Evolving Neuro–Fuzzy network modeling approach based on recursive fuzzy instrumental variable

Article type: Research Article

Authors: Rocha Filho, Orlando Donato | de Oliveira, Ginalber Luiz Serra^*

Affiliations: Federal Institute of Education, Science and Technology, São Luis, MA, Brazil

Correspondence: [*] Corresponding author. Ginalber Luiz Serra de Oliveira, Federal Institute of Education, Science and Technology, São Luis, MA, Brazil. Tel.: +55 98 32189088; Fax: +55 98 3218 9001; E-mail: [email protected].

Abstract: In this paper an evolving Neuro–Fuzzy Network Modeling based on recursive parameter estimation with fuzzy instrumental variable method, is proposed. The proposed methodology presents an online evolving clustering algorithm composed of participatory learning based on the maximum likelihood norm. To avoid the curse of dimensionality in relation to the number of evolving rules, the algorithm uses an online adaptive norm strategy in the creation of fuzzy rules. The performance of the proposed methodology is concerned to benchmark problems: experiments considering the convergence analysis, by proposal of three Lemmas and one Theorem, of the fuzzy instrumental variable applied to the parametric estimation of nonlinear systems in a noise environment; nonlinear systems identification are performed and compared to evaluate the performance of the approach proposed with other models of evolving systems widely cited in the literature and statistical analysis of experimental results from black box modeling of a helicopter with two degrees of freedom are used for the purpose of show the performance and efficiency the proposed approach.

Keywords: Evolving Neuro–Fuzzy, Takagi–Sugeno, black box modeling fuzzy instrumental variable

DOI: 10.3233/JIFS-16569

Journal: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 6, pp. 4159-4172, 2017