Application of Wilcoxon Norm for increased Outlier Insensitivity in Function Approximation Problems

In system theory, characterization and identification are fundamental problems. When the plant behavior is completely unknown, it may be characterized using certain model and then, its identification may be carried out with some artificial neural networks(ANN) (like multilayer perceptron(MLP) or functional link artificial neural network(FLANN) ) or Radial Basis Functions(RBF) using some learning rules such as the back propagation (BP) algorithm. They offer flexibility, adaptability and versatility, for the use of a variety of approaches to meet a specific goal, depending upon the circumstances and the requirements of the design specifications. The first aim of the present thesis is to provide a framework for the systematic design of adaptation laws for nonlinear system identification and channel equalization. While constructing an artificial neural network or a radial basis function neural network, the designer is often faced with the problem of choosing a network of the right size for the task. Using a smaller neural network decreases the cost of computation and increases generalization ability. However, a network which is too small may never solve the problem, while a larger network might be able to. Transmission bandwidth being one of the most precious resources in digital communication, Communication channels are usually modeled as band-limited linear finite impulse response (FIR) filters with low pass frequency response

Various nonlinear models and their identification, equalization and linearization

System identification is a pre-requisite to analysis of a dynamic system and design of an appropriate controller for improving its performance. The more accurate the mathematical model identified for a system, the more effective will be the controller designed for it. The identification of nonlinear systems is a topic which has received considerable attention over the last two decades. Generally speaking, when it is difficult to model practical systems by mathematical analysis method, system identification may be an efficient way to overcome the shortage of mechanism analysis method. The goal of the modeling is to find a simple and efficient model which is in accord with the practical system. In many cases, linear models are not suitable to present these systems and nonlinear models have to be considered. Since there are nonlinear effects in practical systems, e.g. harmonic generation, intermediation, desensitization, gain expansion and chaos, we can infer that most control systems are nonlinear. Nonlinear models are more widely used in practice, because most phenomena are nonlinear in nature. Indeed, for many dynamic systems the use of nonlinear models is often of great interest and generally characterizes adequately physical processes over their whole operating range. Thus, accuracy and performance of the control law increase significantly. Therefore, nonlinear system modeling is much more important than linear system identification. We will deal with various nonlinear models and their processing

On Applications of New Soft and Evolutionary Computing Techniques to Direct and Inverse Modeling Problems

Adaptive direct modeling or system identification and adaptive inverse modeling or channel equalization find extensive applications in telecommunication, control system, instrumentation, power system engineering and geophysics. If the plants or systems are nonlinear, dynamic, Hammerstein and multiple-input and multiple-output (MIMO) types, the identification task becomes very difficult. Further, the existing conventional methods like the least mean square (LMS) and recursive least square (RLS) algorithms do not provide satisfactory training to develop accurate direct and inverse models. Very often these (LMS and RLS) derivative based algorithms do not lead to optimal solutions in pole-zero and Hammerstein type system identification problem as they have tendency to be trapped by local minima. In many practical situations the output data are contaminated with impulsive type outliers in addition to measurement noise. The density of the outliers may be up to 50%, which means that about 50% of the available data are affected by outliers. The strength of these outliers may be two to five times the maximum amplitude of the signal. Under such adverse conditions the available learning algorithms are not effective in imparting satisfactory training to update the weights of the adaptive models. As a result the resultant direct and inverse models become inaccurate and improper. Hence there are three important issues which need attention to be resolved. These are : (i) Development of accurate direct and inverse models of complex plants using some novel architecture and new learning techniques. (ii) Development of new training rules which alleviates local minima problem during training and thus help in generating improved adaptive models. (iii) Development of robust training strategy which is less sensitive to outliers in training and thus to create identification and equalization models which are robust against outliers. These issues are addressed in this thesis and corresponding contribution are outlined in seven Chapters. In addition, one Chapter on introduction, another on required architectures and algorithms and last Chapter on conclusion and scope for further research work are embodied in the thesis. A new cascaded low complexity functional link artificial neural network (FLANN) structure is proposed and the corresponding learning algorithm is derived and used to identify nonlinear dynamic plants. In terms of identification performance this model is shown to outperform the multilayer perceptron and FLANN model. A novel method of identification of IIR plants is proposed using comprehensive learning particle swarm optimization (CLPSO) algorithm. It is shown that the new approach is more accurate in identification and takes less CPU time compared to those obtained by existing recursive LMS (RLMS), genetic algorithm (GA) and PSO based approaches. The bacterial foraging optimization (BFO) and PSO are used to develop efficient learning algorithms to train models to identify nonlinear dynamic and MIMO plants. The new scheme takes less computational effort, more accurate and consumes less input samples for training. Robust identification and equalization of complex plants have been carried out using outliers in training sets through minimization of robust norms using PSO and BFO based methods. This method yields robust performance both in equalization and identification tasks. Identification of Hammerstein plants has been achieved successfully using PSO, new clonal PSO (CPSO) and immunized PSO (IPSO) algorithms. Finally the thesis proposes a distributed approach to identification of plants by developing two distributed learning algorithms : incremental PSO and diffusion PSO. It is shown that the new approach is more efficient in terms of accuracy and training time compared to centralized PSO based approach. In addition a robust distributed approach for identification is proposed and its performance has been evaluated. In essence the thesis proposed many new and efficient algorithms and structure for identification and equalization task such as distributed algorithms, robust algorithms, algorithms for ploe-zero identification and Hammerstein models. All these new methods are shown to be better in terms of performance, speed of computation or accuracy of results

Support Vector Regression aplicado à previsão de taxas de câmbio

Dissertação (mestrado) — Universidade de Brasília, Faculdade de Economia, Administração, Contabilidade e Gestão Pública, Programa de Pós-Graduação em Administração, 2016.O presente estudo realizou a previsão da taxa spot de 15 pares de câmbio mediante a aplicação de um algoritmo de aprendizado de máquinas – Support Vector Regression – com base em um modelo fundamentalista composto por 13 variáveis explicativas. Para a estimação das previsões, foram consideradas 9 funções Kernel extraídas da literatura científica, totalizando assim 135 modelos verificados. As previsões foram comparadas com o benchmark Random Walke avaliadas em relação à taxa de acerto direcional do câmbio e às métricas de erro RMSE (raiz quadrada do erro quadrático médio) e MAE (erro absoluto médio). A significância estatística do incremento de poder explicativo dos modelos SVR em relação ao Random Walk foi verificada mediante a aplicação do Reality Check Test de White (2000). Os resultados mostram que os modelos SVR obtiveram desempenho preditivo satisfatório em relação ao benchmark, com vários dos modelos propostos apresentando forte significância estatística de superioridade preditiva.Por outro lado, observou-se que várias funções Kernel comumente utilizadas na literatura científica não lograram êxito em superar o Random Walk, apontando para uma possível lacuna no estado da arte de aprendizado de máquinas aplicada à previsão de taxas de câmbio. Por fim, discutiu-se acerca das implicações dos resultados obtidos para o desenvolvimento futuro da agenda de pesquisa correlata.This paper aims to forecast the spot exchange rate of 15 currency pairs by applying a machinelearning algorithm – Support Vector Regression – based on a fundamentalist model composedof 13 explanatory variables. The predictions’ estimation were obtained by applying 9different Kernel functions extracted from the scientific literature, resulting in a total of 135 modelsverified. The predictions were compared to the Random Walk benchmark and evaluated for directionalaccuracy rate of exchange pradictions and error performance indices RMSE (root meansquare error) and MAE (mean absolute error). The statistical significance of the explanatorypower gain via SVR models with respect to the Random Walk was checked by applying White(2000)’s Reality Check Test. The results show that SVR models achieved satisfactory predictiveperformance relative to the benchmark, with several of the proposed models showing strong statisticalsignificance of predictive superiority. Furthermore, the results showed that mainstreamKernel functions commonly used in the scientific literature failed to outperform the RandomWalk,indicating a possible gap in the state of art of machine learning methods applications to exchangerates forecasting. Finally, the paper presents a discussion about the implications of the obtainedresults for the future development of related research agendas