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卷积神经网络求解有限元单元刚度矩阵

贾光辉 于云瑞 王丹

贾光辉, 于云瑞, 王丹等 . 卷积神经网络求解有限元单元刚度矩阵[J]. 北京航空航天大学学报, 2020, 46(3): 481-487. doi: 10.13700/j.bh.1001-5965.2019.0134
引用本文: 贾光辉, 于云瑞, 王丹等 . 卷积神经网络求解有限元单元刚度矩阵[J]. 北京航空航天大学学报, 2020, 46(3): 481-487. doi: 10.13700/j.bh.1001-5965.2019.0134
JIA Guanghui, YU Yunrui, WANG Danet al. Solving finite element stiffness matrix based on convolutional neural network[J]. Journal of Beijing University of Aeronautics and Astronautics, 2020, 46(3): 481-487. doi: 10.13700/j.bh.1001-5965.2019.0134(in Chinese)
Citation: JIA Guanghui, YU Yunrui, WANG Danet al. Solving finite element stiffness matrix based on convolutional neural network[J]. Journal of Beijing University of Aeronautics and Astronautics, 2020, 46(3): 481-487. doi: 10.13700/j.bh.1001-5965.2019.0134(in Chinese)

卷积神经网络求解有限元单元刚度矩阵

doi: 10.13700/j.bh.1001-5965.2019.0134
详细信息
    作者简介:

    贾光辉, 男, 博士, 副教授, 硕士生导师。主要研究方向:飞行器结构分析与撞击动力学响应; E-mail:jiaguanghui@buaa.edu.cn

    于云瑞, 男, 硕士研究生。主要研究方向:深度学习与传统结构分析的结合

    王丹, 女, 博士, 高级工程师。主要研究方向:飞行器总体设计

    通讯作者:

    贾光辉, E-mail:jiaguanghui@buaa.edu.cn

  • 中图分类号: TP301.6

Solving finite element stiffness matrix based on convolutional neural network

More Information
  • 摘要:

    随着深度学习在众多领域的成功应用与快速发展,将深度学习与传统的结构分析相融合已经成为了新的研究方向。在求解有限元单元刚度矩阵的具体问题上,研究了卷积神经网络在结构分析上的应用。以四边形平面应力单元为例,基于卷积神经网络,提出了一个求解有限元总体刚度矩阵的神经网络模型;同时分析了网络的学习效果与网络卷积核数目、训练样本数目之间的关系。计算实例表明,在一定范围内,网络的学习能力随着卷积核数目、训练样本数目的增加而不断提升。在现实应用时,可以根据具体的精度要求而设定相应的卷积神经网络。卷积神经网络训练完成后,单元刚度矩阵的计算具有实时性,且精度满足工程要求。

     

  • 图 1  LeakyReLU激活函数

    Figure 1.  LeakyReLU activation function

    图 2  平面四边形单元

    Figure 2.  Planar quadrilateral unit

    图 3  数据处理之后的平面四边形单元

    Figure 3.  Planar quadrilateral unit after data processing

    图 4  图像的RGB三通道数据存储

    Figure 4.  Data storage of a three-channel RGB picture

    图 5  平面四边形单元的数据存储

    Figure 5.  Data storage of planar quadrilateral unit

    图 6  补零操作后平面四边形单元的数据存储

    Figure 6.  Data storage of planar quadrilateral unit after padding zero

    图 7  平面四边形单元所需求解的刚度矩阵元素

    Figure 7.  Stiffness matrix elements to be solved for a planar quadrilateral unit

    图 8  卷积神经网络示意图

    Figure 8.  Schematic diagram of convolutional neural network

    图 9  预测误差与卷积核数目的关系

    Figure 9.  Relationship between prediction error and number of convolution kernels

    图 10  预测误差与训练样本数目的关系

    Figure 10.  Relationship between prediction error and number of training samples

    表  1  平面四边形单元所需求解单元刚度矩阵元素的真实值与预测值对比

    Table  1.   Comparison between real and predicted values of stiffness matrix elements to be solved for a planar quadrilateral unit

    单元刚度矩阵元素 真实值 预测值
    k12 0.167 0.167
    k13 -0.893 -0.893
    k14 -0.033 -0.033
    k15 -0.485 -0.485
    k16 -0.167 -0.167
    k17 0.408 0.407
    k18 0.033 0.034
    k23 0.033 0.033
    k24 -0.276 -0.276
    k25 -0.167 -0.167
    k26 -0.241 -0.241
    k27 -0.033 -0.033
    k28 0.035 0.034
    k34 -0.167 -0.167
    k35 0.408 0.409
    k36 -0.033 -0.033
    k37 -0.485 -0.486
    k38 0.167 0.167
    k45 0.033 0.033
    k46 0.035 0.036
    k47 0.167 0.167
    k48 -0.241 -0.242
    k56 0.167 0.167
    k57 -0.893 -0.894
    k58 -0.033 -0.033
    k67 0.033 0.033
    k68 -0.276 -0.276
    k78 -0.167 -0.167
    注:真实值的输入为经过平移和归一化操作之后的平面四边形单元的4个节点坐标值,分别对应:x1=-0.387, y1=-1;x2=0.387, y2=-1;x3=0.387, y3=1;x4=-0.387, y4=1。
    下载: 导出CSV
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出版历程
  • 收稿日期:  2019-04-01
  • 录用日期:  2019-10-11
  • 网络出版日期:  2020-03-20

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