Bayesian uncertainty quantification and propagation for discrete element simulations of granular materials

摘要

Predictions in the behavior of granular materials using Discrete Element Methods (DEM) hinge on the employed interaction potentials. Here we introduce a data driven, Bayesian framework to quantify DEM predictions. Our approach relies on experimentally measured coefficients of restitution for single steel particle-wall collisions. The calibration data entail both tangential and normal coefficients of restitution, for varying impact angles and speeds of the bouncing particle. The parametric uncertainty in multiple Force-Displacement models is estimated using an enhanced Transitional Markov Chain Monte Carlo implemented efficiently on parallel computer architectures. In turn, the parametric model uncertainties are propagated to predict Quantities of Interest (Qol) for two testbed applications: silo discharge and vibration induced mass-segregation. This work demonstrates that the classical way of calibrating DEM potentials, through parameter optimization, is insufficient and it fails to provide robust predictions. The present Bayesian framework provides robust predictions for the behavior of granular materials using DEM simulations. Most importantly the results demonstrate the importance of including parametric and modeling uncertainties in the potentials employed in Discrete Element Methods.