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In this paper, fuzzy models with orthonormal basis functions (OBF) framework are employed for modeling the nonlinear dynamics of biological treatment processes. These models are consisting of a linear part describing the system dynamics (Laguerre filters) followed by a non-linear static part (fuzzy system). The training procedure contains of two main steps: 1) obtaining the optimum time-scale and the order of truncated Laguerre network as the linear part and 2) defining membership functions, corresponding rules and adjusting the consequent parameters of fuzzy system as the nonlinear part. A comparison between the responses of the developed model and the original plant was performed in order to validate the accuracy of the developed model.
Wydawca
Rocznik
Tom
Strony
343--356
Opis fizyczny
Bibliogr. 27 poz., rys., tab.
Twórcy
autor
- Department of Mechanical Engineering, University of Guilan, Rasht, 4199613769 Guilan, Iran
autor
- Department of Chemistry, University of Guilan, Rasht, 4199613769 Guilan, Iran
autor
- WASTE, University of Stuttgart, 70569 Stuttgart, Germany
autor
- Department of Mechanical Engineering, Politecnico di Milano, 20156 Milan, Italy
Bibliografia
- [1] Y.J. Chan, M.F. Chong, C.L. Law, D.G. Hassell, A review on anaerobic–aerobic treatment of industrial and municipal wastewater, Chemical Engineering Journal, 155, 2009, 1-18.
- [2] K.V. Gernaey, M.C.M. van Loosdrecht, M. Henze, M. Lind, S.B. Jrgensen, Activated sludge wastewater treatment plant modelling and simulation: state of the art, Environmental Modelling & Software, 19, 2004, 763-783.
- [3] I. Iacopozzi, V. Innocenti, S. Marsili-Libelli, E. Giusti, A modified Activated Sludge Model No. 3 (ASM3) with two-step nitrification – denitrification, Environmental Modelling & Software,22, 2007, 847-861.
- [4] L. Ljung, Perspectives on system identification, Annual Reviews in Control, 34, 2010, 1-12.
- [5] E.K. Juuso, Integration of intelligent systems in development of smart adaptive systems, International Journal of Approximate Reasoning, 35, 2004, 307-337.
- [6] Y.L. Hsu, J.S. Wang, A Wiener-type recurrent neural network and its control strategy for nonlinear dynamic applications, Journal of Process Control, 19, 2009, 942-953.
- [7] U. Mehta, S. Majhi, Identification of a class of Wiener and Hammerstein-type nonlinear processes with monotonic static gains, ISA Transactions, 49, 2010, 501-509.
- [8] R.J.G.B. Campello, F.J. Von Zuben, W.C. Amaral, L.A.C. Meleiro, R. Maciel Filho, Hierarchical fuzzy models within the framework of orthonormal basis functions and their application to bioprocess control, Chemical Engineering Science, 58, 2003, 4259- 4270.
- [9] I. Łkrjanca, S. Blai, O. Agamennoni, Identification of dynamical systems with a robust interval fuzzy model, Automatica, 41, 2005, 327-332.
- [10] H. He, Fuzzy modeling and fuzzy control (book review), IEEE Computational Intelligence Magazine, 3, 2008, 8-10.
- [11] R. Liutkeviius, Fuzzy Hammerstein Model of Nonlinear Plant, Nonlinear Analysis: Modelling and Control, 13, 2008, 201-212.
- [12] B. Wahlberg, P.M. Makila, Approximation of stable linear dynamical systems using Laguerre and Kautz functions, Automatica, 32, 1996, 693-708.
- [13] M. Alci, M.H. Asyali, Nonlinear system identification via Laguerre network based fuzzy systems, Fuzzy Sets and Systems, 160, 2009, 3518-3529.
- [14] R. Babuka, H. Verbruggen, Neuro-fuzzy methods for nonlinear system identification, Annual Reviews in Control, 27, 2003, 73-85.
- [15] M.A. Masnadi-Shirazi, M. Aleshams, Laguerre discrete-time filter design, Computers and Electrical Engineering, 29, 2003, 173-192.
- [16] T. Takagi, M. Sugeno, fuzzy identification of systems and its applications to modeling and control,”IEEE Transactions on Systems, Man and Cybernetics, 15, 1985, 116-132.
- [17] Y. Fu, G.A. Dumont, An optimum time scale for discrete Laguerre network, IEEE Transaction on Automatic Control, 38, 1993, 934-938.
- [18] T.O. E. Silva, On the determination of the optimal pole position of Laguerre filters, IEEE Transaction of Signal Processing, 43, 1999, 2079-2087.
- [19] A.N. Venkat, P. Vijaysai, R.D. Gudi, Identification of complex nonlinear processes based on fuzzy decomposition of the steady state space, Journal of Process Control, 13, 2003, 473-488.
- [20] G. Beliakov, M. King, Density based fuzzy cmeans clustering of non-convex patterns, European Journal of Operational Research, 173, 2006, 717-728
- [21] B. Feil, J. Abonyi, F. Szeifert, Model order selection of nonlinear input-output models - a clustering based approach, Journal of Process Control, 14, 2004, 593-602.
- [22] Y. Zhang,W.Wang, X. Zhang, Y. Li, A cluster validity index for fuzzy clustering, Information Sciences, 178, 2008, 1205-1218.
- [23] X.L. Xie, G. Beni, A validity measure for fuzzy clustering, IEEE Transaction on Pattern Analyzing Machine Intelligence, 13, 1991, 841-847.
- [24] G. Olsson, J.F. Andrews, The dissolved oxygen profile - a valuable tool for control of the activated sludge process, Water Research, 12, 1978, 985-1004.
- [25] L.K. Wang, N.K. Shammas, Y.T. Hung, Advanced Biological Treatment Processes, Volume 9, in: the Handbook of Environmental Engineering series, Humana Press, 2009.
- [26] F. Nejjari, A. Benhammou, B. Dahhou, G. Roux, Non-linear multivariable adaptive control of an activated sludge wastewater treatment process, International Journal of Adaptive Control and Signal Process, 13, 1999, 347-365.
- [27] A. Janczak, Identification of Nonlinear Systems Using Neural Networks and Polynomial Models: A Block-Oriented Approach, Springer-Verlag, Berlin, 2004.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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