A hierarchical Bayesian approach for calibration of stochastic material models
A hierarchical Bayesian approach for calibration of stochastic material models
复制标题
用于校准随机材料模型的分层贝叶斯方法
DOI：
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
T. Dodwell
中科院分区：
文献类型：
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作者：
Nikolaos Papadimas;T. Dodwell
摘要 本文将校准材料本构模型的传统挑战重新定义为分层概率框架。我们考虑一个贝叶斯框架，其中材料参数被分配分布，然后根据实验数据进行更新。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，而是对可能的实验样本群体推断模型参数。在此过程中，我们还试图捕捉不同优惠券材料的固有变异性，以及测试重复性的不确定性。在本文中，我们使用分层贝叶斯模型来解决这个问题。然而，普通的计算方法成本高昂。我们的策略边缘化每个单独的实验，将推理问题的维度减少到仅超参数——这些参数仅描述材料模型的总体统计数据。重要的是，这个边缘化步骤要求我们得出一个近似的可能性，为此，我们利用模拟器（在采样之前离线构建）和贝叶斯求积，使我们能够捕获该数值近似中的不确定性。重要的是，我们的方法使得材料模型的分层贝叶斯校准计算变得可行。该方法在两个不同的示例中进行了测试。第一个是使用合成数据的简单弹簧模型的压缩测试；第二个是一个更复杂的示例，使用真实的实验数据来拟合 3D 打印钢材的随机弹塑性模型。
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.
离散和连续时间内医疗保健相关病原体传播模型的有效参数估计。
DOI：
10.1093/imammb/dqt021
发表时间：
2015
期刊：
Mathematical medicine and biology : a journal of the IMA
影响因子：
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作者：
Thomas,Alun;Redd,Andrew;Khader,Karim;Leecaster,Molly;Greene,Tom;Samore,Matthew
通讯作者：
Samore,Matthew