## 5 Conclusions  
(1) Based on the DIC method, the failure process of red sandstone specimens with different prefabricated cracks under compression was investigated. The results reveal that obvious premonitory failure information, such as strain concentration areas, appears on the specimen surface before the macro-cracks can be observed, and the obtained premonitory failure information is consistent with the emergence and expansion morphology of the macro-cracks observed later.  
(2) RA-AF signals generated during red sandstone failure indicate that as the inclination angle of the prefabricated crack in red sandstone increases, the macroscopic deformation and failure mode gradually transforms from tensile splitting failure to tensile-shear mixed failure. The HF-LA, IF-LA, and LF-LA dominant frequency signals are denser around the stress peak, while the IF-HA and HF-LA dominant frequency signals only appear near the macroscopic failure of specimens.  
(3) A comprehensive evaluation method based on multi-source information fusion monitoring was established. The initial crack expansion time and failure limit time obtained by the derivative function of the multi-source information function advanced by 20.72% and 26.71%, respectively, suggesting that the forewarning of red sandstone failure by levels is realized with multi-source information fusion.  
Next, this study will continue to conduct DIC-AE fusion data analysis on other coal and rock specimens in the hope of achieving the graded early warning of precursor signals prior to the failure of different coal and rock masses.  
Conceptualization and methodology, Z.C.; experiment and validation, G.Q.; data curation, Q.Y. and X.L. supervision, All authors have read and agreed to the published version of the manuscript.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{**Stage**} & \multirow{2}{*}{**Unit**} & **Typical** & **Multi-Source** & \multicolumn{2}{c}{**Comparison Results**} \\  & & & **Stress–Strain** & **Information** & **Initial Crack** & **Failure Limit** \\  & & & **Curve** & **Derivation Curve** & **Expansion Time** & **Time** \\ \hline \multirow{3}{*}{1} & Crack closure stage & \multirow{3}{*}{s} & \multirow{3}{*}{[0, 315]} & \multirow{3}{*}{[0, 64]} & The result & The result \\  & (stable period) & & & & obtained by the & obtained by the \\  & Elastic deformation & & & & derivative & derivative \\
2 & stage & \multirow{3}{*}{s} & \multirow{3}{*}{[315, 502]} & \multirow{3}{*}{[64, 166]} & functions is & functions is \\  & (development period) & & & & 20.72\% earlier & 26.71\% earlier \\  & Crack expansion stage & & & & than that & than that \\
3 & (energy storage & \multirow{3}{*}{s} & \multirow{3}{*}{[502, 543]} & \multirow{3}{*}{[166, 398]} & obtained by & obtained by \\  & period) & & & direct & direct \\
4 & Post-peak failure stage & \multirow{3}{*}{s} & \multirow{3}{*}{[543, 547]} & \multirow{3}{*}{[398, 547]} & observation. & observation. \\
4 & (failure period) & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 4: Relation between the premonitory limit and the bearing limit in the failure stages.  
**Funding:** This paper was funded by the Key Research and Development Program of Xuzhou (KC23292) and the Open Fund of the Key Laboratory of Deep Earth Science and Engineering (Sichuan University) (DUSE202306).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.  
**Conflicts of Interest:** The authors declare no conflicts of interest.