Acceleration of Uncertainty Updating in the Description of Transport Processes in Heterogeneous Materials

TL;DR

This paper introduces a novel approach using stochastic Galerkin methods and polynomial chaos expansions to significantly accelerate Bayesian uncertainty updating in the simulation of heat and moisture transport in heterogeneous materials, improving efficiency and reliability.

Contribution

It proposes a new stochastic computational technique that replaces traditional finite element simulations with polynomial chaos expansions for faster Bayesian updating.

Findings

Accelerated uncertainty updating using stochastic Galerkin methods.

Effective modeling of heat and moisture transport in heterogeneous materials.

Reduced computational cost compared to classical sampling methods.

Abstract

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'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.