Method for Reconstructing the Shape of Surface Corrosion Defects Using B-splines

Abstract

In this paper, the theoretical foundations of a method for reconstructing the geometry of corrosion defects in ferromagnetic objects based on magnetic leakage field data have been considered. The proposed approach relies on a parametric description of the defect as a spline surface, the structure of which is formed based on the characteristic distribution features of magnetic field strength components and their spatial derivatives. The coordinates of the defect region boundaries are determined by the extrema of the first derivative of the normal component of the magnetic field along the magnetization direction, while the locations of internal control points are determined by the extrema of the tangential component within the found boundaries. The depths of the control points are refined through an optimization procedure by minimizing the standard deviation between the calculated and target magnetic fields. The feasibility of the approach has been demonstrated in a numerical experiment with a symmetric corrosion defect. It has been shown that the method makes it possible to reproduce the general shape of the defect region and achieve good agreement in terms of its integral characteristics. The relative error in volume reconstruction has been 2.4%, which confirms the possibility of using the proposed approach as a basis for further solving the inverse problem of reconstructing the geometry of defects based on magnetic non-destructive testing data.