GA optimization of OBF TS fuzzy models with linear and non linear local models

OBF (Orthonormal Basis Function) Fuzzy models have shown to be a promising approach to the areas of nonlinear system identification and control since they exhibit several advantages over those dynamic model topologies usually adopted in the literature. Although encouraging application results have been obtained, no automatic procedure had yet been developed to optimize the design parameters of these models. This paper elaborates on the use of a genetic algorithm (GA) especially designed for this task, in which a fitness function based on the Akaike information criterion plays a key role by considering both model accuracy and parsimony aspects. The use of linear (actually affine) and nonlinear local models is also investigated. The proposed methodology is evaluated in the modeling of a real nonlinear magnetic levitation system

Identificação e controle de processos via desenvolvimentos em séries ortonormais. Parte A: identificação

In this paper, an overview about the identification of dynamic systems using orthonormal basis function models, such as those based on Laguerre and Kautz functions, is presented. The mathematical foundations of these models as well as their advantages and limitations are discussed within the contexts of linear, robust, and nonlinear identification. The discussions comprise a broad bibliographical survey on the subject and a comparative analysis involving some specific model realizations, namely, linear, Volterra, fuzzy, and neural models within the orthonormal basis function framework. Theoretical and practical issues regarding the identification of these models are also presented and illustrated by means of two case studies related to a polymerization process.O presente artigo apresenta uma visão geral do estado da arte na área de identificação de sistemas utilizando modelos dinâmicos com estrutura desenvolvida através de bases de funções ortonormais, como as funções de Laguerre, Kautz ou funções ortonormais generalizadas. Discute-se as vantagens e possíveis limitações desse tipo de estrutura bem como os fundamentos matemáticos dos modelos correspondentes nos contextos de identificação linear, linear com incertezas paramétricas (identificação robusta) e não linear, incluindo uma revisão bibliográfica abrangente sobre o tema. Diferentes realizações de modelos com funções de base ortonormal, a saber, modelos lineares, de Volterra, fuzzy e neurais, são detalhadas e discutidas comparativamente em termos de capacidade de representação, parcimônia, complexidade de projeto e interpretabilidade. Aspectos práticos da identificação desses modelos são também apresentados e ilustrados através de dois casos de estudo envolvendo um processo simulado de polimerização isotérmica.301321Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq

Modelagem de Sistemas Dinâmicos Não Lineares via RBF-GOBF.

Trata-se neste trabalho trata da modelagem e identificação de sistemas dinâmicos não lineares estáveis representáveis por modelos de Wiener por um estrutura formada por bases de funções ortonormais generalizadas (Generalized Orthonormal Basis Functions - GOBF) com funções internas e redes neurais com funções de base radial (Radial Basis Functions - RBF). Os modelos GOBF com funções internas são capazes de representar dinâmicas lineares intrincadas com uma parametrização que se vale apenas de valores reais, sejam os polos do sistema a ser representado complexos e/ou reais. Com informações de entrada e saída do sistema a ser identificado é possível obter um modelo GOBF-RBF inicial. Os clusters que determinam os parâmetros inciais das RBFs (centros das funções gaussianas e larguras ou spreads) são obtidos pelo método fuzzy C-means, o qual é inicializado com um número de centros pré-determinado, obtido pela técnica subtractive clustering, garantindo clusters com volume e densidade apropriados. São propostas duas técnicas para o ajuste dos parâmetros da estrutura. A primeira delas se baseia em um método de otimização não linear e os gradientes exatos da estrutura. Apresenta-se um procedimento para a obtenção dos cálculos analíticos dos gradientes de saída do modelo GOBF-RBF em relação a seus parâmetros (polos da base ortonormal, centros, larguras e pesos de saída da rede RBF). A segunda proposta se vale de um método metaheurístico chamado otimização por enxame de partículas com comportamento quântico. As metodologias são validadas com suas aplicações em três diferentes sistemas não lineares associados a modelos de processos práticos

Design Of Obf-ts Fuzzy Models Based On Multiple Clustering Validity Criteria

Takagi-Sugeno Fuzzy Models within the framework of Orthonormal Basis Functions (OBF-TS Fuzzy Models) have shown to be an effective approach to nonlinear system identification and control due to several advantages they exhibit over those dynamic model topologies most commonly adopted in the literature. Despite all the theoretical advances and encouraging application results obtained so far, the automatic determination of the number of local OBF models remains an issue. This paper elaborates on the use of a mixture of clustering validity criteria to automatically determine the number of local models based on product space fuzzy clustering of I/O data. © 2007 IEEE.2336339Babuška, R., (1998) Fuzzy Modeling for Control, , KluwerBezdek, J.C., Pal, N.R., Some new indexes of cluster validity (1998) IEEE Trans. on Systems, Man and Cybernetics B, 28 (3), pp. 301-315Campello, R.J.G.B., Hruschka, E.R., A fuzzy extension of the silhouette width criterion for cluster analysis (2006) Fuzzy Sets and Systems, 157, pp. 2858-2875R. J. G. B. Campello, L. A. C. Meleiro, W. C. Amaral, and R. M. Filho. Identification of a bioprocess using Laguerre function based models. In World Congress of Chemical Engineering, page CD, Melbourne, Australia, 2001R. J. G. B. Campello, L. A. C. Meleiro, and W. C. Amaral. Takagi-sugeno fuzzy models within orthonormal basis function framework and their application to process control. In IEEE Int. Conf. Fuzzy Systems, pages 1399-1404, Honolulu, USA, 2002R. J. G. B. Campello, L. A. C. Meleiro, and W. C. Amaral. Control of a bioprocess using orthonormal basis function fuzzy models. In IEEE Int. Conf. Fuzzy Systems, pages 801-806, Budapest, Hungary, 2004Campello, R.J.G.B., Von Zuben, F.J., Amaral, W.C., Meleiro, L.A.C., Maciel Filho, R., Hierarchical fuzzy models within the framework of orthonormal basis functions and their application to bioprocess control (2003) Chemical Engineering Science, 58, pp. 4259-4270Heuberger, P.S.C., Van den Hof, P.M.J., Wahlberg, B., (2005) Modelling and Identification with Rational Orthogonal Basis Functions, , SpringerHöppner, F., Klawonn, F., Kruse, R., Runkler, T., (1999) Fuzzy Cluster Analysis: Methods for Classification, Data Analysis and Image Recognition, , John Wiley & SonsMedeiros, A.V., Amaral, W.C., Campello, R.J.G.B., GA optimization of generalized OBF TS fuzzy models with global and local estimation approaches (2006) Proc. IEEE Int. Conf. Fuzzy Systems, pp. 8494-8501. , Vancouver, CanadaMedeiros, A.V., Amaral, W.C., Campello, R.J.G.B., GA optimization of OBF TS fuzzy models with linear and non linear local models (2006) Proc. Brazilian Symposium on Neural Networks, , Ribeirão Preto, BrazilMedeiros, A.V., (2006) Modeling of Nonlinear Dynamic Systems using Fuzzy Systems, Genetic Algorithms and Orthonormal Basis Functions, , Master's Degree Thesis, School of Electrical and Computer Engineering FEEC, UNICAMP, Brazil, Jan, In PortugueseNelles, O., (2001) Nonlinear System Identification, , Springer-VerlagG. H. C. Oliveira, R. J. G. B. Campello, and W. C. Amaral. Fuzzy models within orthonormal basis function framework. In IEEE Int. Conf. Fuzzy Systems, pages 957-962, Seoul, Korea, 1999Johansen, R.S.T.A., Murray-Smith, R., On the interpretation and identification of dynamic takagi-sugeno fuzzy models (2000) IEEE Transactions on Fuzzy Systems, 8 (3), pp. 297-31

Identification And Control Of Processes Via Developments In The Orthonormal Series Part A: Identification _net Identificação E Controle De Processos Via Desenvolvimentos Em Séries Ortonormais. Parte A: Identificação

In this paper, an overview about the identification of dynamic systems using orthonormal basis function models, such as those based on Laguerre and Kautz functions, is presented. The mathematical foundations of these models as well as their advantages and limitations are discussed within the contexts of linear, robust, and nonlinear identification. The discussions comprise a broad bibliographical survey on the subject and a comparative analysis involving some specific model realizations, namely, linear, Volterra, fuzzy, and neural models within the orthonormal basis function framework. Theoretical and practical issues regarding the identification of these models are also presented and illustrated by means of two case studies related to a polymerization process.183301321Aguirre, L.A., (2004) Introdução à Identificação de Sistemas: Técnicas Lineares e Não Lineares Aplicadas a Sistemas Reais, , 2 edn, Editora UFMGAguirre, L.A., Correa, M.V., Cassini, C., Nonlinearities in NARX polynomial models: Representation and estimation (2002) IEE Proc. 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