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Cutting stresses introduced by punching influence the magnetic characteristics of electrical steels. A nondestructive experimental method used for measuring flux distributions in laminations is the needle probe method. The probe signals can be simulated by solving the two-dimensional nonlinear diffusion equation for the magnetic field in combination with a proper Preisach model. The Preisach parameters in several subregions of the steel sheet which best fit the input probe signals are obtained by solving the inverse problem. The method used for minimizing the cost function is the space mapping technique. This technique combines the fine model, which uses the finite element method, with a semianalytical coarse model, which reduces the nonlinear problem to a linear problem.