A hierarchical Bayesian approach for calibration of stochastic material models

IF 2.4 Q3 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE DataCentric Engineering Pub Date : 2021-12-17 DOI:10.1017/dce.2021.20
Nikolaos Papadimas, T. Dodwell
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引用次数: 7

Abstract

Abstract This article recasts the traditional challenge of calibrating a material constitutive model into a hierarchical probabilistic framework. We consider a Bayesian framework where material parameters are assigned distributions, which are then updated given experimental data. Importantly, in true engineering setting, we are not interested in inferring the parameters for a single experiment, but rather inferring the model parameters over the population of possible experimental samples. In doing so, we seek to also capture the inherent variability of the material from coupon-to-coupon, as well as uncertainties around the repeatability of the test. In this article, we address this problem using a hierarchical Bayesian model. However, a vanilla computational approach is prohibitively expensive. Our strategy marginalizes over each individual experiment, decreasing the dimension of our inference problem to only the hyperparameter—those parameter describing the population statistics of the material model only. Importantly, this marginalization step, requires us to derive an approximate likelihood, for which, we exploit an emulator (built offline prior to sampling) and Bayesian quadrature, allowing us to capture the uncertainty in this numerical approximation. Importantly, our approach renders hierarchical Bayesian calibration of material models computational feasible. The approach is tested in two different examples. The first is a compression test of simple spring model using synthetic data; the second, a more complex example using real experiment data to fit a stochastic elastoplastic model for 3D-printed steel.
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随机材料模型的分层贝叶斯校正方法
摘要:本文将传统的材料本构模型的校准问题转化为一个层次概率框架。我们考虑一个贝叶斯框架,其中材料参数被分配分布,然后根据实验数据更新。重要的是,在真正的工程环境中,我们对推断单个实验的参数不感兴趣,而是推断可能实验样本总体上的模型参数。在这样做的过程中,我们还试图捕获材料从优惠券到优惠券的固有可变性,以及围绕测试可重复性的不确定性。在本文中,我们使用分层贝叶斯模型来解决这个问题。然而,普通的计算方法是非常昂贵的。我们的策略将每个单独的实验边缘化,将我们的推理问题的维度降低到只有超参数-那些只描述材料模型的总体统计的参数。重要的是,这个边缘化步骤需要我们推导出一个近似的似然,为此,我们利用模拟器(在采样之前离线构建)和贝叶斯正交,允许我们捕获这个数值近似中的不确定性。重要的是,我们的方法使材料模型的分层贝叶斯校准在计算上可行。该方法在两个不同的示例中进行了测试。首先利用合成数据对简单弹簧模型进行压缩试验;第二,一个更复杂的例子,使用实际实验数据拟合3d打印钢的随机弹塑性模型。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
DataCentric Engineering
DataCentric Engineering Engineering-General Engineering
CiteScore
5.60
自引率
0.00%
发文量
26
审稿时长
12 weeks
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