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

Anna Kučerová*, Jan Skora, Bojana Rosić, Hermann G. Matthies

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

22 Citations (Scopus)


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 updating procedure such as Bayesian inference. The classical probabilistic setting of the identification process in Bayes' 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.

Original languageEnglish
Pages (from-to)4862-4872
Number of pages11
JournalJournal of computational and applied mathematics
Issue number18
Publication statusPublished - 1 Dec 2012
Externally publishedYes


  • Bayesian inference
  • Coupled heat and moisture transport
  • Karhunen-Loève expansion
  • Polynomial chaos expansion
  • Stochastic finite elements
  • Uncertainty updating


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