# Heuristic Global Optimization for Thermal Model Reduction and Correlation in Aerospace Applications
## 4 Results
### Heuristic Methods Benchmark Results
#### 4.3.3 Best Fitness Function Results  
The best correlated reduced TMM simulation results of the Simple Model are presented in Figure 12a,b, where the simulation temperature results and temperature differences between DTMM and RTMM, respectively, are presented Additionally, the uncertainty of the RTMM was assessed by changing the model parameters, i.e., node mass and emissivity, with a variation of \(\pm 5\%\), for each node. The uncertainty was estimated with Equation (18).  
\[Uncertainty_{Node}=\sqrt{\sum_{\text{Sensitive cases}}(T_{\text{Nominal case}}-T_{\text{Sensitive case}})^{2}}, \tag{18}\]  
This figure displays the transient temperatures for each node (e.g., 10, 20, and 30) over a 24 h orbit, similar to Section 4.1. However, now these results have already been correlated with the DTMM results. This correlation was made by using the Cultural Algorithm (CA) best correlation adjustment factors from a previous optimization exercise. These adjustment factors, \(KGL\) and \(KGR\), are now:  
* \(\text{KGL}_{0,10}=1.69\);
* \(\text{KGL}_{10,20}=1.22\);
* \(\text{KGL}_{20,30}=1.33\);
* \(\text{KGR}_{10}=1.04\);
* \(\text{KGR}_{20}=0.65\);  
Figure 11: \(FF_{\text{Optimized}}\) average for each heuristic method.  
Figure 12: Correlated RTMM with Cultural Algorithm (CA) with lowest \(FF_{\text{Optimized}}\) value: (**a**) RTMM temperature results. (**b**) Temperature difference between DTMM and RTMM, including the model uncertainty.  
* KGR\({}_{30}=1.05\). Despite the 90 min exposure to solar radiation during each orbital period, the nodes ultimately reach equilibrium temperatures, as shown in Figure 12a. Specifically;
* Node 10 stabilizes at an average temperature of approximately 40.68 \({}^{\circ}\)C.
* Node 20 stabilizes at an average temperature of approximately 80.98 \({}^{\circ}\)C.
* Node 30 stabilizes at an average temperature of approximately \(-1.34\)\({}^{\circ}\)C.  
Similar to the analysis conducted in Figure 7c, where temperature differences between the DTMM and RTMM were compared without any RTMM model corrections or correlations, we now examine the temperature differences with optimization applied. The new results show significantly smaller temperature differences, as shown in Figure 12b.  
As in the previous comparison in Section 4.1 relative to Figure 7c, both models begin at the same initial temperature of 25 \({}^{\circ}\)C due to identical initial conditions.  
As the simulation progresses, temperature differences between the two models begin to emerge. These differences increase over time but eventually stabilize at steady-state conditions. The steady-state average temperatures for each node are as follows:  
* Node 10 temperature difference stabilizes at an average of approximately \(0.55\)\({}^{\circ}\)C \(\pm\) 2.8 \({}^{\circ}\)C.
* Node 20 temperature difference stabilizes at an average of approximately \(-0.46\)\({}^{\circ}\)C \(\pm\) 2.4 \({}^{\circ}\)C.
* Node 30 temperature difference stabilizes at an average of approximately \(-0.77\)\({}^{\circ}\)C \(\pm\) 1.8 \({}^{\circ}\)C. These temperature differences in Figure 12b were obtained with adjustments applied to the RTMM, using the Cultural Algorithm (CA) optimization method, which achieved the fitness function value of \(FF=95.87\). It is also interesting to note that the RTMM uncertainty due to variations in mass and external surface emissivity within \(\pm 5\%\) shows that it is possible to exceed the 3 \({}^{\circ}\)C limit specified in typical standards [1]. This exceedance of the 3 \({}^{\circ}\)C limit could be considered significant; however, it does not imply that the difference between the DTMM and RTMM is on the order of 3 \({}^{\circ}\)C, which is still considered very low.