[pt] Este trabalho tem por objetivo investigar a redução do custo computacional associado ao cálculo das principais estatísticas das saídas dos modelos de propagação de incertezas. Para tal, apresentamos uma implementação alternativa ao método tradicional de Monte Carlo, chamado Caos Polinomial; que é adequado a problemas onde o número de variáveis de incerteza não é muito alto. No método Caos Polinomial, o valor esperado e a variância das saídas do simulador são diretamente estimados, como funções de distribuições de probabilidade de variáveis de incerteza na entrada do simulador. A principal vantagem do método de Caos Polinomial é que o número de pontos necessários para uma boa estimativa das estatísticas da saída de um simulador, comparado com Monte Carlo, é menor. Aplicações de Caos Polinomial em reservatórios de petróleo serão apresentadas para a propagação de até quatro variáveis, apesar do método poder ser aplicado a problemas de dimensões maiores. Nossos principais resultados são aplicados a dois modelos de reservatórios de petróleo sintéticos. / [en] In this work we investigate the reduction of the computational cost of the calculus of statistical moments of simulator s output in uncertainties propagation s models. For do that, we present an alternative s implementation to the traditional Monte Carlo s Method, called Polynomial Chaos; that is adequate to problems where the number of uncertain variables is not so high. In the Polynomial Chaos method, the expectation and the variance of the simulator s output are directly estimated, as functions of the probability distribuition of the uncertain variables in simulator input. The great advantage of Polynomial Chaos is that number of points necessary for a good estimation of the output statistics have smaller magnitude, compared to the Monte Carlo Method. Applications of Polynomial Chaos on oil reservoir simulations will be presented. As it is just a preliminar implementation, we just treat propagation s problems with at most four uncertainties variables, despite of the method being applicable to problems with more dimensions. Our main results are applied to two models of synthetic oil reservoirs.

[pt] Este trabalho analisa a propagação de uma doença epidemiológica com uma abordagem estocástica. Na análise, o número de indivíduos que cada membro infectado da população pode infectar é modelado como uma variável aleatória e o número de indivíduos infectados ao longo do tempo é modelado como um processo estocástico de ramificação. O foco do trabalho é caracterizar a influência do modelo probabilístico da variável aleatória que modela o contágio entre indivíduos na disseminação da doença e na probabilidade de extinção, e analisar a influência de uma vacinação em massa no controle da propagação da doença. A comparação é feita com base em histogramas e estatísticas amostrais do número de indivíduos infectados ao longo do tempo, como média e variância. Os modelos estatísticos referentes à parte que trata de uma população não vacinada são calculados usando simulações de Monte Carlo para 3 diferentes famílias de variáveis aleatórias: binomial, geométrica-1 e geométrica-0. Para cada família, 21 distribuições diferentes foram selecionadas e, para cada distribuição, 4000 simulações do processo de ramificação foram computadas. Os modelos estatísticos referentes a uma população parcialmente vacinada foram calculados usando simulações de Monte Carlo para a família de variável aleatória binomial. Para essa família, 21 distribuições diferentes foram selecionadas e, para cada uma delas foram escolhidas 6 diferentes percentagens de população vacinada. Para cada percentagem, foram analisadas vacinas com 4 diferentes eficácias. No total, foram realizadas 2.2 milhões de simulações, caracterizando o problema como big data. / [en] This work analyzes the spread of an epidemiological disease with a stochastic approach. In the analysis, the number of individuals that each infected member of the population can infect is modeled as a random variable and the number of infected individuals over time is modeled as a stochastic branching process. The focus of the work is to characterize the influence of the probabilistic model of the random variable that models contagion between individuals on the spread of the disease and the probability of extinction, and to analyze the influence of mass vaccination in controlling the spread of a disease. The comparison is based on histograms and sample statistics of the number of infected individuals over time, such as mean and variance. Statistical models for the chapter dealing with a vaccine free population are calculated using Monte Carlo simulations for 3 different families of random variables: binomial, geometric-1 and geometric-0. For each of the 3 families, 21 different distributions were selected and, for each distribution, 4000 simulations of the branching process were computed. Statistical models for a partially vaccinated population were calculated using Monte Carlo simulations for one family of random variable: the binomial. For it, 21 different distributions were selected and, for each of them, 6 different percentages of the vaccinated population were chosen. For each of them, 4 different vaccine efficacy were stipulated. In total, 2.2 million simulations were performed, featuring a big data problem.

In the future, hydropower plants are expected to operate more flexibly. This will lead to a more varied operation of the turbine and the generator, such as more start and stop in order to stabilise the frequency in the grid. Studies show that these transient operations are more costly in terms of fatigue degradation, i.e. consumption of fatigue life. Vattenfall has developed a methodology with the aim to analyse fatigue loads, acting on the runner and the rotor in hydropower units during operation. With a numerical model, the loads are assessed with input data gathered from measurements together with given data on several parameters. Some of the input data are bearing structure stiffness, bearing oil properties, and point of action of forces, etc. Several of these input parameters are subject to a degree of uncertainty, which affect the assessed fatigue load, determined with the methodology. This study will focus on analysing one fatigue force component acting on the runner. The aim with this study is to answer the following research questions: (i) Which input parameters, that are subject to a degree of uncertainty, contribute the most to the combined standard uncertainty in the assessed fatigue force? (ii) How much does the combined standard uncertainty in the assessed fatigue force amount to? (iii) How does the uncertainty in the assessed fatigue force affect the fatigue damage?. The combined standard uncertainty in the fatigue force is determined with methods in uncertainty propagation. In order to evaluate the effect from the uncertainty in the fatigue load on the fatigue damage, a statistical analysis of the ratio between the fatigue damage associated with a probability of exceedance and the expected fatigue damage is conducted. From the results it can be observed that the governing uncertainty parameter is the offset of the shaft displacement signal, which amount to 40 % of the combined standard uncertainty in the fatigue force. Of the nine analysed uncertainty parameters, three parameters are bearing properties parameters, i.e. the bearing clearance, the oil film temperature and the point of action of bearing forces, which amount to 47.5 % of the combined standard uncertainty in the fatigue force. Therefore, in order to decrease the uncertainties, focus should be kept on the bearing properties. Given each parameters uncertainty, the ratio between the combined standard uncertainty in the fatigue force and the expected fatigue force amount to 7 %. This corresponds to a ratio between the standard uncertainty in the fatigue damage and the expected fatigue damage of 35 %, due to the value of the index of S-N curve of five. Given the standard uncertainty in the fatigue force together with the index of S-N-curve, the ratio between the fatigue force associated with a probability of exceedance and the expected fatigue force can be assessed, i.e. the fatigue force ratio. Consequently, the fatigue force ratio amount to 1.32 for a probability of 0.0032 %, 1.09 for a probability of 10 % and 1.04 for a probability of 30 %. These probabilities correspond to the fatigue damage ratios, i.e. the ratios between the fatigue damage associated with a probability of exceedance and the expected fatigue damage of 4, 1.56 and 1.20. Thereby, the uncertainty in the fatigue force can greatly affect the uncertainty in the fatigue damage, dependent on the value of the index of S-N-curve. The results from this study imply the importance of considering the uncertainties in fatigue load assessments. These results provide support for assessing load levels for runner dimensioning to finally, be able to derive a correct margin of safety. This in order to not underestimate fatigue damage and thereby decrease the risk for unexpected fatigue failure. / Det finns ett förväntat behov av att kraftproduktionen i vattenkraftverk skall vara mer flexibel i framtiden. Detta leder till mer varierande driftlägen för turbinen och generatorn, såsom fler start och stop med syfte att stabilisera frekvensen i elnätet. Studier påvisar att transienta driftlägen är mer kostsamma i form av utmattningsdegradering, d.v.s. konsumtion av utmattningsliv. Vattenfall har utvecklat en metodik för att analysera inverkan av utmattningslaster verkande på löphjulet och rotorn i vattenkraftsaggregat under drift. Med en numerisk modell kan utmattningslasterna bedömas. Den ingående datan till modellen är bland annat är uppmätta storheter och given data på parameterar. Några av de ingående storheterna är lagerstyvhet, angreppspunkter för lagerkrafter och lageroljans egenskaper, etc. Flera av dessa ingående parametrar innehar osäkerheter, vilket påverkar bedömningen av utmattningslasterna. Denna studie kommer att fokusera på en kraftkomponent verkande på löphjulet. Malet med detta arbete är att svara på följande forskningsfrågor: (i) Vilka ingående parametrar, som innehar en osäkerhet, bidrar med en styrande osäkerhet i den bedömda kraften? (ii) Hur mycket uppgår den kombinerade standardosäkerheten i den bedömda kraften till? (iii) Hur påverkar kraftens osäkerhet utmattningsskadan? Den kombinerade standardosäkerheten i kraften är beräknad med metoder i fortplantning av osäkerheter. För att kunna bedöma påverkan på delskadan givet osäkerheten i kraften, så sker en statistisk analys av förhållandet mellan delskadan sammanhängande med en sannolikhet för överskridande och den förväntade delskadan. Resultatet påvisar att den styrande ingående parametern är offset i signalen för axelförskjutning, vilken uppgår till 40 % av den kombinerade standardosäkerheten i utmattningskraften. Av de nio analyserade parametrarna härrör tre av dessa lageregenskaper, d.v.s. lagerspel, oljetemperatur och angreppspunkter för lagerkrafterna, vilka tillsammans uppgår till 47.5 % av den kombinerade standardosäkerheten i utmattningskraften. Därför, för att reducera den totala osäkerheten bör fokus ligga på lageregenskaperna. Givet alla standardosäkerheter i de analyserade parametrarna så uppgår förhållandet mellan standardosäkerheten i utmattningskraften och den förväntade utmattningskraften på löphjulet till 7 %. Detta motsvarar att förhållandet mellan standardosäkerheten i delskadan och väntevärdet för delskadan uppkommer till 35 %, givet ett index av S-N-kurvan på fem. Givet standardosäkerheten i kraften och index av S-N-kurvan, kan förhållandet mellan utmattningskraften förenad med en sannolikhet för överskridande, och den förväntade utmattningskraften, d.v.s. kvoten av utmattningskraften, utvärderas. Detta resulterar att kvoten av utmattningskraften uppgår till 1.32 för en sannolikhet för överskridande på 0.0032 %, 1.09 för en sannolikhet på 10 % och 1.04 för en sannolikhet på 30 %. Dessa sannolikheter motsvarar att kvoten av delskadan, d.v.s. kvoten mellan delskadan förenad med en sannolikhet för överskridande, och den förväntade delskadan uppgår till 4, 1.56 och 1.20. Därför kan osäkerheten i utmattningskraften påverka osäkerheten i delskadan med en betydande faktor, beroende på värdet på index av S-N-kurvan. Således, resultaten från denna studie påvisar betydelsen att beakta osäkerheterna i de ingående parameterna vid bedömning av utmattningslast. Dessa resultat tillhandahåller stöd vid bedömning av lastnivåer för dimensionering av löphjul, för att slutligen kunna erhålla en korrekt säkerhetsmarginal. Detta för att inte underskatta utmattningsskadan och därmed minska risken oför oväntat utmattningshaveri.

Pour commercialiser un véhicule, les constructeurs automobiles doivent se soumettre à la réglementation sur le bruit extérieur. Le règlement de la commission économique pour l'Europe, ECE R51.03, spécifie les niveaux admissibles que peut rayonner un véhicule automobile en roulage. Ce règlement est entré en vigueur depuis le 1er juillet 2016 pour remplacer l'ancien règlement ECE R51.02 (changement de méthode d’essai et sévérisation des niveaux de bruit admissibles). La diminution drastique des niveaux sonores tolérés se fait en trois étapes : passage de 74 dB (A) sous l'ancien règlement, à 68 dB (A) en 2024. Par conséquent, les constructeurs ainsi que les fournisseurs automobiles seront confrontés à un grand défi pour atteindre cet objectif. Ainsi, l'objectif de ces travaux de thèse consiste à développer une aide à la modélisation totale du bruit de passage d’un véhicule, comme le préconisent les essais réglementaires. Le but est de construire des modèles optimaux pour prévoir et évaluer avec précision le bruit que peut rayonner un véhicule en roulage plus tôt dans son cycle de développement, i.e. avant l'étape d'industrialisation. Il faut alors se placer dans la recherche d'un compromis entre précision des estimations, sensibilité aux paramètres, robustesse de la méthode et efficacité numérique. / Currently, to put a vehicle on market, car manufacturers must comply to a certification test of exterior noise. The regulation of the United Nations Economic Commission for Europe, ECE R51-03, specifies permissible levels a rolling motor vehicle can emit. This regulation is applied since July 1st, 2016, to replace the old regulation ECE R51-02 (test method change and tightening of permissible levels). The drastic reduction in noise levels will be done in 3 steps: from 74 dB (A) under the old regulation to 68 dB (A) in 2024. Therefore, manufacturers as well as their suppliers will face a great challenge to achieve this goal. The objective of this thesis is to develop an aid to the modeling of the pass-by noise of a vehicle, as called for in regulatory testing. The goal is to predict and evaluate accurately the noise emissions earlier in the vehicle development cycle, i.e. before the industrialization stage. We must then seek a trade-off between accuracy of estimates, sensitivity to parameters, robustness of the method and numerical efficiency.

Ces travaux de thèse portent sur l'étude expérimentale et numérique de structures mécaniques non-linéaires soumises à des vibrations sinusoïdales et aléatoires. L'étude prend en compte l'existence d'incertitudes au sein du protocole expérimentale et de la modélisation. Les études expérimentales menées au CEA/CESTA montrent que la réponse des structures assemblées à des sollicitations vibratoires est fortement dépendante du niveau d'excitation d'une part, et que la réponse obtenue possède une variabilité, parfois importante. Ces résultats expérimentaux ne peuvent pas être reproduits en simulation avec la méthode de simulation vibratoire linéaire déterministe classique.L'objectif de ces travaux est de proposer et de mettre en place des méthodes numériques pour étudier ces réponses non-linéaires, et de quantifier et propager les incertitudes pertinentes au sein des calculs. Cet objectif passe par l'étude de maquettes d'essai de complexité croissante et sujettes aux mêmes phénomènes vibratoires que les objets d'étude industriels du CEA/CESTA. Les méthodes de simulation vibratoire non-linéaires et les techniques numériques développées dans le monde académique sont adaptées et utilisées dans le contexte industriel du CEA/CESTA.Le premier objet d'étude est une poutre métallique bi-encastrée, dont la non-linéarité est d'origine géométrique. Le modèle associé à cette poutre est un oscillateur de Duffing à un degré de liberté très détaillé dans la littérature scientifique, et qui permet de valider les développements numériques effectués, sur les aspects de l'excitation aléatoire et de la propagation d'incertitudes. Dans un premier temps, les méthodes de tir et d'équilibrage harmonique sont étendues au cas de l'excitation aléatoire et validées sur cette structure académique par comparaison à l'expérience. Dans un second temps, une méthode de propagation d'incertitude non-intrusive est implémentée pour prendre en compte les incertitudes de modélisation identifiées.Le second objet d'étude est une maquette comportant un plot élastomère reliant une masselotte à un bâti. Le comportement non-linéaire de l'élastomère est au c\oe ur de ces travaux de thèse. De nombreux essais vibratoires sont réalisés dans un premier temps pour identifier un modèle non-linéaire de l'élastomère juste suffisant. Dans un second temps, le modèle développé est validé par comparaison aux essais en utilisant et adaptant les méthodes étendues lors de l'étude de la poutre bi-encastrée.Enfin, une maquette d'étude se rapprochant d'un cas d'application industriel est étudiée : la maquette Harmonie-Gamma. Elle compte des interfaces frottantes et des liaisons élastomères. Les essais vibratoires réalisés permettent d'identifier le comportement dynamique linéaire et non-linéaire du système et d'étudier l'évolution de la réponse en fonction du niveau d'excitation. Un modèle numérique est réalisé par éléments finis puis réduit par une méthode de sous-structuration. Les relations non-linéaires sont introduites au niveau des liaisons frottantes et élastomères. La réponse vibratoire de la structure est simulée par la méthode d'équilibrage harmonique couplée à un algorithme de continuation. Les comparaisons essais / calculs sont menées pour les excitations de type sinus balayé et aléatoire, et permettent d'analyser l'apport de chaque non-linéarité dans la réponse de la structure. / This PhD work focuses on the experimental and numerical study of nonlinear structures subjected to both harmonic and random vibrations, in the presence of modeling and experimental uncertainties. Experimental studies undertaken at the CEA / CESTA show a strong dependence of the jointed structures towards the excitation level, as well as a variability in the response for a given excitation level. These experimental results cannot be simulated using the classical determinist linear vibration simulation method.The objective of this work is to propose and set up numerical methods to study these nonlinear responses, while quantifying and propagating the relevant uncertainties in the simulations. This objective involves the study of structural assemblies of increasing complexity and subjected to the same vibratory phenomena as CEA / CESTA industrial structures. Advanced nonlinear numerical methods developed in academia are applied in the CEA / CESTA industrial context.The first test structure is a clamped-clamped steel beam that has a geometrical nonlinearity. The beam is modeled by a Duffing oscillator which is a widely studied model in the field of nonlinear dynamics. This allows for a validation of the numerical developments proposed in this work, first on the issue of random vibrations, and second on the issue of the propagation of uncertainties. The simulations are based on two techniques of reference (shooting method and harmonic balance method). Firstly, the simulation results are validated by comparison with the experimental results for random vibrations. Secondly, the harmonic balance method is used in adequation with a non-intrusive polynomial chaos in order to take into accounts the modeling uncertainties.The second test structure is a mass linked to a solid casing via a vibration-absorbing elastomeric material of biconical shape surrounded by a cage of aluminum. The nonlinear behavior of the elastomer is at the heart of this work. Various vibration tests were performed on this structure in order to identify the simplest nonlinear model possible to answer our queries. The identified model is validated through comparisons between the simulation results and the experimental results for both sine-swept and random vibrations.The central assembly of this work is an industrial assembly with friction joints and vibration-absorbing elastomeric joints, named Harmonie-Gamma. The vibration tests performed exhibit resonance modes as well as a strong dependency of the response with the excitation level. A numerical finite element model is developed and reduced with a substructuration technique. The resulting nonlinear reduced model is simulated using an harmonic balance method with a continuation method. The simulated responses are compared with the experiments and allow for an analysis of coupled nonlinearities in the CEA / CESTA industrial context.

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.

[pt] A medição da velocidade de fluidos tem relevância considerável em aplicações industriais e científicas, nas quais medições com baixa incerteza são geralmente requeridas. Nesta tese, tem-se como objetivo projetar e modelar um sistema de medição de velocidade de vento utilizando fusão de dados das informações dos tempos de trânsito obtidas pelas técnicas de detecção de limiar e diferença de fase. Para este propósito, este trabalho é composto por duas partes principais. Na primeira parte, apresenta-se uma análise da propagação de incertezas das técnicas de detecção de limiar e diferença de fase considerando duas estruturas para a medição da velocidade do vento, e faz-se a comparação das faixas de medição e suas incertezas associadas para cada estrutura de medição. Na segunda parte deste trabalho, faz-se um estudo das técnicas de fusão de dados aplicadas a instrumentação e medição, identificandose duas técnicas principais baseadas em: (a) estimação de máxima probabilidade (MLE – Maximum Likelihood Estimation), (b) relação de compatibilidade fuzzy e operadores OWA (Order Weighted Average) com agregação parcial. Em seguida, estas técnicas de fusão são aplicadas para a estimação do tempo de trânsito, considerando-se várias medições independentes do tempo de trânsito obtidas pelas técnicas de detecção de limiar e diferença de fase. Finalmente, realiza-se uma análise da incerteza quantificando-se a incerteza de cada medição sobre o resultado final de fusão. Apresenta-se um estudo de caso englobando estas duas partes do trabalho, desenvolvendo-se o projeto e modelagem de um instrumento de medição de velocidade do vento com baixa incerteza, considerando-se as incertezas associadas, e o uso de técnicas adequadas de fusão de dados para prover informações com maior exatidão e confiabilidade. Resultados experimentais são realizados em um túnel de vento de baixa velocidade com o objetivo de verificar a consistência dos estudos teóricos apresentados. / [en] Flow speed measurement has considerable relevance in industrial and scientific applications, where measurements with low uncertainty are required. In this work, a system for wind speed measurement using ultrasonic transducers is designed and modelled. This system makes use of data fusion techniques for the time-of-flight estimation, combining independent information provided by the threshold detection and phase difference methods. For this purpose, this work consists of two main parts. The first part presents an analysis of uncertainty and error propagation concerning the threshold detection and phase difference techniques and considering two structures for the wind speed measurement. Measurement ranges are associated uncertainties are then compared for each of those estrutures. In the second part of this work, data fusion techniques applied to instrumentation and measurement are studied; two main techniques are singled out: (a) Maximum Likelihood Estimation (MLE), (b) Fuzzy compatibility relation and Order Weighted Average (OWA) operators with partial aggregation. These fusion techniques are then applied to the time-of-flight estimation, by considering several independent measurements obtained through the threshold detection and phase difference techniques. Finally, uncertainty analysis is carried out by quantifying the influence of each independent measurement on the global fusion result. A case study is also presented, where an instrument for wind speed measurements with low uncertainty is designed and modelled. Appropriate techniques of data fusion aimed at improving accuracy and realiability are considered. Experiments are performed in a wind tunnel in order to verify the consistency of the results in view of the theoretical studies.