Efficient and robust Levenberg–Marquardt Algorithm based on damping parameters for parameter inversion in underground metal target detection
The Levenberg–Marquardt (LM) algorithm has been widely used to solve nonlinear least-squares problems in underground target detection. However, the LM algorithm has an unsatisfactory performance of convergence due to the influence of noise in the environment. Therefore, a new modified LM (NMLM) algo...
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| Vydáno v: | Computers & geosciences Ročník 176; s. 105354 |
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| Jazyk: | angličtina |
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Elsevier Ltd
01.07.2023
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| ISSN: | 0098-3004, 1873-7803 |
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| Abstract | The Levenberg–Marquardt (LM) algorithm has been widely used to solve nonlinear least-squares problems in underground target detection. However, the LM algorithm has an unsatisfactory performance of convergence due to the influence of noise in the environment. Therefore, a new modified LM (NMLM) algorithm has been proposed in this paper to improve its accuracy and efficiency of parameter estimation with low SNR. The NMLM algorithm can also converge globally under certain conditions and converge quadratically under the error-bound condition, which updates based on the gain ratio and determines the damping factor based on the gradient value. An experimental investigation has been conducted under different SNRs and the amount of data, and the results indicate the new algorithm can accurately and quickly estimate the parameters of underground metal targets under the lower SNRs and smaller amounts of data. More specifically, the estimation accuracy of position, principal axes polarizability, and orientation of the metal target can be increased by up to 1.6 cm, 0.00013, and 2.31 degree, respectively. This paper also verifies that the new algorithm finds the optimal solution for standard numerical problems with low errors and a finite number of iterations.
•A new LM algorithm is proposed to improve the accuracy and convergence of the result.•The performances are analyzed by comparing conventional and NMLM algorithms.•The performance of the NMLM algorithm on the common optimization problem is analyzed. |
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| AbstractList | The Levenberg–Marquardt (LM) algorithm has been widely used to solve nonlinear least-squares problems in underground target detection. However, the LM algorithm has an unsatisfactory performance of convergence due to the influence of noise in the environment. Therefore, a new modified LM (NMLM) algorithm has been proposed in this paper to improve its accuracy and efficiency of parameter estimation with low SNR. The NMLM algorithm can also converge globally under certain conditions and converge quadratically under the error-bound condition, which updates based on the gain ratio and determines the damping factor based on the gradient value. An experimental investigation has been conducted under different SNRs and the amount of data, and the results indicate the new algorithm can accurately and quickly estimate the parameters of underground metal targets under the lower SNRs and smaller amounts of data. More specifically, the estimation accuracy of position, principal axes polarizability, and orientation of the metal target can be increased by up to 1.6 cm, 0.00013, and 2.31 degree, respectively. This paper also verifies that the new algorithm finds the optimal solution for standard numerical problems with low errors and a finite number of iterations.
•A new LM algorithm is proposed to improve the accuracy and convergence of the result.•The performances are analyzed by comparing conventional and NMLM algorithms.•The performance of the NMLM algorithm on the common optimization problem is analyzed. The Levenberg-Marquardt (LM) algorithm has been widely used to solve nonlinear least-squares problems in underground target detection. However, the LM algorithm has an unsatisfactory performance of convergence due to the influence of noise in the environment. Therefore, a new modified LM (NMLM) algorithm has been proposed in this paper to improve its accuracy and efficiency of parameter estimation with low SNR. The NMLM algorithm can also converge globally under certain conditions and converge quadratically under the error-bound condition, which updates based on the gain ratio and determines the damping factor based on the gradient value. An experimental investigation has been conducted under different SNRs and the amount of data, and the results indicate the new algorithm can accurately and quickly estimate the parameters of underground metal targets under the lower SNRs and smaller amounts of data. More specifically, the estimation accuracy of position, principal axes polarizability, and orientation of the metal target can be increased by up to 1.6 cm, 0.00013, and 2.31 degree, respectively. This paper also verifies that the new algorithm finds the optimal solution for standard numerical problems with low errors and a finite number of iterations. |
| ArticleNumber | 105354 |
| Author | Wan, Yadong Wang, Peng Shi, Haodong Wang, Xiaofen Zhang, Xiaotong Liu, Wen |
| Author_xml | – sequence: 1 givenname: Xiaofen orcidid: 0000-0003-0903-2044 surname: Wang fullname: Wang, Xiaofen email: b20200343@xs.ustb.edu.cn organization: School of Computer and Communication Engineering, University of Science and Technology Beijing, 30th Xueyuan Road, Haidian District, Beijing, 100083, China – sequence: 2 givenname: Peng surname: Wang fullname: Wang, Peng email: wangp503@chinaunicom.cn organization: China Unicom Smart City Research Institute, 9th South Capital Gymnasium Road, Haidian District, Beijing, 100033, China – sequence: 3 givenname: Xiaotong surname: Zhang fullname: Zhang, Xiaotong email: zxt@ies.ustb.edu.cn organization: School of Computer and Communication Engineering, University of Science and Technology Beijing, 30th Xueyuan Road, Haidian District, Beijing, 100083, China – sequence: 4 givenname: Yadong surname: Wan fullname: Wan, Yadong email: wyd@ustb.edu.cn organization: School of Computer and Communication Engineering, University of Science and Technology Beijing, 30th Xueyuan Road, Haidian District, Beijing, 100083, China – sequence: 5 givenname: Wen surname: Liu fullname: Liu, Wen email: g20208815@xs.ustb.edu.cn organization: School of Computer and Communication Engineering, University of Science and Technology Beijing, 30th Xueyuan Road, Haidian District, Beijing, 100083, China – sequence: 6 givenname: Haodong surname: Shi fullname: Shi, Haodong email: g20208825@xs.ustb.edu.cn organization: School of Computer and Communication Engineering, University of Science and Technology Beijing, 30th Xueyuan Road, Haidian District, Beijing, 100083, China |
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| Cites_doi | 10.1093/comjnl/3.3.175 10.1016/j.measurement.2020.108330 10.1109/JSEN.2017.2676460 10.1109/ACCESS.2020.3008176 10.1090/qam/10666 10.1137/0111030 10.1109/JSEN.2019.2944752 10.1007/s10957-020-01666-1 10.1109/TIM.2019.2917236 10.1109/TNN.2010.2045657 10.3390/drones6010011 10.1109/JSEN.2022.3175502 10.1093/gji/ggaa483 10.1007/s10915-017-0488-6 10.1109/ACCESS.2021.3049308 10.3390/rs13122343 10.1016/j.ndteint.2021.102571 10.1080/10556788.2016.1179737 10.1007/s00607-004-0083-1 |
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| Keywords | Damping parameter Underground target detection Parameter inversion Levenberg–Marquardt Electromagnetic induction |
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| Snippet | The Levenberg–Marquardt (LM) algorithm has been widely used to solve nonlinear least-squares problems in underground target detection. However, the LM... The Levenberg-Marquardt (LM) algorithm has been widely used to solve nonlinear least-squares problems in underground target detection. However, the LM... |
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| SubjectTerms | algorithms computers Damping parameter Electromagnetic induction least squares Levenberg–Marquardt metals Parameter inversion solutions Underground target detection |
| Title | Efficient and robust Levenberg–Marquardt Algorithm based on damping parameters for parameter inversion in underground metal target detection |
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