## 3 Results
### Simulated Flame Temperature Measurement and Thermal Damage Assessment  
In this study, for safety reasons, the experiment was conducted in an open clearing in the forest, causing no damage to the surrounding trees. A simulated deflagration flame experiment with a solid fuel was conducted, and the multispectral image of the simulated flame was acquired using a multispectral camera at a frame rate of 200 Hz, as shown in Figure 6. The brightness of the flame at 0 ms was the largest, the brightness of the flame at 100 ms decreased a little, and the brightness of the multispectral image at 200 ms did not change much. There was also a small area of rekindling phenomenon with the presence of bright light. The flame brightness gradually decreased from 300 ms. The multispectral camera captured a multispectral image of the simulated deflagration flame. The system integrated the blackbody furnace calibration function with a dual annealing multi-objective constraint optimization algorithm to optimize the emissivity of each channel, ensuring that the constraint function approached zero. This process guaranteed that the temperature calculated for each channel closely aligned with the average temperature across all channels, effectively mitigating the influence of emissivity. The method enabled the determination of the two-dimensional real temperature distribution of the exploding fireball. A flowchart illustrating the multispectral temperature solving process is presented in Figure 7.  
In order to have a clearer understanding of the emissivity optimization process and to obtain the true temperature, this paper shows the process of optimizing the emissivity and solving the temperature in Figure 8.  
The complete 25-band multispectral image of the deflagration flame was iteratively optimized using the double annealing multi-objective constrained optimization algorithm. In this way, the two-dimensional temperature distribution of the deflagration flame with the effect of the emissivity eliminated was finally obtained, as shown in Figure 9. \begin{table}
\begin{tabular}{c c c c} \hline
**Bands (nm)** & \(A_{\lambda i}\) & \(B_{i}\) & \(\mathbf{R^{2}}\) \\ \hline  
\hline \end{tabular}
\end{table} 
Table 3: _Cont._Figure 6: 25-band multi-spectral images of the simulates deflagration flames. Figure 7: Flowchart of multispectral temperature solution. The temperature of the simulated deflagration flame was also collected with the calibrated CIT-3 MD2-T0830&T0409-W34-HS2 us two-color pyrometer and multispectral camera; a maximum temperature profile comparison graph is shown in Figure 10. The maximum temperature of the deflagration flame measured by the colorimetric pyrometer TC was 2953.07 K, and the maximum temperature measured by the multispectral camera was 2920 K, with a relative measurement error of 1.12%. The overall temperature trend of the two methods was consistent, with a maximum relative measurement error of 1.81%. Figure 8: Emissivity optimization process. Figure 9: Temperature distribution of the simulated deflagration flames. According to the principle of radiative temperature measurement, the equivalent average temperature [24]\(T_{ave}\) was used to represent the surface temperature of the fire. \[T_{ave}=\sqrt{\sum_{i}^{n}\frac{T_{i}^{4}}{n}} \tag{20}\]  
The equivalent average temperature \(T_{ave}\) of the equivalent thermal radiation intensity on the surface of the simulated deflagration flame was between 1500 K and 2200 K. The overall temperature trend function is presented in the form of a 2 nd-order fit function, with a good fit optimality of 0.991, as shown in Figure 11.  
Figure 11: Equivalent average temperature _Tave_ of the simulated deflagration flames. Figure 10: Comparison of temperature and error plots of the simulated deflagration flames. Figure 12 illustrates the simulation of the deflagration flame. At 0 ms, the fireball diameter reached a maximum value of 15.68 m. Between 300 ms and 500 ms, the fireball diameter initially decreased before increasing again, with a diameter of 10.05 m recorded at 500 ms.