Nonlinear Dynamic System Identification Using Volterra Series: Multi-Objective Optimization Approach
Sayed Mohammad Reza Loghmanian*,**, Rubiyah Yusof**,
and Marzuki Khalid**
*Faculty of Engineering, Islamic Azad University, Mobarakeh Branch, Isfahan, Iran
**Centre for Artificial Intelligence and Robotics (CAIRO), Universiti Teknologi Malaysia, International Campus, Jalan Semarak, 54100 Kuala Lumpur, Malaysia
In this paper, identification of the nonlinear dynamic systems based on an optimized Volterra model structure is presented. Model structure selection is an important step in system identification, which involves the selection of variables and terms of a model. The key task is choosing a compact model representation where only significant terms are selected from among all the possible ones while also taking good performance into account. An automated algorithm based on multi-objective optimization is proposed for this purpose. The developed model should fulfill two criteria or objectives, namely, high prediction accuracy and optimum model structure. A genetic algorithm is applied to search the significant Volterra kernels from among all possible candidate model combinations. The result shows that the proposed algorithm is able to correctly identify the simulated examples and adequately model the nonlinear discrete dynamic system.
and Marzuki Khalid, “Nonlinear Dynamic System Identification Using Volterra Series: Multi-Objective Optimization Approach,” J. Adv. Comput. Intell. Intell. Inform., Vol.16, No.4, pp. 489-495, 2012.
-  O. Nelles, “Nonlinear System Identification; From Classical Approaches to Neural Networks and Fuzzy Models,” Springer, Germany, 2001.
-  M. J. Korenberg, “A Robust Orthogonal Algorithm for System Identification and Time-Series Analysis,” Biol. Cybern., Vol.60, pp. 267-276, 1989.
-  R. H. M. Abbas and M. M. Bayoumi, “An adaptive evolutionary algorithm for Volterra system identification,” Pattern Recognition Letters, Vol.26, No.1, pp. 109-119, 2005.
-  L. Yao, “Genetic Algorithm Based Identification of Nonlinear Systems by Sparse Volterra Filters,” IEEE Trans. Signal Process., Vol.47, No.12, pp. 3433-3435, 1999.
-  H. M. Abbas and M. M. Bayoumi, “Volterra System Identification Using Adaptive Genetic Algorithms,” Applied Soft Computing, Vol.5, pp. 75-86, 2004.
-  S. M. R. Loghmanian, R. Ahmad, and H. Jamaluddin, “Multiobjective Optimization of Neural Network Structure for System Identification Using Genetic Algorithm,” Int. J. of Computer Sciences and Engineering Systems, Vol.5, No.3, 2011.
-  L. Li and S. A. Billings, “Analysis of Nonlinear Oscillators Using Volterra Series in the Frequency Domain,” J. of Sound and Vibration, Vol.330, pp. 337-355, 2011.
-  S. Boyd and L. O. Chua, “Fading Memory and the Problem of Approximating Nonlinear Operators with Volterra Series,” IEEE Trans. on Circuits and Systems, Vol.32, No.11, pp. 1150-1161, 1985.
-  Q. Zhang, B. Suki, D. Westwick, and K. R. Lutchen, “Factors Affecting Volterra Kernel Estimation: Emphasis on Lung Tissue Viscoelasticity,” Annals of Biomedical Engineering, Vol.26, pp. 103-116, 1998.
-  W. M. Ling and D. E. Rivera, “Control Relevant Model Reduction of Volterra Series Models,” J. of Process Control, Vol.8, No.2, pp. 79-88, 1998.
-  J.Wray and G. Green, “Calculation of the Volterra Kernels of Nonlinear Dynamic Systems Using an Artificial Neural Network,” Biol. Cybern., Vol.71, pp. 187-195, 1994.
-  A. Rosa, R. J. G. B. Campello, and W. C. Ameral, “Choice of Free Parameters in Expansions of Discrete Time Volterra Models Using Kautz Functions,” Automatica, Vol.43, pp. 1084-1091, 2007.
-  D. Mirri, G. Iuculano, P. A. Traverso, G. Pasini, and F. Filicori, “Non-linear dynamic system modelling based on modified Volterra series approaches,” Measurement, Vol.33, No.1, pp. 9-21, 2003.
-  H. Tang, Y. H. Liao, J. Y. Cao, and H. Xie, “Fault Diagnosis Approach Based on Volterra Models,” Mechanical Systems and Signal Processing, Vol.24, pp. 1099-1113, 2010.
-  W. Suleiman and A. Monin, “New Method for Identifying Finite Degree Volterra Series,” Automatica, Vol.44, pp. 488-497, 2008.
-  H. M. Abbas and M. M. Bayoumi, “Volterra system identification using adaptive genetic algorithms,” Applied Soft Computing, Vol.5, No.1, pp. 75-86, 2004.
-  J. D. Schaffer, “Some Experiments in Machine Learning Using Vector Evaluated Genetic Algorithm,” K. Deb (Ed.), Multi-objective Optimization Using Evolutionary Algorithms, John Wiley, Chichester, 1984.
-  K. Deb, “Multi-objective Optimization Using Evolutionary Algorithms,” John Wiley, Chichester, 2001.
-  N. Srinivas and K. Deb, “Multi-objective Optimization Using Nondominated Sorting in Genetic Algorithms,” Evolutionary Computation, Vol.2, No.3, pp. 221-248, 1994.
-  K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II,” IEEE Trans. on Evolutionary Computation, Vol.6, No.2, pp. 182-197, 2002.
-  K. Tsuchida, H. Sato, H. Aguirre, and K. Tanaka, “Analysis of NSGA-II and NSGA-II with CDAS, and Proposal of an Enhanced CDASMechanism,” J. of Advanced Computational Intelligence and Intelligent Informatics, Vol.13, No.4, pp. 470-480, 2009.
-  S. Y. Fakhouri, “Identification of the Volterra Kernels of Nonlinear Systems,” IEE Proc., Vol.127, No.6, pp. 296-304, 1980.
-  S. M. R. Loghmanian, H. Jamaluddin, R. Ahmad, R. Yusof, and M. Khalid, “Structure optimization of neural network for dynamic system modeling using multi-objective genetic algorithm,” Neural Comput & Applic, DOI 10.1007/s00521-011-0560-3.
-  K. Deb and S. Jain, “Running Performance Metrics for EvolutionaryMulti-objective Optimization, Technical Report 2002004,” Kan-GAL, Indian Institute of Technology, Kanpur 208016, 2002.
-  S. A. Billings and W. S. F. Voon, “Correlation Based Model Validity Tests for Nonlinear Models,” Int. J. Control., Vol.44, No.1, pp. 235-244, 1986.
This article is published under a Creative Commons Attribution-NoDerivatives 4.0 International License.