Electrical engineering & Electromechanics (May 2025)
Simplified method for analytically determining the external magnetostatic field of uncertain extended technical objects based on near-field measurements
Abstract
Introduction. An important scientific and technical problem of magnetism of uncertain extended energy-saturated objects - such as naval vessels and submarines is implementation of strict requirements for magnetic silence based on mathematical modeling of magnetic field, adequate to its real measurements. The purpose of the work is to develop a simplified analytical method for determining the external magnetostatic field of extended technical objects with uncertain magnetic field sources based on near-field measurement data using spherical and spheroidal sources in a Cartesian coordinate system. Methodology. Forward problems of magnetostatics solved based on developed method of analytical calculation of magnetostatic field induction of spherical and spheroidal sources in Cartesian coordinate system based on near-field measurements. Geometric inverse problems of magnetostatics for solving prediction and control problems of magnetic silence of technical object calculated based on vector games solution. Both vector games payoff calculated as forward problems solutions Wolfram Mathematica software package used. Results. The results of prediction of magnetic field magnitude in far zone of extended technical objects based on designed multispheroidal magnetic field model in form of spatial elongated spheroidal harmonics in prolate spheroidal coordinate system and in form of multispherical magnetic field model in form of spatial spherical harmonics in spherical coordinate system using measurements near field and taking into account magnetic characteristics uncertainty of extracted technical objects. Originality. For the first time, a method of simplifying the mathematical modeling of the magnetic field of an uncertain long energy- saturated object developed based on development and application of method of analytical calculation of induction of magnetostatic fields of spherical and spheroidal sources in the Cartesian coordinate system. Unlike known methods developed method allows modeling magnetic field directly in Cartesian coordinate system based on near-field measurements without finding magnetic induction projection in prolate spheroidal coordinate system and in spherical coordinate system without their translation from prolate spheroidal coordinate system and in spherical coordinate system in Cartesian coordinate system and vice versa. Practical value. The possibility of a more than 10 times calculation time reduction of magnetic field induction of magnetic field elongated spheroidal sources and the possibility of a more than 4 times calculation time reduction of magnetic field induction of magnetic field spherical sources when magnetic field calculating of uncertain extended energy-saturated object based on development and application of analytical calculation method of magnetostatic field induction of spherical and spheroidal sources in the Cartesian coordinate system based on near-field measurements shown. References 50, tables 2, figures 4.
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