Bojana Petkovć, Marek Ziolkowski, Hannes Toepfer and Jens Haueisen
The purpose of this paper is to derive a new stress tensor for calculating the Lorentz force acting on an arbitrarily shaped nonmagnetic conductive specimen moving in the field of…
Abstract
Purpose
The purpose of this paper is to derive a new stress tensor for calculating the Lorentz force acting on an arbitrarily shaped nonmagnetic conductive specimen moving in the field of a permanent magnet. The stress tensor allows for a transition from a volume to a surface integral for force calculation.
Design/methodology/approach
This paper derives a new stress tensor which consists of two parts: the first part corresponds to the scaled Poynting vector and the second part corresponds to the velocity term. This paper converts the triple integral over the volume of the conductor to a double integral over its surface, where the subintegral functions are continuous through the different compartments of the model. Numerical results and comparison to the standard volume discretization using the finite element method are given.
Findings
This paper evaluated the performance of the new stress tensor computation on a thick and thin cuboid, a thin disk, a sphere and a thin cuboid containing a surface defect. The integrals are valid for any geometry of the specimen and the position and orientation of the magnet. The normalized root mean square errors are below 0.26% with respect to a reference finite element solution applying volume integration.
Originality/value
Tensor elements are continuous throughout the model, allowing integration directly over the conductor surface.
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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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Keywords
Roland Eichardt, Daniel Strohmeier, Alexander Hunold, René Machts, Jens Haueisen, Gregor Oelsner, Christian B. Schmidt, Volkmar Schultze, Ronny Stolz and Uwe Graichen
The purpose of this paper is to present a simulation study using a model of a new optically pumped magnetometer sensor for application in the field of magnetoencephalography. The…
Abstract
Purpose
The purpose of this paper is to present a simulation study using a model of a new optically pumped magnetometer sensor for application in the field of magnetoencephalography. The effects of sensor distance and orientation on the measurement information and the sensitivity to neuronal sources are investigated. Further, this paper uses a combinatorial optimization approach for sensor placement to measure spontaneous activity in the region of the occipital cortex.
Design/methodology/approach
This paper studies the effects of sensor distance and orientation on sensitivity to cortical sources and measurement information. A three-compartment model of the head, using the boundary element method, is applied. For sensor setup optimization, a combinatorial optimization scheme is developed.
Findings
The sensor distance to sources considerably affects the sensitivity and the retrieved information. A specific arrangement of four sensors for measuring spontaneous activity over the occipital part of the head is optimized by effectively avoiding position conflicts.
Research limitations/implications
Individual head models, as well as more detailed noise and signal models, will increase the significance for specific-use cases in future studies.
Originality/value
Effects of sensor distance and orientation are specifically evaluated for a new optically pumped magnetometer. A discrete optimization scheme for sensor optimization is introduced. The presented methodology is applicable for other sensor characterization and optimization problems. The findings contribute significantly to the development of new sensors.
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Roland Eichardt, Daniel Baumgarten, Luca Di Rienzo, Sven Linzen, Volkmar Schultze and Jens Haueisen
The purpose of this paper is to examine the localisation of ferromagnetic objects buried in the underground. More specifically, it deals with the reconstruction of the…
Abstract
Purpose
The purpose of this paper is to examine the localisation of ferromagnetic objects buried in the underground. More specifically, it deals with the reconstruction of the XY‐positions, the depths (Z‐positions), the number, and the extension of the objects based on geomagnetic measurements. This paper introduces a minimum‐norm reconstruction approach and evaluates its performance in a simulation study.
Design/methodology/approach
A minimum‐L2‐norm estimation based on the truncated singular value decomposition method with lead field weighting is proposed in order to localise geomagnetic sources. The sensor setup and positions are taken from real measurements. The source space is formed by an automatically generated grid. At each grid point, a magneto‐static dipole is assumed.
Findings
Sources with different depths and XY‐positions could be successfully reconstructed. The proposed approach is not overly sensitive to errors/noise in measurement values and sensor positions.
Originality/value
The approach described in this paper can be used for applications like geoprospection, archaeology, mine clearing, and the clean‐up of former waste deposits.
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Luca Di Rienzo and Jens Haueisen
To define a methodology for comparing sensor arrays for solving magnetostatic linear inverse problems.
Abstract
Purpose
To define a methodology for comparing sensor arrays for solving magnetostatic linear inverse problems.
Design/methodology/approach
A singular value decomposition related projection method is used for comparing sensor arrays and we applied it to a biomagnetic inverse problem, as an example. Furthermore, a theoretical reference sensor system is introduced and used as a benchmark for the analysed sensor arrays.
Findings
The method has turned out to be effective in comparing three different theoretical sensor arrays, showing the superiority of the two arrays constituted by three‐axial sensors.
Research limitations/implications
The method has been applied only to the case of over‐determined problems. The underdetermined case will be considered in future work.
Practical implications
From the applicative point of view, the illustrated methodology is useful when one has to choose between existing sensor arrays or in the design phase of a new sensor array.
Originality/value
A new methodology is proposed for comparing sensor arrays. The advantage of the methodology are to take into account the regularization in the solution of the inverse problem and to be general, not depending on a particular source configuration.
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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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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.
Details
Keywords
Luca Di Rienzo, Jens Haueisen and Cesare Mario Arturi
To demonstrate the improvement of three‐axial magnetic sensors systems for magnetocardiography when using minimum norm solutions (MNS).
Abstract
Purpose
To demonstrate the improvement of three‐axial magnetic sensors systems for magnetocardiography when using minimum norm solutions (MNS).
Design/methodology/approach
The thesis is proved by using figures of merit and by means of repeated numerical simulations, starting from a BEM model for forward calculations.
Findings
We found out that both for under‐determined and over‐determined problems two figures of merit show better performance of a three‐axial sensor system when compared with two mono‐axial sensor systems. We also showed the positive impact of three component magnetic field data on MNS by means of repeated simulations.
Research limitations/implications
The analysis is limited to theoretical sensor systems and can be applied also to realistic measurement set‐ups. Noise is considered uncorrelated. The analysis could be carried out with the help of other figures of merit. More refined models for the human body could be adopted.
Practical implications
The use of three axial sensor systems is encouraged in the field of magnetocardiography.
Originality/value
Numerical analysis of inversion algorithms using three‐dimensional magnetic field data in magnetocardiography have been never carried out.