Marc Lambert

Detection of Defects in Wiring Networks Using Time Domain Reflectometry

A new technique is proposed to reconstruct faulty wiring networks from the time-domain reflectometry (TDR) response. The developed method is also for characterization of defects in the branches of the network. The direct problem (propagation along the cables) is modeled by RLCG circuit parameters computed by finite element method (FEM) and the finite-difference time domain (FDTD) method. Genetic algorithms (GAs) are used to solve the inverse problem. The proposed method allows to accurately locate wire faults. Some examples are presented to validate and illustrate the ability of this reconstruction method.

Multiple-Shape Reconstruction by Means of Multiregion Level Sets

In the framework of inverse scattering techniques for microwave imaging, this paper proposes an approach based on the integration between a multiscaling procedure and the level-set-based optimization in order to properly deal with the shape reconstruction of multiple and disconnected homogeneous scatterers. The effectiveness and robustness of the proposed approach is assessed against both synthetic and experimental data. A selected set of results concerned with complex shapes is presented and discussed.

Adaptive Metamodels for Crack Characterization in Eddy-Current Testing

In the framework of nondestructive eddy-current testing, an inversion method is proposed. It relies on a metamodel-based optimization method: a fast optimization by means of a particle swarm algorithm is performed wherein the exact forward computations are replaced by an appropriate metamodel. The latter is obtained by radial basis function interpolation over a database previously generated by sequential design. Both synthetically generated and laboratory-controlled experimental data are used to illustrate its performances. Comparisons to inversions by support vector machines, now common for defect characterization, are carried out. The proposed method appears to be an useful tool for decision analysis, highlighting the likeliest results.

Electromagnetic Modeling of a Damaged Ferromagnetic Metal Tube by a Volume Integral Equation Formulation

We propose a volume integral equation formulation for eddy-current nondestructive evaluation of ferromagnetic tubes affected by volumetric defects. We solve the system of integral equations (introduced into the model by application of Greens theorem) by the method of moments for both fictitious electric and magnetic currents within the defects, and calculate variations of impedance of the probes by the reciprocity theorem. We have made thorough comparisons of our results with finite-element-method simulations and with experimental data as well.

Nonlinear inversion of a buried object in transverse electric scattering

A method for reconstructing the material properties of a buried bounded inhomogeneous object from measured scattered field data at the surface of the Earths interface is presented. This work extends the method previously developed for the homogeneous transverse electric (TE) case to the more complicated case of a buried object. In the TE case, the magnetic field is polarized along the axis of an inhomogeneous cylinder of arbitrary cross section, and the corresponding integral equation contains derivatives of both the background Greens function and the field. The nonlinear inversion, however, can be formulated from an electric field integral equation for the two transversal components of the electric field. The integrand is a product of the background Greens function, the contrast, and the electric field vector; however, in the case of a buried object the background Greens function is the one pertaining to a two-media configuration. The derivatives are operative outside the integral. In this paper the latter formulation will be taken as the point of departure to develop a nonlinear inversion scheme based upon the modified gradient method. In the inversion scheme the positivity of the material parameters has to be ensured in order to obtain a convergent inversion scheme. Numerical results are presented in which the reconstruction of the contrast is shown and compared in the case of TE excitation as well as transverse magnetic (TM) excitation.

Dyad-based model of the electric field in a conductive cylinder at eddy-current frequencies

We propose a rigorous model of the electromagnetic field in a conductive circular cylinder illuminated by an arbitrarily shaped and oriented current-carrying coil placed nearby for nondestructive evaluation at eddy-current frequencies. The model is based on a dyadic field formulation, and its modularity enables handy generalizations to a multilayered cylindrical structure that might be affected by various defects. We give a variety of numerical results about the primary electric field within the cylinder in both canonical and practical cases in order to illustrate pros and cons of the solution method. The results agree quite well with known analytical results (which are available only in highly symmetrical cases), and fairly well with results yielded at high computational cost by an industrial finite-element code in more general cases. We discuss in detail the conditions for reaching a good numerical accuracy (involving some suitable regularization) while preserving both generality and small computational burden of the resulting computer code.

Conductive masses in a half-space Earth in the diffusive regime: fast hybrid modeling of a low-contrast ellipsoid

Electromagnetic three-component magnetic probes at diffusion frequencies are now available for use in slim mineral-exploration boreholes. When a source is operated at or below the surface of the Earth in the vicinity of a conductive orebody, these probes provide, after appropriate processing, the secondary vector magnetic field attributed to this body. Proper inversion of the resulting datasets requires as a first step a clear understanding of the electromagnetic interaction of model signals with model bodies. In this paper, the response of a conductive ellipsoid buried at shallow depth in a half-space Earth is investigate by a novel hybrid approach combining the localized nonlinear approximation and the low frequency scattering theory. The ellipsoidal shape indeed fits a large class of scatterers and yet is amenable to analytical calculations in the intricate world of ellipsoidal harmonics, while the localized nonlinear approximation is known to provide fairly accurate results at least for low contrasts of conductivity between a scattering body and its host medium. In addition, weak coupling of the body to the interface is assumed. The primary field accounts for the presence of the interface, but multiple reflection of the secondary field on this interface is neglected. After analyzing the theoretical bases of the approach, numerical simulations in several geometrical and electrical configurations illustrate how estimators of the secondary magnetic field along a nearby borehole behave with respect to a general-purpose method-of-moments (MoM) code. Perspectives of the investigation and extensions, in particular, to two-body systems, strong coupling to the interface, and high contrast cases, are discussed.

Solution of Inverse Problems in Nondestructive Testing by a Kriging-Based Surrogate Model

The inverse problems of electromagnetic nondestructive testing are often solved via the solution of several forward problems. For the latter, precise numerical simulators are available in most of the cases, but the associated computational cost is usually high. Surrogate models (or metamodels)-which are getting more and more widespread in electromagnetics-might be promising alternatives to heavy simulations. Traditionally, such surrogates are used to replace the forward model. However, in this paper the direct use of surrogate models for the solution of inverse problems is studied and illustrated via eddy-current testing examples.

Electromagnetic scattering by a triaxial homogeneous penetrable ellipsoid: Low‐frequency derivation and testing of the localized nonlinear approximation

The field resulting from the illumination by a localized time-harmonic low-frequency source (typically a magnetic dipole) of a voluminous lossy dielectric body placed in a lossy dielectric embedding is determined within the framework of the localized nonlinear approximation by means of a low-frequency Rayleigh analysis. It is sketched (1) how one derives a low-frequency series expansion in positive integral powers of (jk), where k is the embedding complex wavenumber, of the depolarization dyad that relates the background electric field to the total electric field inside the body; (2) how this expansion is used to determine the magnetic field resulting outside the body and how the corresponding series expansion of this field, up to the power 5 in (jk), follows once the series expansion of the incident electric field in the body volume is known up to the same power; and (3) how the needed nonzero coefficients of the depolarization dyad (up to the power 3 in (jk)) are obtained, for a general triaxial ellipsoid and after careful reduction for the geometrically degenerate geometries, with the help of the elliptical harmonic theory. Numerical results obtained by this hybrid low-frequency approach illustrate its capability to provide accurate magnetic fields at low computational cost, in particular, in comparison with a general purpose method-of-moments code.

Kriging for Eddy-Current Testing Problems

Accurate numerical simulation of Eddy-Current Testing (ECT) experiments usually requires large computational efforts. So, a natural idea is to build a cheap approximation of the expensive-to-run simulator. This paper presents an approximation method based on functional kriging. Kriging is widely used in other domains, but is still unused in the ECT community. Its main idea is to build a random process model of the simulator. The extension of kriging to the case of functional output data (which is the typical case in ECT) is a recent development of mathematics. The paper introduces functional kriging and illustrates its performance via numerical examples using an ECT simulator based on a surface integral method. A comparison with other classical data interpolation methods is also carried out.