基于POD-RBF方法的管道内壁几何识别

余波; 陶盈盈

doi:10.21656/1000-0887.430168

基于POD-RBF方法的管道内壁几何识别

doi: 10.21656/1000-0887.430168

余波^{1, 2, ,},
陶盈盈¹

1.
合肥工业大学土木与水利工程学院工程力学系，合肥 230009
2.
大连理工大学工业装备结构分析国家重点实验室，辽宁大连 116024

基金项目:

国家自然科学基金(面上项目) 11872166

详细信息

通讯作者:
余波(1983—)，男，教授，博士生导师(通讯作者. E-mail: yubochina@hfut.edu.cn)

中图分类号: O302
计量
- 文章访问数: 427
- HTML全文浏览量: 191
- PDF下载量: 59
- 被引次数: 0
出版历程
- 收稿日期: 2022-05-18
- 修回日期: 2022-10-04
- 刊出日期: 2023-04-01

Identification of Pipeline Inner Wall Geometry Based on the POD-RBF Method

YU Bo^{1, 2
, ,},
TAO Yingying¹

1.
Department of Engineering Mechanics, School of Civil Engineering, Hefei University of Technology, Hefei 230009, P.R.China
2.
State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, Liaoning 116024, P.R.China

摘要

摘要: 针对天然气、石油等管道内部被腐蚀问题，基于本征正交分解-径向基函数(POD-RBF)提出了一种管道内壁几何识别方法. 考虑静磁场并建立管道的简化有限元模型，构建变几何样本库，实现了POD-RBF对任意形状的响应预测. 该方法在降阶分析的同时避免了迭代过程中因几何的改变需反复求解刚度矩阵，在很大程度上提高了计算效率. 采用灰狼优化(GWO)算法对目标函数实施优化，避免了在变几何过程中灵敏度的求解. 算例结果显示，该文方法可高效准确地反演管道内壁的几何形状，即使在引入噪声后GWO算法仍具有较好的稳定性.
- 管道内壁几何形状识别 /
- 降阶代理模型 /
- 本征正交分解 /
- 径向基函数 /
- 灰狼优化算法
Abstract: Based on the proper orthogonal decomposition-radial basis function (POD-RBF), a geometric identification method for pipeline inner wall was proposed to solve the internal corrosion detection problem of natural gas and oil pipelines. In view of the static magnetic field, the simplified finite element model for the pipelines was established, and the variable-geometry sample library was constructed, to realize the response prediction of arbitrary geometry by the POD-RBF. The proposed method achieves reduced-order analysis and avoids repeated solution of the stiffness matrix due to the geometrical change during the identification process. Hence, it can significantly improve the computation efficiency. Finally, the grey wolf optimization (GWO) algorithm was used to optimize the objective function and avoid the calculation of the sensitivity in the process of geometry change. The numerical examples show that, the proposed method has high efficiency and accuracy in the geometric identification of the pipeline inner wall, with good stability even under introduced noises.
- identification of pipeline inner wall geometry /
- reduced-order surrogate model /
- proper orthogonal decomposition /
- radial basis function /
- grey wolf optimization algorithm

HTML全文

图 1 求解域示意图

Figure 1. The diagram of the solution domain

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图 2 灰狼的等级制度

Figure 2. The hierarchy of gray wolves

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图 3 圆型管道内壁

Figure 3. The inner wall of the circular pipeline

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图 4 有限元网格

Figure 4. The FEM mesh

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图 5 磁场强度大小

Figure 5. The magnetic field intensity

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图 6 参考点磁势的误差

注为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.

Figure 6. The magnetic potential errors at the reference points

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图 7 不同样本数量对应的目标函数值

Figure 7. Objective function values with different sample sizes

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图 8 不同样本数量对应的几何参数

Figure 8. Geometric parameters with different sample sizes

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图 9 椭圆型管道内壁

Figure 9. The inner wall of the elliptical pipeline

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图 10 不同基函数的识别过程

Figure 10. The identification processes with different basis functions

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图 11 不规则几何形状的管道内壁

Figure 11. The inner wall of the pipeline with irregular geometry

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图 12 δ=0时的识别结果

Figure 12. The identified results with δ=0

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图 13 δ=1%时的识别结果

Figure 13. The identified results with δ=1%

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图 14 δ=2%时的识别结果

Figure 14. The identified results with δ=2%

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图 15 δ=3%时的识别结果

Figure 15. The identified results with δ=3%

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图 16 采用不同管道内壁几何计算的磁势云图

Figure 16. The calculated magnetic potential contours with different pipeline inner wall geometries

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表 1 识别结果

Table 1. The identified results

sample feature	N=10	N=20	N=40
α_p/m	0.532 89	0.532 98	0.533 01
absolute error Δα_p/m	1.1×10^－4	2.0×10^－5	1.0×10^－5
relative error δ/%	0.020 6	0.003 8	0.001 9

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表 2 不同方案下的识别结果

Table 2. Identification results with different schemes

scheme	real radius R_r/m	identified radius R_i/m	relative error δ/%
1	0.45	0.499 02	10.892 1
2	0.46	0.499 14	8.508 5
3	0.47	0.499 48	6.271 8
4	0.48	0.499 90	4.145 9
5	0.49	0.500 57	2.156 1
6	0.50	0.501 22	0.244 6
7	0.51	0.514 09	0.800 9
8	0.53	0.529 95	0.009 9
9	0.55	0.549 94	0.011 0
10	0.57	0.569 93	0.013 0
11	0.59	0.590 20	0.034 6
12	0.60	0.599 99	0.001 6
13	0.61	0.605 79	0.689 8
14	0.62	0.609 70	1.660 9
15	0.63	0.612 84	2.723 5
16	0.64	0.615 56	3.818 5
17	0.65	0.617 77	4.957 9
18	0.66	0.619 81	6.089 3
19	0.67	0.621 66	7.214 4
20	0.68	0.623 50	8.309 2
21	0.69	0.625 25	9.384 0

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表 3 识别结果

Table 3. The identified results

error level δ/%	the corresponding parameterα_p/m
0	[0.525 41, 0.576 20, 0.524 89, 0.544 12, 0.514 53, 0.529 19, 0.529 58, 0.565 94, 0.486 45, 0.548 11, 0.530 33, 0.578 42]^T
1	[0.546 53, 0.562 76, 0.541 14, 0.556 05, 0.541 27, 0.572 85, 0.537 73, 0.565 71, 0.520 06, 0.556 62, 0.545 09, 0.564 27]^T
2	[0.534 33, 0.564 35, 0.542 28, 0.538 52, 0.550 63, 0.535 66, 0.548 13, 0.564 59, 0.509 82, 0.551 63, 0.532 63, 0.576 50]^T
3	[0.530 88, 0.504 95, 0.513 75, 0.539 59, 0.534 85, 0.536 71, 0.550 55, 0.534 37, 0.550 73, 0.573 37, 0.563 28, 0.564 12]^T

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