Magnetic dipole modeling combined with material sensitivity analysis for solving an inverse problem of thin ferromagnetic sheet

This paper presents an efficient methodology for determining the underwater field anomaly due to the remanent magnetization of a ferromagnetic ship hull by utilizing a magnetic dipole modeling technique combined with material sensitivity analysis. The complicated 3D structure of the hull is replaced with an equivalent magnetic dipole array placed in a 2D plane, of which the optimal dipole moment values will be easily sought out with the aid of material sensitivity analysis. To achieve this, a material sensitivity formula, which contains the first-order gradient information of an objective function with respect to the magnetic dipoles, is analytically derived by exploiting the augmented objective function and adjoint variable method. The proposed method leads to easy numerical implementation and also dramatically reducing system unknowns of the 3D inverse problem considered. Finally, the validity of the method has been tested with real measurements of a scale model ship as well as numerical results of our previous work, which adopted the magnetic charge method in conjunction with material sensitivity analysis.