Nonlinear system identification using least squares support vector machine tuned by an adaptive particle swarm optimization

AbstractIn this paper, we present a method for nonlinear system identification. The proposed method adopts least squares support vector machine (LSSVM) to approximate a nonlinear autoregressive model with eXogeneous (NARX). First, the orders of NARX model are determined from input–output data via Lipschitz quotient criterion. Then, an LSSVM model is used to approximate the NARX model. To obtain an efficient LSSVM model, a novel particle swarm optimization with adaptive inertia weight is proposed to tune the hyper-parameters of LSSVM. Two experimental results are given to illustrate the effectiveness of the proposed method.

[1]  Ali Belmehdi,et al.  Multi-objective optimization of TSK fuzzy models , 2008, 2008 5th International Multi-Conference on Systems, Signals and Devices.

[2]  Kumpati S. Narendra,et al.  Identification and control of dynamical systems using neural networks , 1990, IEEE Trans. Neural Networks.

[3]  Fernando José Von Zuben,et al.  Hybridizing mixtures of experts with support vector machines: Investigation into nonlinear dynamic systems identification , 2007, Inf. Sci..

[4]  Johan A. K. Suykens,et al.  Least Squares Support Vector Machine Classifiers , 1999, Neural Processing Letters.

[5]  Bidyadhar Subudhi,et al.  A differential evolution based neural network approach to nonlinear system identification , 2011, Appl. Soft Comput..

[6]  Om P. Malik,et al.  Identification of nonlinear systems by Takagi-Sugeno fuzzy logic grey box modeling for real-time control , 2005 .

[7]  Hsiao-Ping Huang,et al.  Identification of Block-Oriented Nonlinear Processes Using Designed Relay Feedback Tests , 2005 .

[8]  Qi Wu,et al.  The forecasting model based on wavelet nu-support vector machine , 2009, Expert Syst. Appl..

[9]  Arthur L. Dexter,et al.  On-line identification of computationally undemanding evolving fuzzy models , 2007, Fuzzy Sets Syst..

[10]  Zhao Lu,et al.  Linear programming support vector regression with wavelet kernel: A new approach to nonlinear dynamical systems identification , 2009, Math. Comput. Simul..

[11]  Jiashu Zhang,et al.  Nonlinear dynamic system identification using pipelined functional link artificial recurrent neural network , 2009, Neurocomputing.

[12]  Zhao Lu,et al.  Non-Mercer hybrid kernel for linear programming support vector regression in nonlinear systems identification , 2009, Appl. Soft Comput..

[13]  Y. K. Wong,et al.  Nonlinear system identification using optimized dynamic neural network , 2009, Neurocomputing.

[14]  G. P. Gualtieri,et al.  A modified Volterra series approach for nonlinear dynamic systems modeling , 2002 .

[15]  Shutao Li,et al.  Tuning SVM parameters by using a hybrid CLPSO-BFGS algorithm , 2010, Neurocomputing.

[16]  Xiaoli Zhang,et al.  An ACO-based algorithm for parameter optimization of support vector machines , 2010, Expert Syst. Appl..

[17]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[18]  Vladimir Vapnik,et al.  Statistical learning theory , 1998 .

[19]  Leon O. Chua,et al.  Fading memory and the problem of approximating nonlinear operators with volterra series , 1985 .

[20]  Chia-Feng Juang,et al.  TS-fuzzy system-based support vector regression , 2009, Fuzzy Sets Syst..

[21]  José Luis Rojo-Álvarez,et al.  Support vector method for robust ARMA system identification , 2004, IEEE Transactions on Signal Processing.

[22]  E. Bai,et al.  Block Oriented Nonlinear System Identification , 2010 .

[23]  Yanchun Liang,et al.  Identification and control of nonlinear systems by a dissimilation particle swarm optimization-based Elman neural network , 2008 .

[24]  James Kennedy,et al.  Particle swarm optimization , 2002, Proceedings of ICNN'95 - International Conference on Neural Networks.

[25]  Nong Zhang,et al.  Application of evolving Takagi-Sugeno fuzzy model to nonlinear system identification , 2008, Appl. Soft Comput..

[26]  Mohammad Mehdi Ebadzadeh,et al.  A novel particle swarm optimization algorithm with adaptive inertia weight , 2011, Appl. Soft Comput..

[27]  Xiangdong He,et al.  A New Method for Identifying Orders of Input-Output Models for Nonlinear Dynamic Systems , 1993, 1993 American Control Conference.

[28]  Pakkiriswamy Aadaleesan,et al.  Nonlinear system identification using Wiener type Laguerre–Wavelet network model , 2008 .

[29]  Mehmet Karaköse,et al.  A multi-objective artificial immune algorithm for parameter optimization in support vector machine , 2011, Appl. Soft Comput..

[30]  Musa H. Asyali,et al.  Nonlinear system identification via Laguerre network based fuzzy systems , 2009, Fuzzy Sets Syst..

[31]  Ling Zhuang,et al.  Prediction of silicon content in hot metal using support vector regression based on chaos particle swarm optimization , 2009, Expert Syst. Appl..

[32]  X. C. Guo,et al.  A novel LS-SVMs hyper-parameter selection based on particle swarm optimization , 2008, Neurocomputing.

[33]  Feng Qian,et al.  Identification and control of nonlinear systems by a time-delay recurrent neural network , 2009, Neurocomputing.

[34]  A. Bagis.  Fuzzy rule base design using tabu search algorithm for nonlinear system modeling. , 2008, ISA transactions.

[35]  H. Akaike.  A new look at the statistical model identification , 1974 .

[36]  Shuichi Adachi,et al.  A New System Identification Method Based on Support Vector Machines , 2001 .

[37]  Yue Shi,et al.  A modified particle swarm optimizer , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[38]  H. Toivonen,et al.  Support vector method for identification of Wiener models , 2009 .