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Mathematical Problems in Engineering
Volume 2018, Article ID 7452863, 11 pages
Research Article

Inverse Problem Solution and Regularization Parameter Selection for Current Distribution Reconstruction in Switching Arcs by Inverting Magnetic Fields

State Key Lab of Electrical Insulation and Power Equipment, School of Electrical Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China

Correspondence should be addressed to Guogang Zhang; nc.ude.utjx.liam@gnahzgg

Received 8 February 2017; Accepted 14 November 2017; Published 4 January 2018

Academic Editor: Salvatore Alfonzetti

Copyright © 2018 Jinlong Dong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Current density distribution in electric arcs inside low voltage circuit breakers is a crucial parameter for us to understand the complex physical behavior during the arcing process. In this paper, we investigate the inverse problem of reconstructing the current density distribution in arcs by inverting the magnetic fields. A simplified 2D arc chamber is considered. The aim of this paper is the computational side of the regularization method, regularization parameter selection strategies, and the estimation of systematic error. To address the ill-posedness of the inverse problem, Tikhonov regularization is analyzed, with the regularization parameter chosen by Morozov’s discrepancy principle, the L-curve, the generalized cross-validation, and the quasi-optimality criteria. The provided range of regularization parameter selection strategies is much wider than in the previous works. Effects of several features on the performance of these criteria have been investigated, including the signal-to-noise ratio, dimension of measurement space, and the measurement distance. The numerical simulations show that the generalized cross-validation and quasi-optimality criteria provide a more satisfactory performance on the robustness and accuracy. Moreover, an optimal measurement distance can be expected when using a planner sensor array to perform magnetic measurements.