Efficient Uncertainty Analysis of External Heat Flux of Solar Radiation with External Heat Flux Expansion for Spacecraft Thermal Design

Abstract

Designing spacecraft involves a careful equilibrium to avoid overengineering or underdesigning, which underscores the importance of employing thermal uncertainty analysis. A key part of this analysis is modeling thermal conditions, but this is often a computationally heavy process. This is largely because ray-tracing calculations require determining the external heat flux of solar radiation across different operating conditions. Ray emission varies across conditions, which can lead to inefficient resource use in uncertainty calculations. Our study aims to address this by introducing a new approach to calculating the external heat flux of solar radiation that is better suited for uncertainty analysis than previous approaches. Our formula only requires ray tracing to be performed for one condition rather than for every condition. The other conditions are handled by simple matrix budgeting, negating the need for complicated ray tracing. In the aforementioned analytical procedure, certain matrices demonstrate sparsity properties. By exploiting this characteristic, optimization computations can be executed by utilizing sparse matrix algorithms. We tested this new formula, which we call the external heat flux expansion (EHFE) formula, on a specific spacecraft and compared the results with those obtained using the traditional method. Our findings suggest that the EHFE formula is ideal for calculating uncertainty. It significantly improves computational efficiency while maintaining accuracy. The formula is also user-adjustable, allowing the accuracy of uncertainty calculation results of the external heat flux of solar radiation to be fine-tuned by changing the value of the cutoff factor. This work establishes an essential theoretical framework pivotal to addressing inherent uncertainties in the thermal design of upcoming deep-space exploration spacecraft, solar observatory satellites, and space solar power stations.