Adaptive Neuro-Fuzzy Black-Box Modeling Based on Instrumental Variable Evolving Algorithm
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Adaptive Neuro-Fuzzy Black-Box Modeling Based on Instrumental Variable Evolving Algorithm Orlando Rocha1 · Ginalber Serra1
Received: 15 April 2016 / Revised: 23 August 2016 / Accepted: 17 October 2016 © Brazilian Society for Automatics–SBA 2016
Abstract In this paper, an online identification algorithm for instrumental variable-based evolving neuro-fuzzy modeling applied to dynamic systems in noisy environment is proposed. The adopted methodology is based on neuro-fuzzy inference system with Takagi–Sugeno evolving structure, which employs an adaptive distance norm based on the maximum likelihood criterion with instrumental variable recursive parameter estimation. The application and performance analysis of the proposed algorithm is based on black-box modeling of a 2DOF Helicopter with errors in variables. Keywords Evolving neuro-fuzzy · Takagi–Sugeno · Black-box modeling
1 Introduction Batch fuzzy clustering algorithms play an important role in modeling from experimental data. However, these algorithms require an initial condition from expert, that is, the number of initial fuzzy clusters so that the algorithm can be performed (Babuska et al. 2010; Baruah and Angelov 2012). Furthermore, data clustering is the aim at major engineering problems in different areas such as manufacturing, control and signal processing, motivating the proposal of new modeling methodologies (Skrjanc 2015; Dovzan et al. 2015). An important problem in data clustering is the esti-
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Ginalber Serra [email protected] Orlando Rocha [email protected]
1
Federal Institute of Education, Science and Technology, São Luís, MA, Brazil
mation of the number of clusters from a non-stationary data set, which is not a new issue, so there are several comprehensive works dealing with adaptive, incremental, evolving clustering (Sayed-Mouchaweh and Lughofer 2012) and the detecting of clusters with varying volume, uncertain shapes, unequal sizes and variable densities (Baruah and Angelov 2012; Skrjanc 2015; Petelin and Kocijan 2014). In many case studies cited in the literature, it appears that the clustering task is not restricted to data sets in batch (offline ), but it can be applied to non-stationary stream data set (online ). Therefore, once these data structures are dynamic, the clustering algorithm should be able to evolve as data are read (Costa et al. 2015; Baruah et al. 2014; Pratama et al. 2014). According to (Lughofer 2011; Lughofer et al. 2015), the evolving models are data-driven models, which adapt automatically, dynamically extend and evolve the structure when a new sample data is read from dynamic system. So, evolving models are able of supporting time-varying flow data and changing your nature over time and space (Baruah et al. 2014; Lughofer 2011; Lughofer et al. 2015). Within the concept of evolving systems (models), there is the evolving fuzzy systems that combine the best features of fuzzy systems (universal approximation capabilities in connection with comprehensability and understandability aspects) with concept of evol
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