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

*Corresponding author for this work

    Research output: Contribution to journalArticleAcademicpeer-review

    7 Citations (Scopus)
    21 Downloads (Pure)

    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
    Early online date8 Mar 2019
    DOIs
    Publication statusPublished - 15 Jun 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

    Cite this

    @article{fc2b476cd4fd43509eaddae89cf7ae7c,
    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 = "0045-7825",
    publisher = "Elsevier",

    }

    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 journalArticleAcademicpeer-review

    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

    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 - 0045-7825

    ER -