Magnetostatic Permeability Tomography in Material Inspection

Structural materials in reinforced concrete, often made of iron, are sometimes damaged due to acid, rain or salty wind. The magnetic permeability of the damaged materials change due to this damage. In this paper we study an advance monitoring system based on a magnetostatic permeability tomography (MPT) technique. The magnetostatic field is applied to the material from the external surfaces and the measurement data for inspection are the normal components of the resulting magnetostatic fields in the surface. Knowing the tangential component of the applied field and normal component of the measured field uniquely defines the permeability distributions. In practise, excitation and sensing coils can be used for the measurement configuration, in order to gather the data from the surface. The problem of the permeability reconstruction is then a nonlinear and ill-posed inverse problem. We employed a regularised Gauss-Newton method to recover the permeability distribution. The forward problem is to simulate the measurement process. We have implemented a 3D edge-based finite element package to solve the magnetostatic problem via a formulation based on magnetic vector potentials. For the Jacobian matrix and the sensitivity analysis we derived an efficient formulation based on the reciprocity theorem. The results of the forward problem and the sensitivity map will be presented in this paper. We also show the results of 3D permeability reconstruction for a numerically simulated MPT system. The system consists of 8 coils which are used to apply the primary field and measuring the resulting field. The images are reconstructed using synthetically generated data with 28 independent scanning measurements with added noise. The high contrast and low contrast permeability reconstruction will be discussed.