Review of Methods for Solving Inverse Problems of Identification of the Magnetization of Permanent Magnets in Electrical Devices

Abstract

The article shows the need for identification of permanent magnets by studying the distribution of magnetization over their volume by solving inverse problems. The main approaches to solving inverse problems are considered: minimization of some functional and multiple solution of the direct problem of calculating the magnetic field; solution of an ill-posed problem and determination, using regularization methods, of a pseudosolution that is stable to small perturbations. An overview of the work performed aimed at improving the theoretical and practical approaches to solving these problems is given. New mathematical models and methods for calculating the magnetic field have been developed, which provide a decrease in the number of unknown parameters, an improvement in stability and a decrease in time consumption in the problems of identifying the magnetization of permanent magnets in electrical devices. The influence of the experimental data error on the solution result is estimated. Examples of solving test problems and experimental studies are given, which have shown the effectiveness of the proposed methods and approaches. The results obtained can also be used to solve direct and inverse problems of electrical engineering.