Research on the Grounding Grid Electrical Impedance Imaging Algorithm Based on Improved Tikhonov and Lp Regularization
Lele He
,
Lei Yang
,
Xiaoheng Yan
,
Weihua Chen
and
Shangfei Huang
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.
