Propagation of Uncertainties in Pyrolysis Kinetic Parameters Using Polynomial Chaos Methods

This master thesis addresses two challenges for the propagation of uncertainties related to the pyrolysis process in thermal protection materials, which are the high computational cost of numerical simulations and the correlation between input uncertainties. Due to this high computational cost, classical techniques such as Monte Carlo simulations are not applicable. In this respect, we propose exploring the so-called method of polynomial chaos, which consists in using a set of orthogonal polynomials to build a cheaper surrogate model from a limited number of runs of the reference model. First, some theoretical and computational aspects of the polynomial chaos are presented in details, then different test cases are considered in order to assess the relevance of the method in producing a surrogate model for complex pyrolysis and thermal ablation processes. In summary, the goal of this thesis is to successfully demonstrate the possibility of computing a cheap and accurate surrogate model for complex pyrolysis processes in moderately high dimensions when the uncertainties on the input parameters are correlated.