State-Space Recursive Fuzzy Modeling Approach Based on Evolving Data Clustering
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State-Space Recursive Fuzzy Modeling Approach Based on Evolving Data Clustering Luís Miguel Magalhães Torres1 · Ginalber Luiz de Oliveira Serra2 Received: 21 December 2017 / Revised: 21 April 2018 / Accepted: 6 June 2018 © Brazilian Society for Automatics–SBA 2018
Abstract In this paper, an online evolving fuzzy Takagi–Sugeno state-space model identification approach for multivariable dynamic systems is proposed. The proposed methodology presents an evolving fuzzy clustering algorithm based on the concept of recursive density estimation for online antecedent structure adaptation according to the data. For estimation of the minimum realization state-space models in the consequent of the fuzzy rules is proposed a recursive methodology based on the eigensystem realization fuzzy algorithm using the system fuzzy Markov parameters obtained recursively from experimental data. Experimental results from the modeling of multivariable nonlinear evaporator process are presented. Keywords Evolving fuzzy systems · Multivariable dynamic systems · State space · System identification
1 Introduction
1.1 State of Art
The acquisition of mathematical models capable of representing real physical systems is of extreme importance in the most diverse areas of science and engineering. These models can be used in many applications such as fault diagnosis (Forrai 2017; Xia et al. 2016), design of control systems (Costa and Serra 2017; Noshadi et al. 2016; Liu et al. 2016), development of soft sensor for process monitoring (Huang et al. 2015; Zhou et al. 2014; Souza et al. 2016). Such applications require that the models must be able to represent the most diverse characteristics of the dynamic system under analysis, such as nonlinearities, temporal parameters variations, uncertainty, among many others.
To deal with the nonlinearities present in many practical systems, a wide variety of models has been largely researched by the scientific community. Hammerstein and Wiener models are block-oriented whose structure consists of two parts: a linear dynamic model and a static nonlinearity (CastroGarcia et al. 2017; Mzyk and Wachel 2017; Li and Qiliang 2017). Another classic approach for identification of nonlinear systems is Volterra Series (Prawin and Rao 2017; Maachou et al. 2014; Cheng et al. 2017). This kind of model is an extension of the convolution integral of linear systems by a series of multi-dimensional convolution integral. With the advent of computational intelligence techniques, approaches like neural networks (Zhao et al. 2014; Raj and Sivanandan 2017; Sahoo and Chakraverty 2017) and Takagi–Sugeno (TS) fuzzy models (Cheung et al. 2014; Precup et al. 2014; Cervantes et al. 2016) are also applied for identification of nonlinear dynamic systems. From the proposal of TS fuzzy models to the present day, this type of inference system has been highly used for modeling of complex systems (Takagi and Sugeno 1985; Chang et al. 2016; Tsai and Chen 2017). In Salgado et al. (2017) is proposed a mixed fuzzy clustering algorithm to derive Takag
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