Multivariable State-Space Recursive Identification Algorithm Based on Evolving Type-2 Neural-Fuzzy Inference System
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Multivariable State-Space Recursive Identification Algorithm Based on Evolving Type-2 Neural-Fuzzy Inference System Anderson Pablo Freitas Evangelista1 · Ginalber Luiz de Oliveira Serra2 Received: 14 February 2019 / Revised: 9 August 2019 / Accepted: 24 September 2019 © Brazilian Society for Automatics–SBA 2019
Abstract In this paper, a novel approach for state-space evolving type-2 neural-fuzzy identification of multivariable dynamic systems is proposed. According to adopted methodology, conditions for creating and merging clusters are used to perform the structural adaptation of the neural-fuzzy model. The center and shape of each cluster are estimated, defining all rules in the interval type-2 neural-fuzzy inference system. The degree of uncertainty on the shape of type-2 membership functions is computed through an extended Kalman filter-based learning mechanism. Once the type-2 membership functions (upper and lower membership values) are estimated, the fuzzy Markov parameters are computed from experimental data, and for each incoming information, the parameters of state-space linear models in the consequent proposition of inference system are recursively estimated. The efficiency and applicability of the proposed methodology are demonstrated through experimental results of modeling of an industrial dryer. Keywords Type-2 neural-fuzzy inference system · Interval type-2 fuzzy sets · Evolving systems · Fuzzy state-space identification
1 Introduction Quite often, the knowledge that is used to design a fuzzy system can be uncertain. According to Mendel and John (2002), there are, at least, four resources of uncertainties to built a fuzzy system: (1) the meanings of words which are used in the antecedent/consequent proposition of rules can be uncertain, i.e., words have different meanings for different people; (2) when the knowledge is extracted from a group of experts who do not agree among themselves; (3) measurements that activate a type-1 fuzzy system may be noisy and therefore uncertain; (4) the data set used to tune parameters of fuzzy systems may contain uncertainty and noise. Therefore, type-1 fuzzy systems are not able to handle severe uncertainties because their membership functions are crisp. To deal
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Ginalber Luiz de Oliveira Serra [email protected] Anderson Pablo Freitas Evangelista [email protected]
1
Federal University of Maranhão, Av. dos Portugueses, 1966, Bacanga, São Luís, MA CEP 65080-805, Brazil
2
Federal Institute of Education, Science and Technology of Maranhao, Av. Getúlio Vargas, 04, Monte Castelo, São Luís, MA CEP 65030-005, Brazil
with the uncertainties mentioned above, type-2 fuzzy systems were proposed, where their membership functions are themselves fuzzy (ZADEH 1975).
1.1 State-of-the-Art The concept of a type-2 fuzzy set was introduced by Zadeh as an extension of the concept of ordinary fuzzy set (type-1 fuzzy set) (ZADEH 1975). However, the first works specifically dealing with type-2 fuzzy sets were published in the 1990s. In Karnik and Mendel (1998),
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