![]() ![]() ![]() Sheinker used the finite element method and the LASSO algorithm to model the magnetic field based on 55 magnetic dipoles uniformly distributed on the surface of the ship model 5. Jeung Giwoo presented an effective method for determining underwater magnetic field anomalies caused by residual magnetization of ferromagnetic hulls using a magnetic dipole modeling technique combined with material sensitivity analysis 16. In recent years, many scholars have carried out relevant research on ship magnetic field modeling. The hybrid ellipsoid and magnetic dipole array model simulates the target magnetic field with high accuracy and is suitable for near-field conditions. 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. Ship magnetic field equivalent source models include single magnetic dipole model 9, 10, 11, 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. 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. The magnetic field equivalent source method is a simple and effective numerical calculation method for ship magnetic field reconstruction compared with the finite element method 5, 6 and boundary element method 7, whose basic principle is to replace the original ferromagnetic objects by using several magnetic sources with analytical solutions, which is widely used because of its advantages of high stability, high accuracy and high computational efficiency 8. The finite element method for simulating and synthesizing ship magnetic field data has the advantage of high accuracy, but the disadvantage is that it needs to measure the complete envelope, which is difficult in practice and has high computational complexity 3, 4. Ship's magnetic field is the disturbed magnetic field generated by ferromagnetic ship disturbing the magnetic field around the earth, and there are four main sources of ship's magnetic field generation 1, 2. The modeling results based on the ship model test data show that the composite model can be used for modeling the magnetic field of ships, and compared with the hybrid model, it reduces the number of coefficient matrix conditions and improves the computational efficiency on the basis of retaining a higher modeling accuracy, and it can be effectively applied in related scientific research and engineering. Finally, a ship model test is designed to compare and analyze the effectiveness of the composite and hybrid models in four aspects: the number of coefficient matrix conditions of the model equation set, the relative error of magnetic field fitting, the relative error of magnetic field extrapolation, and the computational time complexity. Secondly, the set of equations for calculating the magnetic moments of the composite model is established, and for the problem of solving the pathological set of equations, the least-squares estimation, stepwise regression method, Tikhonov, and truncated singular value decomposition regularization methods are introduced in terms of the magnetic field, and generalized cross-validation is used to solve the optimal regularization parameters. First, the improved composite model of the ship's magnetic field is established based on the magnetic dipole array model with 3-axis magnetic moment, the magnetic dipole array model with only x-axis magnetic moment, and the ellipsoid model. In order to simultaneously maintain the ship magnetic field modeling accuracy, reduce the number of coefficient matrix conditions and the model computational complexity, an improved composite model is designed by introducing the magnetic dipole array model with a single-axis magnetic moment on the basis of the hybrid ellipsoid and magnetic dipole array model.
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