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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摘要

电阻抗成像（EIT）技术作为一种非侵入式成像方法,已成为接地网腐蚀诊断的研究重点之一,然而现有算法下的图像重构效果均不理想。为了对变电站接地网进行准确的腐蚀诊断,该文提出了一种L₁-L₂弹性范数算法对接地网EIT逆问题模型进行修正,以获得更接近真实值的接地网电阻率的解,进而提高腐蚀诊断的准确性。首先,介绍了EIT技术在接地网腐蚀诊断中的基本原理;其次,对L₁范数、L₂范数、一步牛顿法（NOSER）以及L₁-L₂弹性范数等四种算法作用下的接地网仿真模型进行算例分析,并搭建镀锌钢模型进行实验验证;最后,引入图像相关系数和图像相对误差等评价标准对四种算法下重构的接地网图像进行评价。结果表明,该文所提算法在改善接地网EIT技术病态性与欠定性方面效果良好,与其他三种算法相比,图像相关系数平均提升了32.19%、相对误差平均降低了22.54%。该算法的提出增强了EIT技术在接地网腐蚀诊断中的应用。

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关键词 ：电阻抗成像, 接地网, 腐蚀诊断, 算法, 弹性范数

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

收稿日期: 2024-01-11

PACS:

TM12

基金资助:

智能电网四川省重点实验室开放基金资助项目（2022-IEPGKLSP-KFYB02）

通讯作者: 张维哲男,1997年生,硕士研究生,研究方向为接地网腐蚀诊断。E-mail：245647583@qq.com

作者简介: 张承乾女,1980年生,副教授,硕士生导师,研究方向为电力系统故障诊断、信号处理等。E-mail：47188203@qq.com

引用本文:

张维哲, 张承乾, 刘建生, 张亮, 马文博. 基于弹性范数的接地网电阻抗成像算法[J]. 电工技术学报, 0, (): 240072-240072. Zhang Weizhe, Zhang Chengqian, Liu Jiansheng, Zhang Liang, Ma Wenbo. Grounding Grid Electrical Impedance Tomography Algorithm Based on Elastic Norm. Transactions of China Electrotechnical Society, 0, (): 240072-240072.

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