Multi-objective optimization of ship magnetic field modeling method

Abstract

Ship magnetic field modeling is not only beneficial to understanding the characteristics of ship magnetic field, but also can predict the space distribution of ship magnetic field, which has an important application in ship protection and underwater weapons. Aiming at the problems of low modeling accuracy and poor stability in establishing the ship magnetic field hybrid model, a method of establishing a high precision stablity model is proposed in this paper. A hybrid model of magnetic field of a ship is established by using a uniformly magnetized rotating ellipsoid and a magnetic dipole array. Since the number and positions of magnetic dipoles in the hybrid model have an important effect on the modeling accuracy and stability, the fitting error function representing the modeling accuracy and the coefficient matrix condition number function representing the stability of the model are constructed by taking the magnetic dipole parameters as unknown variables. The multi-objective function is constructed by combining the fitting error function with the coefficient matrix conditional number function, which indirectly transforms the modeling problem into a multi-objective optimization problem. The multi-objective function is solved by using the multi-objective particle swarm optimization algorithm, and an optional set of modeling solution results is obtained. In order to select the best results from the optional set, the corresponding selection rules are designed based on the modeling accuracy. The proposed method is validated by the measured data of three kinds of ship models, the modeling results show that the relative error of the model is less than 3%, and the conversion error is less than 6%, which verifies that the proposed method can effectively model the ship magnetic field. Though the measurement data error exists, the modeling solution results from the proposed method have the best stability, which verifies that the modeling method proposed in this work has good stability. Compared with the two existing modeling methods, the proposed method has very good modeling accuracy and stability. Finally, the actual data of a ship on the sea are used for modeling, and the modeling results further verify that the proposed method has high modeling accuracy and conversion accuracy, and can be effectively applied to the relevant projects.

A CGLS-based method for solving magnetic moments of hybrid-model magnetic targets

“…At the same time, the measured magnetic field needs to be extrapolated to other depths. In general, the magnetic target can be equivalent to a hybrid model of ellipsoid and magnetic dipole array [9], as shown in figure 1. The ellipsoid is located in the center of the magnetic target, its long axis is equal to the length of the magnetic target, and its short axis is equal to the width of the magnetic target, which is used to fit the macro magnetic field of the magnetic target.…”

“…Once the location of the magnetic source has been determined, the parameters can be identified based on the magnetic field measurements. The equivalent source models of the magnetic target magnetic field have many models, such as the single magnetic dipole model [1][2][3][4], magnetic monopole model [5], magnetic dipole array model, multi-magnetic dipole model [6][7][8], mono-ellipsoid model, ellipsoid and magnetic dipoles array hybrid model [9], ellipsoid harmonic model [10], and so on. The single magnetic dipole model has few unknown parameters and a small number of calculations, which are suitable for far-field conditions, but it cannot accurately simulate the target magnetic field in the near field.…”

An improved composite ship magnetic field model with ellipsoid and magnetic dipole arrays

“…Ship magnetic field modeling refers to the construction of some kind of model to accurately reflect the spatial distribution law of the ship magnetic field, and at the same time, it is necessary to extrapolate the measured magnetic field to the location of other depths, which can usually be equivalent to the ship as a hybrid model of ellipsoid and magnetic dipole array 14 , in order to further enhance the accuracy of magnetic field simulation on the ship while taking into account the complexity of the model, the introduction of a uniaxial magnetic moment on the basis of the hybrid model of the In order to further improve the magnetic field simulation accuracy of the ship while taking into account the model complexity, the magnetic dipole array model with uniaxial magnetic moment is introduced on the basis of the hybrid model, and the improved composite equivalent source magnetic field model of the ship is designed. Considering that the ship is in a stable and direct sailing state in a short period of time, the ship's intrinsic magnetic field and induced magnetic field can be studied together, so the intrinsic magnetic moment and induced magnetic moment of the magnetic dipole are no longer considered differently.…”

“…The problem of calculating the magnetic moment of a ship's magnetic field model can be regarded as a problem of solving a system of overdetermined Equations. 14 . For the problem of solving the overdetermined equations, the least squares estimation, stepwise regression method 14 , Tikhonov-GCV, and TSVD-GCV regularization methods are used to solve the problem, respectively.…”

“…And the equivalent source method can invert the model parameters based on the magnetic field measurements once the location of the magnetic sources is determined. Ship magnetic field equivalent source models include single magnetic dipole model 9 – 12 , magnetic monopole model 13 , magnetic dipole array model, multiple magnetic dipole model 5 , single ellipsoid model, hybrid ellipsoid and magnetic dipole array model 14 , and long ellipsoid harmonic model 15 . The single magnetic dipole model has fewer unknown parameters, less computational effort, and is suitable for far-field conditions, but cannot accurately simulate the target magnetic field in the near field.…”