Parameter identification for phase-field modeling of fracture: a Bayesian approach with sampling-free update
Parameter identification for phase-field modeling of fracture: a Bayesian approach with sampling-free update
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DOI：
10.1007/s00466-020-01942-x
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发表时间：
2020-11
影响因子：
4.1
通讯作者：
T. Wu;B. Rosic;L. Lorenzis;H. Matthies
中科院分区：
文献类型：
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作者：
T. Wu;B. Rosic;L. Lorenzis;H. Matthies
裂缝的相场建模在过去十年中得到了广泛的应用，因为相关的计算框架在模拟三维任意复杂的裂缝过程方面具有灵活性。然而，数值预测很大程度上受到材料力学性能不确定性的影响，这些不确定性源于未解决的非均质性和使用有噪声的实验数据。本工作的目的是应用贝叶斯方法来估计相场模型的体积和剪切模量、抗拉强度和断裂韧性，从而在实验数据的帮助下提高模拟的准确性。传统的贝叶斯后验概率密度函数估计方法采用采样方案，通常需要大量的模型估计才能达到预期的收敛效果，计算成本很高。为了缓解这个问题，我们采用了一种更有效的方法，称为无采样线性贝叶斯更新，它依赖于给定实验数据的参数条件期望的评估。通过对三点弯曲试验（观察）的实验数据进行在线和离线调节，确定水泥砂浆的力学性能。在在线方法中，随着新的实验信息的输入，参数值被依次更新。相比之下，离线方法仅在实验完成后提供实验数据的全部历史时使用。通过在一组未使用的实验数据上验证相场断裂模型，讨论和比较了两种估计版本。
Phase-field modeling of fracture has gained popularity within the last decade due to the flexibility of the related computational framework in simulating three-dimensional arbitrarily complicated fracture processes. However, the numerical predictions are greatly affected by the presence of uncertainties in the mechanical properties of the material originating from unresolved heterogeneities and the use of noisy experimental data. The objective of this work is to apply the Bayesian approach to estimate bulk and shear moduli, tensile strength and fracture toughness of the phase-field model, thus improving accuracy of the simulations with the help of experimental data. Conventional approaches for estimating the Bayesian posterior probability density function adopt sampling schemes, which often require a large amount of model estimations to achieve the desired convergence, thus resulting in a high computational cost. In order to alleviate this problem, we employ a more efficient approach called sampling-free linear Bayesian update, which relies on the evaluation of the conditional expectation of parameters given experimental data. We identify the mechanical properties of cement mortar byconditioningon the experimental data of the three-point bending test (observations) in an online and offline manner. In the online approach the parameter values are sequentially updated on the fly as the new experimental information comes in. In contrast, the offline approach is used only when the whole history of experimental data is provided once the experiment is performed. Both versions of estimation are discussed and compared by validating the phase-field fracture model on an unused set of experimental data.