Novel framework for Bayesian inference of material properties of ablative thermal protection systems

The work performed in this thesis allows the assessment of PICA thermal conductivity ratio and cold wall stagnation point heat flux by harnessing the powerful tool of Bayesian Inference. As part of the inference framework, that has been implemented on MATLAB using UQLab, the McDougall thermal model has been used. Before implementing it in the framework, a study about the model precision (for the calculation of temperature histories at specific thermocouple locations) when varying mesh size and timestep has been performed. By exploring the uncertain nature of these parameters, the inference framework allowed the definition of the posterior distributions of α and q0, using available experimental results from (1). Posterior distributions of the inferred parameters, obtained using some thermocouples, have then been used to estimate the temperature evolution in other thermocouples, in order to validate the posteriors previously calculated. This result can then be used to guide precisely the material and heat shield design process. This approach has also been crucial as it served to find out which thermocouple placements are more informative about a certain parameter. In particular, through the Kullback Leibler Divergence, it has been possible to find that TC8, TC5-TC8, TC6-TC8, TC5-TC7-TC8, and TC6-TC7-TC8 thermocouples set, as visualized in Fig. 3.1, allow for the highest information gain about the inferred parameters. The study of the correlation factor between the parameters has been essential, as it served as an indicator of how much the variables are dependent. Through the correlation factor, it has been discovered that TC5 and TC6 offer the lowest correlation between α and q0. This indicated the possibility of performing a sequential inference analysis: using TC5 or TC6 for assessing a posterior distribution for q0, and another set for assessing the α posterior. Results of the sequential analysis have then been compared with the ones obtained inferring both parameters in the same simulation.