Benefits of virtual calibration for discrete element parameter estimation from bulk experiments

Abstract

Calibration remains an important challenge in the estimation of discrete element parameters. Importantly, the usability of the discrete element method (DEM) is directly dependent on the quality of the parameter estimation. Numerous approaches have been developed to characterize discrete element parameters directly from experimental data, often characterized by insufficient data and overparametrized models, which needlessly to say often fits the experimental data very well. However, if the quality of the parameter vector is properly investigated or critically interpreted for quality and uniqueness the applicability for applications distinct from the experimental setup remain indecisive. This study proposes a virtual calibration on simulated data to be conducted before the actual calibration on experimental data is pursued. The reason being that for the virtual experiment we know the answer of the optimal parameter vector beforehand, hence we can investigate and map the effect of aleatoric uncertainty spatially over the parameter domain. This mapping allows us to differentiate between model parameters that can be uniquely defined and those that require additional information to be uniquely defined for a given an experimental setup. Our results show that certain parameter vectors can be identified more uniquely than others. This implies that using the same experimental setup certain materials can be better identified than other materials. The approach we propose allows us to estimate the identifiability of various parameter vectors or equivalently various materials using the same experimental setup. As a consequence, our proposed approach can inform the calibrator when additional experimental data through an additional experimental setup is required to finally obtain a sufficiently calibrated DEM model. In summary, we need to identify the correct model parameters as opposed merely model parameters that matches the desired output to ensure that we can achieve some sensible measure of extrapolation from the calibrated experimental setup.