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ARTICLE IN PRESS Neurocomputing 73 (2009) 517–524
Contents lists available at ScienceDirect
Neurocomputing journal homepage: www.elsevier.com/locate/neucom
A novel hybrid algorithm for creating self-organizing fuzzy neural networks Omid Khayat a,, Mohammad Mehdi Ebadzadeh a, Hamid Reza Shahdoosti a, Ramin Rajaei b, Iman Khajehnasiri c a
Department of Biomedical Engineering, Amirkabir University of Technology, Tehran, Iran Computer Engineering Department, Amirkabir University of Technology, Tehran, Iran c Electrical Engineering Department, Sharif University of Technology, Tehran, Iran b
a r t i c l e in fo
abstract
Available online 6 August 2009
A novel hybrid algorithm based on a genetic algorithm and particle swarm optimization to design a fuzzy neural network, named self-organizing fuzzy neural network based on GA and PSO (SOFNNGAPSO), to implement Takagi–Sugeno (TS) type fuzzy models is proposed in this paper. The proposed algorithm, as a new hybrid algorithm, consists of two phases. A tuning based on TS’s fuzzy model is applied to identify the fuzzy structure, and also a fuzzy cluster validity index is utilized to determine the optimal number of clusters. To obtain a more precision model, GA and PSO are performed to conduct fine tuning for the obtained parameter set of the premise parts and consequent parts in the aforementioned fuzzy model. The proposed algorithm is successfully applied to three tested examples. & 2009 Elsevier B.V. All rights reserved.
Keywords: Self-organizing Fuzzy neural network Genetic algorithm Particle swarm optimization Xie–Beni index
1. Introduction Fuzzy systems, as model-free approaches, provide a high-level, approximate human reasoning ability. It has been shown that fuzzy systems could serve as a powerful tool for system modeling and control [17,35]. A fuzzy system is intrinsically a rule-based system which is composed of a set of linguistic rules in the form of ‘‘IF–THEN’’. As there is no formal and effective way of knowledge acquisition, it is difficult for a designer to acquire appropriate fuzzy rules from numerical training data [36]. In addition, fuzzy systems lack adaptability for possible changes in the reasoning environment. Fuzzy model is one of the most important techniques in fuzzy logic, which has advantages of excellent capability to deal with complex systems [1,4,38]. For building a fuzzy model, the most important issue is the structure identification and parameters estimation. The structure identification concerns about the appropriate number of fuzzy rules, and the parameter estimation is related to the calculation of parameters that represent a reliable system. Within various fuzzy model techniques, one of the most outstanding models was proposed by Takagi and Sugeno [33]. This fuzzy model is capable of describing a complex system using
Corresponding author. Tel.: +98 915 164 3065.
E-mail addresses: [email protected] (O. Khayat), [email protected] (M.M. Ebadzadeh), [email protected] (H.R. Shahdoosti), [email protected] (R. Rajaei), [email protected] (I. Khajehnasiri). 0925-2312/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.neucom.2009.06.013
sufficient rules and training data [4,6,31]. However, this fuzzy model must define fuzzy subspaces in advance, and then the parameters in consequences are obtained through a Kalman filter type of estimation [4]. Various alternative approaches for modeling Takagi and Sugeno’s fuzzy rules have been proposed in the literature [7,9,17,23,24]. In general, the input space is decomposed into fuzzy subspaces according to the input data and then the system or function approximation is approximated in each subspace by a simple linear regression function. The most drawbacks of the aforementioned approaches do not account for the interaction between input and output variables [4]. Recently, some authors have employed two phases of learning for fuzzy model: the coarse learning phase and the fine-tuning phase [4,21,22,34]. The idea is to formulate fuzzy structure with input and output variables of the system, and the parameter set of premise parts and consequent parts are approximately first determined. Moreover, the parameter set of premise parts and consequent are precisely adjusted by the fine-tuning phase to improve the modeling accuracy. However, the coarse-tuning phase does not incorporate the validity index in fuzzy models, and the number of fuzzy rules is not determined by optimization algorithms. In the fine-tuning phase, the gradient descent approach is used to adjust the parameter set of premise parts and consequent parts. Due to the property of gradient descent approach, the found parameter set may be trapped in local optimum [17,29,30]. This paper proposes a novel hybrid algorithm to design a fuzzy neural network to implement Takagi–Sugeno (TS) models [33]. One of the main novelties of the proposed algorithm is
Contents lists available at ScienceDirect
Neurocomputing journal homepage: www.elsevier.com/locate/neucom
A novel hybrid algorithm for creating self-organizing fuzzy neural networks Omid Khayat a,, Mohammad Mehdi Ebadzadeh a, Hamid Reza Shahdoosti a, Ramin Rajaei b, Iman Khajehnasiri c a
Department of Biomedical Engineering, Amirkabir University of Technology, Tehran, Iran Computer Engineering Department, Amirkabir University of Technology, Tehran, Iran c Electrical Engineering Department, Sharif University of Technology, Tehran, Iran b
a r t i c l e in fo
abstract
Available online 6 August 2009
A novel hybrid algorithm based on a genetic algorithm and particle swarm optimization to design a fuzzy neural network, named self-organizing fuzzy neural network based on GA and PSO (SOFNNGAPSO), to implement Takagi–Sugeno (TS) type fuzzy models is proposed in this paper. The proposed algorithm, as a new hybrid algorithm, consists of two phases. A tuning based on TS’s fuzzy model is applied to identify the fuzzy structure, and also a fuzzy cluster validity index is utilized to determine the optimal number of clusters. To obtain a more precision model, GA and PSO are performed to conduct fine tuning for the obtained parameter set of the premise parts and consequent parts in the aforementioned fuzzy model. The proposed algorithm is successfully applied to three tested examples. & 2009 Elsevier B.V. All rights reserved.
Keywords: Self-organizing Fuzzy neural network Genetic algorithm Particle swarm optimization Xie–Beni index
1. Introduction Fuzzy systems, as model-free approaches, provide a high-level, approximate human reasoning ability. It has been shown that fuzzy systems could serve as a powerful tool for system modeling and control [17,35]. A fuzzy system is intrinsically a rule-based system which is composed of a set of linguistic rules in the form of ‘‘IF–THEN’’. As there is no formal and effective way of knowledge acquisition, it is difficult for a designer to acquire appropriate fuzzy rules from numerical training data [36]. In addition, fuzzy systems lack adaptability for possible changes in the reasoning environment. Fuzzy model is one of the most important techniques in fuzzy logic, which has advantages of excellent capability to deal with complex systems [1,4,38]. For building a fuzzy model, the most important issue is the structure identification and parameters estimation. The structure identification concerns about the appropriate number of fuzzy rules, and the parameter estimation is related to the calculation of parameters that represent a reliable system. Within various fuzzy model techniques, one of the most outstanding models was proposed by Takagi and Sugeno [33]. This fuzzy model is capable of describing a complex system using
Corresponding author. Tel.: +98 915 164 3065.
E-mail addresses: [email protected] (O. Khayat), [email protected] (M.M. Ebadzadeh), [email protected] (H.R. Shahdoosti), [email protected] (R. Rajaei), [email protected] (I. Khajehnasiri). 0925-2312/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.neucom.2009.06.013
sufficient rules and training data [4,6,31]. However, this fuzzy model must define fuzzy subspaces in advance, and then the parameters in consequences are obtained through a Kalman filter type of estimation [4]. Various alternative approaches for modeling Takagi and Sugeno’s fuzzy rules have been proposed in the literature [7,9,17,23,24]. In general, the input space is decomposed into fuzzy subspaces according to the input data and then the system or function approximation is approximated in each subspace by a simple linear regression function. The most drawbacks of the aforementioned approaches do not account for the interaction between input and output variables [4]. Recently, some authors have employed two phases of learning for fuzzy model: the coarse learning phase and the fine-tuning phase [4,21,22,34]. The idea is to formulate fuzzy structure with input and output variables of the system, and the parameter set of premise parts and consequent parts are approximately first determined. Moreover, the parameter set of premise parts and consequent are precisely adjusted by the fine-tuning phase to improve the modeling accuracy. However, the coarse-tuning phase does not incorporate the validity index in fuzzy models, and the number of fuzzy rules is not determined by optimization algorithms. In the fine-tuning phase, the gradient descent approach is used to adjust the parameter set of premise parts and consequent parts. Due to the property of gradient descent approach, the found parameter set may be trapped in local optimum [17,29,30]. This paper proposes a novel hybrid algorithm to design a fuzzy neural network to implement Takagi–Sugeno (TS) models [33]. One of the main novelties of the proposed algorithm is
