We develop a stochastic parametrization, based on a 'simple' deterministic model for the dynamics of steady longshore currents, that produces ensembles that are statistically consistent with field observations of these currents. Unlike deterministic models, stochastic parameterization incorporates randomness and hence can only match the observations in a statistical sense. Unlike statistical emulators, in which the model is tuned to the statistical structure of the observation, stochastic parametrization are not directly tuned to match the statistics of the observations. Rather, stochastic parameterization combines deterministic, i.e physics based models with stochastic models for the "missing physics" to create hybrid models, that are stochastic, but yet can be used for making predictions, especially in the context of data assimilation. We introduce a novel measure of the utility of stochastic models of complex processes, that we call consistency of sensitivity. A model with poor consistency of sensitivity requires a great deal of tuning of parameters and has a very narrow range of realistic parameters leading to outcomes consistent with a reasonable spectrum of physical outcomes. We apply this metric to our stochastic parametrization and show that, the loss of certainty inherent in model due to its stochastic nature is offset by the model's resulting consistency of sensitivity. In particular, the stochastic model still retains the forward sensitivity of the deterministic model and hence respects important structural/physical constraints, yet has a broader range of parameters capable of producing outcomes consistent with the field data used in evaluating the model. This leads to an expanded range of model applicability. We show, in the context of data assimilation, the stochastic parametrization of longshore currents achieves good results in capturing the statistics of observation that were not used in tuning the model.

This diploma thesis based on a result of the European Union's intention to increase the share of electricity produced from renewable energy sources in the total production, Slovak Republic currently subsidises building gasifier power plants (high efficiency combined production) to produce electricity and thermal energy from the biomass. Therefore, this thesis aims to build a financial plan of gasifier, which will be used for the evaluation of the investment from the point of view of an investor. Valuation depends mainly on the economic benefits of the project with regards to the assessment of business environment. The work contains a sensitivity analysis to determine what impact on the value of the cash flows will make a percentage change in one variable.

When we develop and use species distribution models to predict species' current or potential distributions, we are faced with the trade-offs between model generality, precision, and realism. It is important to know how to improve and validate model generality while maintaining good model precision and realism. However, it is difficult for ecologists to evaluate species distribution models using field-sampled data alone because the true species response function to environmental or ecological factors is unknown. Species distribution models should be able to approximate the true characteristics and distributions of species if ecologists want to use them as reliable tools. Simulated data provide the advantage of being able to know the true species-environment relationships and control the causal factors of interest to obtain insights into the effects of these factors on model performance. I used a case study on Bythotrephes longimanus distributions from several hundred Ontario lakes and a simulation study to explore the effects on model performance caused by several factors: the choice of predictor variables, the model evaluation methods, the quantity and quality of the data used for developing models, and the strengths and weaknesses of different species distribution models. Linear discriminant analysis, multiple logistic regression, random forests, and artificial neural networks were compared in both studies. Results based on field data sampled from lakes indicated that the predictive performance of the four models was more variable when developed on abiotic (physical and chemical) conditions alone, whereas the generality of these models improved when including biotic (relevant species) information. When using simulated data, although the overall performance of random forests and artificial neural networks was better than linear discriminant analysis and multiple logistic regression, linear discriminant analysis and multiple logistic regression had relatively good and stable model sensitivity at different sample size and detection limit levels, which may be useful for predicting species presences when data are limited. Random forests performed consistently well at different sample size levels, but was more sensitive to high detection limit. The performance of artificial neural networks was affected by both sample size and detection limit, and it was more sensitive to small sample size.

When we develop and use species distribution models to predict species' current or potential distributions, we are faced with the trade-offs between model generality, precision, and realism. It is important to know how to improve and validate model generality while maintaining good model precision and realism. However, it is difficult for ecologists to evaluate species distribution models using field-sampled data alone because the true species response function to environmental or ecological factors is unknown. Species distribution models should be able to approximate the true characteristics and distributions of species if ecologists want to use them as reliable tools. Simulated data provide the advantage of being able to know the true species-environment relationships and control the causal factors of interest to obtain insights into the effects of these factors on model performance. I used a case study on Bythotrephes longimanus distributions from several hundred Ontario lakes and a simulation study to explore the effects on model performance caused by several factors: the choice of predictor variables, the model evaluation methods, the quantity and quality of the data used for developing models, and the strengths and weaknesses of different species distribution models. Linear discriminant analysis, multiple logistic regression, random forests, and artificial neural networks were compared in both studies. Results based on field data sampled from lakes indicated that the predictive performance of the four models was more variable when developed on abiotic (physical and chemical) conditions alone, whereas the generality of these models improved when including biotic (relevant species) information. When using simulated data, although the overall performance of random forests and artificial neural networks was better than linear discriminant analysis and multiple logistic regression, linear discriminant analysis and multiple logistic regression had relatively good and stable model sensitivity at different sample size and detection limit levels, which may be useful for predicting species presences when data are limited. Random forests performed consistently well at different sample size levels, but was more sensitive to high detection limit. The performance of artificial neural networks was affected by both sample size and detection limit, and it was more sensitive to small sample size.

Diploma thesis is focused on advanced reliability analysis of structures solved by non--linear finite element analysis. Specifically, semi--probabilistic methods for determination of design value of resistance, sensitivity analysis and surrogate model created by polynomial chaos expansion are described in the diploma thesis. Described methods are applied on prestressed reinforced concrete roof girder.

Pour mieux comprendre et traiter les troubles musculosquelettiques présents à l’épaule, une meilleure connaissance de la contribution et de la fonction de chaque muscle de l’articulation glénohumérale est nécessaire. L’analyse des forces musculaires et articulaires est une étape importante pour comprendre les mécanismes de blessures et les pathologies. Ces forces musculaires peuvent être estimées de façon non invasive grâce à des modèles musculosquelettiques. Le défi est de prédire de façon physiologique les trajectoires musculaires et les bras de levier afin de s’assurer d’avoir une cohérence des forces musculaires dans les modèles musculosquelettiques. L’objectif de cette thèse était d’améliorer la géométrie musculaire des modèles musculosquelettiques de l’épaule en passant par plusieurs méthodes différentes d’implémentation des trajectoires musculaires. À cet égard, nos objectifs spécifiques étaient de : (1) améliorer la géométrie musculaire des modèles multicorps rigides grâce à l’implémentation de contraintes transverses; (2) évaluer la fiabilité d’un modèle éléments finis pour l’estimation des bras de levier et (3) tester la sensibilité de la prédiction des bras de levier aux incertitudes sur les zones d’insertions musculaires; (4) établir une base de données de bras de levier 3D pour des mouvements de grande amplitude; (5) quantifier de façon expérimentale les changements architecturaux des muscles entre l’état au repos et différents niveaux de contraction isométrique. (1) Deux modèles multicorps rigides de la coiffe des rotateurs ont été développés : un modèle classique intégrant une représentation des lignes d’action en 1D et un modèle possédant des contraintes transverses entre les lignes d’action permettant une représentation 2D. La représentation 2D avec des contraintes transverses permet une représentation plus physiologique des trajectoires musculaires et des bras de levier que les modèles classiques 1D. Toutefois, lors de mouvement allant au-delà de 90° d’élévation du bras, lorsque les points d’origine et d’insertion se rapprochent, les bras de levier et les longueurs musculaires sont mal estimés, car le modèle ne prend pas en compte les déformations du volume musculaire. (2) Un modèle éléments finis a été développé à partir de données d’imagerie médicale. Ce modèle permet une estimation des bras de levier fidèle aux données d’IRM. Contrairement aux modèles multicorps rigides, notre modèle élément finis rend compte du fait qu’un même muscle peut avoir plusieurs actions selon la position de sa ligne d’action par rapport au centre de rotation de l’articulation. (3) Le modèle a également servi à faire une étude de sensibilité des bras de levier : les zones d’insertion des différents muscles de la coiffe des rotateurs et du deltoïde ont été déplacées et les bras de levier associés calculés. Les résultats montrent qu’une variation de 10 mm des points d’insertion sur la tête humérale peut amener un muscle à changer de fonction (par exemple adduction plutôt que d’abduction). (4) Une collecte de données expérimentales effectuées sur quatre épaules a permis de collecter les bras de levier du deltoïde et des muscles de la coiffe des rotateurs pour des mouvements de grande amplitude. Ces résultats permettent de mieux comprendre le rôle des muscles de l’articulation glénohumérale lors de la réalisation de différents mouvements. Le deltoïde antérieur a une grande action en flexion et en adduction; le deltoïde moyen est un fort abducteur; le deltoïde postérieur agit en extension. Contrairement au deltoïde, l’infra-épineux et le petit rond ont principalement une fonction de rotateur externe. (5) Une collecte de données impliquant 14 sujets a été réalisée dans le but de quantifier les changements de géométrie musculaire et d’angle de pennation associés à la contraction pour les muscles du biceps, triceps et deltoïde. Les angles de pennation ont été obtenus grâce à un système d’échographie et les changements de géométrie externe des muscles ont été mesurés grâce à un capteur de structure. Les résultats montrent que les changements architecturaux pour les muscles étudiés se produisent principalement entre 0 et 25% de contraction maximale volontaire (aucune différence significative observée entre 25 et 50%). Le muscle le plus affecté par les changements architecturaux est le biceps. Cette thèse a évalué différentes approches de modélisation de la géométrie musculaire : l’approche la plus bio-fidèle étant finalement la modélisation par éléments finis, car elle permet de prendre en compte les interactions entre les structures et les déformations musculaires. De plus, nous avons montré l’importance d’estimer avec rigueur les paramètres d’entrée (zones d’insertions musculaires) des modèles et de bien évaluer la bio-fidèlité des modèles développés avant de les utiliser dans des contextes cliniques. Dans ce but, de nouvelles données ont été acquises en termes de déformations musculaires et d’angle de pennation pour permettre l’évaluation de modèle intégrant de l’activation musculaire. / Understanding and treating musculoskeletal disorders of the shoulder requires additional knowledge of the contribution and function of each muscle of the glenohumeral joint. The analysis of muscle and joint forces is an important step in understanding injury mechanisms and pathologies. These muscle forces can be estimated non-invasively using musculoskeletal models. The challenge is to physiologically predict muscle trajectories and moment arms to ensure consistency of muscle forces in musculoskeletal models. The aim of this thesis was to improve muscle geometry in musculoskeletal models of the shoulder by testing several different techniques for implementing muscle trajectories. Our specific objectives were to: (1) improve muscle geometry of rigid multibody models by using transverse constraints; (2) assess the reliability of a finite element model for estimating moment arms and (3) evaluate the sensitivity of moment arm predictions to uncertainties in muscle insertion areas; (4) create a database of 3D moment arms for movements with high ranges of motion; (5) experimentally quantify muscles’ architectural changes between resting state and different levels of isometric contractions. (1) Two rigid multibody models of the rotator cuff were developed: a classic model representing muscles with lines of action in 1D and a 2D model with transverse constraints between lines of action of a single muscle. The 2D model (with transverse constraints) gives a more physiological representation of muscle trajectories and moment arms than the classical 1D model. However, for arm movements beyond 90° of elevation, when the origin and insertion points get closer, moment arms and muscle lengths are misestimated due to the mode’s inability to account for muscle volume deformations. (2) A finite element model of the glenohumeral joint was developed based on medical imaging. Moment arms were computed and compared to the literature and MRI data. Our finite element model produces moment arms consistent with the literature and MRI data. Unlike rigid multibody models, our finite element model accounts for the fact that one muscle can have several actions depending on the position of its line of action relative to the centre of rotation of the joint. (3) The model was used to study moment arm sensitivity: insertion areas of rotator cuff muscles and the deltoid were moved, and associated moment arms have been computed. Results showed that a 10 mm variation in insertion points on the humeral head could cause a muscle to change function (for example performing adduction rather than abduction). (4) The 3D moment arms were assessed on four post-mortem human surrogates during movements with high ranges of motion. Results of the study gave us a better understanding of muscle functions during different movements. The main findings of the study were that the anterior deltoid was the largest flexor and had an adduction component, the median deltoid was a strong abductor, and the posterior deltoid acted in extension. Unlike the deltoid, the infraspinatus and teres minor were the largest external rotators of the shoulder. (5) Experimental measurements were performed on 14 subjects in order to quantify changes in muscle geometry and pennation angles associated with different levels of contraction for the biceps, triceps and deltoid. Pennation angles were measured on subjects using a portable ultrasound system. External muscle deformations were measured with an iPad equipped with a structure sensor. Changes in muscle architecture for the biceps, triceps and deltoid during isometric contractions occurred mostly between 0 and 25% of maximal voluntary contraction (no significant difference was observed between 25 and 50%). Changes were higher for the biceps than other muscles. This thesis evaluated different approaches to model muscle geometry: the approach leading to the most physiological result was the finite element model due to modeling of the interactions between structure and muscle deformations. Additionally, we demonstrated the importance of rigorously estimating input parameters (muscle insertion areas) and of properly evaluating the bio-fidelity of the models developed before using them in clinical contexts. New data was acquired regarding muscle deformations and pennation angles to evaluate models integrating muscle activation.

Die Dissertation erforscht die Unsicherheit, Sensitivität und Grenzen großskaliger Erosionsmodelle. Die Modellierung basiert auf der allgemeinen Bodenabtragsgleichung (ABAG), Sedimenteintragsverhältnissen (SDR) und europäischen Daten. Für mehrere Regionen Europas wird die Bedeutung der Unsicherheit topographischer Modellparameter, ABAG-Faktoren und kritischer Schwebstofffrachten für die Anwendbarkeit empirischer Modelle zur Beschreibung von Sedimentfrachten und SDR von Flusseinzugsgebieten untersucht. Der Vergleich alternativer Modellparameter sowie Kalibrierungs- und Validierungsdaten zeigt, dass schon grundlegende Modellentscheidungen mit großen Unsicherheiten behaftet sind. Zur Vermeidung falscher Modellvorhersagen sind kalibrierte Modelle genau zu dokumentieren. Auch wenn die geschickte Wahl nicht-topographischer Algorithmen die Modellgüte regionaler Anwendungen verbessern kann, so gibt es nicht die generell beste Lösung. Die Ergebnisse zeigen auch, dass SDR-Modelle stets mit Sedimentfrachten und SDR kalibriert und evaluiert werden sollten. Mit diesem Ansatz werden eine neue europäische Bodenabtragskarte und ein verbessertes SDR-Modell für Einzugsgebiete nördlich der Alpen und in Südosteuropa abgeleitet. In anderen Regionen Europas ist das SDR-Modell bedingt nutzbar. Die Studien zur jährlichen Variabilität der Bodenerosion zeigen, dass jahreszeitlich gewichtete Niederschlagsdaten geeigneter als ungewichtete sind. Trotz zufriedenstellender Modellergebnisse überwinden weder sorgfältige Algorithmenwahl noch Modellverbesserungen die Grenzen europaweiter SDR-Modelle. Diese bestehen aus der Diskrepanz zwischen modellierten Bodenabtrags- und maßgeblich zur beobachteten bzw. kritischen Sedimentfracht beitragenden Prozessen sowie der außergewöhnlich hohen Sedimentmobilisierung durch Hochwässer. Die Integration von nicht von der ABAG beschriebenen Prozessen und von Starkregentagen sowie die Disaggregation kritischer Frachten sollte daher weiter erforscht werden. / This dissertation thesis addresses the uncertainty, sensitivity and limitations of large-scale erosion models. The modelling framework consists of the universal soil loss equation (USLE), sediment delivery ratios (SDR) and European data. For several European regions, the relevance of the uncertainty in topographic model parameters, USLE factors and critical yields of suspended solids for the applicability of empirical models to predict sediment yields and SDR of river catchments is systematically evaluated. The comparison of alternative model parameters as well as calibration and validation data shows that even basic modelling decisions are associated with great uncertainties. Consequently, calibrated models have to be well-documented to avoid misapplication. Although careful choices of non-topographic algorithms can also be helpful to improve the model quality in regional applications, there is no definitive universal solution. The results also show that SDR models should always be calibrated and evaluated against sediment yields and SDR. With this approach, a new European soil loss map and an improved SDR model for river catchments north of the Alps and in Southeast Europe are derived. For other parts of Europe, the SDR model is of limited use. The studies on the annual variability of soil erosion reveal that seasonally weighted rainfall data is more appropriate than unweighted data. Despite satisfactory model results, neither the careful algorithm choice nor model improvements overcome the limitations of pan-European SDR models. These limitations are related to the mismatch of modelled soil loss processes and the relevant processes contributing to the observed or critical sediment load as well as the extraordinary sediment mobilisation during floods. Therefore, further research on integrating non-USLE processes and heavy-rainfall data as well as on disaggregating critical yields is needed.