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基于机器学习方法的有限元等效应力解的改善研究
发表时间：2018-10-15 浏览量：2071 下载量：327
| 全部作者： | 赵亚飞，韦广梅，李海滨，李劲波，吴鹏辉 |
| 作者单位： | 内蒙古工业大学理学院 |
| 摘 要： | 选取一简化为平面应力问题的各向同性且受均布载荷的等截面悬臂深梁为研究实例，以Mises应力为应力考察量、高斯积分点为样本点、单元角结点为改善点，比较BP神经网络、支持向量机（support vector machine，SVM）、高斯过程回归（Gaussian process regression，GPR）3种机器学习方法对有限元应力解的改善效果。4结点单元有限元模型和8结点单元有限元模型的计算结果表明：1）3种机器学习方法的应力改善效果均较传统有限元整体应力修匀明显，其中边界结点改善效果尤为显著；2）4结点模型（大样本）的改善效果，3种机器学习方法改善后的结点总体误差均比样本点的总体误差小，BP神经网络稍优于SVM，GPR效果最佳；3）8结点模型（小样本）的改善效果，GPR和SVM的改善效果明显优于BP神经网络，GPR总体误差与SVM相当，但较SVM的各点误差波动小；4）GPR方法较SVM方法，能够给出置信区间，输出具有概率意义。基于机器学习方法进行有限元应力解改善是可行的，且较之经典方法，机器学习方法可以直接给出改善效果更好的Mises应力。 |
| 关 键 词： | 固体力学；有限元；应力改善；机器学习方法；Mises应力 |
| Title： | Improvement of finite element equivalent stress solution based on machine learning methods |
| Author： | ZHAO Yafei, WEI Guangmei, LI Haibin, LI Jinbo, WU Penghui |
| Organization： | College of Sciences, Inner Mongolia University of Technology |
| Abstract： | This paper compares the three machine learning methods of BP neural network, support vector machine (SVM) and Gaussian process regression (GPR) to improve the stress solution of finite element method. The example is a homogeneous cantilever beam with uniform load, which is simplified as plane stress problem. The stress is measured by Mises stress, Gaussian integral point is taken as the sample point, and the element angle node is the improvement point. The calculation results of 4-node finite element model and 8-node element finite element model show that: 1) The stress improvement effects of the three machine learning methods are obviously better than that of the traditional finite element method, and the improvement effect of the boundary nodes are particularly significant; 2) The improvement effects of 4-node model (large sample) is that the overall error of the three machine learning methods is smaller than that of the sample point, and BP neural network is slightly better than SVM, GPR is the best; 3) The improvement effects of 8-node model (small sample) is that the improvement effects of GPR and SVM are obviously better than that of BP neural network, and the overall error of GPR is similar to that of SVM, but the error of each point is less than that of SVM; 4) Compared with the SVM method, the GPR method can give the confidence interval and the output has the probability significance. It is concluded that the improvement of finite element stress solution based on machine learning methods is feasible. Compared with the classical method, machine learning method can directly give the better Mises stress with better effect. |
| Key words： | solid mechanics; finite element; stress improvement; machine learning method; Mises stress |
| 发表期数： | 2018年10月第19期 |
| 引用格式： | 赵亚飞，韦广梅，李海滨，等. 基于机器学习方法的有限元等效应力解的改善研究[J]. 中国科技论文在线精品论文，2018，11（19）：1966-1976. |
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