Bayesian Updating of Aleatory Uncertainties in Heterogeneous Materials

Advances in meta-modelling and increasing computational capacity of modern computerspermitted many researches to focus on parameter identification in probabilistic setting. Increasinglypopular Bayesian inference allows to estimate model parameters together with corresponding epistemicuncertainties from indirect experimental measurements. However in case of a heterogeneousmaterial model, the identification procedure has to be able to quantify the aleatory uncertainties capturingthe variability of the material properties. Parameter identification of a heterogeneous materialmodel can be formulated as a search for probabilistic description of its parameters providing the distributionof the model response corresponding to the distribution of the observed data, i.e. a stochasticinversion problem. By prescribing a specific type of probability distribution to the model parameterswith corresponding uncertain moments, the task changes to the identification of these so-calledhyperparameters of the distribution which can be inferred in the Bayesian way.