Identification of random material properties as stochastic inversion problem
DOI:
https://doi.org/10.14311/AP.2026.66.0155Keywords:
heterogeneous material, uncertainty, stochastic inversion, hierarchical Bayesian model, transformation of variables, principal component analysis, Markov chain Monte Carlo, polynomial chaosAbstract
Heterogeneity of many building materials complicates numerical modelling of structural behaviour. The material randomicity can be manifested by different values of the material parameters of each material specimen. To capture the inherent variability of heterogeneous materials, the model parameters describing the material properties are considered as random variables and their identification consists in solving a stochastic inversion problem. The stochastic inversion is based on searching for a probabilistic description of the model parameters that provides the model response distribution corresponding to the distribution of the observations. The paper presents two different formulations of the stochastic inversion problem. The first formulation arises from the Bayesian inference of uncertain statistical moments of a prescribed parameters’ distribution, whereas the second is centered on a nonlinear transformation of the random model parameters from the observed data distribution.
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