MPEG audio compression techniques significantly reduces the storage and transmission requirements for high quality digital audio. However, compression complicates the processing of audio in many applications. If a compressed audio signal is to be processed, a direct method would be to decode the compressed signal, process the decoded signal and re-encode it. This is computationally expensive due to the complexity of the MPEG filter bank. This thesis deals with processing of MPEG compressed audio. The main contributions of this thesis are a) Extracting wavelet coefficients in the MPEG compressed domain. b) Wavelet based pitch extraction in MPEG compressed domain. c) Time Scale Modifications of MPEG audio. d) Watermarking of MPEG audio. The research contributions starts with a technique for calculating several levels of wavelet coefficients from the output of the MPEG analysis filter bank. The technique exploits the toeplitz structure which arises when the MPEG and wavelet filter banks are represented in a matrix form, The computational complexity for extracting several levels of wavelet coefficients after decoding the compressed signal and directly from the output of the MPEG analysis filter bank are compared. The proposed technique is found to be computationally efficient for extracting higher levels of wavelet coefficients. Extracting pitch in the compressed domain becomes essential when large multimedia databases need to be indexed. For example one may be interested in listening to a particular speaker or to listen to male female audio segments in a multimedia document. For this application, pitch information is one of the very basic and important features required. Pitch is basically the time interval between two successive glottal closures. Glottal closures are accompanied by sharp transients in the speech signal which in turn gives rise to a local maxima in the wavelet coefficients. Pitch can be calculated by finding the time interval between two successive maxima in the wavelet coefficients. It is shown that the computational complexity for extracting pitch in the compressed domain is less than 7% of the uncompressed domain processing. An algorithm for extracting pitch in the compressed domain is proposed. The result of this algorithm for synthetic signals, and utterances of words by male/female is reported. In a number of important applications, one needs to modify an audio signal to render it more useful than its original. Typical applications include changing the time evolution of an audio signal (increase or decrease the rate of articulation of a speaker),or to adapt a given audio sequence to a given video sequence. In this thesis, time scale modifications are obtained in the subband domain such that when the modified subband signals are given to the MPEG synthesis filter bank, the desired time scale modification of the decoded signal is achieved. This is done by making use of sinusoidal modeling [I]. Here, each of the subband signal is modeled in terms of parameters such as amplitude phase and frequencies and are subsequently synthesised by using these parameters with Ls = k La where Ls is the length of the synthesis window , k is the time scale factor and La is the length of the analysis window. As the PCM version of the time scaled signal is not available, psychoacoustic model based bit allocation cannot be used. Hence a new bit allocation is done by using a subband coding algorithm. This method has been satisfactorily tested for time scale expansion and compression of speech and music signals. The recent growth of multimedia systems has increased the need for protecting digital media. Digital watermarking has been proposed as a method for protecting digital documents. The watermark needs to be added to the signal in such a way that it does not cause audible distortions. However the idea behind the lossy MPEC encoders is to remove or make insignificant those portions of the signal which does not affect human hearing. This renders the watermark insignificant and hence proving ownership of the signal becomes difficult when an audio signal is compressed. The existing compressed domain methods merely change the bits or the scale factors according to a key. Though simple, these methods are not robust to attacks. Further these methods require original signal to be available in the verification process. In this thesis we propose a watermarking method based on spread spectrum technique which does not require original signal during the verification process. It is also shown to be more robust than the existing methods. In our method the watermark is spread across many subband samples. Here two factors need to be considered, a) the watermark is to be embedded only in those subbands which will make the addition of the noise inaudible. b) The watermark should be added to those subbands which has sufficient bit allocation so that the watermark does not become insignificant due to lack of bit allocation. Embedding the watermark in the lower subbands would cause distortion and in the higher subbands would prove futile as the bit allocation in these subbands are practically zero. Considering a11 these factors, one can introduce noise to samples across many frames corresponding to subbands 4 to 8. In the verification process, it is sufficient to have the key/code and the possibly attacked signal. This method has been satisfactorily tested for robustness to scalefactor, LSB change and MPEG decoding and re-encoding.

Les progrès en anesthésie et en réanimation ont pour objectifs la réduction de la durée de surveillance et l'amélioration de la qualité de la récupération. Pour le cas particulier de l'assistance respiratoire, la capacité de surveiller et d'optimiser l'adaptation entre le patient et sa machine d'assistance est déterminante pour la qualité et la conduite des soins. Ce travail de thèse concerne dans sa première partie la mise en place et la validation d'un outil instrumental permettant de caractériser un comportement respiratoire par l'étude cycle à cycle du délai d'activation inspiratoire entre les muscles des voies aériennes supérieures et de la cage thoracique. Cet outil doit prendre en compte les contraintes imposées par le milieu clinique telle qu'une mesure non-invasive des muscles respiratoires. Il repose sur une mesure électromyographique (EMG) de surface des muscles respiratoires. La mesure cycle à cycle et par voie de surface du délai d'activation est un véritable challenge dans un environnement clinique qui est fortement perturbé. La démarche choisie ici est double avec en parallèle : i) La mise en place d'un outil de détection d'évènements menée sous supervision. ii) La définition d'un protocole original sur sujets sains prenant en compte les contraintes cliniques et permettant de valider l'outil et de constituer une base de connaissances pour envisager l'automatisation des procédés dans un travail futur. D'un point de vue physiologique, l'influence de la fréquence respiratoire sur le délai d'activation de l'inspiration n'a pas été étudiée à ce jour. Ce délai a donc été mesuré en condition de normocapnie à différentes fréquences respiratoires imposées par un stimulus sonore. Une étude statistique montre que l'instrument permet de distinguer deux situations physiologiques du protocole expérimental, ce qui en dé- montre la sensibilité. La deuxième partie de ce travail de thèse s'inscrit dans le cadre d'une optimisation des méthodes de détection de singularités d'intérêt. La solution choisie ici se base sur l'intensité structurelle qui calcule la "densité" de maxima d'ondelettes à différentes échelles et permet une localisation des singularités d'un signal bruité. Une formulation de cet outil qui utilise la transformée de Berkner est proposée. Celle-ci permet le chaînage des maxima d'ondelette afin de positionner précisément les amers du signal. Le filtrage de l'artefact ECG dans l'EMG diaphragmatique sans signal de référence est proposé comme exemple d'application. / Better care in an anaesthesia and critical care could be achieved by reducing monitoring duration and improving the quality of recovery. For the particular case of respiratory assistance, the capacity to track and optimize patient-ventilator synchrony is essential to quality care. As a first step, this thesis adresses the development and validation of an instrument which characterizes respiratory behavior by studying the time lag between onset of upper airway muscles and rib cage muscles, cycle by cycle during respiration. This tool must take into account the constraints imposed by the clinical environment ; measuring respiratory muscles by surface electromyographic measurements (EMG). Measurement of the onset time lag, cycle by cycle and non invasively, is a true challenge in a critical care clinical environment. Here the approach is two-fold : i) The development of a tool for events detection. ii) The definition of an original protocol on healthy subjects. The tool development constitutes a knowledge bases to eventually develop automation of the processes in future work. From a physiological point of view, the influence of respiratory rate on the EMG onset time lag during inspiration has not been studied. Thus we measured this time lag in normocapnia at various respiratory rates imposed by a sound stimulus. Statistically, the instrumental tool can distinguish two physiological situations in this experimental protocol, which confirms its sensitivity. The second step of this thesis is part of an optimization of events detection methods with singularities of interest. The chosen solution is based on structural intensity which computes the "density" of the locations of the modulus maxima of a wavelet representation along various scales in order to identify singularities of an unknown signal. An improvement is proposed by applying Berkner transform which allows maxima linkage to insure accurate localization of landmarks. An application to cancel ECG interference in diaphragmatic EMG without a reference signal is also proposed. / Réalisé en cotutelle avec l'Université Joseph Fourier École Doctorale Ingénierie pour la Santé,la Cognition et l'Environnement (France)

L'objectif général de la thèse est d'améliorer la modélisation numérique RANS des flux thermiques turbulents notamment en proposant un modèle fonctionnant dans les trois régimes de convection thermique (forcée, mixte et naturelle).Pour ce faire, un état des lieux, non exhaustif, des modèles des flux thermiques utilisant les approches algébriques et à équations de transport, est effectué. Puis, le modèle EB-RSM (Elliptic Blending-Reynolds Stress Model) étant utilisé pour modéliser la turbulence, le principe de la pondération elliptique est appliqué aux modèles des flux thermiques turbulents algébriques EB-GGDH (EB-General Gradient Diffusion Hypothesis), EB-AFM (EB-Algebraic Flux Model) et à équations de transport EB-DFM (EB-Differential Flux Model). Une attention particulière a été apportée aux échelles de temps et de longueur utilisées pour ces modèles. Il en résulte qu'utiliser une échelle de longueur thermique différente de l'échelle de longueur dynamique et une échelle de temps mixte dans le terme de flottabilité de l'équation de la dissipation turbulente est préférable.Pour valider les formulations retenues, nous avons effectué des tests pour des fluides usuels (nombre de Prandtl de l’ordre de 1) dans les trois régimes de convection à l'aide de l'outil de calcul Code_Saturne sur des configurations académiques, semi-académiques et industrielles.Des résultats satisfaisants ont été obtenus en associant l'EB-RSM et le GGDH en convection forcée ou mixte et l'EB-RSM aux modèles EB-DFM et AFM en convection naturelle. / The PhD main objective is to improve the turbulent heat flux RANS modelling especially by proposing a model working in the three thermal convection regime (forced, mixed and natural).In order to achieve this, a non-exhaustive state of art of heat flux model, using algebraic approach and transport equations, is done. Then, as EB-RSM model (Elliptic Blending-Reynolds Stress Model) is used to model turbulence, elliptic blending approach is apply to algebraic turbulent heat flux model EB-GGDH (EB-General Gradient Diffusion Hypothesis), EB-AFM (EB-Algebraic Flux Model) and transport equation model EB-DFM (EB-Differential Flux Model). Special attention was paid to time and length scales used with these models. It follows that using a thermal length scale different from dynamic length scale and a mixed time scale in the buoyant term of turbulent dissipation equation is better.To validate these models, some test were done for common fluids (Prandtl number in the order of 1) in the three convection regimes with the tool Code_Saturne on academic, mid-academic and industrial cases.Good results were obtained combining EB-RSM with GGDH in forced or mixed convection and EB-RSM with EB-DFM or AFM in natural convection.

Notre travail porte sur une analyse des pratiques de classe au cours de la mise en œuvre d’une séquence d’enseignement sur les circuits électriques en 5ème. Nous étudions la vie du savoir, son évolution et sa continuité à travers ces pratiques. Nos outils théoriques s'appuient largement sur la Théorie de l’Action Conjointe en Didactique (TACD) qui permet la description de la pratique en fournissant des outils pour cette description notamment la notion de jeu. Nous étudions dans un premier temps les effets des pratiques de classe sur la vie du savoir, ensuite nous effectuons une étude sur la continuité du savoir. Notre analyse des effets des pratiques de classe sur la vie du savoir se fonde principalement sur notre analyse en jeux et elle est complétée par une analyse au niveau microscopiques en facettes qui représentent des parties du discours de l’ordre d’une phrase ou d’une intervention portant sur un élément de savoir. L’étude de l’ensemble des jeux des séances analysées nous a permis de distinguer certains jeux particuliers du point de vue du développement du savoir. L’étude de ces jeux nous a permis de montrer l’influence des actions du professeur et des élèves sur l’évolution du savoir. Une comparaison avec ce qui était prévu par le professeur selon les propositions des concepteurs de la séquence montre deux cas de développement suivant la façon dont le professeur prend l’activité effective des élèves en considération. Dans un cas il y a un élargissement et une densification du savoir autour d’une notion, les éléments de savoirs introduits sont en cohérence et continuité avec ceux déjà introduits, et dans l’autre cas il apparaît une dispersion des éléments de savoir autour d’une notion, les éléments de savoir introduits n’ont pas ou peu de lien avec l’enjeu de savoir.Dans notre étude nous considérons que la continuité du savoir est établie grâce à des liens créés entre éléments de savoir, méthode, procédure ou discussions à propos de ces éléments, qui peuvent avoir été en jeu à différents moments de leur enseignement., Pour cette étude la méthodologie est adaptée à la définition de la continuité et à nos données, elle inclut une analyse microscopique en facettes nourrie dans certains cas par l’analyse en jeux. Nous avons construit des catégories du fonctionnement du savoir qui permettent de relier des éléments de savoir introduits à différents moments de l’enseignement. Pour cela nous avons fait appel aux niveaux de modélisation ainsi qu’aux taches épistémiques comme définir, interpréter, décrire, comparer, etc.Cette analyse a montré que le développement du savoir est principalement initié par le champ expérimental et non par des relations entre concepts. Les nouveaux concepts sont introduits lors du passage d’une description entre objets et événements à une conceptualisation ou relation entre concepts. Cette introduction est assez souvent imposée et peut expliquer des discontinuités repérées dans la séquence.Pour terminer nous proposons des perspectives pour la formation des maitres et la conception de séquences. / Our work is focused on the analysis of classroom practices during a physics teaching sequence on electrical circuits in 7th grade. We study the life of knowledge, its evolution and continuity through these practices. Our theoretical tools are largely based on the Joint Action Theory in Didactics (JATD) that allows us to describe the practices by providing tools for this description especially the concept of the learning games. We first study the effects of classroom practices on the knowledge’s life, then we study the continuity of knowledge.Our analysis of classroom practices’effects on the life of knowledge is based primarily on our learning games analysis and is completed by a microscopic level analysis of facets that represent parts of a speech at the level of a sentence or an intervention on an element of knowledge. The study of the whole learning games analysed in the studied sessions allowed us to distinguish some particular learning games from the development of knowledge perspective. The study of these games allowed us to show the influence of the actions of the teacher and students on the evolution of knowledge. A comparison with what was planned by the teacher according to the proposals of the designers of the sequence shows two cases of development according to the way the teacher takes into considerationthe actual activity of the students. In one case there is an enlargement and densification of knowledge about a concept, elements of knowledge are introduced in consistency and continuity with those already introduced. In the other case there is dispersion of knowledge elements around a concept, elements of knowledge introduced has no or little connection with the knowledge at stake.In our study we consider that the continuity of knowledge is established through links between elements of knowledge, methods, procedures or discussions about these elements, at different teaching moments. Thus, in order to study the continuity of knowledge, we built a methodology adapted to this definition and our data by relying on microscopic analysis of facets completed in some cases by our learning games analysis. We built categories of processing knowledge that allows to connect different elements of knowledge introduced at different teaching moments. For this purpose, we used the modelling levels as well as the epistemic tasks such as defining, interpreting, describing, comparing, etc. This analysis ha shown that the development of knowledge is mainly initiated by the experimental field and not by relations between concepts. The new concepts are introduced during the passage of a description between objects and events to a conceptualization or relationship between concepts. This introduction is often imposed and may explain discontinuity of knowledge identified in the sequence.Finally, we offer perspectives for teacher training and sequences design.

Ce manuscrit porte sur la modélisation et l'estimation de certaines non-stationnarités dans les signaux audio. Nous nous intéressons particulièrement à une classe de modèles de sons que nous nommons timbre*dynamique dans lesquels un signal stationnaire, associé au phénomène physique à l'origine du son, est déformé au cours du temps par un opérateur linéaire unitaire, appelé opérateur de déformation, associé à l'évolution temporelle des caractéristiques de ce phénomène physique. Les signaux audio sont modélisés comme des processus gaussiens généralisés et nous donnons dans un premier temps un ensemble d'outils mathématiques qui étendent certaines notions utilisées en traitement du signal au cas des processus stochastiques généralisés.Nous introduisons ensuite les opérateurs de déformations étudiés dans ce manuscrit. L'opérateur de modulation fréquentielle qui est l'opérateur de multiplication par une fonction à valeurs complexes de module unité, et l'opérateur de changement d'horloge qui est la version unitaire de l'opérateur de composition.Lorsque ces opérateurs agissent sur des processus stationnaires les processus déformés possèdent localement des propriétés de stationnarité et les opérateurs de déformation peuvent être approximés par des opérateurs de translation dans les plans temps-fréquence et temps-échelle. Nous donnons alors des bornes pour les erreurs d'approximation correspondantes. Nous développons ensuite un estimateur de maximum de vraisemblance approché des fonctions de dilatation et de modulation. L'algorithme proposé est testé et validé sur des signaux synthétiques et des sons naurels. / This manuscript deals with the modeling and estimation of certain non-stationarities in audio signals. We are particularly interested in a sound class models which we call dynamic*timbre in which a stationary signal, associated with the physical phenomenon causing the sound, is deformed over time by a linear unitary operator, called deformation operator, associated with the temporal evolution of the characteristics of this physical phenomenon.Audio signals are modeled as generalized Gaussian processes. We give first a set of mathematical tools that extend some classical notions used in signal processing in case of generalized stochastic processes.We then introduce the two deformations operators studied in this manuscript. The frequency modulation operator is the multiplication operator by a complex-valued function of unit module and the time-warping operator is the unit version of the composition operator by a bijective function.When these operators act on generalized stationary processes, deformed process are non-stationary generalized process which locally have stationarity properties and deformation operators can be approximated by translation operators in the time-frequency plans and time-scale.We give accurate versions of these approximations, as well as bounds for the corresponding approximation errors.Based on these approximations, we develop an approximated maximum likelihood estimator of the warping and modulation functions. The proposed algorithm is tested and validated on synthetic signals. Its application to natural sounds confirm the validity of the timbre*dynamic model in this context.

Cette thèse est une contribution au calcul des variations et à la théorie du contrôle optimal dans les cadres discret, plus généralement time scale, et fractionnaire. Ces deux domaines ont récemment connu un développement considérable dû pour l’un à son application en informatique et pour l’autre à son essor dans des problèmes physiques de diffusion anormale. Que ce soit dans le cadre time scale ou dans le cadre fractionnaire, nos objectifs sont de : a) développer un calcul des variations et étendre quelques résultats classiques (voir plus bas); b) établir un principe du maximum de Pontryagin (PMP en abrégé) pour des problèmes de contrôle optimal. Dans ce but, nous généralisons plusieurs méthodes variationnelles usuelles, allant du simple calcul des variations au principe variationnel d’Ekeland (couplé avec la technique des variations-aiguilles), en passant par l’étude d’invariances variationnelles par des groupes de transformations. Les démonstrations des PMPs nous amènent également à employer des théorèmes de point fixe et à prendre en considération la technique des multiplicateurs de Lagrange ou encore une méthode basée sur un théorème d’inversion locale conique. Ce manuscrit est donc composé de deux parties : la Partie 1 traite de problèmes variationnels posés sur time scale et la Partie 2 est consacrée à leurs pendants fractionnaires. Dans chacune de ces deux parties, nous suivons l’organisation suivante : 1. détermination de l’équation d’Euler-Lagrange caractérisant les points critiques d’une fonctionnelle Lagrangienne ; 2. énoncé d’un théorème de type Noether assurant l’existence d’une constante de mouvement pour les équations d’Euler-Lagrange admettant une symétrie ; 3. énoncé d’un théorème de type Tonelli assurant l’existence d’un minimiseur pour une fonctionnelle Lagrangienne et donc, par la même occasion, d’une solution pour l’équation d’Euler-Lagrange associée (uniquement en Partie 2) ; 4. énoncé d’un PMP (version forte en Partie 1, version faible en Partie 2) donnant une condition nécessaire pour les trajectoires qui sont solutions de problèmes de contrôle optimal généraux non-linéaires ; 5. détermination d’une condition de type Helmholtz caractérisant les équations provenant d’un calcul des variations (uniquement en Partie 1 et uniquement dans les cas purement continu et purement discret). Des théorèmes de type Cauchy-Lipschitz nécessaires à l’étude de problèmes de contrôle optimal sont démontrés en Annexe. / This dissertation deals with the mathematical fields called calculus of variations and optimal control theory. More precisely, we develop some aspects of these two domains in discrete, more generally time scale, and fractional frameworks. Indeed, these two settings have recently experience a significant development due to its applications in computing for the first one and to its emergence in physical contexts of anomalous diffusion for the second one. In both frameworks, our goals are: a) to develop a calculus of variations and extend some classical results (see below); b) to state a Pontryagin maximum principle (denoted in short PMP) for optimal control problems. Towards these purposes, we generalize several classical variational methods, including the Ekeland’s variational principle (combined with needle-like variations) as well as variational invariances via the action of groups of transformations. Furthermore, the investigations for PMPs lead us to use fixed point theorems and to consider the Lagrange multiplier technique and a method based on a conic implicit function theorem. This manuscript is made up of two parts : Part A deals with variational problems on time scale and Part B is devoted to their fractional analogues. In each of these parts, we follow (with minor differences) the following organization: 1. obtaining of an Euler-Lagrange equation characterizing the critical points of a Lagrangian functional; 2. statement of a Noether-type theorem ensuring the existence of a constant of motion for Euler-Lagrange equations admitting a symmetry;3. statement of a Tonelli-type theorem ensuring the existence of a minimizer for a Lagrangian functional and, consequently, of a solution for the corresponding Euler-Lagrange equation (only in Part B); 4. statement of a PMP (strong version in Part A and weak version in Part B) giving a necessary condition for the solutions of general nonlinear optimal control problems; 5. obtaining of a Helmholtz condition characterizing the equations deriving from a calculus of variations (only in Part A and only in the purely continuous and purely discrete cases). Some Picard-Lindelöf type theorems necessary for the analysis of optimal control problems are obtained in Appendices.

Monte-Carlo calculations are used to simulate the stochastic effects of fast neutron-induced chemical changes in the radiolysis of the ferrous sulfate (Fricke) dosimeter. To study the dependence of the yield of ferric ions, G(Fe[superscript 3+]), on fast neutron energy, we have simulated, at 25 [degree centigrade], the oxidation of ferrous ions in aerated aqueous 0.4 M H[subscript 2]SO[subscript 4] (pH 0.46) solutions when subjected to ~0.5-10 MeV incident neutrons, as a function of time up to ~50 s. The radiation effects due to fast neutrons are estimated on the basis of track segment (or"escape") yields calculated for the first four recoil protons with appropriate weighting according to the energy deposited by each of these protons. For example, a 0.8-MeV neutron generates recoil protons of 0.505, 0.186, 0.069, and 0.025 MeV, with linear energy transfer (LET) values of ~41, 69, 82, and 62 keV/[micro]m, respectively. In doing so, we consider that further recoils make only a negligible contribution to radiation processes. Our results show that the radiolysis of dilute aqueous solutions by fast neutrons produces smaller radical yields and larger molecular yields (relative to the corresponding yields for the radiolysis of water by [superscript 60]Co [gamma]-rays or fast electrons) due to the high LET associated to fast neutrons. The effect of recoil ions of oxygen, which is also taken into account in the calculations, is shown to decrease G(Fe[superscript 3+]) by about 10%. Our calculated values of G(Fe[superscript 3+]) are found to increase slightly with increasing neutron energy over the energy range covered in this study, in good agreement with available experimental data. We have also simulated the effect of temperature on the G(Fe[superscript 3+]) values in the fast neutron radiolysis of the Fricke dosimeter from 25 to 300 [degree centigrade]. Our results show an increase of G(Fe[superscript 3+]) with increasing temperature, which is readily explained by an increase in the yields of free radicals and a decrease in those of molecular products. For 0.8-MeV incident neutrons (the only case for which experimental data are available in the literature), there is a ~23% increase in G(Fe[superscript 3+]) on going from 25 to 300 [degree centigrade]. Although these results are in reasonable agreement with experiment, more experimental data, in particular for different incident neutron energies, would be needed to test more rigorously our Fe[superscript 3+] ion yield results at elevated temperatures.

在這篇論文中，我們討論的是一階非線性衝擊動態方程的週期邊界值問題。利用Schaefer定理及Banach固定點定理，我們得到一些解的存在性結果。 / In this thesis, we are concernd with nonlinear first-order periodic boundary value problems of impulsive dynamic equations on time scales. By using Schaefer’s theorem and Banach’s fixed point theorem we acquire some new existence results.

Cette thèse est une contribution au problème du pronostic des systèmes complexes. Plus précisément, elle concerne l'approche basée modèles et est composée de trois contributions principales. Tout d'abord, dans une première contribution une définition du concept de pronostic est proposée et est positionnée par rapport aux concepts de diagnostic et de diagnostic prédictif. Pour cela, une notion de contrainte temporelle a été introduite afin de donner toute pertinence à la prédiction réalisée. Il a également été montré comment le pronostic est lié à la notion d'accessibilité en temps fini.La deuxième contribution est dédiée à l'utilisation des observateurs à convergence en temps fini pour la problématique du pronostic. Une méthodologie de pronostic est présentée pour les systèmes non linéaires à échelle de temps multiple. Puis, une troisième contribution est introduite par l'utilisation des observateurs par intervalle pour le pronostic. Une méthodologie de pronostic est proposée pour les systèmes non linéaires incertains à échelle de temps multiple. Pour illustrer les différents résultats théoriques, des simulations ont été conduites sur un modèle de comportement d'un oscillateur électromécanique. / This thesis is a contribution to the problem of a complex system prognosis. More precisely, it concerns the model-based prognosis approach and the thesis is divided into three main contributions. First of all, a definition of prognosis concept is proposed as a first contribution and is positionned in reference to the diagnosis and predictive diagnosis concepts. For that, a notion of temporal constraint is introduced to give all pertinence to the prediction achieved. It is also shown how prognosis is linked to the finite time reachability notion. The second contribution is dedicated to the use of finite time convergence observer for the prognosis problem. A prognosis methodology is presented for nonlinear multiple time scale systems. Then, a last contribution is introduced through the use of interval observer for the prognosis problem. A pronognosis methodology is proposed for nonlinear uncertain multiple time scale systems. To illustrate the theorical results, simulations are achieved based on a model of an electromechanical oscillator system.

Trabalhos prévios mostram que a variabilidade do gelo marinho antártico em diversas escalas temporais está intimamente relacionada a mecanismos de teleconexões trópicos-extratrópicos. Com base nesta hipótese, este trabalho pretende estabelecer a resposta da passagem dos trens de ondas em latitudes médias, associados a fenômenos de escala intrasazonal (20-100 dias) como a Oscilação de Madden-Julian (Madden-Julian Oscillation ou MJO), nas camadas superiores do Oceano Austral (OA) e impactos no gelo marinho antártico. O período investigado neste estudo é 19892007, com ênfase no inverno e sobre o mar de Ross, localizado no setor Pacífico austral (região diretamente afetada pela passagem dos trens de ondas de latitudes médias). Composições com defasagens (lag composites) de anomalias intrasazonais da tensão de cisalhamento do vento (zonal e meridional) mostram que correntes oceânicas são geradas em resposta a essa forçante atmosférica sobre o oceano no setor Pacífico austral. O transporte zonal e meridional de massa na camada de Ekman oceânica indica que divergência de massa nessa camada precede os eventos extremos intrasazonais de retração do gelo marinho em Ross (EIR). Em contraste, convergência precede períodos de eventos extremos intrasazonais de expansão do gelo marinho em Ross (EIE). A divergência (convergência) de massa na camada de Ekman associada com anomalias intrasazonais do bombeamento de Ekman resulta em ressurgência (subsidência) que precede a ocorrência de EIR (EIE). Alguns trabalhos mostram que águas intermediárias antárticas, que são relativamente mais quentes no inverno em relação às águas superficiais que estão próximas ao ponto de congelamento (ou congeladas), são dirigidas para a superfície do oceano pelo bombeamento de Ekman e ocasionam o derretimento do gelo marinho. Anomalias do transporte meridional de calor na camada de Ekman oceânica mostram que durante os EIR (EIE), calor é transportado para dentro (fora) do mar de Ross entre 15 e 8 dias (12 e 8 dias) precedentes aos EIR (EIE). Anomalias intrasazonais do fluxo de calor na interface ar-mar mostram que precedendo o dia de observação dos EIR (EIE) o fluxo de calor é direcionado da atmosfera para o oceano (do oceano para a atmosfera), sendo essa configuração associada a um ganho (perda) de calor no oceano superior em Ross. Em todas as composições, observa-se a mudança de fase das anomalias nos dias posteriores (lags positivos) ao dia dos EIG e são consistentes com a propagação do modo conhecido como Pacific-South-American (PSA), identificado nesse trabalho por meio de anomalias intrasazonais da altura geopotencial em 200 hPa. Além disso, uma diferença notada em alguns casos nas lag-composities é que em períodos de MJO ativa, as anomalias parecem estar mais deslocadas para o sul do que em períodos de MJO inativa. Em períodos de MJO inativa foram observados 15 (13) eventos de EIR (EIE), enquanto que, em períodos de MJO ativa observou-se 25 (24) eventos de EIR (EIE). Observa-se ainda que há uma maior quantidade de ciclones quando a MJO está presente. Por exemplo, o número de ciclones com duração a partir de 12 horas para períodos sem MJO foi igual a 146 para os EIR e 130 para os EIE. Já o número de ciclones para períodos com MJO foi igual a 311 para os EIR e 278 para os EIE. Com isso, observa-se claramente o papel da MJO na circulação de latitudes média e possíveis associações com o gelo marinho, pois é sabido que a atividade ciclônica está relacionada à advecção de massas de ar sobre o gelo marinho, além da advecção do próprio gelo marinho. Para investigar em detalhes a interação oceano-atmosfera-gelo marinho foram examinados casos persistentes de EIR e EIE. Os casos mais persistentes de EIR (EIE) tiveram durações de 34 e 30 (26 e 25) dias, sendo esses os casos analisados. Mostra-se que as anomalias intrasazonais da circulação atmosférica em baixos níveis (em 850 hPa) estão associadas a advecções quentes (frias) na proporção de aproximadamente 0,5 1 (0,1 1) m.s-1 em períodos precedentes aos EIR (EIE). No geral, anomalias em latitudes médias da circulação atmosférica ciclônicas (anti-ciclônicas) e divergência (convergência) das correntes oceânicas superficiais aparecem relacionadas à ressurgência (subsidência) da ordem de 0,1 0,3 m2.s-1 em algumas pêntadas anteriores a pêntada que corresponde ao início dos supercasos de EIR (EIE). Os padrões mudam de fase com o tempo, o que sugere a propagação de um padrão de onda em escala intrasazonal. Estas anomalias mostram-se abrangendo dimensões espaciais que compreendem grande parte do setor Pacífico austral, incluindo o mar de Ross. Impactos associados a estas anomalias podem ser verificados diretamente no mar de Ross através das análises da concentração do gelo marinho em Ross. Anomalias intrasazonais negativas (positivas) da concentração do gelo marinho predominam sobre o campo do gelo marinho do mar de Ross nas primeiras pêntadas a partir daquela que indica o início dos casos persistentes de EIR (EIE). Durante os períodos de EIR, as anomalias intrasazonais negativas da concentração do gelo mostram-se da ordem de aproximadamente 5% a 10% no interior do mar de Ross e entre 15% a 30% nas bordas do gelo marinho de Ross. Já durante os períodos de EIE, as anomalias intrasazonais positivas da concentração do gelo marinho em Ross mostram-se da ordem de 10% a 30% nas bordas do gelo marinho do mar de Ross. Esse resultado mostra que a resposta do gelo marinho aos padrões atmosféricos e oceânicos em escala intrasazonal possui uma defasagem entre 5 e 1 pêntada(s). No geral, este trabalho cumpriu o objetivo de verificar as respostas do oceano às anomalias da circulação atmosférica e impactos associados no gelo marinho, em escala intrasazonal. / Previous works show that antarctic sea ice variability on several time-scales is close related to tropics-extratropics teleconections mechanisms. Based on this hyphotesis, this work intend to verify the responses in oceanic upper layers of Austral Ocean on intraseasonal time-scale (20-100 days) phenomenom and impacts on sea ice due to anomalous atmospheric circulation associated to the Madden-Julian Oscillation (MJO). The period analysed in this study is from 1989 to 2007, with emphasis on winter season and on Ross Sea (located at austral Pacific sector). Lag composities of zonal and meridional intraseasonal wind stress anomalies show that oceanic currents are generated as a response of these atmospheric forcings on austral Pacific sector. Zonal and meridional mass transport on oceanic Ekman layer, which are perpendicular and to the left of wind stress at Southern Hemisphere (SH), indicate that Ekman mass divergence precedes intraseasonal Ross sea ice extreme retraction (EIR). In contrast, convergence precedes the periods of extreme intraseasonal Ross sea ice expantion (EIE). Divergence (convergence) on oceanic Ekman layer associated to intraseasonal Ekman pumping anomalies results in upwelling (downwelling) wich precedes the occurrence of EIR (EIE). Some works have already shown that intermediate antarctic waters, wich are relatively warmer in the wintertime when compared to superficial waters that are next to the freezing point (or freezed), are headed to ocean surface due to Ekman pumping, generating sea ice melt. Intraseasonal anomalies of sea-air heat flux show that days before EIR (EIE) occurrences, the flux is headed from atmosphere to the ocean (from ocean to the atmosphere), which configuration is associated to the earn (loss) of heat at Ross upper ocean. In all compositions, the change of anomalies phase on the days before EI occurrence (positive lags) is clearly noticed and is consistent to the propagations of the mode known as Pacific South American (PSA), revealed in intraseasonal anomalies of geopotencial height at 200 hPa. Furthermore, in some cases (as in the case of Ekman pumping and Sverdrup transport) the anomalies seem to be deplaced southward in active MJO periods than in inactive MJO periods. In inactive MJO periods were observed 15 (13) EIR (EIE) events, while in active MJO periods were observed 25 (24) EIR (EIE) events. Furthermore, the number of cyclones during EIR periods was bigger than during EIE periods. In addiction, more cyclones were observed when MJO is active. For example, the number of cyclones with duration of 6 (12) hours without MJO was equal to 174 (146) during EIR events and 169 (130) during EIE events. However, the number of cyclones with active MJO was equal to 393 (311) in EIR events and 364 (278) in EIE events. In order to investigate in details the interaction between ocean-atmosphere-sea ice, it was examinated persistents cases of EIR and EIE events. The cases more persistents of EIR (EIE) events had durations of 34 and 30 (26 and 25) days, which were the analised cases. It was observed that intraseasonal anomalies of atmospheric circulation at lower levels (in 850 hPa) and intraseasonal anomalies of superficial ocean currents were associates to hot (cold) advection during periods before EIR (EIR) events. In general, the medium latitude cyclonic (anticyclonic) anomalies of atmospheric circulation and divergence (convergence) of superficial ocean currents seem to be linked to upwelling (downwelling) in some pentads before the pentad which is correspondent to the beggining of EIR (EIE) supercases. The patterns observed change their phases along the time, suggesting the propagation of extratropical intraseasonal wave train pattern. Negatives (positives) intraseasonal anomalies of sea ice concentration were observed above Ross Sea in the first pentads after the beggining of EIR (EIE) persistents cases. This result shows that sea ice response to atmospheric and to oceanic patterns on intraseasonal time-scales has a lag between 5 and 1 pentad(s). In general, this work contributed to better understand the oceanic responses due to anomalies in atmospheric circulation and related impacts on sea ice, on intraseasonal time-scale.