Bayesian identification of fibrous insulation thermal conductivity towards design of spacecraft thermal protection systems

Abstract

The design of spacecraft thermal protection systems (TPS) requires accurate knowledge of thermal transport properties across wide ranges of temperature and pressure. For fibrous insulation, conventional measurement techniques in laboratory settings are typically limited to temperatures much lower than what is reached in atmosphere entry scenarios. Moreover, it is often the case that only temperature measurements are available, meaning that the thermal conductivity of the insulation must be indirectly inferred as an inverse problem. We propose a Bayesian framework using information field theory (IFT) to reconstruct the thermal conductivity of high-temperature fibrous insulation from sparse experimental data. Under IFT, the conductivity is represented as a Gaussian process, and the physics is enforced via a physics-informed prior over the temperature derived from the heat equation. Bayes's rule produces an infinite-dimensional posterior distribution that quantifies uncertainty about the conductivity which can be evaluated in extrapolation regimes. We apply the method to Opacified Fibrous Insulation with both synthetic and experimental data to reconstruct the thermal conductivity beyond the experimental regime. The inferred conductivities are validated against reference data and then propagated into high-fidelity digital twins of flexible TPS performance under Mars and Earth entry trajectories. The results show that IFT yields accurate predictions with quantified uncertainty, enabling robust TPS sizing in regimes inaccessible to direct measurement.