Ingeniero Civil de Minas / El presente trabajo trata de la estimación geoestadística de recursos de un yacimiento de fierro que ha sido explorado mediante sondajes de diamantina. Las muestras disponibles contienen información sobre: coordenada espacial, ley de fierro total, ley de sílice, razón de recuperación o magnetismo y densidad de roca (que en verdad está calculada a partir de la ley de fierro, no medida). Una particularidad que presenta la base de datos es el sub-muestreo del magnetismo, del cual se encuentra información solo en 17 de los 70 sondajes, o en 1219 de las 8373 muestras, para ser más preciso. En el cálculo de recursos, lo que se suma son tonelajes de roca y de finos, no leyes. Aun así, lo que se estima usualmente es ley, ya que es lo más simple. Sin embargo, multiplicar a posteriori las estimaciones para obtener los finos y tonelajes introduce sesgo. Por lo tanto este caso de estudio trata con este sesgo al tomar dos enfoques separados a la estimación: El tradicional, con leyes y uno menos convencional, estimando contenidos de fierro sílice y fierro magnético directamente (contenido definido como ley*densidad). En ambos enfoques se utiliza co-kriging al especificar la estructura de la correlación espacial de las variables de entrada a través del modelamiento de los variogramas directos y cruzados, así como las posibles relaciones lineales entre sus medias. Esto último se ve motivado al observar fuertes dependencias lineales durante el análisis exploratorio; y lleva a implementar una variante al co-kriging ordinario tradicional que busca mejorar las estimaciones al restringir las medias de las variables, aun asumiéndolas desconocidas. Comparando ambos enfoques resulta en diferencias de aproximadamente 55 millones de toneladas de mineral y de más de 4% en la ley media estimada. Estas diferencias podrían ser explicadas ya que el primer enfoque estima variables no aditivas (ley, razón de magnetismo), mientras que el segundo enfoque estima variables aditivas directamente (contenido de fierro) y por lo tanto es más confiable desde el punto de vista teórico. Esta explicación además se apoya en una validación realizada con una técnica de partición de muestra (jack-knife), el cual indica que el segundo enfoque tiene una mayor precisión de estimación. Se recomienda entonces para la estimación de yacimientos de fierro evitar trabajar con variables no aditivas como leyes, y trabajar directamente con contenidos de metal, para los cuales la suma entre varios bloques tiene un sentido físico. Se espera que, en el futuro, más atención sea prestada a la medición directa de la densidad de roca en vez de calcularla a partir de la ley; ya que es crucial a la hora de analizar y calcular tonelajes y contenidos de metal.

Great Smoky Mountains National Park (GRSM) received 12.5 million visitors in 2020. With a high traffic volume, it is imperative roadways remain open and free from obstruction. Annual unanticipated rockfall events in GRSM often obstruct traffic flow. Using the Unstable Slope Management Program for Federal Land Management Agencies (USMP for FLMA) protocols, this study analyzes high priority unstable rock slopes through 1) creation of an unstable slope geodatabase and 2) generation of a final rockfall risk model using Co-Kriging from a preliminary risk model and susceptibility model. A secondary goal of this study is to provide risk estimation for the three most traveled transportation corridors within GRSM, as well as investigate current rockfall hazard warning sign location to ultimately improve visitor safety with regards to rockfall hazards.

No description available.

O planejamento de lavra de curto prazo é normalmente executado utilizando-se número reduzido de informações de sondagem. Para aprimorar o gerenciamento de riscos geológicos no planejamento de lavra de curto prazo é necessário utilizar um universo maior de informações. Como é normalmente inviável obter novas informações de sondagem, esta dissertação propõe uma metodologia de utilização de amostras de pó de perfuratriz (a partir de furos de desmonte) como uma fonte de informação secundária e assim aprimorar a qualidade das estimativas. Neste sentido, foi adotada uma técnica de co-estimativa da variável P2O5 das sondagens (variável primária) em conjunto com a variável P2O5 do desmonte (variável secundária) baseado no modelo Marcoviano MM2, pelo qual é possível combinar as duas informações (sondagem e desmonte) na estimativa de um modelo de blocos. Este processo permitiu a modelagem de atributos geológicos de forma mais detalhada o que contribuiu para uma melhor interface entre o planejamento de curto prazo e a operação da mina. A metodologia proposta também possibilitou acessar uma população maior de informações geológicas o que contribui para a criação de planos operacionais mais aderentes aos objetivos de produção mensal ou semanal, e, ao mesmo tempo, respeitando o sequenciamento importado do planejamento de longo e médio prazo. Como resultado, foi demonstrado que é possível criar programas operacionais mais precisos com base em estimativas de áreas próximas à lavra mesmo quando apenas um pequeno número de informações primárias (sondagens) esteja disponível. / Short-term mine planning is normally carried out over a limited number of drillhole information. In order to improve the management of geological risks in mine planning, a larger population of samples is required. However, it is normally very difficult to obtain additional drillhole samples once mining takes place. This research addresses that issue by proposing a methodology for the incorporation of additional information from blastholes (secondary information) to the original drillhole samples (primary information). A co-estimation technique for using P2O5 samples from the drillholes (primary variable) in conjunction with P2O5 from blastholes (secondary variable) based on the Markovian estimation model (MM2), through which is possible to combine both sources of information for a better estimation of mineable blocks. This process has allowed more detailed modeling of geological attributes and a better interface between short-term mine planning and mine operations. The proposed methodology also allowed the access to a larger sample population which meant more accurate mine plans for the daily and weekly mine schedules. As a result, it has been demonstrated that it is possible to crate operational plans that are more precise through the use of models that are properly estimated even in those areas where only a small amount of primary information (drillhole samples) is available.

This work is on Gaussian-process based approximation of a code which can be run at different levels of accuracy. The goal is to improve the predictions of a surrogate model of a complex computer code using fast approximations of it. A new formulation of a co-kriging based method has been proposed. In particular this formulation allows for fast implementation and for closed-form expressions for the predictive mean and variance for universal co-kriging in the multi-fidelity framework, which is a breakthrough as it really allows for the practical application of such a method in real cases. Furthermore, fast cross validation, sequential experimental design and sensitivity analysis methods have been extended to the multi-fidelity co-kriging framework. This thesis also deals with a conjecture about the dependence of the learning curve (ie the decay rate of the mean square error) with respect to the smoothness of the underlying function. A proof in a fairly general situation (which includes the classical models of Gaussian-process based metamodels with stationary covariance functions) has been obtained while the previous proofs hold only for degenerate kernels (ie when the process is in fact finite-dimensional). This result allows for addressing rigorously practical questions such as the optimal allocation of the budget between different levels of codes in the multi-fidelity framework.

O planejamento de lavra de curto prazo é normalmente executado utilizando-se número reduzido de informações de sondagem. Para aprimorar o gerenciamento de riscos geológicos no planejamento de lavra de curto prazo é necessário utilizar um universo maior de informações. Como é normalmente inviável obter novas informações de sondagem, esta dissertação propõe uma metodologia de utilização de amostras de pó de perfuratriz (a partir de furos de desmonte) como uma fonte de informação secundária e assim aprimorar a qualidade das estimativas. Neste sentido, foi adotada uma técnica de co-estimativa da variável P2O5 das sondagens (variável primária) em conjunto com a variável P2O5 do desmonte (variável secundária) baseado no modelo Marcoviano MM2, pelo qual é possível combinar as duas informações (sondagem e desmonte) na estimativa de um modelo de blocos. Este processo permitiu a modelagem de atributos geológicos de forma mais detalhada o que contribuiu para uma melhor interface entre o planejamento de curto prazo e a operação da mina. A metodologia proposta também possibilitou acessar uma população maior de informações geológicas o que contribui para a criação de planos operacionais mais aderentes aos objetivos de produção mensal ou semanal, e, ao mesmo tempo, respeitando o sequenciamento importado do planejamento de longo e médio prazo. Como resultado, foi demonstrado que é possível criar programas operacionais mais precisos com base em estimativas de áreas próximas à lavra mesmo quando apenas um pequeno número de informações primárias (sondagens) esteja disponível. / Short-term mine planning is normally carried out over a limited number of drillhole information. In order to improve the management of geological risks in mine planning, a larger population of samples is required. However, it is normally very difficult to obtain additional drillhole samples once mining takes place. This research addresses that issue by proposing a methodology for the incorporation of additional information from blastholes (secondary information) to the original drillhole samples (primary information). A co-estimation technique for using P2O5 samples from the drillholes (primary variable) in conjunction with P2O5 from blastholes (secondary variable) based on the Markovian estimation model (MM2), through which is possible to combine both sources of information for a better estimation of mineable blocks. This process has allowed more detailed modeling of geological attributes and a better interface between short-term mine planning and mine operations. The proposed methodology also allowed the access to a larger sample population which meant more accurate mine plans for the daily and weekly mine schedules. As a result, it has been demonstrated that it is possible to crate operational plans that are more precise through the use of models that are properly estimated even in those areas where only a small amount of primary information (drillhole samples) is available.

<p dir="ltr"> The need to develop reliable hypersonic capabilities is of critical import today. Among the most prominent tools used in recent efforts to overcome the challenges of developing hypersonic vehicles are NASA's Configuration Based Aerodynamics (CBAERO) and surrogate modeling techniques. This work presents the development of a tool, CBAERO Surrogate (CBAS), which leverages the advantages of both CBAERO and surrogate models to create a simple and streamlined method for building an aerodynamic database for any given vehicle geometry. CBAS is capable of interfacing with CBAERO directly and builds Kriging or Co-Kriging surrogate models for key aerodynamic parameters without significant user or computational effort. Two applicable geometries representing hypersonic vehicles have been used within CBAS and the resulting Kriging and Co-Kriging surrogate models evaluated against experimental data. These results show that the Kriging model predictions are accurate to CBAERO's level of fidelity, while the Co-Kriging model predictions fall within 0.5%-5% of the experimental data. These Co-Kriging models produced by CBAS are 10%-50% more accurate than CBAERO and the Kriging models and offer a higher fidelity solution while maintaining low computational expense. Based on these initial results, there are promising advancements to obtain in future work by incorporating CBAS to additional applications.</p>

The biodiversity is distributed heterogeneously across the Earth. Although the discussion about which factors determine the spatial patterns of species diversity remains controversial, to know the components of biodiversity themselves is a challenge even bigger in certain regions. So, to know how much still remains to be studied or discovered is fundamental to the science, and the lack of knowledge about the species geographical distribution is known as one of the main problems faced in biodiversity research, especially in “Megadiverse” countries like Brazil. Historically, the Caatinga biome has been recognized as one of the most unknown and less valued according to its biodiversity, because the erroneous idea that the biome would have low diversity and endemism rates, and high degrees of degradation. Considering the dominance of the Family Fabaceae in the Caatinga, in both richness and abundance, we investigated the spatial pattern of Fabaceae species richness on the biome looking for determine which are the factors responsible for the spatial variation on its species richness. Moreover, we elaborated a spatial statistical model for the diversity of Fabaceae in the Caatinga, utilizing the spatial structure of the know assemblages and their environmental determinants, in order to estimate the shortfall of knowledge about the distribution (Wallacean shortfall) of the family in the Caatinga. We obtained 220,781 registers, less than 25% were valid. From these registers, we found 1,310 species in 198 genera. The predict richness vary from 92 to 283 species across the space and was better described by the sampling effort, the soil properties and the topography. With the measure of discrepancy between predicted and the observed values of species richness, we estimated the Wallacean shortfall, reaching 192 species in one single locality. The total number of species found in this work represents an expressive improvement on the know species richness of the family in the Caatinga. The selection of non-climatic factors as the main predictors of richness indicate the major influence of topography and soil on regional scale. The importance of substrate on the establishment of plant communities on the semiarid, as well. The estimated Wallacean shortfall evidences a chronical and spatially heterogeneous deficiency on knowledge of the regional flora. The persistence of such expressive gaps on the knowledge, plus the reduced coverage of protected areas on the biome shows a currently risk of significantly losses of biological diversity, with serious implications for the conservation of the biome. / A biodiversidade é distribuída de forma heterogênea através do planeta Terra. Embora a discussão sobre quais fatores determinam os padrões espaciais da biodiversidade continue controversa, o simples conhecimento dos seus componentes é um desafio ainda maior em algumas regiões. Assim, conhecer o quanto ainda há para ser estudado ou descoberto é fundamental para a ciência, e a falta de conhecimento sobre a distribuição geográfica das espécies é considerado um dos principais problemas enfrentados em estudos sobre a biodiversidade, especialmente em países “megadiversos” como o Brasil. O Bioma Caatinga tem sido historicamente reconhecido com um dos menos conhecidos e valorizados quanto a diversidade biológica, devido à ideia equivocada de sua baixa diversidade e endemismo e elevado grau de antropização. Considerando a dominância da família Fabaceae na Caatinga, quanto à riqueza e abundância regional, investigamos o padrão espacial da riqueza de espécies de Fabaceae no bioma, buscando determinar quais os fatores ambientais responsáveis pela variação espacial da sua riqueza de espécies. Além disso, elaboramos um modelo estatístico espacial de diversidade de Fabaceae na Caatinga a partir da estrutura espacial das assembleias conhecidas e dos seus determinantes ambientais, a fim de estimar o déficit de conhecimento sobre a distribuição (déficit wallaceano) da Família na Caatinga. Obtivemos 220.781 registros, dos quais menos de 25% foram válidos. A partir desses registros, encontramos o total de 1.310 espécies de 198 gêneros. A riqueza predita pelo modelo espacial variou de 92 a 283 espécies ao longo do espaço e foi melhor descrita pelo esforço amostral, aspectos do solo e topografia. A partir da medida de discrepância entre valores preditos e observados de riqueza de espécies, estimamos valores de déficit Wallaceano, chegando a 192 espécies em uma única localidade. O número total de espécies encontrado neste trabalho representa um incremento expressivo na riqueza conhecida de espécies da família na Caatinga. A seleção de fatores não climático como principais preditores de riqueza indica maior influência da topografia e do solo na escala regional. E também a importância do substrato no estabelecimento de comunidades vegetais no semiárido. O déficit Wallaceano estimado evidencia uma deficiência crônica e espacialmente heterogênea no conhecimento da flora regional. A persistência de lacunas tão expressivas no conhecimento, somada a cobertura reduzida de áreas protegidas no Bioma evidencia um risco corrente de perdas significativas de diversidade biológica com sérias implicações para a conservação do Bioma.

Les travaux présentés portent sur l'étude de modèles numériques multi-fidèles, déterministes ou stochastiques. Plus précisément, les modèles considérés disposent d'un paramètre réglant la qualité de la simulation, comme une taille de maille dans un modèle par différences finies, ou un nombre d'échantillons dans un modèle de Monte-Carlo. Dans ce cas, il est possible de lancer des simulations basse fidélité, rapides mais grossières, et des simulations haute fidélité, fiables mais coûteuses. L'intérêt d'une approche multi-fidèle est de combiner les résultats obtenus aux différents niveaux de fidélité afin d'économiser du temps de simulation. La méthode considérée est fondée sur une approche bayésienne. Le simulateur est décrit par un modèle de processus gaussiens multi-niveaux développé dans la littérature que nous adaptons aux cas stochastiques dans une approche complètement bayésienne. Ce méta-modèle du simulateur permet d'obtenir des estimations de quantités d'intérêt, accompagnés d'une mesure de l'incertitude associée. L'objectif est alors de choisir de nouvelles expériences à lancer afin d'améliorer les estimations. En particulier, la planification doit sélectionner le niveau de fidélité réalisant le meilleur compromis entre coût d'observation et gain d'information. Pour cela, nous proposons une stratégie séquentielle adaptée au cas où les coûts d'observation sont variables. Cette stratégie, intitulée "Maximal Rate of Uncertainty Reduction" (MRUR), consiste à choisir le point d'observation maximisant le rapport entre la réduction d'incertitude et le coût. La méthodologie est illustrée en sécurité incendie, où nous cherchons à estimer des probabilités de défaillance d'un système de désenfumage. / The presented works focus on the study of multi-fidelity numerical models, deterministic or stochastic. More precisely, the considered models have a parameter which rules the quality of the simulation, as a mesh size in a finite difference model or a number of samples in a Monte-Carlo model. In that case, the numerical model can run low-fidelity simulations, fast but coarse, or high-fidelity simulations, accurate but expensive. A multi-fidelity approach aims to combine results coming from different levels of fidelity in order to save computational time. The considered method is based on a Bayesian approach. The simulator is described by a state-of-art multilevel Gaussian process model which we adapt to stochastic cases in a fully-Bayesian approach. This meta-model of the simulator allows estimating any quantity of interest with a measure of uncertainty. The goal is to choose new experiments to run in order to improve the estimations. In particular, the design must select the level of fidelity meeting the best trade-off between cost of observation and information gain. To do this, we propose a sequential strategy dedicated to the cases of variable costs, called Maximum Rate of Uncertainty Reduction (MRUR), which consists of choosing the input point maximizing the ratio between the uncertainty reduction and the cost. The methodology is illustrated in fire safety science, where we estimate probabilities of failure of a fire protection system.

La conception optimale de turbomachines repose usuellement sur des méthodes itératives avec des évaluations soit expérimentales, soit numériques qui peuvent conduire à des coûts élevés en raison des nombreuses manipulations ou de l’utilisation intensive de CPU. Afin de limiter ces coûts et de raccourcir les temps de développement, le présent travail propose d’intégrer une méthode de paramétrisation et de métamodélisation dans un cycle de conception d’une turbomachine axiale basse vitesse. La paramétrisation, réalisée par l’étude de sensibilité d’ordre élevé des équations de Navier-Stokes, permet de construire une base de données paramétrée qui contient non seulement les résultats d’évaluations, mais aussi les dérivées simples et les dérivées croisées des objectifs en fonction des paramètres. La plus grande quantité d’informations apportée par les dérivées est avantageusement utilisée lors de la construction de métamodèles, en particulier avec une méthode de Co-Krigeage employée pour coupler plusieurs bases de données. L’intérêt économique de la méthode par rapport à une méthode classique sans dérivée réside dans l’utilisation d’un nombre réduit de points d’évaluation. Lorsque ce nombre de points est véritablement faible, il peut arriver qu’une seule valeur de référence soit disponible pour une ou plusieurs dimensions, et nécessite une hypothèse de répartition d’erreur. Pour ces dimensions, le Co-Krigeage fonctionne comme une extrapolation de Taylor à partir d’un point et de ses dérivées. Cette approche a été expérimentée avec la construction d’un méta-modèle pour une hélice présentant un moyeu conique. La méthodologie fait appel à un couplage de bases de données issues de deux géométries et deux points de fonctionnement. La précision de la surface de réponse a permis de conduire une optimisation avec un algorithme génétique NSGA-2, et les deux optima sélectionnés répondent pour l’un à une maximisation du rendement, et pour l’autre à un élargissement de la plage de fonctionnement. Les résultats d’optimisation sont finalement validés par des simulations numériques supplémentaires. / The turbomachinery optimal design usually relies on some iterative methods with either experimental or numerical evaluations that can lead to high cost due to numerous manipulations and intensive usage of CPU. In order to limit the cost and shorten the development time, the present thesis work proposes to integrate a parameterization method and the meta-modelization method in an optimal design cycle of an axial low speed turbomachine. The parameterization, realized by the high order sensitivity study of Navier-Stokes equations, allows to construct a parameterized database that contains not only the evaluations results, but also the simple and cross derivatives of objectives as a function of parameters. Enriched information brought by the derivatives are utilized during the meta-model construction, particularly by the Co-Kriging method employed to couple several databases. Compared to classical methods that are without derivatives, the economic benefit of the proposed method lies in the use of less reference points. Provided the number of reference points is small, chances are a unique point presenting at one or several dimensions, which requires a hypothesis on the error distribution. For those dimensions, the Co-Kriging works like a Taylor extrapolation from the reference point making the most of its derivatives. This approach has been experimented on the construction of a meta-model for a conic hub fan. The methodology recalls the coupling of databases based on two fan geometries and two operating points. The precision of the meta-model allows to perform an optimization with help of NSGA-2, one of the optima selected reaches the maximum efficiency, and another covers a large operating range. The optimization results are eventually validated by further numerical simulations.