## 5 Conclusions  
This paper presents a comprehensive and systematic methodology for correcting the thermal network model, with the aim of improving the accuracy of temperature prediction and thermal performance acquisition for aerial cameras. Based on the thermally sensitive analysis results of our previous work, the passive thermal control optimization design is carried out, including the optimization of the frame insulation structure and the convective heat transfer coefficients, which ensures that the values of the key thermal parameters are kept within the optimum ranges. A comparative analysis of the temperature variation trend reveals a discrepancy between the calculated and measured temperature curves for the window barrel. Analysis of the heat transfer pathways shows that the original thermal network lacked convective and radiative heat transfer between the window barrel and the lens. After increasing the convective and radiative resistances between the window barrel and the lens, the calculated temperature values for both the window and the window barrel are in agreement with the measured values, thereby indicating the effectiveness of the structural correction. The Monte Carlo algorithm is used to explore the parameter spaces for critical parameters within their respective value ranges and uniform distribution patterns, using sampling numbers of 3000, 6000, and 12,000. The optimal parameter values are then derived by satisfying the tolerance limit condition and minimizing the objective function. As a result, the temperature predicted by the revised model shows significantly improved accuracy, with the maximum discrepancy between the predicted and experimental results reduced from 33.8% to 4.6%. Furthermore, the discrepancy between the calculated and measured temperatures decreases as the number of samples increases. This is evidenced by the reduction of the RMSE from 1.82 \({}^{\circ}\)C to 1.44 \({}^{\circ}\)C. Consequently, the precision of parameter corrections is enhanced with the expansion of the sampling data.  
Compared to the previous work, the optimized thermal network model with structure and parameter correction by the Monte Carlo algorithm shows a significant improvement in the accuracy of temperature prediction. The proposed correction method provides the basis for a digital twin system of airborne cameras. In practical applications, the inability to attach sensors to the surface of optical components precludes the possibility of obtaining the online operating temperature of the optical system by direct measurement. In contrast, the digital twin system offers the potential to predict the online temperature of aerospace optical systems with a high degree of accuracy, thereby ensuring the imaging quality of the optical system through timely temperature adjustment.  
Y.F.: Conceptualization, methodology, investigation, validation, formal analysis, writing--original draft. W.F.: Conceptualization, methodology. Z.R.: Data curation, writing--review and editing. B.L.: Resources, funding acquisition, project administration. J.L.: Software. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China, grant number 42104174.  
The data are available from the corresponding author on reasonable request.  
The authors declare no conflicts of interest.