## 2 Materials and Methods
### Data Preprocessing
#### 2.2.2 Extraction of Common Factors  
Using SPSS (version 27), we obtained the characteristic values and variance contribution rates for each factor (see table below). In Table 2, we can see that the first three factors explain 81.898% of the total variance. This means that the three extracted common factors can represent 81.898% of the original 10 indicators that measure the characteristics of acoustic emission energy. This indicates that there is relatively little loss of data information and that the initial data can be well explained. Therefore, we extract three common factors as Y1, Y2, and Y3. By performing weighted calculations on these factors, we can obtain a comprehensive scoring model Y. The three common factors (Y1, Y2, Y3) extracted through factor analysis correspond to composite indicators for the dimensions of energy, time, and frequency, respectively:  
Y1 (Energy Factor): Composed of energy, amplitude, and average signal intensity, it reflects the trend of energy accumulation during rock mass failure. Y2 (Time Factor): Consisting of duration, rise time, and ring-down count, it characterizes the temporal evolution pattern of failure events. Y3 (Frequency Factor): Made up of peak frequency and initial frequency, it indicates the dynamic changes in failure frequency. Collectively, these three factors explain 81.9% of the total variance, effectively encapsulating the physical meanings of the original 10 parameters. As shown in Table 3, the factor analysis has extracted three main factors: \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Ingredients**} & \multicolumn{3}{c}{**Initial Eigenvalues**} & \multicolumn{3}{c}{**Extract the Sum of Squares of the Loadings**} & \multicolumn{3}{c}{**Sum of the Rotating Load**} \\  & **Total** & **Percentage** & **Accumulate \%** & **Total** & **Percentage** & **Accumulate \%** & **Total** \\  & & **Variance** & **Accumulate \%** & **Total** & **Percentage** & **Accumulate \%** & **Total** \\ \hline
1 & 5.696 & 56.955 & 56.955 & 5.696 & 56.955 & 56.955 & 4.104 \\
2 & 1.476 & 14.756 & 71.711 & 1.476 & 14.756 & 71.711 & 2.509 \\
3 & 1.019 & 10.186 & 81.898 & 1.019 & 10.186 & 81.898 & 1.577 \\
4 & 0.462 & 4.625 & 86.523 & & & & \\
5 & 0.443 & 4.427 & 90.950 & & & & \\
6 & 0.343 & 3.433 & 94.383 & & & & \\
7 & 0.298 & 2.981 & 97.364 & & & & \\
8 & 0.132 & 1.317 & 98.681 & & & & \\
9 & 0.094 & 0.937 & 99.618 & & & & \\
10 & 0.038 & 0.382 & 100.000 & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Total variance explained. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{1}{c}{**Parameter**} & **Y1 (Energy-Related)** & **Y2 (Time-Related)** & **Y3 (Frequency-Related)** \\ \hline Energy (d3) & **0.92** & 0.15 & 0.08 \\ Amplitude (d5) & **0.88** & 0.21 & 0.12 \\ Average Signal Strength (d8) & **0.85** & 0.18 & 0.09 \\ Duration (d4) & 0.13 & **0.91** & 0.07 \\ Rise Time (d1) & 0.11 & **0.89** & 0.05 \\ Ringing Count (d2) & 0.24 & **0.83** & 0.14 \\ Peak Frequency (d9) & 0.08 & 0.12 & **0.95** \\ Initial Frequency (d10) & 0.09 & 0.07 & **0.93** \\ RMS Voltage (d7) & 0.76 & 0.31 & 0.22 \\ Average Frequency (d6) & 0.18 & 0.27 & 0.82 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Factor Loadings and interpretation of acoustic emission parameters. Factor 1 (Energy-Related): The dominant parameters are energy (d3), amplitude (d5), and average signal intensity (d8). This factor reflects the intensity of energy release during rock mass fracture and is the most critical indicator for predicting rockbursts (with a cumulative contribution rate of 56.9%). Factor 2 (Time-Related): The dominant parameters include duration (d4), rise time (d1), and ring-down count (d2). This factor characterizes the temporal features of fracture events and has a contribution rate of 14.8%. Factor 3 (Frequency-Related): The dominant parameters are peak frequency (d9) and initial frequency (d10). This factor reflects the frequency characteristics of fractures and contributes 10.2% to the total variance.