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浙江大学学报(工学版)
浙江大学学报(工学版)  2022, Vol. 56 Issue (1): 202-212    DOI: 10.3785/j.issn.1008-973X.2022.01.023
航空航天技术     
基于支持向量回归的一维频率域航空电磁反演
姚禹1(),张志厚1,*(),石泽玉1,刘鹏飞1,赵思为2,张天一1,赵明浩1
1. 西南交通大学 地球科学与环境工程学院，四川 成都 611756
2. 中铁二院成都地勘岩土工程有限责任公司，四川 成都 610031
Airborne electromagnetic inversion in one-dimensional frequency-domain based on support vector regression
Yu YAO1(),Zhi-hou ZHANG1,*(),Ze-yu SHI1,Peng-fei LIU1,Si-wei ZHAO2,Tian-yi ZHANG1,Ming-hao ZHAO1
1. Faculty of Geosciences and Environmental Engineering, Southwest Jiaotong University, Chengdu 611756, China
2. China Railway Eryuan Geotechnical Engineering Limited Company, Chengdu 610031, China
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摘要：

为了提高一维频率域航空电磁的反演精度，将机器学习方法应用于航空电磁数据的反演中，提出基于多输出最小二乘支持向量回归（MLS-SVR）的一维频率域航空电磁端到端反演方法. 对不同地电模型进行正演计算，获得样本数据集；搭建MLS-SVR模型框架，输入端为归一化后的垂直磁场分量，输出端为地电模型参数；利用网格寻优和K-折交叉验证进行调参；利用MLS-SVR模型进行反演. 试验结果表明，利用MLS-SVR可以准确地反演出各地电模型参数，与单输出支持向量回归(S-SVR)和多输出支持向量回归（M-SVR）算法相比，该反演方法的精度更高，实测数据反演表明了该方法的有效性.
关键词： 航空电磁;  一维频率域反演;  多输出;  端到端;  最小二乘支持向量机    
Abstract:

The machine learning method was applied to the inversion of airborne electromagnetic data in order to improve the accuracy of airborne electromagnetic inversion in one-dimensional frequency-domain. An end-to-end inversion method of one-dimensional frequency-domain airborne electromagnetic data was proposed based on multiple-output least square support vector regression (MLS-SVR). Forward calculations of different geological models were conducted to obtain sample data set. The framework of MLS-SVR model was constructed. The input end was normalized vertical magnetic field component, and the output end was geological parameters. Then the grid-search method and the K-fold cross-validation method were applied to search for the best parameters of the MLS-SVR model. The parameters of geological model were predicted via MLS-SVR. The experimental results show that the geological parameters can be accurately predicted with MLS-SVR. MLS-SVR has the advantage of high-precision compared with single support vector regression (S-SVR) and multiple-output support vector regression (M-SVR). The inversion of the measured data shows the effectiveness of the method.
Key words: airborne electromagnetic    one-dimensional frequency-domain inversion    multiple output    end-to-end    least square support vector machine
收稿日期: 2021-02-03 出版日期: 2022-01-05
CLC:  P 631  
基金资助: 四川省科技厅计划资助项目(2019YFG0460，2020YFG303，2021YJ0031)；国家重点研发计划资助项目(2018YFC1505401)；中国中铁股份有限公司科技研究开发计划资助项目(CZ01-重点-05)
通讯作者: 张志厚     E-mail: 1298170964@qq.com;logicprimer@163.com
作者简介: 姚禹（1997—），男，硕士生，从事基于机器学习的航空电磁数据处理研究. orcid.org/0000-0002-7732-7111. E-mail： 1298170964@qq.com
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姚禹
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引用本文:

姚禹,张志厚,石泽玉,刘鹏飞,赵思为,张天一,赵明浩. 基于支持向量回归的一维频率域航空电磁反演[J]. 浙江大学学报(工学版), 2022, 56(1): 202-212.

Yu YAO,Zhi-hou ZHANG,Ze-yu SHI,Peng-fei LIU,Si-wei ZHAO,Tian-yi ZHANG,Ming-hao ZHAO. Airborne electromagnetic inversion in one-dimensional frequency-domain based on support vector regression. Journal of ZheJiang University (Engineering Science), 2022, 56(1): 202-212.

链接本文:

https://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2022.01.023    或    https://www.zjujournals.com/eng/CN/Y2022/V56/I1/202

图 1  固定翼频率域航空电磁数据采集示意图
图 2  通过高斯径向基函数将数据集映射至高维空间
算法 RMSE
$ \mathop \rho \nolimits_1 $ $ \mathop \rho \nolimits_2 $ $ \mathop h\nolimits_1 $
S-SVR 1.36 6.02 4.91
M-SVR 2.12 4.15 3.40
MLS-SVR 1.87 3.81 2.98
表 1  最优参数对应的地电参数RMSE
样本
序号 		理论值 S-SVR M-SVR MLS-SVR
$ \mathop \rho \nolimits_1 $/ $(\Omega \cdot {\text{m)}}$ $ \mathop \rho \nolimits_2 $/ $(\Omega \cdot {\text{m)}}$ $ \mathop h\nolimits_1 $/m $ \mathop \rho \nolimits_1 $/ $(\Omega \cdot {\text{m)}}$ $ \mathop \rho \nolimits_2 $/ $(\Omega \cdot {\text{m)}}$ $ \mathop h\nolimits_1 $/m $ \mathop \rho \nolimits_1 $/ $(\Omega \cdot {\text{m)}}$ $ \mathop \rho \nolimits_2 $/ $(\Omega \cdot {\text{m)}}$ $ \mathop h\nolimits_1 $/m $ \mathop \rho \nolimits_1 $/ $(\Omega \cdot {\text{m)}}$ $ \mathop \rho \nolimits_2 $/ $(\Omega \cdot {\text{m)}}$ $ \mathop h\nolimits_1 $/m
1 450 800 120 443.59 733.92 127.25 435.77 763.59 114.64 437.50 766.28 116.56
2 700 300 90 712.68 323.52 84.25 721.26 313.92 86.42 719.74 311.50 84.96
3 300 850 135 307.43 780.45 126.34 315.78 806.77 130.26 312.91 815.14 129.35
4 800 450 75 814.91 410.32 70.02 773.95 429.66 73.33 778.90 433.25 72.59
5 550 750 45 540.66 697.64 40.30 532.74 725.71 43.66 535.42 727.57 44.01
表 2  2层模型5组数据不同方法的反演结果对比
反演
方法 		相对误差/% 平均值
1 2 3 4 5
S-SVR 5.33 5.35 5.69 5.77 6.37 5.70
M-SVR 4.06 3.89 4.65 3.33 3.12 3.81
MLS-SVR 3.29 4.08 4.19 3.19 2.61 3.47
表 3  2层模型5组数据不同方法的反演相对误差对比
图 3  2层理论模型不同方法的反演结果对比
算法 RMSE
$ {\rho _{\text{1}}} $ $ \rho {}_{\text{2}} $ $ {\rho _{\text{3}}} $ $ \mathop h\nolimits_1 $ $ \mathop h\nolimits_2 $
S-SVR 1.89 7.85 8.95 5.75 8.39
M-SVR 2.54 5.70 7.40 4.52 6.14
MLS-SVR 2.13 5.41 7.11 3.85 5.89
表 4  各参数RMSE
样本序号 理论值 MLS-SVR反演值
$\;{\rho _{\text{1} } }$/ $(\Omega \cdot {\text{m)}}$ $\;{\rho _{\text{2} } }$/ $(\Omega \cdot {\text{m)}}$ $\;{\rho _{\text{3} } }$/ $(\Omega \cdot {\text{m)}}$ $ \mathop h\nolimits_1 $/m $ \mathop h\nolimits_2 $/m $\;{\rho _{\text{1} } }$/ $(\Omega \cdot {\text{m)}}$ $\;{\rho _{\text{2} } }$/ $(\Omega \cdot {\text{m)}}$ $\; {\rho _{\text{3} } }$/ $(\Omega \cdot {\text{m)}}$ $ \mathop h\nolimits_1 $/m $ {h_2} $/m
1 150 600 400 45 75 155.67 624.09 375.66 43.07 69.33
2 200 400 600 75 30 193.96 374.77 560.14 71.66 27.96
3 800 450 600 90 30 830.16 428.69 568.43 95.55 32.43
4 700 400 200 45 45 667.45 426.08 214.88 42.86 48.01
5 800 350 700 60 75 834.56 369.25 749.94 63.22 69.91
表 5  3层模型的MLS-SVR反演结果
反演方法 相对误差/% 平均值
1 2 3 4 5
S-SVR 6.49 7.54 7.66 8.01 7.09 7.36
M-SVR 5.88 6.01 5.19 6.44 5.91 6.14
MLS-SVR 5.14 5.44 5.61 6.14 5.82 5.63
表 6  3层模型5组数据各反演方法的相对误差
图 4  3层理论模型不同方法的反演结果对比
图 5  2种5层理论模型MLS-SVR反演结果
序号 相对误差/%
无噪声 3%噪声 5%噪声
1 3.84 4.60 4.90
2 4.01 5.29 5.71
3 3.33 4.78 5.49
4 2.86 4.15 4.93
5 4.44 5.17 5.77
6 5.51 7.03 8.77
7 5.85 6.96 9.01
8 6.04 7.19 8.61
9 6.41 6.99 8.83
10 6.23 7.25 9.21
平均值 4.85 5.94 7.12
表 7  无噪声数据与含3%、5%高斯随机噪声数据反演相对误差对比
图 6  实测数据Occam反演方法
图 7  实测数据Occam反演方法、SVD反演方法结果与MLS-SVR反演方法结果对比图
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