Optimization Approach to Estimate Hammerstein–Wiener Nonlinear Blocks in Presence of Noise and Disturbance
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Optimization Approach to Estimate Hammerstein–Wiener Nonlinear Blocks in Presence of Noise and Disturbance

Authors: Leili Esmaeilani, Jafar Ghaisari, Mohsen Ahmadian


Hammerstein–Wiener model is a block-oriented model where a linear dynamic system is surrounded by two static nonlinearities at its input and output and could be used to model various processes. This paper contains an optimization approach method for analysing the problem of Hammerstein–Wiener systems identification. The method relies on reformulate the identification problem; solve it as constraint quadratic problem and analysing its solutions. During the formulation of the problem, effects of adding noise to both input and output signals of nonlinear blocks and disturbance to linear block, in the emerged equations are discussed. Additionally, the possible parametric form of matrix operations to reduce the equation size is presented. To analyse the possible solutions to the mentioned system of equations, a method to reduce the difference between the number of equations and number of unknown variables by formulate and importing existing knowledge about nonlinear functions is presented. Obtained equations are applied to an instance H–W system to validate the results and illustrate the proposed method.

Keywords: Identification, Hammerstein-Wiener, optimization, quantization.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1314875

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[1] F. Giri and E.-W. Bai, "Block-oriented Nonlinear System Identification," London: Springer-Verlag, 2010.
[2] M. Hong and S. Cheng, "Hammerstein–Wiener Model Predictive Control of Continuous Stirred Tank Reactor," Electronics and Signal Processing, ed: Springer, 2011, pp. 235-242.
[3] T. Patikirikorala, L. Wang, A. Colman, and J. Han, "Hammerstein–Wiener nonlinear model based predictive control for relative QoS performance and resource management of software systems," Control Engineering Practice, vol. 20, pp. 49-61, 2012.
[4] J. C. Gómez, A. Jutan, and E. Baeyens. "Wiener model identification and predictive control of a pH neutralisation process," IEE Proceedings Control Theory and Applications 151(3), 329-338, 2004.
[5] A. Nemati and M. Faieghi, "The Performance Comparison of ANFIS and Hammerstein–Wiener Models for BLDC Motors," Electronics and Signal Processing, ed: Springer, 2011, pp. 29-37.
[6] K. Elleuch and A. Chaari, "Modeling and identification of hammerstein system by using triangular basis functions," International Journal of Electrical, Computer, Energetic, Electronic and Communication Engineering, vol. 1, p. 1, 2011.
[7] F. Lindsten, T. B. Schön, and M. I. Jordan, "Bayesian semiparametric Wiener system identification," Automatica, vol. 49, pp. 2053-2063, 2013.
[8] E.W. Bai, "An optimal two-stage identification algorithm for Hammerstein–Wiener nonlinear systems," Automatica, vol. 34, pp. 333-338, 1998.
[9] E.W. Bai, "A blind approach to the Hammerstein–Wiener model identification," Automatica, vol. 38, pp. 967-979, 2002.
[10] Y. Zhu, "Estimation of an N–L–N Hammerstein–Wiener model," Automatica, vol. 38, pp. 1607-1614, 9// 2002.
[11] P. Crama and J. Schoukens, "Hammerstein–Wiener system estimator initialization," Automatica, vol. 40, pp. 1543-1550, 2004.
[12] B. Ni, M. Gilson, and H. Garnier, "Refined instrumental variable method for Hammerstein–Wiener continuous-time model identification," IET Control Theory & Applications, vol. 7, pp. 1276-1286, 2013.
[13] A. Wills, T. B. Schön, L. Ljung, and B. Ninness, "Identification of Hammerstein–Wiener models," Automatica, vol. 49, pp. 70-81, 2013.
[14] G. Golub and W. Kahan, "Calculating the singular values and pseudo-inverse of a matrix," Journal of the Society for Industrial and Applied Mathematics, Series B: Numerical Analysis, vol. 2, pp. 205-224, 1965.
[15] R. Bouldin, "The pseudo-inverse of a product," SIAM Journal on Applied Mathematics, vol. 24, pp. 489-495, 1973.
[16] P. E. Gill, W. Murray, and M. H. Wright, "Practical optimization," New York: Academic Press, 1981.
[17] T. F. Coleman and Y. Li, "A reflective Newton method for minimizing a quadratic function subject to bounds on some of the variables," SIAM Journal on Optimization, vol. 6, pp. 1040-1058, 1996.