Nonlinear System Identification Using Hammerstein-Wiener Neural Network and subspace algorithms

Subject Areas : Embedded Systems

Maryam  Ashtari Mahini ¹ (Dept of Computer Engineering. Science and Research Branch, Islamic Azad University, Tehran, Iran.)
Mohammad  Teshnehlab ² (Department of Computer Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran.)
Mojtaba  Ahmadieh khanehsar ³ (Department of Control Engineering, Semnan University, Semnan, Iran.)

Received: 2015-01-12 Accepted : 2015-03-12 Published : 2015-08-01

Keywords: nonlinear system identification, Neural Network, Hammerstein-Wiener model, state space and subspace identification,

Abstract :

Neural networks are applicable in identification systems from input-output data. In this report, we analyze theHammerstein-Wiener models and identify them. TheHammerstein-Wiener systems are the simplest type of block orientednonlinear systems where the linear dynamic block issandwiched in between two static nonlinear blocks, whichappear in many engineering applications; the aim of nonlinearsystem identification by Hammerstein-Wiener neural networkis finding model order, state matrices and system matrices. Wepropose a robust approach for identifying the nonlinear systemby neural network and subspace algorithms. The subspacealgorithms are mathematically well-established and noniterativeidentification process. The use of subspace algorithmmakes it possible to directly obtain the state space model.Moreover the order of state space model is achieved usingsubspace algorithm. Consequently, by applying the proposedalgorithm, the mean squared error decreases to 0.01 which isless than the results obtained using most approaches in theliterature.

References:

[1] A.Atiya, and C.Ji. "How initial conditions affect generalization performance in large networks." IEEE Trans. Neural Netw., vol. 8, no. 2, 1997,pp. 448-451.
[2] A.Hagenblad. aspects of the identification of wiener model. sweden, 1999.
[3] A.Wills, and B.Ninness. "Generalised Hammerstein-Wiener System Estimation and a Benchmark Application." n.d.
[4] Bai, E.W. "A blind approach to the Hammerstein-Wiener model identification." Automatica, 38(6), 2002,pp. 967–979.
[5] Ch.Yan, and J. Wang and Q.Zhang. " Subspace identification methods for Hammerstein systems: rank constraint and dimension problem." International Journal of Control, 2010.
[6] D.Wang, F.Ding. "Extended stochastic gradient identification algorithms for Hammerstein-Wiener ARMAX." Computers & Mathematics with Applications, 56(12), 2008 ,pp.157-3164.
[7] E.Eskinat, S.H. Johnson and W.L. Luyben. "Use of Hammerstein model in Identification of nonlinear system." AIChE Journal, February ,Vol. 37, No. 2, 1991 .
[8] E.W.Bai. "An optimal two-stage identification algorithm forHammerstein-Wiener nonlinear systems." Automatica, vol. 34, no. 3, 1998.
[9] F.Giri, and E.W.Bai. "Block-oriented nonlinear system identification." springer, 2010.
[10] F.Taringou, O. Hamm, B.rinivasan, R.Malhame and F.M.Ghannouchi. "Behaviour modelling of wideband RF transmitters using Hammerstein-Wiener models." IET Circuits Devices& Systems, 4(4), 2010,pp. 282-290.
[11] F.Z.Chaoui, F.Giri, Y.Rochdi, M.Haloua, and A.Naitali. "system identification based on Hammerstein model." International Journal of, 2005,pp. 430-442.
[12] G.B.Giannakis, E.Serpedin. "A bibliography on nonlinear system identification." signal process,vol. 83 ,no. 3, 2001,pp. 533-580.
[13] H.AI-Duwaish, N.M.Karim, and V.Chandrasekar. "Use of multilayer feedforward neural networks in identification and control of Wiener model." IEE Proceedings of Control Theory and Applications, Vol. 143, 1996,pp. 255-258.
[14] H.Al-Duwaish, and W.Naeem. "Nonlinear Model Predictive Control of Hammerstein and Wiener models Using Genetic Algorithms." Electrical Engineering Department/King Fahd University of Petroleum and Minerals, n.d.
[15] H.J. Palanthandalam-Madapusi, D.S. Bernstein and A.J. Ridley. "Identifying periodicallyswitching block-structured models to predictmagnetic-fieldfluctuations." IEEE control systems magazine , 2007.
[16] H.J.Palanthandalam-Madapusi, J.A.Ridley, and D.S.Bernstein. "Identification and Prediction of Ionospheric Dynamics Using a Hammerstein-Wiener Model with Radial Basis Functions." Proceedings of the American control conference, Vols 1-7, 2005, pp. 5052-5057.
[17] I.Goethals, K.Pelckmans, L.Hoegaerts, J.Suykens, and B.DeMoor. "Subspace intersection identification of Hammerstein-Wiener systems." 44th IEEE Conference on Decision and Control & European Control conference, vols 1-8, 2005, pp. 7108-7113.
[18] I.Goethals, L.Hoegaerts, V.Verdult, J.A.K.Suykens, B.Moor, and K.U.Leuven. "Subspace Identification of Hammerstein-Wiener systems using Kernel Canonical Correlation Analysis." 2004.
[19] J.Sh.Wang, Y.Hsu. "dynamic nonlinear system identification using a wiener-type recurrent network with OKID algorithm." n.d.
[20] J.Voros. "An Iterative Method for Hammerstein-Wiener Systems Parameter Identification." Journal of Electrical engineering, 55(11-22), 2004, pp. 328-331.
[21] J.Wang, Q.Zhang, and L.Ljung. Revisiting Hammerstein system identification through the Two-Stage Algorithm for bilinear parameter estimation. Technical report from Automatic Control at Linköpings universitet, Sweden: Automatica, Vol 45, 2010.
[22] M.Schukens, E.W.Bai, and Y.Rolain. "Identification of Hammerstein-Wiener systems." 16th IFAC Symposium on System Identification, 2012.
[23] N.J.Juang, and R.S.Pappa. "An eigensystem realization algorithm for modal parameter identification and model reduction." Journal of Guidance, Vol. 8, 1985, pp. 620-627.
[24] P.Crama, and J.Schoukens. "Hammerstein-Wiener system estimator initialization." Automatica, 40(9), 2004, pp. 1543-1550.
[25] P.V.Overchee, and B.D.Moor. "N4SID :subspace algorithms for the identification of combined deterministic-stochastic system." 1996.
[26] P.V.Overchee ,”Subspace identification for linear system.”, Kluwer academic publisher, 1996.
[27] R.Abbasi-Asl, and R.Khorsandi and B.Vosooghi-Vahdat. "Hammerstein-Wiener Model: A New Approach to the estimation of formal neural information." basic and clinical neuro science, 2012.
[28] R.Abrahamsson, S.M.Kay, and P.Stoica. "Estimation of the parameters of a bilinear model with applications to submarine detection and system identification." digital signal processing 17(4), 2007, pp. 756-773.
[29] Y.C.Zhu. "Estimation of an N-L-N Hammerstein-Wiener model." Automativa 38, 2002, pp. 1607-1614.
[30] Y.Ch.Chen, J.Sh.Wang. "A Hammerstein-Wiener Recurrent Neural Network with Frequency - Domain Eigensystem Realization Algorithm for Unknown system identification." Journal of Universal Computer Science, vol. 15, no. 13 , 2009: 2547-2565.
[31] Y.Chen, J.Sh.Wang. "A Fully Automated Recurrent Neural Network for Unknown Dynamic System Identification and Control." IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR PAPERS, VOL. 53, NO. 6, 2006.
[32] E.Abd-Elrady , L.Gan, "identification of Hammerstein and Wiener models using Spectral Magnitude Matching", Proceedings of the 17th World Congress,2008
[33] A. Wills, T. Schön, L. Ljung and B. Ninness, "Identification of Hammerstein-Wiener models",Automatica, (49), 1, 2013,pp. 70-81.
[34] CH. Xi, F. Hai-Tao, "Recursive Identification for Hammerstein Systems with State-space Model", Acta Automatica Sinica, Vol. 36, No. 10, 2010