Parametric Reconstruction of Permittivity Graded Materials Based on Electrical Capacitance Tomography

Abstract

This paper presents our simulation study on the applicability of electrical capacitance tomography (ECT) for permittivity functionally graded material ( $\boldsymbol{\varepsilon}$ -FGM) testing. Firstly, a 2D multi-layer $\boldsymbol{\varepsilon}$ -FGM model with 8 electrodes is established in COMSOL software. Subsequently, the forward problem of this model is solved using finite element method (FEM), in which various permittivity distribution patterns (descending, V-shape, etc.) are involved. In addition, several ECT reconstruction methods, including linear back projection (LBP), Tikhonov regularization and Landweber algorithm, are studied for their applicability on the $\boldsymbol{\varepsilon}$ -FGM problems. The results show that LBP algorithm has the fastest computing speed but poor reconstruction results. Tikhonov regularization algorithm method provides acceptable results in local domain and additionally appears smoothing effect caused by L2 regularization. What's more, Landweber method shows high accuracy in reconstruction process and low sensitivity to the measurement errors and noise. This work investigates the measuring of permittivity distributions inside $\boldsymbol{\varepsilon}$ -FGM by using ECT method, which is helpful for the research of $\boldsymbol{\varepsilon}$ -FGM insulation and represents a new idea of measuring permittivity graded materials.