Solving the Inverse Geometric Problem of Magnetostatics for Corrosion Defects with Allowance for Nonlinear Properties of Ferromagnet

Abstract—A method is proposed for solving the inverse problem of magnetostatics with allowance for a nonlinear dependence of the relative magnetic permeability of a ferromagnet on the applied external field. The method has been investigated for metal loss defects located on the ferromagnetic-plate side opposite to magnetic transducers, without imposing any conditions on defect shape. The ferromagnetic plate is magnetized in the direction of the abscissa axis; the dependence of the magnetic induction of metal on the applied external magnetic field corresponds to a nonlinear segment of the magnetization curve. The problem has been solved for the three-dimensional case. Defects were simulated and the direct problem was solved with software developed by the authors in FORTRAN language. The program for constructing lines of force and solving the inverse problem of reconstructing magnetic field components was written using the Scilab package of applied mathematical programs.