## 6 Conclusions  
In this paper, the spacecraft and infrared heating cage spacing, partition height, partition arc length, curvature, circumferential relationship, radial relationship, and other variables are considered, and the PSO-SVR is used to establish the angular coefficient relationship model of spacecraft and infrared heating cage of different shapes. The data generated by the Monte Carlo simulation are known results for the model to train and generalize. Then, the rapid prediction model of heat flux simulation of the infrared heating cage, which can satisfy the accuracy requirement, is established. Finally, a rapid prognostic model for the infrared heating cage heat flow simulation is established to meet the accuracy requirements. When using the model, only key parameters, such as the spacing of infrared heating cages and the height of partitions, are inputted into the model. The results of angular coefficients of different partition intervals and the heat flow distribution of the spacecraft surface arrival can be obtained rapidly, thus eliminating the complex heat flow simulation process and realizing the rapid prediction of the heat flow of infrared heating cages. For the planar, cylindrical, and circular truncated conic configurations, five sets of partition parameters are randomly generated, and the angular coefficients are calculated by the rapid prognostic model and the Monte Carlo method, respectively. The angular coefficients obtained by the rapid prognostic model are very similar to those obtained by Monte Carlo simulation, and the maximum error is 0.003, which meets the application requirements. The angular coefficient obtained by the rapid prognostic model is 0.915, and the time taken is 0.002 s, which is 29,750 times more efficient. The Monte Carlo method takes an average of 59.5 s for each calculation, and the rapid prognostic model takes an average of 0.002 s for each calculation, which is significantly more efficient than the Monte Carlo simulation method.  
On this basis, the vacuum thermal test of a small thermal control star is used as a case study to verify the training results of the rapid prognostic model. It can be found that the prognostic error gradually decreases with the increase in the heat flow. The maximum error is 6.1%, which occurs at working condition 3A, and the average error is 4.29%, which meets the requirements of engineering applications.  
Conceptualization, X.S.; Methodology, X.S. and G.L.; Software, T.Q.; Validation, X.S. and H.J.; Formal analysis, T.Q.; Investigation, H.J.; Resources, G.L.; Writing--original draft, X.S. and H.J.; Writing--review & editing, T.Q. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy concerns.  
The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline  & & **Working Condition** & **Working Condition** & **Working Condition** & **Working Condition** & **Working Condition** \\  & & **3A** & **3B** & **3C** & **3D** & **3E** \\ \hline \multirow{4}{*}{\(-\)X surface infrared heating cage} & Actual heat flow arriving (W/m\({}^{2}\)) & 55.5 & 1672.9 & 1661.6 & 2093.5 & 1410.6 \\  & Modeled predicted heat flow (W/m\({}^{2}\)) & 58.7 & 1639.4 & 1626.7 & 2047.4 & 1469.8 \\  & Error (\%) & 5.9 & 2.0 & 2.1 & 2.2 & 4.2 \\ \hline \end{tabular}
\end{table}
Table 6: _Cont._