An Innovative External Heat Flow Expansion Formula for Efficient Uncertainty Analysis in Spacecraft Earth Radiation Heat Flow Calculations

Abstract

Thermal uncertainty analysis of spacecraft is an important method to avoid overdesign and underdesign problems. In the context of uncertainty analysis, thermal models representing multiple operating conditions must be invoked repeatedly, leading to substantial computational costs. The ray tracing calculation of Earth infrared and albedo radiation heat flux is an important reason for the slow calculation speed. As the rays emitted during external heat flux calculations under different operating conditions are independent and unconnected, the rays produced across various conditions are effectively wasted. In this study, the external heat flow equation is thoroughly expanded and the derived factors are clustered and analyzed to develop a novel formula for calculating external heat flow. When this formula is employed to compute the uncertain external heat flux, only one condition necessitates ray tracing, while the remaining conditions utilize simple matrix operations in place of complex ray tracing. Within the aforementioned procedure, certain matrices demonstrate sparse characteristics. The optimization calculations for these matrices can, therefore, benefit from the application of sparse matrix optimization algorithms. Using a spacecraft as an example, the uncertain external heat flux calculation outcomes of the new and traditional formulas are compared and assessed. The findings reveal that the new formula is highly suitable for estimating uncertain Earth radiation heat flow, with a marked improvement in efficiency. The accuracy is essentially equivalent to that of the traditional formula and the calculation precision can be dynamically adjusted to meet user requirements. The methodology can be further generalized to assess the uncertainties associated with radiative external heat fluxes for other celestial bodies within the solar system. This offers a valuable theoretical framework for addressing the uncertainties in the thermal design of deep space exploration vehicles.