Magnetic Signature Description of Ellipsoid-Shape Vessel Using 3D Multi-Dipole Model Fitted on Cardinal Directions

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.