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Sergey А. Nekrasov, 
South Russian state Polytechnic University (NPI), 
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Abstract
The article is devoted to the methods of nondestructive control of magnetization of permanent magnets on the basis of solving the
inverse problem of magnetostatics. New are the results related to the optimization of the location of the induction measurement points,
including taking into account the differences in the measurement error at different measurement points. According to the practice of
magnetic flaw detection, the influence of the field of external currents was not taken into account. The presence of a ferromagnetic
frame was taken into account. An approach based on the integral equation of magnetostatics is used to identify magnetization. A scalar
magnetic potential is introduced for a stationary field. The corresponding numerical method (cells) is applied to solve the integral equa-
tion of magnetostatics. The volume of magnetic material is divided into cells (elementary parallelepipeds). Within the cell, the magneti-
zation is considered constant. Integrals over the cell region are calculated analytically, and the strength for points outside the volume
of the magnetic material is calculated from the corresponding analytical relations. For Slough regularization, the Tikhonov method based
on minimization of a functional with some regularization parameter is used, which leads to SLOUGH with a square matrix. Due to the
presence of measurement errors, different measurement points are characterized by different information content. The weighted sum
method was used to account for this. The weight factor is taken inversely proportional to the measurement error. The minimized func-
tional in the regularization method in connection with the noted circumstance takes the form of a weighted sum, where the weight
coefficients are inversely proportional to the measurement errors. Identification of magnetization in the region of a rectangular per-
manent magnet located on a ferromagnetic base is considered as a model problem. Optimization of the location of measurement points
is considered. In order to improve the adequacy of the model, the weighted sum method was used. The weight of the term was taken
inversely proportional to the measurement error. The use of optimization and the method of weight coefficients significantly increas-
es the efficiency of the considered technique.