# Heuristic Global Optimization for Thermal Model Reduction and Correlation in Aerospace Applications
## 4 Results  
### DTMM vs. RTMM: Without Correlation  
All nodes are initialized at 25 \({}^{\circ}\)C. The simulation covers 24 h, divided into 5000 time steps. The ODE system is solved using odeint from scipy.integrate. The simulation was run on the SPYDER IDE using an AMD 5900X CPU with 64 GB of RAM. The detailed TMM simulation results are presented in Figure 7a. This figure displays the transient average temperatures (mass-weighted) for each node pair (e.g., 10-11, 20-21, and 30-31) over a 24 h orbit. These results offer a comprehensive view of the system's thermal behaviour, emphasizing the dynamic interplay between conduction, radiation, and solar input. Despite the 90 min exposure to solar radiation during each orbital period, the nodes ultimately reach equilibrium temperatures. Specifically,  
* Nodes 10-11 stabilize at an average temperature of approximately 41 \({}^{\circ}\)C.
* Nodes 20-21 stabilize at an average temperature of approximately 80.25 \({}^{\circ}\)C.
* Nodes 30-31 stabilize at an average temperature of approximately 0 \({}^{\circ}\)C.  
It is important to note that the temperatures shown in Figure 7a primarily reflect the behaviour of Nodes 10, 20, and 30, which together account for 90% of the system's total mass (30 kg) relative to the overall system mass of 33 kg. This mass distribution naturally causes the thermal characteristics of these nodes to dominate the system's response. The reduced TMM simulation results of the Simple Model are presented in Figure 7b. This figure displays the transient temperatures for each node (e.g., 10, 20, and 30) over a 24 h orbit. These results offer a comprehensive view of the system's thermal behaviour, emphasizing the dynamic interplay between conduction, radiation, and solar input. Despite the 90 min exposure to solar radiation during each orbital period, the nodes ultimately reach equilibrium temperatures. Specifically,  
Node 10 stabilizes at an average temperature of approximately 34.31 \({}^{\circ}\)C.  
Node 20 stabilizes at an average temperature of approximately 72.86 \({}^{\circ}\)C.  
Node 30 stabilizes at an average temperature of approximately \(-1.41\)\({}^{\circ}\)C.  
A comparison of the temperature results for Nodes 10, 20, and 30 between the detailed and reduced TMMs is presented in Figure 7c. Initially, both models start at the same temperature of 25 \({}^{\circ}\)C, as they share identical initial conditions. As a result, the temperature difference between the detailed and reduced TMMs is 0 \({}^{\circ}\)C at the start of the simulation (\(t=0\) s), as shown in Figure 7c. 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 6.5 \({}^{\circ}\)C.  
Node 20 temperature difference stabilizes at an average of approximately 7.7 \({}^{\circ}\)C.  
Node 30 temperature difference stabilizes at an average of approximately \(-2.0\)\({}^{\circ}\)C.  
These temperature difference results in Figure 7c were obtained without any adjustments applied to either the DTMM or RTMM. Because the DTMM features the highest number of nodes and, therefore, provides the most detailed results, its output is considered the temperature reference value. This assumption mirrors the approach used during thermal test correlations, where measured thermal test data serve as the \"temperature reference,\" and the thermal model is refined accordingly to match those reference values. Figure 7: Simulation temperature results without correlation: (a) DTMM. (b) RTMM. (c) Difference between DTMM and RTMM. In addition to examining the temperature differences between the DTMM and RTMM, it is also important to evaluate a global fitness value.