Avec la généralisation de la construction des bâtiments basse consommation, passifs et à énergie positive, mais aussi la rénovation du parc existant, il est indispensable d’avoir recours à la simulation pour évaluer, entre autres, les performances énergétique et environnementale atteintes par ces nouveaux bâtiments. Les attentes en termes de garantie de performance énergétique étant de plus en plus importantes, il est primordial de s’assurer de la fiabilité des outils de simulation utilisés. En effet, les codes de simulation doivent être capables de représenter le comportement de ces nouveaux types de bâtiments de la façon la plus juste et fidèle possible. De plus, les incertitudes liées aussi bien aux paramètres de conception qu’aux différentes sollicitations ainsi qu’aux usages des bâtiments doivent être prises en compte pour pouvoir garantir la performance du bâtiment sur sa durée de vie.Cette thèse s’est intéressée à la validation expérimentale de modèles appliquée à un bâtiment de type cellule test. Cette méthodologie de validation se déroule en plusieurs étapes au cours desquelles on évalue la qualité du modèle en termes de justesse et de fidélité. Plusieurs cas d’études ont été menés sur lesquels nous avons pu identifier les paramètres les plus influents sur la sortie du modèle, examiner l’influence du pas de temps sur le processus de validation expérimentale, analyser l’influence de l’initialisation et confirmer l’aptitude de la méthodologie à tester le modèle. / Construction of low, passive and positive energy buildings is generalizing and existing buildings are being renovated. For this reason, it is essential to use simulation in order to estimate, among other things, energy and environmental performances reached by these new buildings. Expectations regarding guarantee of energy performance being more and more important, it is crucial to ensure the reliability of simulation tools being used. Indeed, simulation codes should reflect the behavior of these new kinds of buildings in the most consistent and accurate manner. Moreover, the uncertainty related to design parameters, as well as solicitations and building uses have to be taken into account in order to guarantee building energy performance during its lifetime.This thesis investigates the empirical validation of models applied to a test cell building. This validation process is divided into several steps, during which the quality of the model is evaluated as far as consistency and accuracy are concerned. Several study cases were carried out, from which we were able to identify the most influential parameters on model output, inspect the influence of time step on the empirical validation process, analyze the influence of initialization and confirm methodology’s ability to test the model.

<p>The coupled transport of water and heat, involving freezing and thawing, in the road structure and its immediate environment is important to consider for optimal design and maintenance of roads and when assessing solute transport, of e.g. de-icing salt, from roads. The objective of this study was to develop mechanistic models, and measurement techniques, suitable to describe and understand water flow and heat flux in road structures exposed to a cold climate. </p><p>Freezing and thawing was accounted for by implementing new routines in two numerical models (HYDRUS1D/2D). The sensitivity of the model output to changes in parameter values and operational hydrological data was investigated by uncertainty and sensitivity analyses. The effect of rainfall event characteristics and asphalt fractures on the subsurface flow pattern was investigated by scenario modelling. The performance of water content reflectometers (WCR), measuring water content, was evaluated using measurements in two road structure materials. A numerical model was used to simulate WCR sensor response. The freezing/thawing routines were stable and provided results in agreement with laboratory measurements. Frost depth, thawing period, and freezing-induced water redistribution in a model road was greatly affected by groundwater level and type of subgrade. The simulated subsurface flow patterns corresponded well with published field observations. A new method was successful in enabling the application of time domain reflectometer (TDR) calibration equations to WCR output. The observed distortion in sampling volume for one of the road materials could be explained by the WCR sensor numerical model. Soil physical, hydrological, and hydraulic modules proved successful in simulating the coupled transport of water and heat in and on the road structure. It was demonstrated in this thesis that numerical models can improve the interpretation and explanation of measurements. The HYDRUS model was an accurate and pedagogical tool, clearly useful in road design and management.</p>

The coupled transport of water and heat, involving freezing and thawing, in the road structure and its immediate environment is important to consider for optimal design and maintenance of roads and when assessing solute transport, of e.g. de-icing salt, from roads. The objective of this study was to develop mechanistic models, and measurement techniques, suitable to describe and understand water flow and heat flux in road structures exposed to a cold climate. Freezing and thawing was accounted for by implementing new routines in two numerical models (HYDRUS1D/2D). The sensitivity of the model output to changes in parameter values and operational hydrological data was investigated by uncertainty and sensitivity analyses. The effect of rainfall event characteristics and asphalt fractures on the subsurface flow pattern was investigated by scenario modelling. The performance of water content reflectometers (WCR), measuring water content, was evaluated using measurements in two road structure materials. A numerical model was used to simulate WCR sensor response. The freezing/thawing routines were stable and provided results in agreement with laboratory measurements. Frost depth, thawing period, and freezing-induced water redistribution in a model road was greatly affected by groundwater level and type of subgrade. The simulated subsurface flow patterns corresponded well with published field observations. A new method was successful in enabling the application of time domain reflectometer (TDR) calibration equations to WCR output. The observed distortion in sampling volume for one of the road materials could be explained by the WCR sensor numerical model. Soil physical, hydrological, and hydraulic modules proved successful in simulating the coupled transport of water and heat in and on the road structure. It was demonstrated in this thesis that numerical models can improve the interpretation and explanation of measurements. The HYDRUS model was an accurate and pedagogical tool, clearly useful in road design and management.

Rubber like materials find wide applications in damping treatment of structures, vibration isolations and they appear prominently in the form of hoses in many structures such as aircraft engines. The study reported in this thesis addresses a few issues in computational modeling of vibration of structures with some of its components made up of rubber like materials. Specifically, the study explores the use of fractional derivatives in representing the constitutive laws of such material and focuses its attention on problems of parameter identification in linear time invariant systems with fractional order damping models. The thesis is divided into four chapters and two annexures. A review of literature related to mathematical modeling of damping with emphasis on fractional order derivative models is presented in chapter 1. The review covers lternatives available for modeling energy dissipation that include viscous, structural and hybrid damping models. The advantages of using fractional order derivative models in this context is pointed out and papers dealing with solution of differential equations with fractional order derivatives are reviewed. Issues related to finite element modeling and random vibration analysis of systems with fractional order damping models are also covered. The review recognizes the problems of system parameter identification based on inverse eigensensitivity and inverse FRF sensitivity as problems requiring further research. The problem of determination of derivatives of eigensolutions and FRF-s with respect to system parameters of linear time invariant systems with fractional order damping models is considered in chapter 2. The eigensolutions here are obtained as solutions of a generalized asymmetric eigenvalue problem. The order of system matrices here depends upon the mechanical degrees of freedom and also somewhat artificially on the fractional order of the derivative terms. The formulary for first and second order eigenderivatives are developed taking account of these features. This derivation also takes into account the various orthogonality relations satisfied by the complex valued eigenvectors. The system FRF-s are obtained by a straight forward inversion of the system dynamic stiffness matrix and also by using a series solution in terms of system eigensolutions. As might be expected, the two solutions lead to identical results. The first and the second order derivatives of FRF-s are obtained based on system dynamic matrix and without taking recourse to modal summation. Numerical examples that bring out various facets of eigensolutions, FRF-s and their sensitivities are presented with reference to single and multi degree freedom systems. The application sensitivity analysis developed in chapter 2 to problems of system parameter identification is considered in chapter 3. Methods based on inverse eigensensitivity and inverse FRF sensitivity are outlined. The scope of these methods cover first and second order analyses and applications to single and multi degree freedom systems. While most illustrations are based on synthetic measurement data, limited efforts are also made to implement the identification methods using laboratory measurement data. The experimental work has involved the measurement of FRF-s on a system consisting of two steel tubes connected by a rubber hose. The two system identification methods are shown to perform well especially when information on second order sensitivity are included in the analysis. The method based on inverse eigensolution is shown to become increasingly unwieldy to apply as the order of the system matrices increases while the FRF based method does not suffer from this drawback. The FRF based method also has the advantage that the prior knowledge of order of fractional order derivative terms is not needed in its implementation while such knowledge is assumed in the method based on eigensolutions. While the methods are shown to perform satisfactorily when synthetic measurement data is used, their success is not uniformly good when laboratory measurement data are employed. Chapter 4 presents a summary of contributions made in the thesis and also enlists a few suggestions for further research. Annexure I provides a précis of elementary notion of fractional order derivatives and integrals. A case study on finite element analysis of aircraft engine component made up of metallic and rubber materials is outlined in Annexure II and the study points towards possible advantages of using fractional order damping models in the study of such structures.

This thesis consists of a summary and four scientific articles. All four articles consider various aspects of stochastic differential equations and the purpose of the summary is to provide an introduction to this subject and to supply the notions required in order to fully understand the articles. In the first article we conduct a thorough study of the multi-dimensional Skorohod problem in time-dependent domains. In particular we prove the existence of cádlág solutions to the Skorohod problem with oblique reflection in time-independent domains with corners. We use this existence result to construct weak solutions to stochastic differential equations with oblique reflection in time-dependent domains. In the process of obtaining these results we also establish convergence results for sequences of solutions to the Skorohod problem and a number of estimates for solutions, with bounded jumps, to the Skorohod problem. The second article considers the problem of determining the sensitivities of a solution to a second order parabolic partial differential equation with respect to perturbations in the parameters of the equation. We derive an approximate representation of the sensitivities and an estimate of the discretization error arising in the sensitivity approximation. We apply these theoretical results to the problem of determining the sensitivities of the price of European swaptions in a LIBOR market model with respect to perturbations in the volatility structure (the so-called ‘Greeks’). The third article treats stopped diffusions in time-dependent graph domains with low regularity. We compare, numerically, the performance of one adaptive and three non-adaptive numerical methods with respect to order of convergence, efficiency and stability. In particular we investigate if the performance of the algorithms can be improved by a transformation which increases the regularity of the domain but, at the same time, reduces the regularity of the parameters of the diffusion. In the fourth article we use the existence results obtained in Article I to construct a projected Euler scheme for weak approximation of stochastic differential equations with oblique reflection in time-dependent domains. We prove theoretically that the order of convergence of the proposed algorithm is 1/2 and conduct numerical simulations which support this claim.

Despite their important ecosystem benefits for terrestrial and marine flora and fauna and the human livelihood mangrove forests suffer a high loss rate mainly due to human activity. Aside from these impacts, natural forest disturbances exist more commonly in mangroves compared to other forests as a direct consequence of their exposed coastal location. Within this thesis I investigate the influence of natural disturbance regimes on the mangrove forest dynamics focusing in particular on the ecological role of disturbances, disturbance patterns, forest structure, succession behavior and long-term vulnerability evaluation. The study areas were set in the Indian River Lagoon in Florida (USA) and in Can Gio an UNESCO Biosphere Reserve (Vietnam). In addition, theoretical simulation studies were carried out to complement the field studies. Thereby, in our study at the Indian River Lagoon site I investigated the ecosystem response to hurricane events of an artificially impounded mangrove forest. In Can Gio, the suitability of lightning strike – caused gaps for setting a homogenous plantation into more natural-like state according to species composition and forest structure was analyzed. Finally, a theoretical simulation study was carried out to compare lightning strike and hurricane events regarding their homogenization and heterogenization effects on the spatio-temporal forest structure. The findings of the field study in the Indian River Lagoon indicate that hurricane events had a severe impact on forest areas in higher successional stages by creating open patches, whereas areas in lower successional stages remained largely undisturbed. Furthermore, the impoundment determines the species selection of the post-hurricane succession by favoring flooding-tolerant species. However, regeneration was found to be impaired by the artificially high inundation regime at some disturbed patches. The lightning-strike disturbances enhance the species composition in the monospecific plantation in Can Gio by providing a sufficient light regime for entering seeds to establish. In addition, lightning-strike gaps increased the plantation structure complexity. Regenerating lightning-strike gaps remained as “green islands” within windthrow sites in the plantation due to their low stature and provided seeds for surrounding disturbed areas thereby accelerating their recolonization. The results of the simulation analysis of a theoretical landscape showed that in the simulated highly complex natural mature forests all disturbance regimes entail homogenization on the spatial structure compared to an undisturbed scenario. The hurricane scenario showed an increased temporal variation of the forest dynamics whereas lightning-strike gaps were not able to contribute to additional heterogeneity in the simulated area, despite of having the same tree mortality probability during disturbances. The interaction of the large-scale impoundment in the Indian River Lagoon and medium-sized hurricane events is characterized by partially impeded post-hurricane regeneration. In contrast, small-scaled lightning strikes influenced the regeneration of medium-sized windthrow sites positively within the homogenous plantation. We therefore suggest management activities aimed at creating small clearances within the plantation in Can Gio to simulate additional small-scale disturbances in order to facilitate heterogenization of the plantation structure. Natural disturbances are found to be able to enhance the species diversity and the interactions of ecological processes. In particular, where sustainable management strategies focused on maintaining ecosystem services especially in restored sites or plantations act as a supportive part. Natural disturbances are an integral component of mangrove forests and fulfill specific ecological functions. However, our findings indicate that these disturbances, on top of altered environmental conditions associated with climate change and direct human impacts, might jeopardize the natural development in unnatural forest structures as on plantations or restored sites. This thesis gives an extensive overview about the effect of various disturbances in different mangrove forest systems, including semi-natural forests and strongly modified plantations, on species composition and forest structure. Field studies and simulation analyses contribute in equal parts to the results of the thesis.

We have considered the bilevel programming problem in the case where the lower-level problem admits more than one optimal solution. It is well-known in the literature that in such a situation, the problem is ill-posed from the view point of scalar objective optimization. Thus the optimistic and pessimistic approaches have been suggested earlier in the literature to deal with it in this case. In the thesis, we have developed a unified approach to derive necessary optimality conditions for both the optimistic and pessimistic bilevel programs, which is based on advanced tools from variational analysis. We have obtained various constraint qualifications and stationarity conditions depending on some constructive representations of the solution set-valued mapping of the follower’s problem. In the auxiliary developments, we have provided rules for the generalized differentiation and robust Lipschitzian properties for the lower-level solution setvalued map, which are of a fundamental interest for other areas of nonlinear and nonsmooth optimization. Some of the results of the aforementioned theory have then been applied to derive stationarity conditions for some well-known transportation problems having the bilevel structure.

Mathematical models of signal transduction pathways are characterized by a large number of proteins and uncertain parameters, yet only a limited amount of quantitative data is available. The dissertation addresses this problem using two different approaches: the first approach deals with a model simplification procedure for signaling pathways that reduces the model size but retains the physical interpretation of the remaining states, while the second approach deals with creating rich data sets by computing transcription factor profiles from fluorescent images of green-fluorescent-protein (GFP) reporter cells. For the first approach a model simplification procedure for signaling pathway models is presented. The technique makes use of sensitivity and observability analysis to select the retained proteins for the simplified model. The presented technique is applied to an IL-6 signaling pathway model. It is found that the model size can be significantly reduced and the simplified model is able to adequately predict the dynamics of key proteins of the signaling pathway. An approach for quantitatively determining transcription factor profiles from GFP reporter data is developed as the second major contribution of this work. The procedure analyzes fluorescent images to determine fluorescence intensity profiles using principal component analysis and K-means clustering, and then computes the transcription factor concentration from the fluorescence intensity profiles by solving an inverse problem involving a model describing transcription, translation, and activation of green fluorescent proteins. Activation profiles of the transcription factors NF-κB, nuclear STAT3, and C/EBPβ are obtained using the presented approach. The data for NF-κB is used to develop a model for TNF-α signal transduction while the data for nuclear STAT3 and C/EBPβ is used to verify the simplified IL-6 model. Finally, an approach is developed to compute the distribution of transcription factor profiles among a population of cells. This approach consists of an algorithm for identifying individual fluorescent cells from fluorescent images, and an algorithm to compute the distribution of transcription factor profiles from the fluorescence intensity distribution by solving an inverse problem. The technique is applied to experimental data to derive the distribution of NF-κB concentrations from fluorescent images of a NF-κB GFP reporter system.

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Les données manquantes sont fréquentes dans les enquêtes et peuvent entraîner d’importantes erreurs d’estimation de paramètres. Ce mémoire méthodologique en sociologie porte sur l’influence des données manquantes sur l’estimation de l’effet d’un programme de prévention. Les deux premières sections exposent les possibilités de biais engendrées par les données manquantes et présentent les approches théoriques permettant de les décrire. La troisième section porte sur les méthodes de traitement des données manquantes. Les méthodes classiques sont décrites ainsi que trois méthodes récentes. La quatrième section contient une présentation de l’Enquête longitudinale et expérimentale de Montréal (ELEM) et une description des données utilisées. La cinquième expose les analyses effectuées, elle contient : la méthode d’analyse de l’effet d’une intervention à partir de données longitudinales, une description approfondie des données manquantes de l’ELEM ainsi qu’un diagnostic des schémas et du mécanisme. La sixième section contient les résultats de l’estimation de l’effet du programme selon différents postulats concernant le mécanisme des données manquantes et selon quatre méthodes : l’analyse des cas complets, le maximum de vraisemblance, la pondération et l’imputation multiple. Ils indiquent (I) que le postulat sur le type de mécanisme MAR des données manquantes semble influencer l’estimation de l’effet du programme et que (II) les estimations obtenues par différentes méthodes d’estimation mènent à des conclusions similaires sur l’effet de l’intervention. / Missing data are common in empirical research and can lead to significant errors in parameters’ estimation. This dissertation in the field of methodological sociology addresses the influence of missing data on the estimation of the impact of a prevention program. The first two sections outline the potential bias caused by missing data and present the theoretical background to describe them. The third section focuses on methods for handling missing data, conventional methods are exposed as well as three recent ones. The fourth section contains a description of the Montreal Longitudinal Experimental Study (MLES) and of the data used. The fifth section presents the analysis performed, it contains: the method for analysing the effect of an intervention from longitudinal data, a detailed description of the missing data of MLES and a diagnosis of patterns and mechanisms. The sixth section contains the results of estimating the effect of the program under different assumptions about the mechanism of missing data and by four methods: complete case analysis, maximum likelihood, weighting and multiple imputation. They indicate (I) that the assumption on the type of MAR mechanism seems to affect the estimate of the program’s impact and, (II) that the estimates obtained using different estimation methods leads to similar conclusions about the intervention’s effect.