论文标题

贝叶斯多尺度CNN框架,可预测具有微观特征的结构中的局部应力场

A Bayesian multiscale CNN framework to predict local stress fields in structures with microscale features

论文作者

Krokos, Vasilis, Xuan, Viet Bui, Bordas, Stéphane P. A., Young, Philippe, Kerfriden, Pierre

论文摘要

由于有限元素的直接数值模拟的高计算成本,多尺度计算建模是具有挑战性的。为了解决此问题,并发多尺度方法使用较便宜的宏观替代解决方案作为微观滑动窗口的边界条件。在实施和成本方面,显微镜问题仍然是数值挑战性的操作。在这项工作中,我们建议通过编码器卷积神经网络替换局部微观尺度解决方案,该卷积神经网络将在未解决的显微镜特征周围生成细微的应力校正,而无需先前的局部微观镜头问题。我们部署了一种贝叶斯方法,提供可靠的间隔来评估预测的不确定性,然后将其用于研究选择性学习框架的优点。我们将展示该方法使用线性化和有限的应变弹性理论预测多孔结构中等效应力场的能力。

Multiscale computational modelling is challenging due to the high computational cost of direct numerical simulation by finite elements. To address this issue, concurrent multiscale methods use the solution of cheaper macroscale surrogates as boundary conditions to microscale sliding windows. The microscale problems remain a numerically challenging operation both in terms of implementation and cost. In this work we propose to replace the local microscale solution by an Encoder-Decoder Convolutional Neural Network that will generate fine-scale stress corrections to coarse predictions around unresolved microscale features, without prior parametrisation of local microscale problems. We deploy a Bayesian approach providing credible intervals to evaluate the uncertainty of the predictions, which is then used to investigate the merits of a selective learning framework. We will demonstrate the capability of the approach to predict equivalent stress fields in porous structures using linearised and finite strain elasticity theories.

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