## Liste des publications

#### Bayesian Pressure Snake forWeld Defect Detection

Image Segmentation plays a key role in automatic weld defect detectionand classification in radiographic testing. Among the segmentation methods,boundary extraction based on deformable models is a powerful techniqueto describe the shape and then deduce after the analysis stage, the type of thedefect under investigation. This paper describes a method for automatic estimationof the contours of weld defect in radiographic images. The method uses astatistical formulation of contour estimation by exploiting statistical pressuresnake based on non-parametric modeling of the image. Here the edge energy isreplaced by a region energy which is a function of statistical characteristics ofarea of interest. Voir les détails

**Mots clés : **Snake, images segmentation, pdf estimation, radiographic images, Non Destructive Inspection

#### Comparison of Simulation Methods of Pulsed Ultrasonic Fields Radiated in Isotropic Solids

The modelling of pulsed ultrasonic fields radiated by transducers in materials of various types is of particular interest in industrial applications of non destructive testing. Knowledge of the ultrasonic field allows defining and optimizing the control conditions. For the calculation of harmonic and pulsed ultrasonic fields, various methods have been used such as exact, semi-analytical, asymptotic and purely numerical methods. In this work, these methods are reviewed for the case of a planar and circular ultrasonic source coupled to a semi-infinite isotropic solid. In the second part, the solution of a semi-analytical method, which uses particular approximations, is compared to that of an exact one. The numerical calculations achieved by using the exact method are very tedious but allow the interpretation of physical phenomena involved. In contrast to that, the semi-analytic one permits the calculations to be undertaken in a more reasonable time. However, Rayleigh waves and head waves are not revealed by this method. Voir les détails

**Mots clés : **Ultrasound, NDT, Pulsed field, Isotropic Solid, Transducer.

#### Characterization of Grains Size by Ultrasounds

A mechanical or thermal treatment of a material can change, among other things, the average grains size. It depends on temperature, holding time, cooling condition or rolling stress. The average grain size, as well as its influence on the propagation velocity and attenuation coefficient of ultrasonic waves, also affects the wave frequency propagating through the material. Grain size is an indicator of material fatigue. It can therefore be used in monitoring or fatigue damage prevention. In this paper, we study the effect of various heat treatments hence different steel average grain sizes on the ultrasonic wave frequency after crossing the material. We have performed the same experimental study on aluminum samples. The different grain sizes are obtained by rolling. The frequency shift measurement of longitudinal waves is achieved by immersion with two probes of different frequencies 2.25 and 5 MHz. The experimental results are shown as curves giving the frequencies depending on the grain size. Heat treatments on steel and aluminum rolling performed on the samples have yielded a grain sizes gradient. Our results are consistent with the theory because of the important path in the sample and in this case the down shift frequency is paramount. They show a direct relationship between the frequency shift and the average grain size. It is therefore possible to trace quantitatively to an average grains size from the frequency of an ultrasonic wave that has passed through this material and hence its thermal or mechanical fatigue state. Voir les détails

**Mots clés : **Attenuation, Frequency Spectrum, Grain Size, Scattering, Ultrasound (US)

#### Numerical approximation and umbral calculus

We show that any operator P, invariant by translation, can be developed as P=∑ n≥0 a n Q n ,(1) where Q n is a sequence of well defined operators. By using the umbral calculus, this generalizes the result of G. C. Rota et al. [Finite operator calculus, J. Math. Anal. Appl. 42, 685–760 (1973)]. Our idea consists in choosing a Δ-sequence (Q n ) n∈ℕ defined as Q 0 =I(Identity),forn=0,Q n =1 h n1 h n2 ⋯h nn Δ h n1 Δ h n2 ⋯Δ h nn ,forn≠0, where Δ h is the difference operator: 1 hΔ h f(x)=f(x+h)-f(x) h,forh≠0,f ' (x),forh=0, while (h ij ) is a double sequence of arbitrary parameters. Our goal is to find parameters (h ij ) minimizing the absolute values of the functions a n (h n1 ,h n2 ,⋯,h nn ) and to determine, experimentally, on a representative class of functions: • What are the values of the h ij that minimize an for n=4 or n=5? • Does, by the accelerated convergence of the series of operators (1) with an optimum choice of the h ij , this imply an accelerated convergence of the corresponding series of functions (in case of convergence of course)? A positive answer would open a perspective in the process of the acceleration of the convergence of numerical series. It is noted that (1) is independent of the choice of these parameters, therefore we exploit this idea in the approximation of certain operators encountered in numerical analysis. Voir les détails

**Mots clés : **Numerical approximation

#### Design and Optimisation of Circular and Inductors for Silicon-based RFIC Application

In this paper, spiral inductors for RF application, which are designed on a silicon substrate by using standards 0.35 µ m CMOS technology, are described. Analyzed and designed with ASITIC (a tool from the University of Berkeley), which accurately takes into account the parasitic effects. This study shows the possibility of obtaining an optimal inductance having a high quality factor of 15. This result is carried out without resorting to the specific processes such as the digging of the substrate under the inductors or the use of a thick layer in gold. The use of circular form, with optimization of geometrical parameters like spacing between two adjacent turn, the track width and the number of turns, can ensure high quality factors. Voir les détails

**Mots clés : **circular inductor, high quality factors., RF application

#### Deconvolution of ultrasonic echoes using Bernoulli-Gaussian processes for composite materials inspection

In this work, we present an approach of deconvolution ill-posed problems of superimposed signals in time. A priori information must be taken into account to solve this problem. The a priori information translates the physical properties of the ultrasonic signals. The defect impulse response is modelled as a Bernoulli-Gaussian sequence. Deconvolution becomes the detection problem of the optimal Bernoulli sequence and estimation of the associated complex amplitudes. A simulation study on defect detection was realised, and results were validated experimentally on Carbon fiber-reinforced polymer multi-layered composite materials (CFRP) with and without delamination defects taken from aircraft. Voir les détails

**Mots clés : **composite materials, blind deconvolution, processes BG

#### Piezoelectric transformer: Comparison between a model and an analytical verification

In this paper, a study comparing a model of a composite piezoelectric transformer, based on the corresponding electrical equivalent circuit, and the direct calculation solving the mechanical fundamental equations constrained by the appropriate boundary conditions is presented. The approach is simplified considering vibrations only along one direction, neglecting the coupling phenomena existing along the other directions. The electrical equivalent circuit of the transformer is obtained from the equivalent circuit referred for the isolated piezoelectric oscillators. In this paper, each electrical equivalent circuit is placed on a cascade in order to conserve the continuity of dis- placements and stress at the junction. Voir les détails

**Mots clés : **Piezoelectricity, Transformer, Modeling; Equivalent circuit, Analytical verification, Voltage gain, Boundary conditions

#### Detection of delamination defects in CFRP materials using ultrasonic signal processing

In this paper, signal processing techniques are tested for their ability to resolve echoes associated with delaminations in carbon fiber-reinforced polymer multi-layered composite materials (CFRP) detected by ultrasonic methods. These methods include split spectrum processing (SSP) and the expectation–maximization (EM) algorithm. A simulation study on defect detection was performed, and results were validated experimentally on CFRP with and without delamination defects taken from aircraft. Comparison of the methods for their ability to resolve echoes are made. Voir les détails

**Mots clés : **Ultrasonic NDE, composite materials, CFRP, SSP, Deconvolution, EM algorithm

#### Effect of solution treatment temperature on the precipitation kinetic of σ-phase in 2205 duplex stainless steel welds

The effect of the prior solution treatment temperature on the δ-ferrite transformation in 2205 duplex stainless welds after aging at 850 °C has been studied. Microstructural examination showed that the σ-phase and M_{23}C_{6} chromium carbides precipitate at the δ/γ interfaces and within the δ-ferrite grains. Increasing the solution treatment temperature from 1050 to 1250 °C delays the σ-phase formation and favours the precipitation of intragranular secondary austenite γ_{2}. The simulation of the σ-phase precipitation kinetic in the base metal, HAZ and weld metal, indicates a good agreement between the experimental fitted data and the modified Johnson–Mehl–Avrami model. The results indicate a marked sensitivity of the σ-phase precipitation kinetic to the solution treatment temperature. A high precipitation rate corresponds to a fine grained structure with ferrite enriched in σ forming elements (Cr, Mo)
Voir les détails

**Mots clés : **duplex stainless steel, welding, ageing, precipitation kinetic, Johnson-Mehl-Avrami model

#### Phase transformation and mechanical behavior in annealed 2205 duplex stainless steel welds

The phase transformations and mechanical behaviour during welding and subsequent annealing treatment of 2205 duplex stainless steel have been investigated. Detailed microstructural examination showed the presence of higher ferrite amounts in the heat affected zone (HAZ), while higher amounts of austenite were recorded in the centre region of the weld metal. Annealing treatments in the temperature range of 800–1000 °C resulted in a precipitation of σ phase and M_{23}C_{6} chromium carbides at the γ/δ interfaces that were found to be preferential precipitation sites. Above 1050 °C, the volume fraction of δ ferrite increases with annealing temperature. The increase of δ ferrite occurs at a faster rate in the HAZ than in the base metal and fusion zone. Optimal mechanical properties and an acceptable ferrite/austenite ratio throughout the weld regions corresponds to annealing at 1050 °C. Fractographic examinations showed that the mode of failure changed from quasi-cleavage fracture to dimple rupture with an increase in the annealing temperature from 850 to 1050 °C
Voir les détails

**Mots clés : **duplex stainless steel, welding, Annealing, microstructure, impact toughness, tensile tests