Iterative sequential algorithm for inversion of an operator. Application to the restoration of the images given by a multi-element eddy current sensor

Iterative methods are commonly used in signal processing, to restore a signal smoothed by a linear operator H, in presence of noise. In this paper, we present an original sequential method which relies on a recursive feed back control loop including the operator H. It is based on the use of only a small fixed number of iterations, with a predetermined sequence of gain factors k,, . We demonstrate that the sequence k„ can be choosen in order to approximate the optimal Wiener inverse filter corresponding to a particular crude assumption on the input signal statistics . This is ofparticular interest if H is a non stationary filter, or a non linear filter with a varying local linear approximation . It is this kind of non linear filtering that we encountered in a practical situation in the design of a multi-element eddy carrent sensor. The performance of our algorithm is illustrated in this application, in order to improve the depth image of a metallic body given by the sensor .Les techniques d'estimation utilisées en traitement du signal nécessitent fréquemment l'emploi de méthodes itératives, qui permettent de restituer au mieux le signal d'entrée d'un système à partir de l'observation . Dans cet article, nous effectuons une brève synthèse des méthodes d'inversion, et présentons un algorithme original mettant en jeu l'opérateur H à inverser et une séquence de gains de correction k,,, choisie pour obtenir la meilleure approximation du filtre optimal de Wiener inverse correspondant à des hypothèses assez simples sur les propriétés statistiques du signal d'entrée. L'analyse détaillée des performances de ce schéma itératif est menée dans le cas d'un opérateur H linéaire en présence de bruit, mais nous montrons qu'elle s'étend sous certaines conditions à des systèmes non linéaires . Les développements théoriques sont ensuite illustrés par une application en restauration de profil pour un multicapteurs à courants de Foucault

Modélisation de capteurs inductifs pour la mesure à travers une paroi métallique amagnétique

Cet article présente une application originale utilisant les capteurs inductifs destinés à la mesure de déplacement d'une pièce magnétique à travers une paroi métallique amagnétique. Grâce à une analyse physique du problème, un modèle analytique permettant la prédétermination et l'optimisation des performances du système est élaboré, puis confronté avec succès aux résultats expérimentaux

The distributed sources method: a concept for open magnetic cores modelling

This paper presents a original method for open magnetic cores modelling. It is called the distributed point source method. It is based on a spatial distribution of point sources located on the core surfaces emitting the magnetic flux, called the active surfaces. Compared to Finite Elements methods, the DSPM method requires only the meshing of these active surfaces, which considerably reduces the solving process time. In this paper, the DSPM method is applied on a magnetic cylindrical core, placed in free space

Modélisation de capteurs inductifs pour la mesure à travers une paroi métallique amagnétique

In this paper, an interesting application of magnetic sensors used for distance measurement through a metallic medium is presented. By a careful physical analysis of this problem, an original modelling for predetermination and optimisation of the performances of this system is achieved, and successfully compared with experimental results.Cet article présente une application originale utilisant les capteurs inductifs destinés à la mesure de déplacement d'une pièce magnétique à travers une paroi métallique amagnétique. Grâce à une analyse physique du problème, un modèle analytique permettant la prédétermination et l'optimisation des performances du système est élaboré, puis confronté avec succès aux résultats expérimentaux

The DPSM method and its application to NDE problems with interfaces modelling

This paper deals with the new results of the distributed point source method (DPSM). This method has been first developed at the SATIE lab, located at the École Normale Supérieure of Cachan, France. This method now allows the modelling of interactions between an incident wave and an obstacle. It can be applied in the non destructive testing area, using eddy currents or ultrasonic waves

Modélisation d'une structure multicapteur à courants de Foucault destinée à l'analyse de profil

This paper deals with original eddy current sensors set in a linear structure, leading the way to new metrology and profilemetry applications. A physical model is being presented, giving good results in sensors image « deconvolution ». Interests of this system are demonstrated through some examples in robotic industry.Cet article présente une structure originale de capteurs à courants de Foucault dont l'association en ligne permet d'envisager pour cette technologie, de nouvelles applications en métrologie et en relevé de profils. La présentation d'un modèle physique et son utilisation lors de phases de « déconvolution » de l'image sont ensuite illustrées par quelques exemples d'applications industrielles en robotique

Semi-analytical modeling of an eddy current imaging system for the characterization of defects in metallic structures

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Distributed point source method for the modeling of a three-dimensional eddy current NDE problem

This paper deals with modeling in electromagnetism in the field of eddy current for Non Destructive Evaluation. Several techniques could be used to diagnose structural damages. In eddy current application, a magnetic field generates by an excitation coil (or primary coil), interacts with a conductive target and generates eddy current. Variations in the phase and the magnitude of these eddy currents can be monitored using a second receivera coil. Variations in the physical properties (electrical conductivity, magnetic permeability,.) or the presence of any flaw in the target will cause a change in eddy current and a corresponding change in the phase and amplitude of measured signal. The interpretation of the signals requires a good understanding of the interaction between eddy current and structure. Therefore, researchers need analytical or numerical techniques to obtain a clear understanding of wave propagation behaviors. However, modeling of wave scattering phenomenon by conventional numerical techniques such as finite elements requires very fine mesh and heavy computational power. To go further, an innovative implementation of a semi-analytical modeling method, called the Distributed Points Source Method (DPSM), has been developed and used. The DPSM has already shown great potentialities for the versatile and computationally efficient modeling of complex electrostatic, electromagnetic or ultrasounic problems. In this paper, we report on a new implementation of the DPSM, called differential DPSM, which shows interesting prospects for the modeling of complex eddy current problems. In parallel, an Eddy Current Imager (ECI) has been recently developed in our laboratory in the aim of imaging cracks in metallic structures. In this paper, a simplified modeling of the ECI is presented using DPSM technique, the basics of DPSM formalism being firstly developed. A comparison between experimental and computed data obtained for a millimetric surface defect is presented in the form of complex magnetic cartographies. The obtained results show good agreement. Then, imaging in the case of a buried object in a metallic target is discussed. The effect of 2 parameters (the conductivity and the depth of the buried object) on the magnetic field which is computed at the surface of the material through our DPSM modeling is presented. The objective is to predict the sensor behavior for different values of these parameters, and to plot some arrays of curves, which can be used as calibration curves for the sensora's user