Geodesic
Direct and inverse problems of electromagnetic conrol
Sibirskij žurnal industrialʹnoj matematiki, Tome 21 (2018) no. 1, pp. 90-104.

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A mathematic model is suggested of the direct and universe problems of flaw detection. The direct problem consists in determining the complex amplitude of EMF in the through-type-induction-transducer–air gap–ferromagnetic cylinder system. In the direct problem, the distribution laws of magnetic permeability and electrical conduction are assumed to be known. A formula is obtained for calculating the complex amplitude of EMF in the class of piecewise-constant dependences of electromagnetic parameters. The inverse problem of flaw detection for a ferromagnetic cylinder consists in determining the magnetic permeability based on the measured values of the moduli of the EMF amplitudes in the system on a fixed frequency grid. An approximate solution of the inverse problem is searched in the class of piecewise-constant functions. Tikhonov's method of regularization is used to solve the inverse problem. The results of numerical and physical modeling are presented.
Keywords: direct problem of flaw detection, inverse problem of flaw detection, ferromagnetic cylinder, magnetic permeability, piecewise-constant functions, method of regularization. 
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V. N. Stepanov. Direct and inverse problems of electromagnetic conrol. Sibirskij žurnal industrialʹnoj matematiki, Tome 21 (2018) no. 1, pp. 90-104. http://geodesic.mathdoc.fr/item/SJIM_2018_21_1_a8/

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