## 3 Results and Analysis
### IR and AE Combined Instability Precursors of Different Coal Impact Types  
The damage and failure of coal under load generate IR and AE signals. The IR and AE signals have sensitivity and are precursors to stress and internal damage changes in  
Figure 6: Distribution characteristics of AF-RA of different coal impact types under different loading stages.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Crack Type** & **Type** & **Stage I** & **Stage II** & **Stage III** & **Stage IV** \\ \hline \multirow{3}{*}{Tensile crack} & No impact & 76.40 & 68.44 & 53.93 & 60.08 \\  & Weak impact & 88.94 & 73.58 & 59.86 & 49.14 \\  & Strong impact & 90.60 & 79.07 & 68.93 & 46.26 \\ \hline \multirow{3}{*}{Shear crack} & No impact & 23.60 & 31.56 & 46.07 & 39.92 \\  & Weak impact & 11.06 & 26.42 & 40.14 & 50.86 \\ \cline{1-1}  & Strong impact & 9.40 & 20.93 & 31.07 & 53.74 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Proportion of tensile and shear cracks at different stages.  
the coal rock mass [37; 38]. This paper combines the advantages of IR and AE signals to establish a combined IR and AE sensitivity index, K, for different coal impact types.  
The formula is as follows:  
\[K_{i+1}=\frac{(A_{i}+B_{i})\sigma_{i}}{\sigma_{\max}} \tag{3}\]  
where \(A_{i}\) is the variation coefficient of IRT, \(B_{i}\) is the variation coefficient of AE signal, \(\sigma_{i}\) is the stress at moment \(i\), and \(\sigma_{\max}\) is the peak stress.  
Among them, the formula for the variation coefficient \(A_{i}\) of IRT is:  
\[A_{i}=\frac{S_{xi}}{\frac{\sum\limits_{i=1}^{n}x_{i}}{n}} \tag{4}\]  
The formula for the variation coefficient \(B_{i}\) of AE signal is:  
\[B_{i}=\frac{S_{yi}}{\frac{\sum\limits_{i=1}^{n}y_{i}}{n}} \tag{5}\]  
Among them, \(S_{xi}\) and \(S_{yi}\) are as follows:  
\[S_{xi}=\sqrt{\sum\limits_{i=1}^{n}\frac{(x_{i}-\overline{x})^{2}}{n}} \tag{6}\]  
\[S_{yi}=\sqrt{\sum\limits_{i=1}^{n}\frac{(y_{i}-\overline{y})^{2}}{n}} \tag{7}\]  
where \(x_{i}\) is the IRT value at time \(i\), \(S_{xi}\) is the standard deviation of IRT, \(y_{i}\) is the AE energy at time \(i\), and \(S_{yi}\) is the standard deviation of AE energy.  
The combined index \(K\) value represents the degree of mutation of the IRT and AE signals during the coal body failure. The larger the \(K\) value, the greater the fluctuation and sensitivity of the IRT and AE signals. According to Formula (3), the IRT and AE sensitive combined index \(K\) for different coal impact types is calculated as shown in Figure 7. When the combined index \(K\) appears dense and increases rapidly, the coal body will be unstable and failure. In this paper, the moment P is defined as the precursor time of the coal body instability failure (Figure 7). From the variation in the combined index \(K\), it can be seen that there are significant differences in the peak value and instability precursor time of the combined index \(K\) for different coal impact types. The peak values of the combined index \(K\) for no-, weak-, and strong-impact coal are 5.63, 21.54, and 264.93, respectively, indicating that strong-impact coal has the strongest IRT and AE sensitivity, followed by weak-impact coal, and no-impact coal has the weakest sensitivity. The IRT and AE sensitive instability precursor time of no-, weak-, and strong-impact coal is 71.23 s, 126.50 s, and 171.74 s, respectively, for 55.2%, 66.3%, and 93.4% of the coal body instability failure. Therefore, as the impact tendency increases, the IRT and AE sensitivity of the coal gradually increases, but the occurrence time of the instability precursors becomes later and later.