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基于BP神经网络的I型金属夹芯板极限强度预测

卫钰汶 仲强 王德禹

卫钰汶, 仲强, 王德禹. 基于BP神经网络的I型金属夹芯板极限强度预测[J]. 中国舰船研究, 2022, 17(2): 125–134 doi: 10.19693/j.issn.1673-3185.02335
引用本文: 卫钰汶, 仲强, 王德禹. 基于BP神经网络的I型金属夹芯板极限强度预测[J]. 中国舰船研究, 2022, 17(2): 125–134 doi: 10.19693/j.issn.1673-3185.02335
WEI Y W, ZHONG Q, WANG D Y. Ultimate strength prediction of I-core sandwich plate based on BP neural network[J]. Chinese Journal of Ship Research, 2022, 17(2): 125–134 doi: 10.19693/j.issn.1673-3185.02335
Citation: WEI Y W, ZHONG Q, WANG D Y. Ultimate strength prediction of I-core sandwich plate based on BP neural network[J]. Chinese Journal of Ship Research, 2022, 17(2): 125–134 doi: 10.19693/j.issn.1673-3185.02335

基于BP神经网络的I型金属夹芯板极限强度预测

doi: 10.19693/j.issn.1673-3185.02335
基金项目: 国家自然科学基金资助项目(51979163)
详细信息
    作者简介:

    卫钰汶,女,1998年生,硕士生。研究方向:船体结构极限强度。E-mail:yuwenwei@sjtu.edu.cn

    仲强,男,1990年生,博士生。研究方向:船体结构极限强度。E-mail:zhongqiang@sjtu.edu.cn

    王德禹,男,1963年生,博士,教授,博士生导师。研究方向:船舶与海洋工程结构力学,结构优化设计与可靠性分析,结构极限强度与试验技术研究。E-mail:dywang@sjtu.edu.cn

    通信作者:

    王德禹

  • 中图分类号: U661.43

Ultimate strength prediction of I-core sandwich plate based on BP neural network

知识共享许可协议
基于BP神经网络的I型金属夹芯板极限强度预测卫钰汶,等创作,采用知识共享署名4.0国际许可协议进行许可。
  • 摘要:   目的  针对过去对I型金属夹芯板的极限强度评估不完善的问题,提出一种采用 BP人工神经网络的方法来定量确定各相关参数对I型金属夹芯板极限强度的影响。  方法  首先,采用非线性有限元法研究I型金属夹芯板在面内轴向压缩载荷条件下的极限强度;然后,构造BP神经网络以对不同面板柔度系数βp、腹板柔度系数βw和梁柱柔度系数λ下I型金属夹芯板的极限强度进行预测;最后,提出采用人工神经网络权值和偏置法预测I型金属夹芯板极限强度的公式。  结果  针对所计算的算例尺寸,显示采用BP神经网络方法的极限强度预测的均方差MSE和相关系数R分别为0.001 2和0.981 8,所构建的神经网络模型具有较好的预测精度,最大误差不超过10%。  结论  所得结论可为I型金属夹芯板在船体结构中的应用提供参考。
  • 图  1  I型金属夹芯板结构示意图

    Figure  1.  Schematic diagram of I-core sandwich panels

    图  3  纵向1/2+1+1/2跨(边界条件代替强横梁)模型示意图

    Figure  3.  Schematic diagram of longitudinal 1/2+1+1/2 spans (boundary conditions instead of strong beams) model

    图  4  纵向单跨(边界条件代替强构件)模型示意图

    Figure  4.  Schematic diagram of longitudinal 1 span (boundary conditions instead of strong members) model

    图  2  纵向三跨(有实际强构件)模型示意图

    Figure  2.  Schematic diagram of longitudinal 3 spans model with actual strong members

    图  5  不同模型范围下I型金属夹芯板轴压下载荷−端缩曲线对比

    Figure  5.  Comparison of load-deformation curves for I-core sandwich panels under axial compression with different range of models

    图  6  I型金属夹芯板轴压下载荷−端缩曲线对比

    Figure  6.  Comparison of load-deformation curves for I-core sandwich panel under axial compression

    图  7  模型试验与有限元仿真失效模式对比

    Figure  7.  Comparison of the failure mode by the FE analysis and model test

    图  8  预测I型金属夹芯板极限强度与屈服强度比的BP神经网络结构

    Figure  8.  Architecture of BP neural network for prediction of ultimate strength to yield strength ratio of I-core sandwich panels

    图  9  训练集中${{{\sigma _{{\rm{u}}}}} \mathord{\left/ {\vphantom {{{\sigma _{{\rm{u}}}}} {{\sigma _{{\rm{Y}}}}}}} \right. } {{\sigma _{{\rm{Y}}}}}}$的期待值与预测值的相关图

    Figure  9.  Correlation between the expected data and predicted outputs for ${{{\sigma _{{\rm{u}}}}} \mathord{\left/ {\vphantom {{{\sigma _{{\rm{u}}}}} {{\sigma _{{\rm{Y}}}}}}} \right. } {{\sigma _{{\rm{Y}}}}}}$ in training set

    图  10  验证集中${{{\sigma _{{\rm{u}}}}} \mathord{\left/ {\vphantom {{{\sigma _{{\rm{u}}}}} {{\sigma _{{\rm{Y}}}}}}} \right. } {{\sigma _{{\rm{Y}}}}}}$的期待值与预测值的相关图

    Figure  10.  Correlation between the expected data and predicted outputs for ${{{\sigma _{{\rm{u}}}}} \mathord{\left/ {\vphantom {{{\sigma _{{\rm{u}}}}} {{\sigma _{{\rm{Y}}}}}}} \right. } {{\sigma _{{\rm{Y}}}}}}$ in validation set

    图  11  测试集中${{{\sigma _{{\rm{u}}}}} \mathord{\left/ {\vphantom {{{\sigma _{{\rm{u}}}}} {{\sigma _{{\rm{Y}}}}}}} \right. } {{\sigma _{{\rm{Y}}}}}}$的期待值与预测值的相关图

    Figure  11.  Correlation between the expected data and predicted outputs for ${{{\sigma _{{\rm{u}}}}} \mathord{\left/ {\vphantom {{{\sigma _{{\rm{u}}}}} {{\sigma _{{\rm{Y}}}}}}} \right. } {{\sigma _{{\rm{Y}}}}}}$ in testing set

    图  12  全部集中${{{\sigma _{{\rm{u}}}}} \mathord{\left/ {\vphantom {{{\sigma _{{\rm{u}}}}} {{\sigma _{{\rm{Y}}}}}}} \right. } {{\sigma _{{\rm{Y}}}}}}$的期待值与预测值的相关图

    Figure  12.  Correlation between the expected data and predicted outputs for ${{{\sigma _{{\rm{u}}}}} \mathord{\left/ {\vphantom {{{\sigma _{{\rm{u}}}}} {{\sigma _{{\rm{Y}}}}}}} \right. } {{\sigma _{{\rm{Y}}}}}}$ in whole set

    图  13  测试集中${{{\sigma _{{\rm{u}}}}} \mathord{\left/ {\vphantom {{{\sigma _{{\rm{u}}}}} {{\sigma _{{\rm{Y}}}}}}} \right. } {{\sigma _{{\rm{Y}}}}}}$的期待值与预测值间误差

    Figure  13.  Error between the expected data and predicted outputs for ${{{\sigma _{{\rm{u}}}}} \mathord{\left/ {\vphantom {{{\sigma _{{\rm{u}}}}} {{\sigma _{{\rm{Y}}}}}}} \right. } {{\sigma _{{\rm{Y}}}}}}$ in testing set

    图  14  ${{{\sigma _{{\rm{u}}}}} \mathord{\left/ {\vphantom {{{\sigma _{{\rm{u}}}}} {{\sigma _{{\rm{Y}}}}}}} \right. } {{\sigma _{{\rm{Y}}}}}}$中期待值与预测值间误差

    Figure  14.  Error between the expected data and predicted outputs for ${{{\sigma _{{\rm{u}}}}} \mathord{\left/ {\vphantom {{{\sigma _{{\rm{u}}}}} {{\sigma _{{\rm{Y}}}}}}} \right. } {{\sigma _{{\rm{Y}}}}}}$

    图  15  输入变量βpβwλ对I型金属夹芯板结构${{{\sigma _{{\rm{u}}}}} \mathord{\left/ {\vphantom {{{\sigma _{{\rm{u}}}}} {{\sigma _{{\rm{Y}}}}}}} \right. } {{\sigma _{{\rm{Y}}}}}}$的影响程度

    Figure  15.  Relative importance of the input variables βp, βw, λ on the response variable of ${{{\sigma _{{\rm{u}}}}} \mathord{\left/ {\vphantom {{{\sigma _{{\rm{u}}}}} {{\sigma _{{\rm{Y}}}}}}} \right. } {{\sigma _{{\rm{Y}}}}}}$ of I-core sandwich panels

    表  1  I型金属夹芯板几何尺寸和材料参数

    Table  1.   Geometrical size and material parameters of I-core sandwich panels

    参数数值
    上下面板厚度tp /mm2,3,4
    腹板厚度tw /mm2,4,6,8
    腹板高度hw /mm40,60,80
    腹板间距dw /mm80,120,160
    横梁间距a/mm2 500,3 000,3 500
    屈曲半波数e15
    屈服强度σY /MPa235,315,390
    下载: 导出CSV

    表  2  纵向三跨(有实际强构件)模型的边界条件

    Table  2.   Boundary condition of longitudinal 3 spans model with actual strong members

    施加范围UxUyUzRxRyRz
    A1-B1,A1'-B1',
    A2-B2,A2'-B2'
    000
    A1-A2,A1'-A2'位移
    载荷
    0000
    B1-B2,B1'-B2'00000
    C1-D1,C2-D2,E1-F1,E2-F2,
    G1-H1,G2-H2,J1-K1,J2-K2
    0
    下载: 导出CSV

    表  3  纵向1/2+1+1/2跨(边界条件代替强横梁)模型的边界条件

    Table  3.   Boundary condition of longitudinal 1/2+1+1/2 spans (boundary conditions instead of strong beams) model

    施加范围UxUyUzRxRyRz
    A1-B1,A1'-B1',
    A2-B2,A2'-B2'
    000
    A1-A2,A1'-A2'位移载荷00
    B1-B2,B1'-B2'000
    K1-K2,L1-L200
    下载: 导出CSV

    表  4  纵向单跨(边界条件代替强构件)模型的边界条件

    Table  4.   Boundary condition of longitudinal 1 span (boundary conditions instead of strong members) model

    施加范围UxUyUzRxRyRz
    A1-B1,A1'-B1',
    A2-B2,A2'-B2'
    000
    A1-A2,A1'-A2'位移载荷0000
    B1-B2,B1'-B2'00000
    下载: 导出CSV

    表  5  不同网格密度下的I型金属夹芯板数值计算结果

    Table  5.   Numerical results of I-core sandwich panels with different mesh densities

    网格大小/mmσu /MPa
    1/8hw183.671 7
    1/4hw184.319 9
    1/2hw189.535 6
    hw207.345 3
    下载: 导出CSV

    表  6  不同训练函数的训练效果对比

    Table  6.   Performance comparison of different training function

    函数算法迭代次数迭代精度
    TrainlmLevenberg-Marquardt法250.002 0
    Traingd梯度递减法1 0000.012 1
    Traingdm带动量因子的梯度递减法1 0000.034 7
    Traingda带自适应学习率的梯度递减法1 0000.005 9
    Traingdx带自适应学习率和动量因子的梯度递减法1 0000.010 1
    下载: 导出CSV

    表  7  不同隐藏层层数及神经元个数的训练效果对比

    Table  7.   Performance comparison of different number of neurons

    隐藏层1的
    神经元个数
    隐藏层2的
    神经元个数
    迭代次数迭代精度
    301 0000.002 2
    401 0000.003 4
    501 0000.002 5
    601 0000.002 7
    702350.002 0
    803600.002 0
    90250.002 0
    100720.001 9
    1101330.002 0
    120710.001 9
    33710.002 0
    341500.002 0
    351530.001 9
    361920.001 9
    37520.002 0
    382890.002 0
    39850.002 0
    下载: 导出CSV

    表  8  有限元仿真结果

    Table  8.   The results of FE simulation

    序号λβpβwσuY序号λβpβwσuY
    16.370 61.351 00.675 50.880 7333.185 30.675 51.351 00.954 9
    26.715 41.351 00.337 80.892 1343.357 70.675 50.675 50.992 9
    37.003 71.351 00.225 20.850 4353.501 90.675 50.450 30.996 8
    47.249 11.351 00.168 90.795 4363.624 50.675 50.337 80.996 7
    56.099 10.900 70.675 50.944 7376.240 02.026 50.675 50.581 4
    66.352 80.900 70.337 80.982 0386.492 92.026 50.337 80.604 5
    76.576 60.900 70.225 20.981 9396.715 42.026 50.225 20.585 9
    86.775 90.900 70.168 90.976 4406.913 02.026 50.168 90.565 0
    95.894 50.675 50.675 50.953 1416.006 71.351 00.675 50.710 8
    106.094 40.675 50.337 80.996 0426.187 31.351 00.337 80.788 9
    116.276 10.675 50.225 20.997 4436.352 81.351 00.225 20.776 7
    126.442 20.675 50.168 90.996 9446.505 01.351 00.168 90.760 1
    134.431 31.351 01.013 30.861 6455.823 31.013 30.675 50.751 6
    144.731 11.351 00.506 60.872 9465.963 41.013 30.337 80.882 1
    154.965 21.351 00.337 80.856 0476.094 41.013 30.225 20.891 3
    165.153 81.351 00.253 30.830 8486.217 41.013 30.168 90.883 9
    174.247 10.900 71.013 30.928 1494.311 52.026 51.013 30.669 0
    184.476 90.900 70.506 60.974 1504.540 32.026 50.506 60.714 0
    194.669 20.900 70.337 80.974 6514.731 12.026 50.337 80.703 6
    204.832 70.900 70.253 30.970 2524.893 02.026 50.253 30.685 6
    214.119 30.675 51.013 30.942 9534.160 01.351 01.013 30.801 5
    224.304 90.675 50.506 60.992 0544.328 61.351 00.506 60.852 6
    234.466 40.675 50.337 80.995 1554.476 91.351 00.337 80.851 7
    244.608 40.675 50.253 30.992 0564.608 61.351 00.253 30.837 3
    253.429 31.351 01.351 00.900 3574.051 01.013 31.013 30.847 2
    263.692 61.351 00.675 50.918 6584.184 21.013 30.506 60.907 1
    273.886 91.351 00.450 30.902 4594.304 91.013 30.337 80.913 6
    284.036 61.351 00.337 80.883 4604.414 91.013 30.253 30.909 0
    293.282 40.900 71.351 00.943 7613.319 02.026 51.351 00.714 7
    303.491 50.900 70.675 50.980 0623.527 02.026 50.675 50.775 6
    313.658 40.900 70.450 30.979 4633.692 62.026 50.450 30.783 6
    323.795 10.900 70.337 80.969 3643.828 02.026 50.337 80.777 2
    下载: 导出CSV

    表  9  I型金属夹芯板极限强度预测方程参数值

    Table  9.   Parameter values of prediction equation for ultimate strength of I-core sandwich panels

    kjiwijbjwjkbk
    11115.787 83−8.060 5−1.134 293.508 448
    2−1.317 5
    31.242 68
    21−3.184 6714.235 290.202 705
    2−12.944 9
    3−1.725 95
    31−5.953 611.084 991−0.376 16
    211.236 42
    30.961 726
    4129.143 18−14.747 20.815 201
    2−3.361 12
    34.365 897
    510.309 728−3.401 43−0.135 02
    215.531 94
    3−12.604 4
    61−1.301 16−1.886 73−2.492 59
    2−6.731 54
    38.029 399
    716.911 944−9.691 39−0.172 38
    212.653 35
    36.526 226
    812.203 4711.637 875−2.538 26
    26.820 759
    3−7.541 44
    91−6.343 715.825 7580.036 682
    2−13.337 1
    3−3.522 82
    下载: 导出CSV

    表  10  I型金属夹芯板参数

    Table  10.   Parameters of I-core sandwich panels

    序号λβpβwσuY
    14.962 20.965 00.562 90.921 4
    25.131 20.965 00.337 80.949 6
    35.283 20.965 00.241 30.945 0
    45.829 02.346 20.651 70.502 8
    56.013 82.346 20.391 00.512 9
    66.180 72.346 20.279 30.502 2
    75.638 61.675 90.651 70.618 2
    85.779 21.675 90.391 00.648 9
    95.909 61.675 90.279 30.647 4
    104.927 61.740 41.015 30.675 8
    115.174 91.740 40.609 20.679 8
    125.380 01.740 40.435 10.666 9
    134.943 51.243 20.609 20.852 1
    145.116 11.243 20.435 10.851 7
    153.713 22.026 50.788 10.681 2
    163.859 82.026 50.472 90.705 2
    173.987 52.026 50.337 80.709 6
    183.596 21.447 50.788 10.801 5
    193.710 21.447 50.472 90.829 8
    203.813 21.447 50.337 80.834 1
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-03-30
  • 修回日期:  2021-05-25
  • 网络出版日期:  2022-04-06
  • 刊出日期:  2022-04-20

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