Abstract
Despite their structural simplicity, Wiener and Hammerstein nonlinear model structures have been effective in many application areas, where linear modelling has failed, e.g., the chemical process industry [5, 13], microwave and radio frequency (RF) technology [4, 7, 19], seismology [21], biology [8], physiology and psychophysics [14]. They can also be used in model predictive control [28, 29].
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References
Abed-Meraim, K., Qiu, W., Hua, Y.: Blind system identification. Proc IEEE 85(8), 1310–1322 (1997)
Bai, E.: A blind approach to the Hammerstein–Wiener model identification. Automatica 38(6), 967–979 (2002)
Billings, S., Fakhouri, S.: Identification of systems containing linear dynamic and static nonlinear elements. Automatica 18(1), 15–26 (1982)
Clark, C., Chrisikos, G., Muha, M., Moulthrop, A., Silva, C.: Time-domain envelope measurement technique with application to wideband power amplifier modeling. IEEE Trans. Microw. Theory Tech. 46(12), 2531–2540 (1998)
Eskinat, E., Johnson, S., Luyben, W.: Use of Hammerstein models in identification of nonlinear systems. AIChE Journal 37(2), 255 (1991)
Fletcher, R.: Practical methods of optimization, 2nd edn. Wiley-Interscience, New York (1991)
Greblicki, W.: Nonlinearity estimation in Hammerstein systems based on ordered observations. IEEE Trans. Signal Process 44(5), 1224–1233 (1996)
Hunter, I., Korenberg, M.: The identification of nonlinear biological systems: Wiener and Hammerstein cascade models. Biological Cybernetics 55(2), 135–144 (1986)
Kalouptsidis, N., Koukoulas, P.: Blind identification of Volterra-Hammerstein systems. IEEE Trans. Signal Process 53(8), 2777–2787 (2005)
Kaplan, W.: Advanced calculus, 4th edn. Addison-Wesley, Reading (1993)
Ljung, L.: System identification: theory for the user, 2nd edn. Prentice Hall, Upper Saddle River (1999)
Marquardt, D.: An algorithm for least-squares estimation of nonlinear parameters. SIAM J. Appl. Math. 11(2), 431–441 (1963)
Norquay, S., Palazoglu, A., Romagnoli, J.: Application of Wiener model predictive control (WMPC) to a pH neutralization experiment. IEEE Trans. Control Syst. Technol. 7(4), 437–445 (1999)
Nykamp, D., Ringach, D.: Full identification of a linear-nonlinear system via cross-correlation analysis. Journal of Vision 2(1), 1–11 (2002)
Peeters, B., De Roeck, G.: Stochastic system identification for operational modal analysis: a review. Journal of Dynamic Systems, Measurement, and Control 123(4), 659–667 (2001)
Pintelon, R., Schoukens, J.: Box–Jenkins identification revisited – Part I: Theory. Automatica 42(1), 63–75 (2006)
Pintelon, R., Schoukens, J., Vandersteen, G., Rolain, Y.: Identification of invariants of (over)parameterized models: finite sample results. IEEE Trans. Autom. Control 44(5), 1073–1077 (1999)
Prakriya, S., Hatzinakos, D.: Blind identification of LTI-ZMNL-LTI nonlinear channel models. IEEE Trans. Signal Process 43(12), 3007–3013 (1995)
Prakriya, S., Hatzinakos, D.: Blind identification of linear subsystems of LTI-ZMNL-LTI models with cyclostationary inputs. IEEE Trans. Signal Process 45(8), 2023–2036 (1997)
Schoukens, J., Nemeth, J., Crama, P., Rolain, Y., Pintelon, R.: Fast approximate identification of nonlinear systems. Automatica 39(7), 1267–1274 (2003)
Taleb, A., Solé, J., Jutten, C.: Quasi-nonparametric blind inversion of Wiener systems. IEEE Trans. Signal Process 49(5), 917–924 (2001)
Tjärnström, F.: Computing uncertainty regions with simultaneous confidence degree using bootstrap. In: Proc. 12th IFAC Symp. System Identification, Santa Barbara, CA, pp. 522–527 (2000)
Tong, L., Perreau, S.: Multichannel blind identification: from subspace to maximum likelihood methods. Proc. IEEE 86(10), 1951–1968 (1998)
Vanbeylen, L.: Calculation of the Fisher information matrix for blind ML Hammerstein identification. Tech. rep., Vrije Universiteit Brussel (2007), http://wwwir.vub.ac.be/elec/Papers%20on%20webPapers/slashLaurentVBeylen/FisherHamm.pdf
Vanbeylen, L., Pintelon, R., Schoukens, J.: Blind maximum likelihood identification of Hammerstein systems. Automatica 44(12), 3139–3146 (2008)
Vanbeylen, L., Pintelon, R., de Groen, P.: Blind maximum likelihood identification of Wiener systems with measurement noise. In: Proc. 15th IFAC Symp. System Identification, Saint Malo, France, pp. 1686–1691 (2009a)
Vanbeylen, L., Pintelon, R., Schoukens, J.: Blind maximum-likelihood identification of Wiener systems. IEEE Trans Signal Process 57(8), 3017–3029 (2009b)
Wang, W., Henriksen, R.: Generalized predictive control of nonlinear systems of the Hammerstein form. Modeling, Identification and Control 15(4), 253–262 (1994)
Zhu, Y.: Identification of Hammerstein models for control using ASYM. International Journal of Control 73(18), 1692–1702 (2000)
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Vanbeylen, L., Pintelon, R. (2010). Blind Maximum-likelihood Identification of Wiener and Hammerstein Nonlinear Block Structures. In: Giri, F., Bai, EW. (eds) Block-oriented Nonlinear System Identification. Lecture Notes in Control and Information Sciences, vol 404. Springer, London. https://doi.org/10.1007/978-1-84996-513-2_17
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DOI: https://doi.org/10.1007/978-1-84996-513-2_17
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