# Heuristic Global Optimization for Thermal Model Reduction and Correlation in Aerospace Applications
## 1 Introduction  
Thermal model reduction and test data correlation are vital for developing aerospace systems, ensuring that simulation models accurately predict flight conditions. Traditionally, these tasks have been handled manually, a process that is both time-consuming and prone to error--especially under the tight schedules typical of final flight predictions. The complexity of these thermal models, characterized by numerous parameters and nonlinear behaviours (notably due to radiation effects), challenges conventional optimization methods, which were designed for simpler, linear problems. Model reduction involves breaking down a detailed thermal mathematical model into specific node categories: kept nodes (essential for control and accuracy), suppressed nodes (with minimal impact), and grouped nodes (condensed for simplification). Each step of the reduction is verified through defined test cases, ensuring that adjustments do not compromise model integrity. However, a significant hurdle is the prevalence of local optima in global optimization. Traditional algorithms, such as gradient-based methods, can prematurely converge on suboptimal solutions. In contrast, global search techniques--like Genetic Algorithms, simulated annealing, and hybrid approaches combining broad exploration with local refinement--can more effectively navigate complex search spaces. The objective of this study is to evaluate heuristic global optimization methods, particularly continuous techniques, for enhancing thermal model correlation in aerospace applications. By identifying more efficient optimization strategies and developing supportive software tools, the research seeks to reduce manual intervention, improve model accuracy, and ultimately contribute to more reliable flight predictions and increased mission success. This article employs the PRISMA methodology to guide the literature review process. The review begins with a standard literature review (see Section 2), followed by a systematic review incorporating bibliometric considerations (Section 2.1). Subsequently, the research questions are defined (Section 2.2), the inclusion and exclusion criteria are established (Section 2.3), the data extraction methods are described (Section 2.4), and the final analysis is presented (Section 2.5). An application case is then presented (Section 3), demonstrating thermal model reduction and correlation. A detailed thermal mathematical model (DTMM) and a reduced thermal mathematical model (RTMM) are developed for a simple aerospace instrument. Thermal model reduction, as defined in the ECSS standard [1], is essential in aerospace engineering due to frequent model exchanges throughout a project's lifecycle. Subsystem developers often provide models for system model integration. When multiple teams contribute to a system-level model, controlling complexity is vital to avoid excessive size and overhead. Although modern tools offer high computational power, thermal analyses still involve repeated runs for sensitivity studies, test correlation, and design validation. Thus, model simplification remains necessary. The goal is to produce a RTMM that replicates the DTMM's input/output behaviour with minimal loss of accuracy. While RTMMs improve efficiency, some accuracy is sacrificed. Often, recipients only require thermal behaviour at interfaces rather than detailed internal distributions. A typical acceptable deviation between DTMM and RTMM is 2 \({}^{\circ}\)C to 3 \({}^{\circ}\)C, which in many cases is a challenge to meet and often requires significant correlation effort. The results section (Section 4) is organized to illustrate the evolution of the reduction and correlation process through the application of various heuristic methods. Initially, a comparison between the DTMM and an uncorrelated RTMM is provided (Section 4.1). This is followed by an examination of the application and optimization of different heuristic methods.