# Simulation and Catastrophe Detection of Spontaneous Combustion Processes in Suffide Ores
## 3 Results
### Optimization for Wavelet Functions  
Figure 8 shows the reconstruction temperature increment sequence at point (A) after wavelet function (demy) reconstruction. The blue line represents the original temperature sequence at measurement point A, depicting minute-by-minute changes in the raw temperature of the sulfide ore. The temperature changes remain relatively stable before 200 min; however, after 200 min, significant fluctuations and peaks are observed; these peaks represent the maximum increments in the sulfide ore temperature. These changes are heavily influenced by the high-temperature test chamber, which obscures information about the ore's spontaneous combustion, making it unsuitable for direct prediction.  
The red line represents the low-frequency reconstruction sequence at measurement point A, illustrating the changes attributable to the test chamber. It closely matches the trends in the original temperature increment sequence, confirming that the high-temperature test chamber mainly affects the ore's temperature changes.  
The green line represents the high-frequency reconstruction sequence, excluding the influence of the high-temperature test chamber and reflecting the intrinsic changes in the ore's self-heating. Before 200 min, the ore's temperature changes are relatively stable; however, at 200 min, there is a noticeable peak corresponding to the rapid temperature increase observed in Figure 5 at the same time point. Unlike the original temperature sequence, the high-frequency reconstruction sequence captures intricate details, encompassing sub-microscopic changes throughout the oxidation and spontaneous combustion process of the entire ore heap. Therefore, these peaks represent the maximum temperature variations generated solely by the self-heating of the sulfide ore, indicating significant temperature fluctuations.  
These high-frequency details are crucial for understanding the dynamic changes in the ore's self-heating and combustion, laying the foundation for catastrophe detection.  
According to the method described in Section 2.3.2, sym2, rbio5.5, bior5.5, bior5.5, db2, db2, and db2 are selected as the wavelet functions for wavelet decomposition and reconstruction of measurement points A, B, C, D, E, F, G, and H, respectively.  
The high-frequency reconstruction sequences obtained by wavelet decomposition and reconstruction using the respective optimized wavelet functions at each measurement point, i.e., the sequences containing the information of spontaneous combustion of sulfide ore heap, are taken as examples at measurement points A, B, C, and D. The results are shown in Figure 9. By comparing the high-frequency reconstruction sequences of each measurement point, the result of temporal and spatial differences in the spontaneous combustion processes in different regions can be obtained.  
Figure 8: The wavelet reconstruction result of the measurement point (A) (dmey).  
Moreover, by comparing the high-frequency reconstruction sequence of point A reconstructed by the sym2 wavelet function and that by the demy wavelet function, a big difference between the two can be found. The former is finer and fuller than the latter and can better reflect the spontaneous combustion information. It also shows the importance of wavelet function optimization.