Bayesian inference for the identification of model parameters in atmospheric entry problems

Abstract

When a spacecraft undergoes atmospheric entry, it is submitted to extreme heating resulting from the formation of an hypersonic shock, requiring the use of a thermal protection system (TPS). Ablative heat shield composed of phenolic resin (PICA) protect the vehicle, notably due to the pyrolysis process. The pyrolysis is the thermal degradation of the resin resulting from the exposition to elevated temperatures. When the ablative material is heated, it reacts by releasing gases and forming char. The pyrolysis gases released in the porous material can move towards the surface of the TPS and create a heat blockage effect.

The chemical model of the pyrolysis process requires the identification of model parameters that fits experimental measurements. Probabilistic methods for the identification of these parameters allows the quantification of the uncertainties resulting from error an experimental measurements. Current probabilistic methods used in the estimation of parameters for the pyrolysis process are based on Metropolis-Hastings, which can require a certain amount of tuning to explore the probability density of the parameters such that more robust alternative are sought. Inference methods, such as Hamiltonian Monte Carlo, that use information on the geometry of the posterior density are good candidate due to the low amount of tuning they usually require.

The goal of this work is to develop these methods and apply them to the estimation of parameters in pyrolysis models. To do so, an efficient method for the computation of the gradients required had to be developed using a discrete adjoint method based on the numerical solution of the pyrolysis model. The Hamiltonian Monte Carlo algorithm and a method based on a system of dynamical stochastic differential equations were considered and applied to a simplified pyrolysis model to which it provided satisfactory results. It was then extended to a multiple reaction model, showing promising results.