基于弹性范数的接地网电阻抗成像算法

doi:10.19595/j.cnki.1000-6753.tces.240072

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Abstract Electrical Impedance Tomography (EIT) technology, as a non-invasive imaging method, has become one of the important research points in the diagnosis of grounding grid corrosion. Because the mathematical model of EIT inverse problem of grounding grid has the defects of highly pathological, underqualitative and nonlinear, under the existing algorithm, the error between the iterative solution of grounding grid resistivity and the real solution is large, which results in the low spatial resolution of the reconstructed image of grounding grid and serious edge artifacts. In order to solve the existing problems, this paper proposes an electrical impedance imaging algorithm of grounding grid based on L₁-L₂ elastic norm, which restrains and revises the mathematical model of EIT inverse problem of grounding grid, improves the spatial resolution of the reconstructed image of grounding grid, reduces edge artifacts, and improves the efficiency of corrosion diagnosis.
Firstly, the constraint ability of three norm algorithms, L₁, L₂ and L₁-L₂, to the inverse problem of ground grid EIT is analyzed and compared. Secondly, simulation experiments of single branch and double branch corrosion conditions are set up. At the same time, in order to better evaluate the robustness and data processing ability of the algorithm, 5 dB Gaussian white noise is added to all boundary potential measurement data during unknown topology imaging. It can be seen from the simulation results that all the four algorithms can perform imaging corrosion diagnosis for the grounding grid with known topology, but for the unknown grounding grid topology, the quality of reconstructed images under the four algorithms is very different, and serious "false diagnosis" occurs under the L₁ norm algorithm. The stability of the reconstructed structure under L₂ norm algorithm is poor. NOSER algorithm is difficult to reconstruct the basic contours of the grounding grid in most cases. Under the L₁-L₂ elastic norm algorithm, not only the contour edge of the grounding grid can be clearly seen, but also the corrosion branch can be accurately located and diagnosed. Thirdly, the image correlation coefficient (ICC) and image relative error (IRE), which are commonly used in EIT field, are introduced to evaluate the reconstructed images of the ground grid with unknown topology. The results show that L₁-L₂ elastic norm algorithm has the smallest relative error and the largest correlation coefficient. Under the proposed algorithm, the relative error of the reconstructed image is reduced by 22.54% on average and the correlation coefficient is increased by 32.19% on average. It shows that the resistivity solution of grounding grid under this algorithm is closer to the real value. Finally, the effectiveness of the proposed algorithm is further verified by building a galvanized steel model and conducting experiments.
The following conclusions can be drawn from the simulation analysis and real experiments: (1) For the L₁-L₂ elastic norm algorithm, when the regularization parameter α is set to 0.03 and the weight factor ω is set to 0.4, a high-resolution impedance reconfiguration of the grounding grid can be obtained. (2) L₁-L₂ elastic norm has the advantages of both L₁-L₂ norm and L₂ norm, which can effectively improve the ill-condition and underquality of EIT inverse problem of grounding grid, and also has good robustness to Gaussian white noise, so that the mathematical model of grounding grid can obtain an approximate solution closer to the real solution. (3) L₁-L₂ elastic norm algorithm has the smallest relative error and the highest correlation coefficient compared with the other three commonly used algorithms mentioned in this paper, even though the imaging speed is not the fastest among EIT imaging algorithms for grounding grid. The imaging results are best in the acceptable time range.

Key words： Electrical impedance tomography grounding grid corrosion diagnosis algorithm elastic norm

Received: 11 January 2024

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	Zhang Weizhe
	Zhang Chengqian
	Liu Jiansheng
	Zhang Liang
	Ma Wenbo

Cite this article:

Zhang Weizhe,Zhang Chengqian,Liu Jiansheng等. Grounding Grid Electrical Impedance Tomography Algorithm Based on Elastic Norm[J]. Transactions of China Electrotechnical Society, 2025, 40(3): 676-688.

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https://dgjsxb.ces-transaction.com/EN/10.19595/j.cnki.1000-6753.tces.240072 OR https://dgjsxb.ces-transaction.com/EN/Y2025/V40/I3/676

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