# Simulation and Catastrophe Detection of Spontaneous Combustion Processes in Suffide Ores
## 4 Conclusions and Discussion  
(1) Simulation experiments on the whole unsteady process of spontaneous combustion of sulfide ore heap have shown spatial differences in the response of sulfide ore heap to environmental temperature changes. The whole unsteady process of spontaneous combustion of sulfide ore heap inevitably has at least one catastrophe point corresponding to a critical temperature. Once this temperature is exceeded, the ore heap is considered to have transitioned to an unsafe state. This process can be divided into four stages by reconstructing the temperature field: surface temperature rise more significant than internal temperature rise, internal temperature rise more significant than surface temperature rise, a substantial increase in surface temperature rise exceeding internal temperature rise, and a significant increase in internal temperature rise exceeding surface temperature rise.  
Experimental uncertainties include the structure of the ore and the singularity of ore selection. The structure of the ore is a multi-void medium with anisotropy, so the results of repeated experiments may be slightly different. The ore was selected from the same mine, and the results may differ for ores from other mines, which is the direction of the follow-up research in this study.  
(2) The information on the non-stationary whole process of spontaneous combustion of sulfide ore heap is extracted from the measured temperature-time series by wavelet  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Measurement Point**} & \multirow{2}{*}{**Catastrophe Point**} & \multicolumn{2}{c}{**Mean of Sample Entropy**} & \multirow{2}{*}{**Catastrophe Temperature / C**} \\ \cline{3-3}  & & **I.** & **II.** & \\ \hline A & 1027 & 0.581 & 0.649 & 113.9 \\ D & 842 & 0.483 & 0.598 & 111.8 \\ E & 834 & 0.551 & 0.603 & 108.2 \\ \hline H & 839 & 0.566 & 0.647 & 110.9 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Results of catastrophe analysis for measurement points A, D, E, and H.  
technique. A new quantitative method is developed to select wavelet functions appropriate for different measurement points by combining the Fuzzy Comprehensive Evaluation and Entropy Weight Method. The method can efficiently extract high-frequency reconstruction sequences containing information about the process of spontaneous combustion of sulfide ore heap.  
(3) Catastrophe detection by sample entropy in the whole unsteady process of spontaneous combustion of sulfide ore heap indicates that not all areas within the ore heap exhibit significant catastrophe. Under the combined effects of ventilation and heat storage, there are noticeable differences in the spontaneous combustion process among different regions. The catastrophe temperature ranges from 108.2 \({}^{\circ}\)C to 113.9 \({}^{\circ}\)C. Based on the trend of sample entropy variation, the whole unsteady process of spontaneous combustion is divided into four stages: region (I) represents the relatively stable stage of oxidation and self-heating development, region (II) represents the stage of significant self-heating/approaching combustion, region (III) represents the stage of high-speed oxidation/combustion, and region (IV) represents the post-effect. Region (II) is the catastrophe stage.  
W.P.: funding acquisition, methodology, supervision, writing--review and editing. S.W.: funding acquisition, data curation, investigation, methodology, writing--original draft. R.Y.: project administration, writing--review and editing. Y.K.: writing--review and editing. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Natural Science Foundation of China (Grant No. 52274247), the Natural Science Foundation of Hunan Province (Grant No. 2022 JJ30050), and the Fundamental Research Funds for the Central Universities of Central South University (Grant No. 2024 ZZTS0669).  
Not applicable.  
Data Availability Statement: Data will be provided upon request.  
The authors declare no conflicts of interest.