PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

Dimensionality reduction in kernel-based identification of Wiener system by cyclostationary excitations

Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The topic of nonparametric estimation of nonlinear characteristics in the Wiener system is examined. In this regard, the traditional kernel algorithm faces difficulties stemming from the dimensionality associated with the memory length of the dynamic block. A particular class of input sequences has been proposed, which aids in reducing dimensionality and consequently improves the convergence rate of the estimator to the true characteristics. A theoretical analysis of the suggested method is presented.
Twórcy
autor
  • Wrocław University of Science and Technology, Poland
  • Wrocław University of Science and Technology, Poland
Bibliografia
  • [1] M. Ławryńczuk, Computationally Efficient Model Predictive Control Algorithms, ser. Studies in Systems, Decision and Control. Springer Cham, 2014, vol. 3. [Online]. Available: https://doi.org/10.1007/978-3-319-04229-9
  • [2] F. Giri and E.-W. Bai, Block-oriented nonlinear system identification. Springer, 2010, vol. 1. [Online]. Available: https://doi.org/10.1007/978-1-84996-513-2
  • [3] W. Härdle, Applied Nonparametric Regression, ser. Econometric Society Monographs. Cambridge University Press, 1990. [Online]. Available: https://doi.org/10.1017/CCOL0521382483
  • [4] L. Györfi, M. Kohler, A. Krzy˙zak, H. Walk et al., A distribution-free theory of nonparametric regression. Springer, 2002, vol. 1. [Online]. Available: https://doi.org/10.1007/b97848
  • [5] W. Greblicki and M. Pawlak, Nonparametric system identification. Cambridge University Press, Cambridge, 2008, vol. 10. [Online]. Available: https://doi.org/10.1017/CBO9780511536687
  • [6] G. Mzyk and G. Maik, “Nonparametric identification of Wiener system with a subclass of wide-sense cyclostationary excitations,” International Journal of Adaptive Control and Signal Processing, vol. 38, no. 1, pp. 323-341, 2024. [Online]. Available: https://doi.org/10.1002/acs.3702
  • [7] G. Mzyk, “Identification of time-varying non-linear systems with adaptive bootstrap-based tracking,” Mechanical Systems and Signal Processing, vol. 223, p. 111896, 2025. [Online]. Available: https://doi.org/10.1016/j.ymssp.2024.111896
  • [8] J. P. Cunningham and Z. Ghahramani, “Linear dimensionality reduction: Survey, insights, and generalizations,” The Journal of Machine Learning Research, vol. 16, no. 1, pp. 2859-2900, 2015. [Online]. Available: https://dl.acm.org/doi/10.5555/2789272.2912091
  • [9] J. P. Cunningham and B. M. Yu, “Dimensionality reduction for large-scale neural recordings,” Nature neuroscience, vol. 17, no. 11, pp. 1500-1509, 2014. [Online]. Available: https://doi.org/10.1038/nn.3776
  • [10] W. Jia, M. Sun, J. Lian, and S. Hou, “Feature dimensionality reduction: a review,” Complex & Intelligent Systems, vol. 8, no. 3, pp. 2663-2693, 2022. [Online]. Available: https://doi.org/10.1007/s40747-021-00637-x
  • [11] L. Ljung, “Perspectives on system identification,” Annual Reviews in Control, vol. 34, no. 1, pp. 1-12, 2010. [Online]. Available: https://doi.org/10.1016/j.arcontrol.2009.12.001
  • [12] S. T. Roweis and L. K. Saul, “Nonlinear dimensionality reduction by locally linear embedding,” Science, vol. 290, no. 5500, pp. 2323-2326, 2000. [Online]. Available: https://doi.org/10.1126/science.290.5500.2323
  • [13] G. Rega and H. Troger, “Dimension reduction of dynamical systems: methods, models, applications,” Nonlinear Dynamics, vol. 41, pp. 1-15, 2005. [Online]. Available: https://doi.org/10.1007/s11071-005-2790-3
  • [14] M. Cenedese, J. Axås, H. Yang, M. Eriten, and G. Haller, “Data-driven nonlinear model reduction to spectral submanifolds in mechanical systems,” Philosophical Transactions of the Royal Society A, vol. 380, no. 2229, p. 20210194, 2022. [Online]. Available: https://doi.org/10.1098/rsta.2021.0194
  • [15] J. Li, Y. Wang, X. Jin, Z. Huang, and I. Elishakoff, “Data-driven method for dimension reduction of nonlinear randomly vibrating systems,” Nonlinear Dynamics, vol. 105, no. 2, pp. 1297-1311, 2021. [Online]. Available: https://doi.org/10.1007/s11071-021-06601-1
  • [16] A. Juditsky, H. Hjalmarsson, A. Benveniste, B. Delyon, L. Ljung, J. Sjöberg, and Q. Zhang, “Nonlinear black-box models in system identification: Mathematical foundations,” Automatica, vol. 31, no. 12, pp. 1725-1750, 1995. [Online]. Available: https://doi.org/10.1016/0005-1098(95)00119-1
  • [17] H. Peng, F. Long, and C. Ding, “Feature selection based on mutual information criteria of max-dependency, max-relevance, and min-redundancy,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 27, no. 8, pp. 1226-1238, 2005. [Online]. Available: https://doi.org/10.1109/TPAMI.2005.159
  • [18] H. Akaike, “A new look at the statistical model identification,” IEEE Transactions on Automatic Control, vol. 19, no. 6, pp. 716-723, 1974. [Online]. Available: https://doi.org/10.1109/TAC.1974.1100705
  • [19] R. Tibshirani, “Regression shrinkage and selection via the lasso,” Journal of the Royal Statistical Society Series B: Statistical Methodology, vol. 58, no. 1, pp. 267-288, 1996. [Online]. Available: https://doi.org/10.1111/j.2517-6161.1996.tb02080.x
  • [20] G. Mzyk, Z. Hasiewicz, and P. Mielcarek, “Kernel identification of non-linear systems with general structure,” Algorithms, vol. 13, no. 12, p. 328, 2020. [Online]. Available: https://doi.org/10.3390/a13120328
  • [21] R. Pintelon and J. Schoukens, System identification: a frequency domain approach. John Wiley & Sons, 2012. [Online]. Available: https://doi.org/10.1002/9781118287422
  • [22] L. McInnes, J. Healy, and J. Melville, “UMAP: Uniform manifold approximation and projection for dimension reduction,” arXiv preprint arXiv:1802.03426, 2018. [Online]. Available: https://doi.org/10.48550/arXiv.1802.03426
  • [23] P. Wachel, P. Śliwiński, and Z. Hasiewicz, “Nonparametric identification of MISO Hammerstein system from structured data,” Journal of Systems Science and Systems Engineering, vol. 24, no. 1, pp. 68-80, 2015. [Online]. Available: https://doi.org/10.1007/s11518-014-5256-7
  • [24] G. Maik, G. Mzyk, and P. Wachel, “Exponential excitations for effective identification of Wiener system,” International Journal of Control, vol. 97, no. 9, pp. 1956-1966, 2024. [Online]. Available: https://doi.org/10.1080/00207179.2023.2246070
  • [25] G. Maik and G. Mzyk, “Randomly initiated cyclostationary excitations for dimensionality reduction in Wiener system identification,” in System Dependability - Theory and Applications, W. Zamojski, J. Mazurkiewicz, J. Sugier, T. Walkowiak, and J. Kacprzyk, Eds. Cham: Springer Nature Switzerland, 2024, pp. 143-151. [Online]. Available: https://doi.org/10.1007/978-3-031-61857-4 14
  • [26] G. Mzyk, “A censored sample mean approach to nonparametric identification of nonlinearities in Wiener systems,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 54, no. 10, pp. 897-901, 2007. [Online]. Available: https://doi.org/10.1109/TCSII.2007.901634
  • [27] G. Mzyk and P. Wachel, “Kernel-based identification of Wiener-Hammerstein system,” Automatica, vol. 83, pp. 275-281, 2017. [Online]. Available: https://doi.org/10.1016/j.automatica.2017.06.038
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-1a6f97c8-82bf-42c5-937c-b76870b67216
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.