基于XFEM和GA-BP神经网络的裂纹智能识别研究

毛晓敏; 张慧华; 纪晓磊; 韩尚宇

doi:10.21656/1000-0887.420250

基于XFEM和GA-BP神经网络的裂纹智能识别研究

doi: 10.21656/1000-0887.420250

南昌航空大学土木建筑学院，南昌 330063

基金项目: 国家自然科学基金（12062015；52068054）；江西省自然科学基金（20192BAB202001;20212BAB211016）

详细信息

作者简介:
毛晓敏（1996—），女，硕士生（E-mail：3194197173@qq.com）

张慧华（1982—），男，教授，博士（通讯作者. E-mail：hhzhang@nchu.edu.cn）

中图分类号: O241.82; TP183
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- 被引次数: 0
出版历程
- 收稿日期: 2021-08-25
- 录用日期: 2022-02-01
- 修回日期: 2021-12-20
- 网络出版日期: 2022-10-15
- 刊出日期: 2022-11-30

Intelligent Crack Recognition Based on XFEM and GA-BP Neural Networks

School of Civil Engineering and Architecture, Nanchang Hangkong University, Nanchang 330063, P.R.China

摘要

摘要:
基于扩展有限元法(XFEM)和经遗传算法(GA)优化的误差反向传播多层前馈(BP)神经网络(GA-BP)算法，建立了识别结构中裂纹的反演分析模型。模型通过XFEM正向分析获得的测点位移数据训练GA-BP神经网络，并在此基础上利用该网络进行裂纹反向识别。通过两个典型算例对模型的可行性和精度进行了验证，并探讨了网格密度、测点布置、输入数据噪声等对网络识别精度的影响。结果表明，该文的方法可反演线弹性断裂力学重点关注的直线裂纹的几何信息且具有较好的容噪性能，此外，GA-BP神经网络的预测精度较传统BP神经网络普遍更高。
- 扩展有限元法 /
- 遗传算法 /
- BP神经网络 /
- 反演分析 /
- 裂纹
Abstract:
Based on the extended finite element method (XFEM) and the error back propagation (BP) multilayer feedforward neural network algorithm optimized by the genetic algorithm (GA), an inverse analysis model for identifying cracks in structures was established. The GA-BP neural network was trained by the displacement data of measuring points obtained by the XFEM forward analysis, and the network was used for crack inverse identification. The feasibility and accuracy of the model were verified with 2 typical examples, and the effects of the mesh density, the measuring point layout and the input data noise on the accuracy of network recognition were discussed. The results show that, the proposed method can invert the geometric information of straight cracks, which is the major focus of linear elastic fracture mechanics, and has good noise tolerance. Besides, the GA-BP neural network has higher accuracy than the traditional BP neural network in general.
- extended finite element method /
- genetic algorithm /
- BP neural network /
- inverse analysis /
- crack

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图 1 含裂纹结构及测点示意图

Figure 1. Schematic diagram of the structure with cracks and the measuring points

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图 2 GA优化BP神经网络的流程图

Figure 2. The flow chart of the BP neural network optimized by GA

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图 3 BP神经网络的结构模型

Figure 3. The structure of the BP neural network

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图 4 XFEM与GA-BP神经网络算法开展裂纹识别的流程图

Figure 4. The flow chart of crack identification based on the XFEM and the GA-BP neural network algorithm

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图 5 单向拉伸作用下含单边裂纹的矩形板

Figure 5. A rectangular plate with an edge crack under uniaxial tension

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图 6 XFEM网格：(a) 120个单元； (b) 435个单元； (c) 780个单元； (d) 1 540个单元

Figure 6. XFEM meshes: (a) 120 elements; (b) 435 elements; (c) 780 elements; (d) 1 540 elements

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图 7 测点布置方案：(a) 方案1，14个测点； (b) 方案2，12个测点； (c) 方案3，10个测点； (d) 方案4，8个测点；(e) 方案5，6个测点； (f) 方案6，4个测点

Figure 7. Layouts of measuring points: (a) scheme 1, 14 points; (b) scheme 2, 12 points; (c) scheme 3, 10 points; (d) scheme 4, 8 points; (e) scheme 5, 6 points; (f) scheme 6, 4 points

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图 8 不同噪声下X_A预测的相对误差绝对值

Figure 8. Absolute values of relative errors of predicted X_A under various noises

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图 9 单向拉伸荷载作用下含双斜裂纹的方板

Figure 9. A square plate with two inclined cracks under uniaxial tension

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图 10 XFEM网格和测点布置 (a=0.5 m)

Figure 10. The XFEM mesh and measuring points (a=0.5 m)

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图 11 不同噪声下，X_A，X_B，X_C和X_D预测值的相对误差绝对值

Figure 11. Absolute values of relative errors of predicted X_A, X_B, X_C and X_D under different noises

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图 12 不同噪声下，Y_A，Y_B，Y_C和Y_D预测值的相对误差绝对值

Figure 12. Absolute values of relative errors of predicted Y_A, Y_B, Y_C and Y_D under different noises

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表 1 不同网格下的$ {K_{\rm I}} $(单位：MPa·m^1/2)

Table 1. $ {K_{\rm I}} $ for different meshes (unit: MPa·m^1/2)

XFEM solution				reference solution
120 elements	435 elements	780 elements	1540 elements	reference solution
2.5743 （6.86%）	2.6801 （3.03%）	2.7209 （1.55%）	2.7224 （1.50%）	2.7639

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表 2 测点坐标

Table 2. Coordinates of measuring points

number	X	Y	number	X	Y
1	0.0000	0.7692	8	1.3000	6.0000
2	0.0000	1.5385	9	2.0000	5.2308
3	0.0000	2.3077	10	2.0000	4.4615
4	0.0000	3.6923	11	2.0000	3.6923
5	0.0000	4.4615	12	2.0000	2.3077
6	0.0000	5.2308	13	2.0000	1.5385
7	0.7000	6.0000	14	2.0000	0.7692

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表 3 GA-BP神经网络对X_A的训练输出结果

Table 3. Training results of the GA-BP neural network for X_A

crack length a/m	true X_A	training X_A	relative error e_k/%
0.5	0.5000	0.5057	1.14
0.6	0.6000	0.6004	0.07
0.7	0.7000	0.6991	−0.13
0.8	0.8000	0.7996	−0.05
0.9	0.9000	0.9003	0.03
1.0	1.0000	1.0004	0.04
1.1	1.1000	1.0999	−0.01
1.2	1.2000	1.1994	−0.05
1.3	1.3000	1.2999	−0.01
1.4	1.4000	1.4010	0.07

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表 4 BP与GA-BP神经网络预测的X_A值

Table 4. Prediction of X_A by BP and GA-BP neural networks

layout scheme of measuring points	number of measuring points	number of hidden layer neurons	true X_A	BP prediction X_A	relative error e_k/%	GA-BP prediction X_A	relative error e_k/%
1	14	4	1.5000	1.4756	1.63	1.4958	0.28
2	12	4		1.4968	0.21	1.4862	0.92
3	10	8		1.5977	6.51	1.4979	0.14
4	8	4		1.4911	0.59	1.4837	1.08
5	6	3		1.5210	1.40	1.4979	0.14
6	4	3		1.5518	3.45	1.4676	2.16

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表 6 GA-BP神经网络对裂尖B坐标的训练值

Table 6. Training coordinates of crack tip B by the GA-BP neural network

crack length a/m	true X_B	training X_B	true Y_B	training Y_B
0.500	0.8768	0.8769	1.6768	1.6806
0.528	0.8868	0.8873	1.6868	1.6913
0.556	0.8968	0.8953	1.6968	1.6974
0.585	0.9068	0.9084	1.7068	1.7109
0.613	0.9168	0.9170	1.7168	1.7218
0.641	0.9268	0.9257	1.7268	1.7299
0.670	0.9368	0.9380	1.7368	1.7406
0.698	0.9468	0.9462	1.7468	1.7449

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表 7 GA-BP神经网络对裂尖C坐标的训练值

Table 7. Training coordinates of crack tip C by the GA-BP neural network

crack length a/m	true X_C	training X_C	true Y_C	training Y_C
0.500	1.1232	1.1236	0.6768	0.6744
0.528	1.1132	1.1128	0.6868	0.6841
0.556	1.1032	1.1046	0.6968	0.6941
0.585	1.0932	1.0910	0.7068	0.7027
0.613	1.0832	1.0826	0.7168	0.7121
0.641	1.0732	1.0739	0.7268	0.7225
0.670	1.0632	1.0620	0.7368	0.7329
0.698	1.0532	1.0543	0.7468	0.7438

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表 5 GA-BP神经网络对裂尖A坐标的训练值

Table 5. Training coordinates of crack tip A by the GA-BP neural network

crack length a/m	true X_A	training X_A	true Y_A	training Y_A
0.500	0.5232	0.5238	1.3232	1.3194
0.528	0.5132	0.5127	1.3132	1.3088
0.556	0.5032	0.5044	1.3032	1.3031
0.585	0.4932	0.4906	1.2932	1.2893
0.613	0.4832	0.4823	1.2832	1.2783
0.641	0.4732	0.4738	1.2732	1.2703
0.670	0.4632	0.4622	1.2632	1.2594
0.698	0.4532	0.4549	1.2532	1.2556

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表 8 GA-BP神经网络对裂尖D坐标的训练值

Table 8. Training coordinates of crack tip D by the GA-BP neural network

crack length a/m	true X_D	training X_D	true Y_D	training Y_D
0.500	1.4768	1.4748	0.3232	0.3258
0.528	1.4868	1.4872	0.3132	0.3160
0.556	1.4968	1.4962	0.3032	0.3049
0.585	1.5068	1.5113	0.2932	0.2971
0.613	1.5168	1.5192	0.2832	0.2879
0.641	1.5268	1.5272	0.2732	0.2772
0.670	1.5368	1.5377	0.2632	0.2671
0.698	1.5468	1.5433	0.2532	0.2553

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表 9 BP与GA-BP神经网络对裂尖A、B的预测值

Table 9. Prediction of crack tips A and B by BP and GA-BP neural networks

crack length a/m		X_A	relative error e_k/%	Y_A	relative error e_k/%	X_B	relative error e_k/%	Y_B	relative error e_k/%
0.726	true value	0.4432	−	1.2432	−	0.9568	−	1.7568	−
	BP	0.4465	0.74	1.2491	0.47	0.9558	0.11	1.7515	0.30
	GA-BP	0.4435	0.07	1.2433	0.01	0.9564	0.04	1.7566	0.01
0.755	true value	0.4332	−	1.2332	−	0.9668	−	1.7668	−
	BP	0.4411	1.82	1.2534	1.64	0.9637	0.32	1.7482	1.05
	GA-BP	0.4345	0.29	1.2336	0.03	0.9658	0.10	1.7663	0.03
0.783	true value	0.4232	−	1.2232	−	0.9768	−	1.7768	−
	BP	0.4350	2.79	1.2529	2.43	0.9729	0.40	1.7492	1.55
	GA-BP	0.4264	0.77	1.2248	0.13	0.9739	0.30	1.7750	0.10

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表 10 BP与GA-BP神经网络对裂尖C、D的预测值

Table 10. Prediction of crack tips C and D by BP and GA-BP neural networks

crack length a/m		X_C	relative error e_k/%	Y_C	relative error e_k/%	X_D	relative error e_k/%	Y_D	relative error e_k/%
0.726	true value	1.0432	−	0.7568	−	1.5568	−	0.2432	−
	BP	1.0454	0.22	0.7541	0.36	1.5492	0.49	0.2446	0.56
	GA-BP	1.0436	0.04	0.7567	0.02	1.5563	0.03	0.2433	0.05
0.755	true value	1.0332	−	0.7668	−	1.5668	−	0.2332	−
	BP	1.0390	0.56	0.7656	0.16	1.5495	1.11	0.2306	1.10
	GA-BP	1.0342	0.10	0.7664	0.05	1.5658	0.06	0.2336	0.17
0.783	true value	1.0232	−	0.7768	−	1.5768	−	0.2232	−
	BP	1.0318	0.84	0.7753	0.19	1.5492	1.75	0.2196	1.59
	GA-BP	1.0262	0.29	0.7752	0.21	1.5739	0.19	0.2248	0.72

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