Acceleration of uncertainty updating in the description of transport processes in heterogeneous materials

Anna Kučerová, Jan Sýkora, Bojana Rosić, Hermann G. Matthies
2012 Journal of Computational and Applied Mathematics  
The prediction of thermo-mechanical behaviour of heterogeneous materials such as heat and moisture transport is strongly influenced by the uncertainty in parameters. Such materials occur e.g. in historic buildings, and the durability assessment of these therefore needs a reliable and probabilistic simulation of transport processes, which is related to the suitable identification of material parameters. In order to include expert knowledge as well as experimental results, one can employ an
more » ... ng procedure such as Bayesian inference. The classical probabilistic setting of the identification process in Bayes's form requires the solution of a stochastic forward problem via computationally expensive sampling techniques, which makes the method almost impractical. In this paper novel stochastic computational techniques such as the stochastic Galerkin method are applied in order to accelerate the updating procedure. The idea is to replace the computationally expensive forward simulation via the conventional finite element (FE) method by the evaluation of a polynomial chaos expansion (PCE). Such an approximation of the FE model for the forward simulation perfectly suits the Bayesian updating. The presented uncertainty updating techniques are applied to the numerical model of coupled heat and moisture transport in heterogeneous materials with spatially varying coefficients defined by random fields.
doi:10.1016/j.cam.2012.02.003 fatcat:pn63f54axnfodifwuw5fbvwxny