基于弹性范数的接地网电阻抗成像算法  

Grounding Grid Electrical Impedance Tomography Algorithm Based on Elastic Norm

作　　者：张维哲 张承乾 刘建生[1] 张亮 马文博 Zhang Weizhe;Zhang Chengqian;Liu Jiansheng;Zhang Liang;Ma Wenbo(School of Electrical Engineering and Information Southwest Petroleum University,Chengdu 610500 China)

机构地区：[1]西南石油大学电气信息学院,成都610500

出　　处：《电工技术学报》2025年第3期676-688,共13页Transactions of China Electrotechnical Society

基　　金：智能电网四川省重点实验室开放基金资助项目(2022-IEPGKLSPKFYB02)。

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L_(1)-L_(2)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L_(1)范数、L_(2)范数、一步牛顿法(NOSER)以及L_(1)-L_(2)弹性范数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。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 L_(1)-L_(2) 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,L_(1),L_(2) and L_(1)-L_(2),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 L_(1) norm algorithm.The stability of the reconstructed structure under L_(2) norm algorithm is poor.NOSER algorithm is difficult to reconstruct the basic contours of the grounding grid in most cases.Under the L_(1)-L_(2) elastic norm algorithm,not only the contour edge of the grounding grid can

关 键 词：电阻抗成像 接地网 腐蚀诊断 算法 弹性范数 

分 类 号：TM12[电气工程—电工理论与新技术]