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Batterimodeller används för att representera batterier. För ändamål som batterihanteringssystem används idag främst empiriska modeller som representerar ett batteri med en motsvarande kretsmodell. Några nackdelar för dessa modeller ligger i dess oförmåga att simulera interna tillstånd och en tidskrävande parametriseringsprocess. Dessa nackdelar motiverar ingenjörer att vända sig till modeller som är baserade på fysiska lagar som ett alternativ eftersom de kan ge insikt i vad som händer inuti batteriet. Batterimodellerna som är baserade på de fysiska lagarna har alltför krävande beräkningar för att kunna användas för vissa applikationer, som batterihanteringssystem. Singel-partikelmodellen (SPM) är en fysikbaserad modell som används i detta avhandlingsprojekt. Syftet med projektet var att hitta en metod för att parametrisera SPM för nya kommersiella cylindriska HTPFR18650 1100mAh 3.2V litiumjärnfosfatceller. En litteraturundersökning och experiment användes för att extrahera parametervärdena. 17 parametrar valdes från litteraturundersökningen eftersom de kunde användas för att parametrisera modellen. Geometriska parametrar hittades genom en cellöppning. Tre typer av icke-destruktiva experiment som var inspirerade av litteraturen utfördes för att extrahera värden för de andra icke-geometriska parametrarna. Ett cykeltest med låg strömhastighet utfördes för att få en pseudo-OCV-kurva och för att extrahera kapacitetsrelaterade parametrarna. En känslighetsanalys genomfördes för galvanostatisk intermittent titreringsteknik testet (GITT) och pulstestet för de parametrar som var kopplade till transportoch kinetiska fenomen. Python matematisk batterimodellering (PyBaMM) användes för att simulera experimenten. Parametersamlingen Prada 2013 användes som standardvärden. Standardvärdena för de valda parametrarna ersattes av de värden som hittades genom experiment. Känslighetsanalysen visade att några av de valda parametrarna var känsliga för experimenten medan andra inte var det. Parametrarna extraherades genom fysiska relationer och genom att anpassa parametervärde för simuleringen så att den passar den experimentella datan under urladdningsförloppet. Värden för 14 av de 17 parametrarna extraherades i metoden. Den parametriserade modellen validerades mot två potentiella applikationer, en för ett batterielfordon och den andra för ett mild-hybridfordon. Den parametriserade modellen visade att den negativa partikelradien inte kan hittas med den föreslagna parametriseringsmetoden. Simuleringen visade sig också matchade den experimentella datan bättre under urladdning av cellerna jämfört till uppladdning. Flera förbättringar för framtida arbete har föreslagits, såsom att utvidgning av känslighetsanalysen, att erhålla OCV-kurvan från GITT istället för att använda pseudo-OCVkurvan, att använda strängare gränser vid kurvanpassningarna samt att skapa mer optimala tester för att extrahera parametervärdena. / Battery models are used to represent batteries. For purposes like battery management systems, empirical based models like the equivalent circuit models are widely used. These models have downsides regarding for example inability to simulate internal states and parametrization time that make engineers look at physics-based models as an alternative. The physics-based models are made up of physical relationships that offer insights into what is happening inside the battery. These are too computationally demanding to be used for certain applications, like battery managements systems. The Single Particle Model (SPM) is a physics-based model that is utilized in this thesis project. The aim of the project is to find a method to parametrize the SPM for fresh commercial cylindrical HTPFR18650 1100mAh 3.2V lithium iron phosphate cells. Literature survey and experiments were used to extract the parameter values. 17 parameters were selected from the literature survey since they could be used to parametrize the model. Geometrical parameters were found through a cell opening. Three types of nondestructive experiments inspired by literature were performed to extract values for the other non-geometric parameters. A low-rate cycling test was performed to get pseudo-OCV curve and to extract capacity related parameters. A sensitivity analysis is done for the GITT and the Pulse test for the parameters that were connected to the transport and kinetic phenomena. Python mathematical battery modelling (PyBaMM) was used to simulate the experiments. The Prada 2013 parameter set was be used as default values. The default values for the selected parameters were replaced by the values found through experiments. The sensitivity analysis showed that some of the selected parameters were sensitive while others were not. The parameters were extracted through physical relations and through curve fitting procedures during discharge. Values for 14 out of the 17 parameters were extracted in the method. The parametrized model was validated against two potential applications, one for a battery electric vehicle and the other for a mild hybrid. The parametrized model showed that the negative particle radius cannot be found through the proposed parametrization procedure. The simulation matched the experimental data better for discharging cells than charging cells. Several improvements for future work have been suggested such as extending the sensitivity analysis, obtaining the OCV-curve from GITT instead of low-rate cycling, having stricter bounds for the curve fitting as well as creating more optimal tests to extract the parameter values.

Conformational dynamics are important to the function of biological molecules. While many experimental techniques (e.g. X-ray crystallography and NMR spectroscopy) have been developed for providing the structure of functional conformations, it is exceptionally challenging to understand conformational dynamics from experimental characterization. Molecular dynamics (MD) simulations is a powerful tool for probing conformational dynamics. The timescale resolution of MD simulations enables people to investigate intermediate conformations and transition pathways in atomic detail. Recent advancements in computer hardware have increased the timescales accessible to MD simulations. Meanwhile, more accurate and specific force fields have been developed to accurately model a variety biological system of different sizes. My graduate research has been focused on using MD simulations to study the conformational dynamics of proteins. Markov State Model (MSM) based approaches are extensively applied to investigate a variety of folding and/or binding mechanisms in atomic detail. Another focus of my work has been developing a Bayesian inference-based approach called BICePs to reconcile experimental measurements with simulation data to determine conformational ensembles and to validate force fields. / Chemistry

In modern combat aircraft, the most common localization method integrates a Global Navigation Satellite System (GNSS) with an Inertial Navigation System (INS). Although GNSS is the optimal choice for navigation, there are situations when the GNSS satellite signal is unavailable. This can happen due to various reasons such as jamming, physical obstacles, or technical failures. An alternative method to GNSS is utilizing Signals of Opportunity (SOP), which leverages signals not intended for navigation, such as those from cellular towers. These signals are transmitted from non-controllable sources, and challenges may arise due to the lack of guarantee regarding their quality and availability. Therefore, it is crucial that any estimation method utilizing SOP is robust to ensure accurate aircraft localization. This thesis investigates three different localization approaches to address this challenge. This study explores SOP sources with both known and unknown positions. For known signal source positions, an Extended Kalman Filter (EKF) based solution is utilized as a baseline to evaluate how well unknown signal sources can be used to estimate the aircraft's location. To address the challenge of unknown signal source positions, an EKF combined with a Simultaneous Localization and Mapping (SLAM) method, referred to as EKF SLAM, is used. In this case, the sources are introduced through two different approaches. The first approach, undelayed initialization, introduces the signal source directly when observed. The second approach, delayed initialization, involves inverse depth parameterization (IDP) and preprocessing of the signal source position before fully introducing it into the aircraft system. While both approaches outperform an unassisted INS approach, they do not achieve the same level of performance as when the source positions are known. Moreover, various factors, including the aircraft's trajectory, measurement noise, measurement frequency, and the initial covariance of new landmarks, influence the performance of the EKF SLAM approaches. Additionally, delayed initialization is strongly influenced by a threshold assessing landmark position estimate linearity, underscoring its sensitivity to accuracy. The concept behind delayed initialization aims to reduce the error of the signal source position before it is introduced to the system. This method has been proven to significantly reduce the signal source position error. However, its robustness is influenced by several factors, including the parallax angle, sudden changes in the aircraft's direction, and particularly the initial covariance of a landmark estimate. The accuracy of the aircraft's position is crucial, resulting in a trade-off between preprocessing and rapidly initializing a signal source position to the aircraft system. In contrast, undelayed initialization is less sensitive to trajectory changes, even though it introduces the signal sources with greater initial error. There is a significant difference in computational time when comparing known and unknown sources. As the number of sources increases, the computational time for unknown sources is more affected than for known sources. The delayed source initialization method increases computational time due to its preprocessing, especially as more sources are used. Conversely, initializing sources directly reduces the computational time, as no preprocessing is required. / I moderna stridsflygplan är den vanligaste lokaliseringsmetoden att integrera ett Global Navigation Satellite System (GNSS) med ett Inertial Navigation System (INS). Även om GNSS är det optimala valet för navigation finns det situationer när GNSS-satellitsignalen inte är tillgänglig. Detta kan inträffa på grund av olika orsaker som störningar, fysiska hinder eller tekniska fel. En alternativ metod till GNSS är att använda Signals of Opportunity (SOP), som utnyttjar signaler som inte är avsedda för navigation, till exempel de från mobilmaster. Dessa signaler kommer från okontrollerbara källor, vilket kan medföra utmaningar på grund av att deras kvalitet och tillgänglighet inte kan garanteras. Därför är det viktigt att varje lokaliseringsmetod som använder SOP är robust för att säkerställa en bra och korrekt flygplans positionering. Detta examensarbete undersöker tre olika lokaliseringsmetoder för att hantera denna utmaning. Denna studie utforskar SOP-källor med både kända och okända positioner. För kända positioner används en lösning baserad på ett Extended Kalman Filter (EKF) som en baslinje för att utvärdera hur väl okända signalkällor kan användas för att uppskatta flygplanets position. För att hantera utmaningen med okända signalkällors positioner används ett EKF kombinerad med en metod vid namn Simultaneous Localization and Mapping (SLAM), även kallad EKF SLAM. I detta fall introduceras källorna genom två olika tillvägagångssätt. Det första tillvägagångssättet, ofördröjd initialisering, introducerar signalkällan direkt när den observeras. Det andra tillvägagångssättet, fördröjd initialisering, involverar inverse depth parameterization (IDP) och förbearbetning av signalkällans position innan den introduceras i flygplanets lokaliseringssystem. Även om båda tillvägagångssätten presterar bättre än en oassisterad INS-metod uppnår de inte samma prestandanivå som när källornas position är kända. Dessutom påverkar olika faktorer prestandan hos EKF SLAM-metoderna, vilka främst är flygplanets flygbana, mätbrus, mätfrekvens och den initiala kovariansen av nya landmärken. Dessutom påverkas fördröjd initialisering starkt av en tröskel som bedömer linjäritet hos landmärkes positionen, vilket understryker dess känslighet för noggrannhet. Konceptet bakom fördröjd initialisering syftar till att minska felet i signalkällans position innan den introduceras i lokaliseringssystemet. Denna metod har visat sig kunna minska felet i signalkällans position avsevärt. Emellertid påverkas dess robusthet av flera faktorer, inklusive parallaxvinkeln, plötsliga förändringar i flygplanets riktning och särskilt den initiala kovariansen av uppskattningen av ett landmärkes position. Noggrannheten i flygplanets position är avgörande, vilket resulterar i en avvägning mellan förbearbetning och snabb initialisering av en signalkällas position till flygplanets lokaliseringssystem. Till skillnad från fördröjd initialisering är ofördröjd initialisering mindre känslig för förändringar i flygbanan, även om den introducerar signalkällorna med större initialt fel. Det finns en anmärkningsvärd skillnad i beräkningstid när man jämför kända och okända källors. När antalet källor ökar påverkas beräkningstiden för okända källor mer än för kända källor. Den fördröjda källinitialiseringsmetoden ökar beräkningstiden på grund av dess förbearbetning, särskilt när många källor används. Däremot minskar beräkningstiden när källor initialiseras direkt, eftersom ingen förbearbetning krävs.

This thesis deals with different computational techniques related to some classes of nonlinear response regimes of engineering interest. The work is mainly divided into two parts. In the first part different numeric-analytic integration techniques for nonlinear oscillators are developed. In the second part, procedures for handling arbitrarily large rotations are addressed and a few novel developments are reported in the process. To begin the first part, we have proposed an explicit numeric-analytic technique, based on the Adomian decomposition method, for integrating strongly nonlinear oscillators. Numerical experiments suggest that this method, like most other numerical techniques, is versatile and can accurately solve strongly nonlinear and chaotic systems with relatively larger step-sizes. It is then demonstrated that the procedure may also be effectively employed for solving two-point boundary value problems with the help of a shooting algorithm. This has been followed up with the derivation and numerical exploration of variants of a recently developed numeric-analytic technique, the multi-step transversal linearization (MTrL), in the context of nonlinear oscillators of relevance in engineering dynamics. A considerable generalization and improvement over the original form of a MTrL strategy is achieved in this study. Finally, we have used the concept of MTrL method on the nonlinear variational (rate) equation corresponding to a nonlinear oscillator and thus derive another family of numeric-analytic techniques, presently referred to as the multi-step tangential linearization (MTnL). A comparison of relative errors through the MTrL and MTnL techniques consistently indicate a superior quality of approximation via the MTrL route. In the second part of the thesis, a scheme for numerical integration of rigid body rotation is proposed using only rudimentary tensor analysis. The equations of motion are rewritten in terms of rotation vectors lying in same tangent spaces, thereby facilitating vector space operations consistent with the underlying geometric structure of rotation. One of the most important findings of this part of the dissertation is that the existing constant-preserving algorithms are not necessarily accurate enough and may not be ideally applicable to cases wherein numerical accuracy is of primary importance. In contrast, the proposed rotation-algorithms, the higher order ones in particular, are significantly more accurate for conservative rotational systems for reasonably long time. Similar accuracy is expected for dissipative rotational systems as well. The operators relating rotation variables corresponding to different tangent spaces are also investigated and this should provide further insight into the understanding of rotation vector parametrization. A rotation update is next proposed in terms of rotation vectors. This update, employed along with interpolation of relative rotations, gives a strain-objective and path independent finite element implementation of a geometrically exact beam. The method has the computational advantage of requiring considerably less nodal variables due to the use of rotation vector parametrization. We have proposed a new isoparametric interpolation of nodal quaternions for computing the rotation field within an element. This should be a computationally efficient alternative to the interpolation of local rotations. It has been proved that the proposed interpolation of rotation leads to the objectivity of strain measures. Several numerical experiments are conducted to demonstrate the frame invariance, path-independence and other superior aspects of the present approach vis-`a-vis the existing methods based on the rotation vector parametrization. It is emphasized that, in order to develop an objective finite element formulation, the use of relative rotation is not mandatory and an interpolation of total rotation variables conforming with the rotation manifold should suffice.

Dans cette thèse, nous proposons des solutions pour la conception de systèmes de contrôle actif de vibration robustes (AVC). Le manuscrit de thèse comporte deux grandes parties.Dans la première, les problèmes d'incertitude paramétrique dans les systèmes de contrôle actif de vibration sont étudiés. En plus des incertitudes sur la fréquence des perturbations, nous avons trouvé que la présence de zéros complexes peu amortis soulevait des problèmes de conception difficiles, même pour des systèmes et des modèles parfaitement connus. Dans ce contexte, nous avons proposé des solutions pour le problème linéaire. Une procédure améliorée d'identification en boucle fermée a été développée pour réduire les incertitudes dans l'identification de ces zéros. Pour traiter les incertitudes sur la perturbation, l'adaptation de la fréquence est de toute façon incontournable.La seconde partie est consacrée au développement et/ou à l'amélioration de deux algorithmes, désormais classiques, de compensation par feedback adaptatif direct, fondés sur la paramétrisation de Youla-Kučera. Le premier résulte de l'amélioration d'un précédent travail (Landau et al., 2005) ; les contributions concernent la synthèse du contrôleur central robuste et l'utilisation optionnelle de la surparamétrisation du filtre Q-FIR (réponse à temps fini) avec pour effet de minimiser l'effet « waterbed » sur la fonction de sensibilité de sortie. Le second algorithme présente une structure hybride directe/indirecte qui utilise un filtre Q-IIR (à temps de réponse infini). Les améliorations sont dues principalement au dénominateur du filtre, obtenu à partir d'une estimation de la perturbation. Cette solution permet également de simplifier la conception du contrôleur central.Les algorithmes ont été testés, comparés et validés sur un procédé réel du laboratoire Gipsa-lab, dans le cadre d'un benchmark international. / In this thesis, solutions for the design of robust Active Vibration Control (AVC) systems are presented. The thesis report is composed of two main parts.In the first part of the thesis uncertainties issues in Active Vibration Control systems are examined. In addition of the uncertainties on the frequency of the disturbances it has been found that the presence of low damped complex zeros raise difficult design problems even if plant and models are perfectly known. Solutions for the linear control in this context have been proposed. In order to reduce the uncertainties in the identification of low complex zeros and improved closed loop identification procedure has been developed. To handle the uncertainties on the disturbance frequency adaptation has any way to be used.The second part is concerned with the further development and/or the improvement of the now classical direct adaptive feedback compensation algorithms using Youla Kucera controller parametrization. Two new solutions have been proposed in this context. The first one results from the improvement of a previous work (Landau et al., 2005). The contributions are a new robust central controller design to the optional use of over parameterization of the Q-FIR filter which aims to ensure a small waterbed effect for the output sensitivity function and therefore reducing the unwanted amplification. The second algorithm presents a mixed direct/indirect structure which uses a Q-IIR filter. The improvements are mainly the effect of the Q filter denominator, which is obtained from a disturbance identification. This solution in addition drastically simplifies the design of the central controller.The algorithms have been tested, compared and validated on an international benchmark setup available at the Control System Department of GIPSA-Lab, Grenoble, France.

Finding a topologically accurate approximation of a real planar algebraic curve is a classic problem in Computer Aided Geometric Design. Algorithms describing the topology search primarily the singular points and are usually based on algebraic techniques applied directly to the curve equation. In this thesis we propose a more geometric approach, taking into account the subsequent high-precision approximation. Our algorithm is primarily based on the identification and approximation of smooth monotonous curve segments, which can in certain cases cross the singularities of the curve. To find the characteristic points we use not only the primary algebraic equation of the curve but also, and more importantly, its implicit support function representation. Using the rational Puiseux series, we describe local properties of curve branches at the points of interest and exploit them to find their connectivity. The support function representation is also used for an approximation of the segments. In this way, we obtain an approximate graph of the entire curve with several nice properties. It approximates the curve within a given Hausdorff distance. The actual error can be measured efficiently. The ap- proximate curve and its offsets are piecewise rational. And the question of topological equivalence of the...

Depuis les années 80 la cartographie optique est devenu un outil important pour l'étude et la compréhension des arythmies cardiaques. Cette expérience permet la visualisation de flux de fluorescence à la surface du tissu ; fluorescence qui est directement liée au potentiel transmembranaire. Dans les observations en surface se cachent des informations sur la distribution en trois dimensions de ce potentiel. Nous souhaitons exploiter ces informations surfaciques afin de reconstruire le front de dépolarisation dans l'épaisseur. Pour cela nous avons développé une méthode basée sur la résolution d'un problème inverse. Le modèle direct est composée de deux équations de diffusion et d'une paramétrisation du front de dépolarisation. La résolution du problème inverse permet l'identification des caractéristiques du front. La méthode a été testée sur des données in silico avec différentes manières de caractériser le front (sphère qui croît au cours du temps, équation eikonale). Les résultats obtenus sont très satisfaisants et comparés à une méthode développée par Khait et al. [1]. Le passage à l'étude sur données expérimentales a mis en évidence un problème au niveau du modèle. Nous détaillons ici les pistes explorées pour améliorer le modèle : illumination constante, paramètres optiques, précision de l'approximation de diffusion. Plusieurs problèmes inverses sont considérés dans ce manuscrit, ce qui implique plusieurs fonctionnelles à minimiser et plusieurs gradients associés. Pour chaque cas, le calcul du gradient est explicité, le plus souvent par la méthode de l'adjoint. La méthode développée a aussi été appliquée à des données autres que la cartographie optique cardiaque. / Since the 80's optical mapping has become an important tool for the study and the understanding of cardiac arythmias. This experiment allows the visualization of fluorescence fluxes through tissue surface. The fluorescence is directly related to the transmembrane potential. Information about its three-dimension distribution is hidden in the data on the surfaces. Our aim is to exploit this surface measurements to reconstruct the depolarization front in the thickness. For that purpose we developed a method based on the resolution of an inverse problem. The forward problem is made of two diffusion equations and the parametrization of the wavefront. The inverse problem resolution enables the identification of the front characteristics. The method has been tested on in silico data with different ways to parameter the front (expanding sphere, eikonal equation). The obtained results are very satisfying, and compared to a method derived by Khait et al. [1]. Moving to experimental data put in light an incoherence in the model. We detail the possible causes we explored to improve the model : constant illumination, optical parameters, accuracy of the diffusion approximation. Several inverse problems are considered in this manuscript, that involves several cost functions and associated gradients. For each case, the calculation of the gradient is explicit, often with the gradient method. The presented method was also applied on data other than cardiac optical mapping.

Durant l’épisode de canicule-sécheresse de 2003, les peuplements de douglas et de hêtres en Bourgogne ont été lourdement affectés, présentant des symptômes de dépérissement et de surmortalité. Cet épisode semble être la première occurrence d’aléas climatiques attendus dans un futur proche et remet en question leur pérennité en Bourgogne puisque leur vulnérabilité au climat est attribuable à l'amplitude et au cumul des contraintes hydriques exercées durant leur cycle de végétation. Dans le contexte du changement climatique et en réponses aux demandes des gestionnaires forestiers qui s’appuient partiellement sur une cartographie de l’évolution des contraintes climatiques jusqu’à la fin de ce siècle, ce travail explore la capacité d’une chaîne de modélisation hydroclimatique haute résolution couplant le modèle de climat régional WRF alimenté par les réanalyses ERA-Interim au modèle de bilan hydrique Biljou© ˆ simuler des indices de déficit hydrique pour ces deux essences. La première partie de ce travail propose une analyse de la capacité du modèle WRF à simuler chacune des variables atmosphériques de surface qui sont utilisées en entrée du modèle du bilan hydrique. L’analyse de la capacité du modèle à simuler ces variables repose (i) sur une approche comparative directe entre les données simulées par WRF et les observations enregistrées par le réseau de stations Météo-France et les réanalyses SAFRAN à l’échelle de la région, de la station, et du peuplement forestier, (ii) sur une approche indirecte utilisant l’évapotranspiration potentielle (ETP) et la relation entre les indices de croissance radiale et les indices de déficit hydrique calculés par le modèle d’impact pour les deux essences. Les résultats montrent une amélioration significative des données ERA-Interim par le modèle WRF pour chacune des variables ainsi qu’une capacité certaine à les spatialiser à haute résolution. Toutefois, la bonne reproduction de l’ETP par WRF, combinée à la faible corrélation entre la moyenne annuelle des indices de déficit hydrique estimés avec les données WRF et la moyenne annuelle des indices de croissance radiale montrent que les difficultés de WRF à simuler le déficit hydrique sont principalement imputables à ses biais de précipitations. La seconde partie propose l’application d’une post-correction statistique aux données de précipitations WRF. Bien que cette méthode améliore significativement la distribution spatiale des précipitations, leurs variabilités saisonnière et interannuelle et surtout les cumuls précipités, les données post-corrigées ne permettent pas de reproduire un indice de déficit hydrique suffisamment proche de celui estimé à partir des observations ou des analyses SAFRAN. Deux nouvelles simulations résolvant explicitement les processus convectifs et utilisant un guidage spectral ont permis de montrer à partir de deux années types que cette déficience est imputable à l’incapacité de la méthode de correction à résoudre les différences de timing de la variabilité climatique transitoire simulée par WRF. Deux types d’erreurs de modélisation climatique, survenant indépendamment, sont donc d'une importance primordiale pour les études d'impact: (i) la chronologie des événements pluvieux ; (ii) la distribution statistique des précipitations quotidiennes. La combinaison de ces deux éléments contrôle le nombre de jours franchissant le seuil de 40% de réserve relative en eau du sol et indirectement l’intensité des indices de déficit hydrique. / During the 2003 drought and heat wave event, douglas-fir and common beech stands in Burgundy have been heavily affected, and presented symptoms of dieback and mortality. This event seems to be the first occurrence of expected climatic changes in the near future and questions their sustainability in Burgundy since their climate vulnerability is mainly due to the amplitude and accumulated water constraints exercised during their growing cycle. In the context of climate change and in order to provide information to forest managers who partly rely on a mapping of the climatic constraints until the end of this century, this work explores the ability of a high resolution hydroclimatic modelling chain, coupling the regional climate model WRF to the daily lumped water balance model Biljou© in order to simulate soil water deficit indices for these two species. The first part of this paper analyzes the capacity of WRF model to simulate each surface atmospheric variable used as input for the water balance computation. The analysis of model's ability to simulate these variables is based on (i) a direct and comparative approach between WRF simulated data and observations recorded by the Météo-France stations network and SAFRAN reanalyses across the whole region, over stations and forest stands, (ii) on an indirect approach using the potential evapotranspiration and soil water deficit index calculated by Biljou©. Results show a significant improvement upon the ERA-Interim data for each variable and a strong ability to produce reliable data at high resolution. However, the WRF capability to estimate a realist potential evapotranspiration, combined to the the low correlation between the average annual soil water deficit and radial growth indexes, show that the WRF deficiencies in simulating water deficit are mainly attributable to its precipitation biases. The second part proposes to apply a statistical post-correction to the WRF precipitation data. Although this method significantly improves the spatial distribution of precipitation, their seasonal and interannual variability and precipitation amounts, post-corrected data do not produce a water deficit index sufficiently close to those ones estimated from observations or SAFRAN reanalysis. Two new simulations explicitly solving convective processes and using a spectral nudging have shown that this deficiency is mainly attributable to the inability of the correction method to solve timing differences of the transient climate variability simulated by WRF. This work showed that two types of climate modeling errors occurring independently, are major issues for impact studies: (i) the timing of precipitations events ; (ii) the statistical distribution of daily precipitation. Combined together, they control the number of days crossing the 40% threshold of relative extractable water and indirectly the soil water deficit index intensity.

This diploma thesis is focused on the design of a product family of portable veterinary x-ray generators. The thesis deals with the possibilities of using parameterization when designing products which are part of a product series. The main body of the thesis lies in the design of a parametric script which generates variations of portable veterinary x-ray generators depending on the size and position of the inner components. The outer surfaces are defined by algorithms from the input parameters. It is possible to alter the individual attributes (e.g. the progresion of curves, the dimensions of component parts and the proportions between the individual parts). The output from the parametric script is three size-variations of the product.