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Bandwidth selection for kernel generalized regression neural networks in identification of hammerstein systems

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper addresses the issue of data-driven smoothing parameter (bandwidth) selection in the context of nonparametric system identification of dynamic systems. In particular, we examine the identification problem of the block-oriented Hammerstein cascade system. A class of kernel-type Generalized Regression Neural Networks (GRNN) is employed as the identification algorithm. The statistical accuracy of the kernel GRNN estimate is critically influenced by the choice of the bandwidth. Given the need of data-driven bandwidth specification we propose several automatic selection methods that are compared by means of simulation studies. Our experiments reveal that the method referred to as the partitioned cross-validation algorithm can be recommended as the practical procedure for the bandwidth choice for the kernel GRNN estimate in terms of its statistical accuracy and implementation aspects.
Rocznik
Strony
181--194
Opis fizyczny
Bibliogr. 35 poz., rys.
Twórcy
autor
  • Department of Electrical & Computer Engineering University of Manitoba, Canada
  • Department of Electrical & Computer Engineering University of Manitoba, Canada
  • Information Technology Institute, University of Social Sciences, Lodz, Poland
Bibliografia
  • [1] K. Hunt, M. Munih, N. Donaldson, F. Barr, Investigation of the Hammerstein hypothesis in the modeling of electrically stimulated muscle, IEEE Transactions on Biomedical Engineering 45 (1998) 998–1009.
  • [2] T. Kara, I. Eker, Nonlinear modeling and identification of a DC motor for bidirectional operation with real time experiments, Energy Conversion and Management 45 (2004) 1087–1106.
  • [3] T. Quatieri, D. Reynolds, G. O’Leary, Estimation of handset nonlinearity with application to speaker recognition, IEEE Transactions on Speech and Audio Processing 8 (2000) 567–584.
  • [4] J. Turunen, J. Tanttu, P. Loula, Hammerstein model for speech coding, EURASIP Journal on Applied Signal Processing (2003) 1238–1249.
  • [5] E. Capobianco, Hammerstein system representation of financial volatility processes, The European Physical Journal B 27 (2002) 201–211.
  • [6] W. Greblicki, M. Pawlak, Nonparametric System Identification, Cambridge University Press, 2008.
  • [7] L. Ljung, System Identification: Theory for the User, Prentice Hall, New Jersey, 1987.
  • [8] F. Giri, E. Bai, Block-Oriented Nonlinear System Identification, Springer-Verlag, 2010.
  • [9] H.-F. Chen, W. Zhao, Recursive Identification and Parameter Estimation, CRC Press, 2014.
  • [10] R. Pintelon, J. Schoukens, System Identification: A Frequency Domain Approach, John Wiley & Sons, 2012.
  • [11] S. A. Billings, Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains, John Wiley & Sons, 2013.
  • [12] W. Greblicki, M. Pawlak, The weighted nearest neighbor estimate for Hammerstein system identification, IEEE Transactions on Automatic Control 64 (2019) 1550–1565.
  • [13] W. Greblicki, M. Pawlak, Hammerstein system identification with the nearest neighbor algorithm, IEEE Transactions on Information Theory 63 (2017) 4746–4757.
  • [14] J. G. Smith, S. Kamat, K. Madhavan, Modeling of ph process using wavenet based Hammerstein model, Journal of Process Control 17 (6) (2007) 551–561.
  • [15] K. Fruzzetti, A. Palazoğlu, K. McDonald, Nolinear model predictive control using Hammerstein models, Journal of Process Control 7 (1) (1997) 31–41.
  • [16] L. Jia, X. Li, M.-S. Chiu, Correlation analysis based mimo neuro-fuzzy Hammerstein model with noises, Journal of Process Control 41 (2016) 76–91.
  • [17] J. Wang, Q. Zhang, Detection of asymmetric control valve stiction from oscillatory data using an extended Hammerstein system identification method, Journal of Process Control 24 (1) (2014) 1–12.
  • [18] W. Wu, D.-W. Jhao, Control of a direct internal reforming molten carbonate fuel cell system using wavelet network-based Hammerstein models, Journal of Process Control 22 (3) (2012) 653–658.
  • [19] C. Qi, H.-T. Zhang, H.-X. Li, A multi-channel spatio-temporal Hammerstein modeling approach for nonlinear distributed parameter processes, Journal of Process Control 19 (1) (2009) 85–99.
  • [20] G. Harnischmacher, W. Marquardt, A multi-variate Hammerstein model for processes with input directionality, Journal of Process Control 17 (2007) 539–550.
  • [21] M. Pawlak, On the series expansion approach to the identification of Hammerstein systems, IEEE Transactions on Automatic Control 36 (6) (1991) 763–767.
  • [22] D. Specht, A general regression neural network, IEEE Transactions on Neural Networks 2 (1991) 568–576.
  • [23] P. Duda, M. Jaworski, L. Rutkowski, Convergent time-varying regression models for data streams: Tracking concept drift by the recursive Parzen-based generalized regression neural networks, International Journal of Neural Systems 28 (2018) 1750048.
  • [24] J. S. Marron, Automatic smoothing parameter selection: a survey, Empirical Economics 13 (3-4) (1988) 187–208.
  • [25] W. Härdle, P. Hall, J. S. Marron, How far are automatically chosen regression smoothing parameters from their optimum?, Journal of the American Statistical Association 83 (401) (1988) 86–95.
  • [26] J. Rice, Bandwidth choice for nonparametric regression, The Annals of Statistics (1984) 1215–1230.
  • [27] T. Gasser, A. Kneip, W. Köhler, A flexible and fast method for automatic smoothing, Journal of the American Statistical Association 86 (415) (1991) 643–652.
  • [28] J. S. Marron, Partitioned cross-validation, Econometric Reviews 6 (2) (1987) 271–283.
  • [29] C.-K. Chu, J. S. Marron, Comparison of two bandwidth selectors with dependent errors, The Annals of Statistics (1991) 1906–1918.
  • [30] N. Altman, Kernel smoothing of data with correlated errors, Journal of the American Statistical Association 85 (411) (1990) 749–759.
  • [31] J. Hart, P. Vieu, Data-driven bandwidth choice for density estimation based on dependent data, The Annals of Statistics 18 (2) (1990) 873–890.
  • [32] K. D. Brabanter, J. D. Brabanter, J. Suykens, Kernel regression in the presence of correlated errors, The Journal of Machine Learning Research 12 (2011) 1955–1976.
  • [33] Q. Yao, H. Tong, Cross-validatory bandwidth selections for regression estimation based on dependent data, Journal of Statistical Planning and Inference 68 (2) (1998) 387–415.
  • [34] A. Quintela del Río, Comparison of bandwidth selectors in nonparametric regression under dependence, Computational Statistics & Data Analysis 21 (5) (1996) 563–580.
  • [35] I. Goethals, K. Pelckmans, J. Suykens, B. De Moor, Identification of MIMO Hammerstein models using least squares support vector machines, Automatica 41 (2005) 1263–1272.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-e920eb14-c371-4647-bf02-eaf9beedec2d
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