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The article presents a continuation of the research on the 3D multi-dipole model applied to the reproduction of magnetic signatures of ferromagnetic objects. The model structure has been modified to improve its flexibility - model parameters determined by optimization can now be located in the cuboid contour representing the object’s hull. To stiffen the model, the training dataset was expanded to data collected from all four cardinal directions. The robustness of the modified multi-dipole model was verified with various noise levels applied to the synthetic data. A comprehensive numerical verification of the proposed methodology was performed using only data not involved in determining the modified multi-dipole model parameters: the data from intercardinal directions and from different depth were used for cross-validation. An analysis of the influence of initial conditions on the optimization process was carried out. In addition to the gradient optimization method, an evolutionary strategy was also used. Regularization was carried out to search for effective model parameterization. New verification methods were also applied based on the balance of magnetic moments and on the average width of the fit error interval. The results of the performed experiments have shown high robustness of the modified multi-dipole model, even in the face of high noise in the input data. The most significant advantage of the model is its predictive ability, enabling determination of magnetic signatures in any directions and depths with high accuracy.

The paper presents the construction of a multi-dipole model that allows reproducing magnetic signatures of ferromagnetic objects. The virtual object used in the paper is an ellipsoid, which is the source of synthetic data. To make the situation more realistic, noise is added to the synthetic data. Two significant improvements compared to previous work are presented. Three-axial magnetometers are introduced instead of uniaxial magnetometers. However, a more important change is the modification of the model structure that allows placing dipoles on the entire plane, e.g. object's deck. The multi-dipole model consists of an a priori assumed number of permanent and induced single-dipole models. Each single dipole is described by three magnetic moments and, depending on the applied approach, one or two dipole position parameters. The non-linear least-squares optimization method is used to determine model parameters. To assess the quality of magnetic signature reproduction, qualitative and quantitative forms are used. The final quality assessment is based on differences between the reference fields and the fields determined from the multi-dipole model. The applied modifications bring significant improvement, however, only their combined application allows to restore magnetic signatures with good quality for directions other than for which the data were available.