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基于SBFEM和深度学习的裂纹状缺陷反演模型

江守燕 万晨 孙立国 杜成斌

江守燕, 万晨, 孙立国, 杜成斌. 基于SBFEM和深度学习的裂纹状缺陷反演模型. 力学学报, 2021, 53(10): 2724-2735 doi: 10.6052/0459-1879-21-360
引用本文: 江守燕, 万晨, 孙立国, 杜成斌. 基于SBFEM和深度学习的裂纹状缺陷反演模型. 力学学报, 2021, 53(10): 2724-2735 doi: 10.6052/0459-1879-21-360
Jiang Shouyan, Wan Chen, Sun Liguo, Du Chengbin. Crack-like defect inversion model based on SBFEM and deep learning. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(10): 2724-2735 doi: 10.6052/0459-1879-21-360
Citation: Jiang Shouyan, Wan Chen, Sun Liguo, Du Chengbin. Crack-like defect inversion model based on SBFEM and deep learning. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(10): 2724-2735 doi: 10.6052/0459-1879-21-360

基于SBFEM和深度学习的裂纹状缺陷反演模型

doi: 10.6052/0459-1879-21-360
基金项目: 国家重点研发计划(2018YFE0122400), 中央高校基本科研业务费专项资金(B210202097)和国家自然科学基金(51579084)资助项目
详细信息
    作者简介:

    江守燕, 副教授, 主要研究方向: 计算力学和虚拟仿真. E-mail: syjiang@hhu.edu.cn

  • 中图分类号: TB115

CRACK-LIKE DEFECT INVERSION MODEL BASED ON SBFEM AND DEEP LEARNING

  • 摘要: 结构内部缺陷的识别是结构健康监测的重要研究内容, 而当前以无损检测为主的结构安全检测多以定性分析为主, 定量识别缺陷的尺度较困难. 本文将比例边界有限元法(scaled boundary finite element methods, SBFEM)和深度学习相结合, 提出了基于Lamb波在结构中传播时的反馈信号定量识别结构内部裂纹状缺陷的反演模型. 通过随机生成缺陷信息(位置、大小), 采用SBFEM模拟Lamb波在含不同缺陷信息的结构中的信号传播过程, SBFEM仅需对结构边界离散可最小化网格重划分过程, 大大提高了计算效率. Lamb波在含裂纹状缺陷结构中传播时观测点的反馈信号包含大量的裂纹信息, 基于这一特性可为深度学习模型提供足够多的反映问题特性的训练数据. 建议的缺陷反演模型规避了传统反分析问题的目标函数极小化迭代过程, 在保证计算精度的前提下大大减少了计算成本. 对含单裂纹和多裂纹板的数值算例进行分析, 结果表明: 建立的缺陷识别模型能够准确地量化结构内部的缺陷, 对浅表裂纹亦有很好的识别效果, 且对于含噪信号模型仍具有较好的鲁棒性.

     

  • 图  1  比例边界有限元S域和S单元示意图

    Figure  1.  Schematic diagram of S-domain and S-element in SBFEM

    图  2  缺陷识别流程图

    Figure  2.  Flow chart of defect identification

    图  3  深度学习网络结构图

    Figure  3.  Deep learning network structure chart

    图  4  单缺陷板几何尺寸及SBFEM边界离散

    Figure  4.  Geometric dimension of single cracked plate and boundary discretization of SBFEM

    图  5  实测的观测点动位移响应

    Figure  5.  Measured dynamic displacement responses of observation point

    图  6  网络的精度和损失函数随训练过程变化曲线

    Figure  6.  Accuracy and loss function varies as epoch increases

    图  7  测试集反演结果图

    Figure  7.  Inversion results of test sets

    图  8  单裂纹1000次反演结果正态分布拟合图

    Figure  8.  Fitting diagram of normal distribution of 1000 inversion results of single crack

    图  9  不同深度裂纹的反演结果

    Figure  9.  Inversion results of cracks with different depths

    图  10  不同样本数量的缺陷反演结果

    Figure  10.  Inversion results with different training samples

    图  11  多裂纹板示意图

    Figure  11.  Schematic diagram of multi crack plate

    12  多裂纹测试集反演结果图

    12.  Inversion results of multi crack on test sets

    图  12  多裂纹测试集反演结果图(续)

    Figure  12.  Inversion results of multi crack on test sets (continued)

    表  1  搭建的卷积神经网络模型参数

    Table  1.   Parameters of convolution neural network model

    ParameterValue
    input layer size 2000 × 3000 × 1
    convolution layer number 3
    convolution kernel size 5 × 1
    number of pooling layers 3
    pooled core size 3 × 1
    number of fully connected layers 2
    optimizer RMSprop
    optimizer learning rate 0.0001
    number of batches 18
    maximum number of iterations 24
    下载: 导出CSV

    表  2  单开口裂纹的反演结果和误差

    Table  2.   Inversion results and errors of single crack

    Identified parametersTrue resultsIdentified resultsError /%
    ${x}_{\mathrm{c} }/\mathrm{m}\mathrm{m}$9090.0210.023
    $\alpha/ (^ \circ )$2.52.4950.200
    $d/\mathrm{m}\mathrm{m}$10.9613.900
    下载: 导出CSV

    表  3  多裂纹的反演结果和误差

    Table  3.   Inversion results and errors of multi cracks

    Identified parametersTrue resultsIdentified resultsError /%
    crack 1${x}_{\mathrm{c}1}/\mathrm{m}\mathrm{m}$61.20061.2770.126
    ${\alpha }_{1}/(^ \circ )$2.5002.5010.040
    ${d}_{1}/\mathrm{m}\mathrm{m}$1.0000.9950.500
    crack 2${x}_{\mathrm{c}2}/\mathrm{m}\mathrm{m}$133.200133.1370.047
    ${\alpha }_{2}/(^ \circ )$2.0002.0633.150
    ${d}_{2}/\mathrm{m}\mathrm{m}$0.8000.7882.500
    下载: 导出CSV

    表  4  不同样本数量时多裂纹反演结果

    Table  4.   Inversion results and errors of multi cracks with different training samples

    Identified parametersTrue resultsNumber of training samples
    1000Error /%1250Error /%1500Error /%2000Error /%
    crack 1 ${x}_{\mathrm{c}1}/\mathrm{m}\mathrm{m}$ 61.200 59.899 2.126 61.479 0.456 61.287 0.142 61.277 0.126
    ${\alpha }_{1}/(^ \circ )$ 2.500 2.529 1.160 2.504 0.160 2.504 0.160 2.501 0.040
    ${d}_{1}/\mathrm{m}\mathrm{m}$ 1.000 0.917 8.300 0.920 8.000 0.984 1.600 0.995 0.500
    crack 2 ${x}_{\mathrm{c}2}/\mathrm{m}\mathrm{m}$ 133.200 132.243 0.718 131.777 1.068 133.358 0.119 133.137 0.047
    ${\alpha }_{2}/(^ \circ )$ 2.000 2.533 26.650 2.518 25.900 2.055 2.750 2.063 3.150
    ${d}_{2}/\mathrm{m}\mathrm{m}$ 0.800 0.733 8.375 0.724 9.500 0.824 3.000 0.780 2.500
    下载: 导出CSV

    表  5  引入5%噪声的反演结果

    Table  5.   Inversion results with 5% noise

    Identified parametersTrue resultsIdentified resultsError/%
    crack 1 ${x}_{\mathrm{c}1}/\mathrm{m}\mathrm{m}$ 61.200 61.813 1.002
    ${\alpha }_{1}/(^ \circ )$ 2.500 2.453 1.880
    ${d}_{1}/\mathrm{m}\mathrm{m}$ 1.000 0.972 2.800
    crack 2 ${x}_{\mathrm{c}2}/\mathrm{m}\mathrm{m}$ 133.200 132.881 0.239
    ${\alpha }_{2}/(^ \circ )$ 2.000 2.160 8.000
    ${d}_{2}/\mathrm{m}\mathrm{m}$ 0.800 0.780 2.500
    下载: 导出CSV

    表  6  引入10%噪声的反演结果

    Table  6.   Inversion results with 10% noise

    Identified parametersTrue resultsIdentified resultsError/%
    crack 1 ${x}_{\mathrm{c}1}/\mathrm{m}\mathrm{m}$ 61.200 61.992 1.294
    ${\alpha }_{1}/(^ \circ )$ 2.500 2.597 3.880
    ${d}_{1}/\mathrm{m}\mathrm{m}$ 1.000 0.925 7.500
    crack 2 ${x}_{\mathrm{c}2}/\mathrm{m}\mathrm{m}$ 133.200 132.424 0.583
    ${\alpha }_{2}/(^ \circ )$ 2.000 2.407 20.350
    ${d}_{2}/\mathrm{m}\mathrm{m}$ 0.800 0.718 10.250
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-07-27
  • 录用日期:  2021-09-26
  • 网络出版日期:  2021-09-27
  • 刊出日期:  2021-10-26

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