Nonlinear System Identification with a Real–Coded Genetic Algorithm (RCGA)

Cherif, Imen; Fnaiech, Farhat

doi:10.1515/amcs-2015-0062

Abstract

This paper is devoted to the blind identification problem of a special class of nonlinear systems, namely, Volterra models, using a real-coded genetic algorithm (RCGA). The model input is assumed to be a stationary Gaussian sequence or an independent identically distributed (i.i.d.) process. The order of the Volterra series is assumed to be known. The fitness function is defined as the difference between the calculated cumulant values and analytical equations in which the kernels and the input variances are considered. Simulation results and a comparative study for the proposed method and some existing techniques are given. They clearly show that the RCGA identification method performs better in terms of precision, time of convergence and simplicity of programming.

References

Annaswamy, A.S. and Yu, H. (1996). Adaptive neural networks: A new approach to parameter estimation, IEEE Transactions on Neural Networks7(4): 907–918.10.1109/72.50893418263486
Search in Google Scholar
Attar, P.J. and Dowell, E.H. (2005). A reduced order system ID approach to the modelling of nonlinear structural behavior in aeroelasticity, Journal of Fluids and Structures21(5–7): 531–542.10.1016/j.jfluidstructs.2005.08.012
Search in Google Scholar
Cherif, I., Abid, S., Fnaiech, F. and Favier, G. (2004). Volterra kernels identification using higher order moments for different input signals, IEEE-ISCCSP, Hammamet, Tunisia, pp. 845–848.
Search in Google Scholar
Cherif, I., Abid, S. and Fnaiech, F. (2005). Blind identification of quadratic systems under i.i.d. excitation using genetic algorithms, 8th International Symposium on Signal Processing and its Applications ISSPA’2005, Sydney, Australia, pp. 463–466.
Search in Google Scholar
Cherif I., Abid S., and Fnaiech, F. (2007). Blind nonlinear system identification under Gaussian and/or i.i.d. excitation using genetic algorithms, IEEE International Conference on Signal Processing and Communication ICSPC 2007, Dubai, UAE, pp. 644–647.
Search in Google Scholar
Cherif, I., Abid, S., Fnaiech, F. (2012). Nonlinear blind identification with three dimensional tensor analysis, Mathematical Problems in Engineering2012, Article ID: 284815.10.1155/2012/284815
Search in Google Scholar
Glentis, G.O.A., Koukoulas, P. and Kalouptsidis, N. (1999). Efficient algorithms for Volterra system identification, IEEE Transactions on Signal Processing47(11): 3042–3057.10.1109/78.796438
Search in Google Scholar
Greblicki, W. (2001). Recursive identification of Wiener systems, International Journal of Applied Mathematics and Computer Science11(4): 977–991.
Search in Google Scholar
Herrera, F., Lozano, M., and Verdegay, J.L. (1998). Tackling real-coded genetic algorithms: Operators and tools for behavioural analysis, Artificial Intelligence Review12(4): 265–319.10.1023/A:1006504901164
Search in Google Scholar
Koukoulas, P. and Kalouptsidis, N. (1996). On blind identification of quadratic systems, EUSIPCO’96, Trieste, Italy, pp. 1929–1932.
Search in Google Scholar
Koukoulas, P. and Kalouptsidis, N. (1997). Third order system identification, International Conference on Acoustic Speech and Signal Processing: ICASSP’97, Munich, Germany, pp. 2405–2408.
Search in Google Scholar
Koukoulas, P. and Kalouptsidis, N. (2000). Second order Volterra system identification, IEEE Transactions on Signal Processing48(12): 3574–3577.10.1109/78.887051
Search in Google Scholar
Kalouptsidis, N. and Koukoulas, P. (2005). Blind identification of Volterra–Hammerstein systems, IEEE Transactions on Signal Processing53(8): 2777–2787.10.1109/TSP.2005.850357
Search in Google Scholar
Mathlouthi H., Abderrahim K., Msahli F. and Gerard F. (2009). Crosscumulants based approaches for the structure identification of Volterra models, International Journal of Automation and Computing6(4): 420–430.10.1007/s11633-009-0420-0
Search in Google Scholar
Mendel J.M. (1991). Tutorial on higher order statistics (spectra) in signal processing and system theory: Theoretical results and some applications, Proceedings of the IEEE79(3): 278–305.10.1109/5.75086
Search in Google Scholar
Ozertem, U. and Erdogmus, D. (2009). Second-order Volterra system identification with noisy input-output measurements, IEEE Signal Processing Letters16(1): 18–21.10.1109/LSP.2008.2008478
Search in Google Scholar
Orjuela, R., Marx, B., Ragot, J. and Maquin D. (2013). Nonlinear system identification using heterogeneous multiple models, International Journal of Applied Mathematics and Computer Science23(1): 103–115, DOI: 10.2478/amcs-2013-0009.10.2478/amcs-2013-0009
Search in Google Scholar
Phan, M.Q., Longman, R.W., Lee, S.C. and Lee, J.-W. (2003). System identification from multiple-trial data corrupted by non-repeating periodic disturbances, International Journal of Applied Mathematics and Computer Science13(2): 185–192.
Search in Google Scholar
Stathaki, T. and Scohyers, A. (1997). A constrained optimisation approach to the blind estimation of Volterra kernels, IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP-97, Munich, Germany, pp. 2373–2376.
Search in Google Scholar
Stoica, P. and Soderstorm, T. (1982). Instrumental variable methods for identification of Hammerstein systems, International Journal of Control35(3): 459–476.10.1080/00207178208922632
Search in Google Scholar
Tan, H.Z. and Chow, T.W.S. (2000). Blind identification of quadratic nonlinear models using neural networks with higher order cumulants, IEEE Transactions on Industrial Electronics47(3): 687–696.10.1109/41.847909
Search in Google Scholar
Tseng, C.H. and Powers, E.J. (1995). Identification of cubic systems using higher order moments of i.i.d. signals, IEEE Transactions on Signal Processing43(7): 1733–1735.
Search in Google Scholar
Tsoulkas, V., Koukoulas, P. and Kalouptsidis, N. (2001). Identification of input-output bilinear system using cumulants, IEEE Transactions on Signal Processing49(11): 2753–2761.10.1109/78.960423
Search in Google Scholar
Vasconcelos, J.A., Ramirez, J.A., Takahashi, R.H.C. and Saldanha, R.R. (2001). Improvement in genetic algorithms, IEEE Transactions on Magnetics37(5): 3414–3417.10.1109/20.952626
Search in Google Scholar
Zhang, S. and Constantinides, A.G. (1992). Lagrange programming neural networks, IEEE Transactions on Circuits and Systems: Analog and Digital Signal Processing39(7): 441–452.10.1109/82.160169
Search in Google Scholar

Nonlinear System Identification with a Real–Coded Genetic Algorithm (RCGA)

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