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No description available.

In this dissertation, we propose decentralized and scalable algorithms for Gaussian process (GP) training and prediction in multi-agent systems. The first challenge is to compute a spatial field that represents underwater acoustic communication performance from a set of measurements. We compare kriging to cokriging with vehicle range as a secondary variable using a simple approximate linear-log model of the communication performance. Next, we propose a model-based learning methodology for the prediction of underwater acoustic performance using a realistic propagation model. The methodology consists of two steps: i) estimation of the covariance matrix by evaluating candidate functions with estimated parameters; and ii) prediction of communication performance. Covariance estimation is addressed with a multi-stage iterative training method that produces unbiased and robust results with nested models. The efficiency of the framework is validated with simulations and experimental data from field trials. The second challenge is to perform predictions at unvisited locations with a team of agents and limited inter-agent information exchange. To decentralize the implementation of GP training, we employ the alternating direction method of multipliers (ADMM). A closed-form solution of the decentralized proximal ADMM is provided for the case of GP hyper-parameter training with maximum likelihood estimation. Multiple aggregation techniques for GP prediction are decentralized with the use of iterative and consensus methods. In addition, we propose a covariance-based nearest neighbor selection strategy that enables a subset of agents to perform predictions. Empirical evaluations illustrate the efficiency of the proposed methods / Doctor of Philosophy / In this dissertation, we propose decentralized and scalable algorithms for collaborative multiagent learning. Mobile robots, such as autonomous underwater vehicles (AUVs), can use predictions of communication performance to anticipate where they are likely to be connected to the communication network. The first challenge is to predict the acoustic communication performance of AUVs from a set of measurements. We compare two methodologies using a simple model of communication performance. Next, we propose a model-based learning methodology for the prediction of underwater acoustic performance using a realistic model. The methodology first estimates the covariance matrix and then predicts the communication performance. The efficiency of the framework is validated with simulations and experimental data from field trials. The second challenge regards the efficient execution of Gaussian processes using multiple agents and communicating as little as possible. We propose decentralized algorithms that facilitate local computations at the expense of inter-agent communications. Moreover, we propose a nearest neighbor selection strategy that enables a subset of agents to participate in the prediction. Illustrative examples with real world data are provided to validate the efficiency of the algorithms.

Due to advancements in supercomputing and algorithms for finite element analysis, today's computer simulation models often contain complex calculations that can result in a wealth of knowledge. Gaussian processes (GPs) are highly desirable models for computer experiments for their predictive accuracy and uncertainty quantification. This dissertation addresses GP modeling when data abounds as well as GP adaptive design when simulator expense severely limits the amount of collected data. For data-rich problems, I introduce a localized sparse covariance GP that preserves the flexibility and predictive accuracy of a GP's predictive surface while saving computational time. This locally induced Gaussian process (LIGP) incorporates latent design points, inducing points, with a local Gaussian process built from a subset of the data. Various methods are introduced for the design of the inducing points. LIGP is then extended to adapt to stochastic data with replicates, estimating noise while relying upon the unique design locations for computation. I also address the goal of identifying a contour when data collection resources are limited through entropy-based adaptive design. Unlike existing methods, the entropy-based contour locator (ECL) adaptive design promotes exploration in the design space, performing well in higher dimensions and when the contour corresponds to a high/low quantile. ECL adaptive design can join with importance sampling for the purpose of reducing uncertainty in reliability estimation. / Doctor of Philosophy / Due to advancements in supercomputing and physics-based algorithms, today's computer simulation models often contain complex calculations that can produce larger amounts of data than through physical experiments. Computer experiments conducted with simulation models are sought-after ways to gather knowledge about physical problems but come with design and modeling challenges. In this dissertation, I address both data size extremes - building prediction models with large data sets and designing computer experiments when scarce resources limit the amount of data. For the former, I introduce a strategy of constructing a series of models including small subsets of observed data along with a set of unobserved data locations (inducing points). This methodology also contains the ability to perform calculations with only unique data locations when replicates exist in the data. The locally induced model produces accurate predictions while saving computing time. Various methods are introduced to decide the locations of these inducing points. The focus then shifts to designing an experiment for the purpose of accurate prediction around a particular output quantity of interest (contour). A experimental design approach is detailed that selects new sample locations one-at-a-time through a function to maximize the amount of information gain in the contour region for the overall model. This work is combined with an existing method to estimate the true volume of the contour.

In modern mining industry, new resource efficient and climate resilient methods have been gaining traction. Commissioned efforts to improve the efficiency of European mining is further helping us to such goals. Orexplore AB's X-ray technology for analyzing drill cores is currently involved in two such project. Orexplore AB wishes to incorporate geostatistics (spatial statistics) into their analyzing process in order to further extend the information gained from the mineral data. The geostatistical method implemented here is ordinary kriging which is an interpolation method that, given measured data, predicts intermediate values governed by prior covariance models. Ordinary kriging facilitates prediction of mineral concentrations on a continuous grid in 1-D up to 3-D. Intermediate values are predicted on a Gaussian process regression line, governed by prior covariances. The covariance is modeled by fitting a model to a calculated experimental variogram. Mineral concentrations are available along the lateral surface of the drill core. Ordinary kriging is implemented to sequentially predict mineral concentrations on shorter sections of the drill core, one mineral at a time. Interpolation of mineral concentrations is performed on the data considered in 1-D and 3-D. The validation is performed by calculating the corresponding density at each section that concentrations are predicted on and compare each such value to measured densities. The performance of the model is evaluated by subjective visual evaluation of the fit of the interpolation line, its smoothness, together with the variance. Moreover, the fit is tested through cross-validation using different metrics that evaluates the variance and prediction errors of different models. The results concluded that this method accurately reproduces the measured concentrations while performing well according to the above mentioned metrics, but does not outperform the measured concentrations when evaluated against the measured densities. However, the method was successful in providing information of the minerals in the drill core by producing mineral concentrations on a continuous grid. The method also produced mineral concentrations in 3-D that reproduced the measured densities well. It can be concluded that ordinary kriging implemented according to the methodology described in this report efficiently produces mineral concentrations that can be used to obtain information of the distribution of concentrations in the interior of the drill core. / I den moderna gruvindustrin har nya resurseffektiva och klimatbeständiga metoder ökat i efterfråga. Beställda projekt för att förbättra effektiviteten gällande den europeiska gruvdriften bidrar till denna effekt ytterligare. Orexplore AB:s röntgenteknologi för analys av borrkärnor är för närvarande involverad i två sådana projekt. Orexplore AB vill integrera geostatistik (spatial statistik) i sin analysprocess för att ytterligare vidga informationen från mineraldatan. Den geostatistiska metoden som implementeras här är ordinary kriging, som är en interpolationsmetod som, givet uppmätta data, skattar mellanliggande värden betingade av kovariansmodeller. Ordinary kriging tillåter skattning av mineralkoncentrationer på ett kontinuerligt nät i 1-D upp till 3-D. Mellanliggande värden skattas enligt en Gaussisk process-regressionslinje. Kovariansen modelleras genom att passa en modell till ett beräknat experimentellt variogram. Mineralkoncentrationer är tillgängliga längs borrkärnans mantelyta. Ordinary kriging implementeras för att sekventiellt skatta mineralkoncentrationer på kortare delar av borrkärnan, ett mineral i taget. Interpolering av mineralkoncentrationer utförs på datan betraktad i 1-D och 3-D. Valideringen utförs genom att utifrån de skattade koncentrationerna beräkna den motsvarande densiteten vid varje sektion som koncentrationer skattas på och jämföra varje sådant värde med uppmätta densiteter. Undersökning av modellen utförs genom subjektiv visuell utvärdering av interpolationslinjens passning av datan, dess mjukhet, tillsammans med variansen. Dessutom testas passformen genom korsvalidering med olika mätvärden som utvärderar varians- och skattningsfel för olika modeller. Slutsatsen från resultaten är att denna metod reproducerar de uppmätta koncentrationerna väl samtidigt som den presterar bra enligt de mätvärden som utvärderas, men överträffar ej de uppmätta koncentrationerna vid utvärdering mot de uppmätta densiteterna. Metoden var emellertid framgångsrik med att tillhandahålla information om mineralerna i borrkärnan genom att producera mineralkoncentrationer på ett kontinuerligt rutnät. Metoden producerade också mineralkoncentrationer i 3-D som reproducerade de uppmätta densiteterna väl. Slutsatsen dras att ordinary kriging, implementerad enligt den metod som beskrivs i denna rapport, effektivt skattar mineralkoncentrationer som kan användas för att få information om fördelningen av koncentrationer i det inre av borrkärnan.

<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>

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Extreme Value Theory nds application in problems concerning low probability but high consequence events. In hydrology the study of heavy rainfall is important in regional ood risk assessment. In particular, the N-year return level is a key output of an extreme value analysis, hence care needs to be taken to ensure that the model is accurate and that the level of imprecision in the parameter estimates is made explicit. Rainfall is a process that evolves over time and space. Therefore, it is anticipated that at extreme levels the process would continue to show temporal and spatial correlation. In this study interest is in whether any trends in heavy rainfall can be detected for the Western Cape. The focus is on obtaining the 50-year daily winter rainfall return level and investigating whether this quantity is homogenous over the study area. The study is carried out in two stages. In the rst stage, the point process approach to extreme value theory is applied to arrive at the return level estimates at each of the fteen sites. Stationarity is assumed for the series at each station, thus an issue to deal with is that of short-range temporal correlation of threshold exceedances. The proportion of exceedances is found to be smaller (approximately 0.01) for stations towards the east such as Jonkersberg, Plettenbergbay and Tygerhoek. This can be attributed to rainfall values being mostly low, with few instances where large amounts of rainfall were observed. Looking at the parameters of the point process extreme value model, the location parameter estimate appears stable over the region in contrast to the scale parameter estimate which shows an increase towards in a south easterly direction. While the model is shown to t exceedances at each station adequately, the degree of uncertainty is large for stations such as Tygerhoek, where the maximum observed rainfall value is approximately twice as large as the high rainfall values. This situation was also observed at other stations and in such cases removal of these high rainfall values was avoided to minimize the risk of obtaining inaccurate return level estimates. The key result is an N-year rainfall return level estimate at each site. Interest is in mapping an estimate of the 50-year daily winter rainfall return level, however to evaluate the adequacy of the model at each site the 25-year return level is considered since a 25 year return period is well within the range of the observed data. The 25-year daily winter rainfall return level estimate for Ladismith is the smallest at 22:42 mm. This can be attributed to the station's generally low observed winter rainfall values. In contrast, the return level estimate for Tygerhoek is high, almost six times larger than that of Ladismith at 119:16 mm. Visually design values show di erences between sites, therefore it is of interest to investigate whether these di erences can be modelled. The second stage is the geostatistical analysis of the 50-year 24-hour rainfall return level The aim here is to quantify the degree of spatial variation in the 50-year 24-hour rainfall return level estimates and to use that association to predict values at unobserved sites within the study region. A tool for quantifying spatial variation is the variogram model. Estimation of the parameters of this model require a su ciently large sample, which is a challenge in this study since there is only fteen stations and therefore only fteen observations for the geostatistical analysis. To address this challenge, observations are expanded in space and time and then standardized and to create a larger pool of data from which the variogram is estimated. The obtained estimates are used in ordinary and universal kriging to derive the 50-year 24-hour winter rainfall return level maps. It is shown that 50-year daily winter design rainfall over most of the Western Cape lies between 40 mm and 80 mm, but rises sharply as one moves towards the east coast of the region. This is largely due to the in uence of large design values obtained for Tygerhoek. In ordinary kriging prediction uncertainty is lowest around observed values and is large if the distance from these points increases. Overall, prediction uncertainty maps show that ordinary kriging performs better than universal kriging where a linear regional trend in design values is included.

O inventário florestal é uma das principais ferramentas na gestão dos recursos florestais, uma vez que as informações geradas por ele são utilizadas ao longo de toda a cadeia produtiva do setor. Desta forma, erros nas estimativas volumétricas dos inventários florestais devem ser controlados. Inúmeras informações podem ser obtidas a partir de imagens orbitais ou aerotransportadas, uma vez que podem cobrir facilmente toda a área de interesse, e estão comumente disponíveis em empresas florestais ou ao usuário final. A utilização de preditores derivados das imagens pode trazer benefícios para as estimativas do inventário florestal. Desta forma, a aplicação de técnicas de regressão linear múltipla (RLM) ganhou espaço no setor devido a sua facilidade de aplicação. Porém, a RLM não leva em consideração a dependência espacial entre as unidades amostrais, sendo que a geoestatística pode ser utilizada para predizer a distribuição espacial do estoque de madeira (VTCC) para uma dada região. A modelagem geoestatística mais simples como a krigagem ordinária (KO), por considerar apenas a dependência espacial entre os pontos não amostrados, pode apresentar erros de predição nestes locais. Tais erros podem ser reduzidos com a aplicação de técnicas mais robustas como a Krigagem com Deriva Externa (KDE), pois esta agrega as informações obtidas das imagens com a distribuição espacial do volume. Buscando-se avaliar as vantagens da integração do Sensoriamento Remoto (SR) ao inventário florestal foram testados 4 tipos diferentes de imagens; as oriundas dos satélites LANDSAT8, RAPIDEYE e GEOEYE, e as provenientes de aeronaves (Imagens Aerotransportadas). Avaliou-se também diferentes tipos de estimativas para a predição volumétrica sendo estas RLM, KDE e KO. A melhor estimativa serviu de variável auxiliar para o estimador de regressão (ER), sendo os resultados comparados com a abordagem tradicional da amostragem aleatória simples (AAS). Os resultados demonstraram por meio da validação cruzada que as estimativas da KDE foram mais eficientes que as estimativas da KO e da RLM. Os melhores preditores (variáveis auxiliares) foram aqueles derivados do satélite LANDSAT8 e do satélite RAPIDEYE. Obteve-se como produto das estimativas de KDE e RLM mapas capazes de detectar áreas com mortalidade ou anomalias em meio a formação florestal. A utilização de uma estimativa de KDE utilizando imagens LANDSAT8 como medida auxiliar para o ER permitiu reduzir o erro amostral da AAS de 3,87% para 2,34%. Da maneira tradicional, tal redução de erro apenas seria possível com um aumento de mais 99 unidades amostrais. / Forest Inventory (FI) is one of the main tools for managing forest resources, once the information derived from FI is used along the sector production chain. When estimating volume, errors resulting from FI are common, therefore these errors must be controlled. Once orbital or airborne imaging data are easily acquired for an entire area, and are commonly available in forest companies or for the end user, much information can be obtained from these products. The use of predictor derived from images can be of significant benefits to forest inventory estimates. For that reason, the application of linear multiple regression (LMR) techniques have taken place in the forest sector, due to the facilities of its application. However, the LMR technique does not take the spatial dependence among sample units in consideration, the geostatistics utilized to predict the spatial distribution of the wood stock (VTCC) for a specific region. Simpler geostatistical modeling as the ordinary kriging (OK), just takes in consideration the spatial dependence among non-sampled points, because of that, prediction errors can be found. Such errors can be reduced when techniques that are more robust are applied, such as the kriging with external drift (KED) approach. This technique aggregates the information obtained from the images with the spatial distribution of the volume. In order to evaluate the advantages of Remote Sensing and Forest Inventory integration, we considered 4 different types of images, from the satellites LANSAT 8, RAPIDEYE, GEOEYE and from airborne images. When predicting volume, three different approaches were evaluated: LMR, EDK, OK. The best model among those evaluated, served as auxiliary variable for the regression estimator (RE). The result were then compared to the traditional approach, simple random sampling (SRS).This approach showed, through a cross-validation, that the KDE estimates were more efficiently than the OK and the LMR. The best predictor model (auxiliary variables) were derived from LADNSAT 8 and RAPIDEYE satellites. There is a significant advantage to using the KDE and LMR approaches, as it allows for a spatial representation of areas with mortality or anomalies, in a forest environment. The combination of KDE approach and LANDSAT 8 images as an auxiliary method for the RE, abled the decrease of the sampling error of SRS from 3.87% to 2.34%.The traditional approaches to conduct plantation inventories would allow for this error reduction, only if there were an increase of 99 more sampling units.

O inventário florestal é uma das principais ferramentas na gestão dos recursos florestais, uma vez que as informações geradas por ele são utilizadas ao longo de toda a cadeia produtiva do setor. Desta forma, erros nas estimativas volumétricas dos inventários florestais devem ser controlados. Inúmeras informações podem ser obtidas a partir de imagens orbitais ou aerotransportadas, uma vez que podem cobrir facilmente toda a área de interesse, e estão comumente disponíveis em empresas florestais ou ao usuário final. A utilização de preditores derivados das imagens pode trazer benefícios para as estimativas do inventário florestal. Desta forma, a aplicação de técnicas de regressão linear múltipla (RLM) ganhou espaço no setor devido a sua facilidade de aplicação. Porém, a RLM não leva em consideração a dependência espacial entre as unidades amostrais, sendo que a geoestatística pode ser utilizada para predizer a distribuição espacial do estoque de madeira (VTCC) para uma dada região. A modelagem geoestatística mais simples como a krigagem ordinária (KO), por considerar apenas a dependência espacial entre os pontos não amostrados, pode apresentar erros de predição nestes locais. Tais erros podem ser reduzidos com a aplicação de técnicas mais robustas como a Krigagem com Deriva Externa (KDE), pois esta agrega as informações obtidas das imagens com a distribuição espacial do volume. Buscando-se avaliar as vantagens da integração do Sensoriamento Remoto (SR) ao inventário florestal foram testados 4 tipos diferentes de imagens; as oriundas dos satélites LANDSAT8, RAPIDEYE e GEOEYE, e as provenientes de aeronaves (Imagens Aerotransportadas). Avaliou-se também diferentes tipos de estimativas para a predição volumétrica sendo estas RLM, KDE e KO. A melhor estimativa serviu de variável auxiliar para o estimador de regressão (ER), sendo os resultados comparados com a abordagem tradicional da amostragem aleatória simples (AAS). Os resultados demonstraram por meio da validação cruzada que as estimativas da KDE foram mais eficientes que as estimativas da KO e da RLM. Os melhores preditores (variáveis auxiliares) foram aqueles derivados do satélite LANDSAT8 e do satélite RAPIDEYE. Obteve-se como produto das estimativas de KDE e RLM mapas capazes de detectar áreas com mortalidade ou anomalias em meio a formação florestal. A utilização de uma estimativa de KDE utilizando imagens LANDSAT8 como medida auxiliar para o ER permitiu reduzir o erro amostral da AAS de 3,87% para 2,34%. Da maneira tradicional, tal redução de erro apenas seria possível com um aumento de mais 99 unidades amostrais. / Forest Inventory (FI) is one of the main tools for managing forest resources, once the information derived from FI is used along the sector production chain. When estimating volume, errors resulting from FI are common, therefore these errors must be controlled. Once orbital or airborne imaging data are easily acquired for an entire area, and are commonly available in forest companies or for the end user, much information can be obtained from these products. The use of predictor derived from images can be of significant benefits to forest inventory estimates. For that reason, the application of linear multiple regression (LMR) techniques have taken place in the forest sector, due to the facilities of its application. However, the LMR technique does not take the spatial dependence among sample units in consideration, the geostatistics utilized to predict the spatial distribution of the wood stock (VTCC) for a specific region. Simpler geostatistical modeling as the ordinary kriging (OK), just takes in consideration the spatial dependence among non-sampled points, because of that, prediction errors can be found. Such errors can be reduced when techniques that are more robust are applied, such as the kriging with external drift (KED) approach. This technique aggregates the information obtained from the images with the spatial distribution of the volume. In order to evaluate the advantages of Remote Sensing and Forest Inventory integration, we considered 4 different types of images, from the satellites LANSAT 8, RAPIDEYE, GEOEYE and from airborne images. When predicting volume, three different approaches were evaluated: LMR, EDK, OK. The best model among those evaluated, served as auxiliary variable for the regression estimator (RE). The result were then compared to the traditional approach, simple random sampling (SRS).This approach showed, through a cross-validation, that the KDE estimates were more efficiently than the OK and the LMR. The best predictor model (auxiliary variables) were derived from LADNSAT 8 and RAPIDEYE satellites. There is a significant advantage to using the KDE and LMR approaches, as it allows for a spatial representation of areas with mortality or anomalies, in a forest environment. The combination of KDE approach and LANDSAT 8 images as an auxiliary method for the RE, abled the decrease of the sampling error of SRS from 3.87% to 2.34%.The traditional approaches to conduct plantation inventories would allow for this error reduction, only if there were an increase of 99 more sampling units.