{"title":"Optimization Approach to Estimate Hammerstein\u2013Wiener Nonlinear Blocks in Presence of Noise and Disturbance","authors":"Leili Esmaeilani, Jafar Ghaisari, Mohsen Ahmadian","volume":132,"journal":"International Journal of Electrical and Information Engineering","pagesStart":1227,"pagesEnd":1235,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10008365","abstract":"Hammerstein–Wiener model is a block-oriented model
\r\nwhere a linear dynamic system is surrounded by two static
\r\nnonlinearities at its input and output and could be used to model
\r\nvarious processes. This paper contains an optimization approach
\r\nmethod for analysing the problem of Hammerstein–Wiener systems
\r\nidentification. The method relies on reformulate the identification
\r\nproblem; solve it as constraint quadratic problem and analysing its
\r\nsolutions. During the formulation of the problem, effects of adding
\r\nnoise to both input and output signals of nonlinear blocks and
\r\ndisturbance to linear block, in the emerged equations are discussed.
\r\nAdditionally, the possible parametric form of matrix operations
\r\nto reduce the equation size is presented. To analyse the possible
\r\nsolutions to the mentioned system of equations, a method to reduce
\r\nthe difference between the number of equations and number of
\r\nunknown variables by formulate and importing existing knowledge
\r\nabout nonlinear functions is presented. Obtained equations are applied
\r\nto an instance H–W system to validate the results and illustrate the
\r\nproposed method.","references":"[1] F. Giri and E.-W. Bai, \"Block-oriented Nonlinear System Identification,\"\r\nLondon: Springer-Verlag, 2010.\r\n[2] M. Hong and S. Cheng, \"Hammerstein\u2013Wiener Model Predictive Control\r\nof Continuous Stirred Tank Reactor,\" Electronics and Signal Processing,\r\ned: Springer, 2011, pp. 235-242.\r\n[3] T. Patikirikorala, L. Wang, A. Colman, and J. Han, \"Hammerstein\u2013Wiener\r\nnonlinear model based predictive control for relative QoS performance\r\nand resource management of software systems,\" Control Engineering\r\nPractice, vol. 20, pp. 49-61, 2012.\r\n[4] J. C. G\u00f3mez, A. Jutan, and E. Baeyens. \"Wiener model identification\r\nand predictive control of a pH neutralisation process,\" IEE Proceedings\r\nControl Theory and Applications 151(3), 329-338, 2004.\r\n[5] A. Nemati and M. Faieghi, \"The Performance Comparison of ANFIS and\r\nHammerstein\u2013Wiener Models for BLDC Motors,\" Electronics and Signal\r\nProcessing, ed: Springer, 2011, pp. 29-37.\r\n[6] K. Elleuch and A. Chaari, \"Modeling and identification of hammerstein\r\nsystem by using triangular basis functions,\" International Journal\r\nof Electrical, Computer, Energetic, Electronic and Communication\r\nEngineering, vol. 1, p. 1, 2011.\r\n[7] F. Lindsten, T. B. Sch\u00f6n, and M. I. Jordan, \"Bayesian semiparametric\r\nWiener system identification,\" Automatica, vol. 49, pp. 2053-2063, 2013.\r\n[8] E.W. Bai, \"An optimal two-stage identification algorithm for\r\nHammerstein\u2013Wiener nonlinear systems,\" Automatica, vol. 34, pp.\r\n333-338, 1998.\r\n[9] E.W. Bai, \"A blind approach to the Hammerstein\u2013Wiener model\r\nidentification,\" Automatica, vol. 38, pp. 967-979, 2002.\r\n[10] Y. Zhu, \"Estimation of an N\u2013L\u2013N Hammerstein\u2013Wiener model,\"\r\nAutomatica, vol. 38, pp. 1607-1614, 9\/\/ 2002.\r\n[11] P. Crama and J. Schoukens, \"Hammerstein\u2013Wiener system estimator\r\ninitialization,\" Automatica, vol. 40, pp. 1543-1550, 2004.\r\n[12] B. Ni, M. Gilson, and H. Garnier, \"Refined instrumental variable\r\nmethod for Hammerstein\u2013Wiener continuous-time model identification,\"\r\nIET Control Theory & Applications, vol. 7, pp. 1276-1286, 2013.\r\n[13] A. Wills, T. B. Sch\u00f6n, L. Ljung, and B. Ninness, \"Identification of\r\nHammerstein\u2013Wiener models,\" Automatica, vol. 49, pp. 70-81, 2013.\r\n[14] G. Golub and W. Kahan, \"Calculating the singular values and\r\npseudo-inverse of a matrix,\" Journal of the Society for Industrial and\r\nApplied Mathematics, Series B: Numerical Analysis, vol. 2, pp. 205-224,\r\n1965.\r\n[15] R. Bouldin, \"The pseudo-inverse of a product,\" SIAM Journal on\r\nApplied Mathematics, vol. 24, pp. 489-495, 1973.\r\n[16] P. E. Gill, W. Murray, and M. H. Wright, \"Practical optimization,\" New\r\nYork: Academic Press, 1981.\r\n[17] T. F. Coleman and Y. Li, \"A reflective Newton method for minimizing\r\na quadratic function subject to bounds on some of the variables,\" SIAM\r\nJournal on Optimization, vol. 6, pp. 1040-1058, 1996.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 132, 2017"}