Determination of the Uncertainty Bounds of a Continuous Distillation Code: Effect of Input Variability and Model Uncertainty

AbstractIn this work, the effect of input variability and model uncertainty on the distillate composition of a continuous distillation tower is studied. To do that, we developed a stationary distillation code by combining mass and energy balance equations with a liquid-vapor equilibrium model and tray efficiency correlations. Feed and model uncertainties were modeled by using normal and uniform distributions respectively. A Monte Carlo propagation method was used to determine the upper and lower uncertainty margins of the distillate composition. The results of the application to a methanol-water distillation showed that the model uncertainty is as high as that of the feed variability. The information can be useful for the robust design of distillation towers

Microwave Non‐Destructive Testing of Non‐Dispersive and Dispersive Media Using High‐Resolution Methods

This chapter discusses the principle and application of two model‐based algorithms for processing non‐dispersive and dispersive ground penetrating radar (GPR) data over layered medium under monostatic antenna configuration. Both algorithms have been selected for their super‐time resolution capability and reduced computational burden; they allow GPR to measure a layer thickness smaller than the fraction of the dominant wavelength. For non‐dispersive data, the ESPRIT algorithm is generalized to handle different kinds of data models encountered in experiments and in the literature. For dispersive data, the proposed adaptation of the MPM algorithm allows recovering the full‐time resolution and jointly estimating the time delays and quality factors of a layered medium with reduced bias. Both processing techniques are applied to probe‐layered roadways for NDT&E purposes

EM characterization of concretes focused on water and chloride content in the frame of multi-linear experimental designs

GPR 2016, 16th International Conference of Ground Penetrating Radar, HONG KONG, CHINE, 13-/06/2016 - 16/06/2016This study is devoted to the electromagnetic (EM) characterization of concrete mixes within the ground-penetrating radar frequency band. Defining two specific experimental designs, water and chloride contents are studied in order to establish their relative sensitivity compared to the other parameters describing the mixes.The evaluation of the complex dielectric properties is carried out in laboratory on 24 and 36 different concrete samples (for the moisture and chloride studies respectively), for which composition parameters are the aggregate nature, the cement nature, the cement content and the water to cement ratio and conditions are the water saturation degree or the chloride content. In the case of the chloride experimental design, the mixes are tested dry and saturated.EM characterization is performed using a coaxial-cylindrical cell working in the frequency band [50 MHz - ~1000 MHz]. The models of relative permittivity associated to the experimental designs are multi-linear polynomials of the 4 or 5 chosen engineer parameters, depending to the study. The exploitation of the sets of data consist in a calculation level of the coefficients of the models independently for the real and the imaginary parts of the relative permittivity, for different frequencies. This reveals the significant relationship between the dielectric properties and the composition parameters, and their evolution function of the frequency.Raw results in terms of the real and imaginary parts of the dielectric permittivity along frequencies are presented for the different concretes, in dry and saturated conditions for the chloride experimental design, and the sensitivity of the parameters are discussed

A comparison of phase-shift and one-port coaxial cell permittivity measurements for GPR applications

The coarse and loose nature of unbound granular road materials presents a number of challenges for conventional permittivity characterisation approaches. An alternative that appears better suited to these materials involves measuring the phase-shift at discrete frequencies through a sample of known thickness. To validate this approach against more established methods, a comparison is required on materials that can be easily measured using either method. To this end phase-shift measurements were undertaken on a range of solid dielectric slabs including various types of stone, plastic and an artificial material. Permittivity predictions from this method were then compared to results from a one-port coaxial cell. As an additional comparison, and to better understand the results, the phase-shift test setup was also modelled using GPRMax software. To improve the predictions, reverberations within the test apparatus were minimized by isolating the direct wave using time-domain Blackman windowing. However, the narrow window necessary for this particular test setup also degraded the ability to detect frequency-dependent permittivity changes. Overall the phase-shift approach produced real relative permittivity predictions similar to that from the one-port coaxial cell. Despite limitations in the current approach, the results validate the phase-shift approach as a simple and rapid method of characterizing the permittivity of larger dielectric material samples of constant thickness

Effect of water and chloride contents and carbonation on the electromagnetic characterization of concretes on the GPR frequency band through designs of experiment

Water content, chloride content and carbonation are three durability indicators that affect not only concrete properties and integrity, but also the ground penetrating radar (GPR) response. This article characterizes the effect of water and chloride contents as well as carbonation on the high-frequency electromagnetic (EM) properties of concretes using a coaxial-cylindrical cell operating within the large frequency band from 50 MHz to appprox. 1000 MHz, thus making possible to study dispersion effects on the complex relative permittivity of various concretes. During a second step, three specific designs of experiment (DoE), involving water and chloride contents, and then carbonation, are designed and studied in order to establish the relative sensitivity of these parameters compared to others in describing the mixes at three different frequencies. The complex dielectric properties are evaluated in the laboratory on many concrete specimens (numbering 24, 36 and 24 for the moisture, chloride and carbonation studies respectively). For these evaluations, the composition parameters consist of nature of aggregate, nature of cement, cement content and water-to-cement ratio (W/C) while conditions are described by degree of water saturation, chloride content or carbonation. In the case of the chloride and carbonation DoEs, the mixes are tested under both dry and saturated conditions. The models describing complex relative permittivity, in association with the designs of experiment, are multilinear polynomials of the 4 or 5 identified engineering parameters, to be chosen depending on the study. The interpretation of datasets entails in independent calculation of model coefficients for the real and imaginary parts of relative permittivity, at the three chosen frequencies. This approach reveals the significant relationships existing between dielectric properties and composition parameters as well as their evolution versus frequency.The major results of this work can be summarized as follow:- The degree of water saturation amounts to about 80% on µ'r variability and 60% to 15% versus frequency on µ'r variability, for the first campaign.- The chloride content, while only visible in saturated mixes, represents approx. 40% and 50% with porosity (via the W/C ratio) accounting for some 30% and 40% on µ'r and µ'r variabilities, respectively.- Lastly, carbonation, while also only visible in saturated mixes, corresponds to a weight of about 14% in low frequencies and vanishes at high frequencies for µ'r variability; this amount rises to roughly 24% for µ'r variability

Modélisation et expérimentation radar impulsionnel et à sauts de fréquence pour l'auscultation de milieux stratifiés du génie civil

Dans cette thèse, nous avons étudié deux configurations d auscultation radar dans le but de remonter de manière non destructive à la connaissance des paramètres géométriques et électromagnétiques (EM) d un milieu stratifié, représentant des couches traitées de chaussées. Tout d abord, nous avons étudié le champ d une source ponctuelle, et dérivé les expressions mathématiques du champ reçu par un récepteur (les antennes étant assimilées à des dipôles électriques élémentaires) au-dessus d un milieu stratifié. Ensuite nous avons étudié une configuration d antennes au contact du milieu, en mode bistatique et avec une technique impulsionnelle. On a calculé le champ temporel reçu par le récepteur dans le cas de multicouche sans puis avec pertes, et proposé un modèle de propagation d onde EM. Selon ce modèle, on a développé un modèle inverse en pointant les temps d arrivée des ondes, fonction du milieu et de la distance entre émetteur et récepteur. La méthode de gradient a été utilisée pour reconstruire les permittivités et épaisseurs des couches. Enfin, une configuration d antenne découplée du milieu, en mode monostatique avec une technique à sauts de fréquence, a été étudiée. On a proposé un modèle direct utilisant la fonction de Green d un dipôle électrique élémentaire horizontal placé au-dessus d un multicouche. Pour remonter aux paramètres recherchés, nous avons retenu comme technique d optimisation globale la méthode de MSL . Dans la phase expérimentale, une procédure d étalonnage a été nécessaire pour remonter aux valeurs de la fonction de green à partir des mesures. Pour les deux configurations, des expérimentations ont validé notre modèle direct et inverse.In this thesis, we have studied two configurations of Penetrating Ground Radar (GPR) in order to survey non-destructively the geometrical and electromagnetic parameters of layered media that represent treated layers of road. First of all, we have studied the electric field of a point source, and derived the mathematical expressions of the field received by a receiver (antennas being simplified to elementary electric dipoles) over a layered medium. Then we have studied a configuration of antennas coupled with layered medium, on bi-static mode and with the impulse technique. We have calculated the transient field received by the receiver in the case of the medium without then with losses, and proposed a model of EM wave propagation. According to this model, we have developed an inverse model by picking propagation times of the waves, which are related to the medium and the distance between transmitter and receiver. The method of gradient has been used to estimate permittivities and thicknesses of the layers. Finally, an other configuration of air-coupled antenna, in mono-static mode with the step-frequency technique, has been studied. We have proposed a direct model using the function of Green of a horizontal elementary electric dipole placed over a layered medium. To estimate the parameters of the medium, the technique of global optimization has been adopted with the method "MSL". In the experimental phase, a procedure of calibration has been necessary to extract the values of the function of Green from measures. Experimentations have been done for both configurations in the sake of validation of our direct and inverse models.NANTES-BU Sciences (441092104) / SudocNANTES-BU Technologie (441092105) / SudocSudocFranceF

Caractérisation électromagnétique des matériaux traités de génie civil dans la bande de fréquences 50 MHz - 13 GHz

L'objectif de ce mémoire de thèse est l'identification et la mise au point de techniques permettant la mesure de la permittivité complexe des bétons dans le domaine de fréquence de fonctionnement des radar géophysiques. Deux techniques types ont été développées : une cellule en transition linge coaxiale/guide cylindrique (50 MHz 1,6 GHz) et deux sondes en guide d'onde rectangulaire (bandes spectrales retenues : [4 7 GHz] et [7 13 GHz]). Outre leurs caractères large bande et peu destructif, des simulations nume riques réalisées à l'aide d'un logiciel électromagnétique 3D ont montré que ces techniques présentent les avantages d'avoir une grande profondeur de pénétration, ainsi qu'une bonne sensibilité de mesure. Elles permettent alors de satisfaire le critère du Volume Élémentaire Représentatif (VER - taille minimale du matériau pour avoir des mesures représentatives). L'étude théorique des sondes/cellule a nécessité l'analyse des problèmes direct et inverse. L'étude du problème direct permet de calculer le coefficient de réflexion en fonction des propriétés diélectriques du matériau à caractériser. Le calcul de la permittivité à partir du coefficient de réflexion mesuré définit le problème inverse. Après la conception des dispositifs de mesure, les logiciels de dépouillement des données et d'étalonnage ont été validés sur des matériaux étalons. Enfin, Les mesures réalisées sur différents mélanges de béton ont montré que la nature des granulats joue un rôle prépondérant sur la variation de la permittivité, que la taille maximale des granulats influence la permittivité dans le domaine centimétrique, et que cette dernière varie linéairement en fonction de la compacité.The aim of this work is the identification and the development of techniques allowing the measurement of the complex permittivity of concrete in the frequency range of the geophysical radar or GPR (Ground Penetration Radar). Two typical techniques were developed: a coaxial/cylindrical waveguide cell (50 MHz - 1,6 GHz) and two ended rectangular waveguide probes (spectral bands: [ 4 - 7 GHz ] and [ 7 - 13 GHz ]). These methods presented the advantages that they are broadband and less destructive. In addition, the numerical simulations carried out with a 3D electromagnetic software showed that these techniques presented a great penetration depth, as well as a good sensitivity of measurement. Then, Tthey make it possible to satisfy the Representative Elementary Volume criterion (REV - minimal size of material to have representative measurements). The theoretical study of the probes/cellule required the analysis of the direct and inverse problems. The study of the direct problem allowed the calculation of the reflection coefficient according to the dielectric properties of the material under test. The calculation of the permittivity from the measured reflection coefficient defines the inverse problem. After the design of the measurement devices, the developed softwares have been validated by testing different materials with known permittivity. The measurements carried out on different mixtures showed that the type of the aggregates influence considerably the variation of the permittivity, the maximum size of the aggregates influences the permittivity in the centimetric wave range, and this latter varies linearly according to the compacity.NANTES-BU Sciences (441092104) / SudocNANTES-BU Technologie (441092105) / SudocSudocFranceF

Determination of concrete water content by coupling electromagnetic methods: Coaxial/cylindrical transition line with capacitive probes

This paper deals with the development and the validation of an innovative, easy-to-use and on site technique for determination of concrete water content. The on-site technique is the capacitive probe, able to characterize in situ dielectric media in the 30-35 MHz frequency band (around 33 MHz). For the evaluation of water content in various civil engineering structures, a calibration methodology has to be developed and is presented herein. It is based on the complex permittivity estimation of various dispersive concretes, which is carried out by a cylindrical coaxial electromagnetic (EM) transition line allowing the characterization in laboratory of material samples in a large GPR frequency bandwidth [50-600 MHz]. This methodology consists then on a coupling between the results of both the capacitive probes and the coaxial EM cell extrapolated at low frequency (33 MHz). The extrapolation procedure used to link physically the results of the two techniques is provided by the 4parameter-variant of Jonscher's model which is parameterized to obtain dispersion curves of the complex permittivity for very wide frequency bands. The methodology is checked by a parametric study that associates the 4p-variant of Jonscher's model with the physical and hydric characteristics of the six concrete mix designs representing high performance and ordinary concretes at various hydric states. The surface testing results measured by capacitive probes on slabs are successfully compared to the extrapolated results obtained on cores

Apport de techniques de traitement du signal super et haute résolution à l'amélioration des performances du radar-chaussée

Dans le domaine du génie civil, l'auscultation de couches minces de chaussée (de l'ordre de 2 cm d'épaisseur) est mal résolue par les techniques radar actuelles de Contrôle Non Destructif. Dans ce contexte, cette thèse a pour objectif d'améliorer, d'un facteur 3 à 6, la résolution temporelle des radars actuels par des techniques de traitement du signal dites super et haute résolution. Dans un premier temps, les méthodes super et haute résolution les plus connues de la littérature (LSMYW, MUSIC, ESPRIT, Min-Norm) sont évaluées à partir de signaux simulés. Les résultats montrent les variations de l'erreur quadratique moyenne sur l'épaisseur estimée de matériau, en fonction du rapport signal à bruit et du retard différentiel entre échos. Un critère de précision sur la mesure d'épaisseur permet de déduire la limite de résolution temporelle de chacun des algorithmes. Pour des échos fortement corrélés, on propose une optimisation du paramétrage de la technique de moyennage en sous-bande de fréquences. Quelque soit le niveau de corrélation, la limite de résolution temporelle obtenue permet de montrer la faisabilité de l'application. Dans un second temps, le document se focalise sur l'amélioration de techniques haute résolution de complexité calculatoire plus réduite. Tout d'abord, une version généralisée de l'algoritme ESPRIT (G-ESPRIT) est proposée, pour tenir compte de la forme de l'impulsion radar et des caractéristiques d'un bruit quelconque. Ensuite, deux méthodes linéaires à sous-espaces (OPM et SWEDE) sont introduites. Une version polynomiale d'OPM (root-OPM) permet d'accélérer la recherche des retards de propagation. La méthode SWEDE est transposée à l'estimation de retards; une nouvelle procédure de blanchiment permet d'améliorer ses performances (FBD-SWEDE). Puis, trois nouveaux algorithmes de traitement sont proposés, alliant les avantages calculatoires des algorithmes SWEDE et ESPRIT (ESPRIT-WED, AV-ESPRIT-WED, G-ESPRIT-WED). Enfin, toutes les méthodes de traitement présentées dans ce document sont expérimentées sur des signaux radar impulsionnel et à sauts de fréquence, obtenus sur un milieu-modèle monocouche et bicouche. La mise en oeuvre des algorithmes est détaillée. Les résultats permettent d'une part de valider les résultats théoriques et de montrer la faisabilité de la mesure de couches minces de chaussée à l'aide d'un radar de 2 GHz de largeur de bande.In the field of civil engineering, the pavement survey of the top-layer of roadways is hardly performed by the current radar Non Destructive Techniques. Thanks to the use of special signal processing techniques applied to time delay estimation (TDE), this thesis aims at improving the time resolution of the processing of radar data by 3 at least. At first, the most well-known super and high resolution techniques (LSMYW, MUSIC, ESPRIT, Min-Norm) are performed on simulated data. The performance of algorithhms are assessed in terms of the root mean square error on the estimated thickness of pavement material. For highly correlated echoes, the sub-band smoothing techniques is optimized. The ultimate time resolution of each algorithm is attached to a given accuracy on thickness. Whatever the correlation magnitude is, the performances of algorithms are sufficient to fullfil the required criterion for the NDT application. Then, among the subspace algorithms, the study focusses on those which require a lower computational cost. The ESPRIT algorithm is reconsidered and extended to the signal model with the radar pulse and any noise characteristics accounted for in the mathematical formalism. Moreover, two linear subspace algorithms (OPM and SWEDE) are introduced. A polynomial solution is proposed for OPM (root-OPM) to perform the TDE faster. SWEDE is formulated to the TDE, and a more efficient whitening technique is proposed to improve its performance (FBD-SWEDE). At last, the principle of both SWEDE and ESPRIT algorithms are joined to propose three new algorithms applied to the TDE of radar signal (ESPRIT-WED, AV-ESPRIT-WED, G-ESPRIT-WED). Endly, the algorithms are tested on radar data, which are obtained from measurements on one layer and two-layers media. The implementation of algorithms is detailed for both types of GPR devices (step-frequency and pulse radars). The results are found in accordance with the simulated results and allow us to conclude on the feasibility of the thin pavement thickness measurement from a 2 GHz radar bandwidth.NANTES-BU Sciences (441092104) / SudocSudocFranceF