Probabilistic and statistical aspects of extremes of univariate processes have been extensively studied, and recent developments in extremes have focused on multivariate theory and its application. Multivariate extreme value theory encompasses two separate aspects: marginal features, which may be handled by standard univariate methods, and dependence features. Both will be examined in this study. First we focus on testing independence in multivariate extremes. All existing score tests of independence in multivariate extreme values have non-regular properties that arise due to violations of the usual regularity conditions of maximum likelihood. Some of these violations may be dealt with using standard techniques, for example when independence corresponds to a boundary point of the parameter space of the underlying model. However, another type of regularity violation, the infinite second moment of the score function, is more difficult to deal with and has important consequences for applications, resulting in score statistics with non-standard normalisation and poor rates of convergence. We propose a likelihood based approach that provides asymptotically normal score tests of independence with regular normalisation and rapid convergence. The resulting tests are straightforward to implement and are beneficial in practical situations with realistic amounts of data. A fundamental issue in applied multivariate extreme value (MEV) analysis is modelling dependence within joint tail regions. The primary aim of the remainder of this thesis is to develop a pseudo-polar framework for modelling extremal dependence that extends the existing classical results for multivariate extremes to encompass asymptotically independent tails. Accordingly, a constructional procedure for obtaining parametric asymptotically independent joint tail models is developed. The practical application of this framework is analysed through applications to bivariate simulated and environmental data, and joint estimation of dependence and marginal parameters via likelihood methodology is detailed. Inference under our models is examined and tests of extremal asymptotic independence and asymmetry are derived which are useful for model selection. In contrast to the classical MEV approach, which concentrates on the distribution of the normalised componentwise maxima, our framework is based on modelling joint tails and focuses directly on the tail structure of the joint survivor function. Consequently, this framework provides significant extensions of both the theoretical and applicable tools of joint tail modelling. Analogous point process theory is developed and the classical componentwise maxima result for multivariate extremes is extended to the asymptotically independent case. Finally, methods for simulating from two of our bivariate parametric models are provided.

The presence of different types of defects is an important reality for manufacturers and users of engineering materials. Generally, the defects are either considered to be the unwanted products of impurities in the raw materials or to have been introduced during the manufacturing process. In high-quality steel materials, such as tool steel, the defects are usually non-metallic inclusions such as oxides or sulfides. Traditional methods for purity control during standard manufacturing practice are usually based on the light optical microscopy scanning of polished surfaces and some statistical evaluation of the results. Yet, as the steel manufacturing process has improved, large defects have become increasingly rare. A major disadvantage of the traditional quality control methods is that the accuracy decreases proportionally to the increased rarity of the largest defects unless large areas are examined. However, the use of very high cycle fatigue to 109 cycles has been shown to be a powerful method to locate the largest defects in steel samples. The distribution of the located defects may then be modelled using extreme value statistics. This work presents new methods for determining the volume distribution of large defects in high-quality steels, based on ultrasonic fatigue and the Generalized Extreme Value (GEV) distribution. The methods have been developed and verified by extensive experimental testing, including over 400 fatigue test specimens. Further, a method for reducing the distributions into one single ranking variable has been proposed, as well as a way to estimate an ideal endurance strength at different life lengths using the observed defects and endurance limits. The methods can not only be used to discriminate between different materials made by different process routes, but also to differentiate between different batches of the same material. It is also shown that all modes of the GEV are to be found in different steel materials, thereby challenging a common assumption that the Gumbel distribution, a special case of the GEV, is the appropriate distribution choice when determining the distribution of defects. The new methods have been compared to traditional quality control methods used in common practice (surface scanning using LOM/SEM and ultrasound C-scan), and suggest a greater number of large defects present in the steel than could otherwise be detected.

A limpeza dos aços está diretamente associada ao conteúdo de óxidos dos mesmos, sendo que os diferentes tipos de inclusões não-metálicas presentes podem prejudicar desde os processos de fabricação e conformação até as características necessárias para a aplicação do produto final. As inclusões se formam e se modificam ao longo dos processos de fabricação, e estão relacionadas principalmente às práticas de refino secundário e de lingotamento. Essas inclusões estão sempre presentes nos aços, de modo que é impossível se produzir um aço completamente livre das mesmas. Atualmente, existe uma série de pesquisas buscando o desenvolvimento de práticas e de processos para incrementar a limpeza dos aços. Entre essas está o desenvolvimento de novos materiais refratários adequados às diversas etapas de uma Aciaria. Com especial importância na limpeza dos aços estão as práticas e tecnologias aplicadas no lingotamento contínuo. Neste trabalho foi avaliada a influência do uso de nitrogênio injetado através de poros no colo das válvulas submersas sobre a lingotabilidade e limpeza dos produtos laminados a partir de tarugos. Para este estudo foram testadas diferentes vazões de gás e depois mensurado seu efeito. As técnicas utilizadas para a avaliação foram: verificação da abertura dos tampões; índice de sucateamento nas linhas de inspeção; severidade em ultrassom pelo método de imersão; análise dos teores de oxigênio total e nitrogênio e análise pelo método de distribuição de valores extremos da maior inclusão estimada. Os resultados práticos foram então comparados entre os lotes escolhidos para o teste. Verificou-se através dos dados coletados boa compatibilidade entre as diferentes variáveis e coerência dos resultados com os relatos da literatura. O uso de gás nitrogênio se mostrou ser potencialmente benéfico para a melhoria da limpeza e lingotabilidade do aço, apesar de mais testes serem necessários para a validação das hipóteses levantadas. / The steel cleanliness is directly associated to its inclusion content. The different kind of non-metallic inclusion can harm from the manufacturing and forming processes up to the demanding characteristics for the final products. The inclusions are formed and modified along the steel manufacturing process, and they are related mainly to the secondary refining and casting of steel. These inclusions are always present in the steel, so it is hardly possible to produce steels completely free of them. Nowadays, there are several fields of research concerning with the development of practices and processes to improve steel cleanliness. The development of new lining materials which are suitable for each melting shop step is one of these fields. With special importance over the steel cleanliness issue, the practices and technologies applied to the continuous casting process can be cited. In this work, the influence of nitrogen injection though the pores of the submerged entry nozzle over the castability and cleanliness of rolled products was evaluated. For this study, different gas flows were tested and then measured its effects. The techniques used for the evaluation were: stopper rod opening; rejection index during the inspection lines; severity in immersion ultra-sonic inspection; total oxygen and nitrogen content analysis and largest inclusion diameter estimated by extreme values distribution. The practical results for each lot of steel were then compared. It was verified from, the collected data, good compatibility between these different variables and coherency of the results with the experiences reported in the literature. The use of nitrogen gas showed itself to be potentially good for the improvement of cleanliness and castability of steel, though more trials are necessary for the validation of the considered hypothesis.

Made available in DSpace on 2010-04-20T21:00:17Z (GMT). No. of bitstreams: 3 arturbarros.pdf.jpg: 12128 bytes, checksum: 744fd0a3f0778e232eb725f44b15daed (MD5) arturbarros.pdf: 250112 bytes, checksum: c94304851268e3cb4fd4bfd921552561 (MD5) arturbarros.pdf.txt: 87173 bytes, checksum: 3b94e98f278f3b862e89788c63559743 (MD5) Previous issue date: 2008-01-08T00:00:00Z / O objetivo deste trabalho é analisar o desempenho de estimadores de volatilidade que utilizam valores extremos (máximo, mínimo, abertura e fechamento) para ativos no mercado brasileiro. Discute-se o viés dos estimadores usando como referências o estimador clássico, a volatilidade realizada e a volatilidade implícita de 1 mês da série de opções no dinheiro (ATM - at the money); discute-se a eficiência quanto à previsibilidade da volatilidade futura usando o estimador clássico e a volatilidade implícita defasados um período para frente como variáveis dependentes e a eficiência em si, isto é, quanto ao tamanho da variância do estima-dor. Como representantes de ativos brasileiros, foram escolhidos a paridade BRL/USD spot e o Índice Bovespa. Além de bastante líquidos, esses dois ativos têm bastante importância no mercado brasileiro, seja como benchmark para investimentos, bem como ativos-base para muitos derivativos operados na Bolsa de Mercadorias e Futuros (BM&F) e na Bolsa de Va-lores de São Paulo (Bovespa). A volatilidade do ativo-base é uma das variáveis para o apre-çamento de derivativos como opções; muitas estratégias são montadas, no mercado financei-ro, utilizando-a como referência. A volatilidade também é bastante usada no gerenciamento de riscos, em modelos como o Value at Risk (VaR), por exemplo. / The objective of this work is to analyze the performance of estimators of volatility using extreme values (maximum, minimum, opening and closing) for assets in the Brazilian market. It is discussed the bias of estimators using classical estimator, the realized volatility and the implied volatility of 1 month of the options at the money (ATM) as references, it is discussed the efficiency about the predictability of future volatility using classical estimator and implied volatility delayed for a period ahead as dependent variables and efficiency itself, that is, about the size of the variance of the estimator. As representatives of Brazilian assets, it was chosen the parity BRL/USD spot and the Bovespa index. Besides fairly liquid, these two assets are very important in the Brazilian market as benchmark for investments and underlying for many derivatives operated in the Bolsa de Mercadorias e Futuros (BM&F) and in the Bolsa de Valores de São Paulo (Bovespa). The volatility of the underlying is one of the variables for derivatives pricing such as options. Many strategies are built in financial market volatility using it as a reference. The volatility is also used in the management of risk, in models such as Value at Risk (VaR), for example.

A limpeza dos aços está diretamente associada ao conteúdo de óxidos dos mesmos, sendo que os diferentes tipos de inclusões não-metálicas presentes podem prejudicar desde os processos de fabricação e conformação até as características necessárias para a aplicação do produto final. As inclusões se formam e se modificam ao longo dos processos de fabricação, e estão relacionadas principalmente às práticas de refino secundário e de lingotamento. Essas inclusões estão sempre presentes nos aços, de modo que é impossível se produzir um aço completamente livre das mesmas. Atualmente, existe uma série de pesquisas buscando o desenvolvimento de práticas e de processos para incrementar a limpeza dos aços. Entre essas está o desenvolvimento de novos materiais refratários adequados às diversas etapas de uma Aciaria. Com especial importância na limpeza dos aços estão as práticas e tecnologias aplicadas no lingotamento contínuo. Neste trabalho foi avaliada a influência do uso de nitrogênio injetado através de poros no colo das válvulas submersas sobre a lingotabilidade e limpeza dos produtos laminados a partir de tarugos. Para este estudo foram testadas diferentes vazões de gás e depois mensurado seu efeito. As técnicas utilizadas para a avaliação foram: verificação da abertura dos tampões; índice de sucateamento nas linhas de inspeção; severidade em ultrassom pelo método de imersão; análise dos teores de oxigênio total e nitrogênio e análise pelo método de distribuição de valores extremos da maior inclusão estimada. Os resultados práticos foram então comparados entre os lotes escolhidos para o teste. Verificou-se através dos dados coletados boa compatibilidade entre as diferentes variáveis e coerência dos resultados com os relatos da literatura. O uso de gás nitrogênio se mostrou ser potencialmente benéfico para a melhoria da limpeza e lingotabilidade do aço, apesar de mais testes serem necessários para a validação das hipóteses levantadas. / The steel cleanliness is directly associated to its inclusion content. The different kind of non-metallic inclusion can harm from the manufacturing and forming processes up to the demanding characteristics for the final products. The inclusions are formed and modified along the steel manufacturing process, and they are related mainly to the secondary refining and casting of steel. These inclusions are always present in the steel, so it is hardly possible to produce steels completely free of them. Nowadays, there are several fields of research concerning with the development of practices and processes to improve steel cleanliness. The development of new lining materials which are suitable for each melting shop step is one of these fields. With special importance over the steel cleanliness issue, the practices and technologies applied to the continuous casting process can be cited. In this work, the influence of nitrogen injection though the pores of the submerged entry nozzle over the castability and cleanliness of rolled products was evaluated. For this study, different gas flows were tested and then measured its effects. The techniques used for the evaluation were: stopper rod opening; rejection index during the inspection lines; severity in immersion ultra-sonic inspection; total oxygen and nitrogen content analysis and largest inclusion diameter estimated by extreme values distribution. The practical results for each lot of steel were then compared. It was verified from, the collected data, good compatibility between these different variables and coherency of the results with the experiences reported in the literature. The use of nitrogen gas showed itself to be potentially good for the improvement of cleanliness and castability of steel, though more trials are necessary for the validation of the considered hypothesis.

A limpeza dos aços está diretamente associada ao conteúdo de óxidos dos mesmos, sendo que os diferentes tipos de inclusões não-metálicas presentes podem prejudicar desde os processos de fabricação e conformação até as características necessárias para a aplicação do produto final. As inclusões se formam e se modificam ao longo dos processos de fabricação, e estão relacionadas principalmente às práticas de refino secundário e de lingotamento. Essas inclusões estão sempre presentes nos aços, de modo que é impossível se produzir um aço completamente livre das mesmas. Atualmente, existe uma série de pesquisas buscando o desenvolvimento de práticas e de processos para incrementar a limpeza dos aços. Entre essas está o desenvolvimento de novos materiais refratários adequados às diversas etapas de uma Aciaria. Com especial importância na limpeza dos aços estão as práticas e tecnologias aplicadas no lingotamento contínuo. Neste trabalho foi avaliada a influência do uso de nitrogênio injetado através de poros no colo das válvulas submersas sobre a lingotabilidade e limpeza dos produtos laminados a partir de tarugos. Para este estudo foram testadas diferentes vazões de gás e depois mensurado seu efeito. As técnicas utilizadas para a avaliação foram: verificação da abertura dos tampões; índice de sucateamento nas linhas de inspeção; severidade em ultrassom pelo método de imersão; análise dos teores de oxigênio total e nitrogênio e análise pelo método de distribuição de valores extremos da maior inclusão estimada. Os resultados práticos foram então comparados entre os lotes escolhidos para o teste. Verificou-se através dos dados coletados boa compatibilidade entre as diferentes variáveis e coerência dos resultados com os relatos da literatura. O uso de gás nitrogênio se mostrou ser potencialmente benéfico para a melhoria da limpeza e lingotabilidade do aço, apesar de mais testes serem necessários para a validação das hipóteses levantadas. / The steel cleanliness is directly associated to its inclusion content. The different kind of non-metallic inclusion can harm from the manufacturing and forming processes up to the demanding characteristics for the final products. The inclusions are formed and modified along the steel manufacturing process, and they are related mainly to the secondary refining and casting of steel. These inclusions are always present in the steel, so it is hardly possible to produce steels completely free of them. Nowadays, there are several fields of research concerning with the development of practices and processes to improve steel cleanliness. The development of new lining materials which are suitable for each melting shop step is one of these fields. With special importance over the steel cleanliness issue, the practices and technologies applied to the continuous casting process can be cited. In this work, the influence of nitrogen injection though the pores of the submerged entry nozzle over the castability and cleanliness of rolled products was evaluated. For this study, different gas flows were tested and then measured its effects. The techniques used for the evaluation were: stopper rod opening; rejection index during the inspection lines; severity in immersion ultra-sonic inspection; total oxygen and nitrogen content analysis and largest inclusion diameter estimated by extreme values distribution. The practical results for each lot of steel were then compared. It was verified from, the collected data, good compatibility between these different variables and coherency of the results with the experiences reported in the literature. The use of nitrogen gas showed itself to be potentially good for the improvement of cleanliness and castability of steel, though more trials are necessary for the validation of the considered hypothesis.

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第18562号 / 工博第3923号 / 新制||工||1603(附属図書館) / 31462 / 京都大学大学院工学研究科社会基盤工学専攻 / (主査)教授 寶 馨, 教授 中北 英一, 教授 田中 茂信 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

Traffic load model in standard or specification for bridge design should guarantee all newly designed bridges to have sufficient security margin for future traffic. Many different methods have been used to model extreme traffic load effects on bridges for predicting characteristic value for short or long return period. In order to provide some guidance on selecting parameter estimation when applying POT to bridge traffic loading, we focus on the effect that method used to estimate the parameters of the GPD has on the accuracy of the estimated characteristic values. Through this qualitative discussion on the methods, several available methods for traffic loading are selected. Numerical simulation data, Monte Carlo simulation traffic load effects and in-field traffic load effect measurements are analyzed and presented. Literature points out that the traffic load effect is induced by loading event that involves different number of vehicles, and the distribution of the load effects from different loading events are not identically distributed, which violates the assumption of classic extreme value theory that the underlying distribution should be identically independent distributed. Methods using mixture distribution (exponential or generalized extreme value) has been proposed in the literature to model the extreme traffic load effect by loading event. However, the traffic loading may be also importance if the bridge encounter traffic induced fatigue problem, components like orthotropic steel deck is governed by traffic induced fatigue load effects. We intend to explore the influence of traffic load on the fatigue behaviour of orthotropic steel deck, especially the influence of the loading position in terms of transverse location of vehicle. Measurements of transverse location of vehicle collected from by weigh-in-motion (WIM) systems in 2010 and 2011 four French highways showed a completely different distribution model of transverse location of vehicle to that recommended in EC1. Stress spectrum analysis and fatigue damage calculation was performed on the stresses induced traffic on orthotropic steel deck of Millau cable-stayed bridge. By comparing the stresses and damages induced by different traffic patterns (through distributions of transverse location of vehicle), it was found that the histogram of stress spectrum and cumulative fatigue damage were significantly affected by the distribution of transverse location of vehicle. Therefore, numerical analysis that integrates finite element modelling and traffic data with distributions of transverse location of vehicles can help to make an accurate predetermination of which welded connections should be sampled to represent the health of the deck

Ces dernières décennies, nous avons assisté à l'émergence du concept de copule en modélisation statistique. Les copules permettent de faire une analyse séparée des marges et de la structure de dépendance induite par une distribution statistique. Cette séparation facilite l'incorporation de lois non gaussiennes, et en particulier la prise en compte des dépendances non linéaires entre les variables aléatoires. La finance et l'hydrologie sont deux exemples de sciences où les copules sont très utilisées. Cependant, bien qu'il existe beaucoup de familles de copules bivariées, le choix reste limité en plus grande dimension: la construction de copules multivariées/en grande dimension reste un problème ouvert aujourd'hui. Cette thèse présente trois contributions à la modélisation et à l'inférence de copules en grande dimension. Le premier modèle proposé s'écrit comme un produit de copules bivariées, où chaque copule bivariée se combine aux autres via un graphe en arbre. Elle permet de prendre en compte les différents degrés de dépendance entre les différentes paires. La seconde copule est un modèle à facteurs basé sur une classe nonparamétrique de copules bivariées. Elle permet d'obtenir un bon équilibre entre flexibilité et facilité d'utilisation. Cette thèse traite également de l'inférence paramétrique de copules dans le cas général, en établissant les propriétés asymptotiques d'un estimateur des moindres carrés pondérés basé sur les coefficients de dépendance. Les modèles et méthodes proposés sont appliqués sur des données hydrologiques (pluies et débits de rivières). / In the last decades, copulas have been more and more used in statistical modeling. Their popularity owes much to the fact that they allow to separate the analysis of the margins from the analysis of the dependence structure induced by the underlying distribution. This renders easier the modeling of non Gaussian distributions, and, in particular, it allows to take into account non linear dependencies between random variables. Finance and hydrology are two examples of scientific fields where the use of copulas is nowadays standard. However, while many bivariate families exist in the literature, multivariate/high dimensional copulas are much more difficult to construct. This thesis presents three contributions to copula modeling and inference, with an emphasis on high dimensional problems. The first model writes as a product of bivariate copulas and is underlain by a tree structure where each edge represents a bivariate copula. Hence, we are able to model different pairs with different dependence properties. The second one is a factor model built on a nonparametric class of bivariate copulas. It exhibits a good balance between tractability and flexibility. This thesis also deals with the parametric inference of copula models in general. Indeed, the asymptotic properties of a weighted least-squares estimator based on dependence coefficients are established. The models and methods have been applied to hydrological data (flow rates and rain falls).

Les précipitations extrêmes en France sont responsables de phénomènes d'inondations entraînant la perte de vies humaines et des millions d'euros en dégâts matériels. Mesurer le risque associé à ces événements météorologiques rares fait appel à la théorie statistique des valeurs extrêmes, qui propose plusieurs approches permettant d'évaluer des scénarios catastrophes. Cette thèse s'intéresse en particulier à trois mesures de risque faisant intervenir à la fois des lois de probabilité jointes et des méthodes de prédiction spatiale liées à la géostatistique.Dans un premier temps, plusieurs modèles spatiaux de valeurs extrêmes construits sur des données de maxima annuels sont évalués dans une étude comparative sous la forme d'un article. La comparaison des méthodes est menée en se servant de simulations construites à partir de données réelles de maxima annuels de précipitations en France et porte sur des critères liés aux deux mesures de risque que sont le niveau de retour centennal et le coefficient extrémal.Un modèle en particulier, le processus max-stable et hiérarchique de Reich et Shaby (2012) est étudié en détail et fait l'objet d'une implémentation sous la forme d'un package R dédié à la simulation et à l'estimation par cette méthode.Dans un second temps, les données journalières dépassant un seuil élevé sont modélisées dans un cadre spatial dans le but d'estimer une probabilité d'échec conditionnelle. Plusieurs estimateurs de cette mesure sont proposés en se concentrant d'une part sur des méthodes paramétriques liées aux processus Pareto et d'autre part sur deux approches non paramétriques. Les méthodes sont construites de sorte que la dépendance temporelle observable dans les valeurs journalière soit prise en compte lors de l'estimation.Tout au long de la thèse, les méthodes développées sont appliquées sur des données journalières de précipitations en France / Extreme precipitation in France are responsible for flooding events that cause people's deaths and billions of euros in material damage. Measuring the risk associated to these rare meteorological events is possible thanks to the extreme value theory which allows the estimation of such catastrophic scenarios. This thesis focus on three risk measures involving joint probabilities and spatial prediction methods related to geostatistics.In a first time, several spatial models for extreme values built on annual maxima are evaluated in a comparative study in the form of an article. This comparison is performed using simulated data from real annual maxima of precipitation in France. It is also based on two criteria linked to risk measures: the hundred years return level and the extremal coefficient. One particular model is presented in details: the one of Reich and Shaby (2012). This model is implemented under a R package entirely dedicated to its estimation and simulation procedures.In a second time, exceedances of spatial daily data are modelled in order to estimate a conditional failure probability. Several estimators of this measure are proposed, based on the one hand on parametric methods involving Pareto processes and on the other hand on non parametric approaches. The temporal dependence in extremes is also considered with care when estimating this probability.Along this thesis, the methods are applied on daily data of precipitation in France