## 5 Validation of a Rapid Prognostic Technique for Infrared Heated Cages
### Rapid Prognostic Model Training Results and Case Validation  
In order to facilitate the analytical calculations, the following simplifying assumptions are required in this paper:  
1. All instruments are simplified into hexahedra according to their equivalent radiant area;
2. All heat pipes are simplified as rectangular;
3. The inner and outer skins of the heat dissipation surface area are divided into nodes, and the hatch plate in the multi-layer area is divided into nodes with the corresponding multi-layer outer surface;
4. Consider the thermal conductivity between the inner and outer skin nodes of the honeycomb panel and between the inner and outer skin nodes of the heat dissipation surface, and the thermal conductivity between the nodes of the outer surface of the multilayer is neglected;
5. Only the thermal conductivity of the honeycomb core along the perpendicular skin direction is considered, while the thermal conductivity of the honeycomb core along the parallel skin direction is not considered.  
The critical setup parameters for PSO and SVR that would aid in replicating results are as follows.  
PSO: w = 0.5, c\({}_{1}\) = 1, c\({}_{2}\) = 1; SVR: C = 10.  
The heat flow simulation capability of the heat control star infrared heating cage was predicted by the rapid prognostic model and compared with the measured data, and the results are shown in Table 6. It can be seen that the prognostic error gradually decreases with the increase in heat flow. The maximum error is 6.1%, which occurs at working condition 3A, and the average error is 4.29%.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & **Working Condition** & **Working Condition** & **Working Condition** & **Working Condition** & **Working Condition** \\  & & **3A** & **3B** & **3C** & **3D** & **3E** \\ \hline \multirow{4}{*}{
\begin{tabular}{c} +Y surface infrared heating cage \\ \end{tabular} } & Actual heat flow arriving (W/m\({}^{2}\)) & 55.5 & 304.7 & 361.4 & 455.3 & 306.5 \\  & Modeled predicted heat flow (W/m\({}^{2}\)) & 58.8 & 322.3 & 341.1 & 482.6 & 297.3 \\  & Error (\%) & 6.1 & 5.8 & 5.6 & 6.0 & 3.0 \\ \hline \hline \end{tabular}
\end{table}
Table 6: PSO-SVR model accuracy analysis.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Infrared Heating Cage Heating Conditions** & **Working Condition 3A** & **Working Condition 3B** & **Working Condition 3C** & **Working Condition 3D** & **Working Condition 3E** \\ \hline +Y-side infrared heating cage black sheet 1 (actual temperature \({}^{\circ}\)C) & \(-\)73.7 & \(-\)4.3 & 7.3 & 24.3 & \(-\)4.3 \\ +Y-side infrared heating cage heat flow1 (W/m\({}^{2}\)) & 89.73 & 296.23 & 350.76 & 443.85 & 296.23 \\ +Y surface infrared heating cage black film 2 (actual temperature \({}^{\circ}\)C) & \(-\)68.0 & \(-\)0.4 & 11.4 & 28.0 & 0.3 \\ +Y-side infrared heating cage heat flow2 (W/m\({}^{2}\)) & 100.43 & 313.79 & 371.72 & 466.35 & 317.03 \\ +Y surface infrared heating cage heat flow & 5.63 & 2.88 & 2.90 & 2.47 & 3.39 \\ inhomogeneity (\%) & & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 5: +Y surface infrared heating cage heat flow unevenness.