Vol. 106
Latest Volume
All Volumes
PIERB 109 [2024] PIERB 108 [2024] PIERB 107 [2024] PIERB 106 [2024] PIERB 105 [2024] PIERB 104 [2024] PIERB 103 [2023] PIERB 102 [2023] PIERB 101 [2023] PIERB 100 [2023] PIERB 99 [2023] PIERB 98 [2023] PIERB 97 [2022] PIERB 96 [2022] PIERB 95 [2022] PIERB 94 [2021] PIERB 93 [2021] PIERB 92 [2021] PIERB 91 [2021] PIERB 90 [2021] PIERB 89 [2020] PIERB 88 [2020] PIERB 87 [2020] PIERB 86 [2020] PIERB 85 [2019] PIERB 84 [2019] PIERB 83 [2019] PIERB 82 [2018] PIERB 81 [2018] PIERB 80 [2018] PIERB 79 [2017] PIERB 78 [2017] PIERB 77 [2017] PIERB 76 [2017] PIERB 75 [2017] PIERB 74 [2017] PIERB 73 [2017] PIERB 72 [2017] PIERB 71 [2016] PIERB 70 [2016] PIERB 69 [2016] PIERB 68 [2016] PIERB 67 [2016] PIERB 66 [2016] PIERB 65 [2016] PIERB 64 [2015] PIERB 63 [2015] PIERB 62 [2015] PIERB 61 [2014] PIERB 60 [2014] PIERB 59 [2014] PIERB 58 [2014] PIERB 57 [2014] PIERB 56 [2013] PIERB 55 [2013] PIERB 54 [2013] PIERB 53 [2013] PIERB 52 [2013] PIERB 51 [2013] PIERB 50 [2013] PIERB 49 [2013] PIERB 48 [2013] PIERB 47 [2013] PIERB 46 [2013] PIERB 45 [2012] PIERB 44 [2012] PIERB 43 [2012] PIERB 42 [2012] PIERB 41 [2012] PIERB 40 [2012] PIERB 39 [2012] PIERB 38 [2012] PIERB 37 [2012] PIERB 36 [2012] PIERB 35 [2011] PIERB 34 [2011] PIERB 33 [2011] PIERB 32 [2011] PIERB 31 [2011] PIERB 30 [2011] PIERB 29 [2011] PIERB 28 [2011] PIERB 27 [2011] PIERB 26 [2010] PIERB 25 [2010] PIERB 24 [2010] PIERB 23 [2010] PIERB 22 [2010] PIERB 21 [2010] PIERB 20 [2010] PIERB 19 [2010] PIERB 18 [2009] PIERB 17 [2009] PIERB 16 [2009] PIERB 15 [2009] PIERB 14 [2009] PIERB 13 [2009] PIERB 12 [2009] PIERB 11 [2009] PIERB 10 [2008] PIERB 9 [2008] PIERB 8 [2008] PIERB 7 [2008] PIERB 6 [2008] PIERB 5 [2008] PIERB 4 [2008] PIERB 3 [2008] PIERB 2 [2008] PIERB 1 [2008]
2024-05-06
Research on the Grounding Grid Electrical Impedance Imaging Algorithm Based on Improved Tikhonov and Lp Regularization
By
Progress In Electromagnetics Research B, Vol. 106, 1-16, 2024
Abstract
In this paper, an improved hybrid regularized grounded network imaging algorithm (ITR-Lp) combining Tikhonov regularization and Lp regularization is proposed; through the improvement of the filtering function, the correction of small magnitude for large singular values and increasing magnitude of correction with decreasing singular values for small singular values is implemented for the improvement of the convergence of the solution. The proposed algorithm constructs a regularization matrix to achieve selective correction of singular values and improve the convergence of the solution, while Lp regularization is used to enhance the sparsity of the solution and improve the boundary contrast. the effect of node distribution on convergence is investigated, and finally the ITR-Lp algorithm is validated by simulation and experiment. The results show that the ITR-Lp algorithm proposed in this paper achieves the lowest resistivity relative errors of 0.1695 and 0.1089 for resistive networks with 1 corrosion and 2 corrosions, respectively. The method has good convergence and boundary contrast, which effectively improves the pathology of the inverse problem of imaging the electrical impedance tomography of grounding grid.
Citation
Lele He, Lei Yang, Xiaoheng Yan, Weihua Chen, and Shangfei Huang, "Research on the Grounding Grid Electrical Impedance Imaging Algorithm Based on Improved Tikhonov and Lp Regularization," Progress In Electromagnetics Research B, Vol. 106, 1-16, 2024.
doi:10.2528/PIERB24031403
References

1. Fu, Zhihong, Xiujuan Wang, Qian Wang, Xiaobin Xu, Nengyi Fu, and Shanqiang Qin, "Advances and challenges of corrosion and topology detection of grounding grid," Applied Sciences, Vol. 9, No. 11, 2290, 2019.

2. Zhang, Cheng, Yuxiang Liao, Xue Gao, Jing Zhao, Yuan Yuan, and Ruijin Liao, "Research advances of soil corrosion of grounding grids," Micromachines, Vol. 12, No. 5, 513, 2021.

3. Alam, A. K. M. Monsurul, Miodrag Kandic, Douglas J. Thomson, and Greg E. Bridges, "Rod insertion TDR for detecting corrosion damage in vertical grounding electrodes," IEEE Transactions on Power Delivery, Vol. 38, No. 2, 1230-1238, 2023.

4. Yu, Cigong, Zhihong Fu, Qian Wang, Heng-Ming Tai, and Shanqiang Qin, "A novel method for fault diagnosis of grounding grids," IEEE Transactions on Industry Applications, Vol. 51, No. 6, 5182-5188, 2015.

5. Lu, Caijiang, Tianyi Zhang, Shaoheng Sun, Zhongqing Cao, Mingyong Xin, Guoqiang Fu, Tao Wang, and Xi Wang, "Fault diagnosis of tower grounding conductor based on the electromagnetic measurement and neural network," IEEE Transactions on Instrumentation and Measurement, Vol. 71, 1-9, 2022.

6. Liang, Guanghui, Shangjie Ren, Shu Zhao, and Feng Dong, "A Lagrange-Newton method for EIT/UT dual-modality image reconstruction," Sensors, Vol. 19, No. 9, 1966, 2019.
doi:10.3390/s19091966

7. Liu, Shengheng, Hancong Wu, Yongming Huang, Yunjie Yang, and Jiabin Jia, "Accelerated structure-aware sparse Bayesian learning for three-dimensional electrical impedance tomography," IEEE Transactions on Industrial Informatics, Vol. 15, No. 9, 5033-5041, 2019.

8. Wang, Xiujuan, Zhihong Fu, Yao Wang, Renkuan Liu, and Lin Chen, "A non-destructive testing method for fault detection of substation grounding grids," Sensors, Vol. 19, No. 9, 2046, 2019.
doi:10.3390/s19092046

9. Liu, Kai, Fan Yang, Songyang Zhang, Liwei Zhu, Jiayuan Hu, Xiaoyu Wang, and Ullah Irfan, "Research on grounding grids imaging reconstruction based on magnetic detection electrical impedance tomography," IEEE Transactions on Magnetics, Vol. 54, No. 3, 1-4, 2018.

10. Yang, Fan, Yongan Wang, Manling Dong, Xiaokuo Kou, Degui Yao, Xing Li, Bing Gao, and Irfan Ullah, "A cycle voltage measurement method and application in grounding grids fault location," Energies, Vol. 10, No. 11, 1929, 2017.

11. Li, Xing, Fan Yang, Julan Ming, Ammad Jadoon, and Sheng Han, "Imaging the corrosion in grounding grid branch with inner-source electrical impedance tomography," Energies, Vol. 11, No. 7, 1739, 2018.

12. Chen, Yanhao, Yu Xiang, Ziyu Shi, Jing Lu, and Yujiang Wang, "Tikhonov regularized penalty matrix construction method based on the magnitude of singular values and its application in near-field acoustic holography," Mechanical Systems and Signal Processing, Vol. 170, 108870, 2022.

13. Chen, Yutong and Hua Yan, "Reconstruction of complex temperature field based on improved Tikhonov regularization," Journal of Physics: Conference Series, Vol. 1754, No. 1, 012207, IOP Publishing, 2021.

14. Dimas, Christos, Nikolaos Uzunoglu, and Paul P. Sotiriadis, "An efficient point-matching method-of-moments for 2D and 3D electrical impedance tomography using radial basis functions," IEEE Transactions on Biomedical Engineering, Vol. 69, No. 2, 783-794, 2021.

15. Estatico, C., M. Pastorino, and A. Randazzo, "A novel microwave imaging approach based on regularization in Lp Banach spaces," IEEE Transactions on Antennas and Propagation, Vol. 60, No. 7, 3373-3381, 2012.
doi:10.1109/TAP.2012.2196925

16. Zhang, Lingling, Genqi Xu, Qian Xue, Huaxiang Wang, and Yanbin Xu, "An iterative thresholding algorithm for the inverse problem of electrical resistance tomography," Flow Measurement and Instrumentation, Vol. 33, 244-250, 2013.

17. Liu, Xianglong and Ze Liu, "A novel algorithm based on L1-Lp norm for inverse problem of electromagnetic tomography," Flow Measurement and Instrumentation, Vol. 65, 318-326, 2019.

18. Li, Jia, Shihong Yue, Mingliang Ding, Ziqiang Cui, and Huaxiang Wang, "Adaptive Lp regularization for electrical impedance tomography," IEEE Sensors Journal, Vol. 19, No. 24, 12297-12305, 2019.
doi:10.1109/JSEN.2019.2940070

19. Zhu, Wei, "Image denoising using Lp-norm of mean curvature of image surface," Journal of Scientific Computing, Vol. 83, No. 2, 32, 2020.

20. Hua, Ping, Eung Je Woo, John G. Webster, and Willis J. Tompkins, "Finite element modeling of electrode-skin contact impedance in electrical impedance tomography," IEEE Transactions on Biomedical Engineering, Vol. 40, No. 4, 335-343, 1993.

21. Zhang, Xueying, Guizhi Xu, Shuai Zhang, Yongjian Li, Youguang Guo, Ying Li, Youhua Wang, and Weili Yan, "A numerical computation forward problem model of electrical impedance tomography based on generalized finite element method," IEEE Transactions on Magnetics, Vol. 50, No. 2, 1045-1048, 2014.

22. Shi, Yanyan, Zuguang Rao, Can Wang, Yue Fan, Xinsong Zhang, and Meng Wang, "Total variation regularization based on iteratively reweighted least-squares method for electrical resistance tomography," IEEE Transactions on Instrumentation and Measurement, Vol. 69, No. 6, 3576-3586, 2019.

23. Song, Yizhuang, Yanying Wang, and Dong Liu, "A nonlinear weighted anisotropic total variation regularization for electrical impedance tomography," IEEE Transactions on Instrumentation and Measurement, Vol. 71, 1-13, 2022.

24. Cheney, Margaret, David Isaacson, Jonathan C. Newell, S. Simske, and J. Goble, "NOSER: An algorithm for solving the inverse conductivity problem," International Journal of Imaging Systems and Technology, Vol. 2, No. 2, 66-75, 1990.

25. Cheng, Wei, Yingying Lu, and Zhousuo Zhang, "Tikhonov regularization-based operational transfer path analysis," Mechanical Systems and Signal Processing, Vol. 75, 494-514, 2016.

26. Zong, Zheng, Yusong Wang, Siyuan He, and Zhun Wei, "Adaptively regularized bases-expansion subspace optimization methods for electrical impedance tomography," IEEE Transactions on Biomedical Engineering, Vol. 69, No. 10, 3098-3108, 2022.

27. Ramlau, Ronny and Elena Resmerita, "Convergence rates for regularization with sparsity constraints," Electronic Transactions on Numerical Analysis, Vol. 37, 87-104, 2010.

28. Engl, Heinz Werner, Martin Hanke, and Andreas Neubauer, Regularization of Inverse Problems, Vol. 375, Springer Science & Business Media, 1996.
doi:10.1007/978-94-009-1740-8

29. Wang, Zheng, Yanbin Xu, Yang Pei, and Feng Dong, "A method of spatially adaptive Lp regularization for electrical tomography," 2017 IEEE International Instrumentation and Measurement Technology Conference (I2MTC), 1-6, IEEE, 2017.

30. Zhao, Jia, Yanbin Xu, and Feng Dong, "An Lq–Lp optimization framework for image reconstruction of electrical resistance tomography," Measurement Science and Technology, Vol. 25, No. 12, 125402, 2014.

31. Hu, Jia-Yuan, Jian-Gen Hu, Dao-Lin Lan, Ju-Lan Ming, Yu-Tong Zhou, and Yan-Wei Li, "Corrosion evaluation of the grounding grid in transformer substation using electrical impedance tomography technology," IECON 2017 - 43rd Annual Conference of the IEEE Industrial Electronics Society, 5033-5038, IEEE, 2017.

32. Li, Chun-Na, Yuan-Hai Shao, Wei-Jie Chen, Zhen Wang, and Nai-Yang Deng, "Generalized two-dimensional linear discriminant analysis with regularization," Neural Networks, Vol. 142, 73-91, 2021.

33. Sabett, Christiana, Ariel Hafftka, Kyle Sexton, and Richard G. Spencer, "L1, Lp, L2, and elastic net penalties for regularization of Gaussian component distributions in magnetic resonance relaxometry," Concepts in Magnetic Resonance Part A, Vol. 46, No. 2, e21427, 2017.

34. Chen, Maomao, Han Su, Yuan Zhou, Chuangjian Cai, Dong Zhang, and Jianwen Luo, "Automatic selection of regularization parameters for dynamic fluorescence molecular tomography: A comparison of L-curve and U-curve methods," Biomedical Optics Express, Vol. 7, No. 12, 5021-5041, 2016.