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Online sequential extreme learning machine for transient electromagnetic nonlinear inversion |
LI Rui-You( ), ZHANG Huai-Qing( ), WU Zhao |
State Key Laboratory of Power Transmission Equipment & System Security and New Technology, Chongqing University, Chongqing 400044, China |
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Abstract The traditional transient electromagnetic inversion method using artificial neural network based on gradient descent method is inefficient and can not guarantee global convergence. In order to solve these problems, this paper proposes a transient electromagnetic inversion method based on on online sequential extreme learning machine (OSELM). This approaches is used for inversion of high-dimensional exploration data obtained by transient electromagnetic method. Firstly, the hidden layer parameters (input weight and deviation) are randomly set to simplify the learning process of the model. Then, the prediction samples obtained from the test are added to the training samples as the next update information, and the online sequential extreme learning machine prediction model is established to maximize the inverse accuracy. Finally, the inversion results of two classical TEM layered geoelectric models and a quasi two-dimensional geoelectric model show that the proposed method can solve the problem of nonlinear modeling and high-dimensional data for TEM inversion, and a comparison with extreme learning machine (ELM) shows that this method has more accurate inversion, better generalization ability and higher calculation efficiency, which provides a new idea for the application of neural network in geophysical inversion.
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Received: 23 November 2020
Published: 20 August 2021
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Corresponding Authors:
ZHANG Huai-Qing
E-mail: 1378546842@qq.com;zhanghuaiqing@cqu.edu.cn
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Schematic diagram of the layered geoelectric model and TEM method
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五层模型 | ρ/(Ω·m) h/m | | ρ1 | ρ2 | ρ3 | ρ4 | ρ5 | h1 | h2 | h3 | h4 | pmin | 10 | 5 | 1 | 20 | 100 | 10 | 10 | 5 | 10 | | pmax | 1 000 | 500 | 100 | 2000 | 10 000 | 1 000 | 1000 | 500 | 10 000 | | 九层模型 | ρ/(Ω·m) h/m | | ρ1 | ρ2 | ρ3 | ρ4 | ρ5 | ρ6 | ρ7 | ρ8 | ρ9 | h1 | h2 | h3 | h4 | h5 | h6 | h7 | h8 | pmin | 10 | 1 | 10 | 1 | 10 | 5 | 13 | 10 | 10 | 2 | 2 | 2 | 2 | 6 | 2 | 3 | 1 | pmax | 1 000 | 100 | 1 000 | 100 | 1 000 | 500 | 1 300 | 1 000 | 1 000 | 200 | 200 | 200 | 200 | 600 | 200 | 300 | 100 |
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Maximum and minimum values of parameters in each layer for five-layer and nine-layer geoelectric model
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ELM neural network structure
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Block diagram of the calculation flow of the OSELM algorithm
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Algorithm | 5层模型 | 9层模型 | R2 | RRMSE | APE/% | Time/s | R2 | RRMSE | APE/% | Time/s | OSELM | 0.9978 | 0.1148 | 6.465 | 0.0089 | 0.9975 | 0.1542 | 8.372 | 0.0089 | ELM | 0.9978 | 0.1540 | 8.174 | 0.0097 | 0.9974 | 0.1904 | 10.218 | 0.0099 |
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Comparison of inversion performance for two ELM methods
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五层模型 | ρ/(Ω·m) h/m | | ρ1 | ρ2 | ρ3 | ρ4 | ρ5 | h1 | h2 | h3 | h4 | 理论值 | 100 | 50 | 10 | 200 | 1000 | 100 | 100 | 50 | 100 | | 九层模型 | ρ/(Ω·m) h/m | | ρ1 | ρ2 | ρ3 | ρ4 | ρ5 | ρ6 | ρ7 | ρ8 | ρ9 | h1 | h2 | h3 | h4 | h5 | h6 | h7 | h8 | 理论值 | 100 | 10 | 100 | 10 | 100 | 50 | 130 | 100 | 100 | 20 | 20 | 20 | 20 | 60 | 20 | 30 | 10 |
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Theoretical values of five-layered and nine-layered geoelectric model inversion
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Inversion results of different algorithms for of 5-layer(a) and 9-layer(b) geoelectric models
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Forward response curves of 5-layer(a) and 9-layer(b) geoelectric models
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Schematic diagram of quasi two dimensional model and measurement position
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Inversion results of OSELM method (a) and ELM method (b) of quasi-two-dimensional geoelectric model
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