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

机译：用于DEM模型的快速和自动校准的迭代贝叶斯过滤框架

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摘要

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. (C) 2019 The Author(s). Published by Elsevier B. V.
机译：粒状材料的非线性，历史依赖性宏观行为植根于组成颗粒之间的微机械和不可逆的塑性变形中，反映了微观结构的变化。离散元素方法（DEM）可以预测由颗粒间相互作用引起的微观结构的演变。然而，接触和颗粒水平的微机械参数通常是未知的，因为颗粒材料相对于它们的表面，形状，紊乱和各向异性的多样性。所提出的迭代贝叶斯滤波器包括递归更新模型参数的后部分布并迭代该过程。在高可能参数空间中从提案密度汲取新的样本。在迭代上，提案密度在后部模式附近逐渐局部地定位，这允许自动变焦朝向最佳解决方案。 Dirichlet工艺高斯混合物训练，通过稀疏和高尺寸数据从先前的迭代训练，以更新提案密度。例如，估计微机械参数的概率分布，对粒状组件的实验测量应力 - 应变行为进行调节。选择四个微机械参数，即接触级杨氏模量，颗粒间摩擦，滚动刚度和滚动摩擦，与宏观行为密切相关。从3D X射线计算机断层摄影图像获得先验粒子配置。每个微机械参数的后验期望在四个迭代中收敛，导致实验数据与数值预测之间的优异协议。作为新的结果，所提出的框架提供了更深入地了解微机械参数之间的相关性以及微观和宏观参数/数量之间的相关性，包括它们的不确定性。因此，迭代贝叶斯过滤框架具有巨大的潜力，可以在粒状材料中量化参数不确定性及其在各种尺度上的传播。 （c）2019年作者。 elsevier b. v.

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