This thesis consists of two parts. The first part focuses on design and analysis for computer experiments and the second part deals with binary time series and its application to kinetic studies in micropipette experiments. The first part of the thesis addresses three problems. The first problem is concerned with optimal design of computer experiments. Latin hypercube designs (LHDs) have been used extensively for computer experiments. A multi-objective optimization approach is proposed to find good LHDs by combining correlation and distance performance measures. Several examples are presented to show that the obtained designs are good in terms of both criteria. The second problem is related to the analysis of computer experiments. Kriging is the most popular method for approximating complex computer models. Here a modified kriging method is proposed, which has an unknown mean model. Therefore it is called blind kriging. The unknown mean model is identified from experimental data using a Bayesian variable selection technique. Many examples are presented which show remarkable improvement in prediction using blind kriging over ordinary kriging. The third problem is related to computer experiments with nested and branching factors. Design and analysis of experiments with branching and nested factors are challenging and have not received much attention in the literature. Motivated by a computer experiment in a machining process, we develop optimal LHDs and kriging methods that can accommodate branching and nested factors. Through the application of the proposed methods, optimal machining conditions and tool edge geometry are attained, which resulted in a remarkable improvement in the machining process. The second part of the thesis deals with binary time series analysis with application to cell adhesion frequency experiments. Motivated by the analysis of repeated adhesion tests, a binary time series model incorporating random effects is developed in this chapter. A goodness-of-fit statistic is introduced to assess the adequacy of distribution assumptions on the dependent binary data with random effects. Application of the proposed methodology to real data from a T-cell experiment reveals some interesting information. These results provide some quantitative evidence to the speculation that cells can have ¡§memory¡¨ in their adhesion behavior.

This thesis presents a comparison of the development of the concentrations of nitrogen oxides and sulfur dioxide in the air in the Usti region. The work described generally air pollution and related terms such as the sources of pollution emission, immission and atmospheric deposition. The study also evaluated pollution nitrogen oxides and sutur dioxide in the Usti region. This work describes the methods that were used in the calculations and evaluations. It also deals with the selecting appropriate measuring stations to handle the development of the concentrations of these substances in the air. The aim of this work is to find trends in time series of concentrations of NOx and SO2 and statistical evaluation of development levels in selected cities Ústí Region. The next section is evaluated spatial analysis of the concentration of nitrogen oxides and sulfur dioxide in the air in the Ústí Region. This area was chosen primarily because it is characterized by significant air pollution.

Terrain surfaces conserve human activities in terms of textures and structures. With reference to archaeological questions, the geological archive is investigated by means of models regarding anthropogenic traces. In doing so, the high-resolution digital terrain model is of inestimable value for the decoding of the archive. The evaluation of these terrain models and the reconstruction of historical surfaces is still a challenging issue. Due to the data collection by means of LiDAR systems (light detection and ranging) and despite their subsequent pre-processing and filtering, recently anthropogenic artefacts are still present in the digital terrain model. Analysis have shown that elements, such as contour lines and channels, can well be extracted from a highresolution digital terrain model. This way, channels in settlement areas show a clear anthropogenic character. This fact can also be observed for contour lines. Some contour lines representing a possibly natural ground surface and avoid anthropogenic artefacts. Comparable to channels, noticeable patterns of contour lines become visible in areas with anthropogenic artefacts. The presented work ow uses functionalities of ArcGIS and the programming language R.¹ The method starts with the extraction of contour lines from the digital terrain model. Through macroscopic analyses based on geomorphological expert knowledge, contour lines are selected representing the natural geomorphological character of the surface. In a first step, points are determined along each contour line in regular intervals. This points and the corresponding height information which is taken from an original digital terrain model is saved as a point cloud. Using the programme library gstat, a variographic analysis and the use of a Kriging-procedure based on this follow. The result is a digital terrain model filtered considering geomorphological expert knowledge showing no human degradation in terms of artefacts, preserving the landscape-genetic character and can be called a prehistoric terrain model.

Currently in archaeological studies digital elevation models are mainly used especially in terms of shaded reliefs for the prospection of archaeological sites. Hesse (2010) provides a supporting software tool for the determination of local relief models during the prospection using LiDAR scans. Furthermore the search for relicts from WW2 is also in the focus of his research.¹ In James et al. (2006) the determined contour lines were used to reconstruct locations of archaeological artefacts such as buildings.² This study is much more and presents an innovative workflow of determining historical high resolution terrain surfaces using recent high resolution terrain models and sedimentological expert knowledge. Based on archaeological field studies (Franconian Saale near Bad Neustadt in Germany) the sedimentological analyses shows that archaeological interesting horizon and geomorphological expert knowledge in combination with particle size analyses (Köhn, DIN ISO 11277) are useful components for reconstructing surfaces of the early Middle Ages.³ Furthermore the paper traces how it is possible to use additional information (extracted from a recent digital terrain model) to support the process of determination historical surfaces. Conceptual this research is based on methodology of geomorphometry and geo-statistics. The basic idea is that the working procedure is based on the different input data. One aims at tracking the quantitative data and the other aims at processing the qualitative data. Thus, the first quantitative data were available for further processing, which were later processed with the qualitative data to convert them to historical heights. In the final stage of the work ow all gathered information are stored in a large data matrix for spatial interpolation using the geostatistical method of Kriging. Besides the historical surface, the algorithm also provides a first estimation of accuracy of the modelling. The presented workflow is characterized by a high exibility and the opportunity to include new available data in the process at any time.

In this report we attempt to provide insights in how interpolation can be used for creating heat maps showing residence prices for different residence markets in Sweden. More specifically, three interpolation methods are implemented and are then used on three Swedish residence markets. These three residence markets are of varying characteristics such as size and residence type. Data of residence sales and the physical definitions of the residence markets were collected. As residence sales are never identical, residence sales were preprocessed to make them comparable. For comparison, a so-called external predictor was used as an extra parameter for the interpolation method. In this report, distance to nearest public transportation was used as an external predictor. The interpolated heat maps were compared and evaluated using both quantitative and qualitative approaches. Results show that each interpolation method has its own strengths and weaknesses, and that using an external predictor results in better heat maps compared to only using residence price as predictor. Kriging was found to be the most robust method and consistently resulted in the best interpolated heat maps for all residence markets. On the other hand, it was also the most time-consuming interpolation method. / Den här rapporten försöker ge insikter i hur interpolation kan användas för att skapa färgdiagram över bostadspriser för olika bostadsmarknader i Sverige. Mer specifikt implementeras tre interpolationsmetoder som sedan används på tre olika svenska bostadsmarknader. Dessa tre bostadsmarknader är av olika karaktär med hänsyn till storlek och bostadstyp. Bostadsförsäljningsdata och de fysiska definitionerna för bostadsmarknaderna samlades in. Eftersom bostadsförsäljningar aldrig är identiska, behandlas de först i syfte att göra dem jämförbara. En extern indikator, vilket är en extra parameter för interpolationsmetoder, undersöktes även. I den här rapporten användes avståndet till närmaste kollektiva transportmedel som extern indikator. De interpolerade färgdiagrammen jämfördes och utvärderades både med en kvantiativ och en kvalitativ metod. Resultaten visar att varje interpolationsmetod har sina styrkor och svagheter och att användandet av en extern indikator alltid renderade i ett bättre färgdiagram jämfört med att endast använda bostadspris som indikator. Kriging bedöms vara den mest robusta interpolationsmetoden och interpolerade även de bästa färgdiagrammen för alla bostadsmarknader. Samtidigt var det även den mest tidskrävande interpolationsmetoden.

In this thesis a Gaussian process regression (GPR) model and a Kalman filter (KF) model were developed and applied to a trajectory prediction problem. The main subject of the thesis is GPR, where the intended purpose of the KF is to compare it to the GPR model. The input data for the models consists of two noisy spherical angle coordinates of a moving target relative to a moving guided projectile. In order to perform trajectory predictions the models need to estimate the distance between the target and guided projectile since there are only two coordinates available and an estimation of three coordinates is desired. The distance estimation was done by a Low Speed Approximation. The trajectories investigated were harmonic-exponential, exponential-spiral and linear. The results showed issues with the hyperparameters of the GPR model which may be related to the preprocessing of the trajectory data. However, the GPR model did outperform the KF model when there was acceleration, despite the issues with the hyperparameters. The KF model outperformed the GPR model when the target trajectory behaved linearly. The results indicate that GPR has potential as a trajectory prediction algorithm. / I denna avhandling utvecklades och tillämpades en Gaussisk process regression (GPR)-modell och en Kalman Filter (KF)-modell på ett positionspredikteringsproblem. Huvudämnet för avhandlingen är GPR medan det avsedda syftet med KF är att jämföra den med GPR-modellen. Modellernas indata består av två brusiga sfäriska vinkelkoordinater av ett rörligt mål i förhållande till en styrd projektil. För att modellerna ska kunna utföra positionsprediktering så behöver avståndet mellan målet och den styrda projektilen skattas, eftersom det endast finns två tillgängliga koordinater och en uppskattning av tre koordinater önskas. Avståndsberäkningen gjordes baserat på ett antagande om att hastigheten för målet är liten relativt hastigheten för den styrda projektilen, i avhandlingen är denna approximation benämnd Low Speed Approximation. De undersökta banorna var harmonisk-exponentiell, exponentiell-spiral och linjär. Resultaten visade problem med hyperparametrarna för GPR-modellen, vilket kan vara relaterat till förbehandlingen av bandatan. Trots problem med hyperparametrarna så presterade GPR-modellen bättre än KF-modellen när det fanns acceleration. KF-modellen presterade bättre än GPR-modellen när målets bana betedde sig linjärt. Resultaten indikerar att GPR har potential som en algoritm för positionsprediktering.

The purpose of this study is to investigate the importance of prior information about hydraulic conductivity (K) by Kriging, using point K data and/or residual covariance, on improvements of K estimates at the North Campus Research Site (NCRS). Among many methods that can characterize the mean or detail distribution of hydraulic conductivity (K), the Cooper-Jacob straight line solution, Kriging using point K data, single-well pumping tests inversion and Hydraulic Tomography (HT) have been compared in this study, using the head data collected from 15 cross-hole pumping tests collected at NCRS, where 9 existing wells were installed with packer system and the pressure responses at different intervals in different wells were monitored with transducers. It is found that the HT method, which fuse all the available pumping test data, yields more accurate and consistent results. However, many studies have indicated that the hydraulic data combined with geologic investigation will improve the HT estimates. Thus, in this study, hard data of K obtained by permeameter (227 data points) are brought in using Kriging and combined with HT to yield better estimate K field. Moreover, the validations of unused tests indicate that the estimated K obtained using collected K information makes more accurate predictions.

A novel concept of multiple deterministic analyses is proposed to design safer and more damage-tolerant structures, particularly when excited by dynamic including seismic loading in time domain. Since the presence of numerous sources of uncertainty cannot be avoided or overlooked, the underlying risk is estimated to compare design alternatives. To generate the implicit performance functions explicitly, the basic response surface method is significantly improved. Then, several surrogate models are proposed. The advanced factorial design and Kriging method are used as the major building blocks. Using these basic schemes, seven alternatives are proposed. Accuracies of these schemes are verified using basic Monte Carlo simulations. After verifying all seven alternatives, the capabilities of the three most desirable schemes are compared using a case study. They correctly identified and correlated damaged states of structural elements in terms of probability of failure using only few hundreds of deterministic analyses. The modified Kriging method appears to be the best technique considering both efficiency and accuracy. Estimating the probability of failure, the post-Northridge seismic design criteria are found to be appropriate. After verifying the proposed method, a Site-Specific seismic safety assessment method for nonlinear structural systems is proposed to generate a suite of ground excitation time histories. The information of risk is used to design a structure more damage-tolerant. The proposed procedure is verified and showcased by estimating risks associated with three buildings designed by professional experts in the Los Angeles area satisfying the post-Northridge design criteria for the overall lateral deflection and inter-story drift. The accuracy of the estimated risk is again verified using the Monte Carlo simulation technique. In all cases, the probabilities of collapse are found to be less than 10% when excited by the risk-targeted maximum considered earthquake ground motion satisfying the intent of the code. The spread in the reliability indexes for each building for both limit states cannot be overlooked, indicating the significance of the frequency contents. The inter story drift is found to be more critical than the overall lateral displacement. The reliability indexes for both limit states are similar only for few cases. The author believes that the proposed methodology is an alternative to the classical random vibration and simulation approaches. The proposed site-specific seismic safety assessment procedure can be used by practicing engineers for routine applications. The proposed reliability methodology is not problem-specific. It is capable of handling systems with different levels of complexity and scalability, and it is robust enough for multi-disciplinary routine applications. In order to show the multi-disciplinary application of the proposed methodology, the probability of failure of lead-free solders in Ball Grid Array 225 surface-mount packaging for a given loading cycle is estimated. The accuracy of the proposed methodology is verified with the help of Monte Carlo simulation. After the verification, probability of failure versus loading cycles profile is calculated. Such a comprehensive study of its lifetime behavior and the corresponding reliability analyses can be useful for sensitive applications.

Dans le contexte actuel de transition énergétique, les acteurs de la production électrique (dont EDF) s'orientent de plus en plus vers les technologies "bas carbone", permettant de développer leur mix énergétique et d'assurer une production toujours plus respectueuse de l'environnement. Parmi l'ensemble des alternatives progressivement industrialisées au cours de ces dernières décennies, l'énergie éolienne voit son développement s'accélérer. De nouveaux projets voient le jour, notamment avec le développement de parcs éoliens posés en mer le long des côtes françaises.Afin de garantir une sécurité maximale des installations vis-à-vis des défaillances mécaniques, les ingénieurs doivent mettre en place un ensemble de vérifications ayant pour but d'assurer l'intégrité structurelle pendant une durée de vie donnée. Cette étape, nécessaire à la certification et donc à l'industrialisation du projet, exige un investissement numérique important. Dans le cas particulier de l'estimation de l'endommagement à durée de vie, un ensemble complet d'analyses doit être effectué afin de simuler les réactions structurelles en différents points de la conception et ce, pour l'ensemble des conditions environnementales de chargement possibles (cas de charge). Au total, quelques milliers de simulations correspondant à l'ensemble des situations probables sont à prévoir pour la seule estimation de l'endommagement à durée de vie. De plus, la prise en compte des différents phénomènes physiques du problème (aérodynamique, hydrodynamique, mécanique élastique), ainsi que la considération des non-linéarités des réponses liées à l'asservissement de la turbine, impliquent l'utilisation de codes de résolution temporels et multi-physiques coûteux pour chacune des situations de chargement à simuler.Afin de réduire l'investissement lié à l'estimation de cet endommagement, l'utilisation de méthodes numériques de substitution (également appelées métamodèles) est une alternative prometteuse. Ces méthodologies ont montré leur efficacité dans divers domaines de l'ingénierie permettant d'approcher, par diverses hypothèses statistiques, la réponse de modèles numériques en ne considérant qu'un nombre réduit de simulations.Ce travail de thèse s'est focalisé sur le développement d'outils numériques pour le dimensionnement efficace des structures éoliennes en mer et plus particulièrement sur l'utilisation des métamodèles de Krigeage (ou méthode de régression par processus gaussien) pour l'estimation de l'endommagement mécanique. Sous certaines hypothèses, cette méthode de substitution se prête particulièrement bien à l'approximation des réponses de modèles physiques, notamment grâce à la mise en place facilitée d'architectures itératives d'enrichissement ("active learning strategy"). Deux domaines ont principalement été étudiés : l'estimation rapide des quantités d'endommagement structurel par le développement de la méthode "Adaptive Kriging for Damage Assessment" (AK-DA) et les possibilités d'utilisation de cette dernière dans le cadre d'études de la fiabilité conceptuelle au regard de la tenue à l'endommagement. L'applicabilité de ces méthodes a été illustrée via l'utilisation d'exemples numériques inspirés du contexte industriel et de ses contraintes. / The mechanical certification of wind turbine structures is required for the funding of newoffshore projects on the French coasts. In order to ensure a maximal safety level of installations,a series of structural analyzes are required by the certification bodies. Amongst all, thedamage based computations represent an important numerical effort for EDF. The presentedworks focus on the applicability and the performances of Kriging metamodels for the estimationof the lifetime cumulated damage of offshore wind turbine structures (AK-DA approach)and the damage based reliability assessment of new designs (AK-MCS/AK-DA coupling).

O presente trabalho tem como objetivo principal a classificação do risco de infestação por regiões de culturas vegetais por plantas daninhas. Os riscos por regiões são obtidos por um sistema de classificação fuzzy, usando métodos de Krigagem e análise de imagens. A infestação é descrita por atributos da cobertura foliar, densidade de sementes, extensão dos agrupamentos de sementes e competitividade, obtidos a partir das amostras de densidades de sementes e de plantas daninhas, da cobertura foliar e da biomassa de plantas daninhas. O atributo da cobertura foliar indica a porcentagem de ocupação das plantas emergentes e é obtido a partir de um mapa de cobertura foliar, construído usando Krigagem. O atributo da densidade de sementes caracteriza a localização das sementes que podem germinar e é obtido a partir de um mapa da distribuição da produção de sementes das plantas daninhas, também construído usando Krigagem. O atributo da extensão dos agrupamentos de sementes reflete a influência das sementes vizinhas em uma certa localização e também é obtido a partir do mapa de distribuição da produção de sementes. O atributo da competitividade entre plantas daninhas e cultura é obtido a partir de um sistema neurofuzzy, utilizando amostras de densidade e de biomassa das plantas daninhas. Para reunir os riscos de infestação semelhantes, os valores de risco inferidos por região pelo sistema fuzzy são agrupados considerando valores e localizações próximas utilizando o método k-médias com coeficiente de variação. Uma abordagem probabilística com redes de classificação Bayesianas é também empregada para a obtenção de um conjunto de regras linguísticas para classificar a competitividade e o risco de infestação, por motivo de comparação. Resultados para o risco de infestação são obtidos para uma área experimental em uma cultura de milho indicando a existência de riscos diferenciados que são explicados pela perda de rendimento da cultura. / The goal of this work is the classification of the risk of infestation per regions of a crop by weeds. The risks per regions are obtained by a fuzzy classification system, using kriging and image analysis. The infestation is described by attributes of the weed coverage, weed seed density, weed seed patches and competitiveness, obtained from weed seeds and weed densities, weed coverage and biomass. The attribute of the weed coverage indicates the percentage of infested surface of the emergent weeds which is obtained from a weed coverage map built with kriging. The attribute of the weed seed density is obtained from a weed seed production map also built with kriging which characterizes the locations of seeds which can germinate. The attribute of the weed seed patches is also obtained by the weed seed production map which reflects how the seeds contribute to weed proliferation in the surroundings. The attribute of the competitiveness among weeds and crop is obtained from a neurofuzzy system, using the weeds density and biomass of the plants. In order to aggregate the similar risks of infestation, the values of risks per region inferred by the fuzzy system are clustered according to similar values and locations using the k-means method with a variation coefficient. A probabilistic approach with Bayesian networks classifiers is also considered to obtain a set of linguistic rules to classify the competitiveness and the risk of infestation, for comparison purposes. Results for the risk of infestation are obtained for an experimental area in a corn crop which indicate the existence of different risks, explained by the yield loss of the crop.