The forward and inverse problems in magnetic induction tomography of low conductivity structures

Abstract

Purpose

The purpose of this paper is to develop a magnetic induction tomography (MIT) system as well as the conductivity reconstruction algorithms (inverse problem).

Design/methodology/approach

In order to define and verify the solution of the inverse problem, the forward problem is formulated using mathematical model of the system. The forward problem is solved using the finite element method. The optimization of the excitation unit is based on the numerical solutions of the direct problem. All the dimensions and shape of the excitation system are optimized in order to focus the main part of the magnetic field in the vicinity of the receiver. Finally, two formulations of the inverse problem are discussed: based on the inversion of the Biot‐Savart law; and based on the artificial neural networks.

Findings

The formulation of the forward problem of the considered MIT system is given. The construction of the exciter unit that focuses the main part of the magnetic field in the vicinity of the receiver is proposed. Two formulations of the inverse problem are discussed. First using the inversion of the Biot‐Savart law and second using the artificial neural network. The neural networks seem to be promising tools for reconstructing the MIT images.

Originality/value

This paper demonstrates a real‐life MIT system whose performance is satisfactorily predicted by mathematical models. The original design of the exciter is shown. The new approach to the inverse problem in MIT – the use of the artificial neural network – is presented.

Citation

Palka, R., Gratkowski, S., Stawicki, K. and Baniukiewicz, P. (2009), "The forward and inverse problems in magnetic induction tomography of low conductivity structures", Engineering Computations, Vol. 26 No. 7, pp. 843-856. https://doi.org/10.1108/02644400910985206