Clustering discretization methods for generation of material performance databases in machine learning and design optimization
Clustering discretization methods for generation of material performance databases in machine learning and design optimization
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DOI：
10.1007/s00466-019-01716-0
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发表时间：
2019-08-01
影响因子：
4.1
通讯作者：
Liu, Wing Kam
中科院分区：
文献类型：
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作者：
Li, Hengyang;Kafka, Orion L.;Liu, Wing Kam
机械科学和工程可以使用机器学习。然而，数据集仍然相对稀缺；幸运的是，已知的控制方程可以补充这些数据。本文总结并概括了三种降阶方法：自洽聚类分析、虚拟聚类分析和有限元聚类分析。这些方法具有两阶段结构：无监督学习有助于降低模型复杂性，机械方程提供预测。这些预测定义了适合训练神经网络的数据库。前馈神经网络解决前向问题，例如替换本构定律或均质化例程。卷积神经网络解决逆问题或者是分类器，例如提取边界条件或确定是否发生损坏。我们将解释如何应用这些网络，然后提供一个实际练习：（a）具有非线性弹性材料行为和（b）在微观结构损伤约束下的结构的拓扑优化。这导致微结构敏感设计的计算量仅比传统线弹性分析多一点。
Mechanical science and engineering can use machine learning. However, data sets have remained relatively scarce; fortunately, known governing equations can supplement these data. This paper summarizes and generalizes three reduced order methods: self-consistent clustering analysis, virtual clustering analysis, and FEM-clustering analysis. These approaches have two-stage structures: unsupervised learning facilitates model complexity reduction and mechanistic equations provide predictions. These predictions define databases appropriate for training neural networks. The feed forward neural network solves forward problems, e.g., replacing constitutive laws or homogenization routines. The convolutional neural network solves inverse problems or is a classifier, e.g., extracting boundary conditions or determining if damage occurs. We will explain how these networks are applied, then provide a practical exercise: topology optimization of a structure (a) with non-linear elastic material behavior and (b) under a microstructural damage constraint. This results in microstructure-sensitive designs with computational effort only slightly more than for a conventional linear elastic analysis.