Identifying elastoplastic parameters with Bayes’ theorem considering output error, input error and model uncertainty

We discuss Bayesian inference for the identification of elastoplastic material parameters. In addition to errors in the stress measurements, which are commonly considered, we furthermore consider errors in the strain measurements. Since a difference between the model and the experimental data may still be present if the data is not contaminated by noise, we also incorporate the possible error of the model itself. The three formulations to describe model uncertainty in this contribution are: (1) a random variable which is taken from a normal distribution with constant parameters, (2) a random variable which is taken from anormal distribution with an input-dependent mean, and (3) a Gaussian random process with a stationary covariance function. Our results show that incorporating model uncertainty often, but not always, improves the results. If the error in the strain is considered as well, the results improve even more.

The authors would like to acknowledge the financial support from the University of Luxembourg and the European Research Council Starting Independent Research Grant (ERC Stg grant agreement No. 279578) entitled \Towards real time multiscale simulation of cutting in nonlinear materials with applications to surgical simulation and computer guided surgery.