Наталья Алексеевна Евдокимова, старший преподаватель, кафедра ≪Математический анализ≫, Южно-Уральский государственный университет (г. Челябинск, Российская Федерация), naevdok@math.susu.ac.ru. N.A. Evdokimova, South Ural State University (Chelyabinsk, Russian Federation). Дмитрий Витальевич Лукьяненко, кандидат физико-математических наук, кафедра ≪Математика≫, Физический факультет, Московский государственный университет имени М.В. Ломоносова(г. Москва, Российская Федерация), lukyanenko@physics.msu.ru. D.V. Lukyanenko, M.V. Lomonosov Moscow State University (Moscow, Russian Federation). Анатолий Григорьевич Ягола, доктор физико-математических наук, профессор, кафедра ≪Математика≫, Физический факультет, Московский государственный университет имени М.В. Ломоносова(г. Москва, Российская Федерация), yagola@physics.msu.ru. A.G. Yagola, M. V. Lomonosov Moscow State University (Moscow, Russian Federation)
Abstract Recovery of magnetic target parameters from magnetic sensor measurements has attracted wide interests and found many practical applications. However, difficulties present in identifying the permanent magnetization due to the complications of magnetization distributions over the ship body, and errors and noises of measurement data degrade the accuracy and quality of the parameter identification. In this paper, we use a two step sequential solutions to solve the inversion problem. In the first step, a numerical model is built and used to determine the induced magnetization of the ship. In the second step, we solve a type of continuous magnetization inversion problem by solving 2D Fredholm integral equation of the 1st kind. We use parallel computing which allows solve the inverse problem with high accuracy. In additional, Tikhonov regularization has been applied in solving the inversion problems. The proposed methods have been validated using simulation data with added noises.
Inversion of ill-posed problem from measurement data have been proposed use: i) Conjugate gradient projection method with regularization; ii) Conditional gradient method with regularization; iii) SVD with constraints with regularization method and iv) The method for solving two-dimensional integral equation of convolution type for vector functions using DFT method for Tikhonov functional. The performance of the proposed approach is demonstrated using simulated data with added noises.
