## 3 Result and Discussion
### Adaptability Test  
The interlayer pressure distribution may be greatly affected by the vacuum conditions. In order to verify the adaptability of the ELM algorithm, four additional distributions of interlayer pressure are used to test the algorithm. Four additional test sample sets are presented in Figure 7. They can be distinguished by the maximum interlayer pressures, which are 10-times, 30-times, 50-times, and 70-times the ideal vacuum chamber pressure (\(1\times 10^{-3}\) Pa). The values of the interlayer pressure at nine positions are given, and it is assumed that the corresponding reflector's temperature at the same position can be measured. Besides the cold and hot boundary temperatures at the positions with the near ideal vacuum pressure, seven temperatures of the internal layers may be measured by temperature sensors with the random uncertainty of 0.5-1 K. The hypothetical random measuring errors of the seven temperature sensors are listed in Table 3. It has been proven that the classical LBL model can be used to predict the reflector temperatures and the thermal insulation of MLIs precisely. Hence, the reflector temperatures of these seven points are determined by solving the modified LBL model in this study. Then they are added to the hypothetical random measuring errors, respectively, to be used as the input data of the inversion algorithm (ELM). It should be noted that the reflector temperatures of the MLI should be measured. The testing result is shown in Figure 8. It can be seen that the ELM algorithm has good recognition ability for the distribution trends of different layers. This indicates that the algorithm can capture the change trend of the pressure distribution well and conduct \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Point** & **1** & **2** & **3** & **4** & **5** & **6** & **7** \\ \hline Error/K & +0.68 & +0.70, & \(-\)0.76 & \(-\)0.93 & \(-\)0.82 & +0.50 & \(-\)0.56 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Hypothetical measuring error at seven temperature sensors. Figure 7: The testing sample set. corresponding processing. However, there may be some minor deviations in specific parts, which may be related to the difficulty of reconstructing some minor features. Overall, the ELM algorithm performs well in processing the pressure distribution trend. Table 4 gives the mean squared error (MSE) of interlayer temperature reconstruction for different testing cases. It can be found that the MSE of the interlayer temperature reconstruction for the four testing cases is below 0.65 K, indicating that the error of the model in reconstructing the interlayer temperature is smaller than the error of the temperature sensor. This result shows that the model performs well in reconstructing the interlayer temperature and can provide reliable reconstruction results. Based on the above analysis, we conclude that the model can effectively reduce the error of temperature reconstruction and adapt well to different interlayer pressure distributions. This indicates that the model can handle the errors in temperature reconstruction well and has strong adaptability. In the process of training ELM neural networks, the number of neurons, the type of sigmoid function, and the number and quality of samples all have an impact on the \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Testing Case** & **1** & **2** & **3** & **4** \\ \hline MSE/K & 0.37 & 0.65 & 0.41 & 0.23 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Mean squared error of reconstruction temperature in each testing case. Figure 8: The testing results of different interlayer pressure distrbutions. (**a**) Testing case 1; (**b**) Testing case 2; (**c**) Testing case 3; (**d**) Testing case 4.  
prediction accuracy. In this study, these key parameters of the ELM model are manually tuned. This may be the limitation of the proposed model. The potential error in the prediction results may be caused by the possibility of local optimization.