Neurofuzzy approach for nonlinear dynamical systems modeling

Orientadores: Fernando Antonio Campos Gomide, Pyramo Pires Costa JuniorTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de ComputaçãoResumo: Este trabalho propõe um procedimento sistemático para obtenção de modelos de sistemas dinâmicos não-lineares complexos utilizando redes neurais nebulosas. As redes neurais nebulosas aplicadas em modelagem são capazes de extrair conhecimento de dados entrada/saída e representar este conhecimento na forma de regras nebulosas do tipo se-então, gerando modelos lingüísticos convenientes para compreensão humana. Duas novas classes de redes neurais nebulosas são propostas a partir de generalizações dos neurônios lógicos AND e OR. Estas generalizações, denominadas unineurons e nullneurons, implementam, além da plasticidade sináptica, outra importante característica dos neurônios biológicos, a plasticidade neuronal. Desta forma, os neurônios propostos neste trabalho são capazes de modificar parâmetros internos em resposta à alterações, permitindo que unineurons e nullneurons variem individualmente de um neurônio AND para um neurônio OR (e vice-e-versa), dependendo da necessidade do problema. Conseqüentemente, uma rede neural nebulosa composta por unineurons e nullneurons é mais geral do que as redes neurais nebulosas similares sugeridas na literatura. Além da introdução de redes neurais com unineurons e nullneurons, um novo algoritmo de treinamento para obtenção de modelos nebulosos de sistemas dinâmicos é proposto utilizando aprendizado participativo. Neste algoritmo, uma nova informação fornecida à rede por meio de um dado entrada/saída é comparada com o conhecimento que já se tem a respeito do sistema. A nova informação só tem influência na atualização do conhecimento se não entrar em conflito com o conhecimento adquirido anteriormente. Como conseqüência, redes neurais nebulosas que utilizam este novo algoritmo de treinamento são mais robustas a dados de treinamento com valores que correspondem a comportamentos anômalos ou mesmo a erros durante a obtenção destes dados. As abordagens propostas foram utilizadas para desenvolver modelos para previsão de séries temporais e modelagem térmica de transformadores de potência. Os resultados experimentais mostram que os modelos aqui propostos são mais robustos e apresentam os melhores desempenhos, tanto em termos de precisão quanto em termos de custos computacionais, quando comparados com abordagens alternativas sugeridas na literaturaAbstract: This work suggests a systematic procedure to develop models of complex nonlinear dynamical systems using neural fuzzy networks. The neural fuzzy networks are able to extract knowledge from input/output data and to encode it explicitly in the form of if-then rules. Therefore, linguistic models are obtained in a form suitable for human understanding. Two new classes of fuzzy neurons are introduced to generalize AND and OR logic neurons. These generalized login neurons, called unineurons and nullneurons, provide a mechanism to implement synaptic plasticity and an important characteristic of biological neurons, the neuronal plasticity. Unineurons and nullneurons achieve synaptic and neuronal plasticity modifying their internal parameters in response to external changes. Thus, unineurons and nullneurons may individually vary from a AND neuron to a OR neuron (and vice-versa), depending upon the necessity of the modeling task. Neural fuzzy networks constructed with unineurons and nullneurons are more general than similar fuzzy neural approaches suggested in literature. Training algorithms for neural fuzzy networks with unineurons and nullneurons are also studied. In particular, a new training algorithm based on the participatory learning is introduced to develop fuzzy models of dynamical systems. In the participatory learning algorithm, a new information brought to the network through an input/output data is first compared with the knowledge that the network already has about the model. The new information influences the update of the knowledge only if it does not conflict with the current knowledge. As a result, neural fuzzy networks trained with participatory learning show greater robustness to training data with anomalous values than their counterparts. The neural fuzzy network and training algorithms suggested herein are used to develop time series forecast models and thermal models of power transformers. Experimental results show that the models proposed here are more robust and perform best in terms of accuracy and computational costs when compared against alternative approaches suggested in the literatureDoutoradoAutomaçãoDoutor em Engenharia Elétric

Neurons And Neural Fuzzy Networks Based On Nullnorms

This paper suggests a new type of elementary unit for neural fuzzy networks based on the concept of nullnorm. A nullnorm is a category of fuzzy set-oriented operators that generalizes triangular norms and conorms. The new unit, called nullneuron, is a generalization of and/or logic-based neurons parametrized by an element u, called the absorbing element. If the absorbing element u = 0, then the nullneuron becomes an and neuron and if u = 1, then the nullneuron becomes a dual or neuron. The paper also addresses two learning schemes for a class of hybrid neural fuzzy networks with nullneurons. The first scheme uses the gradient descent technique and the second reinforcement learning. Both learning schemes adjust not only the weights associated with the inputs of the nullneurons, but also the role of the nullneuron in the network (and or or) by individually adjusting the parameter u of each nullneuron. The neurofuzzy network presented here is more general than alternative approaches discussed in the literature because they allow different triangular norms in the same network structure. Experimental results show that nullneuron-based networks provide accurate results with low computational effort. © 2008 IEEE.123128Box, G.E.P., Jenkins, G.M., (1976) Time Series Analysis- Forecasting and Control, , Holden Day, CA, USA, second editionDelgado, M., Gmez-Skarmeta, A.F., Martin, F., Fuzzy clustering based rapid prototyping for fuzzy rule-based modeling (1997) IEEE Trans. on Fuzzy Systems, 5, pp. 223-233. , MayFigueiredo, M., Ballini, R., Soares, S., Andrade, M., Gomide, F., Learning algorithms for a class of neurofuzzy network and application (2004) IEEE Trans. on System, Man and Cybernetics - Part C, 34 (3), pp. 293-301Gomide, F., Pedrycz, W., (2007) Fuzzy Systems Engineering: Toward Human-Centric Computing, , Wiley Interscience, NJ, USAM. Hell, P. Costa-Jr., and F. Gomide. Nullneurons-based hybrid neurofuzzy network. In Proceedings of Annual Meeting of the North American Fuzzy Information Processing Society, NAFIPS 07, pages 331-336, San Diego-CA, USA, June 2007Hell, M., Costa-Jr, P., Gomide, F., Hybrid neurofuzzy computing with nullneurons (2008) Proceedings of IEEE World Congress on Computational Intelligence - WCCI 2008, , Hong Kong, China, JuneJang, R., Anfis: Adaptive network based fuzzy inference system (1993) IEEE Trans. on Systems Man and Cybernetics, 23 (3), pp. 665-685Lin, C.T., Lee, C.S., (1996) Neural Fuzzy Systems, , Prentice-Hall, NJ, USAPedrycz, W., A identification algorithm in fuzzy relational systems (1984) Fuzzy Sets and Systems, 13, pp. 153-167Pedrycz, W., Neurocomputations in relational systems (1991) IEEE Trans. on Pattern Analysis and Machinne Intelig, 13 (3). , 289-297Pedrycz, W., Logic-based neurocomputing with unineurons (2006) IEEE Trans. on Fuzzy Systems, 14 (6), pp. 860-873Rutkowski, L., Cpalka, K., Design and learning of adjustable quasi-triangular norms with applications to neurofuzzy systems (2005) IEEE Trans. on Neural Networks, 13 (1), pp. 140-151Calvo, B.D.B.T., Fodor, J., The functional equations of frank ans alsina for uninorms and nullnorms (2001) Fuzzy Sets and Systems, 120, pp. 385-394Caminhas, F.G.W., Tavares, H., Pedrycz, W., Fuzzy set based neural networks: Structure, learning and application (1999) Journal of Advanced Computational Intelligence, 3 (3), pp. 151-157Xu, W., Lu, Y.Z., Fuzzy model identification and selflearning for dynamic systems (1987) IEEE Trans. on System, Man and Cybernetics, SMC-17, pp. 683-689. , JulyYager, R., Rybalov, A., Uninorm aggregation operators (1996) Fuzzy Sets and Systems, 80 (1), pp. 111-120Yoshinari, Y., Pedrycz, W., Hirota, K., Construction of fuzzy models through clustering techniques (1993) Fuzzy Sets and Systems, 54, pp. 157-16