An iterative Bayesian filtering framework for fast and automated calibration of DEM models

Hongyang Cheng, Takayuki Shuku, Klaus Thoeni, Pamela Tempone, Stefan Luding, Vanessa Magnanimo

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

The nonlinear, history-dependent macroscopic behavior of a granular material is rooted in the micromechanics between constituent particles and irreversible, plastic deformations reflected by changes in the microstructure. The discrete element method (DEM) can predict the evolution of the microstructure resulting from interparticle interactions. However, micromechanical parameters at contact and particle levels are generally unknown because of the diversity of granular materials with respect to their surfaces, shapes, disorder and anisotropy. The proposed iterative Bayesian filter consists in recursively updating the posterior distribution of model parameters and iterating the process with new samples drawn from a proposal density in highly probable parameter spaces. Over iterations the proposal density is progressively localized near the posterior modes, which allows automated zooming towards optimal solutions. The Dirichlet process Gaussian mixture is trained with sparse and high dimensional data from the previous iteration to update the proposal density. As an example, the probability distribution of the micromechanical parameters is estimated, conditioning on the experimentally measured stress–strain behavior of a granular assembly. Four micromechanical parameters, i.e., contact-level Young's modulus, interparticle friction, rolling stiffness and rolling friction, are chosen as strongly relevant for the macroscopic behavior. The a priori particle configuration is obtained from 3D X-ray computed tomography images. The a posteriori expectation of each micromechanical parameter converges within four iterations, leading to an excellent agreement between the experimental data and the numerical predictions. As new result, the proposed framework provides a deeper understanding of the correlations among micromechanical parameters and between the micro- and macro-parameters/quantities of interest, including their uncertainties. Therefore, the iterative Bayesian filtering framework has a great potential for quantifying parameter uncertainties and their propagation across various scales in granular materials.

Original languageEnglish
Pages (from-to)268-294
Number of pages27
JournalComputer Methods in Applied Mechanics and Engineering
Volume350
DOIs
Publication statusPublished - Jun 15 2019

Fingerprint

Granular materials
Finite difference method
Calibration
Friction
Microstructure
Micromechanics
granular materials
Probability distributions
Tomography
Macros
Plastic deformation
Anisotropy
iteration
proposals
Elastic moduli
Stiffness
X rays
friction
micromechanics
microstructure

Keywords

  • Cyclic oedometric compression
  • Dirichlet process mixture model
  • Discrete element method
  • Iterative parameter estimation
  • Sequential Monte Carlo
  • X-ray tomography

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications

Cite this

An iterative Bayesian filtering framework for fast and automated calibration of DEM models. / Cheng, Hongyang; Shuku, Takayuki; Thoeni, Klaus; Tempone, Pamela; Luding, Stefan; Magnanimo, Vanessa.

In: Computer Methods in Applied Mechanics and Engineering, Vol. 350, 15.06.2019, p. 268-294.

Research output: Contribution to journalArticle

Cheng, Hongyang ; Shuku, Takayuki ; Thoeni, Klaus ; Tempone, Pamela ; Luding, Stefan ; Magnanimo, Vanessa. / An iterative Bayesian filtering framework for fast and automated calibration of DEM models. In: Computer Methods in Applied Mechanics and Engineering. 2019 ; Vol. 350. pp. 268-294.
@article{3841ffd0c237480ab0d0da0a101a65cf,
title = "An iterative Bayesian filtering framework for fast and automated calibration of DEM models",
abstract = "The nonlinear, history-dependent macroscopic behavior of a granular material is rooted in the micromechanics between constituent particles and irreversible, plastic deformations reflected by changes in the microstructure. The discrete element method (DEM) can predict the evolution of the microstructure resulting from interparticle interactions. However, micromechanical parameters at contact and particle levels are generally unknown because of the diversity of granular materials with respect to their surfaces, shapes, disorder and anisotropy. The proposed iterative Bayesian filter consists in recursively updating the posterior distribution of model parameters and iterating the process with new samples drawn from a proposal density in highly probable parameter spaces. Over iterations the proposal density is progressively localized near the posterior modes, which allows automated zooming towards optimal solutions. The Dirichlet process Gaussian mixture is trained with sparse and high dimensional data from the previous iteration to update the proposal density. As an example, the probability distribution of the micromechanical parameters is estimated, conditioning on the experimentally measured stress–strain behavior of a granular assembly. Four micromechanical parameters, i.e., contact-level Young's modulus, interparticle friction, rolling stiffness and rolling friction, are chosen as strongly relevant for the macroscopic behavior. The a priori particle configuration is obtained from 3D X-ray computed tomography images. The a posteriori expectation of each micromechanical parameter converges within four iterations, leading to an excellent agreement between the experimental data and the numerical predictions. As new result, the proposed framework provides a deeper understanding of the correlations among micromechanical parameters and between the micro- and macro-parameters/quantities of interest, including their uncertainties. Therefore, the iterative Bayesian filtering framework has a great potential for quantifying parameter uncertainties and their propagation across various scales in granular materials.",
keywords = "Cyclic oedometric compression, Dirichlet process mixture model, Discrete element method, Iterative parameter estimation, Sequential Monte Carlo, X-ray tomography",
author = "Hongyang Cheng and Takayuki Shuku and Klaus Thoeni and Pamela Tempone and Stefan Luding and Vanessa Magnanimo",
year = "2019",
month = "6",
day = "15",
doi = "10.1016/j.cma.2019.01.027",
language = "English",
volume = "350",
pages = "268--294",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0374-2830",
publisher = "Elsevier",

}

TY - JOUR

T1 - An iterative Bayesian filtering framework for fast and automated calibration of DEM models

AU - Cheng, Hongyang

AU - Shuku, Takayuki

AU - Thoeni, Klaus

AU - Tempone, Pamela

AU - Luding, Stefan

AU - Magnanimo, Vanessa

PY - 2019/6/15

Y1 - 2019/6/15

N2 - The nonlinear, history-dependent macroscopic behavior of a granular material is rooted in the micromechanics between constituent particles and irreversible, plastic deformations reflected by changes in the microstructure. The discrete element method (DEM) can predict the evolution of the microstructure resulting from interparticle interactions. However, micromechanical parameters at contact and particle levels are generally unknown because of the diversity of granular materials with respect to their surfaces, shapes, disorder and anisotropy. The proposed iterative Bayesian filter consists in recursively updating the posterior distribution of model parameters and iterating the process with new samples drawn from a proposal density in highly probable parameter spaces. Over iterations the proposal density is progressively localized near the posterior modes, which allows automated zooming towards optimal solutions. The Dirichlet process Gaussian mixture is trained with sparse and high dimensional data from the previous iteration to update the proposal density. As an example, the probability distribution of the micromechanical parameters is estimated, conditioning on the experimentally measured stress–strain behavior of a granular assembly. Four micromechanical parameters, i.e., contact-level Young's modulus, interparticle friction, rolling stiffness and rolling friction, are chosen as strongly relevant for the macroscopic behavior. The a priori particle configuration is obtained from 3D X-ray computed tomography images. The a posteriori expectation of each micromechanical parameter converges within four iterations, leading to an excellent agreement between the experimental data and the numerical predictions. As new result, the proposed framework provides a deeper understanding of the correlations among micromechanical parameters and between the micro- and macro-parameters/quantities of interest, including their uncertainties. Therefore, the iterative Bayesian filtering framework has a great potential for quantifying parameter uncertainties and their propagation across various scales in granular materials.

AB - The nonlinear, history-dependent macroscopic behavior of a granular material is rooted in the micromechanics between constituent particles and irreversible, plastic deformations reflected by changes in the microstructure. The discrete element method (DEM) can predict the evolution of the microstructure resulting from interparticle interactions. However, micromechanical parameters at contact and particle levels are generally unknown because of the diversity of granular materials with respect to their surfaces, shapes, disorder and anisotropy. The proposed iterative Bayesian filter consists in recursively updating the posterior distribution of model parameters and iterating the process with new samples drawn from a proposal density in highly probable parameter spaces. Over iterations the proposal density is progressively localized near the posterior modes, which allows automated zooming towards optimal solutions. The Dirichlet process Gaussian mixture is trained with sparse and high dimensional data from the previous iteration to update the proposal density. As an example, the probability distribution of the micromechanical parameters is estimated, conditioning on the experimentally measured stress–strain behavior of a granular assembly. Four micromechanical parameters, i.e., contact-level Young's modulus, interparticle friction, rolling stiffness and rolling friction, are chosen as strongly relevant for the macroscopic behavior. The a priori particle configuration is obtained from 3D X-ray computed tomography images. The a posteriori expectation of each micromechanical parameter converges within four iterations, leading to an excellent agreement between the experimental data and the numerical predictions. As new result, the proposed framework provides a deeper understanding of the correlations among micromechanical parameters and between the micro- and macro-parameters/quantities of interest, including their uncertainties. Therefore, the iterative Bayesian filtering framework has a great potential for quantifying parameter uncertainties and their propagation across various scales in granular materials.

KW - Cyclic oedometric compression

KW - Dirichlet process mixture model

KW - Discrete element method

KW - Iterative parameter estimation

KW - Sequential Monte Carlo

KW - X-ray tomography

UR - http://www.scopus.com/inward/record.url?scp=85063104175&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85063104175&partnerID=8YFLogxK

U2 - 10.1016/j.cma.2019.01.027

DO - 10.1016/j.cma.2019.01.027

M3 - Article

AN - SCOPUS:85063104175

VL - 350

SP - 268

EP - 294

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0374-2830

ER -