & 0.2813 & 0.3990 & 0.1918 & 0.1177 & 0.0066 & 0.0036 \\ \hline \end{tabular}
\end{table} 
Table 2: Reconstructed signal energy and distribution coefficient. Figure 10: _Cont._  
Figure 10: The 3546 th effective acoustic emission signal. (**a**) The original AE signal waveform; (**b**) AE signal reconstructed waveform of each frequency band. Three distinct phases can be distinguished in the test process by combining the test phenomenon and the evolution law of the energy distribution coefficients to each frequency band. The three stages are the compaction stage (0-60 s), the quiet period (60-520 s), and the destruction stage (520-635 s). Figure 11: Acoustic emission full-time waveform. Figure 12: Evolution process of the energy distribution coefficients. According to Figure 12, for the frequency band of 0\(\sim\)15.625 kHz, the energy distribution coefficients are mainly concentrated below 0.2 and its moving average has multiple peaks in the destruction stage (up to 0.173). For the frequency band of 15.625\(\sim\)31.250 kHz, the energy distribution coefficients are largely concentrated below 0.1 and its moving average has a single peak in the destruction stage (up to 0.090). For the frequency band of 31.25-62.50 kHz, the energy distribution coefficients are principally concentrated around 0.07, its moving average decreases slowly (from 0.066 to 0.036) during the quiet period and shows peak type during the destruction phase (peak values are 0.131 and 0.146 respectively). For the frequency band of 62.5-125.0 kHz, the energy distribution coefficients are mainly concentrated around 0.18 and its moving average declines steadily at first (from 0.180 to 0.138) in the quiet period, and then rises. There are two peaks in the destruction stage (peak values are 0.202 and 0.208, respectively). For the frequency band of 125-250 kHz, the energy distribution coefficients are mostly concentrated around 0.47 and its moving average appears valley-type (valley value is 0.386 and 0.324, respectively) in the destruction stage. For the frequency band of 250-500 kHz, the energy distribution coefficients are largely concentrated around 0.23 and its moving average rises slowly (from 0.237 to 0.306) during the quiet period. The moving average changed from the valley type (valley value 0.208) to the peak type (peak value 0.388) during the destruction phase. In terms of the density of the energy distribution coefficients, each frequency band appeared intensively in the compaction and destruction stages. From the perspective of the moving average, the energy distribution coefficients of each frequency band are different in the destruction stage, particularly, the trend in the 125-250 kHz frequency band shows a significant valley-type. In the whole process of the experiment, the energy distribution coefficients of the 125-250 kHz frequency band had a more obvious advantage than other frequency bands.