Identification of random material properties as stochastic inversion problem

Abstract

Heterogeneity of many building materials complicates numerical modelling of structural behaviour. The material randomicity can be manifested by different values of material parameters of each material specimen. To capture 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 probabilistic description of model parameters which provides the distribution of the model response corresponding to the distribution of the observed data. 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 while the main idea of the second one utilizes nonlinear transformation of random model parameters from distribution of the observed data.

Figures (22)

• Figure 1: Experimental outputs considered as random variables $Z_t$ due to (a) experimental error $E_t$ (one specimen with deterministic vector of material parameters ${\boldsymbol x}$) and (b) experimental error $E_t$ and stochastic material parameters characterized by random variables ${\boldsymbol X}$ (ensemble of specimens).
• Figure 2: Constitutive equations of the viscoplastic model with non-linear isotropic and kinematic hardening.
• Figure 3: Experimental data: stress-strain curves.
• Figure 4: Sixteen synthetic curves obtained from the numerical model of the cyclic loading test.
• Figure 5: Hierarchical Bayes - verification: Histograms of synthetic experimental inputs, prior (black) and posterior (red) parameters' PDFs corresponding to hyperparameters' mean of prior and mode of posterior (solid lines) accompanied by bounds corresponding to $90$ % of hyperparameters' values (dashed lines).