## 4 Thermal Network Correction
### Correction Results and Discussion  
To investigate the impact of varying sampling numbers on the correction outcomes, parameter spaces are constructed using sampling numbers of 3000, 6000, and 12,000, respectively, adhering to a uniform distribution. Table 3 presents the minimum RMSE values obtained, which quantify the differences between the calculated temperature values and the measured data of the nodes. Alongside the RMSE values, the associated optimal parameter values derived from these minima are provided. Figure 11: The variation of computation time with the sampling number. \begin{table}
\begin{tabular}{c c c c} \hline \hline Sampling number & 3000 & 6000 & 12,000 \\ \hline RMSE (\({}^{\circ}\)C) & 1.82 & 1.58 & 1.44 \\ \hline \(R\)-squared & 0.78 & 0.86 & 0.91 \\ \(k_{1}\) (W-m\({}^{-1,\circ}\)C\({}^{-1}\)) & 0.6 & 1.0 & 1.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Minimum RMSE and R-squared along with optimal parameter values at different sampling numbers. To validate the effectiveness of the parameter correction, the optimal parameter values are imported into the thermal network model for temperature calculations. As illustrated in Figure 12, the transient temperature curves for the central nodes of the lenses (nodes 1, 5, 9) and the node located on the lens barrel (node 13) are presented, with the focus being on the results obtained under heating condition 1. Prior to the implementation of the thermal parameter correction, it is evident that as the duration of the flight progresses, the temperature deviations between the calculated and measured temperatures increase significantly, with the maximum discrepancies reaching 18 \({}^{\circ}\)C for the lens and 22 \({}^{\circ}\)C for the lens barrel, respectively. Following the update of these parameters, a significant reduction in temperature deviations is observed, with the maximum relative error between the predicted and experimental results decreasing from 33.8% to 3.6%. Consequently, the calculated transient temperatures align closely with the measured data, leading to a substantial improvement in the precision of the temperature prediction capabilities of the thermal network model. The use of the modified thermal network model allows for a more accurate prediction of the temperature distribution during the flight of aerial cameras. It also promotes a deeper understanding of thermal characteristics, facilitating the development of a rational and efficient thermal control system. This in turn enables the optimization of imaging quality and the strategic allocation of thermal control resources. Moreover, as the number of samples within the parameter spaces increases from 3000 to 12,000, a notable decline is observed in the RMSE between the calculated and measured temperature values. In particular, the RMSE decreases from 1.82 \({}^{\circ}\)C to 1.44 \({}^{\circ}\)C, and \(R\)-squared increases from 0.78 to 0.91. This is indicative of an improvement in the precision of temperature calculations with the expansion of the sampling data. In the case of the 3000-sample correction, the calculated temperature values of the lens exhibit a high degree of correlation with the measured data, as illustrated in Figure 12a. However, the results of the lens barrel correction are unsatisfactory, with a maximum residual error of 5 \({}^{\circ}\)C, as illustrated in Figure 13a. However, with an increase in the number of samples to 12,000, satisfactory concordances are achieved between the calculated and measured temperature values for both the lens and the lens barrel, with a maximum residual error of 3 \({}^{\circ}\)C, as illustrated in Figure 13b. Moreover, 90% of the discrepancies between the calculated and measured values are within \(\pm\)1.5 \({}^{\circ}\)C, which represents an improvement in temperature prediction accuracy compared to the results of previous studies [10; 28].