Scalar Potential Formulation and Inverse Problem Applied to Thin Magnetic Sheets

Abstract

Our goal is to identify sheet steel magnetization with near field measurements. Indeed, direct calculation of the whole magnetization is impossible because the remanent part of the magnetization is nondeterminist. Consequently, our strategy is to obtain a magnetostatic formulation able to compute magnetic field as close as possible to the sheet and which is adapted to solve an inverse problem. In this paper, a scalar potential integral formulation is introduced and compared to a magnetization formulation. We are especially interested in the magnetic anomaly created by ferromagnetic ships.Index Terms-Inverse problem, magnetization identification, scalar magnetic potential, thin magnetic sheet.

Comparison of Three Modeling Methods for Identifying Unknown Magnetization of Ferromagnetic Thin Plate

“…where t is the thickness of the hull, l is the edge length of each element, S is the whole hull surface, and r means the displacement vector from the magnetic charge to the observation point [3].…”

“…On the other hand, field calculation due to remanent magnetization depends on the magnetic history of the hull, such as mechanical or thermal stress; accordingly, this falls under an inverse problem because there is lack of information about such history. It is usually difficult to predict the field disturbance around the ship due to remanent magnetization [1][2][3][4][5][6]. To date, a few attempts based on the Tikhonov's regularization have been made [1][2][3].…”

“…It is usually difficult to predict the field disturbance around the ship due to remanent magnetization [1][2][3][4][5][6]. To date, a few attempts based on the Tikhonov's regularization have been made [1][2][3]. However, these methods require a very careful selection of the regularization parameter and the sensor position, and also consume considerable computation time, especially for three-dimensional (3D) inverse problems.…”

Identification of Unknown Remanent Magnetization in the Ferromagnetic Ship Hull Utilizing Material Sensitivity Information Combined with Magnetization Modeling

“…When a ship is placed in the earth's magnetic field, steady-state magnetic signatures are created around the hull. This magnetic anomaly depends on the hull's magnetization, which can be classified as induced and remanent magnetization [1][2][3][4][5][6]. The calculus of the induced magnetization is easy to compute [1,2].…”

“…Normally, it is difficult to predict the field disturbance due to the remanent magnetization accurately because there is no information on such history. To date, a few attempts based on the Tikhonov's regularization have been made [1][2][3] but the method requires a very careful choice of the regularization parameter and also takes considerable computation time particularly for threedimensional (3D) inverse problems.…”