3 / 2018-08-22 09:52:17

Parametric Reconstruction of Permittivity Graded Materials Based on Electrical Capacitance Tomography

electrical capacitance tomography, functional graded material, permittivity reconstruction, solid insulation, inverse problem

Increasing demand for equipment miniaturization and higher voltage transmission (e.g. UHVAC and HVDC) has required continual improvements to the insulation system. To improve the insulation performance, it is important to control the electric field distribution in and around the solid insulators. For this, dielectric functionally graded material (d-FGM) with spatially inhomogeneous dielectric property distribution (i.e. relative permittivity  or electrical conductivity ) was proposed, which could be applied to effectively control the electric field distribution. Currently, d-FGM could be fabricated through many techniques. To effectively evaluate the quality of products and give feedback to the manufacturing process, the distribution of or is an important issue. However, this was usually done by invasive methods (cutting and testing, etc.), which is obviously destructive to the insulators and not suitable to the industrial applications.

Here, we investigate a non-destructive detection method for permittivity FGM (-FGM), calling electrical capacitance tomography (ECT). This technology was firstly proposed in the research of multiphase flow imaging. In this technique, the distribution of permittivity in a determined domain is reconstructed from a set of mutual capacitances, which are measured at the domain boundaries. To be more specific, a ECT system are divided into three parts, including capacitance sensors, data acquisition system and image reconstruction algorithm. The capacitance sensors is a set of electrodes placed around the domain, whose mutual capacitance information are obtained by data acquisition system. Then the acquired data are used by image reconstruction algorithm to reconstruct the permittivity distributions inside the domain.

As a non-invasive, fast and low-cost technique, ECT can be a potential solution for measuring the permittivity distribution inside -FGM insulators. However, some technical problems still need further investigation. Firstly, a forward problem which maps the permittivity distribution to a set of capacitance measurements need to be established and solved. Secondly, well-designed reconstruction algorithms are required, since most of the reconstruction problem (i.e., the inverse problem) is mathematical ill-posed. Finally, experimental verification of ECT on d-FGM applications still needs to be studied.

This paper presents our investigation on the applicability of ECT on -FGM testing, which mainly focuses on the first two problems. Firstly, a 2D multi-layer -FGM model with 8 electrodes is established in COMSOL software. The forward problem of this model is solved using finite element method (FEM), in which various permittivity distribution patterns (ascending, 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 -FGM problems. The results show that LBP algorithm has 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 -FGM by using ECT method, which is helpful for the research of -FGM insulation and represents a new idea of measuring permittivity graded materials. Future works will be mainly related to the experimental studies.