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.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.
-
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 
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 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
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 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
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 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
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 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
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 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
下载: 导出CSV
-
[1] 吴中如, 顾冲时. 重大水工混凝土结构病害检测与健康诊断. 北京: 高等教育出版社, 2005(Wu Zhongru, Gu Chongshi. Disease Detection and Health Diagnosis of Large Hydraulic Concrete Structures. Beijing: Higher Education Press, 2005) [2] Rabinovich D, Givoli D, Vigdergauz S. Crack identification by “arrival time” using XFEM and a genetic algorithm. International Journal for Numerical Methods in Engineering, 2009, 77: 337-359 doi: 10.1002/nme.2416 [3] Waisman H, Chatzi E, Smyth AW. Detection and quantification of flaws in structures by the extended finite element method and genetic algorithms. International Journal for Numerical Methods in Engineering, 2010, 82: 303-328 doi: 10.1002/nme.2766 [4] Chatzi EN, Hiriyur B, Waisman H, et al. Experimental application and enhancement of the XFEM-GA algorithm for the detection of flaws in structures. Computers & Structures, 2011, 89: 556-570 [5] Nanthakumar SS, Lahmer T, Rabczuk T. Detection of flaws in piezoelectric structures using extended FEM. International Journal for Numerical Methods in Engineering, 2013, 96: 373-389 doi: 10.1002/nme.4565 [6] 江守燕, 杜成斌. 基于扩展有限元的结构内部缺陷(夹杂) 的反演分析模型. 力学学报, 2015, 47(6): 1037-1045 (Jiang Shouyan, Du Chengbin. Numerical model for identification of internal defect or inclusion based on extended finite element methods. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(6): 1037-1045 (in Chinese) doi: 10.6052/0459-1879-15-134 [7] Sun H, Waisman H, Betti R. Nondestructive identification of multiple flaws in structures using XFEM and a topologically adapting enhanced ABC algorithm. International Journal for Numerical Methods in Engineering, 2013, 95: 871-900 doi: 10.1002/nme.4529 [8] Sun H, Waisman H, Betti R. A multiscale flaw detection algorithm based on XFEM. International Journal for Numerical Methods in Engineering, 2014, 100: 477-503 doi: 10.1002/nme.4741 [9] Yan G, Sun H, Waisman H. A guided Bayesian inference approach for detection of multiple flaws in structures using the extended finite element method. Computers & Structures, 2015, 152: 27-44 [10] 王佳萍, 杜成斌, 江守燕. 扩展有限元与遗传算法相结合的结构缺陷反演分析. 力学与实践, 2017, 39(6): 591-596 (Wang Jiaping, Du Chengbin, Jiang Shouyan. The inverse analysis of internal defects (inclusions) in structures using a combined XFEM and GA method. Mechanics in Engineering, 2017, 39(6): 591-596 (in Chinese) doi: 10.6052/1000-0879-17-176 [11] 王佳萍, 杜成斌, 王翔等. 基于XFEM和改进人工蜂群算法的结构内部缺陷反演. 工程力学, 2019, 36(9): 34-40 (Wang Jiaping, Du Chengbin, Wang Xiang, et al. Inverseanalysis of internal defects in structures using extendedfinite element method and improved artificial bee colonyalgorithm. Engineering Mechanics, 2019, 36(9): 34-40 (in Chinese) [12] Zhao W, Du C, Jiang S. An adaptive multiscale approach for identifying multiple flaws based on XFEM and a discrete artificial fish swarm algorithm. Computer Methods in Applied Mechanics and Engineering, 2018, 339: 341-357 doi: 10.1016/j.cma.2018.04.037 [13] Ma C, Yu T, Lich VL, et al. An effective computational approach based on XFEM and a novel three-step detection algorithm for multiple complex flaw clusters. Computers & Structures, 2017, 193: 207-225 [14] Zhang C, Nanthakumar SS, Lahmer T, et al. Multiple cracks identification for piezoelectric structures. International Journal of Fracture, 2017, 206: 151-169 doi: 10.1007/s10704-017-0206-2 [15] Zhang C, Wang C, Lahmer T, et al. A dynamic XFEM formulation for crack identification. International Journal of Mechanics and Materials in Design, 2016, 12: 427-448 doi: 10.1007/s10999-015-9312-3 [16] Sun H, Waisman H, Betti R. A sweeping window method for detection of flaws using an explicit dynamic XFEM and absorbing boundary layers. International Journal for Numerical Methods in Engineering, 2016, 105: 1014-1040 doi: 10.1002/nme.5006 [17] 江守燕, 赵林鑫, 杜成斌. 基于频率和模态保证准则的结构内部多缺陷反演. 力学学报, 2019, 51(4): 1091-1100 (Jiang Shouyan, Zhao Linxin, Du Chengbin. Identification of multiple flaws in structures based on frequency and modal assurance criteria. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(4): 1091-1100 (in Chinese) doi: 10.6052/0459-1879-19-078 [18] Du C, Zhao W, Jiang S, et al. Dynamic XFEM-based detection of multiple flaws using an improved artificial bee colony algorithm. Computer Methods in Applied Mechanics and Engineering, 2020, 365: 112995 doi: 10.1016/j.cma.2020.112995 [19] Ma C, Yu T, Lich LV, et al. Detection of multiple complicated flaw clusters by dynamic variable-node XFEM with a three-step detection algorithm. European Journal of Mechanics - A/Solids, 2020, 82: 103980 doi: 10.1016/j.euromechsol.2020.103980 [20] Yu T, Bui TQ. Numerical simulation of 2-D weak and strong discontinuities by a novel approach based on XFEM with local mesh refinement. Computers & Structures, 2018, 196: 112-133 [21] Li X, Liu Z, Cui S, et al. Predicting the effective mechanical property of heterogeneous materials by image based modeling and deep learning. Computer Methods in Applied Mechanics and Engineering, 2019, 347: 735-753 doi: 10.1016/j.cma.2019.01.005 [22] Li X, Ning S, Liu Z, et al. Designing phononic crystal with anticipated band gap through a deep learning based data-driven method. Computer Methods in Applied Mechanics and Engineering, 2020, 361: 112737 doi: 10.1016/j.cma.2019.112737 [23] 何存富, 孙雅欣, 吴斌等. 超声导波技术在埋地锚杆检测中的应用研究. 岩土工程学报, 2006, 28(9): 1144-1147 (He Cunfu, Sun Yaxin, Wu Bin, et al. Application of ultrasonic guided waves technology to inspection of bolt embedded in soils. Chinese Journal of Geotechnical Engineering, 2006, 28(9): 1144-1147 (in Chinese) doi: 10.3321/j.issn:1000-4548.2006.09.018 [24] 徐镇凯, 袁志军, 胡济群. 建筑结构检测与加固方法. 工程力学, 2006, 23(SII): 117-130 (Xu Zhenkai, Yuan Zhijun, Hu Jiqun. The inspection and strengthening methods on building structures. Engineering Mechanics, 2006, 23(SII): 117-130 (in Chinese) [25] 刘宏业, 刘申, 吕炎等. 纤维增强复合板中声弹Lamb波的波结构分析. 工程力学, 2020, 37(8): 221-229 (Liu Hongye, Liu Shen, Lv Yan. Wave structure analysis of acoustoelastic Lamb waves in fiber reinforced composite lamina. Engineering Mechanics, 2020, 37(8): 221-229 (in Chinese) doi: 10.6052/j.issn.1000-4750.2019.09.0565 [26] Gravenkamp H, Birk C, Song C. Simulation of elastic guided waves interacting with defects in arbitrarily long structures using the Scaled Boundary Finite Element Method. Journal of Computational Physics, 2015, 295: 438-455 doi: 10.1016/j.jcp.2015.04.032 [27] 张维峰, 冯华. 结构裂纹故障振动检测的小波分析. 力学与实践, 2010, 32(1): 20-23 (Zhang Weifeng, Feng Hua. The wavelet analysis of vibration detection for structure’s crack fault. Mechanics in Engineering, 2010, 32(1): 20-23 (in Chinese) [28] 吴斌, 齐文博, 何存富等. 基于神经网络的超声导波钢杆缺陷识别. 工程力学, 2013, 30(2): 470-476 (Wu Bin, Qi Wenbo, He Cunfu, et al. Recognition of defects o steel rod using ultrasomic guided waves based on neural network. Engineering Mechanics, 2013, 30(2): 470-476 (in Chinese) doi: 10.6052/j.issn.1000-4750.2011.08.0554 [29] Song C. The Scaled Boundary Finite Element Method: Introduction to Theory and Implementation. John Wiley & Sons. Ltd, 2018 [30] Song C, Wolf JP. The scaled boundary finite-element method—alias consistent infinitesimal finite-element cell method—for elastodynamics. Computer Methods in Applied Mechanics and Engineering, 1997, 147: 329-355 doi: 10.1016/S0045-7825(97)00021-2 [31] 陈灯红, 杜成斌. 基于SBFE和改进连分式的有限域动力分析. 力学学报, 2013, 45(2): 297-301 (Chen Denghong, Du Chengbin. Dynamic analysis of bounded domains by SBFE and the improved continuedfraction expansion. Chinese Journal of Theoretical andApplied Mechanics, 2013, 45(2): 297-301 (in Chinese) doi: 10.6052/0459-1879-12-198 [32] Bengio Y, Courville A, Vincent P. Representation learning: A review and new perspectives. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2013, 35(8): 1798-1828 doi: 10.1109/TPAMI.2013.50 [33] Goodfellow I, Bengio Y, Courville A. Deep Learning. Cambridge: MIT Press, 2016 [34] LeCun Y, Bengio Y, Hinton G. Deep Learning. Nature, 2015, 521(7553): 436-444 doi: 10.1038/nature14539 [35] 周飞燕, 金林鹏, 董军. 卷积神经网络研究综述. 计算机学报, 2017, 40(6): 1229-1251 (Zhou Feiyan, Jin Linpeng, Dong Jun. Review of convolutional neural network. Chinese Journal of Computers, 2017, 40(6): 1229-1251 (in Chinese) doi: 10.11897/SP.J.1016.2017.01229 -
下载:
点击查看大图
图(13) / 表(6)
计量
- 文章访问数: 639
- HTML全文浏览量: 185
- PDF下载量: 160
- 被引次数: 0
