This study examined Hurricane Katrina damage in southeast Mississippi to identify stand and site characteristics that may contribute to wind-related damage. Aggregated forest plot-level biometrics were coupled with storm meteorology, topographical features, and soil attributes using GIS techniques to produce damage maps for specific tree species. Regression Tree Analysis was utilized to explore the relationship between damage type and distance variables (distance to coast/storm track). Results indicated that the total damage class had the greatest relationship with distance variables; individual damage classes (shear and blowdown) displayed a better relationship with stand-level variables (Quadratic Mean Diameter, Lorey’s Mean Height, Trees Per Hectare). Logistic regressions identified a negative relationship between damage and height variation, elevation, slope, and aspect and a positive relationship with TPH. For plots/stands nearest to the coast and storm track height variation, TPH, QMD, and LMH consistently predicted damage levels for most species examined.

Gaussian process (GP) regression is the canonical method for nonlinear spatial modeling among the statistics and machine learning communities. Geostatisticians use a subtly different technique known as kriging. I shall highlight key similarities and differences between GPs and kriging through the use of large scale gold mining data. Most importantly GPs are largely hands-off, automatically learning from the data whereas kriging requires an expert human in the loop to guide analysis. To emphasize this, I show an imputation method for left censored values frequently seen in mining data. Oftentimes geologists ignore censored values due to the difficulty of imputing with kriging, but GPs execute imputation with relative ease leading to better estimates of the gold surface. My hope is that this research can serve as a springboard to encourage the mining community to consider using GPs over kriging for diverse utility after GP model fitting. Another common use of GPs that would be inefficient for kriging is Bayesian Optimization (BO). Traditionally BO is designed to find a global optima by sequentially sampling from a function of interest using an acquisition function. When two or more local or global optima of the function of interest have similar objective values, it often makes some sense to target the more "robust" solution with a wider domain of attraction. However, traditional BO weighs these solutions the same, favoring whichever has a slightly better objective value. By combining the idea of expected improvement (EI) from the BO community with mathematical programming's concept of an adversary, I introduce a novel algorithm to target robust solutions called robust expected improvement (REI). The adversary penalizes "peaked" areas of the objective function making those values appear less desirable. REI performs acquisitions using EI on the adversarial space yielding data sets focused on the robust solution that exhibit EI's already proven excellent balance of exploration and exploitation. / Doctor of Philosophy / Since its origins in the 1940's, spatial statistics modeling has adapted to fit different communities. The geostatistics community developed with an emphasis on modeling mining operations and has further evolved to cover a slew of different applications largely focused on two or three physical dimensions. The computer experiments community developed later when these physical experiments started moving into the virtual realm with advances in computer technology. While birthed from the same foundation, computer experimenters often look at ten or sometimes even higher dimension problems. Due to these differences among others, each community tailored their methods to best fit their common problems. My research compares the modern instantiations of the differing methodology on two sets of real gold mining data. Ultimately, I prefer the computer experiments methods for their ease of adaptation to downstream tasks at no cost to model performance. A statistical model is almost never a standalone development; it is created with a specific goal in mind. The first case I show of this is "imputation" of mining data. Mining data often have a detection threshold such that any observation with very small mineral concentrations are recorded at the threshold. Frequently, geostatisticians simply throw out these observations because they cause problems in modeling. Statisticians try to use the information that there is a low concentration combined with the rest of the fully observed data to derive a best guess at the concentration of thresholded locations. Under the geostatistics framework, this is cumbersome, but the computer experiments community consider imputation an easy extension. Another common model task is creating an experiment to best learn a surface. The surface may be a gold deposit on Earth or an unknown virtual function or anything measurable really. To do this, computer experimenters often use "active learning" by sampling one point at a time, using that point to generate a better informed model which suggests a new point to sample, repeating until a satisfactory number of points are sampled. Geostatisticians often prefer "one-shot" experiments by deciding all samples prior to collecting any. Thus the geostatistics framework is not appropriate for active learning. Active learning tries to find the "best" location of the surface with either the maximum or minimum response. I adapt this problem to redefine best to find a "robust" location where the response does not change much even if the location is not perfectly specified. As an example, consider setting operating conditions for a factory. If locations produce a similar amount of product, but one needs an exact pressure setting or else it blows up the factory, the other is certainly preferred. To design experiments to find robust locations, I borrow ideas from the mathematical programming community to develop a novel method for robust active learning.

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Magíster en Minería / Ingeniero Civil de Minas / El objetivo de este trabajo de tesis consiste en utilizar diferentes modelos de kriging en la simulación condicional de leyes para casos donde la ley media (denominada deriva ) varía en el espacio, lo cual generalmente ocurre en la realidad. Con esto se pretende probar la eficiencia de simulaciones con kriging ordinario (KO) y universal (KU) que consideran la ley media variable en el espacio, con los métodos usados hoy en día basados en kriging simple (KS) suponiendo una ley media constante a escala global. Además se busca analizar el efecto que tiene en los resultados el tipo de algoritmo de simulación utilizado. Para esto, distintos modelos de simulación son aplicados a casos sintéticos y a un caso real de estudio. Para los casos sintéticos se crean diferentes escenarios (con y sin deriva, con muchos y pocos datos condicionantes) y se realizan simulaciones condicionales usando el algoritmo de bandas rotantes y el algoritmo secuencial Gaussiano. El caso real de estudio consiste en un yacimiento de hierro donde existe una clara presencia de derivas de la ley de hierro en la dirección vertical para dos unidades geológicas definidas. Para ambos casos (sintéticos y reales) se evalúan diferentes tipos de condicionamiento. Los resultados se analizan considerando la reproducción de la correlación espacial y de las derivas. Para los casos sintéticos los resultados muestran que, independiente del tipo kriging utilizado, el método secuencial reproduce la correlación espacial cuando hay muchos datos condicionantes. Sin embargo, al usar el método secuencial con KO o KU y pocos datos los resultados se deterioran debido a que el error cometido al usar una vecindad móvil se propaga. El método de bandas rotantes funciona bien independiente del número de datos utilizados. Para casos con derivas, los resultados son mejores con KU, debido a que se conoce perfectamente la deriva. El KS y KO suavizan la deriva, más aun cuando es marcada y se tienen pocos datos condicionantes. Para el caso real ambos algoritmos de simulación entregan buenos resultados, siendo mejores con el algoritmo secuencial Respecto al tipo de kriging, en situaciones de extrapolación el KU exagera la deriva. Así el uso de KU estaría limitado a casos con deriva en situaciones de interpolación donde presenta mejoras respecto al KS y KO. Cuando hay muchos datos condicionantes, se pueden usar ambos algoritmos pues entregan resultados parecidos. Sin embargo, cuando hay pocos datos, el método secuencial propaga el error, por lo que convendría usar el método de bandas rotantes. Además, queda en evidencia la mejora que trae usar KO o KU en las simulaciones para casos con deriva, por sobre el KS utilizado hoy de la industria, el que no refleja lo que ocurre a escala local. Estos enfoques son fáciles de implementar y reflejan mejor las propiedades locales de la variable a simular que el enfoque actual basado en KS. Así, la metodología propuesta podría ser usada en otros casos con características similares, como yacimientos con clara existencia de derivas.

Les chercheurs dans le domaine de la conception aérodynamique et de la fabrication des avions ont fait beaucoup d'effort pour améliorer les performances des ailes par des techniques d'optimisation. Le développement de la mécanique des fluides numérique a permis de réduire les dépenses en soufflerie tout en fournissant des résultats convaincants pour simuler des situations compliquées des aéronefs. Dans cette thèse, il a été choisi une partie spéciale et importante de l'avion, à savoir, la structure de l'aile. L'optimisation basée sur la fiabilité est une méthode plus appropriée pour les structures sous incertitudes. Il se bat pour obtenir le meilleur compromis entre le coût et la sécurité tout en tenant compte des incertitudes du système en intégrant des mesures de fiabilité au sein de l'optimisation. Malgré les avantages de l'optimisation de la fiabilité en fonction, son application à un problème d'ingénierie pratique est encore assez difficile. Dans notre travail, l'analyse de l'incertitude dans la simulation numérique est introduite et exprimée par la théorie des probabilités. La simulation de Monte Carlo comme une méthode efficace pour propager les incertitudes dans le modèle d'éléments finis de la structure est ici appliquée pour simuler les situations compliquées qui peuvent se produire. Pour améliorer l'efficacité de la simulation Monte Carlo dans le processus d'échantillonnage, la méthode de l'Hypercube Latin est effectuée. Cependant, l'énorme base de données de l'échantillonnage rend difficile le fait de fournir une évaluation explicite de la fiabilité. L'expansion polynôme du chaos est présentée et discutée. Le modèle de Kriging comme un modèle de substitution joue un rôle important dans l'analyse de la fiabilité. Les méthodes traditionnelles d'optimisation ont des inconvénients à cause du temps de calcul trop long ou de tomber dans un minimum local causant une convergence prématurée. Le recuit simulé est une méthode heuristique basée sur une recherche locale, les Algorithmes Génétiques puisent leur inspiration dans les principes et les mécanismes de la sélection naturelle, qui nous rendent capables d'échapper aux pièges des optimums locaux. Dans l'optimisation de la conception de base de la fiabilité, ces deux méthodes ont été mises en place comme procédure d'optimisation. La boucle de l'analyse de fiabilité est testée sur le modèle de substitution. / Tremendous struggles of researchers in the field of aerodynamic design and aircraft production were made to improve wing airfoil by optimization techniques. The development of computational fluid dynamic (CFD) in computer simulation cuts the expense of aerodynamic experiment while provides convincing results to simulate complicated situation of aircraft. In our work, we chose a special and important part of aircraft, namely, the structure of wing.Reliability based optimization is one of the most appropriate methods for structural design under uncertainties. It struggles to seek for the best compromise between cost and safety while considering system uncertainties by incorporating reliability measures within the optimization. Despite the advantages of reliability based optimization, its application to practical engineering problem is still quite challenging. In our work, uncertainty analysis in numerical simulation is introduced and expressed by probability theory. Monte Carlo simulation as an effective method to propagate the uncertainties in the finite element model of structure is applied to simulate the complicate situations that may occur. To improve efficiency of Monte Carlo simulation in sampling process, Latin Hypercube sampling is performed. However, the huge database of sampling is difficult to provide explicit evaluation of reliability. Polynomial chaos expansion is presented and discussed. Kriging model as a surrogate model play an important role in the reliability analysis.Traditional methods of optimization have disadvantages in unacceptable time-complexity or natural drawbacks of premature convergence because of finding the nearest local optima of low quality. Simulated Annealing is a local search-based heuristic, Genetic Algorithm draws inspiration from the principles and mechanisms of natural selection, that makes us capable of escaping from being trapped into a local optimum. In reliability based design optimization, these two methods were performed as the procedure of optimization. The loop of reliability analysis is running in surrogate model.

Desde a última década, as autoridades aeronáuticas dos países membros da ICAO vem, gradativamente, aumentando as restrições nos níveis de ruído externo de aeronaves, principalmente nas proximidades dos aeroportos. Por isso os novos motores aeronáuticos precisam ter projetos mais silenciosos, tornando as técnicas de predição de ruído de motores cada vez mais importantes. Diferente das técnicas semi-analíticas, que vêm evoluindo nas últimas décadas, as técnicas semiempíricas possuem suas bases lastreadas em técnicas e dados que remontam à década de 70, como as desenvolvidas no projeto ANOPP. Uma bancada de estudos aeroacústicos para um conjunto rotor/estator foi construída no departamento de Engenharia Aeronáutica da Escola de Engenharia de São Carlos, permitindo desenvolver uma metodologia capaz de gerar uma técnica semi-empírica utilizando métodos e dados novos. Tal bancada é capaz de variar a rotação, o espaçamento rotor/estator e controlar a vazão mássica, resultando em 71 configurações avaliadas. Para isso, uma antena de parede com 14 microfones foi usada. O espectro do ruído de banda larga é modelado como um ruído rosa e o ruído tonal é modelado por um comportamento exponencial, resultando em 5 parâmetros: nível do ruído, decaimento linear e fator de forma da banda larga, nível do primeiro tonal e o decaimento exponencial de seus harmônicos. Uma regressão superficial Kriging é utilizada para aproximar os 5 parâmetros utilizando as variáveis do experimento e o estudo mostrou que Mach Tip e RSS são as principais variáveis que definem o ruído, assim como utilizado pelo projeto ANOPP. Assim, um modelo de previsão é definido para o conjunto rotor/estator estudado na bancada, o que permite prever o espectro em condições não ensaiadas. A análise do modelo resultou em uma ferramenta de interpretação dos resultados. Ao modelo são aplicadas 3 técnicas de validação cruzada: leave one out, monte carlo e repeated k-folds e mostrou que o modelo desenvolvido possui um erro médio, do nível do ruído total do espectro, de 2.35 dBs e desvio padrão de 0.91. / Since the last decade, the countries members of ICAO, via its aeronautical authorities, has been gradually increasing the restrictions on external aircraft noise levels, especially in the vicinity of airports. Because that, the new aero-engines need quieter designs, so noise prediction techniques for aero-engines are getting even more important. Semi-analytical techniques have undergone a major evolution since the 70th until nowadays, but semi-empirical techniques still have their bases pegged in techniques and data defined on the 70th, developed in the ANOPP project. An Aeroacoustics Fan Rig to investigate a Rotor/Stator assembly was developed at Aeronautical Engineering Department of São Carlos School of Engineering, allowing the development of a methodology capable of defining a semi-empirical technique based on new data and methods. Such rig is able to vary the rotation, the rotor/stator spacing and mass flow rate, resulting in a set of 71 configurations tested. To measure the noise, a microphone wall antenna with 14 sensors were used. The broadband noise was modeled by a pink noise and the tonal with exponential behavior, resulting in 5 parameters: broadband noise level, decay and form factor and the level and decay of tonal noise. A superficial kriging regression were used to approach the parameters using the experimental variables and the investigation has shown that Mach Tip and RSS are the most important variables that defines the noise, as well on ANOPP. A prediction model for the rotor/stator noise are defined with the 5 approximation of the parameters, that allow to predict the spectra at operations points not measured. The model analyses of the model resulted on a tool for results interpretation. Tree different cross validation techniques are applied to model: leave ou out, Monte Carlo and repeated k-folds. That analysis shows that the model developed has average error of 2.35 dBs and standard deviation of 0.91 for the spectrum level predicted.

Thesis (doctoral)--Universität Trier, 2005. / Includes bibliographical references (p. 118-129).

La presente investigación titulada “Distribución espacial del pH de las precipitaciones pluviales del valle del Mantaro durante el periodo 2005 – 2014” tiene como objetivo determinar la distribución espacial del pH de las precipitaciones pluviales en el Valle del Mantaro durante el periodo 2005 2014; utilizó la estadística descriptiva para la sistematización de información, luego el método geo estadístico Kriging para la interpolación de datos y la generación de los mapas de distribución espacial. Se determinó que durante el periodo 2005-2009 se presentaron precipitaciones con los niveles más bajos de pH, las cuales se concentraron al noroeste del Valle, en la estación de Jauja, con valores desde 5.65, valores que fueron en aumento conforme se dirigía hacia el sur. Durante el segundo periodo de 2010 - 2014, los niveles de pH se mantuvieron contantes en las 4 estaciones, en el rango de 6.94 a 7.14. Asimismo, se determinó a nivel mensual que, las estaciones de Jauja y Huayao presentaron niveles de acidez muy bajos de 4.19 y 3.9 respectivamente. Por tanto, los mapas de distribución espacial determinaron que, los episodios de precipitación durante el periodo 2005-2009 fueron no ácidos, sin embargo, lo niveles de pH más bajos se presentaron en la estación de Jauja, al noroeste del Valle del Mantaro.