Probabilistic calibration of discrete element simulations using the sequential quasi-Monte Carlo filter

Abstract

The calibration of discrete element method (DEM) simulations is typically accomplished in a trial-and-error manner. It generally lacks objectivity and is filled with uncertainties. To deal with these issues, the sequential quasi-Monte Carlo (SQMC) filter is employed as a novel approach to calibrating the DEM models of granular materials. Within the sequential Bayesian framework, the posterior probability density functions (PDFs) of micromechanical parameters, conditioned to the experimentally obtained stress-strain behavior of granular soils, are approximated by independent model trajectories. In this work, two different contact laws are employed in DEM simulations and a granular soil specimen is modeled as polydisperse packing using various numbers of spherical grains. Knowing the evolution of physical states of the material, the proposed probabilistic calibration method can recursively update the posterior PDFs in a five-dimensional parameter space based on the Bayes' rule. Both the identified parameters and posterior PDFs are analyzed to understand the effect of grain configuration and loading conditions. Numerical predictions using parameter sets with the highest posterior probabilities agree well with the experimental results. The advantage of the SQMC filter lies in the estimation of posterior PDFs, from which the robustness of the selected contact laws, the uncertainties of the micromechanical parameters and their interactions are all analyzed. The micro-macro correlations, which are byproducts of the probabilistic calibration, are extracted to provide insights into the multiscale mechanics of dense granular materials.

Grain Learning: Bayesian Calibration of DEM Models and Validation Against Elastic Wave Propagation

“…A novel iterative Bayesian filter is developed to estimate the posterior probability distribution of the micromechanical parameters of a DEM model, conditioned to history-dependent experimental data. The iterative application of conventional sequential Bayesian estimation [2,3] allows the virtual granular material to learn from all previous experimental measurements of the physical system being modeled in a fast and automated manner.…”

A multivariate regression parametric study on DEM input parameters of free-flowing and cohesive powders with experimental data-based validation

“…These results showed that the latter three factors have a significant influence on the porosity. Cheng et al [37] developed a DEM calibration approach of granular soils based on the sequential quasi-Monte Carlo (SQMC) filter. They calibrated the micromechanical parameters of the contact laws against the stress-strain behavior of Toyoura sand in drained triaxial compression conditions at different confining pressures.…”

A hybrid calibration approach to Hertz‐type contact parameters for discrete element models

“…Statistical or optimisation‐based algorithms become popular to determine particle‐scale parameters in DEM as an inverse problem. Existing algorithms include the response surface methodology, artificial neural networks, Latin hypercube sampling and Kriging, random forest, the genetic algorithm, the sequential quasi‐Monte Carlo, and the Bayesian approach . Although these algorithms are useful to quantify a wide range of complex problems, their applications alone still suffer from numerical issues such as local optimum and time‐consuming iterative process.…”