The reproduction of magnetic signatures is an important issue concerning the safety of ship traffic, as well as the identification and classification of vessels. Moreover, military applications of magnetic signatures and their reproduction refer to the activation or protection against activation of magnetic naval mines. Previous works on this subject focused on recording and replicating the signatures under the same conditions as those under which they were measured, e.g., on the same ship courses. In this article, much greater capabilities of the multi-dipole model are presented, including simultaneous identification of permanent and induced magnetism. Determining the dipole values using the data from cardinal directions gives the possibility of determining the magnetic field density at any trajectory (position), direction, or depth, with further reconstruction of the entire magnetic field on the basis of residual measurements. For the purpose of this article, a numerical test model of a corvette-type ship has been modelled in Opera simulation software for different geographical positions. The synthetic data from the simulator served as the data source for determining the parameters of the multi-dipole model and the reference data for the verification of the signatures reconstructed for other positions, directions, and depths than those used to determine the model parameters. To determine all permanent magnetization components, data sets were used for two different values of the external magnetic field vertical component. Finally, as a culmination of the demonstration of model universality, the entire magnetic field around the ship was reproduced for different control points on Earth, and for different courses and depths. Investigating the possibility of reconstructing the magnetic signature at a different geographic location than the place where the measurement was made for model synthesis is the main original issue considered in this paper.

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 a new analytical four-layer (air–water–bottom–non-conductive layer) horizontal electric dipole model which allows an accurate approximation of ship's Underwater Electric Potential (UEP) from a sufficient depth in shallow coastal marine waters. The numerical methods, usually Finite Element Method (FEM) or Boundary Elements Method (BEM), are typically used to estimate the electric field and the distribution of static electric components of UEP around the ship. These methods enable analyses with high accuracy but, compared to other point-electrode methods and the proposed analytical model, they are relatively complex and need high computational time. The developed analytical model proposed in this paper allows real-time calculations without significant loss of accuracy of the UEP estimations. In the model, the problem of boundary values at the borders of individual layers is solved using the reflection/image method and applying the idea of continuity of electric potential at a given boundary between two adjacent layers. Its accuracy is verified based on the synthetic data provided by specialised software packages making use of FEM and BEM numerical methods. A dimensionless quantitative analysis of the relationships between basic parameters of the proposed four-layer analytical model and their impact on the accuracy of representation of individual electric field strength components is also delivered. The relationships between water and bottom conductivity and between water depth and bottom thickness are investigated and described. The obtained results show that the developed model allows detailed and reliable analysis of the electric field, especially in shallow coastal waters.

The paper addresses the innovative issue of minimizing the ship's magnetic signature under any external field conditions, i.e., for arbitrary values of ambient field modulus and magnetic inclination. Varying values of the external field, depending on the current geographical location, affect only the induced part of ship's magnetization. A practical problem in minimizing the ship signature is separating permanent magnetization from induced magnetization. When the ship position changes, a signature measurement has to be made under new magnetic field conditions to update the currents in the coils. This is impractical or even difficult to do (due to the need for a measuring ground), so there is a need to predict the ship's magnetization value in arbitrary geographical location conditions based on the reference signature determined on the measuring ground. In particular, the model predicting the signatures at a new geographical location must be able to separate the two types of magnetization, as permanent magnetization is independent of external conditions. In this paper, a FEM model of the vessel is first embedded in an external field and permanent magnetization is simulated using DC coils placed inside the model. Then, using the previously developed rules for data acquisition and determination of model parameters, a multi-dipole model is synthesized in which the induced and permanent parts are separated. The multi-dipole model thus developed has been successfully confronted with the initial model in FEM environment. The separation of permanent and induced magnetization allows the latter to be scaled according to new values of the external field. In the paper, the situation of determining a signature at one geographical position and its projection onto two other positions is analyzed. Having determined the signature with a high degree of accuracy anywhere in the world, it is possible to perform classical signature minimization by determining DC currents in coils placed inside the ship's hull. The paper also analyzes the effectiveness of ship's signature minimization and the influence of ship's course on the signature value. The advantage of the method presented in this paper is an integrated approach to the issue of scaling and minimization of ship magnetic signature, which has not been presented in the literature on such a scale before.