Dans de nombreuses applications industrielles, les structures en vibration à dimensionner sont en contact avec un fluide (fluide autour des coques des bateaux, réservoirs, échangeurs de chaleur dans les centrales, l’industrie automobile, etc). Cependant, le comportement dynamique de la structure peut être modifié de façon importante par la présence du fluide. Le dimensionnement doit donc prendre en compte les effets de l’interaction fluide-structure.Ces applications nécessitent un couplage efficace. En outre, l’analyse dynamique des systèmes industriels est souvent coûteuse du point de vue numérique. Pour les modèles éléments finis des problèmes couplés fluide-structure, l’importance de la réduction de la taille devient évidente car les degrés de liberté du fluide seront ajoutés à ceux de la structure. Des méthodes de réduction du modèle seront utilisées pour réduire la taille des matrices obtenues.Traditionnellement, l’étude de ces systèmes couplés est fondée sur une démarche déterministe dans laquelle l’ensemble des paramètres utilisés dans le modèle prennent une valeur fixe.Par contre, il suffit d’avoir procédé à quelques expérimentations pour se rendre compte des limites d’une telle modélisation, d’où la nécessité de la prise en compte des incertitudes sur les paramètres du système couplé.Ce travail de thèse s’articule autour de trois études principales. La première consiste à mener une étude déterministe numérique et analytique des problèmes vibro-acoustiques sans réduction de modèles. Cette dernière est basée sur une formulation non symétrique déplacement/pression et une formulation symétrique déplacement/pression et potentiel des vitesses. Dans la deuxième étude, on propose deux méthodes de réduction du modèle : analyse et synthèse modales pour la résolution des problèmes vibro-acoustiques des grandes tailles des systèmes couplés modélisés par la méthode des éléments finis. La méthode de synthèse modale développée couple une méthode de sous-structuration dynamique de type Craig et Bampton et une méthode de sous domaines acoustiques.Enfin, pour tenir compte des incertitudes sur les paramètres du système couplé, on a développé dans la troisième étude une méthode numérique stochastique de synthèse modale étendue à une étude de fiabilité basée sur les approches FORM et SORM pour la résolution de ces problèmes. Ces démarches vont nous permettre de résoudre les problèmes vibro-acoustiques, sans utiliser les méthodes classiques, qui consistent à faire un calcul modal direct allié à la simulation de Monte Carlo demandant un coup de temps très élevé.Plusieurs exemples académiques et industriels ont été traités pour valider les approches proposées.L’étude numérique est conduite en utilisant un code élaboré sous MATLAB couplé au code commercial ANSYS afin d’évaluer la fiabilité du système couplé. La confrontation des résultats numériques, analytiques et expérimentaux nous permet de valider conjointement le processus de calcul et les méthodes proposées dans le domaine de l’analyse fréquentielle et l’étude fiabiliste des structures immergées. D’un point de vue industriel, ces méthodes visent à promouvoir l’introduction de la culture de l’incertain dans les métiers de la conception et encouragent la construction d’un modèle fiable et robuste pour les problèmes d’interaction fluide-structure. / In several industrial applications, the vibrating structures are in contact with a fluid (fluid around the hulls of a boats, reservoirs, heat exchangers in power plants, ...), but the dynamic behavior of the structure can be significantly modified by the presence of the fluid. The sizing must take into account the effects of fluid-structure interaction. These applications require an effective coupling. In addition, the dynamic analysis of the industrial systems is often expensive from the numerical point of view. For the coupling fluid structure finite elements models, the importance of the size reduction becomes obvious because the fluid’s freedom degrees will be added to those of the structure. A proposed condensation method will be used to reduce the matrixes size. Traditionally, the study of the fluid-structure interaction is based on a deterministic approach where all the parameters used in the model have a fixed value. But it suffices having conducted a few experimentations to realize the limitations of such modeling. Hence it need to take into accounts the uncertainty on the parameters of mechanical systems. In this thesis, we deal with the simulation of vibro-acoustic problems. The first part presents a numerical and analytical study of deterministic problems without model’s reduction, based on a non-symmetric formulation displacement/pressure and on a symmetric formulation displacement/pressure and velocity potential. In the second part of this work, two methods are proposed to reduce the model : modal analysis and modal synthesis for solving vibro-acoustic problems of large sizes modeled by finite elements method. The developed modal synthesis method is coupling dynamic substructure of Craig and Bampton type and acoustic subdomain based on a pressure formulation. To take into account the parameter’s uncertainties of the coupled system, we have developed a numerical stochastic method of the modal synthesis and modal analysis extended to reliability study, based on the FORM and SORM approaches. These approaches will allow us to solve the vibro-acoustic problems without using classical procedure. It may become prohibitive in terms of computation time. Several academic and industrial examples are studied to validate the proposed methods. The numerical study is performed using a code developed with MATLAB coupled with the commercial code ANSYS in order to evaluate the reliability of systems. The comparison of numerical, analytical and experimental results enables us to jointly validate the calculation process and the proposed methods in the domain of frequency analysis and reliability study of submerged structures. From the industrial point of view, our research work aim is to promote the introduction of the uncertainty’s culture during modeling in the context of design processes.

The purpose of this thesis was to experimentally investigate the influence of increasing sulfide concentrations on the 34S isotope enrichment in sulfate during dissimilatory sulfate reduction (DSR). Two independent batch culture experiments with different maximum sulfide concentrations of up to 20 mM in the first and up to 40 mM in the second experiment were conducted using the marine sulfate reducer Desulfobacter latus. A comparison of the results from both experiments revealed a distinct offset towards more positive δ34S(SO42-) values in the 'high-sulfide' experiment, compared to the 'low-sulfide' experiment. While a Rayleigh type fractionation model was able to match the slopes - i.e., enrichment factors - of both experiments, it failed to reproduce the proper y-axis intercept in the 'high-sulfide' experiment. I therefore propose a new fractionation model that allows for a backward flow of ambient H2S into the bacterial cell and a subsequent enzymatically mediated oxidation of H2S to sulfate. The new backward flow increases with elevated H2S concentrations and is described as a first order rate constant. Unlike a Rayleigh type fractionation model, my model explains the slope and y-intercept of both experiments with a single parameter set. The new model with H2S-reflux further suggests that it can be used to determine growth kinetic parameters like the half-saturation constant through δ34S measurements. These findings support the hypothesis of microbially mediated, bi-directional S-fluxes between oxidized and reduced sulfur species. Because the S-transport during DSR appears to be bi-directional, great care must be taken when evaluating culture experiments with a Rayleigh type fractionation model, owing to the fact that an evident S-backward flow violates the prerequisites for applying the Rayleigh model. A variable S-backward flow results in variable enrichment factors which increased from -11 (no H2S) to ≈-17 ‰ (40 mM of H2S) in my experiments. I show for the first time the significance of a bi-directional H2S transport across the cell membrane during DSR and its consequences for the 34S-isotope fractionation in sulfate.

The purpose of this thesis was to experimentally investigate the influence of increasing sulfide concentrations on the 34S isotope enrichment in sulfate during dissimilatory sulfate reduction (DSR). Two independent batch culture experiments with different maximum sulfide concentrations of up to 20 mM in the first and up to 40 mM in the second experiment were conducted using the marine sulfate reducer Desulfobacter latus. A comparison of the results from both experiments revealed a distinct offset towards more positive δ34S(SO42-) values in the 'high-sulfide' experiment, compared to the 'low-sulfide' experiment. While a Rayleigh type fractionation model was able to match the slopes - i.e., enrichment factors - of both experiments, it failed to reproduce the proper y-axis intercept in the 'high-sulfide' experiment. I therefore propose a new fractionation model that allows for a backward flow of ambient H2S into the bacterial cell and a subsequent enzymatically mediated oxidation of H2S to sulfate. The new backward flow increases with elevated H2S concentrations and is described as a first order rate constant. Unlike a Rayleigh type fractionation model, my model explains the slope and y-intercept of both experiments with a single parameter set. The new model with H2S-reflux further suggests that it can be used to determine growth kinetic parameters like the half-saturation constant through δ34S measurements. These findings support the hypothesis of microbially mediated, bi-directional S-fluxes between oxidized and reduced sulfur species. Because the S-transport during DSR appears to be bi-directional, great care must be taken when evaluating culture experiments with a Rayleigh type fractionation model, owing to the fact that an evident S-backward flow violates the prerequisites for applying the Rayleigh model. A variable S-backward flow results in variable enrichment factors which increased from -11 (no H2S) to ≈-17 ‰ (40 mM of H2S) in my experiments. I show for the first time the significance of a bi-directional H2S transport across the cell membrane during DSR and its consequences for the 34S-isotope fractionation in sulfate.

Multivariate linear regression methods are widely used statistical tools in data analysis, and were developed when some response variables are studied simultaneously, in which our aim is to study the relationship between predictor variables and response variables through the regression coefficient matrix. The rapid improvements of information technology have brought us a large number of large-scale data, but also brought us great challenges in data processing. When dealing with high dimensional data, the classical least squares estimation is not applicable in multivariate linear regression analysis. In recent years, some approaches have been developed to deal with high-dimensional data problems, among which dimension reduction is one of the main approaches. In some literature, random projection methods were used to reduce dimension in large datasets. In Chapter 2, a new random projection method, with low-rank matrix approximation, is proposed to reduce the dimension of the parameter space in high-dimensional multivariate linear regression model. Some statistical properties of the proposed method are studied and explicit expressions are then derived for the accuracy loss of the method with Gaussian random projection and orthogonal random projection. These expressions are precise rather than being bounds up to constants. In multivariate regression analysis, reduced rank regression is also a dimension reduction method, which has become an important tool for achieving dimension reduction goals due to its simplicity, computational efficiency and good predictive performance. In practical situations, however, the performance of the reduced rank estimator is not satisfactory when the predictor variables are highly correlated or the ratio of signal to noise is small. To overcome this problem, in Chapter 3, we incorporate matrix projections into reduced rank regression method, and then develop reduced rank regression estimators based on random projection and orthogonal projection in high-dimensional multivariate linear regression models. We also propose a consistent estimator of the rank of the coefficient matrix and achieve prediction performance bounds for the proposed estimators based on mean squared errors. Envelope technology is also a popular method in recent years to reduce estimative and predictive variations in multivariate regression, including a class of methods to improve the efficiency without changing the traditional objectives. Variable selection is the process of selecting a subset of relevant features variables for use in model construction. The purpose of using this technology is to avoid the curse of dimensionality, simplify models to make them easier to interpret, shorten training time and reduce overfitting. In Chapter 4, we combine envelope models and a group variable selection method to propose an envelope-based sparse reduced rank regression estimator in high-dimensional multivariate linear regression models, and then establish its consistency, asymptotic normality and oracle property. Tensor data are in frequent use today in a variety of fields in science and engineering. Processing tensor data is a practical but challenging problem. Recently, the prevalence of tensor data has resulted in several envelope tensor versions. In Chapter 5, we incorporate envelope technique into tensor regression analysis and propose a partial tensor envelope model, which leads to a parsimonious version for tensor response regression when some predictors are of special interest, and then consistency and asymptotic normality of the coefficient estimators are proved. The proposed method achieves significant gains in efficiency compared to the standard tensor response regression model in terms of the estimation of the coefficients for the selected predictors. Finally, in Chapter 6, we summarize the work carried out in the thesis, and then suggest some problems of further research interest. / Dissertation / Doctor of Philosophy (PhD)