New Parameter-Identification Method Based on QR Decomposition for Nonlinear Time-Varying Systems
Publication: Journal of Engineering Mechanics
Volume 145, Issue 1
Abstract
A new identification method based on QR decomposition for nonlinear time-varying systems is proposed in this paper, which is applied in a time-varying multiple-degree-of-freedom (MDOF) dynamic system to locate and estimate nonlinearities without a priori knowledge of them. This new procedure provides a continuous-time model with which a MDOF system can be partitioned into a number of different subsystems. After an orthogonalizing algorithm and an error reduction ratio (ERR) process, all information about the masses and linear and nonlinear connections in the subsystems can be detected and estimated with a high degree of accuracy. In this procedure, the time expressions of the time-varying parameters are also given. Because of its simplicity and efficiency, this new method will have wide application in practical engineering. The reliability of the identification method is demonstrated by a numerical example.
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Acknowledgments
This paper is funded by the National Natural Science Foundation of China (Grant No. 11472132) and the National Natural Science Foundation of China (Grant No. 11602105).
References
Ahmed-Ali, T., G. Kenn, and F. Lamnabhi-Lagarrigue. 2009. “Identification of nonlinear systems with time-varying parameters using a sliding-neural network observer.” Neurocomputing 72 (7–9): 1611–1620. https://doi.org/10.1016/j.neucom.2008.09.001.
Apostolikas, G., and S. Tzafestas. 2003. “On-line RBFNN based identification of rapidly time-varying nonlinear systems with optimal structure-adaptation.” Math. Comput. Simul. 63 (1): 1–13. https://doi.org/10.1016/S0378-4754(02)00159-3.
Basu, B., S. Nagarajaiah, and A. Chakraborty. 2008. “Online identification of linear time-varying stiffness of structural systems by wavelet analysis.” Struct. Health. Monit. 7 (1): 21–36. https://doi.org/10.1177/1475921707081968.
Billings, S. A. 2013. Nonlinear system identification: NARMAX methods in the time, frequency, and spatio-temporal domains. Chichester, UK: Wiley.
Billings, S. A., S. Chen, and M. J. Korenberg. 1989. “Identification of MIMO non-linear systems using a forward-regression orthogonal estimator.” Int. J. Control 49 (6): 2157–2189. https://doi.org/10.1080/00207178908559767.
Chen, S., S. A. Billings, and W. Luo. 1989. “Orthogonal least squares methods and their application to non-linear system identification.” Int. J. Control 50 (5): 1873–1896. https://doi.org/10.1080/00207178908953472.
Chen, S. L., and K. C. Ho. 2006. “Identification of linear time varying systems by Haar wavelet.” Int. J. Syst. Sci. 37 (9): 619–628. https://doi.org/10.1080/00207720600774255.
Chesher, A. 1991. “The effect of measurement error.” Biometrika 78 (3): 451–462. https://doi.org/10.1093/biomet/78.3.451.
Feldman, M. 2011. Hilbert transform applications in mechanical vibration. Chichester, UK: Wiley.
Ghanem, R., and F. Romeo. 2000. “A wavelet-based approach for identification of linear time varying dynamical systems.” J. Sound. Vib. 234 (4): 555–576. https://doi.org/10.1006/jsvi.1999.2752.
Green, M., and A. M. Zoubir. 2004. “Selection of a time-varying quadratic Volterra model using a wavelet packet basis expansion.” IEEE. Trans. Signal Process. 52 (10): 2721–2728. https://doi.org/10.1109/TSP.2004.834411.
He, F., H. L. Wei, and S. A. Billings. 2015. “Identification and frequency domain analysis of non-stationary and nonlinear systems using time-varying NARMAX models.” Int. J. Syst. Sci. 46 (11): 2087–2100. https://doi.org/10.1080/00207721.2013.860202.
Ikharia, B. I., and D. T. Westwick. 2006. “A bootstrap term selection method for the identification of time-varying nonlinear systems.” In Proc., Int. Conf. of the IEEE Engineering in Medicine and Biology Society. Piscataway, NJ: IEEE.
Kenné, G., T. Ahmed-Ali, F. Lamnabhi-Lagarrigue, and A. Arzandé. 2008. “Nonlinear systems time-varying parameter estimation: Application to induction motors.” Electr. Power Syst. Res. 78 (11): 1881–1888. https://doi.org/10.1016/j.epsr.2008.03.014.
Li, Y., H. L. Wei, and S. A. Billings. 2011. “Identification of time-varying systems using multi-wavelet basis functions.” IEEE. Trans. Control Syst. Technol. 19 (3): 656–663. https://doi.org/10.1109/TCST.2010.2052257.
Li, Y., H. L. Wei, S. A. Billings, and P. G. Sarrigiannis. 2016. “Identification of nonlinear time-varying systems using an online sliding-window and common model structure selection (CMSS) approach with applications to EEG.” Int. J. Syst. Sci. 47 (11): 2671–2681. https://doi.org/10.1080/00207721.2015.1014448.
Liu, K. 1997. “Identification of linear time-varying systems.” J. Sound. Vib. 206 (4): 487–505. https://doi.org/10.1006/jsvi.1997.1105.
Nordsjo, A. E., and L. H. Zetterberg. 1999. “A recursive prediction error algorithm for identification of certain time-varying nonlinear systems.” In Proc., 1999 IEEE Int. Conf. on Acoustics, Speech and Signal Processing, 1305–1308. Phoenix: IEEE Computer Society.
Nordsjo, A. E., and L. H. Zetterberg. 2001. “Identification of certain time-varying nonlinear Wiener and Hammerstein systems.” IEEE. Trans. Signal Process. 49 (3): 577–592. https://doi.org/10.1109/78.905884.
Ohsumi, A., and T. Kawano. 2002. “Subspace identification for a class of time-varying continuous-time stochastic systems via distribution-based approach.” In Proc., IFAC 15th Triennial World Congress, 241–246. Laxenburg, Austria: International Federation of Automatic Control.
Shi, Z. Y., and S. S. Law. 2007. “Identification of linear time-varying dynamical systems using Hilbert transform and empirical mode decomposition method.” J. Appl. Mech. 74 (2): 223–230. https://doi.org/10.1115/1.2188538.
Tsatsanis, M. K., and G. B. Giannakis. 1993. “Time-varying system identification and model validation using wavelets.” IEEE. Trans. Signal. Process. 41 (12): 3512–3523. https://doi.org/10.1109/78.258089.
Wang, W., T. M. Wang, and H. X. Wei. 2008. “Comparison of nonlinear regression estimation ability of LS-SVM and multilayer forward neural network.” J. Syst. Simul. 20 (1): 236–256. https://doi.org/10.16182/j.cnki.joss.2008.01.050.
Wei, H. L., and S. A. Billings. 2002. “Identification of time-varying systems using multiresolution wavelet models.” Int. J. Syst. Sci. 33 (15): 1217–1228. https://doi.org/10.1080/0020772031000081982.
Wei, H. L., S. A. Billings, and J. J. Liu. 2010. “Time-varying parametric modelling and time-dependent spectral characterisation with applications to EEG signals using multiwavelets.” Int. J. Modell. Ident. Control 9 (3): 215–224. https://doi.org/10.1504/IJMIC.2010.032802.
Worden, K., G. R. Tomlinson, and K. Yagasaki. 2000. Nonlinearity in structural dynamics: Detection, identification and modelling. Abingdon, UK: Taylor & Francis.
Yu, K. P., and S. W. Pang. 2009. “Advances in method of time-varying linear/nonlinear structural system identification and parameter estimate.” Chinese. Sci. Bull. 54 (20): 3147–3156. https://doi.org/10.1360/972008-2471.
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Published In
Journal of Engineering Mechanics
Volume 145 • Issue 1 • January 2019
Copyright
©2018 American Society of Civil Engineers.
History
Received: Nov 21, 2017
Accepted: Jul 6, 2018
Published online: Oct 24, 2018
Published in print: Jan 1, 2019
Discussion open until: Mar 24, 2019
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