Reconstruction of the shape of a flaw in ferromagnetic plate by solving inverse problem of magnetostatics and series of direct problems

The article presents a verification technique for solving the inverse geometric problem of magnetostatics in a soft magnetic ferromagnet plate. The technique involves solving a number of direct problems, in which the shape of the defect obtained by solving the inverse geometric problem of magnetostatics is used as a first approximation, and then increasing or decreasing the depth of the defect without changing the shape of the boundary surface — comparing the topographies of the magnetic field components obtained during measurements above the plate surface and calculated (as a result of solving the direct problem) at the same points of the components of the magnetic stray field from the reconstructed three-dimensional defect. As a result of applying the technique, the geometric parameters of the defect under study can also be refined. Obtaining the initial conditions for solving the inverse problem and solving direct problems of magnetostatics is carried out using the finite element method in the ELMER program. The technique works with one-sided access to any surface of the plate (a defect-free surface or a surface with a defect).