CRACK-LIKE DEFECT INVERSION MODEL BASED ON SBFEM AND DEEP LEARNING
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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.Abstract: The identification of structural internal defects is an important research content of structural health monitoring. At present, the structural safety inspection based on non-destructive testing mainly focuses on qualitative analysis, so it is difficult to identify the scale of defects quantitatively. In this paper, an inversion model is proposed by combing the scaled boundary finite element methods (SBFEM) and deep learning. The identification of crack-like defects can be performed in structures based on the feedback signal of Lamb wave propagation. By randomly generating defect information, i.e. position and size, the SBFEM can be used to simulate the signal propagation process of Lamb wave in structures with defects. The SBFEM only needs to discretize the structure boundary, which can minimize the re-meshing process and greatly improve the computational efficiency. When Lamb wave propagates in a cracked structure, the feedback signal of the observation point can reflect crack information. Based on this characteristic, enough training data reflecting the characteristics of the problem can be provided for the deep learning model. The proposed defect inversion model avoids the iterative process of minimizing the objective function of the traditional inverse problems, and greatly reduces the computational cost on the premise of ensuring accuracy. Numerical examples of plates with single and multiple cracks are analyzed. The results show that the defect identification model can accurately quantify the defects in the structure. It also has a good identification effect for shallow cracks. The model also shows robustness to the noisy signal model.
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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 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 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
Parameter Value 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 
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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 parameters True results Identified results Error /% ${x}_{\mathrm{c} }/\mathrm{m}\mathrm{m}$ 90 90.021 0.023 $\alpha/ (^ \circ )$ 2.5 2.495 0.200 $d/\mathrm{m}\mathrm{m}$ 1 0.961 3.900
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表 3 多裂纹的反演结果和误差
Table 3. Inversion results and errors of multi cracks
Identified parameters True results Identified results Error /% crack 1 ${x}_{\mathrm{c}1}/\mathrm{m}\mathrm{m}$ 61.200 61.277 0.126 ${\alpha }_{1}/(^ \circ )$ 2.500 2.501 0.040 ${d}_{1}/\mathrm{m}\mathrm{m}$ 1.000 0.995 0.500 crack 2 ${x}_{\mathrm{c}2}/\mathrm{m}\mathrm{m}$ 133.200 133.137 0.047 ${\alpha }_{2}/(^ \circ )$ 2.000 2.063 3.150 ${d}_{2}/\mathrm{m}\mathrm{m}$ 0.800 0.788 2.500
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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 parameters True results Number of training samples 1000 Error /% 1250 Error /% 1500 Error /% 2000 Error /% 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
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表 5 引入5%噪声的反演结果
Table 5. Inversion results with 5% noise
Identified parameters True results Identified results Error/% 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
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表 6 引入10%噪声的反演结果
Table 6. Inversion results with 10% noise
Identified parameters True results Identified results Error/% 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
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