Surrogate-based Bayesian Inversion for the Model Calibration of Fire Insulation Panels

We outline an approach for the calibration of a finite element model (FEM) by using a full Bayesian inference approach. The considered FEM describes the heat transfer in insulation when exposed to fire, it uses so-called temperature dependent effective material parameters. These parameters are required for applying the improved component additive method to determine the fire resistance of e.g. timber frame assemblies. After setting up the Bayesian inference problem, we distinguish two approaches to compute the posterior distribution and thus calibrate the sought effective material parameters. The first approach is standard Markov chain Monte Carlo (MCMC) based parameter estimation. In order to alleviate the computational burden typically associated with MCMC computations, we initially construct a surrogate model to be used instead of the computationally expensive FEM code. This model combines a dimensionality reduction technique (principal component analysis), with a sampling-free uncertainty propagation technique (polynomial chaos expansion). A second, novel approach is spectral likelihood expansion (SLE). In this procedure, the likelihood function of the posed Bayesian problem is projected onto an orthogonal basis. Following this projection, the computation of posterior quantities of interest (mean, covariance matrix,...) can be done analytically by post-processing the SLE coefficients. We compare these two posterior computation approaches and showcase their ability to calibrate the sought effective material parameters