This dissertation considers certain issues in support vector machines (SVMs), including a description of their construction, aspects of certain exponential kernels used in some SVMs, and a presentation of an algorithm that computes the necessary elements of their operation with proof of convergence. In its first section, this dissertation provides a reasonably complete description of SVMs and their theoretical basis, along with a few motivating examples and counterexamples. This section may be used as an accessible, stand-alone introduction to the subject of SVMs for the advanced undergraduate. Its second section provides a proof of the positive-definiteness of a certain useful function here called E and dened as follows: Let V be a complex inner product space. Let N be a function that maps a vector from V to its norm. Let p be a real number between 0 and 2 inclusive and for any in V , let ( be N() raised to the p-th power. Finally, let a be a positive real number. Then E() is exp(()). Although the result is not new (other proofs are known but involve deep properties of stochastic processes) this proof is accessible to advanced undergraduates with a decent grasp of linear algebra. Its final section presents an algorithm by Dr. Kallman (preprint), based on earlier Russian work by B.F. Mitchell, V.F Demyanov, and V.N. Malozemov, and proves its convergence. The section also discusses briefly architectural features of the algorithm expected to result in practical speed increases.

In this research project, the Boundary Element Method (BEM) is developed and formulated for the solution of two-dimensional convection-diffusion-reaction problems. A combined approach with the dual reciprocity boundary element method (DRBEM) has been applied to solve steady-state problems with variable velocity and transient problems with constant and variable velocity fields. Further, the radial integration boundary element method (RIBEM) is utilised to handle non-homogeneous problems with variable source term. For all cases, a boundary-only formulation is produced. Initially, the steady-state case with constant velocity is considered, by employing constant boundary elements and a fundamental solution of the adjoint equation. This fundamental solution leads to a singular integral equation. The conservation laws, usually applied to avoid this integration, do not hold when a chemical reaction is taking place. Then, the integrals are successfully computed using Telles' technique. The application of the BEM for this particular equation is discussed in detail in this work. Next, the steady-state problem for variable velocity fields is presented and investigated. The velocity field is divided into an average value plus a perturbation. The perturbation is taken to the right-hand-side of the equation generating a non-homogeneous term. This nonhomogeneous equation is treated by utilising the DRM approach resulting in a boundary-only equation. Then, an integral equation formulation for the transient problem with constant velocity is derived, based on the DRM approach utilising the fundamental solution of the steady-state case. Therefore, the convective terms will be encompassed by the fundamental solution and lie within the boundary integral after application of Greens's second identity, leaving on the right-hand-side of the equation a domain integral involving the time-derivative only. The proposed DRM method needs the time-derivative to be expanded as a series of functions that will allow the domain integral to be moved to the boundary. The expansion required by the DRM uses functions which take into account the geometry and physics of the problem, if velocity-dependent terms are used. After that, a novel DRBEM model for transient convection-diffusion-reaction problems with variable velocity field is investigated and validated. The fundamental solution for the corresponding steady-state problem is adopted in this formulation. The variable velocity is decomposed into an average which is included into the fundamental solution of the corresponding equation with constant coefficients, and a perturbation which is treated using the DRM approximation. The mathematical formulation permits the numerical solution to be represented in terms of boundary-only integrals. Finally, a new formulation for non-homogeneous convection-diffusion-reaction problems with variable source term is achieved using RIBEM. The RIM is adopted to convert the domain integrals into boundary-only integrals. The proposed technique shows very good solution behaviour and accuracy in all cases studied. The convergence of the methods has been examined by implementing different error norm indicators and increasing the number of boundary elements in all cases. Numerical test cases are presented throughout this research work. Their results are sufficiently encouraging to recommend the use of the techniques developed for solution of general convection-diffusion-reaction problems. All the simulated solutions for several examples showed very good agreement with available analytical solutions, with no numerical problems of oscillation and damping of sharp fronts.

Resumo: A previsão de carga, em sistemas de energia elétrica, constitui-se numa atividade de grande importância, tendo em vista que a maioria dos estudos realizados (fluxo de potência, despacho econômico, planejamento da expansão, compra e venda de energia, etc.) somente poderá ser efetivada se houver a disponibilidade de uma boa estimativa da carga a ser atendida. Deste modo, visando contribuir para que o planejamento e operação dos sistemas de energia elétrica ocorram de forma segura, confiável e econômica, foi desenvolvida uma metodologia para previsão de carga, a previsão multinodal, que pode ser entendida como um sistema inteligente que considera vários pontos da rede elétrica durante a realização da previsão. O sistema desenvolvido conta com o uso de uma rede neural artificial composta por vários módulos, sendo esta do tipo perceptron multicamadas, cujo treinamento é baseado no algoritmo retropropagação. Porém, foi realizada uma modificação na função de ativação da rede, em substituição à função usual, a função sigmoide, foram utilizadas as funções de base radial. Tal metodologia foi aplicada ao problema de previsão de cargas elétricas a curto-prazo (24 horas à frente) / Abstract: Load forecasting in electric power systems is a very important activity due to several studies, e.g. power flow, economic dispatch, expansion planning, purchase and sale of energy that are extremely dependent on a good estimate of the load. Thus, contributing to a safe, reliable, economic and secure operation and planning this work is developed, which is an intelligent system for multinodal electric load forecasting considering several points of the network. The multinodal system is based on an artificial neural network composed of several modules. The neural network is a multilayer perceptron trained by backpropagation where the traditional sigmoide is substituted by radial basis functions. The methodology is applied to forecast loads 24 hours in advance / Orientador: Carlos Roberto. Minussi / Coorientador: Francisco Villarreal Alvarado / Banca: Anna Diva Plasencia Lotufo / Banca: Maria do Carmo Gomes da Silveira / Banca: Gelson da Cruz Junior / Banca: Edmárcio Antonio Belati / Doutor

This thesis describes the implementation of a Radial Basis Function (RBF) network to be used in predicting the effectiveness of various strategies for reducing the Vehicle Trip Rate (VTR) of a worksite. Three methods of learning were utilized in training the Gaussian hidden units of the network, those being a) output weight adjustment using the Delta rule b) adjustable reference vectors in conjunction with weight adjustment, and c) a combination of adjustable centers and adjustable sigma values for each RBF neuron with the Delta rule. The justification for utilizing each of the more advanced levels of training is provided using a series of tests and performance comparisons. The network architecture is then selected based upon a series of initial trials for an optimum number of hidden Radial Basis neurons. In a similar manner, the training time is determined after finding a maximum number of epochs during which there is a significant change in the SSE. The network was compared for effectiveness against each of the following methods of data analysis: force-entered regression, backward regression, forward regression, stepwise regression, and two types of back-propagation networks based upon the attributes discovered to be most predictive by these regression techniques. A comparison of the learning methods used on the Radial Basis network shows the third learning strategy to be the most efficient for training, yielding the lowest sum of squared errors (SSE) in the shortest number of training epochs. The result of comparing the RBF implementation against the other methods mentions shows the superiority of the Radial Basis method for predictive ability.

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Radial basis function (RBF) approximation, is a new extremely powerful tool that is promising for high-dimensional problems, such as those arising from pricing of basket options using the Black-Scholes partial differential equation. The main problem for RBF methods have been ill-conditioning as the RBF shape parameter becomes small, corresponding to flat RBFs. This thesis employs a recently developed method called the RBF-QR method to reduce computational cost by improving the conditioning, thereby allowing for the use of a wider range of shape parameter values. Numerical experiments for the one-dimensional case are presented  and a MATLAB implementation is provided. In our thesis, the RBF-QR method performs better  than the RBF-Direct method for small shape parameters. Using Chebyshev points, instead of a standard uniform distribution, can increase the accuracy through clustering of the nodes towards the boundary. The least squares formulation for RBF methods is preferable to the collocation approach because it can result in smaller errors  for the same number of basis functions.

In this thesis, a popular music genre recognition approach for Japanese popular music using SVM (support vector machine) with forward feature selection is proposed. First, various common acoustic features are extracted from the digital signal of popular music songs, including sub-bands, energy, rhythm, tempo, formants. A set of the most appropriate features for the genre identification is then selected by the proposed forward feature selection technique. Experiments conducted on the database consisting of 296 Japanese popular music songs demonstrate that the accuracy of recognition the proposed algorithm can achieve approximately 78.81% and the accuracy is stable when the number of testing music songs is increased.

The selection and modification of kernel functions is a very important problem in the field of support vector learning. However, the kernel function of a support vector machine has great influence on its performance. The kernel function projects the dataset from the original data space into the feature space, and therefore the problems which couldn¡¦t be done in low dimensions could be done in a higher dimension through the transform of the kernel function. In this thesis, we adopt the FCM clustering algorithm to group data patterns into clusters, and then use a statistical approach to calculate the standard deviation of each pattern with respect to the other patterns in the same cluster. Therefore we can make a proper estimation on the distribution of data patterns and assign a proper standard deviation for each pattern. The standard deviation is the same as the variance of a radial basis function. Then we have the origin data patterns and the variance of each data pattern for support vector learning. Experimental results have shown that our approach can derive better kernel functions than other methods, and also can have better learning and generalization abilities.

Meshfree methods have become strong alternatives to conventional numerical methods used in solid mechanics after significant progress in recent years. Radial point interpolation method (RPIM) is a meshfree method based on Galerkin formulation and constructs shape functions which enable easy imposition of essential boundary conditions. This thesis analyses plane elasticity problems using RPIM. A computer code implementing RPIM for the solution of plane elasticity problems is developed. Selected problems are solved and the effect of shape parameters on the accuracy of RPIM with and without polynomial terms added in the interpolation is studied. The optimal shape parameters are determined for plane elasticity problems.

The static synchronous series compensator (SSSC) is a series controller of Flexible AC Transmission Systems (FACTS). It can be controlled by Thyristors, it also has the ability of fast control adjustments and high frequency operation. Through impedance compensation, it is able to control the magnitude and directions of the real power flow in the transmission system. In order to achieve a fast and steady response for real power control in power systems, this thesis proposed a unified intelligent controller, which consists of RBFNN and GA for the SSSC to provide better control features for real power control in the dynamic operations of power systems. Finally, the simulation results of the proposed controllers is compared with the conventional proportional plus integral (PI) controllers to demonstrate the superiority and effectiveness of the unified intelligent controller.