Rafael Psiuk, Alisa Artizada, Daniel Cichon, Hartmut Brauer, Hannes Toepfer and Albert Heuberger
This paper aims to provide a flexible model for a system of inductively coupled loops in a quasi-static magnetic field. The outlined model is used for theoretical analyses on the…
Abstract
Purpose
This paper aims to provide a flexible model for a system of inductively coupled loops in a quasi-static magnetic field. The outlined model is used for theoretical analyses on the magnetic field-based football goal detection system called as GoalRef, where a primary loop generates a magnetic field around the goal. The passive loops are integrated in the football, and a goal is deduced from induced voltages in loop antennas mounted on the goal frame.
Design/methodology/approach
Based on the law of Biot–Savart, the magnetic vector potential of a primary current loop is calculated. The induced voltages in secondary loops are derived by Faraday’s Law. Expressions to calculate induced voltages in elliptically shaped loops and their magnetic field are also presented.
Findings
The induced voltages in secondary loops close to the primary loop are derived by either numerically integrating the primary magnetic flux density over the area of the secondary loop or by integrating the primary magnetic vector potential over the boundary of that loop. Both approaches are examined and compared with respect to accuracy and calculation time. It is shown that using the magnetic vector potential instead of the magnetic flux density can decrease the processing time by a factor of around 100.
Research limitations/implications
Environmental influences like conductive or permeable obstacles are not considered in the model.
Practical implications
The model can be used to investigate the theoretical behavior of inductively coupled systems.
Originality/value
The proposed model provides a flexible, fast and accurate tool for calculations of inductively coupled systems, where the loops can have arbitrary shape, position and orientation.
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Keywords
Eva-Maria Dölker, Bojana Petković, Reinhard Schmidt, Marek Ziolkowski, Hartmut Brauer and Jens Haueisen
Lorentz force evaluation is a non-destructive evaluation method for conducting specimens. The movement of a specimen relative to a permanent magnet leads to Lorentz forces that…
Abstract
Purpose
Lorentz force evaluation is a non-destructive evaluation method for conducting specimens. The movement of a specimen relative to a permanent magnet leads to Lorentz forces that are perturbed in the presence of a defect. This defect response signal (DRS) is used for defect reconstruction. To solve a linear inverse problem for defect reconstruction, an accurate and fast forward computation method is required. As existing forward methods are either too slow or too inaccurate, the purpose of this paper is to propose the single voxel approach (SVA) as a novel method.
Design/methodology/approach
In SVA, the DRS is computed as a superposition of DRSs from single defect voxels, which are calculated in advance, by applying the boundary element source method. This research uses a setup of an isotropic conducting specimen, a spherical permanent magnet and defects of different shapes at different depths. With the help of simulations, this study compares the SVA to the previously proposed approximate forward solution (AFS) and the extended area approach (EAA) using the normalized root mean square error (NRMSE). Simulated data using the finite element method serve as the reference solution.
Findings
SVA shows across all simulations NRMSE values <2.5 per cent compared to <8 per cent for EAA and <12 per cent for AFS.
Originality/value
The superposition principle of SVA allows for the application of linear inverse methods for defect reconstruction while providing sufficient accuracy of the forward method.
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Marek Ziolkowski, Hartmut Brauer and Milko Kuilekov
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…
Abstract
Purpose
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.
Design/methodology/approach
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.
Findings
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.
Originality/value
This paper describes a new technique for the analysis of electromagnetic field which can be also applied in other problems.
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Hartmut Brauer, Marek Ziolkowski and Milko Kuilekov
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…
Abstract
Purpose
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.
Design/methodology/approach
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.
Findings
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.
Originality/value
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.
Details
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Hartmut Brauer, Marek Ziolkowski, Uwe Tenner, Jens Haueisen and Hannes Nowak
Applies four different minimum norm estimations with common regularization techniques, often used in biomedical applications to the solution of the biomagnetic inverse field…
Abstract
Applies four different minimum norm estimations with common regularization techniques, often used in biomedical applications to the solution of the biomagnetic inverse field problem. Magnetic field data measured with a multi‐channel biomagnetometer sensor system in a magnetically shielded room were used to reconstruct the current density distributions generated by an extended current source which was placed inside a human torso phantom. No one of the tested methods is able to estimate the extension of the source. To improve the results as much as possible a priori information of the source space should be taken into account.
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Hartmut Brauer, Konstantin Porzig, Judith Mengelkamp, Matthias Carlstedt, Marek Ziolkowski and Hannes Toepfer
The purpose of this paper is to present a novel electromagnetic non-destructive evaluation technique, so called Lorentz force eddy current testing (LET). This method can be…
Abstract
Purpose
The purpose of this paper is to present a novel electromagnetic non-destructive evaluation technique, so called Lorentz force eddy current testing (LET). This method can be applied for the detection and reconstruction of defects lying deep inside a non-magnetic conducting material.
Design/methodology/approach
In this paper the technique is described in general as well as its experimental realization. Besides that, numerical simulations are performed and compared to experimental data. Using the output data of measurements and simulations, an inverse calculation is performed in order to reconstruct the geometry of a defect by means of sophisticated optimization algorithms.
Findings
The results show that measurement data and numerical simulations are in a good agreement. The applied inverse calculation methods allow to reconstruct the dimensions of the defect in a suitable accuracy.
Originality/value
LET overcomes the frequency dependent skin-depth of traditional eddy current testing due to the use of permanent magnets and low to moderate magnetic Reynolds numbers (0.1-1). This facilitates the possibility to detect subsurface defects in conductive materials.
Details
Keywords
Hartmut Brauer, Marek Ziolkowski, Matthias Dannemann, Milko Kuilekov and Denis Alexeevski
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…
Abstract
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.
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Mehbub‐ur Rahman and René Marklein
The purpose of this paper is to present a time‐domain technique to compute the electromagnetic wave field and to reconstruct the permittivity and electric conductivity profile of…
Abstract
Purpose
The purpose of this paper is to present a time‐domain technique to compute the electromagnetic wave field and to reconstruct the permittivity and electric conductivity profile of a one‐dimensional slab of finite length.
Design/methodology/approach
The forward scattering problem is solved by a Green's function formulation to generate synthetic data that are used as a testbed for the inversion scheme. The inverse scattering problem is solved by reconstructing the unknown permittivity and electric conductivity profile of the medium with the help of an invariant embedding method.
Findings
The Green's operator maps the incident field on either side of the medium to the field at an arbitrary observation point inside the slab and hence, the internal fields can be computed directly without computing the wave field throughout the entire medium. The invariant embedding method requires a finite time trace of reflection data and therefore it is suitable for reconstructing the material parameters in real‐time.
Practical implications
The implemented methods have been validated against synthetic and measured time domain reflectometry data.
Originality/value
This paper fulfils an identified need to determine unknown one‐dimensional profiles and thus plays an important role in electromagnetics, non‐destructive testing, and geophysics.
Details
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P. Di Barba and M.E. Mognaschi
The purpose of the paper is to show that the a posteriori analysis of the Pareto front associated with a given design problem facilitates the task of the decision maker and…
Abstract
Purpose
The purpose of the paper is to show that the a posteriori analysis of the Pareto front associated with a given design problem facilitates the task of the decision maker and possibly helps to identify innovative solutions. The idea is to investigate the similarities existing among non‐dominated solutions.
Design/methodology/approach
A permanent‐magnet alternator for automotive applications is considered as case study. The design problem exhibits six design variables and two energy‐related objective functions. A suitable sampling of the objective space is made and non‐dominated solutions, located along an L‐shaped front, are approximated. Results are assessed by means of a successive optimization using NSGA‐II algorithm.
Findings
From the approximated Pareto front, three optimal devices have been selected and remapped in the design space in order to compare their performance. This is done in terms of iron and copper losses, material costs, rated voltage, and air‐gap induction. Moreover, making the NSGA‐II start from the knee‐point of the front, it is shown that a direct approximation of the two sub‐fronts is possible.
Originality/value
In this paper, a method to sort out the optimal solutions located along the Pareto front is proposed as a possible criterion of decision making; so doing, previously unpredicted solutions might be identified.