The expected growth of civil aviation over the next twenty years places significant emphasis on revolutionary technology development aimed at mitigating the environmental impact of commercial aircraft. As the number of technology alternatives grows along with model complexity, current methods for Pareto finding and multiobjective optimization quickly become computationally infeasible. Coupled with the large uncertainty in the early stages of design, optimal designs are sought while avoiding the computational burden of excessive function calls when a single design change or technology assumption could alter the results. This motivates the need for a robust and efficient evaluation methodology for quantitative assessment of competing concepts. This research presents a novel approach that combines Bayesian adaptive sampling with surrogate-based optimization to efficiently place designs near Pareto frontier intersections of competing concepts. Efficiency is increased over sequential multiobjective optimization by focusing computational resources specifically on the location in the design space where optimality shifts between concepts. At the intersection of Pareto frontiers, the selection decisions are most sensitive to preferences place on the objectives, and small perturbations can lead to vastly different final designs. These concepts are incorporated into an evaluation methodology that ultimately reduces the number of failed cases, infeasible designs, and Pareto dominated solutions across all concepts. A set of algebraic samples along with a truss design problem are presented as canonical examples for the proposed approach. The methodology is applied to the design of ultra-high bypass ratio turbofans to guide NASA's technology development efforts for future aircraft. Geared-drive and variable geometry bypass nozzle concepts are explored as enablers for increased bypass ratio and potential alternatives over traditional configurations. The method is shown to improve sampling efficiency and provide clusters of feasible designs that motivate a shift towards revolutionary technologies that reduce fuel burn, emissions, and noise on future aircraft.

Für die geodätische Überwachung dreidimensionaler Objekte fehlen in der Regel Informationen zur vollständigen Beschreibung der räumlichen Deformation. Um dieses Informationsdefizit zu beheben, können geotechnische Beobachtungen genutzt werden. In der Dissertation wird die Integration dieser Relativmessungen durch ein erweitertes Krigingverfahren gelöst. Dazu werden für den Signal- und Trendanteil der Beobachtungen die nötigen Kovarianz- und Trendmatrizen hergeleitet. Darüberhinaus wird durch die Darstellung der Beobachtungen als lineare Funktionale des Verschiebungsfeldes die Möglichkeit eröffnet, nicht nur das Verschiebungsfeld zu schätzen sondern auch beliebige lineare Funktionale des Verschiebungsfeldes. Das hergeleitete Verfahren wird an zwei praktischen Beispielen demonstriert.

Gegenstand der Arbeit ist die Untersuchung der Anwendbarkeit stochastisch-deterministischer Modelle für die räumliche und zeitliche Vorhersage der Ozonkonzentrationen in Sachsen. Zu diesem Zweck werden die Messwerte des sächsischen Landesmessnetzes von 1995 bis 1999 einer eingehenden statistischen Analyse (deskriptive Analyse, geostatistische Analyse, Zeitreihenanalyse) unterzogen. Bei diesen Analysen werden Repräsentativitätsunterschiede der einzelnen Stationen (städtisch/ländlich) deutlich, die bei Verwendung aller Daten zu einem sehr hohen Nuggeteffekt führen. Um ein realistischeres Bild des Nuggeteffektes zu erhalten, wurde die jeweils am stärksten verkehrsbeeinflusste Station in derselben Stadt aus der Variogrammberechnung ausgeschlossen. Durch die Forschungsarbeit wird gezeigt, dass die Ozonwerte auch nach der Eliminierung räumlicher und zeitlicher Trends eine ausreichende räumliche Autokorrelation besitzen. Schließlich werden geostatistische und zeitreihenanalytische Modelle für die räumliche und zeitliche Vorhersage der sächsischen Ozondaten entwickelt und ihre Genauigkeit überprüft.

Wind generating resources have been increasing more rapidly than any other renewable generating resources. Wind power forecasting is an important issue for deploying higher wind power penetrations on power grids. The existing work on power output forecasting for wind farms has focused on the temporal issues. As wind farm outputs depend on natural wind resources that vary over space and time, spatial analysis and modeling is also needed. Predictions about suitability for locating new wind generating resources can be performed using spatial modeling. In this dissertation, we propose a new approach to spatial prediction of wind farm outputs for grid integration based on Kriging techniques. First, we investigate the characteristics of wind farm outputs. Wind power is variable, uncontrollable, and uncertain compared to traditional generating resources. In order to understand the characteristics of wind power outputs, we study the variability of wind farm outputs using correlation analysis. We estimate the Power Spectrum Density (PSD) from empirical data. Following Apt[1], we classify the estimated PSD into four frequency ranges having different slopes. We subsequently focus on phenomena relating to the slope of the estimated PSD at a low frequency range because our spatial prediction is based on the period over daily to monthly timescales. Since most of the energy is in the lower frequency components (the second, third, and fourth slope regions have much lower spectral density than the first), the conclusion is that the dominant issues regarding energy will be captured by the low frequency behavior. Consequently, most of the issues regarding energy (at least at longer timescales) will be captured by the first slope, since relatively little energy is in the other regions. We propose the slope estimation model of new wind farm production. When the existing wind farms are highly correlated and the slope of each wind farm is estimated at a low frequency range, we can predict the slope with low frequency components of a new wind farm through the proposed spatial interpolation techniques. Second, we propose a new approach, based on Kriging techniques, to predict wind farm outputs. We introduce Kriging techniques for spatial prediction, modeling semivariograms for spatial correlation, and mathematical formulation of the Kriging system. The aim of spatial modeling is to calculate a target value of wind production at unmeasured or new locations based on the existing values that have already been measured at locations considering the spatial correlation relationship between measured values. We propose the multivariate spatial approach based on Co-Kriging to consider multiple variables for better prediction. Co-Kriging is a multivariate spatial technique to predict spatially distributed and correlated variables and it adds auxiliary variables to a single variable of interest at unmeasured locations. Third, we develop the Augmented Kriging-based Model, to predict power outputs at unmeasured or new wind farms that are geographically distributed in a region. The proposed spatial prediction model consists of three stages: collection of wind farm data for spatial analysis, performance of spatial analysis and prediction, and verification of the predicted wind farm outputs. The proposed spatial prediction model provides the univariate prediction based on Universal Kriging techniques and the multivariate prediction based on Universal and Co-Kriging techniques. The proposed multivariate prediction model considers multiple variables: the measured wind power output as a primary variable and the type or hub height of wind turbines, or the slope with low frequency components as a secondary variable. The multivariate problem is solved by Co-Kriging techniques. In addition, we propose $p$ indicator as a categorical variable considering the data configuration of wind farms connected to electrical power grids. Although the interconnection voltage does not influence the wind regime, it does affect transmission system issues such as the level of curtailments, which, in turn, affect power production. Voltage level is therefore used as a proxy to the effect of the transmission system on power output. The Augmented Kriging-based Model (AKM) is implemented in the R system environments and the latest Gstat library is used for the implementation of the AKM. Fourth, we demonstrate the performance of the proposed spatial prediction model based on Kriging techniques in the context of the McCamey and Central areas of ERCOT CREZ. Spatial prediction of ERCOT wind farms is performed in daily, weekly, and monthly time scales for January to September 2009. These time scales all correspond to the lowest frequency range of the estimated PSD. We propose a merit function to provide practical information to find optimal wind farm sites based on spatial wind farm output prediction, including correlation with other wind farms. Our approach can predict what will happen when a new wind farm is added at various locations. Fifth, we propose the Augmented Sequential Outage Checker (ASOC) as a possible approach to study the transmission system, including grid integration of wind-powered generation resources. We analyze cascading outages caused by a combination of thermal overloads, low voltages, and under-frequencies following an initial disturbance using the ASOC. / text

Soil is extremely important for providing food, biomass and raw materials, water and nutrient storage; supporting biodiversity and providing foundations for man-made structures. However, its health is threatened by human activities, which can greatly affect the potential of soils to fulfil their functions and, consequently, result in environmental, economic and social damage. These issues require the characterisation of the impact and spatial extent of the problems. This can be achieved through the creation of detailed and comprehensive soil maps that describe both the spatial and vertical variability of key soil properties. Detailed three-dimensional (3D) digital soil maps can be readily used and embedded into environmental models. Three-dimensional soil mapping is not a new concept. However, only with the recent development of more powerful computers has it become feasible to undertake such data processing. Common techniques to estimate soil properties in the three-dimensional space include geostatistical interpolation, or a combination of depth functions and geostatistics. However, these two methods are both partially flawed. Geostatistical interpolation and kriging in particular, estimate soil properties in unsampled locations using a weighted average of the nearby observations. In order to produce the best possible estimate, this form of interpolation minimises the variance of each weighted average, thus decreasing the standard deviation of the estimates, compared to the soil observations. This appears as a smoothing effect on the data and, as a consequence, kriging interpolation is not reliable when the dataset is not sampled with a sampling designs optimised for geostatistics. Depth function approaches, as they are generally applied in literature, implement a spline regression of the soil profile data that aims to better describe the changes of the soil properties with depth. Subsequently, the spline is resampled at determined depths and, for each of these depths, a bi-dimensional (2D) geostatistical interpolation is performed. Consequently, the 3D soil model is a combination of a series of bi-dimensional slices. This approach can effectively decrease or eliminate any smoothing issues, but the way in which the model is created, by combining several 2D horizontal slices, can potentially lead to erroneous estimations. The fact that the geostatistical interpolation is performed in 2D implies that an unsampled location is estimated only by considering values at the same depth, thus excluding the vertical variability from the mapping, and potentially undermining the accuracy of the method. For these reasons, the literature review identified a clear need for developing, a new method for accurately estimating soil properties in 3D – the target of this research, The method studied in this thesis explores the concept of soil specific depth functions, which are simple mathematical equations, chosen for their ability to describe the general profile pattern of a soil dataset. This way, fitting the depth function to a particular sample becomes a diagnostic tool. If the pattern shown in a particular soil profile is dissimilar to the average pattern described by the depth function, it means that in that region there are localised changes in the soil profiles, and these can be identified from the goodness of fit of the function. This way, areas where soil properties have a homogeneous profile pattern can be easily identified and the depth function can be changed accordingly. The application of this new mapping technique is based on the geostatistical interpolation of the depth function coefficients across the study area. Subsequently, the equation is solved for each interpolated location to create a 3D lattice of soil properties estimations. For this way of mapping, this new methodology was denoted as top-down mapping method. The methodology was assessed through three case studies, where the top-down mapping method was developed, tested, and validated. Three datasets of diverse soil properties and at different spatial extents were selected. The results were validated primarily using cross-validation and, when possible, by comparing the estimates with independently sampled datasets (independent validation). In addition, the results were compared with estimates obtained using established literature methods, such as 3D kriging interpolation and the spline approach, in order to define some basic rule of application. The results indicate that the top-down mapping method can be used in circumstances where the soil profiles present a pattern that can be described by a function with maximum three coefficients. If this condition is met, as it was with key soil properties during the research, the top-down mapping method can be used for obtaining reliable estimates at different spatial extents.

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.

Nors hidromechaninio ežerų valymo darbai vykdomi jau daugelį metų, iki šiol nėra aišku, kaip pasikeičia ežero aplinkosauginė būklė po jo išvalymo, o Lietuvos ir kitų šalių mokslinėje literatūroje informacijos apie valymo sąlygotus metalų ir metaloidų pasiskirstymo dugno nuosėdose pokyčius yra stebėtinai mažai. Disertacijos tyrime buvo taikoma kompleksinė šių pokyčių vertinimo sistema, pasitelkiant ne tik išsamius geocheminius lauko ir laboratorinius tyrimus, bet ir matematinę statistinę analizę bei erdvinę duomenų prognozę ir interpoliaciją. Tyrimų ir analizės rezultatai parodė, kad hidromechaninis ežero valymas sąlygoja nagrinėjamų metalų ir metaloidų kiekių pokyčius ir jų persiskirstymą dugno nuosėdose, kuris yra savitas atskiriems cheminiams elementams, todėl siekiant nustatyti valymo darbų įtaką būtina naudoti indikatorius, leidžiančius įvertinti bendro, kumuliacinio nuosėdų užterštumo lygio pokyčius visų nagrinėjamų elementų atžvilgiu. Vieno iš tokių indikatorių – suminio užterštumo rodiklio Zd verčių statistinė analizė ir erdvinė interpoliacija leido ne tik nustatyti statistiškai patikimą hidromechaninio ežero valymo įtakotą metalų ir metaloidų pokyčių reikšmingumą naujai susiformavusiame paviršiniame dugno nuosėdų sluoksnyje, bet ir pademonstruoti erdvinį šių elementų perskirstymą dugno paviršiaus plote. Disertacijoje pateikiama informacija yra ypač aktuali vertinant Lietuvos ežerų būklę, planuojant ežerų dugno nuosėdų šalinimo darbus ir nustatant jų tikslingumą. / Although hydromechanical lake remediation projects have been carried out over several decades, there still is a lack of evidence about the changes in environmental status after such projects, while scientific literature regarding redistribution of metals and metalloids caused by hydromechanical bottom sediment removal is especially scarce both in Lithuania and in other countries. Research of the dissertation consisted not only of extensive geochemical field work and laboratory analysis, but also methods of mathematical statistics and spatial interpolation. Results of the research and their analysis allowed to conclude that hydromechanical lake remediation results in changes of the contents of metals and metalloids of interest and their spatial redistribution in lake bottom sediments, which are specific to each metal and metalloid, thus cumulative indicators should be used to assess overall changes in sediment quality of remediated lakes. Calculation and statistical analysis of on of such indicators - total sediment contamination index (Zd) and surface interpolation of its values allowed to evaluate statistical significance of changes in contamination degree of the newly formed surface sediment layer and to assess cumulative spatial redistribution of metals and metalloids caused by hydromechanical lake remediation. Data provided in the dissertation is especially significant in preparation and design of future sediment removal projects and in determining their feasibility.

Although hydromechanical lake remediation projects have been carried out over several decades, there still is a lack of evidence about the changes in environmental status after such projects, while scientific literature regarding redistribution of metals and metalloids caused by hydromechanical bottom sediment removal is especially scarce both in Lithuania and in other countries. Research of the dissertation consisted not only of extensive geochemical field work and laboratory analysis, but also methods of mathematical statistics and spatial interpolation. Results of the research and their analysis allowed to conclude that hydromechanical lake remediation results in changes of the contents of metals and metalloids of interest and their spatial redistribution in lake bottom sediments, which are specific to each metal and metalloid, thus cumulative indicators should be used to assess overall changes in sediment quality of remediated lakes. Calculation and statistical analysis of on of such indicators - total sediment contamination index (Zd) and surface interpolation of its values allowed to evaluate statistical significance of changes in contamination degree of the newly formed surface sediment layer and to assess cumulative spatial redistribution of metals and metalloids caused by hydromechanical lake remediation. Data provided in the dissertation is especially significant in preparation and design of future sediment removal projects and in determining their feasibility. / Nors hidromechaninio ežerų valymo darbai vykdomi jau daugelį metų, iki šiol nėra aišku, kaip pasikeičia ežero aplinkosauginė būklė po jo išvalymo, o Lietuvos ir kitų šalių mokslinėje literatūroje informacijos apie valymo sąlygotus metalų ir metaloidų pasiskirstymo dugno nuosėdose pokyčius yra stebėtinai mažai. Disertacijos tyrime buvo taikoma kompleksinė šių pokyčių vertinimo sistema, pasitelkiant ne tik išsamius geocheminius lauko ir laboratorinius tyrimus, bet ir matematinę statistinę analizę bei erdvinę duomenų prognozę ir interpoliaciją. Tyrimų ir analizės rezultatai parodė, kad hidromechaninis ežero valymas sąlygoja nagrinėjamų metalų ir metaloidų kiekių pokyčius ir jų persiskirstymą dugno nuosėdose, kuris yra savitas atskiriems cheminiams elementams, todėl siekiant nustatyti valymo darbų įtaką būtina naudoti indikatorius, leidžiančius įvertinti bendro, kumuliacinio nuosėdų užterštumo lygio pokyčius visų nagrinėjamų elementų atžvilgiu. Vieno iš tokių indikatorių – suminio užterštumo rodiklio Zd verčių statistinė analizė ir erdvinė interpoliacija leido ne tik nustatyti statistiškai patikimą hidromechaninio ežero valymo įtakotą metalų ir metaloidų pokyčių reikšmingumą naujai susiformavusiame paviršiniame dugno nuosėdų sluoksnyje, bet ir pademonstruoti erdvinį šių elementų perskirstymą dugno paviršiaus plote. Disertacijoje pateikiama informacija yra ypač aktuali vertinant Lietuvos ežerų būklę, planuojant ežerų dugno nuosėdų šalinimo darbus ir nustatant jų tikslingumą.

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In Geostatistical modelling of the spatial distribution of rock attributes, the multivariate distribution of a Random Function defines the range of possible values and the spatial relationships among them. Under a decision of stationarity, the Random Function distribution and its statistics are inferred from data within a spatial domain deemed statistically homogenous. Assuming stationary multiGaussianity allows spatial prediction techniques to take advantage of this simple parametric distribution model. These techniques compute the local distributions with surrounding data and global spatially invariant statistics. They often fail to reproduce local changes in the mean, variability and, particularly, the spatial continuity, that are required for geologically realistic modelling of rock attributes. The proposed alternative is to build local Random Function models that are deemed stationary only in relation to the locations where they are defined. The corresponding location-dependent distributions and statistics are inferred by weighting the samples inversely proportional to their distance to anchor locations. These distributions are locally Gaussian transformed. The transformation models carry information on the local histogram. The distance weighted experimental measures of spatial correlation are able to adapt to local changes in the spatial continuity and are semi-automatically fitted by locally defined variogram models. The fields of local variogram and transformation parameters are used in locally stationary spatial prediction algorithms. The resulting attribute models are rich in non-stationary spatial features. This process implies a higher computational demand than the traditional techniques, but, if data is abundant enough to allow a reliable inference of the local statistics, the proposed locally stationary techniques outperform their stationary counterparts in terms of accuracy and precision. These improved models have the potential of providing better decision support for engineering design. / Mining Engineering