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The Element Free Galerkin (EFG) method, which is based on the Moving Least Squares (MLS) approximation, is developed here for vibration, buckling and static analysis of homogenous and FGM plate with curvilinear stiffeners. Numerical results for different stiffeners configurations and boundary conditions are presented. All results are verified using the commercial finite element software ANSYS® and other available results in literature. In addition, the vibration analysis of plates with curvilinear stiffeners is carried out using Ritz method. A 24 by 28 in. curvilinear stiffened panel was machined from 2219-T851 aluminum for experimental validation of the Ritz and meshfree methods of vibration mode shape predictions. Results were obtained for this panel mounted vertically to a steel clamping bracket using acoustic excitation and a laser vibrometer. Experimental results appear to correlate well with the meshfree and Ritz method results. In reality, many engineering structures are subjected to random pressure loads in nature and cannot be assumed to be deterministic. Typical engineering structures include buildings and towers, offshore structures, vehicles and ships, are subjected to random pressure. The vibrations induced from gust loads, engine noise, and other auxiliary electrical system can also produce noise inside aircraft. Consequently, all flight vehicles operate in random vibration environment. These random loads can be modeled by using their statistical properties. The dynamical responses of the structures which are subjected to random excitations are very complicated. To investigate their dynamic responses under random loads, the meshfree method is developed for random vibration analysis of curvilinearly-stiffened plates. Since extensive efforts have been devoted to study the buckling and vibration analysis of stiffened panel to maximize their natural frequencies and critical buckling loads, these structures are subjected to in-plane loading while the vibration analysis is considered. In these cases the natural frequencies calculated by neglecting the in-plane compression are usually over predicted. In order to have more accurate results it might be necessary to take into account the effects of in-plane load since it can change the natural frequency of plate considerably. To provide a better view of the free vibration behavior of the plate with curvilinear stiffeners subjected to axial/biaxial or shear stresses several numerical examples are studied. The FEM analysis of curvilinearly stiffened plate is quite computationally expensive, and the meshfree method seems to be a proper substitution to reduce the CPU time. However it will still require many simulations. Because of the number of simulations may be required in the solution of an engineering optimization problem, many researchers have tried to find approaches and techniques in optimization which can reduce the number of function evaluations. In these problems, surrogate models for analysis and optimization can be very efficient. The basic idea in surrogate model is to reduce computational cost and giving a better understanding of the influence of the design variables on the different objectives and constrains. To use the advantage of both meshfree method and surrogate model in reducing CPU time, the meshfree method is used to generate the sample points and combination of Kriging (a surrogate model) and Genetic Algorithms is used for design of curvilinearly stiffened plate. The meshfree and kriging results and CPU time were compared with those obtained using EBF3PanelOpt. / Ph. D.

Se propusieron innovaciones en la predicción espacio y espacio-temporal, a partir de métodos geoestadísticos y de funciones de base radial (RBF), considerando métodos basados en distancias. En este sentido, por medio de las distancias entre las variables explicativas, incorporadas específicamente en la regresión basada en distancias, se propusieron modificaciones en: el método kriging universal y en la interpolación con splines espacial y espacio-temporal usando las RBF. El método basado en la distancia se utiliza en un modelo Geoestadístico para estimar la tendencia y la estructura de covarianza. Esta estrategia aprovecha al máximo la información existente, debido a la relación entre las observaciones, mediante el uso de una descomposición espectral de una distancia seleccionada y las coordenadas principales correspondientes. Para el método propuesto kriging universal basado en distancias (DBUK), se realizó un estudio de simulación que permitió comparar la capacidad predictiva del método tradicional kriging universal con respecto a kriging universal basado en distancias; mientras que en la interpolación con Splines espacial y espacio-temporal, los estudios de simulación permitieron comparar el funcionamiento de las funciones de base radial espaciales y espaciotemporales, considerando en la tendencia las coordenadas principales generadas a partir de las variables explicativas mixtas mediante el uso del método basado en distancias. El método propuesto DBUK muestra, tanto en las simulaciones como en las aplicaciones, ventajas en la reducción del error con respecto al método clásico de krigeado universal. Esta reducción de los errores se asocia a una mejor modelización de la tendencia y a un menor error en el ajuste y modelado del variograma, al considerar las coordenadas principales obtenidas a partir de las variables explicativas mixtas. Entre muchas otras posibles causas, el error es generado por omisión de variables y por considerar formas funcionales incorrectas. El estudio de simulación muestra que el método propuesto DBUK es mejor que el método de krigeado universal tradicional ya que se encontró una notoria reducción del error, asociada a un RMSPE más pequeño, esta reducción en general fue superior al 10%. El método DBUK podrá producir una mejor estimación de la variable regionalizada si el número de coordenadas principales se incrementa. Esto es posible, incluyendo las coordenadas principales más significativas tanto en modelo de tendencia como en el variograma; se presenta una aplicación que ilustra este hecho. Los métodos propuestos de interpolación espacial basada en distancias con RBF (DBSIRBF) e interpolación espacio-temporal basada en distancias con RBF (DBSTIRBF) analizados mediante una estructura de krigeado considerando en la tendencia las coordenadas principales, presentan un buen funcionamiento al trabajar con vecindarios grandes, indicando en general que se tendrá un menor error asociado a un RMSPE más pequeño En diversos estudios, la detección de variabilidad entre zonas es una tarea muy difícil, y por lo cual los métodos propuestos DBUK, DBSIRBF y DBSTIRBF son útiles de acuerdo a los resultados obtenidos en la tesis, ya que aprovechan al máximo la información existente asociada a las variables explicativas. Aunque la correlación de las variables explicativas puede ser baja con respecto a la variable respuesta, el punto clave en los métodos propuestos es la correlación entre las coordenadas principales (construida con las variables explicativas) y la variable respuesta. Los métodos propuestos se aplicaron a datos agronómicos (Concentración de calcio medido a una profundidad de 0-20 cm de Brasil) y climatológicos (Temperaturas medias diarias de la Tierra en Croacia en el año 2008). Los resultados de validación cruzada “leave-one-out” mostraron un buen rendimiento de los predictores propuestos, lo cual indica que se pueden utilizar como métodos alternos y validos a los tradicionales para el modelado de variables correlacionadas espacialmente y espacio-temporalmente, considerando siempre covariables en la remoción de la tendencia. / Space-time geostatistical analysis based on distances and splines with applications. Innovations were proposed in the space and space-time prediction, based on geostatistical methods and radial basis function (RBF), considering distance-based methods. In this sense, through the distances between the explanatory variables, specifically incorporated in the regression based on distances, changes were proposed in: the universal kriging and interpolation with space and space-time splines using RBF. The distance-based method is used in a geostatistical model to estimate the trend and the covariance structure. This strategy takes full advantage of existing information, because of the relationship between the observations, using a spectral decomposition of a selected distance and the corresponding principal coordinates. For the universal kriging method proposed based on distances (DBUK), we performed a simulation study, which allowed to compare the predictive capacity of traditional universal kriging over universal kriging based on distances. The simulation study shows that the proposed method DBUK, is better than the traditional universal kriging method and was found a marked reduction of error associated with a smaller RMSPE, this reduction was generally greater than 10%. Spatial and spatio-temporal spline interpolation in simulation studies possible to compare the performance of space and spatio-temporal radial basis functions, considering the trend in the principal coordinates generated from the mixed explanatory variables using the method based distances. The proposed spatial interpolation methods based on distances with RBF (DBSIRBF) and spatio-temporal interpolation based on distances RBF (DBSTIRBF) analyzed through kriging structure whereas in the trend the principal coordinates, show good performance when working with large neighborhoods, indicating that in general will have less error associated with a smaller RMSPE. The key point in the proposed methods is the correlation between the principal coordinates (constructed with the explanatory variables) and the response variable. The proposed methods were applied to agronomic data (concentration of calcium measured at a depth of 0-20 cm from Brazil) and climatological (average daily temperature of the Earth in Croatia in 2008). The results of cross-validation "leave-one-out" showed a good performance of the proposed predictors, indicating that can be used as alternative methods to traditional and valid for the modeling of spatially correlated variables in space and time, always considering covariates in the removal of the trend.

Minestis software allows geological domain modeling and resource estimation through an efficient and simplified geostatistics-based workflow. It has been designed for all those, geologists, mining engineers or auditors, for whom quick production of quality models is at the heart of their concerns.

Minestis software allows geological domain modeling and resource estimation through an efficient and simplified geostatistics-based workflow. It has been designed for all those, geologists, mining engineers or auditors, for whom quick production of quality models is at the heart of their concerns.

Recent research using stable isotope analysis has shown a dependence on migrating or breeding populations of vertebrates as vectors for the transfer of marine-derived nutrients within coastal ecosystems. Sable Island, Nova Scotia, Canada supports numerous species of plants, a variety of seabird colonies (including common [Sterna hirundo] and Arctic [Sterna paradisaea] terns), the world’s largest grey seal (Halichoerus grypus) breeding colony, and a self-sustaining population of wild (feral) horses (Equus ferus caballus). I hypothesize that nitrogen cycling within this island ecosystem is highly influenced by the input of nutrients from seals and seabirds (‘biogenic vectors’), affecting primary production and potentially stabilizing higher trophic levels (i.e., horses). To examine this relation I developed a spatially-explicit isoscape for Sable Island through stable isotope analysis of nitrogen (δ15N) in samples (n = 282) of marram grass (Ammophila breviligulata). I incorporated significant variables (i.e., distance to vector colony and distance to shoreline, r2 = 0.41) into the final parsimonious interpolation model using universal co-kriging techniques. The greatest 15N enrichment occurred within the tips and along the perimeter of the island, coinciding with greater densities of grey seals, while the lowest values occurred within the centre of the island. I then identified individual contributions of seal-, tern- and horse-mediated transfer of marine-derived nutrients inland. Marram grass exhibited higher δ15N within seal (μ = 7.5‰) and tern (μ = 5‰) colonies, while horses and biogeochemical processes (i.e., volatilization, ammonification, etc.) most likely contributed to the homogeneity within the centre of the island (μ = 3.6‰). Due to the higher densities, wider distribution, and greater 15N enrichment of marram tissues, grey seals appear to be the most important vector species while seabirds have a more localized effect. The greater availability of N within vector colonies supplemented the local vegetation community, contributing to greater vegetation cover within colony boundaries. This relation had secondary effects on the horse population, which showed correspondingly higher horse δ15N values within the tips of the island (δ15N + 1.6‰) due to consumption of 15N enriched forage. I conclude that biogenic vector species promote nutrient transfer by establishing nutrient gateways which indirectly cause cascading effects throughout the food web.

Afin d'étudier les processus biogéochimiques de l'Océan Austral, des balises posées sur des éléphants de mer ont permis de récolter en 2009-2010 des profils de variables océanographiques (Chlorophylle a (Chl a), température, salinité, lumière) dans une zone s'étalant du sud des îles Kerguelen jusqu'au continent Antarctique. Cette thèse se penche en particulier sur les données de Chl a, car celle-ci est contenue dans les organismes photosynthétiques qui jouent un rôle essentiel de pompe à carbone. Mais les profils verticaux de Chl a, récoltés peu fréquemment, ne permettent pas d'obtenir une cartographie de cette variable dans cette zone de l'océan. Cependant, nous disposons de profils de lumière, échantillonnés plus souvent. L'objectif était alors de développer une méthodologie permettant de reconstruire de manière indirecte les profils de Chl a à partir des profils de lumière, et qui prenne en compte les caractéristiques de ce type de données qui se présentent naturellement comme des données fonctionnelles. Pour cela, nous avons abordé la décomposition des profils à reconstruire ou explicatifs sur une base de splines, ainsi que les questions d'ajustement associées. Un modèle linéaire fonctionnel a été utilisé, permettant de prédire des profils de Chl a à partir des dérivées des profils de lumière. Il est montré que l'utilisation d'un tel modèle permet d'obtenir une bonne qualité de reconstruction pour accéder aux variations hautes fréquences des profils de Chl a à fine échelle. Enfin, une interpolation par krigeage fonctionnel permet de prédire la concentration en Chl a de nuit, car les mesures de lumière acquises à ce moment-là ne peuvent pas être exploitées. / To study biogeochemical processes in the Southern Ocean, tags placed on elephant seals allowed to collect during 2009-2010 oceanographic variables profiles (Chlorophyll a (Chl a), temperature, salinity, light) in an area ranging from southern Kerguelen until the Antarctic continent. This thesis focuses on Chl a data as it is contained in photosynthetic organisms and these ones play an essential role in the oceanic carbon cycle. The infrequently collected vertical Chl a profiles don't provide a mapping of this variable in this area of the ocean. However, we have light profiles sampled more often. The aim of this thesis was then to develop a methodology for reconstructing indirectly Chl a profiles from light profiles, and that takes into account characteristics of this kind of data that naturally occur as functional data. For this, we adressed the profiles decomposition to rebuild or explanations on splines basis, as well as issues related adjustment. A functional linear model was used to predict Chl a profiles from light profiles derivatives. It was shown that the use of such a model provides a good quality of reconstruction to access high frequency variations of Chl a profiles at fine scale. Finally, a functional kriging interpolation predicted the Chl a concentration during night, as light measurements acquired at that time can't be exploited. In the future, the methodology aims to be applied to any type of functional data.

O presente trabalho resulta da aplicação de técnicas geoestatística de análise da variabilidade espacial e de estimativas de dados de sondagem de simples reconhecimento com standard penetration test (SPT) objetivando a caracterização geotécnica de uma área com 44 'KM POT.2', situada na porção nordeste do município de Fortaleza (CE). A caracterização geotécnica desta área compreendeu os seguintes processos: montagem de um banco de dados geotécnicos; aplicação de algoritmos de interpolação para elaboração do modelo digital de terreno (MDT); a aplicação de técnicas geoestatísticas de cokrigagem e krigagem ordinária na elaboração do mapa de superfície freática; a construção de um modelo geológico 3D de superfície; o mapeamento de uma superfície do impenetrável ao amostrador do SPT, auxiliado por geoestatística; a modelagem geoestatística 3D dos dados do índice de resistência à penetração (N) do amostrador do SPT, o que possibilitou a estimativa em bancadas por krigagem ordinária de blocos, do referido índice em diversos níveis altimétricos do terreno. Os dados estimados das bancadas foram tratados no programa ArcView 3.1 em ambiente de sistemas de informações geográficas (SIG) na elaboração de mapas de uso sugerido de fundações, os quais derivam de uma reclassificação, com base em diversos limites de impenetrável ao SPT, dos dados estimados de N, que permitiu a identificação de áreas favoráveis ao uso de um número finito de elementos estruturais de fundação. / This work results from the application of geostatistical techniques on standard penetration test (SPT) data to the geotechnical characterisation of an area with 44 'KM POT.2' situated on the northeastern region of Fortaleza county, northeastern Brazil. The geotechnical characterization involved the following steps: the geotechnical databank development; the performance of the interpolation algorithms and application to the digital elevation model (DEM); estimation and mapping the water table level with ordinary kriging and cokriging techniques; generation of a 3D surface geological model; geostatistical mapping the SPT maximum hard penetration surface; application of 3D geostatistical modeling techniques to SPT database providing bench estimates on blocks. The SPT estimated data were inserted and reclassified on the geographical information system based on the software ESRI ArcView 3.1 in order to produce the suggested foundation maps with references to SPT penetration limits.

Este trabalho apresenta uma nova metodologia para otimizar carteiras de ativos financeiros. A metodologia proposta, baseada em interpoladores universais tais quais as Redes Neurais Artificiais e a Krigagem, permite aproximar a superfície de risco e consequentemente a solução do problema de otimização associado a ela de forma generalizada e aplicável a qualquer medida de risco disponível na literatura. Além disto, a metodologia sugerida permite que sejam relaxadas hipóteses restritivas inerentes às metodologias existentes, simplificando o problema de otimização e permitindo que sejam estimados os erros na aproximação da superfície de risco. Ilustrativamente, aplica-se a metodologia proposta ao problema de composição de carteiras com a Variância (controle), o Valor-em-Risco (VaR) e o Valor-em-Risco Condicional (CVaR) como funções objetivo. Os resultados são comparados àqueles obtidos pelos modelos de Markowitz e Rockafellar, respectivamente. / This work presents a new methodology for optimizing financial asset portfolios. The proposed methodology, based on universal interpolators such as Artificial Neural Networks and the Kriging Method, allows for approximating the risk surface - and thus the optimal solution to the problem - in a generalized fashion and applicable to any risk measure known in literature, relaxing every restrictive hypothesis inherent to the available methods and with the ability to estimate the error in the approximation. Illustratively, the proposed methodology is applied to the portfolio problem with the Variance (control), Value-at-Risk and Conditional Value-at-Risk as objective functions. Results are compared to those obtained by Markowitz and Rockafellar models, respectively.

Santa Maria é um projeto de exploração mineral conduzido pela empresa Votorantim Metais Ltda, com foco nas comodities zinco e chumbo. Localizado no estado do Rio Grande do Sul, próximo das antigas minas de Camaquã e Uruguay, o projeto se encontra em uma região geologicamente fértil para exploração mineral. O depósito de Santa Maria possui informações suficientes para permitir a avaliação dos recursos minerais e também estudos de viabilidade econômica de projeto, entretanto, sua mineralização ocorre de forma heterogênea e condicionada a feições geológicas estruturais complexas, inserindo dúvidas à respeito da forma e volume dos corpos mineralizados. O objetivo desta pesquisa é a avaliação da incerteza associada à modelagem dos corpos mineralizados. Essa avaliação foi realizada através da comparação entre o modelo tridimensional confeccionado por interpretação de seções e outros dois modelos probabilísticos: um gerado por krigagem de indicadoras e outro gerado por simulação sequencial de indicadoras, que permitiu a interpretação da incerteza associada. Com os resultados obtidos foi possível quantificar os valores de volume máximo, mínimo e médio esperado no depósito, além de avaliar regiões de maior e menor confiança. A utilização conjunta dos métodos de krigagem de indicadoras e simulação sequencial de indicadoras se mostrou uma excelente opção para avaliação do modelo interpretado. Através do tratamento dos resultados foi possível obter informações à respeito da variabilidade local e global do depósito e sobre o comportamento espacial da mineralização. Os resultados e interpretações obtidos podem ser aplicados em trabalhos futuros no depósito, como na classificação do recurso mineral, no refinamento do modelo geológico e no planejamento de futuras malhas de sondagem infill. / Santa Maria is a mineral exploration project conducted by Votorantim Metais Ltda, with focus on zinc and lead extraction. The project is located in the state of Rio Grande do Sul, in the vicinities of the old mines of Camaquã and Uruguay, a favorable area for mineral exploration. There is enough information about Santa Maria\'s deposit to allow the estimation of mineral resources and the project\'s economical viability study, however, its mineralization occurs in heterogeneous ways and is conditioned to complex geological structural features, casting doubts about the shape and volume of the ore bodies. The main goal of this research is evaluating the uncertainty associated with the modeling of the orebodies. This evaluation was performed by comparing a three-dimensional model created by section interpretation and other two probabilistic models: one generated by indicator kriging, and the other generated by sequential indicator simulation, which allowed the interpretation of the associated uncertainty. Based on the obtained results, it was possible to quantify the maximum, minimum and average expected volume of the deposit, and also to evaluate the regions of most and least reliability. The joint use of indicator kriging and sequential indicator simulation methods proved to be an excelent tool for evaluating the interpreted model. By processing the results it was possible to obtain information about deposit\'s local and global variability and spatial behavior of mineralization. The obtained results and interpretations can be applied in deposit\'s further sutdies, for instance, to classify the mineral resource, to refine the geological model or to plan future infill drilholes.