A two-stage surrogate model for Neo-Hookean problems based on adaptive proper orthogonal decomposition and hierarchical tensor approximation
A two-stage surrogate model for Neo-Hookean problems based on adaptive proper orthogonal decomposition and hierarchical tensor approximation
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DOI：
10.1016/j.cma.2020.113368
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发表时间：
2020-12-01
影响因子：
7.2
通讯作者：
Reese, Stefanie
中科院分区：
文献类型：
--
作者：
Kastian, Steffen;Moser, Dieter;Reese, Stefanie
在存在不确定性的情况下，评估实际结构的鲁棒性和可靠性在数值上是昂贵的。这激发了模型降阶技术，如适当正交分解（POD），它在完整模型的一组预计算的基础上给出了一个近似模型。这减少了计算时间。在必须进行大量评价的不确定性量化或优化环境中，POD实现的减少通常是不够的。在这种情况下，通常只有少量的数量是值得关注的，进一步减少是可能的。第二次约简可以通过从可能的高维参数空间到每个感兴趣量（qi）的映射来表示。一般来说，从一个未约简的模型构造这样的映射是困难的。因此，本文介绍了结合两种还原方法的两阶段代理模型。该替代模型适用于塑性、硬化和损伤的新胡克模型问题。在这里，模型的知识允许在第一阶段对POD进行自适应选择。这一思想被阐述成一个广义的框架，称为自适应固有正交分解（APOD）。第二阶段由层次张量近似（HTA）组成，该模型易于调整到第一阶段的精度和计算成本，从而使两阶段代理模型成为Neo-Hookean问题不确定性量化和优化的有效选择。此外，在这两个阶段都具备的情况下，利用HTA进行贪婪快照搜索，以改进APOD和POD的基础。如果没有专业知识指导脱机阶段的快照选择，这将非常有用。(C) 2020 Elsevier B.V.版权所有
The evaluation of robustness and reliability of realistic structures in the presence of uncertainty is numerically costly. This motivates model order reduction techniques like the proper orthogonal decomposition (POD), which gives an approximate model on the basis of a set of precomputations of a full model. This reduces the computational time. The reduction achieved by POD is usually not sufficient in the uncertainty quantification or optimization context where a large number of evaluations has to be carried out. In this context, it is also common that only a few quantities are of interest and a further reduction is possible. The second reduction may be represented by a mapping from a possibly high-dimensional parameter space onto each quantity of interest (QoI). In general, it is difficult to construct such a mapping from an unreduced model. Hence, in this paper a two-stage surrogate model that combines both reduction approaches is introduced. This surrogate model is tailored and applied to Neo-Hookean model problems with plasticity, hardening and damage. Here, the knowledge of the model allows an adaptive selection of the POD basis on the first stage. This idea is elaborated into a generalized framework called adaptive proper orthogonal decomposition (APOD). The second stage consists of the hierarchical tensor approximation (HTA) which is easily adjusted to the accuracy and computational cost of the first stage such that the two-stage surrogate model becomes an efficient option for uncertainty quantification and optimization for Neo-Hookean problems. Additionally, with both stages at hand, the HTA is utilized for a greedy snapshot search to improve the basis of APOD and POD. This is useful if no expert knowledge is available to guide the snapshot selection in the offline phase. (C) 2020 Elsevier B.V. All rights reserved.