In this thesis, we analyse multilevel collocation methods involving compactly supported radial basis functions. We focus on linear second-order elliptic bound- ary value problems as well as Darcy's problem. While in the former case we use scalar-valued positive definite functions for constructing multilevel approximants, in the latter case we use matrix-valued functions that are automatically divergence-free. A similar result is presented for interpolating divergence-free vector fields. Even though it had been observed more than a decade ago that the stationary setting, i.e. when the support radii shrink as fast as the mesh norm, does not lead to convergence, it was up to now an open question how the support radii should depend on the mesh norm to ensure convergence. For each case above, we answer this question here thoroughly. Furthermore, we analyse and improve the stability of the linear systems. And lastly, we examine the case when the approximant does not lie in the same space as the solution to the PDE.

Accurate rainfall forecasting using weather radar imagery has always been a crucial and predominant task in the field of meteorology [1], [2], [3] and [4]. Competitive Radial Basis Function Neural Networks (CRBFNN) [5] is one of the methods used for weather radar image based forecasting. Recently, an alternative CRBFNN based approach [6] was introduced to model the precipitation events. The difference between the techniques presented in [5] and [6] is in the approach used to model the rainfall image. Overall, it was shown that the modified CRBFNN approach [6] is more computationally efficient compared to the CRBFNN approach [5]. However, both techniques [5] and [6] share the same prediction stage. In this thesis, a different GRBFNN approach is presented for forecasting Gaussian envelope parameters. The proposed method investigates the concept of parameter dependency among Gaussian envelopes. Experimental results are also presented to illustrate the advantage of parameters prediction over the independent series prediction.

Lui, Fung Yee. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 83-92). / Abstracts in English and Chinese. / Acknowledgement --- p.iii / Abbreviation --- p.xii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Background --- p.1 / Chapter 1.2 --- Related Work --- p.6 / Chapter 1.2.1 --- Parametric Optimization Method and Radial Basis Functions --- p.6 / Chapter 1.3 --- Contribution and Organization of the Dissertation --- p.7 / Chapter 2 --- Level Set Method for Structure Shape and Topology Optimization --- p.8 / Chapter 2.1 --- Primary Ideas of Shape and Topology Optimization --- p.8 / Chapter 2.2 --- Level Set models of implicit moving boundaries --- p.11 / Chapter 2.2.1 --- Representation of the Boundary via Level Set Method --- p.11 / Chapter 2.2.2 --- Hamilton-Jacobin Equations --- p.13 / Chapter 2.3 --- Numerical Techniques --- p.13 / Chapter 2.3.1 --- Sign-distance function --- p.14 / Chapter 2.3.2 --- Discrete Computational Scheme --- p.14 / Chapter 2.3.3 --- Level Set Surface Re-initialization --- p.16 / Chapter 2.3.4 --- Velocity Extension --- p.16 / Chapter 3 --- Structure Topology Optimization with Discrete Level Sets --- p.18 / Chapter 3.1 --- A Level Set Method for Structural Shape and Topology Optimization --- p.18 / Chapter 3.1.1 --- Problem Definition --- p.18 / Chapter 3.2 --- Shape Derivative: an Engineering-oriented Deduction --- p.21 / Chapter 3.2.1 --- Sensitivity Analysis --- p.23 / Chapter 3.2.2 --- Optimization Algorithm --- p.28 / Chapter 3.3 --- Limitations of Discrete Level Set Method --- p.30 / Chapter 4 --- RBF based Parametric Level Set Method --- p.32 / Chapter 4.1 --- Introduction --- p.32 / Chapter 4.2 --- Radial Basis Functions Modeling --- p.33 / Chapter 4.2.1 --- Inverse Multiquadric (IMQ) Radial Basis Functions --- p.38 / Chapter 4.3 --- Parameterized Level Set Method in Structure Topology Optimization --- p.39 / Chapter 4.4 --- Parametric Shape and Topology Structure Optimization Method with Radial Basis Functions --- p.42 / Chapter 4.4.1 --- Changing Coefficient Method --- p.43 / Chapter 4.4.2 --- Moving Knot Method --- p.45 / Chapter 4.4.3 --- Combination of Changing Coefficient and Moving Knot method --- p.46 / Chapter 4.5 --- Numerical Implementation --- p.48 / Chapter 4.5.1 --- Sensitivity Calculation --- p.48 / Chapter 4.5.2 --- Optimization Algorithms --- p.49 / Chapter 4.5.3 --- Numerical Examples --- p.52 / Chapter 4.6 --- Summary --- p.65 / Chapter 5 --- Conclusion and Future Work --- p.80 / Chapter 5.1 --- Conclusion --- p.80 / Chapter 5.2 --- Future Work --- p.81 / Bibliography --- p.83

In order to reduce air pollution and reduce the amount of traffic on highways in the western United States, certain states have set up worksite trip reduction programs. Employers in these states must comply with worksite trip reduction laws and submit trip reduction plans to their respective regulatory agency each year. These plans are currently evaluated manually, and are either rejected or accepted by the agency. There are two major flaws in this system; the first is the amount of time required by the agency to review a plan could be a matter of months, and the second is that human reviewers have subjective opinions regarding the effectiveness of plans. The purpose of this thesis is to develop computer models using Radial Basis Function neural networks, with centers built using the k-means clustering algorithm. These networks will be compared against the performance of a commercial neural network-modeling program known as Predict, as well as the traditional method of selecting RBF neurons from the training set.

We had previously shown that regularization principles lead to approximation schemes, as Radial Basis Functions, which are equivalent to networks with one layer of hidden units, called Regularization Networks. In this paper we show that regularization networks encompass a much broader range of approximation schemes, including many of the popular general additive models, Breiman's hinge functions and some forms of Projection Pursuit Regression. In the probabilistic interpretation of regularization, the different classes of basis functions correspond to different classes of prior probabilities on the approximating function spaces, and therefore to different types of smoothness assumptions. In the final part of the paper, we also show a relation between activation functions of the Gaussian and sigmoidal type.

Thesis (M.S.)--University of Hawaii at Manoa, 2005. / Includes bibliographical references (leaves 63-67). Also available via World Wide Web.

This research develops a memory model capable of performing in a human-like fashion on a maze traversal task. The model is based on and retains the underlying ideas of Minerva 2 but is executed with different mathematical operations and with some added parameters and procedures that enable more capabilities. When applied to the same maze traversal task as was used in a previous experiment with human subjects, the performance of a maze traversal agent with the developed model as its memory emulated the error rates of the human data remarkably well. As well, the maze traversal agent and memory model successfully emulated the human data when it was divided into two groups: fast maze learners and slow maze learners. It was able to account for individual differences in performance, specifically, individual differences in the learning rate. Because forgetting was not applied and therefore all experiences were flawlessly encoded in memory, the model additionally demonstrates that error can be due to interference between memories rather than forgetting. / Thesis (Master, Computing) -- Queen's University, 2008-06-04 13:39:38.179

Submitted by Amanda Silva (amanda.osilva2@ufpe.br) on 2015-03-03T14:16:54Z No. of bitstreams: 2 Dissertação Mariel Cadena da Matta.pdf: 2355898 bytes, checksum: 9c0530af680cf965137a2385d949b799 (MD5) license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) / Made available in DSpace on 2015-03-03T14:16:54Z (GMT). No. of bitstreams: 2 Dissertação Mariel Cadena da Matta.pdf: 2355898 bytes, checksum: 9c0530af680cf965137a2385d949b799 (MD5) license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Previous issue date: 2013 / FACEPE / A Dosimetria citogenética empregando análise de cromossomos dicêntricos é o “padrão ouro” para estimativas da dose absorvida após exposições acidentais às radiações ionizantes. Todavia, este método é laborioso e dispendioso, o que torna necessária a introdução de ferramentas computacionais que dinamizem a contagem dessas aberrações cromossômicas radioinduzidas. Os atuais softwares comerciais, utilizados no processamento de imagens em Biodosimetria, são em sua maioria onerosos e desenvolvidos em sistemas dedicados, não podendo ser adaptados para microscópios de rotina laboratorial. Neste contexto, o objetivo da pesquisa foi o desenvolvimento do software ChromoSomeClassification para processamento de imagens de metáfases de linfócitos (não irradiados e irradiados) coradas com Giemsa a 5%. A principal etapa da análise citogenética automática é a separação correta dos cromossomos do fundo, pois a execução incorreta desta fase compromete o desenvolvimento da classificação automática. Desta maneira, apresentamos uma proposta para a sua resolução baseada no aprimoramento da imagem através das técnicas de mudança do sistema de cores, subtração do background e aumento do contraste pela modificação do histograma. Assim, a segmentação por limiar global simples, seguida por operadores morfológicos e pela técnica de separação de objetos obteve uma taxa de acerto de 88,57%. Deste modo, os cromossomos foram enfileirados e contabilizados, e assim, a etapa mais laboriosa da Dosimetria citogenética foi realizada. As características extraídas dos cromossomos isolados foram armazenadas num banco de dados para que a classificação automática fosse realizada através da Rede Neural com Funções de Ativação de Base Radial (RBF). O software proposto alcançou uma taxa de sensibilidade de 76% e especificidade de 91% que podem ser aprimoradas através do acréscimo do número de objetos ao banco de dados e da extração de mais características dos cromossomos.

This thesis aims to acquire, deepen and promote understanding of computing techniques for high dimensional scattered data approximation with radial basis functions. The main contributions of this thesis include sufficient conditions for the sovability of compactly supported radial basis functions with different shapes, near points preconditioning techniques for high dimensional interpolation systems with compactly supported radial basis functions, a heterogeneous hierarchical radial basis function interpolation scheme, which allows compactly supported radial basis functions of different shapes at the same level, an O(N) algorithm for constructing hierarchical scattered data set andan O(N) algorithm for sparse kernel summation on Cartesian grids. Besides the main contributions, we also investigate the eigenvalue distribution of interpolation matrices related to radial basis functions, and propose a concept of smoothness matching. We look at the problem from different perspectives, giving a systematic and concise description of other relevant theoretical results and numerical techniques. These results are interesting in themselves and become more interesting when placed in the context of the bigger picture. Finally, we solve several real-world problems. Presented applications include 3D implicit surface reconstruction, terrain modelling, high dimensional meteorological data approximation on the earth and scattered spatial environmental data approximation.

Some metals, such as Ti-6Al-4V, have a high elongation to failure when strained at certain rates and temperatures. Superplastic forming is the utilisation of this property, and it can be used to form thin, geometrically complex components. Superplastic forming is a slow process, and this is one of the reasons why it is an expensive manufacturing process. Localised thinning occurs if the specimen is strained too quickly, and components with locally thin wall thickness fail prematurely. The goal of this study is to find a technique that can be used to minimise the forming time while limiting the minimum final thickness. The superplastic forming process is investigated with the finite element method. The finite element method requires a material model which describes the superplastic behaviour of the metal. Several material models are investigated in order to select a material model that can show localised thinning at higher strain rates. The material models are calibrated with stress-strain data, grain size-time data and strain rate sensitivity-strain data. The digitised data from literature is for Ti-6Al-4V with three different initial grain sizes strained at different strain rates at 927 C. The optimisation of the forming time is done with an approximate optimisation algorithm. This algorithm involves fitting a metamodel to simulated data, and using the metamodels to find the optimum instead of using the finite element model directly. One metamodel is fitted to the final forming time results, and another metamodel is fitted to the final minimum thickness results. A regressive radial basis function method is used to construct the metamodels. The interpolating radial basis function method proved to be unreliable at the design space boundaries due to non-smooth finite element results. The non-smooth results are due to the problem being path dependent. The final forming time of the superplastic forming of a rectangular box was successfully minimised while limiting the final minimum thickness. The metamodels predicted that allowing a 4% decrease in the minimum allowable thickness (1.0 mm to 0.96 mm) and a 1 mm gap between the sheet and the die corner the forming time is decreased by 28.84%. The finite element verification indicates that the final minimum thickness reduced by 3.8% and that the gap between the sheet and the die corner is less than 1 mm, resulting in the forming time being reduced by 28.81%. / Dissertation (MEng)--University of Pretoria, 2017. / Mechanical and Aeronautical Engineering / MEng / Unrestricted