  This work develops a multiphase thermomechanical model of porous silica
aerogel and implements an uncertainty analysis framework consisting of the
Sobol methods for global sensitivity analyses and Bayesian inference using a
set of experimental data of silica aerogel. A notable feature of this work is
implementing a new noise model within the Bayesian inversion to account for
data uncertainty and modeling error. The hyper-parameters in the likelihood
balance data misfit and prior contribution to the parameter posteriors and
prevent their biased estimation. The results indicate that the uncertainty in
solid conductivity and elasticity are the most influential parameters affecting
the model output variance. Also, the Bayesian inference shows that despite the
microstructural randomness in the thermal measurements, the model captures the
data with 2% error. However, the model is inadequate in simulating the
stress-strain measurements resulting in significant uncertainty in the
computational prediction of a building insulation component.
