The objective of this study is to characterize the mechanism of drag reduction by comparing the dynamical eigenfunctions of a turbulent pipe flow against those of two known cases of drag reduced flows. The first is forced drag reduction by spanwise wall oscillation, and the second is natural drag reduction found in relaminarizing flow. The dynamics are examined through a Karhunen-Lo`eve (KL) expansion of the direct numerical simulation flow field results. The direct numerical simulation (DNS) is performed using NEK5000, a spectral element Navier-Stokes solver, the first exponentially convergent investigation of DNS of turbulence in a pipe. The base flow is performed at a Reynolds number of Re = 150, resulting in a KL dimension of D_KL = 2130. As in turbulent channel flow, propagating modes are found, characterized with constant phase speed, and contribute of 80.58% of the total fluctuating energy. Based upon wavenumber characteristics and coherent vorticity visualization, four subclasses of propagating modes and two subclasses of non-propagating modes are discovered, qualitatively similar to the horseshoe (hairpin) vortex structure reported in literature. The drag reduced case is performed at the same Reynolds number with a spanwise velocity A+ = 20, a period of T+ = 50, and is driven by a constant pressure gradient. This results in a increase of flow rate by 27 %, and the KL dimension is reduced to D_KL = 102, a 96% reduction. The propagating modes, in particular the wall modes, are pushed away from the wall, resulting in a 34% increase in their advection speed, and a shift away from the wall of the root-mean-square and Reynolds stress peaks. The relaminarizing case observes the chugging motion of the mean flow rate when the Reynolds number is barely turbulent, at Re = 95. This chugging motion is the relaminarization of the flow, resulting in an increased flow rate, and then before complete relaminarization, the flow regains its turbulent state. This occurs because the lift modes, which are responsible for the majority of the energy in the inertial range of the energy spectra, decrease by two or three orders of magnitude. The chugging ends when the wall modes restart the turbulent cascade, and the lift modes are repopulated with energy. A model for the energy path is developed, with energy going from the pressure gradient to the shear modes, then to the roll modes, then to the wall modes, and then finally to the lift modes. It is concluded that drag reduction in a flow can be achieved by disrupting any leg of this model, thus disrupting the self-sustaining mechanism of turbulence. The spanwise wall oscillation shortened the life span of the wall modes, thus limiting their ability to pass energy to the lift modes. Likewise, the low Reynolds number did not provide enough energy to sustain the lift modes, and so relaminarization began. The contribution of this work is twofold. Firstly, the structure of turbulent pipe flow is examined and visualized for the first time using the Karhunen-Lo`eve method. The second, and perhaps greatest contribution of this work, is that the mechanism of drag reduction has been characterized as the link between the wall modes and the lift modes. This will allow future work on developing real methods of drag reduction, and eventually porting it to high Reynolds number flows, like that of an oil pipeline at Re= 40, 000. To achieve this, certain questions remain to be answered, such as what is the most efficient method of disrupting the wall-lift mechanism? Is there a single structure that can be identified and manipulated that gives a similar eect? Once answered, this will allow for a new generation of pipelines to be developed, and considering the implications in petroleum industry alone, will result in a significant contribution to the economy of the world. / Ph. D.

La probabilité de défaillance d’une structure sous séisme est représentée à l’aide de « courbes de fragilité ». Pour les estimer, nous proposons d’enrichir une base de données pré-existante à l’aide du modèle de l’article de F. Poirion et I. Zentner, Stochastic model construction of natural hazards given experimental data, qui se fonde sur la représentation de Karhunen-Loève. Les signaux générés sont triés par classes d’indicateur de nocivité sismique à l’aide d’un algorithme de partitionnement de données. Malgré la ressemblance certaine que présentent plusieurs signaux simulés, et les conséquences que nous tirons de ce problème, ils sont soumis à la structure. Les signaux de réponses résultants sont eux aussi enrichis, en prenant en compte certaines incertitudes afin de construire un intervalle autour de la courbe. La méthode fonctionne pour tout indicateur de nocivité sismique, et permet de s’affranchir de plusieurs hypothèses simplificatrices courantes. Les caractéristiques du scénario sismique sont conservées lors de l’enrichissement, et le processus modélisant le mouvement du sol garde toute sa généralité. Notre démarche est validée d’abord sur un cas simple, puis sur un cas industriel. / The failure probability of a structure under earthquake is represented with « fragility curves ». To estimate them, we propose to enrich a pre-existing data basis using the model of the article Stochastic model construction of natural hazards given experimental data, written by F. Poirion et I. Zentner, which is based on the Karhunen-Loeve expansion. The generated signals are sorted by seismic indicator classes using a data partitioning algorithm. Despite the resemblance between some simulated signals, and the consequences we draw from this problem, the structure is submitted to them. The resulting response signals are also enriched, taking into account uncertainties to construct an interval around the curve. The method works for any seismic indicator, and overcomes several common simplifying assumptions. The characteristics of the seismic scenario are preserved during the enrichment, and the process modeling the ground motion retains its generality. Our approach is first validated on a simple case, then on an industrial case.

Tradicionalmente, a técnica de síntese aditiva com funções base de Fourier é a que tem apresentado melhores resultados no que diz respeito à qualidade dos sons gerados. Entretanto, a carga computacional imposta por esta técnica é extremamente alta, dificultando assim a sua implementação em tempo real. Substituindo as funções de Fourier por outras mais complexas, derivadas das técnicas estatísticas de Karhunen-Loève, consegue-se uma redução na quantidade de operações necessárias. Neste trabalho foi estudado e implementado em microcomputador um modelo de síntese aditiva baseada em análise utilizando a transformada de Karhunen-Loève. / Traditionally, the Fourier based aditive synthesis is the method that have achieved the best results concerning to the quality of the generated sounds. However, the computacional load imposed by this technique is extremely high, difliculting its real time implementation. Substituting the Fourier functions by another set of more complex functions, derived from the Karhunen-Loève statistical techniques, one achieves a reduction on the amount of the necessary operations so as to viabilize its real time implementation.

Tradicionalmente, a técnica de síntese aditiva com funções base de Fourier é a que tem apresentado melhores resultados no que diz respeito à qualidade dos sons gerados. Entretanto, a carga computacional imposta por esta técnica é extremamente alta, dificultando assim a sua implementação em tempo real. Substituindo as funções de Fourier por outras mais complexas, derivadas das técnicas estatísticas de Karhunen-Loève, consegue-se uma redução na quantidade de operações necessárias. Neste trabalho foi estudado e implementado em microcomputador um modelo de síntese aditiva baseada em análise utilizando a transformada de Karhunen-Loève. / Traditionally, the Fourier based aditive synthesis is the method that have achieved the best results concerning to the quality of the generated sounds. However, the computacional load imposed by this technique is extremely high, difliculting its real time implementation. Substituting the Fourier functions by another set of more complex functions, derived from the Karhunen-Loève statistical techniques, one achieves a reduction on the amount of the necessary operations so as to viabilize its real time implementation.

The Karhunen–Loève Transform (KLT) is prevalent nowadays in communication and signal processing. This thesis aims at attaining the KLT in the encoders and achieving the minimum sum rate in the case of Gaussian multiterminal source coding. In the general multiterminal source coding case, the data collected at the terminals will be compressed in a distributed manner, then communicated the fusion center for reconstruction. The data source is assumed to be a Gaussian random vector in this thesis. We introduce the rate-distortion function to formulate the optimization problem. The rate-distortion function focuses on achieving the minimum encoding sum rate, subject to a given distortion. The main purpose in the thesis is to propose a distributed KLT for encoders to deal with the sampled data and produce the minimum sum rate. To determine the distributed Karhunen–Loève transform, we propose three kinds of algorithms. The rst iterative algorithm is derived directly from the saddle point analysis of the optimization problem. Then we come up with another algorithm by combining the original rate-distortion function with Wyner's common information, and this algorithm still has to be solved in an iterative way. Moreover, we also propose algorithms without iterations. This kind of algorithms will generate the unknown variables from the existing variables and calculate the result directly.All those algorithms can make the lower-bound and upper-bound of the minimum sum rate converge, for the gap can be reduced to a relatively small range comparing to the value of the upper-bound and lower-bound. / Thesis / Master of Applied Science (MASc)

Ce travail de thèse est une contribution à l’analyse de santé structurale de la caisse de véhicules militaires terrestres à roues. Appartenant à la gamme 20 - 30 tonnes, de tels véhicules sont déployés dans des contextes opérationnels variés où les conditions de roulage sont sévères et difficilement caractérisables. De plus, faisant face à la concurrence, la fonction mobilité des véhicules est acquise auprès de fournisseurs et n’est plus développée par Nexter Systems. De ce fait, la définition complète de cette fonction n’est plus connue. S’appuyant sur ce contexte, l’objectif principal de la thèse est d’aborder l’état de santé de la structure porteuse par approche probabiliste, afin de maitriser les techniques de calcul permettant la prise en compte de l’aléa intrinsèque des chargements liés à la diversité d’emploi des véhicules militaires terrestres. En particulier, les stratégies les plus pertinentes pour propager les incertitudes de roulage au sein d’un modèle mécanique d’un véhicule terrestre sont définies. Ces travaux décrivent comment il est possible d’exploiter une grandeur d’intérêt au sein du véhicule dans un objectif d’évaluation de la fiabilité par rapport à un critère de dommage donné. Une application sur un démonstrateur entièrement conçu par Nexter Systems illustre l’approche proposée. / This thesis is a contribution to the structural health analysis of the body of ground military vehicles. Belonging to the 20 - 30 tons range, such vehicles are deployed in a variety of operational contexts where driving conditions are severe and difficult to characterize. In addition, due to a growing industrial competition, the mobility function of vehicles is acquired from suppliers and is no longer developed by Nexter Systems. As a result, the complete definition of this function is unknown. Based on this context, the main objective of this thesis is to analyze the health of the vehicle body using a probabilistic approach in order to control the calculation techniques allowing to take into account the random nature of loads related to the use of ground military vehicles. In particular, the most relevant strategies for propagating uncertainties due to the terrain within a vehicle dynamics model are defined. This work describes how it is possible to manage an observation data measured in the vehicle for the purpose of assessing the reliability with respect to a given damage criterion. An application on a demonstrator entirely designed by Nexter Systems illustrates the proposed approach.

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