## 5 Experiments
### Uniaxial Compression Test  
The experimental system includes a loading system and an AE system. An MTS C45.104 testing machine is used in the loading system. The AE instrument utilizes a PCI-Express8 multi-channel AE system manufactured by American Physical Acoustics Company, along with Nano 30 miniature sensors. The sensor has a frequency range of 125-750 kHz, and it is equipped with a 2/4/6 voltage preamplifier that allows for a selectable range of 20, 40, and 60 dB. Before the test, the sampling rate is set to 1 Msample/s. The tests are displacement-controlled at a rate of 1 mm/min.  
All the coal samples tested are taken from Wanglou Coal Mine, Shandong Province, China. All samples are prepared in accordance with the ISRM-suggested shape and size and are processed into cylinders with a diameter of 50 mm and a height of 100 mm. Five samples are prepared, numbered wl-2, wl-3, wl-5, wl-6, and wl-8. The stress-strain curve is shown in Figure 8, and the basic physical and mechanical parameters are shown in Table 3. It can be observed that the uniaxial compressive strength of specimens wl-5, wl-6, and wl-8 is relatively low. This is because coal is a material with significant heterogeneity, con  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multirow{2}{*}{**Metrics**} & \multicolumn{4}{c}{**Simulation AE Signal**} \\ \cline{3-5}  & & **SNR = 5** & **SNR = 10** & **SNR = 8** \\ \hline \multirow{2}{*}{EMD} & ESN & 0.7423 & 0.6490 & 0.7423 \\  & RMSE & 0.3254 & 0.2452 & 0.3154 \\ \hline \multirow{2}{*}{EVMD} & ESN & 0.9047 & 0.9309 & 0.9122 \\  & RMSE & 0.0628 & 0.0942 & 0.0621 \\ \hline \multirow{2}{*}{FCI-VMD} & ESN & 0.9273 & 0.9456 & 0.9742 \\  & RMSE & 0.0412 & 0.0878 & 0.0251 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Evaluation index of three noise reduction methods.  
taining many inherent fractures and voids. Additionally, for coal samples with significant differences in porosity, the uniaxial compressive strength tends to vary significantly.  
The stress-AE count-cumulative AE count curve of coal under uniaxial compression is presented in Figure 9. In the initial stages of low stress, the coal sample undergoes pore compaction, resulting in a relatively small number of AE counts. As the stress gradually increases, microcracks begin to form in the coal sample, leading to a continuous increase in AE counts. When the coal sample approaches its peak strength, a significant number of dense, high-amplitude signals are generated, indicating the occurrence of instability failure. The above observations demonstrate that AE signals can effectively reflect the internal damage and propagation of microcracks in coal. By processing and analyzing the collected AE signals, it becomes possible to assess the stress stage of coal damage, offering a valuable reference for early warning systems pertaining to coal damage and instability.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Number**} & **Density** & **P-Wave Velocity** & **Uniaxial Compressive** & **Young’s** \\  & **(g/cm\({}^{3}\))** & **(m/s)** & **Strength (MPa)** & **Modulus (GPa)** \\ \hline wl-2 & 1.45 & 2023.79 & 12.15 & 2.59 \\ \hline wl-3 & 1.37 & 2050.09 & 12.35 & 2.48 \\ \hline wl-5 & 1.37 & 1550.46 & 9.7 & 2.12 \\ \hline wl-6 & 1.32 & 1981.38 & 8.67 & 2.17 \\ \hline wl-8 & 1.37 & 1532.41 & 6.25 & 1.26 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Physical and mechanical properties of coal samples.  
Figure 8: Stress–strain curve of coal specimens with uniaxial compression tests.