基于刚度的物理信息深度ONet用于结构响应预测
摘要
有限元建模是结构分析中已确立的工具，但建模复杂结构通常需要大量的预处理、巨大的分析工作量和相当的时间。本研究通过引入一种创新方法，来实现结构静态响应的实时预测，该方法利用DeepONet，其物理信息网络方法由结构平衡定律驱动。该方法能够灵活地准确预测各种负载类别和幅度下的响应。训练好的DeepONet可以在几乎一秒钟内为整个域生成解答。这种能力有效地消除了在FE建模中通常需要为每个新案例进行大量重建和分析的需求。我们将该方法应用于两个结构：一个简单的二维梁结构和一个真实桥梁的综合3D模型。为了预测DeepONet的多个变量，我们利用两种策略：分枝/树干以及组合多个DeepONet于单个DeepONet中。在数据驱动训练之外，我们引入了一种新颖的物理信息训练方法。该方法利用结构刚度矩阵来强制基本的平衡和能量守恒原理， resulting in two novel physics-informed loss functions: energy conservation and static equilibrium using the Schur complement。 We use various combinations of loss functions to achieve an error rate of less than 5% with significantly reduced training time. This study shows that DeepONet, enhanced with hybrid loss functions, can accurately and efficiently predict displacements and rotations at each mesh point, with reduced training time.
引用
@article{arxiv.2409.00994,
title = {Physics-informed DeepONet with stiffness-based loss functions for structural response prediction},
author = {Bilal Ahmed and Yuqing Qiu and Diab W. Abueidda and Waleed El-Sekelly and Borja Garcia de Soto and Tarek Abdoun and Mostafa E. Mobasher},
journal= {arXiv preprint arXiv:2409.00994},
year = {2024}
}