Mathematical model of recovery of the reduced magnetic moment of a point dipole for identification of ferromagnetic objects
DOI:
https://doi.org/10.15588/1607-6761-2026-1-4Keywords:
magnetic dipole, inverse magnetometry problem, reduced magnetic moment, integral field characteristic, numerical experiment, object identificationAbstract
Purpose of the work. The purpose of the work is to develop and study a mathematical model for restoring the reduced magnetic moment of a point dipole based on the integral characteristics of the magnetic field, which allows to ensure the correct solution of the inverse problem of magnetometry in conditions of limited a priori information and real noise interference.
Research methods. The work uses mathematical modeling, analytical methods of inverse magnetometry, integral transformations and a numerical experiment to assess the accuracy of restoring the magnetic moment components. To construct the calculated dependencies, the field discretization on a rectangular grid of measuring points and algorithms for minimizing the reconstruction error were used.
Results. A generalized model of the relationship between the measured components of magnetic induction and the components of the magnetic moment vector of the dipole was constructed. A mathematical algorithm for calculating the reduced moment based on the sums of the integral characteristics of the field in the coordinate directions was proposed. A study was conducted for different sizes of the measurement grid, which confirmed the efficiency of the method and showed that the reconstruction error decreases with an increase in the number of measurement points. The results obtained indicate the possibility of reliable identification of the object from a limited set of magnetic field data.
Scientific novelty. A method for restoring the reduced magnetic moment is proposed, which is based not on local field values, but on integral characteristics, which provides increased noise resistance and reduces the influence of medium inhomogeneities. The effectiveness of using the discrete-integral approach in inverse magnetometry problems is shown.
Practical value. The developed model can be used in systems for detecting and classifying ferromagnetic objects in underwater, underground and terrestrial environments, in particular in tasks of non-destructive testing, technical diagnostics and search and rescue operations. The proposed approach allows the implementation of small-sized measuring systems with reduced requirements for the accuracy of sensor positioning.
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Copyright (c) 2026 D.U. Shareyko, I.S. Biliuk, O.V. Savchenko, V.А. Marziavko, A.M. Todosienko
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