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Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

A 3‐D eddy current code, TRIFOU, has been used to simulate eddy currents flowing around cracks in very thick conductors, which is a fully 3‐D situation. The measurement set and the probe have also been simulated so that we can compare numerical and experimental output signals. Storage and CPU‐time requirements are detailed and the expectations of such a program in non‐destructive testing are discussed.

The paper seeks to propose a specific approach based on Dynamic Analysis and Chaos Theory aiming to emphasize the differences into the eddy current signals obtained by related non‐destructive tests, when the inspected specimens have flaws with different shapes.

Non‐linear eddy current analysis is very useful for flaw detection in many in‐service inspections. State‐of‐the‐art technologies allow one to define position and depth of defects, but the shape identification is still an open problem. In this paper, experimental data have been subjected to a dynamical analysis in order to relate the trend of eddy current signals to the shape of analyzed defect.

In particular, a dynamical reconstruction by means of recurrence plots (RPs) has been carried out in order to detect analogies and differentiations between different eddy current signals. Moreover, cross‐correlation between RPs of a reference benchmark and testing eddy current signals has been applied in order to emphasize a different dynamical behaviour and to detect a particular flaw's shape. In this way, a real‐time algorithm for defect shape classification has been performed.

Proposed approach is very interesting, and it is an innovation in non‐destructive testing procedures. In fact, the shape identification of a flaw is still an open challenge. The proposed approach, based on dynamic analysis, gives the key to solve this particular ill‐posed problem, by introducing a relation between the eddy current measurements and the shape of defect existing in the inspected specimen. Very interesting preliminary results have been obtained.

Eddy current imaging is a relatively new technique of electromagnetic nondestructive testing that makes possible an accurate geometrical characterization of flaws. On contrary to the traditional approach to eddy current testing, spatially correlated information, that can be extracted from two‐dimensional eddy current images, is used to infer about flaw shape and dimensions. In general the problem of flaw reconstruction from the eddy current images belongs to the class of three‐dimensional nonlinear inverse problems. These problems can not be solved without properly chosen simplifications. In recent literature most of the authors tried to take advantage from the problem linearization. They used the eddy current image of a small diameter hole as a point spread function (two‐dimensional impulse response) and applied the classical linear filtering to deblur the image. Although this approach results in the restoration of the top view of the flaw it seems to be inadequate for full flaw reconstruction.

Eddy current testing (ECT) is widely used in the non-destructive evaluation of materials in different industries. In this paper, ECT has been used to detect the presence of cracks in boiler tubes. The most important feature in ECT is the way in which the eddy currents are induced and detected in the sample. The authors have tried to design a new sensor that is effective in detecting cracks in boiler tubes. The purpose of this paper is to study the response of this sensor to cracks of different depths and dimensions.

The designed eddy current sensor is equipped with an exciting and a sensing coil. An alternating current is passed through the exciting coil thus producing eddy currents. The sensing coil scans the outer surface of the boiler tube and looks for abrupt changes in output signals resulting from sharp discontinuities in structure.

The sensor designed can detect the position of the crack. The presence of crack is indicated by a reduction in the induced voltage in the sensing coil. The sensor is also used for characterisation of the cracks, and can distinguish between cracks of varying shape, size and depth. The sensitivity of the sensing coil to cracks is dependent on operating conditions, such as frequency and voltage of the excitation signal.

The new sensor designed is used to detect defects in boiler tubes in power plants. However, the operating conditions, such as excitation frequency and amplitude will vary with composition of the boiler tubes.

The new eddy current sensor designed for crack detection is an E-shaped core coil. The shape of the coil provides a high permeability path to the magnetic field lines, thus reducing the loss of the field produced. This helps in improving the sensitivity of the coil, and makes the detection system effective in detecting hairline cracks.

A data fusion approach to the classification of eddy current and ultrasonic measurements is proposed in a context of defect detection/recognition methods for non‐destructive testing/evaluation systems: the purpose is to demonstrate that a multi‐sensor approach that combines the advantages carried by each sensor is able to locate potential cracks on the inspected specimen. Different approaches have been compared: a pixel level data fusion approach, that distinguishes between the defect area and the no‐defect areas, by means of the information carried by the intensity of each pixel of the eddy current and ultrasonic data; a feature level data fusion approach that uses the features computed on the measured data; a symbol level data fusion approach that extracts symbols from the two sensors as complementary information and classifies the data by using these symbols. The experimental results, carried out on an aluminium plate, pointed out the ability of the symbol level proposed approach to classify the input images within a minimum overall error, by taking into account the probability of detection and the probability of false alarm for the defect.

Eddy current testing is a frequently used NDT method at Saab/CSM but recently only single frequency testing has been used. The purpose of our work was to increase both testing speed and sensitivity by using multi‐frequency eddy current testing combined with a scanning system for corrosion detection in multi‐layered structures. The wing of the Saab 2000 aircraft was one specific example for which several samples were manufactured with both artificial (chemically etched) corrosion of various severity and cracks. Using previously determined optimal single frequency as a start, frequency combinations were determined to give increased detectability for the different structures and defects. The influence of different disturbing signals, e.g. signals from rivets, thickness variations, noise, and how to reduce them using the multi‐frequency technique was studied. Tests were also made in “field” conditions to evaluate the system.

The purpose of this paper is to present a new approach for computing by measuring and testing related 3D Eddy currents. In the process, a magnetic vector is formulated from the theoretical setup and obtained results from relevant applications are checked for the consistency of the theory. Besides, cracks detection as well as its propagation is studied through the two parameters: SIF and J-integral. A simulation by a numerical approach using finite-element discretization of 3D governing equations is employed to detect damaged zones and cracks. This approach has been used in the aircraft industry to control cracks. Besides, it makes it possible to highlight the defects of parts while preserving the integrity of the controlled products. Obtained results are compared and agreed with those of other researchers.

Finite-element discretization of 3D for solving problem in eddy current testing is presented in this paper. The main idea is the introduction of categorization for the shape reconstruction using the non-destructive testing by 3D-EC. The results are presented for a simple eddy current problem using the finite-element method as an experimental support.

In this research work, results of the various cases of simulation have been obtained. From these results of various boxes of simulation, one can conclude that the calculation of the impedance in only one point is not enough to confirm the presence or the absence of a defect for materials. Then, this confirmation leads us to the calculation of the impedance along the plate. The detection of an external defect requires the energy of the sensor by high frequencies .The position of defect (internal, in the middle, external) has a large effect on the impedance. The use of this sensor type in industrial application is frequent because of its precision (minimal error) and its low costs. The major disadvantage of this type of sensor lies in the fact that it is unable to detect a defect.

This paper fulfills an identified need to detect cracks in materials and eventually to study their propagation.

For thin cracks, in eddy current testing (ECT), the field‐flaw interaction is equivalent to a current dipole layer on its surface. The dipole density is the solution of an integral equation with a hyperstrong kernel. The variation of coil impedance and eddy current distribution is directly obtained from this density by a surface integration. There is a numerical difficulty to evaluate accurately integrals for the current density near the crack. In fact, due to the singular kernel of a dyadic Green function, the integration is quasi‐singular. A specific regularisation algorithm is developed to overcome this problem and applied to represent eddy current distribution between two cracks.

This paper aims to derive a simple and effective but still a reasonably accurate model for electromagnetic problems with hysteretic magnetic properties and/or induced currents in heterogeneous regions in 2D, meant particularly for non‐destructive testing (NDT) of steel cables by eddy‐currents.

It is assumed that the diffusion of electromagnetic fields in a heterogeneous cable, which consists of many strands, can be described by the Maxwell equations with periodically oscillating coefficients. A computationally efficient model can then be derived. The idea behind this is to replace the heterogeneous material in the cross‐section by a fictitious homogeneous one, whose behaviour at the macroscopic level is a good approximation of the one of the composite material. Such a homogenized model is obtained by employing the two‐scale convergence.

The model is validated based on experimental electromagnetic data from a steel cable (measured magnetic hysteresis loops) to show that the model is applicable for NDT of cables. The model is useful for studying NDT of cables, both for excitation at low frequency (where changes in magnetic properties are investigated) and at higher frequency (eddy current testing). It is valid for a wide range of amplitudes and frequencies.

From the mathematical point of view the model incorporated a non‐local boundary condition that has to be included in the analysis. From the engineering point of view, by solving an inverse problem based on this model and on measured hysteresis loops at several frequencies, a broader range of defects in the cable can be detected.