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To provide a new semi‐analytical procedure which is much faster than FEM and for this reason can be applied in a reconstruction of an interface between two conducting fluids (magnetic fluid dynamics problem) by means of magnetic field tomography.

Three approaches are compared: a simple analytical solution (AS1), a modified semi‐analytical solution (AS2), and the finite element method solution. The modified semi‐analytical approach takes into account an information about azimuthal spatial harmonics received from the Fourier analysis of magnetic flux density distributions calculated by FEM. AS1 and AS2 have been compared for different modes of the interface using FEM solution as a reference.

It is shown that for small perturbations the AS2 in every case provides smaller errors than AS1 although for some modes (14,24) the quality of the solution is still not satisfactory.

This paper describes a new technique for the analysis of electromagnetic field which can be also applied in other problems.

The interface between two conducting fluids in a magnetic fluid dynamics (MFD) problem was identified by means of external magnetic field measurements. Genetic algorithms (GA) were applied to solve the inverse problem.The principal component analysis (PCA) was used to speed up the process of interface reconstruction.

With respect to the experimental results we have designed a general technique for mode identification and/or interface reconstruction. Two main procedures are available to solve the inverse problem, the full interface reconstruction and the principle component analysis (PCA) mode. In the case of full reconstruction, it can be decided whether an algorithm for fast identification of the dominant modes applying a FFT module should be performed or not. The full interface reconstruction applies stochastic optimization methods ((GA) or evolution strategies (ES)) for the estimation of the interface shape characteristics. The main goal of the PCA mode is to find the dominant mode of the interface shape and its amplitude. The PCA mode is realized by means of stochastic optimization methods (GA, ES) and a simple direct searching (DS) using the golden section technique.

PCA with GA procedure enables the identification of the dominant mode of the interface shape between two conducting fluids with sufficient accuracy for simulated magnetic fields. Time of identification is strongly reduced due to a redefinition of the genotype representations in the PCA mode. Accuracy of reconstruction depends on the noise level, i.e. signal to noise ratio and a geometrical model used in the reconstruction phase. The correlation between the noise level and values of cost function for identified modes has been found if a proper geometry modelling is applied.

The paper describes a new, fast technique for solving an inverse field problem of a MFD problem where the interface between two conducting fluids has to be identified using a magnetic field tomography measuring system.

In many industrial applications of magnetic fluid dynamics it is important to control the motion of the surface of liquids. In aluminium electrolysis cells, large surface deformations of the molten aluminium are undesired, and it would be useful to have the possibility to recognize the surface deviation. This includes the problem of reconstructing a free boundary between the conducting fluids. We have investigated how the interface between two fluids of different conductivity assumed in a highly simplified model of an aluminium electrolysis cell could be reconstructed by means of external magnetic field measurements. Forward simulations of the magnetic field generated by the impressed current are done by applying the FEM software code FEMLAB. Several interface shapes which can be realized in experiments are investigated and a strategy for identifying the main interface characteristics using magnetic field measurements as an initial guess to the solution of the inverse problem is proposed.