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Hemmati, Sahar. "Steady-State Co-Kriging Models." Thesis, West Virginia University, 2017. http://pqdtopen.proquest.com/#viewpdf?dispub=10614907.
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<p> In deterministic computer experiments, a computer code can often be run at different levels of complexity/fidelity and a hierarchy of levels of code can be obtained. The higher the fidelity and hence the computational cost, the more accurate output data can be obtained. Methods based on the co-kriging methodology Cressie (2015) for predicting the output of a high-fidelity computer code by combining data generated to varying levels of fidelity have become popular over the last two decades. For instance, Kennedy and O’Hagan (2000) first propose to build a metamodel for multi-level computer codes by using an auto-regressive model structure. Forrester et al. (2007) provide details on estimation of the model parameters and further investigate the use of co-kriging for multi-fidelity optimization based on the efficient global optimization algorithm Jones et al. (1998). Qian and Wu (2008) propose a Bayesian hierarchical modeling approach for combining low-accuracy and high-accuracy experiments. More recently, Gratiet and Cannamela (2015) propose sequential design strategies using fast cross-validation techniques for multi-fidelity computer codes. </p><p> This research intends to extend the co-kriging metamodeling methodology to study steady-state simulation experiments. First, the mathematical structure of co-kriging is extended to take into account heterogeneous simulation output variances. Next, efficient steady-state simulation experimental designs are investigated for co-kriging to achieve a high prediction accuracy for estimation of steady-state parameters. Specifically, designs consisting of replicated longer simulation runs at a few design points and replicated shorter simulation runs at a larger set of design points will be considered. Also, design with no replicated simulation runs at long simulation is studied, along with different methods for calculating the output variance in absence of replicated outputs. </p><p> Stochastic co-kriging (SCK) method is applied to an M/M/1, as well as an M/M/5 queueing system. In both examples, the prediction performance of the SCK model is promising. It is also shown that the SCK method provides better response surfaces compared to the SK method.</p><p>
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Thiesen, Michael Jerome. "A fast layered alternative to kriging." Thesis, Montana State University, 2007. http://etd.lib.montana.edu/etd/2007/thiesen/TheisenM1207.pdf.
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Empirically gathered scientific data often comes in the form of scattered locations, each with an associated measurement. Visualizing scattered data is challenging because we need to estimate the measured values at many regularly spaced intervals in order to render the data to modern displays. Kriging is a common technique for visualizing scattered data that produces high quality output, but is often too slow for large data sets. In this thesis I present Layered Interpolation, an alternative to Kriging based on the idea of fitting fractal noise functions to scattered data. This technique produces output with quality that is comparable to Kriging, but with greatly reduced running time. Layered Interpolation's speed makes it an ideal choice for rendering large scattered data sets to modern high-resolution displays.
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Largueche, Fatima-Zohra. "Assessment of ground contamination using Kriging techniques." Thesis, University of Newcastle Upon Tyne, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.320825.
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Joo, Sin Hen. "Application of Kriging method for drought study." Ohio University / OhioLINK, 1989. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1182439116.
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Nelson, Andrea Joan. "Treed Kriging aerodynamic database modeling and optimization /." May be available electronically:, 2008. http://proquest.umi.com/login?COPT=REJTPTU1MTUmSU5UPTAmVkVSPTI=&clientId=12498.
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Roditis, Ioannis Stavros 1960. "A PERFORMANCE EVALUATION OF THE INDICATOR KRIGING METHOD ON A GOLD DEPOSIT: A COMPARISON WITH THE ORDINARY KRIGING METHOD." Thesis, The University of Arizona, 1986. http://hdl.handle.net/10150/275482.
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Tolosana, Delgado Raimon. "Geostatistics for constrained variables: positive data, compositions and probabilities. Applications to environmental hazard monitoring." Doctoral thesis, Universitat de Girona, 2005. http://hdl.handle.net/10803/7903.
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Aquesta tesi estudia com estimar la distribució de les variables regionalitzades l'espai mostral i l'escala de les quals admeten una estructura d'espai Euclidià. Apliquem el principi del treball en coordenades: triem una base ortonormal, fem estadística sobre les coordenades de les dades, i apliquem els output a la base per tal de recuperar un resultat en el mateix espai original. Aplicant-ho a les variables regionalitzades, obtenim una aproximació única consistent, que generalitza les conegudes propietats de les tècniques de kriging a diversos espais mostrals: dades reals, positives o composicionals (vectors de components positives amb suma constant) són tractades com casos particulars. D'aquesta manera, es generalitza la geostadística lineal, i s'ofereix solucions a coneguts problemes de la no-lineal, tot adaptant la mesura i els criteris de representativitat (i.e., mitjanes) a les dades tractades. L'estimador per a dades positives coincideix amb una mitjana geomètrica ponderada, equivalent a l'estimació de la mediana, sense cap dels problemes del clàssic kriging lognormal. El cas composicional ofereix solucions equivalents, però a més permet estimar vectors de probabilitat multinomial. Amb una aproximació bayesiana preliminar, el kriging de composicions esdevé també una alternativa consistent al kriging indicador. Aquesta tècnica s'empra per estimar funcions de probabilitat de variables qualsevol, malgrat que sovint ofereix estimacions negatives, cosa que s'evita amb l'alternativa proposada. La utilitat d'aquest conjunt de tècniques es comprova estudiant la contaminació per amoníac a una estació de control automàtic de la qualitat de l'aigua de la conca de la Tordera, i es conclou que només fent servir les tècniques proposades hom pot detectar en quins instants l'amoni es transforma en amoníac en una concentració superior a la legalment permesa.<br>This Thesis presents an estimation procedure for the distribution of regionalized variables with sample space and scale admitting an Euclidean structure. We apply the principle of working on coordinates: choose an orthonormal basis; do statistics on the coordinates of your observations on that basis; and, by applying the output to the basis, you will recover a result within the original space. Applying this procedure to regionalized variables, we obtain a unified, consistent method, with the same properties of classical linear kriging techniques, but valid for several sample spaces: real data, positive data and compositions (vectors of positive components summing up to a constant) are regarded as particular cases. In this way we generalize the linear kriging techniques, and offer a solution to several well-known problems of the non-linear ones, by adapting the measure of the space and the averaging criterion (the way means are computed) to the data. The obtained estimator for positive variables is a weighted geometric mean, equivalent to estimate the median, which has none of the drawback of classical lognormal kriging. For compositional data, equivalent results are obtained, but which also serve to treat multinomial probability vectors. By combining this with a preliminary Bayesian estimation, our kriging for compositions become also a valid alternative to indicator kriging, without its order-relation problems (i.e. the rather-usual negative estimates of some probabilities). These techniques are validated by studying the ammonia pollution hazard in an automatic water quality control station placed in a small Mediterranean river. Only the proposed techniques allow us to assess when the secondary pollution by ammonia exceeds the existing legal threshold.
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Toal, David J. J. "Proper orthogonal decomposition & kriging strategies for design." Thesis, University of Southampton, 2009. https://eprints.soton.ac.uk/72023/.
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The proliferation of surrogate modelling techniques have facilitated the application of expensive, high fidelity simulations within design optimisation. Taking considerably fewer function evaluations than direct global optimisation techniques, such as genetic algorithms, surrogate models attempt to construct a surrogate of an objective function from an initial sampling of the design space. These surrogates can then be explored and updated in regions of interest. Kriging is a particularly popular method of constructing a surrogate model due to its ability to accurately represent complicated responses whilst providing an error estimate of the predictor. However, it can be prohibitively expensive to construct a kriging model at high dimensions with a large number of sample points due to the cost associated with the maximum likelihood optimisation. The following thesis aims to address this by reducing the total likelihood optimisation cost through the application of an adjoint of the likelihood function within a hybridised optimisation algorithm and the development of a novel optimisation strategy employing a reparameterisation of the original design problem through proper orthogonal decomposition.
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Wang, Xiang. "Two kriging models, and the expanded readsold package." Ohio University / OhioLINK, 1986. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1183382153.
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Morphet, William James. "Simulation, Kriging, and Visualization of Circular-Spatial Data." DigitalCommons@USU, 2009. https://digitalcommons.usu.edu/etd/386.
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The circular dataimage is defined by displaying direction as the color at the same direction in a color wheel composed of a sequence of two-color gradients with color continuity between gradients. The resulting image of circular-spatial data is continuous with high resolution. Examples include ocean wind direction, Earth's main magnetic field, and rocket nozzle internal combustion flow. The cosineogram is defined as the mean cosine of the angle between random components of direction as a function of distance between observation locations. It expresses the spatial correlation of circular-spatial data. A circular kriging solution is developed based on a model fitted to the cosineogram. A method for simulating circular random fields is given based on a transformation of a Gaussian random field. It is adaptable to any continuous probability distribution. Circular random fields were implemented for selected circular probability distributions. An R software package was created with functions and documentation.
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Liu, Heping Maghsoodloo Saeed. "Taylor Kriging metamodeling for simulation interpolation, sensitivity analysis and optimization." Auburn, Ala., 2009. http://hdl.handle.net/10415/1621.
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Hawe, Glenn. "Kriging methods for constrained multi-objective electromagnetic design optimization." Thesis, University of Southampton, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.444159.
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Asritha, Kotha Sri Lakshmi Kamakshi. "Comparing Random forest and Kriging Methods for Surrogate Modeling." Thesis, Blekinge Tekniska Högskola, Fakulteten för datavetenskaper, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:bth-20230.
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The issue with conducting real experiments in design engineering is the cost factor to find an optimal design that fulfills all design requirements and constraints. An alternate method of a real experiment that is performed by engineers is computer-aided design modeling and computer-simulated experiments. These simulations are conducted to understand functional behavior and to predict possible failure modes in design concepts. However, these simulations may take minutes, hours, days to finish. In order to reduce the time consumption and simulations required for design space exploration, surrogate modeling is used. \par Replacing the original system is the motive of surrogate modeling by finding an approximation function of simulations that is quickly computed. The process of surrogate model generation includes sample selection, model generation, and model evaluation. Using surrogate models in design engineering can help reduce design cycle times and cost by enabling rapid analysis of alternative designs.\par Selecting a suitable surrogate modeling method for a given function with specific requirements is possible by comparing different surrogate modeling methods. These methods can be compared using different application problems and evaluation metrics. In this thesis, we are comparing the random forest model and kriging model based on prediction accuracy. The comparison is performed using mathematical test functions. This thesis conducted quantitative experiments to investigate the performance of methods. After experimental analysis, it is found that the kriging models have higher accuracy compared to random forests. Furthermore, the random forest models have less execution time compared to kriging for studied mathematical test problems.
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Ngwenya, Mzabalazo Z. "Investigating 'optimal' kriging variance estimation :analytic and bootstrap estimators." Master's thesis, University of Cape Town, 2011. http://hdl.handle.net/11427/11265.
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Kriging is a widely used group of techniques for predicting unobserved responses at specified locations using a set of observations obtained from known locations. Kriging predictors are best linear unbiased predictors (BLUPs) and the precision of predictions obtained from them are assessed by the mean squared prediction error (MSPE), commonly termed the kriging variance.
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Clark, Daniel Lee Jr. "Locally Optimized Covariance Kriging for Non-Stationary System Responses." Wright State University / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=wright1464092652.
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YATES, SCOTT RAYMOND. "GEOSTATISTICAL METHODS FOR ESTIMATING SOIL PROPERTIES (KRIGING, COKRIGING, DISJUNCTIVE)." Diss., The University of Arizona, 1985. http://hdl.handle.net/10150/187990.
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Geostatistical methods were investigated in order to find efficient and accurate means for estimating a regionalized random variable in space based on limited sampling. The random variables investigated were (1) the bare soil temperature (BST) and crop canopy temperature (CCT) which were collected from a field located at the University of Arizona's Maricopa Agricultural Center, (2) the bare soil temperature and gravimetric moisture content (GMC) collected from a field located at the Campus Agricultural Center and (3) the electrical conductivity (EC) data collected by Al-Sanabani (1982). The BST was found to exhibit strong spatial auto-correlation (typically greater than 0.65 at 0⁺ lagged distance). The CCT generally showed a weaker spatial correlation (values varied from 0.15 to 0.84) which may be due to the length of time required to obtain an "instantaneous" sample as well as wet soil conditions. The GMC was found to be strongly spatially dependent and at least 71 samples were necessary in order to obtain reasonably well behaved covariance functions. Two linear estimators, the ordinary kriging and cokriging estimators, were investigated and compared in terms of the average kriging variance and the sum of squares error between the actual and estimated values. The estimate was obtained using the jackknifing technique. The results indicate that a significant improvement in the average kriging variance and the sum of squares could be expected by using cokriging for GMC and including 119 BST values in the analysis. A nonlinear estimator in one variable, the disjunctive kriging estimator, was also investigated and was found to offer improvements over the ordinary kriging estimator in terms of the average kriging variance and the sum of squares error. It was found that additional information at the estimation site is a more important consideration than whether the estimator is linear or nonlinear. Disjunctive kriging produces an estimator of the conditional probability that the value at an unsampled location is greater than an arbitrary cutoff level. This latter feature of disjunctive kriging is explored and has implications in aiding management decisions.
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Karnieli, Arnon. "Mapping the Areal Precipitation over Arizona - Using Kriging Technique." Arizona-Nevada Academy of Science, 1988. http://hdl.handle.net/10150/296409.
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From the Proceedings of the 1988 Meetings of the Arizona Section - American Water Resources Association and the Hydrology Section - Arizona-Nevada Academy of Science - April 16, 1988, University of Arizona, Tucson, Arizona<br>The classical methods for interpolating and spatial averaging of precipitation fields fail to quantify the accuracy of the estimate. On the other hand, kriging is an interpolation method for predicting values of regionalized variables at points (punctual kriging) or average values over an area (block kriging). This paper demonstrates the use of the kriging method for mapping and evaluating precipitation data for the state of Arizona. Using 158 rain gage stations with 30 years or more of record, the precipitation over the state has been modeled as a realization of a two dimensional random field taking into consideration the spatial variability conditions. Three data sets have been used: (1) the mean annual precipitation over the state; (2) the mean summer rainy season; and (3) the mean winter rainy season. Validation of the empirical semi-variogram for a constant drift case indicated that the exponential model was appropriate for all the data sets. In addition to a global kriging analysis, the data have been examined under an anisotropic assumption which reflects the topographic structure of the state.
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Tripathi, Suresh. "Variograms and kriging in the analysis of spatial data." Thesis, Edith Cowan University, Research Online, Perth, Western Australia, 1996. https://ro.ecu.edu.au/theses/970.
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This research is in the area of geostatistics and consists essentially of two parts. The first is an investigation of the variogram and cross variogram and the associated kriging and cokriging methods of spatial prediction and the second is an application of these in the analysis of two (original) data sets. In the first part (chapter 1 to chapter 5), the focus is on summarising and illustrating the various techniques of Exploratory Data Analysis (EDA) and some methods used to estimate and model the experimental variograms and cross variograms for a given data set, together with some of the geostatistical methods of kriging and cokriging used for prediction purposes. The research also illustrates some of the many applications of this theory in the earth and environmental sciences. The second part of the thesis (chapter 6) is an application of these geostatistical techniques to the analysis of two (new) data sets. The first data set consists of the Available Phosphate (in ppm) and Potassium (in ppm) from two fields (one cropped and one uncropped) in the Jimperding Brook area of Western Australia. The second data set consists of the number of species of Banksia at various locations within a region of Southwestern Australia.
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Frey, Othmar. "Strukturanalyse und Filterung von Tomographiedaten einer Sandprobe mit Factorial-Kriging." Zürich : ETH, Eidgenössische Technische Hochschule Zürich, Institut für Terrestrische Ökologie, 2002. http://e-collection.ethbib.ethz.ch/show?type=dipl&nr=85.
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Taylor, Simon H. "Techniques and advantages of kriging seismic time and velocity data /." Title page, table of contents and abstract only, 1986. http://web4.library.adelaide.edu.au/theses/09SB/09sbt246.pdf.
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Ali, Arshad. "Advanced sensor positioning in wireless sensor nerworks using kriging interpolation." Thesis, Lancaster University, 2012. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.659448.
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Wireless Sensor Networks (WSN) have an important role to play in applications involving surveillance, security and autonomous systems. Furthermore, recent technological advances have allowed wireless sensor networks to be applied to a plethora of areas such as environment monitoring, traffic control, health, agriculture, medical, home applications, as well as fire fighting, and object tracking. One of the main, generic WSN requirements is the collection of large amounts of data which can be afterwards used in classification and decision making processes. Within such a general WSN framework, this dissertation studies sensor node positioning strategies. Thus given a fixed number of sensors operating in a completely unknown environment, work is focussed on the development of efficient sensor positioning techniques. Efficiency here relates to i) collection of data in order to characterize (for a given accuracy) the environment, with a minimum number of sensor moving steps i.e. as quickly as possible, and ii) the location and tracking of major features of the environment, for example the maxima of data distributions used to form in simulations the data profile of a given environment. Furthermore, the above WSN movement/positioning methodologies are applied to both data static and data dynamic environments. Note that these methodologies contain two key processes: i) data interpolation; and data prediction as applied to trajectories of moving environment features. Thus WSN data is interpolated using a form of Kriging interpolation whereas prediction is performed using a polynomial based approach. Experimentation has been performed using computer simulation of proposed methods and experimental results are presented in the thesis which allows proposed schemes to be compared in terms of different criteria. Results associated to systems employing ground truth data, as a substitute for ideal interpolation and prediction processes, are also presented and are taken as providing bounds of system performance.
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Frez, Ríos Tamara. "Kriging y simulación secuencial de indicadores con proporciones localmente variables." Tesis, Universidad de Chile, 2014. http://www.repositorio.uchile.cl/handle/2250/116844.
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Ingeniera Civil de Minas<br>En la actualidad, los modelos geológicos son generalmente construidos de modo determinístico, imposibilitando la cuantificación de la incertidumbre asociada. Si bien en la minería se le da mayor enfoque a variables continuas como las leyes minerales, un estudio previo de variables categóricas provee subdivisiones con mayor homogeneidad geológica y estadística. Además se es capaz de agregar información importante sobre procesos mineros posteriores.
El kriging de indicadores con proporciones localmente variables posee una limitante teórica que se pretende mejorar con este estudio. Este método utiliza sólo un variograma global para cada indicador. Dada la influencia que se tiene de las medias de los indicadores sobre su varianza, la meseta del variograma varía con esta media, lo que no se está considerando. Se propone un método que sí considere estas variaciones, utilizando una variable indicador transformada, más específicamente, a la variable indicador se le resta su media variable para centrar en cero, y además se estandariza para eliminar el efecto del cambio de varianza.
El análisis se lleva a cabo a través de dos casos de estudio. El primer estudio consta de la estimación por kriging de indicadores tradicional y con la mejora propuesta, sobre una base de datos sintética con un indicador. A este caso también se le realiza un análisis de sensibilidad para revisar los resultados. El segundo caso de estudio consta de la simulación secuencial de indicadores sobre una base de datos real de una veta, contando con información de un muestreo por canales. Se comparan ambas metodologías y se validan los modelos a través de jack-knife.
De las estimaciones resultantes del primer caso, se hace un estudio de los errores promedio y varianza del kriging promedio. Los resultados para ambas metodologías son similares, a excepción de la varianza del kriging, la cual para el método propuesto presenta menores valores y una alta influencia de la media del indicador. Este resultado se mantiene a pesar de disminuir los datos muestreados y cambiar el variograma de los datos sintéticos.
Las simulaciones del caso de estudio real, en ambas metodologías, resultaron similares. De acuerdo a un análisis de errores cuadráticos, se simularon más bloques con menor error para la metodología propuesta que en la tradicional. Mediante un jack-knife se validan los modelos y se comparan sus porcentajes de aciertos. Ambas metodologías poseen porcentajes de aciertos iguales, incluso con distintos modelos variográficos.
En conclusión, si bien el método propuesto muestra mejoras respecto al método tradicional, estas no son lo suficientemente significativas como para declararlo mejor método. Ambas metodologías presentan resultados de alto porcentaje de acierto, pero entre sí son muy similares. A pesar de esto, el nuevo método presenta las ventajas de tener mayor respaldo teórico, menores tiempos de simulación y una mejor cuantificación de los errores de estimación a través de la varianza del kriging.
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Muñoz, Tolosa Leopoldo Andrés. "Uso de Kriging universal en la simulación condicional de leyes." Tesis, Universidad de Chile, 2015. http://repositorio.uchile.cl/handle/2250/134975.
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Magíster en Minería<br>Ingeniero Civil de Minas<br>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.
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Agarwal, Abhijat. "A New Approach to Spatio-Temporal Kriging and Its Applications." The Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1306871646.
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Huang, Deng. "Experimental planning and sequential kriging optimization using variable fidelity data." Connect to this title online, 2005. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1110297243.
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Thesis (Ph. D.)--Ohio State University, 2005.<br>Title from first page of PDF file. Document formatted into pages; contains xi, 120 p.; also includes graphics (some col.). Includes bibliographical references (p. 114-120). Available online via OhioLINK's ETD Center
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McKeown, Michael. "Kriging, selective mining and profitability of the Prince Lyell Mine." Thesis, Federation University Australia, 1996. http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/164936.
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The thesis describes a good kriged resource model which if adopted would enable The Prince Lyell Mine to increase copper production and thus be better able to cope with falling copper prices.<br>Master of Engineering Science
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Mohammadi, Hossein. "Kriging-based black-box global optimization : analysis and new algorithms." Thesis, Lyon, 2016. http://www.theses.fr/2016LYSEM005/document.
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L’«Efficient Global Optimization» (EGO) est une méthode de référence pour l’optimisation globale de fonctions «boites noires» coûteuses. Elle peut cependant rencontrer quelques difficultés, comme le mauvais conditionnement des matrices de covariance des processus Gaussiens (GP) qu’elle utilise, ou encore la lenteur de sa convergence vers l’optimum global. De plus, le choix des paramètres du GP, crucial car il contrôle la famille des fonctions d’approximation utilisées, mériterait une étude plus poussée que celle qui en a été faite jusqu’à présent. Enfin, on peut se demander si l’évaluation classique des paramètres du GP est la plus appropriée à des fins d’optimisation. \\Ce travail est consacré à l'analyse et au traitement des différentes questions soulevées ci-dessus.La première partie de cette thèse contribue à une meilleure compréhension théorique et pratique de l’impact des stratégies de régularisation des processus Gaussiens, développe une nouvelle technique de régularisation, et propose des règles pratiques. Une seconde partie présente un nouvel algorithme combinant EGO et CMA-ES (ce dernier étant un algorithme d’optimisation globale et convergeant). Le nouvel algorithme, nommé EGO-CMA, utilise EGO pour une exploration initiale, puis CMA-ES pour une convergence finale. EGO-CMA améliore les performances des deux algorithmes pris séparément. Dans une troisième partie, l’effet des paramètres du processus Gaussien sur les performances de EGO est soigneusement analysé. Finalement, un nouvel algorithme EGO auto-adaptatif est présenté, dans une nouvelle approche où ces paramètres sont estimés à partir de leur influence sur l’efficacité de l’optimisation elle-même<br>The Efficient Global Optimization (EGO) is regarded as the state-of-the-art algorithm for global optimization of costly black-box functions. Nevertheless, the method has some difficulties such as the ill-conditioning of the GP covariance matrix and the slow convergence to the global optimum. The choice of the parameters of the GP is critical as it controls the functional family of surrogates used by EGO. The effect of different parameters on the performance of EGO needs further investigation. Finally, it is not clear that the way the GP is learned from data points in EGO is the most appropriate in the context of optimization. This work deals with the analysis and the treatment of these different issues. Firstly, this dissertation contributes to a better theoretical and practical understanding of the impact of regularization strategies on GPs and presents a new regularization approach based on distribution-wise GP. Moreover, practical guidelines for choosing a regularization strategy in GP regression are given. Secondly, a new optimization algorithm is introduced that combines EGO and CMA-ES which is a global but converging search. The new algorithm, called EGO-CMA, uses EGO for early exploration and then CMA-ES for final convergence. EGO-CMA improves the performance of both EGO and CMA-ES. Thirdly, the effect of GP parameters on the EGO performance is carefully analyzed. This analysis allows a deeper understanding of the influence of these parameters on the EGO iterates. Finally, a new self-adaptive EGO is presented. With the self-adaptive EGO, we introduce a novel approach for learning parameters directly from their contribution to the optimization
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Sen, Oishik. "Multiscale modeling of multimaterial systems using a Kriging based approach." Diss., University of Iowa, 2016. https://ir.uiowa.edu/etd/2274.
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The present work presents a framework for multiscale modeling of multimaterial flows using surrogate modeling techniques in the particular context of shocks interacting with clusters of particles. The work builds a framework for bridging scales in shock-particle interaction by using ensembles of resolved mesoscale computations of shocked particle laden flows. The information from mesoscale models is “lifted” by constructing metamodels of the closure terms - the thesis analyzes several issues pertaining to surrogate-based multiscale modeling frameworks.
First, to create surrogate models, the effectiveness of several metamodeling techniques, viz. the Polynomial Stochastic Collocation method, Adaptive Stochastic Collocation method, a Radial Basis Function Neural Network, a Kriging Method and a Dynamic Kriging Method is evaluated. The rate of convergence of the error when used to reconstruct hypersurfaces of known functions is studied. For sufficiently large number of training points, Stochastic Collocation methods generally converge faster than the other metamodeling techniques, while the DKG method converges faster when the number of input points is less than 100 in a two-dimensional parameter space. Because the input points correspond to computationally expensive micro/meso-scale computations, the DKG is favored for bridging scales in a multi-scale solver.
After this, closure laws for drag are constructed in the form of surrogate models derived from real-time resolved mesoscale computations of shock-particle interactions. The mesoscale computations are performed to calculate the drag force on a cluster of particles for different values of Mach Number and particle volume fraction. Two Kriging-based methods, viz. the Dynamic Kriging Method (DKG) and the Modified Bayesian Kriging Method (MBKG) are evaluated for their ability to construct surrogate models with sparse data; i.e. using the least number of mesoscale simulations. It is shown that unlike the DKG method, the MBKG method converges monotonically even with noisy input data and is therefore more suitable for surrogate model construction from numerical experiments.
In macroscale models for shock-particle interactions, Subgrid Particle Reynolds’ Stress Equivalent (SPARSE) terms arise because of velocity fluctuations due to fluid-particle interaction in the subgrid/meso scales. Mesoscale computations are performed to calculate the SPARSE terms and the kinetic energy of the fluctuations for different values of Mach Number and particle volume fraction. Closure laws for SPARSE terms are constructed using the MBKG method. It is found that the directions normal and parallel to those of shock propagation are the principal directions of the SPARSE tensor. It is also found that the kinetic energy of the fluctuations is independent of the particle volume fraction and is 12-15% of the incoming shock kinetic energy for higher Mach Numbers.
Finally, the thesis addresses the cost of performing large ensembles of resolved mesoscale computations for constructing surrogates. Variable fidelity techniques are used to construct an initial surrogate from ensembles of coarse-grid, relative inexpensive computations, while the use of resolved high-fidelity simulations is limited to the correction of initial surrogate. Different variable-fidelity techniques, viz the Space Mapping Method, RBFs and the MBKG methods are evaluated based on their ability to correct the initial surrogate. It is found that the MBKG method uses the least number of resolved mesoscale computations to correct the low-fidelity metamodel. Instead of using 56 high-fidelity computations for obtaining a surrogate, the MBKG method constructs surrogates from only 15 resolved computations, resulting in drastic reduction of computational cost.
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Muré, Joseph. "Objective Bayesian analysis of Kriging models with anisotropic correlation kernel." Thesis, Sorbonne Paris Cité, 2018. http://www.theses.fr/2018USPCC069/document.
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Les métamodèles statistiques sont régulièrement confrontés au manque de données qui engendre des difficultés à estimer les paramètres. Le paradigme bayésien fournit un moyen élégant de contourner le problème en décrivant la connaissance que nous avons des paramètres par une loi de probabilité a posteriori au lieu de la résumer par une estimation ponctuelle. Cependant, ce paradigme nécessite de définir une loi a priori adéquate, ce qui est un exercice difficile en l'absence de jugement d'expert. L'école bayésienne objective propose des priors par défaut dans ce genre de situation telle que le prior de référence de Berger-Bernardo. Un tel prior a été calculé par Berger, De Oliveira and Sansó [2001] pour le modèle de krigeage avec noyau de covariance isotrope. Une extension directe au cas des noyaux anisotropes poserait des problèmes théoriques aussi bien que pratiques car la théorie de Berger-Bernardo ne peut s'appliquer qu'à un jeu de paramètres ordonnés. Or dans ce cas de figure, tout ordre serait nécessairement arbitraire. Nous y substituons une solution bayésienne objective fondée sur les posteriors de référence conditionnels. Cette solution est rendue possible par une théorie du compromis entre lois conditionnelles incompatibles. Nous montrons en outre qu'elle est compatible avec le krigeage trans-gaussien. Elle est appliquée à un cas industriel avec des données non-stationnaires afin de calculer des Probabilités de Détection de défauts (POD de l'anglais Probability Of Detection) par tests non-destructifs dans les tubes de générateur de vapeur de centrales nucléaires<br>A recurring problem in surrogate modelling is the scarcity of available data which hinders efforts to estimate model parameters. The Bayesian paradigm offers an elegant way to circumvent the problem by describing knowledge of the parameters by a posterior probability distribution instead of a pointwise estimate. However, it involves defining a prior distribution on the parameter. In the absence of expert opinion, finding an adequate prior can be a trying exercise. The Objective Bayesian school proposes default priors for such can be a trying exercise. The Objective Bayesian school proposes default priors for such situations, like the Berger-Bernardo reference prior. Such a prior was derived by Berger, De Oliveira and Sansó [2001] for the Kriging surrogate model with isotropic covariance kernel. Directly extending it to anisotropic kernels poses theoretical as well as practical problems because the reference prior framework requires ordering the parameters. Any ordering would in this case be arbitrary. Instead, we propose an Objective Bayesian solution for Kriging models with anisotropic covariance kernels based on conditional reference posterior distributions. This solution is made possible by a theory of compromise between incompatible conditional distributions. The work is then shown to be compatible with Trans-Gaussian Kriging. It is applied to an industrial case with nonstationary data in order to derive Probability Of defect Detection (POD) by non-destructive tests in steam generator tubes of nuclear power plants
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Klimprová, Lucie. "Regresní metody pro statistickou analýzu prostorových dat." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2009. http://www.nusl.cz/ntk/nusl-228884.
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Kriging techniques are regression methods used for evaluation of continuous spatial processes. If the covariance structure of process is unknown, then it's necessary to estimate it from the data. The first part of this Master's thesis is devoted to description the kriging method and to estimate of a variogram fuction, which describes the covariance structure of considered process. The second part includes the implementation of kriging method in MATLAB for simulated and real data.
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Naderpour, Nader 1959. "Application of kriging to study spacial variability of soil physical properties." Thesis, McGill University, 1986. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=65963.
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Harris, Paul. "An empirical comparison of kriging methods for nonstationary spatial point prediction." Thesis, University of Newcastle Upon Tyne, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.492440.
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This thesis compares the performance of geostatistical and geostatistical nonparametric hybrid models for providing accurate predictions together with relevant measures of prediction confidence. The key modelling theme is nonstationarity, where models that cater for nonstationary second-order effects nave the potential to provide more accurate results over their stationary counterparts. A comprehensive review and comparison of this particular class of nonstationary predictors is considered missing from the literature. To facilitate this model comparison, models are calibrated to assess the spatial variation in freshwater acidification critical load data across Great Britain, which is shown to be a heterogeneous process requiring a nonstationary modelling approach.
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Freier, Lars [Verfasser]. "Kriging Based Data Analysis and Experimental Design in Biotechnology / Lars Freier." Düsseldorf : Universitäts- und Landesbibliothek der Heinrich-Heine-Universität Düsseldorf, 2018. http://d-nb.info/1152436848/34.
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Rumhy, Mohammed Hamed. "A conditional kriging approach for ascribing permeability distribution in porous media." Thesis, Imperial College London, 1990. http://hdl.handle.net/10044/1/46530.
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Ilyas, Maryam. "Quantification of uncertainties in global temperatures using multi-resolution lattice kriging." Thesis, University College London (University of London), 2018. http://discovery.ucl.ac.uk/10056978/.
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Temperature measurements are subject to uncertainties. Temperature observations are sparsely available over the surface of the earth. The uncertainties in temperatures due to these gaps in spatial coverage is quanti fied using multi-resolution lattice kriging (MRLK). These uncertainties are combined with the existing estimates of the observational uncertainties. It results in a monthly temperature data product from 1850-2016. A new approximate Bayesian methodology is proposed for spatial data analysis. It relies on spatial dependence of the data using the variogram. This methodology is integrated with the multi-resolution lattice kriging (MRLK) model. It results in an approximate Bayesian inference for MRLK. The MRLK with the approximate Bayesian framework is used to generate another temperature data set. It samples the observational and coverage uncertainties in temperatures but also accounts for the model parametric uncertainties. The two sets of monthly temperature data products created in this thesis provide the uncertainties in temperatures at a regional scale. Therefore, a probabilistic El Niño Southern Oscillation (ENSO) index is invented that reflects the regional estimates of temperature uncertainties. This defi nition is applied to both versions of temperature data sets. During the pre-industrial period, fewer temperature measurements are available. Therefore, there is uncertainty in the pre-industrial baseline temperatures. Uncertainties in the pre-industrial baseline are integrated with the observational, coverage and parametric uncertainties. The results suggest that the uncertainties mainly dominate early temperature records. However, the uncertainty in temperatures due to the uncertain pre-industrial baseline stays same throughout the time series.
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Silva, Abel Brasil Ramos da. "Estimation of curves indifference accessibility via urban models and ordered kriging." Universidade Federal do CearÃ, 2013. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=10042.
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Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico<br>O processo de urbanizaÃÃo, crescimento das cidades e estruturaÃÃo urbana ocorrido nas Ãltimas
dÃcadas nas grandes cidades brasileiras vem colocando a questÃo da acessibilidade como fator
relevante na qualidade de vida da populaÃÃo. Neste contexto, analisar rigorosamente o nÃvel de
acessibilidade e o bem-estar dos indivÃduos a partir do momento que deixam suas residÃncias
atà o ponto de execuÃÃo de atividades ou satisfaÃÃo de consumo torna-se uma questÃo de grande
importÃncia cientÃfica ainda pouco explorada de maneira rigorosa. Nesta dissertaÃÃo buscamos
analisar e modelar acessibilidade considerando uma perspectiva teÃrica baseada na metodologia
da maximizaÃÃo da utilidade e na estimaÃÃo de modelos economÃtricos. Para tanto, este estudo
està dividindo em dois eixos de pesquisa: o primeiro, analisa a acessibilidade com o uso de modelos
ordenados generalizados atravÃs de uma base inÃdita de micro dados geo-referenciados
coletada na cidade de Fortaleza, Brasil. Os resultados mostram que variÃveis como renda, posse
de automÃveis, distÃncia, entre outras, sÃo importantes para explicar a acessibilidade dos indivÃduos.
O segundo eixo de anÃlise propÃe e desenvolve, de maneira pioneira, uma superfÃcie de
utilidade espacial atravÃs de tÃcnicas de krigagem. Os resultados mostram que a distÃncia entre
o domicÃlio e o ponto de destino possui uma relaÃÃo bastante heterogÃnea com a acessibilidade,
revelando um padrÃo espacial influenciado pela desigualdade econÃmica da cidade. Esse resultado
coloca em dÃvida suposiÃÃes simplistas tradicionais que assumem uma relaÃÃo linear ou
polinomial entre distÃncia e acessibilidade.<br>The process of urbanization, growth of cities and urban structuring in recent decades among
large Brazilian cities revealed the issue of accessibility as a relevant factor in quality of life.
In this sense, analyzing the level of accessibility and welfare of individuals from where they
leave their homes up to the point of execution of activities or consumer satisfaction becomes
a matter of great scientific importance, yet to be explored in rigorously way. Thus, in this dissertation
we analyze and model urban accessibility considering a theoretical perspective based
on the methodology of utility maximization and estimation of econometric models. Therefore,
this study is divided into two lines of research. The first one analyzes the accessibility using
generalized ordered models through a new geo-referenced micro data set collected in the city
of Fortaleza, Brazil. Our results show that variables such as income, car ownership, distance,
and others are important for explaining accessibility of individuals. The second line of inquiry
proposes and develops, in a pioneering way, a surface of spatial utility by means of Kriging
techniques. The results point to the fact that the distance between home and destination has a
very heterogeneous relationship with accessibility, revealing a spatial pattern greatly influenced
by the prevailing economic inequalities all over the city. This result puts into question simplistic
traditional assumptions that assume a linear or polynomial relation between distance and accessibility.
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Ben, salem Malek. "Model selection and adaptive sampling in surrogate modeling : Kriging and beyond." Thesis, Lyon, 2018. https://tel.archives-ouvertes.fr/tel-03097719.
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Les surfaces de réponses, dites aussi méta-modèles sont généralement utilisées pour remplacer une fonction coûteuse. Ces méta-modèles sont également utilisés pour accélérer l’estimation d’une caractéristique de cette fonction (un optimum, une ligne de niveau, …). Dans ce travail, nous nous sommes intéressés à trois aspects de la méta-modélisation.1/ Il est difficile de choisir le méta-modèle ainsi que ses paramètres les plus appropriés pour un plan d’expérience donné. En effet, il est difficile d'évaluer la qualité d'un méta-modèle sans des données de validation. Nous proposons un critère de qualité de méta-modèle et nous présentons deux algorithmes de sélection en se basant sur ce critère.2/ L’avantage principal de la régression par processus gaussiens (GP) est qu'elle fournit partout une mesure d'incertitude associée à la prédiction. C’est un outil efficace pour construire des stratégies d’échantillonnage séquentiel. Nous proposons un algorithme permettant d'estimer une distribution de prédiction pour n'importe quel méta-modèle, qui permet d’étendre les méthodes d’échantillonnage séquentielles basées sur les GP à tous les méta-modèles. On l'appelle la distribution universelle de prédiction.3/ De nombreux problèmes de conception font appel à un grand nombre de variables ce qui rend l'exploration de l’espace paramétrique difficile. Dans certains cas seules quelques variables sont influentes. Nous proposons un algorithme réalisant simultanément l'apprentissage d'une caractéristique et la réduction de dimension. La méthode est basée sur des résultats théoriques issus du cadre de la régression par processus gaussien. Notre méthode s'appelle l’algorithme Split-and-Doubt<br>Surrogate models are used to replace an expensive-to-evaluate function to speed-up the estimation of a feature of a given function (optimum, contour line, …). Three aspects of surrogate modeling are studied in the work:1/ We proposed two surrogate model selection algorithms. They are based on a novel criterion called the penalized predictive score. 2/ The main advantage of probabilistic approach is that it provides a measure of uncertainty associated with the prediction. This uncertainty is an efficient tool to construct strategies for various problems such as prediction enhancement, optimization or inversion. We defined a universal approach for uncertainty quantification that could be applied for any surrogate model. It is based on a weighted empirical probability measure supported by cross-validation sub-models’ predictions.3/ We present the so-called Split-and-Doubt algorithm that performs sequentially both feature estimation and dimension reduction
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Rehman, Salim Ur. "Semiparametric modeling of cross-semivariograms." Diss., Georgia Institute of Technology, 1995. http://hdl.handle.net/1853/24587.
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Angulo, Argote Juan Daniel. "Metodología para la optimización de la malla de muestreo de corto plazo de lateritas niquelíferas." Tesis, Universidad de Chile, 2018. http://repositorio.uchile.cl/handle/2250/159302.
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Magíster en Minería<br>Las lateritas niquelíferas son una fuente generadora de la materia prima del acero inoxidable, el níquel. Dicho elemento se encuentra presente en diferentes tipos de rocas que son formadas por procesos externos que alteran, meteorizan y por último transforman la roca madre del depósito.
La presencia de diferentes tipos de rocas, desde el punto de vista físico, químico, mecánico y, por último, de su contenido en mineralización en porcentajes (%) de níquel, hierro, magnesio, sílice, alúmina, entre otros, sugiere que cada tipo de roca debe estudiarse en forma propia. Cada perfil de meteorización o dominio geológico, conformado por diferentes tipos de rocas, tiene un comportamiento geoespacial diferente debido al proceso geológico de formación y enriquecimiento del depósito.
Surge entonces la pregunta de cómo diseñar una metodología para muestrear el perfil de meteorización para la optimización de la malla de muestreo a corto plazo, partiendo del muestreo realizado en exploración, para generar el respectivo modelo de recurso.
La metodología que se propone para determinar la malla de muestreo a corto plazo en lateritas niquelíferas, es la siguiente: análisis exploratorio y variográfico de datos espaciales, seguido de la construcción de múltiples escenarios mediante simulación Gaussiana secuencial y, a partir de los escenarios obtenidos, categorización de los recursos en cada dominio geológico usando gráficos tonelaje-ley sobre una ley de corte vs coeficiente de variación condicional (CCV). Lo anterior se aplica a varias mallas de muestreo tentativas para cada dominio geológico y permite estudiar y analizar la relación CBNT (relación costo/benefico, número-tiempo de muestras preparadas-analizadas en el laboratorio, tiempo en perforar cada dominio con su respectiva malla propuesta) para determinar la malla óptima de corto plazo en cada dominio.
Se ilustra la propuesta con un caso de estudio de una zona particular de una laterita niquelífera subdividida en tres dominios geológicos que cubren todo el perfil de meteorización.
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Paulionienė, Laura. "Erdvės - laiko duomenų statistinis modeliavimas, pagrįstas laiko eilučių parametrų erdviniu interpoliavimu." Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2014. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2013~D_20140117_113103-58499.
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Disertaciniame darbe nagrinėjama erdvės – laiko duomenų modeliavimo problema. Dažnai erdvinių duomenų rinkiniai yra gana nedideli, o taškai, kuriuose pasklidę stebėjimai, išsidėstę netaisyklingai. Sprendžiant „erdvinį“ uždavinį, paprastai siekiama inerpoliuoti arba įvertinti erdvinį vidurkį. Laiko eilučių duomenys dažniausiai naudojami ateities reikšmėms prognozuoti. Tuo tarpu erdvės – laiko uždaviniai jungia abu uždavinių tipus. Pasiūlyta keletas originalių erdvinių laiko eilučių modeliavimo metodų. Siūlomi metodai pirmiausia analizuoja vienmates laiko eilutes, o pašalinus laikinę priklausomybė jose, laiko eilučių liekanoms vertinama erdvinė priklausomybė. Tikslas – sudaryti modelį, leidžiantį prognozuoti požymio reikšmę naujame, nestebėtame taške, nauju laiko momentu. Tokio modelio sudarymas remiasi laiko eilučių parametrų erdviniu interpoliavimu.<br>Space – time data modeling problem is analysed. Often spatial data sets are relatively small, and the points, where observations are taken, are located irregularly. When solving spatial task, usually we are interpolating or estimating the spatial average. Time series data usually are used to predict future values. Meanwhile, the space - time tasks combines both types of tasks. Few original modeling methods of spatial time series are proposed. The proposed methods firstly analyzes the univariate time series, and after removing temporal dependence, spatial dependence in the time series of residuals is measured. Aim of this dissertational work - to create time series model at new unobserved location by incorporating spatial interaction thru spatial interpolation of estimated time series parameters. Such a model is based on the spatial interpolation of time series parameters.
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Paulionienė, Laura. "Statistical modelling of spatio-temporal data based on spatial interpolation of time series parameters." Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2014. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2013~D_20140117_113114-31261.
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Space – time data modeling problem is analysed. Often spatial data sets are relatively small, and the points, where observations are taken, are located irregularly. When solving spatial task, usually we are interpolating or estimating the spatial average. Time series data usually are used to predict future values. Meanwhile, the space - time tasks combines both types of tasks. Few original modeling methods of spatial time series are proposed. The proposed methods firstly analyzes the univariate time series, and after removing temporal dependence, spatial dependence in the time series of residuals is measured. Aim of this dissertational work - to create time series model at new unobserved location by incorporating spatial interaction thru spatial interpolation of estimated time series parameters. Such a model is based on the spatial interpolation of time series parameters.<br>Disertaciniame darbe nagrinėjama erdvės – laiko duomenų modeliavimo problema. Dažnai erdvinių duomenų rinkiniai yra gana nedideli, o taškai, kuriuose pasklidę stebėjimai, išsidėstę netaisyklingai. Sprendžiant „erdvinį“ uždavinį, paprastai siekiama inerpoliuoti arba įvertinti erdvinį vidurkį. Laiko eilučių duomenys dažniausiai naudojami ateities reikšmėms prognozuoti. Tuo tarpu erdvės – laiko uždaviniai jungia abu uždavinių tipus. Pasiūlyta keletas originalių erdvinių laiko eilučių modeliavimo metodų. Siūlomi metodai pirmiausia analizuoja vienmates laiko eilutes, o pašalinus laikinę priklausomybė jose, laiko eilučių liekanoms vertinama erdvinė priklausomybė. Tikslas – sudaryti modelį, leidžiantį prognozuoti požymio reikšmę naujame, nestebėtame taške, nauju laiko momentu. Tokio modelio sudarymas remiasi laiko eilučių parametrų erdviniu interpoliavimu.
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Jiang, Dongxiang. "The application of Kriging technique to mathematical modelling of estuarine water quality." Thesis, University of Newcastle Upon Tyne, 1989. http://hdl.handle.net/10443/530.
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It is essential that estuarine modelling and surveying are carried out simultaneously because not only does the latter provide data required by the former but also the former is verified with data from the latter. This study integrates both research subjects from the panoramic point of view, aiming at improving modelling accuracy and reliability and increasing survey efficiency. Partially stratified estuaries are the most difficult types of estuaries to be modelled, in particular, the velocity field in such an estuary. A review of two commonly used methods to determine the velocity field, i. e., theoretical method and empirical method, revealed their inadequacies in real applications. Thus, a new approach using Kriging technique was originated and was tested on a finite element model of water quality. The model was formulated using a Galerkinfinite element method and was programmed in Fortran. Comparison between the simulation results and the field measurements for a salinity intrusion showed a high simulation accuracy. It is believed that the model in combination with the new approach would be a useful tool for estuarine modelling. The generalized Kriging method ensured that the new approach would be appropriate in practice. It was also applied to the investigation of sampling stations in the partially mixed estuary of the River Tees. It is essential to know how many sampling stations should be used and how they should be positioned. Two procedures were designed for solving the survey problems. They were the procedure of overall variance and the procedure of re-estimation. These procedures were capable of quantifing the relative significance of each sampling station and detecting redundant sampling stations. The 1975 survey was investigated, and useful conclusions were obtained.
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Maxwell, Peter. "FFLUX : towards a force field based on interacting quantum atoms and kriging." Thesis, University of Manchester, 2017. https://www.research.manchester.ac.uk/portal/en/theses/fflux-towards-a-force-field-based-on-interacting-quantum-atoms-and-kriging(72a8462a-6907-4f3d-82da-4c182e5a644d).html.
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Force fields have been an integral part of computational chemistry for decades, providing invaluable insight and facilitating the better understanding of biomolecular system behaviour. Despite the many benefits of a force field, there continue to be deficiencies as a result of the classical architecture they are based upon. Some deficiencies, such as a point charge electrostatic description instead of a multipole moment description, have been addressed over time, permitted by the ever-increasing computational power available. However, whilst incorporating such significant improvements has improved force field accuracy, many still fail to describe several chemical effects including polarisation, non-covalent interactions and secondary/tertiary structural effects. Furthermore, force fields often fail to provide consistency when compared with other force fields. In other words, no force field is reliably performing more accurately than others, when applied to a variety of related problems. The work presented herein develops a next-generation force field entitled FFLUX, which features a novel architecture very different to any other force field. FFLUX is designed to capture the relationship between geometry and energy through a machine learning method known as kriging. Instead of a series of parameterised potentials, FFLUX uses a collection of atomic energy kriging models to make energy predictions. The energies describing atoms within FFLUX are obtained from the Interacting Quantum Atoms (IQA) energy partitioning approach, which in turn derives the energies from the electron density and nuclear charges of topological atoms described by Quantum Chemical Topology (QCT). IQA energies are shown to provide a unique insight into the relationship between geometry and energy, allowing the identification of explicit atoms and energies contributing towards torsional barriers within various systems. The IQA energies can be modelled to within 2.6% accuracy, as shown for a series of small systems including weakly bound complexes. The energies also allow an interpretation of how an atom feels its surrounding environment through intra-atomic, covalent and electrostatic energetic descriptions, which typically are seen to converge within a ~7 - 8 A horizon radius around an atom or small system. These energy convergence results are particularly relevant to tackling the transferability theme within force field development. Where energies are seen to converge, a proximity limit on the geometrical description needed for a transferable energy model is defined. Finally, the FFLUX force field is validated through successfully optimising distorted geometries of a series of small molecules, to near-ab initio accuracy.
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Huang, Changwu. "Kriging-assisted evolution strategy for optimization and application in material parameters identification." Thesis, Normandie, 2017. http://www.theses.fr/2017NORMIR05.
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Afin de réduire le coût de calcul pour des problèmes d'optimisation coûteuse, cette thèse a été consacrée à la Stratégie d'Evolution avec Adaptation de Matrice de Covariance assistée par modèle de Krigeage (KA-CMA-ES). Plusieurs algorithmes de KA-CMA-ES ont été développés et étudiés. Une application de ces algorithmes KA-CMA-ES développés est réalisée par l'identification des paramètres matériels avec un modèle constitutif d'endommagement élastoplastique. Les résultats expérimentaux démontrent que les algorithmes KA-CMA-ES développés sont plus efficaces que le CMA-ES standard. Ils justifient autant que le KA-CMA-ES couplé avec ARP-EI est le plus performant par rapport aux autres algorithmes étudiés dans ce travail. Les résultats obtenus par l'algorithme ARP-EI dans l'identification des paramètres matériels montrent que le modèle d'endommagement élastoplastique utilisé est suffisant pour décrire le comportement d'endommage plastique et ductile. Ils prouvent également que la KA-CMA-ES proposée améliore l'efficace de la CMA-ES. Par conséquent, le KA-CMA-ES est plus puissant et efficace que CMA-ES pour des problèmes d'optimisation coûteuse<br>In order to reduce the cost of solving expensive optimization problems, this thesis devoted to Kriging-Assisted Covariance Matrix Adaptation Evolution Strategy (KA-CMA-ES). Several algorithms of KA-CMA-ES were developed and a comprehensive investigation on KA-CMA-ES was performed. Then applications of the developed KA-CMA-ES algorithm were carried out in material parameter identification of an elastic-plastic damage constitutive model. The results of experimental studies demonstrated that the developed KA-CMA-ES algorithms generally are more efficient than the standard CMA-ES and that the KA-CMA-ES using ARP-EI has the best performance among all the investigated KA-CMA-ES algorithms in this work. The results of engineering applications of the algorithm ARP-EI in material parameter identification show that the presented elastic-plastic damage model is adequate to describe the plastic and ductile damage behavior and also prove that the proposed KA-CMA-ES algorithm apparently improve the efficiency of the standard CMA-ES. Therefore, the KA-CMA-ES is more powerful and efficient than CMA-ES for expensive optimization problems
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Wood, Michael James. "An exploration of building design and optimisation methods using Kriging meta-modelling." Thesis, University of Exeter, 2016. http://hdl.handle.net/10871/24974.
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This thesis investigates the application of Kriging meta-modelling techniques in the field of building design and optimisation. In conducting this research, there were two key motivational factors. The first is the need for building designers to have tools that allow low energy buildings to be designed in a fast and efficient manner. The second motivating factor is the need for optimisation tools that account, or help account, for the wide variety of uses that a building might have; so-called Robust Optimisation (RO). This thesis therefore includes an analysis of Kriging meta-modelling and first applies this to simple building problems. I then use this simple building model to determine the effect of the updated UK Test Reference Years (TRYs) on energy consumption. Second, I examine Kriging-based optimisation techniques for a single objective. I then revisit the single-building meta-model to examine the effect of uncertainty on a neighbourhood of buildings and compare the results to the output of a brute-force analysis of a full building simulator. The results show that the Kriging emulation is an effective tool for creating a meta-model of a building. The subsequent use in the analysis of the effect of TRYs on building shows that UK buildings are likely to use less heating in the future but are likely to overheat more. In the final two chapters I use the techniques developed to create a robust building optimisation algorithm as well as using Kriging to improve the optimisation efficiency of the well-known NSGA-II algorithm. I show that the Kriging-based robust optimiser effectively finds more robust solutions than traditional global optimisation. I also show that Kriging techniques can be used to augment NSGA-II so that it finds more diverse solutions to some types of multi-objective optimisation problems. The results show that Kriging has significant potential in this field and I reveal many potential areas of future research. This thesis shows how a Kriging-enhanced NSGA-II multi-objective optimisation algorithm can be used to improve the performance of NSGA-II. This new algorithm has been shown to speed up the convergence of some multi-objective optimisation algorithms significantly. Although further work is required to verify the results for a wider variety of building applications, the initial results are promising.
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Chandra, Sekhar D. "Stochastic engineering simulations using sparse grid collocation method and Kriging based approaches." Thesis, University of Southampton, 2017. https://eprints.soton.ac.uk/418266/.
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The estimation of probabilistic moments is central to robust design process. Typically one would like to estimate the mean and variance of some performance critical metric such as stress, life, etc., of a component in any engineering system, aiming a robustly optimized design that is less sensitive to the input variations/uncertainties. For complex aerospace engineering systems such as aero-engine, a single numerical simulation of any component can often take a substantial amount of time and few samples can be afforded at which the deterministic simulations can be carried out. Considering the variations in the parameters and performing a large number of simulations on such problems is unrealistic and necessitate the improvement of existing UQ approaches. In this study, we present the significance of probabilistic moment estimation approaches for uncertainty quantification and its importance in robust design optimization studies. The background for few popular approaches is provided, where emphasis is put on sparse grid collocation method, adaptive sparse grid collocation approach and Kriging based Bayesian approaches. A non-intrusive multi-point adaptive strategy using sparse grid based collocation design and Kriging based approaches is proposed to reduce the problems arising in high dimensional probabilistic moment estimation studies. The comparison of multi-point adaptive approach with other existing approaches for probabilistic moment estimation in terms of efficiency and accuracy is provided. Further on, the effectiveness of the proposed approach is demonstrated for few mathematical test functions and stochastic structural problems with varying dimensionality and strong interaction among the random variables.
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Schneider, Grant W. "Maximum Likelihood Estimation for Stochastic Differential Equations Using Sequential Kriging-Based Optimization." The Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1406912247.
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Wang, Zeyu. "Reliability Analysis and Updating with Meta-models: An Adaptive Kriging-Based Approach." The Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1574789534726544.
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Wang, Dezhi. "Kriging regression in digital image correlation for error reduction and uncertainty quantification." Thesis, University of Liverpool, 2015. http://livrepository.liverpool.ac.uk/2029379/.
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Digital Image Correlation (DIC) is a widely used full-field measurement technique in the field of experimental mechanics because of its simplicity and ease of implementation. However, owing to the inherent complexity of DIC error sources, the problem of DIC error reduction and uncertainty quantification is still unsolved and has received considerable attention in recent years. The existing work on DIC error reduction is usually focused on specific error sources, e.g. local smoothing techniques are normally applied to reduce errors due to image acquisition noise. Moreover, DIC uncertainty quantification methods are usually derived from a subset-based DIC framework with an assumption of Gaussian image noise. Established methods are normally subject to an ad-hoc choice of parameterisation and might only be able to achieve a local optimum. On the other hand, originally developed in geo-statistics, Kriging is known as optimal interpolation to predict interpolated values using random variables as a realization of a Gaussian process. The Kriging technique has the excellent capability in global optimisation and uncertainty quantification. It is advisable to make an attempt to introduce the Kriging method to DIC to facilitate the solution of error and uncertainty issue. The main purpose of this thesis is to offer a generic and global method that can reduce general DIC errors and quantify measurement uncertainty for displacement and strain results based on Kriging regression from Gaussian Process (GP) and Bayesian perspective. Firstly, a new global DIC approach known as Kriging-DIC was developed through incorporating the Kriging regression model into the classical global DIC algorithm as a full-field shape function. The displacement field of the Region of Interest (RoI) is formulated as a best linear unbiased realisation that contains correlations between all the samples. The measurement errors of control points are accounted for through a global regularisation technique using a global error factor. With the aid of the Mean Squared Error (MSE) determined from the Kriging model, a self-adaptive updating strategy was developed to achieve an optimal control grid without artificial supervision. The developed Kriging DIC method was compared with subset-based DIC, FE-DIC and B-Spline DIC by using synthetic images and open-access experimental data. The effectiveness and robustness of Kriging DIC was verified by numerical examples and an experimental I-section beam test. Secondly, a Kriging-based DIC uncertainty quantification method was proposed to quantify uncertainty of displacement and strain results of the subset-based DIC through a post-processing analysis based on Kriging regression. The subset-by-subset uncertainty was estimated through the subset-based DIC framework and derived as a function of the inverse of the Hessian matrix and residual of Sum of Squared Difference (SSD). This local subset-based uncertainty was then integrated into Kriging regression formula allowing uncertainty quantification of displacement field from a global sense. Based on Cholesky decomposition and covariance matrix solved by the Kriging formula, a multivariate normal sampling process was used to quantify the strain uncertainty whereas displacement gradients were calculated by a Finite Difference technique. Both numerical case studies and an experimental cantilever beam test were employed to test the method, which was found to be able to improve the accuracy of displacement and strain results and quantify corresponding uncertainties. Furthermore, a new approach was developed to calculate strain results by means of Kriging gradients, which was also compared with a state-of-the-art PLS local fitting algorithm. In summary, the main contribution of this thesis is the development of a global DIC algorithm (i.e. Kriging-DIC) and a Kriging-based DIC uncertainty quantification approach. These two methods provide great potential to globally improve DIC measurement accuracy and quantify uncertainties of displacement and strain results.
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Moody, Marla Marie. "Constrained optimal neighborhoods and kernel estimators as improvements to applications of kriging." Diss., The University of Arizona, 1993. http://hdl.handle.net/10150/186233.
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The motivation for this dissertation is to develop innovations in spatial, environmental data analyses, using kriging and kernel estimation, that form a basis for an eventual automation of the calculations. Special consideration should be given to the different requirements for environmental data as compared to the mining data generally used in the evaluation of kriging applications. It is common to use standard search neighborhoods in the applications of kriging. It is one object of this dissertation to develop variable search neighborhoods and to extend the use of these search neighborhoods to experimental variogram calculations. Other objectives include incorporating one dimensional kernel estimation into variogram calculation; and augmenting kriging with two and three dimensional kernel estimators. These three different areas require the development of programs to accomplish the following: (1) Generate elliptical neighborhoods with variable parameters in two dimensions and ellipsoidal neighborhoods with variable parameters in three dimensions; and calculate experimental variograms using these neighborhoods to limit the number of data pairs used and thereby reduce the effects of drift. (2) Calculate experimental variograms with a one dimensional kernel to separate the bin width from the number of points which is not possible with the standard experimental variogram. (3) Use two or three dimensional kernel estimators to provide an alternate to kriging.