# Simulation and Catastrophe Detection of Spontaneous Combustion Processes in Suffide Ores
## 3 Results
### Catastrophe Detection of the Whole Unsteady Process of Spontaneous Combustion of Suffide Ore Heap  
Taking the high-frequency reconstruction sequences of measurement points A, B, C, and D as examples, Figure 10 illustrates the preprocessed high-frequency reconstruction sequences. Compared to Figure 9, Figure 10 shows that after standardization, the temperature increment values on the vertical axis are normalized to a range of 0 to 1, and the horizontal axis is transformed from time to data points. By converting both axes to dimensionless quantities, the subsequent calculation load for catastrophe detection is reduced, and potential errors are avoided. Additionally, the standardized high-frequency reconstructed sequence is more compact compared to Figure 9.  
Catastrophe detection is performed on the high-frequency reconstruction sequences of each preprocessed measurement point, combining sample entropy with the sliding window technique. The sliding window technique involves using a fixed-size window that slides over the data sequence with a set step size, incrementally calculating the target value for the data within each window according to a specified formula. In sample entropy mutation detection, a sliding window width of 225 and a step size of 1 are selected. The sample entropy of the high-frequency reconstruction sequences of the preprocessed data from the eight measurement points is calculated. Specifically, starting from the first data point of each sequence, the sample entropy of 225 temperature increment values is calculated. After each calculation, the window moves forward by one step, and the sample entropy is calculated again for the next 225 temperature increment values, starting from the second data point. This process is repeated to calculate the sample entropy for the entire sequence. The results of the sample entropy detection are shown in Figure 11. In the figure, A to H correspond to the sample entropy catastrophe detection results of the preprocessed  
Figure 10: The preprocessed high-frequency reconstruction sequences (**A**–**D**). Figure 9: The high-frequency reconstruction sequences of measurement points (**A**–**D**). high-frequency reconstructed sequences for points A to H, respectively. I-IV represent the four stages of the spontaneous combustion of sulfide ore, divided into stages I through IV. Figure 11 shows that measurement points A, D, E, and H exhibit significant catastrophe regions (II) among the eight measurement points. This indicates a dynamic structural catastrophe occurred during the spontaneous combustion process in the sulfide ore heap at these four measurement points. In the case of point A, the value of sample entropy in the region (I) varies but not by much. As the window slides, the value of the sample entropy in the region (II) increases abruptly, and the value fluctuation becomes larger. To detect a catastrophe, the complexity of the time series must increase significantly, and its dynamic state must change more obviously. According to the \"Rheology-Catastrophe theory\" [44], the occurrence of a catastrophe is likely to be a transition toward the stage of approaching spontaneous combustion. Additionally, the variation in sample entropy at each measurement point confirms significant differences in the spontaneous combustion process across different areas of the sulfide ore heap. A preliminary explanation for the spatial differences in the whole unsteady process of spontaneous combustion of sulfide ore heap is as follows: The porosity of the loose surface and shallow layers of the ore heap is higher compared to the internal regions, which have lower porosity. Consequently, the surface and shallow layers facilitate better heat dissipation, whereas the interior regions, with reduced porosity, exhibit poorer heat dissipation and improved heat storage conditions. This leads to increased heat accumulation in the interior regions, promoting the progression of oxidation and spontaneous combustion reactions.