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

TL;DR

This work tackles the challenge of determining high-temperature, pressure-dependent thermal conductivity for fibrous insulation used in spacecraft TPS when direct measurements at entry conditions are unavailable. It develops a physics-informed, infinite-dimensional Bayesian framework (information field theory) that couples a temperature field u to a conductivity field k via the steady-state heat equation, with k modeled in log-space as a Gaussian process and u represented by a truncated Fourier basis; the joint posterior p(u,k|d) is sampled with nested stochastic gradient Langevin dynamics to yield uncertainty-quantified reconstructions. The inferred conductivity is then propagated through 1D finite-element TPS models for Mars and Earth entry scenarios, demonstrating accurate median temperature predictions and realistic uncertainty growth with depth, especially in regimes beyond the experimental data. The approach enables robust TPS sizing under extreme, poorly measured conditions and highlights the value of physics-based priors for extrapolation where ground testing is infeasible.

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.

Figures (12)

• Figure 1: Illustration of experimental setup at NASA LaRC
• Figure 2: IFT results at $0.001$ Torr. For each state, we record the resulting posterior median field, the $95\%$ central credible interval, and a few samples from the posterior.
• Figure 3: TPS setup used for entry simulations.
• Figure 4: MSL cold wall heat flux and stagnation used for sizing TPS for Mars entry.
• Figure 5: Temperature profile through the TPS at various points in the Mars entry scenario. At each location, we report the temperature prediction using the reference OFI properties along with the median and credible interval from the IFT-obtained properties.