Les failles sont des zones de rupture de la roche qui affectent le comportement mécanique et fluide des réservoirs. De nombreuses incertitudes existent sur la géométrie et la topologie des réseaux de failles dues à la résolution et la qualité des données, mais aussi aux lacunes d'informations. Des approches stochastiques ont été utilisées dans la littérature pour gérer les incertitudes structurales. Ces méthodes génèrent un ensemble de modèles possibles de failles conditionné par les données disponibles. Dans cette thèse, nous explorons deux principales stratégies de conditionnement de la modélisation stochastique de réseaux de failles. La première stratégie élaborée permet de prendre en compte des observations d'absences de failles sur des données, par exemple, des zones où les réflecteurs sismiques sont continus. Dans ce but, le réservoir est divisé en deux sous-volumes délimités par une enveloppe surfacique 3D : un volume non-faillé et un volume potentiellement-faillé. Les surfaces de failles sont ensuite simulées et optimisées de manière à être entièrement positionnées dans la zone identifiée comme potentiellement faillée. La seconde stratégie de conditionnement présentée dans cette thèse gère les incertitudes relatives à l'interprétation de la segmentation des failles. La méthode génère un ensemble de modèles de segments de failles en-échelon à partir d'une interprétation continue à plus grande échelle d'une faille segmentée. La méthode utilise les variations d'orientations de la faille segmentée pour identifier la position des différents segments la composant. L'impact des différentes configurations de segmentation sur les simulations d'écoulements est étudié / Faults are discontinuities in rock volumes that affect mechanical properties and flow paths of hydrocarbon reservoirs. However, subsurface modeling remains limited by the incompleteness and resolution of available data, so that uncertainties remain on the geometry and the connectivity of fault networks. To assess fault network uncertainties, several stochastic approaches have been introduced in the literature. These methods generate a set of possible fault models conditioned by reservoir data. In this thesis, we investigate two main conditioning strategies of stochastic fault modeling methods. The first one takes into account the observations of the fault absence, for instance, as indicated by seismic reflector continuity. To do this, the reservoir volume is divided into two sub-volumes delimited by a 3D envelope surface: (1) a volume where no faults occur, and (2) a potentially-faulted volume. Then, faults are simulated and optimized in such a way as to be entirely confined to the potentially-faulted volume. The second presented strategy deals with the uncertainties related to the seismic interpretation of fault segmentation. It generates a set of fine-scale segmented faults from a larger-scale and continuous interpretation of the fault. The method uses the orientation variations of the continuous fault to subdivide it into several possible fault segments. The effects of the different segmentation configurations on flow simulations are studied

Dans le cadre de l'élasticité linéaire 3D des microstructures complexes qui ne peuvent pas être simplement décrites en terme de constituants telles que des tissus biologiques, nous proposons, dans ce travail de recherche, une méthodologie d'identification expérimentale multi-échelle du champ stochastique d'élasticité apparent de la microstructure à l'échelle mésoscopique en utilisant des mesures de champ de déplacements aux échelles macroscopique et mésoscopique. On peut alors utiliser cette méthodologie dans le cadre de changement d'échelle pour obtenir des propriétés mécaniques à l'échelle macroscopique. Dans ce contexte, la question majeure est celle de l'identification expérimentale par résolution d'un problème statistique inverse de la modélisation stochastique introduite pour le champ d'élasticité apparent à l'échelle mésoscopique. Cette identification expérimentale permet non seulement de valider la modélisation mais encore de la rendre utile pour des matériaux existants ayant une microstructure complexe. Le présent travail de recherche est une contribution proposée dans ce cadre pour lequel l'expérimentation et validation expérimentale basée sur des mesures simultanées d'imagerie de champ aux échelles macroscopique et mésoscopique sont faites sur de l'os cortical / In the framework of linear elasticity 3D for complex microstructures that cannot be simply described in terms of components such as biological tissues, we propose, in this research work, a methodology for multiscale experimental identification of the apparent elasticity random field of the microstructure at mesoscopic scale using displacement field measurements at macroscopic scale and mesoscopic scale. We can then use this methodology in the case of changing scale to obtain the mechanical properties at macroscale. In this context, the major issue is the experimental identification by solving a statistical inverse problem of the stochastic modeling introduced for the apparent elasticity random field at mesoscale. This experimental identification allows to validate the modeling and makes it useful for existing materials with complex microstructures. This research work is proposed in this context in which experimentation and experimental validation based on simultaneous measurements of field imaging at macroscale and mesoscale are made on the cortical bonemakes it useful for existing materials with complex microstructures. This research work is proposed in this context in which experimentation and experimental validation based on simultaneous measurements of field imaging at macroscale and mesoscale are made on the cortical bone.

Animating trees in wind has long been a problem in computer graphics. Progress on this problem is important for both visual effects and biomechanics and may inform future work on two-way coupling between turbulent flows and deformable objects. Synthetic turbulence added to a coarse fluid simulation has been used to produce convincing animations of turbulent flows, but only considers one-way coupling between fluid and solid. We produce accurate animations of tree motion by creating a two-way coupling between synthetic turbulence and semipermeable proxy geometry. The resulting animations exhibit global wind sheltering effects and branch tips have motion paths which match paths collected from branch tips using motion capture.

The application of stochastic modeling for learning the behavior of multibody dynamics models is investigated. The stochastic modeling technique is also known as Kriging or random function approach. Post-processing data from a simulation run is used to train the stochastic model that estimates the relationship between model inputs, such as the suspension relative displacement and velocity, and the output, for example, sum of suspension forces. Computational efficiency of Multibody Dynamics (MBD) models can be improved by replacing their computationally-intensive subsystems with stochastic predictions. The stochastic modeling technique is able to learn the behavior of a physical system and integrate its behavior in MBS models, resulting in improved real-time simulations and reduced computational effort in models with repeated substructures (for example, modeling a train with a large number of rail vehicles). Since the sampling plan greatly influences the overall accuracy and efficiency of the stochastic predictions, various sampling plans are investigated, and a space-filling Latin Hypercube sampling plan based on the traveling salesman problem (TPS) is suggested for efficiently representing the entire parameter space. The simulation results confirm the expected increased modeling efficiency, although further research is needed for improving the accuracy of the predictions. The prediction accuracy is expected to improve through employing a sampling strategy that considers the discrete nature of the training data and uses infill criteria that considers the shape of the output function and detects sample spaces with high prediction errors. It is recommended that future efforts consider quantifying the computation efficiency of the proposed learning behavior by overcoming the inefficiencies associated with transferring data between multiple software packages, which proved to be a limiting factor in this study. These limitations can be overcome by using the user subroutine functionality of SIMPACK and adding the stochastic modeling technique to its force library. / Ph. D.

Biodiesel has emerged as a promising renewable and clean energy alternative to petrodiesel. While biodiesel has traditionally been prepared through homogeneous basic catalysis, heterogeneous acid catalysis has been investigated recently due to its ability to convert cheaper but high free fatty acid content oils such as waste vegetable oil while decreasing production cost. In this work, the esterification of free fatty acid over sulfated zirconia and activated acidic alumina in a batch reactor was considered. The models of the reaction over the catalysts were developed in two parts. First, a kinetic study was performed using a deterministic model to develop a suitable kinetic expression; the related parameters were subsequently estimated by numerical techniques. Second, a stochastic model was developed to further confirm the nature of the reaction at the molecular level. The esterification of palmitic acid obeyed the Eley-Rideal mechanism in which palmitic acid and methanol are adsorbed on the surface for SO?/ZrO?-550°C and AcAl?O? respectively. The coefficients of determination of the deterministic model were 0.98, 0.99 and 0.99 for SO?/ZrO?-550°C at 40, 60 and 80°C respectively and 0.99, 0.98 and 0.96 for AcAl?O? at the same temperature. The deterministic and stochastic models were in good agreement. / Master of Science

No description available.

No description available.

No description available.

Fundamental diagram, a graphical representation of the relation among traffic flow, speed, and density, has been the foundation of traffic flow theory and transportation engineering for many years. For example, the analysis of traffic dynamics relies on input from this fundamental diagram to find when and where congestion builds up and how it dissipates; traffic engineers use a fundamental diagram to determine how well a highway facility serves its users and how to plan for new facilities in case of capacity expansion. Underlying a fundamental diagram is the relation between traffic speed and density which roughly corresponds to drivers’ speed choices under varying car-following distances. First rigorously documented by Greenshields some seventy-five years ago, such a relation has been explored in many follow-up studies, but these attempts are dominantly deterministic in nature, i.e. they model traffic speed as a function of traffic density. Though these functional speed-density models are able to coarsely explain how traffic slows down as more vehicles are crowded on highways, empirical observations show a wide-scattering of traffic speeds around the values predicted by these models. In addition, functional speed-density models lead to deterministic prediction of traffic dynamics, which lack the power to address the uncertainty brought about by random factors in traffic flow. Therefore, it appears more appropriate to view the speed-density relation as a stochastic process, in which a certain density level gives rise not only to an average value of traffic speed but also to its variation because of the randomness of drivers’ speed choices. The objective of this dissertation is to develop such a stochastic speed-density model to better represent empirical observations and provide a basis for a probabilistic prediction of traffic dynamics. It would be ideal if such a model is formulated with both mathematical elegance and empirical accuracy. The mathematical elegance of the model must include the features of: a single equation (single-regime) with physically meaningful parameters and must be easy to implement. The interpretation of empirical accuracy is twofold; on the one hand, the mean of the stochastic speeddensity model should match the average behavior of the empirical equilibrium speeddensity observations statistically. On the other hand, the magnitude of traffic speed variance is controlled by the variance function which is dependent on the response. Ultimately, it is expected that the stochastic speed-density model is able to reproduce the wide-scattering speed-density relation observed at a highway segment after being calibrated by a set of local parameters and, in return, the model can be used to perform probabilistic prediction of traffic dynamics at this location. The emphasis of this dissertation is on the former (i.e. the development, calibration, and validation of the stochastic speed-density model) with a few numerical applications of the model to demonstrate the latter (i.e. probabilistic prediction). Following the seminal Greenshields model, a great variety of deterministic speeddensity models have been proposed to mathematically represent the empirical speeddensity observations which underlie the fundamental diagram. Observed in the existing speed-density models was their deterministic nature striving to balance two competing goals: mathematical elegance and empirical accuracy. As the latest development of such a pursuit, we show that the stochastic speed-density model can be developed through discretizing a random traffic speed process using the Karhunen- Lo`eve expansion. The stochastic speed-density relationship model is largely motivated by the prevalent randomness exhibited in empirical observations that mainly comes from drivers, vehicles, roads, and environmental conditions. In a general setting, the proposed stochastic speed-density model has two components: deterministic and stochastic. For the deterministic component, we propose to use a family of logistic speed density models to track the average trend of empirical observations. In particular, the five-parameter logistic speed-density model arises as a natural candidate due to the following considerations: (1) The shape of the five-parameter logistic speed-density model can be adjusted by its physically meaningful parameters to match the average behavior of empirical observations. Statistically, the average behavior is modeled by the mean of empirical observations. (2) A three-parameter and four-parameter logistic speed-density model can be obtained by reducing the shape or scale parameter in the five-parameter model, but the counter-effect is the loss of empirical accuracy. (3) The five-parameter model yields the best accuracy compared to three-parameter and four-parameter model. The magnitude of the stochastic component is dominated by the variance of traffic speeds indexed by traffic density. The empirical traffic speed variance increases as density increases to around 25 - 30 veh/km, then starts decreasing as traffic density gets larger. It has been verified by empirical evidence that traffic speed variation shows a parabolic shape which makes the proposed variance function in a suitable formula to model its variation. The variance function is dependent on the logistic speed-density relationship with varying model parameters. A detailed analysis of empirical traffic speed variance can be found in Chapter 6. Modeling results show that by taking care of second-order statistics (i.e., variance and correlation) the proposed stochastic speed-density model is suitable for describing the observed phenomenon as well as for matching the empirical data. Following the results, a stochastic fundamental diagram of traffic flow can be established. On the application side, the stochastic speed-density relationship model can potentially be used for real-time on-line prediction and to explain phenomenons in a similar manner. This enables dynamic control and management systems to anticipate problems before they occur rather than simply reacting to existing conditions. Finally, we will summarize our findings and discuss our future research directions.

The polynomial-chaos expansion (PCE) approach to modeling provides an estimate of the probabilistic response of a dynamic system with uncertainty in the system parameters. A novel adaptive parameter estimation method exploiting the polynomial-chaos representation of a general quarter-car model is presented. Because the uncertainty was assumed to be concentrated in the sprung mass parameter, a novel pseudo mass matrix was developed for generating the state-space PCE model. In order to implement the PCE model in a real-time adaptation routine, a novel technique for representing PCE output equations was also developed. A simple parameter estimation law based on the output error between measured accelerations and PCE acceleration estimates was developed and evaluated through simulation and experiment. Simulation results of the novel adaptation algorithm demonstrate the estimation convergence properties as well as its limitations. The simulation results are further verified by a real-time experimental implementation on a quarter-car test rig. This work presents the first truly real-time implementation of a PCE model. The experimental real-time implementation of the novel adaptive PCE estimation method shows promising results by its ability to converge and maintain a stable estimate of the unknown parameter. / Master of Science