In this paper we compare results of calculations and measurements made for different objects bein... more In this paper we compare results of calculations and measurements made for different objects being tested with magnetic induction tomography system developed and constructed at the
... 4. REFERENCES 1 MVKChari, TGKincaid, "Finite-Element Analysis of Eddy-Current Flaw D... more ... 4. REFERENCES 1 MVKChari, TGKincaid, "Finite-Element Analysis of Eddy-Current Flaw Detection," Eddy-Current Characterization of Materials and Structures, ASTM STP 722, George Birnbaum and George Free, Eds., American Society for Testing and Materials (1981) 59. ...
ABSTRACT Magnetic induction tomography (MIT) is a non-invasive technique for mapping the electric... more ABSTRACT Magnetic induction tomography (MIT) is a non-invasive technique for mapping the electrical properties of tissues. MIT is based on the measurement of perturbations of an alternating magnetic excitation field by the eddy currents induced in a conducting object exposed to the field. In this paper a simulation study of MIT is presented. Different aspects of using the finite element method to solve the 3-D MIT forward problem, which is a precondition of the inverse problems, are discussed.
ABSTRACT The authors have developed a differential type rotational magnetic flux sensor for detec... more ABSTRACT The authors have developed a differential type rotational magnetic flux sensor for detection of a miner reverse-side crack. An equivalent magnetic circuit of the sensor was developed to simplify theoretical analysis. The magnetic circuit showed good agreement with the results of experiments. In this paper, validity of this equivalent magnetic circuit is described.
ABSTRACT In this work, the general form of the solution to Laplace's equation is used to ... more ABSTRACT In this work, the general form of the solution to Laplace's equation is used to derive two formulations of asymptotic boundary conditions (ABC's) suitable for the finite element modeling of axisymmetric electrical field problems with open boundaries. The first formulation works for an arbitrary shape of the finite element region. However, it produces nonsymmetrical matrices. The second formulation works for rectangular outer boundaries and produces symmetric matrices. Both the formulations produce closed-form expressions for the elemental boundary matrices. A simple problem of electrostatic potential is solved as an example
COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 1998
The eddy current method of non-destructive testing uses an alternating current excitation to indu... more The eddy current method of non-destructive testing uses an alternating current excitation to induce secondary currents in a specimen under test. Flaws within the specimen affect the induced currents, causing changes in the impedance of a test coil. In this paper we present a method for obtaining a solution of inverse problems, in which the parameters of defects are unknown
COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 1998
The Faculty of Electrical Engineering at the Technical University of Szczecin, Poland, provides e... more The Faculty of Electrical Engineering at the Technical University of Szczecin, Poland, provides education and training at a technical level as well as up to the Master of Science degree. Electromagnetics and applications are fundamental to electrical engineering and play an important role in the faculty’s curriculum. Because of the vast amount of material to be covered, the essential problem is an appropriate choice of topics. Special care needs to be taken while teaching basic concepts and principles, but nowadays also computer-aided methods. After many years of experience in teaching electromagnetics the authors have proposed new programmes for teaching the subject within the courses offered by the faculty. Some aspects of these programmes are described in the paper.
COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 1992
This paper presents the practical configuration for detecting cracks in material, by applying an ... more This paper presents the practical configuration for detecting cracks in material, by applying an electromagnetic field along the largest dimension of the crack. An electromagnetic field formulation is proposed using Helmholtz's equation and Biot‐ Savart's law. The system equation is solved by using the finite element method (FEM). The exemplary results of calculation ‐ eddy currents lines in material and relative resistance versus probe position are presented.
Purpose-The purpose of this paper is to develop a magnetic induction tomography (MIT) system as w... more Purpose-The purpose of this paper is to develop a magnetic induction tomography (MIT) system as well as the conductivity reconstruction algorithms (inverse problem). Design/methodology/approach-In order to define and verify the solution of the inverse problem, the forward problem is formulated using mathematical model of the system. The forward problem is solved using the finite element method. The optimization of the excitation unit is based on the numerical solutions of the direct problem. All the dimensions and shape of the excitation system are optimized in order to focus the main part of the magnetic field in the vicinity of the receiver. Finally, two formulations of the inverse problem are discussed: based on the inversion of the Biot-Savart law; and based on the artificial neural networks. Findings-The formulation of the forward problem of the considered MIT system is given. The construction of the exciter unit that focuses the main part of the magnetic field in the vicinity of the receiver is proposed. Two formulations of the inverse problem are discussed. First using the inversion of the Biot-Savart law and second using the artificial neural network. The neural networks seem to be promising tools for reconstructing the MIT images. Originality/value-This paper demonstrates a real-life MIT system whose performance is satisfactorily predicted by mathematical models. The original design of the exciter is shown. The new approach to the inverse problem in MIT-the use of the artificial neural network-is presented.
New infinite elements which can be used for a solution of axisymmetric magnetic problems with ope... more New infinite elements which can be used for a solution of axisymmetric magnetic problems with open boundaries are presented. It is supposed that the new elements are being developed for the vector potential A(r,z) and the modified vector potential rA formulation. The elements can represent any type of decay towards infinity, and the element matrix when the decay function is 1/ rho /sup n/, n>or=1, rho /sup 2/=r/sup 2/+z/sup 2/ is given explicity. Standard finite elements for the rA formulation yield very inaccurate results near r=0. The introduction, close to the symmetry axis, of so-called axial elements with special shape functions is proposed. The formulation is so simple that closed-form expressions for the element matrix are obtained. Numerical results are presented for a problem having an analytical solution. >
COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 1995
A basic difficulty encountered in applying the finite element method to unbounded wave problems i... more A basic difficulty encountered in applying the finite element method to unbounded wave problems is that the domain in which the field is to be computed is unbounded, while finite element models are of finite size. There are several ways to overcome this difficulty. The widely used method is to truncate the finite element model at a finite position and apply suitable boundary conditions there. The relevant boundary conditions must absorb the outgoing wave and have been called absorbing boundary conditions (ABC's).
In this paper authors propose an eddy current probe, which is suitable for inspection of low cond... more In this paper authors propose an eddy current probe, which is suitable for inspection of low conductivity structures. The probe consists of an excitation coil and two differentially connected search coils. The detection circuit was designed in this way that a resonance for an operating frequency was obtained. It creates possibility to achieve a high sensitivity of the measuring system.
Contrary to what Dickerson and Mottmann [Am. J. Phys. 84, 413-418 (2016)] state, the temperatures... more Contrary to what Dickerson and Mottmann [Am. J. Phys. 84, 413-418 (2016)] state, the temperatures at which a refrigerator's working fluid absorbs heat need not always lie below those at which it expels heat; nor must a refrigerator's thermodynamic cycle have two adiabats. Moreover, what Dickerson and Mottmann call a "comparison Carnot cycle" cannot always be defined. These conclusions are illustrated here using a counterclockwise Stirling cycle without regeneration. A refrigerator's cold reservoir can absorb some heat and its hot reservoir can expel some heat, so long as the net heat flow is still out of the cold reservoir and into the hot reservoir.
International Journal of Applied Electromagnetics and Mechanics
Magnetic induction tomography, highly promising imaging technique for medical purposes, applies a... more Magnetic induction tomography, highly promising imaging technique for medical purposes, applies a magnetic field from an exciter to induce eddy currents in the object of low conductivity, and the magnetic field from these is then detected by a sensor. The induced eddy currents are proportional to the conductivity distribution. This paper deals with the solution of the fundamental inverse problem existing in magnetic induction tomography, which consists in the reconstruction of the eddy currents distribution basing on the magnetic field measurements. The problem has been solved by the Tikhonov regularization method. The choice of the regularization parameter and the accuracy of the proposed method have also been discussed.
In this paper we compare results of calculations and measurements made for different objects bein... more In this paper we compare results of calculations and measurements made for different objects being tested with magnetic induction tomography system developed and constructed at the
... 4. REFERENCES 1 MVKChari, TGKincaid, "Finite-Element Analysis of Eddy-Current Flaw D... more ... 4. REFERENCES 1 MVKChari, TGKincaid, "Finite-Element Analysis of Eddy-Current Flaw Detection," Eddy-Current Characterization of Materials and Structures, ASTM STP 722, George Birnbaum and George Free, Eds., American Society for Testing and Materials (1981) 59. ...
ABSTRACT Magnetic induction tomography (MIT) is a non-invasive technique for mapping the electric... more ABSTRACT Magnetic induction tomography (MIT) is a non-invasive technique for mapping the electrical properties of tissues. MIT is based on the measurement of perturbations of an alternating magnetic excitation field by the eddy currents induced in a conducting object exposed to the field. In this paper a simulation study of MIT is presented. Different aspects of using the finite element method to solve the 3-D MIT forward problem, which is a precondition of the inverse problems, are discussed.
ABSTRACT The authors have developed a differential type rotational magnetic flux sensor for detec... more ABSTRACT The authors have developed a differential type rotational magnetic flux sensor for detection of a miner reverse-side crack. An equivalent magnetic circuit of the sensor was developed to simplify theoretical analysis. The magnetic circuit showed good agreement with the results of experiments. In this paper, validity of this equivalent magnetic circuit is described.
ABSTRACT In this work, the general form of the solution to Laplace's equation is used to ... more ABSTRACT In this work, the general form of the solution to Laplace's equation is used to derive two formulations of asymptotic boundary conditions (ABC's) suitable for the finite element modeling of axisymmetric electrical field problems with open boundaries. The first formulation works for an arbitrary shape of the finite element region. However, it produces nonsymmetrical matrices. The second formulation works for rectangular outer boundaries and produces symmetric matrices. Both the formulations produce closed-form expressions for the elemental boundary matrices. A simple problem of electrostatic potential is solved as an example
COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 1998
The eddy current method of non-destructive testing uses an alternating current excitation to indu... more The eddy current method of non-destructive testing uses an alternating current excitation to induce secondary currents in a specimen under test. Flaws within the specimen affect the induced currents, causing changes in the impedance of a test coil. In this paper we present a method for obtaining a solution of inverse problems, in which the parameters of defects are unknown
COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 1998
The Faculty of Electrical Engineering at the Technical University of Szczecin, Poland, provides e... more The Faculty of Electrical Engineering at the Technical University of Szczecin, Poland, provides education and training at a technical level as well as up to the Master of Science degree. Electromagnetics and applications are fundamental to electrical engineering and play an important role in the faculty’s curriculum. Because of the vast amount of material to be covered, the essential problem is an appropriate choice of topics. Special care needs to be taken while teaching basic concepts and principles, but nowadays also computer-aided methods. After many years of experience in teaching electromagnetics the authors have proposed new programmes for teaching the subject within the courses offered by the faculty. Some aspects of these programmes are described in the paper.
COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 1992
This paper presents the practical configuration for detecting cracks in material, by applying an ... more This paper presents the practical configuration for detecting cracks in material, by applying an electromagnetic field along the largest dimension of the crack. An electromagnetic field formulation is proposed using Helmholtz's equation and Biot‐ Savart's law. The system equation is solved by using the finite element method (FEM). The exemplary results of calculation ‐ eddy currents lines in material and relative resistance versus probe position are presented.
Purpose-The purpose of this paper is to develop a magnetic induction tomography (MIT) system as w... more Purpose-The purpose of this paper is to develop a magnetic induction tomography (MIT) system as well as the conductivity reconstruction algorithms (inverse problem). Design/methodology/approach-In order to define and verify the solution of the inverse problem, the forward problem is formulated using mathematical model of the system. The forward problem is solved using the finite element method. The optimization of the excitation unit is based on the numerical solutions of the direct problem. All the dimensions and shape of the excitation system are optimized in order to focus the main part of the magnetic field in the vicinity of the receiver. Finally, two formulations of the inverse problem are discussed: based on the inversion of the Biot-Savart law; and based on the artificial neural networks. Findings-The formulation of the forward problem of the considered MIT system is given. The construction of the exciter unit that focuses the main part of the magnetic field in the vicinity of the receiver is proposed. Two formulations of the inverse problem are discussed. First using the inversion of the Biot-Savart law and second using the artificial neural network. The neural networks seem to be promising tools for reconstructing the MIT images. Originality/value-This paper demonstrates a real-life MIT system whose performance is satisfactorily predicted by mathematical models. The original design of the exciter is shown. The new approach to the inverse problem in MIT-the use of the artificial neural network-is presented.
New infinite elements which can be used for a solution of axisymmetric magnetic problems with ope... more New infinite elements which can be used for a solution of axisymmetric magnetic problems with open boundaries are presented. It is supposed that the new elements are being developed for the vector potential A(r,z) and the modified vector potential rA formulation. The elements can represent any type of decay towards infinity, and the element matrix when the decay function is 1/ rho /sup n/, n>or=1, rho /sup 2/=r/sup 2/+z/sup 2/ is given explicity. Standard finite elements for the rA formulation yield very inaccurate results near r=0. The introduction, close to the symmetry axis, of so-called axial elements with special shape functions is proposed. The formulation is so simple that closed-form expressions for the element matrix are obtained. Numerical results are presented for a problem having an analytical solution. >
COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 1995
A basic difficulty encountered in applying the finite element method to unbounded wave problems i... more A basic difficulty encountered in applying the finite element method to unbounded wave problems is that the domain in which the field is to be computed is unbounded, while finite element models are of finite size. There are several ways to overcome this difficulty. The widely used method is to truncate the finite element model at a finite position and apply suitable boundary conditions there. The relevant boundary conditions must absorb the outgoing wave and have been called absorbing boundary conditions (ABC's).
In this paper authors propose an eddy current probe, which is suitable for inspection of low cond... more In this paper authors propose an eddy current probe, which is suitable for inspection of low conductivity structures. The probe consists of an excitation coil and two differentially connected search coils. The detection circuit was designed in this way that a resonance for an operating frequency was obtained. It creates possibility to achieve a high sensitivity of the measuring system.
Contrary to what Dickerson and Mottmann [Am. J. Phys. 84, 413-418 (2016)] state, the temperatures... more Contrary to what Dickerson and Mottmann [Am. J. Phys. 84, 413-418 (2016)] state, the temperatures at which a refrigerator's working fluid absorbs heat need not always lie below those at which it expels heat; nor must a refrigerator's thermodynamic cycle have two adiabats. Moreover, what Dickerson and Mottmann call a "comparison Carnot cycle" cannot always be defined. These conclusions are illustrated here using a counterclockwise Stirling cycle without regeneration. A refrigerator's cold reservoir can absorb some heat and its hot reservoir can expel some heat, so long as the net heat flow is still out of the cold reservoir and into the hot reservoir.
International Journal of Applied Electromagnetics and Mechanics
Magnetic induction tomography, highly promising imaging technique for medical purposes, applies a... more Magnetic induction tomography, highly promising imaging technique for medical purposes, applies a magnetic field from an exciter to induce eddy currents in the object of low conductivity, and the magnetic field from these is then detected by a sensor. The induced eddy currents are proportional to the conductivity distribution. This paper deals with the solution of the fundamental inverse problem existing in magnetic induction tomography, which consists in the reconstruction of the eddy currents distribution basing on the magnetic field measurements. The problem has been solved by the Tikhonov regularization method. The choice of the regularization parameter and the accuracy of the proposed method have also been discussed.
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