Electromagnetic Inverse Problem Research Articles

Inverse Electromagnetic Problems by Field Visualization

The main inverse electromagnetic problems are formulated and solved for testing and inspecting of many devices such as thin-film transformers, inductors, printed circuit boards, motherboards of personal computers, etc. The visualization technique is applied to determine the current distributions and for nondestructive detection of the magnetic materials by locally measured magnetic fields. The image of the field distribution is processed using field theory. The color-source densities have been evaluated from the color distributions of the field data set. It was found that the color-source distribution corresponds to the field source distribution. Generating new color distribution with obtained color-source densities can essentially reduce the noise of the measured field data. With the proposed approach the quality of the images can be essentially improved. The results obtained show that various inverse electromagnetic problems can be successfully solved using visualized information of field distribution and image processing techniques.

Electromagnetic detection of dielectric scatterers using phaseless synthetic and real data and the memetic algorithm

Phaseless data are used to evaluate the application of an electromagnetic inverse-scattering-based procedure for the detection of cylindrical inhomogeneities, which are schematized as multilayer infinite dielectric cylinders with elliptic cross sections. The electromagnetic inverse problem is recast as a global optimization problem and iteratively solved by an efficient memetic algorithm, which combines deterministic and stochastic concepts. Moreover, a recursive analytical procedure is used for the forward-scattering computation. The possibility of localizing and reconstructing the scatterers by using phaseless input data, which would greatly simplify the design of the imaging apparatus, is evaluated both with reference to synthetically produced data and by means of experimental data obtained by a microwave tomograph.

On the Two-dimensional Inverse Scattering Problems in Electromagnetics

In recent years, inverse scattering problems have received much attention because of their important applications. Given the incident and scattered waves, an inverse scattering problem in general is to determine the properties of the scatterer. In radar or sonar a known incident wave and observed scattered wave are used to detect the properties and the presence of aircraft or submarine objects; in MRI scanning, tomography X-rays and ultrasound, scattered waves are used to determine the presence or properties of tumors by detecting density variations, to name a few. In this article, we are concerned with the two-dimensional electromagnetic inverse scattering problem. An iterative algorithm for the transversal electric waves will be given based on a singular domain integral equation formulation. Basic features of a scattering object such as shape, location and index of refraction will be recovered from measurements of the field scattered by the object (when illuminated by electromagnetic waves with the magnetic vector polarized along the cylinder axis). Some numerical experiments are included to illustrate the efficiency of the algorithm.

Numerical methods for locating small dielectric inhomogeneities

We present numerical simulations illustrating the reconstruction of data for electromagnetic inverse problems. Two situations are considered: prescribed electric field and measured magnetic field at the boundary of a medium with cylindrical symmetries, and the analysis of the far field pattern of a scattered field produced by the incidence of an incoming wave on a set of small inhomogeneities.

Error bounds for inverse electromagnetic problems in soil mechanics

This paper explores the possibility of using electrical resistance tomography for the identification of buried objects. The technique requires the solution of both direct and inverse problems, which for noncanonical geometries must be solved by numerical techniques like finite element methods and soft computing. The unknown is the perturbation field, a small fraction of the source field. Therefore, simulation and error estimation tools adopted in the solution process must be both accurate and reliable. This paper shows that complementary formulations readily allow determination of error bounds for global quantities like the electric resistance.

Structural health monitoring of materials by high critical temperature SQUID

Nowadays, tailoring the material properties is essential for advanced product design in engineering systems. The need to provide key information about micro- and macro-structural behaviour of materials, without destructively sectioning the sample, has spurred the development of nondestructive evaluation methodologies. These techniques are required during material production, quality testing of components during manufacturing, and in-service inspection of structural integrity. To ensure the highest possible operational safety along with an economic efficiency, it is necessary to carry out inspections with a high sensitivity and a proven reliability. Due to its unparalleled magnetic field sensitivity over a wide frequency range and large dynamic range, SQUID-based nondestructive evaluation has unique advantages for materials and structures characterization. We will present an overview of eddy-current nondestructive analysis utilizing high T c SQUIDs with an emphasis on examples relevant to the aeronautical industry. These include the detection of deep-lying defects in multi-layer structures of Al–Ti alloys and damage of extremely lightweight graphite/epoxy composites. Both of these can be successfully treated by this approach where conventional electromagnetic probes often fail. In addition some results based on the volume integral formulation, successfully developed to simulate the response of the system to different type of flaws in Al-alloy planar structures and to solve the inverse electromagnetic problem, will be shown.

An improved tabu algorithm applied to global optimizations of inverse problems in electromagnetics

This paper proposes an improved tabu search algorithm for global optimizations of multimodal functions with continuous variables of inverse problems in electromagnetics. The improvements include the introduction of a multistart process, the new neighborhood generating mechanism, and the memorization of the previously searched subspaces as well as the stop criteria for different termination purposes. The numerical results on solving a mathematical test function reveal that the proposed method is more robust in finding the global optimum compared with other kinds of tabu search algorithms. The shape optimization of an electrode demonstrates its value in practical engineering.

Solution strategies for two- and three-dimensionalelectromagnetic inverse problems

We analyse a variety of solution strategies for nonlineartwo-dimensional (2D) and three-dimensional (3D) electromagnetic(EM) inverse problems. To impose a realistic parameterizationon the problem, the finite-difference equations arising fromMaxwell equations are employed in the forward problem. Krylovsubspace methods are then used to solve the resulting linearsystems. Because of the efficiencies of the Krylov methods,they are used as the computational kernel for solving 2D and 3Dinverse problems, where multiple solutions of the forwardproblem are required. We derive relations for computing thefull Hessian matrix and functional gradient that are needed forcomputing the model update, via the Newton iteration. Differentstrategies are then discussed for economically carrying out theNewton iteration for 2D and 3D problems, including theincorporation of constraints necessary to stabilize theinversion process. Two case histories utilizing EM inversionare presented. These include inversion of cross-well data formonitoring electrical conductivity changes arising from anenhanced oil recovery project and the usefulness of cross-wellEM methods to characterize the transport pathwaysfor contaminants in the subsurface.

The method of maximum mutual information for biomedical electromagnetic inverse problems

This paper proposes a new method for biomedical electromagnetic inverse problems based on the technique of maximum mutual information. The new method is different from the conventional methods for it will not depend on the widely used regularization technique. The new method provides a general paradigm for developing algorithms dealing with various biomedical inverse problems that can be described using lead field, including localization and imaging of neural source activities in brain and heart from EEG/MEG and ECG/MCG; it is also possible to apply it to other, electromagnetic inverse problems like electrical impedance tomography. This paper mainly provides the theoretical development, with MEG inverse problems as case studies.

Bayesian evolutionary inversions in computational electromagnetics

Bayesian probability theory and evolutionary optimizations are proposed for solving inverse problems in computational electromagnetics. As a numerical example, a real-world inverse problem from biomedical NMR spectroscopy is presented.

A comparison of optimization techniques for Loney's solenoids design: an alternative Tabu Search algorithm

A global optimization procedure based on Tabu Search metaheuristic is applied to solve electromagnetic inverse problems. In particular, some benchmark problems have been considered consisting of designing systems of Loney's solenoids. The results obtained implementing different Tabu Search strategies are compared to those presented in the literature. The comparison shows that the optimality of the solutions can be noticeably improved without increasing the computational effort. Moreover, the importance of using hybrid heuristics has been highlighted in the case of difficult problems.

A communications theory approach for electromagnetic inverse problems

A new approach to electromagnetic non destructive evaluation (E'NDE) is presented with reference to crack detection in conductive materials by eddy current testing. The key point is the development of a model for E'NDE that allows the original problem to be recast within the framework of digital communications over noisy channels. Consequently, methodologies and techniques originally developed in communications theory can also be applied to E'NDE. However, several questions have to be addressed in order to overcome the gaps between these two fields. Numerical results show the main features of this method.

An electromagnetic inverse problem in chiral media

We consider the inverse boundary value problem for Maxwell’s equations that takes into account the chirality of a body in R3. More precisely, we show that knowledge of a boundary map for the electromagnetic fields determines the electromagnetic parameters, namely the conductivity, electric permittivity, magnetic permeability and chirality, in the interior. We rewrite Maxwell’s equations as a first order perturbation of the Laplacian and construct exponentially growing solutions, and obtain the result in the spirit of complex geometrical optics.

An optimization approach to two‐dimensional time domain electromagnetic inverse problems

An optimization approach to a two‐dimensional electromagnetic inverse problem in the time domain is considered. Wave‐splitting is integrated in the optimization algorithm. The permittivity, permeability, and conductivity are reconstructed by minimizing an objective functional. To speed up the computation time, an explicit expression for the gradient of the objective functional is derived by introducing dual functions and using the Gauss surface divergence theorem. The parameters are then reconstructed by an iterative conjugate gradient algorithm. Numerical results for a simultaneous reconstruction of the permittivity, permeability, and conductivity are presented.

Stability of the inverse electromagnetic inhomogeneous medium problem

We examine the scattering of time-harmonic electromagnetic waves in an inhomogeneous medium. Given two smooth refractive indices whose difference is small with respect to a C2-norm, we show that the maximum norm of the difference of the refractive indices can be estimated by the difference of certain boundary operators associated with the refractive indices. Moreover, using a very strong norm on the far-field patterns, we reconstruct the boundary operators from the far-field patterns and derive continuous dependence of the refractive index on the far-field pattern.

A wave-splitting based optimization approach to multi-dimensional time-domain electromagnetic inverse problems

An optimization approach to a multi-dimensional electromagnetic inverse problem in the time domain is considered. Wave-splitting is integrated in the optimization algorithm. An analysis based on energy estimates is given to show that the wave-splitting provides the best linear combination of the fields for use in this type of inverse problem. The permittivity, permeability and conductivity are reconstructed by minimizing an objective functional. An explicit expression for the gradient of the objective functional is derived by introducing some auxiliary functions and using the Gauss theorem. The parameters are reconstructed by an iterative conjugate gradient algorithm. Numerical results are presented.

Electromagnetic direct and inverse problems for a surface-breaking crack in a conductor at a high frequency

The electromagnetic direct and inverse problems for a surface-breaking crack in a conductor are considered at a high frequency. The direct problem, which is transferred to a two-dimensional potential problem in the unfolded configuration, is solved by a boundary integral equation method. The boundary integral equation (a well-posed Fredholm integral equation of the second kind) for the normal derivative of the potential on the interior boundary of the crack is derived. The potential distribution at the open mouth of the crack is used to determine the shape of the crack. The inverse problem is solved by a genetic algorithm combined with a conjugate gradient method.

Inversion of magnetometer array data by thin-sheet modelling

Summary A conjugate gradient relaxation method is employed in seeking an iterative solution to a particular 3-D electromagnetic inverse problem. The problem, which is non-linear, is that of modelling observed magnetic fluctuation response functions by a thin-sheet earth structure. The method optimizes data misfit and model roughness, and starting from a base model designed on known geology produces a series of improved models. Established thin-sheet algorithms are employed to compute the model responses and sensitivity, and utilization of a parallel computing system enables reasonable execution times. The method is demonstrated by inverting data generated for a synthetic example. Gaussian noise is added to the synthetic data. The inversion scheme has been applied to geomagnetic induction data which have been recorded widely on the Australian continent. Highly conductive structures in models given by the inversion method confirm regional conductivity anomalies indicated by induction arrow patterns, and give more quantitative information about them. The method appears to work well in areas of strong conductivity contrast such as coastlines.

Brain Electrical Tomography Using Algebraic Reconstruction Techniques

ABSTRACTThe localization of the intracranial neural sources of the scalp recorded electroencephalographic (EEG) signals is a major research filed during the last two decades. Evoked Potentials (EPs) are EEG signals produced when external stimuli are presented to subjects. A novel tomographic technique is presented, based on the solution of the inverse electromagnetic problem, using Algebraic Reconstruction Techniques. The electrical activity of the brain is depicted in consecutive projection maps with a resolution of up to 1msec. Results of clinical applications of the method to EP measurements in a group of psychiatric patient and normal controls are presented.

Backus and gilbert method for vector fields

This report describes the theory of Backus and Gilbert with special emphasis for the case of vector fields as required for the solution of the electromagnetic inverse problem. A description of the method is presented with the detailed mathematical derivation of the coefficients that determine the solution for the retrieval of vector fields. Such derivation, to our knowledge, has never been reported in the literature. We also identify some crucial points that can (and had) lead to misuse of this solution and describe some disadvantages of this theory for the case of vector fields suggesting some alternatives to deal with them.