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Shock and Vibration
Volume 2017, Article ID 8176593, 14 pages
https://doi.org/10.1155/2017/8176593
Research Article

Output-Only Modal Parameter Recursive Estimation of Time-Varying Structures via a Kernel Ridge Regression FS-TARMA Approach

School of Aerospace Engineering, Beijing Institute of Technology, Zhongguancun South Street 5, Beijing 100081, China

Correspondence should be addressed to Si-Da Zhou; nc.ude.tib@adisuohz

Received 21 July 2016; Revised 2 November 2016; Accepted 29 November 2016; Published 11 January 2017

Academic Editor: Lu Chen

Copyright © 2017 Zhi-Sai Ma et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. S. W. Doebling, C. R. Farrar, and M. B. Prime, “A summary review of vibration-based damage identification methods,” Shock and Vibration Digest, vol. 30, no. 2, pp. 91–105, 1998. View at Publisher · View at Google Scholar · View at Scopus
  2. E. P. Carden and P. Fanning, “Vibration based condition monitoring: a review,” Structural Health Monitoring, vol. 3, no. 4, pp. 355–377, 2004. View at Publisher · View at Google Scholar · View at Scopus
  3. S. D. Fassois and J. S. Sakellariou, “Time-series methods for fault detection and identification in vibrating structures,” Mathematic, Physical & Engineering Sciences, vol. 365, pp. 411–448, 2007. View at Google Scholar
  4. W. Fan and P. Qiao, “Vibration-based damage identification methods: A Review And Comparative Study,” Structural Health Monitoring, vol. 10, no. 1, pp. 83–111, 2011. View at Publisher · View at Google Scholar · View at Scopus
  5. M. D. Spiridonakos and S. D. Fassois, “An FS-TAR based method for vibration-response-based fault diagnosis in stochastic time-varying structures: experimental application to a pick-and-place mechanism,” Mechanical Systems and Signal Processing, vol. 38, no. 1, pp. 206–222, 2013. View at Publisher · View at Google Scholar · View at Scopus
  6. W. Heylen, S. Lammens, and P. Sas, Modal Analysis Theory and Testing, Katholieke Universiteit Leuven, Leuven, Belgium, 2007.
  7. H. D'Angelo, Linear Time-Varying Systems: Analysis and Synthesis, Allyn & Bacon, Boston, Mass, USA, 1970.
  8. Y. S. Shmaliy, Continuous-Time Systems, Springer, Dordrecht, The Netherlands, 2007.
  9. L. Ljung, System Identification—Theory for the User, Prentice Hall, Upper Saddle River, NJ, USA, 2nd edition, 1999.
  10. M. Niedzwiecki, Identification of Time-Varying Processes, John Wiley & Sons, New York, NY, USA, 2000.
  11. A. G. Poulimenos and S. D. Fassois, “Parametric time-domain methods for non-stationary random vibration modelling and analysis—a critical survey and comparison,” Mechanical Systems and Signal Processing, vol. 20, no. 4, pp. 763–816, 2006. View at Publisher · View at Google Scholar · View at Scopus
  12. M. D. Spiridonakos and S. D. Fassois, “Non-stationary random vibration modelling and analysis via functional series time-dependent ARMA (FS-TARMA) models—a critical survey,” Mechanical Systems and Signal Processing, vol. 47, no. 1-2, pp. 175–224, 2014. View at Publisher · View at Google Scholar · View at Scopus
  13. M. D. Spiridonakos and S. D. Fassois, “Parametric identification of a time-varying structure based on vector vibration response measurements,” Mechanical Systems and Signal Processing, vol. 23, no. 6, pp. 2029–2048, 2009. View at Publisher · View at Google Scholar · View at Scopus
  14. W. Yang, L. Liu, S.-D. Zhou, and Z.-S. Ma, “Moving Kriging shape function modeling of vector TARMA models for modal identification of linear time-varying structural systems,” Journal of Sound and Vibration, vol. 354, pp. 254–277, 2015. View at Publisher · View at Google Scholar · View at Scopus
  15. X. Y. Xie and R. J. Evans, “Discrete time stochastic adaptive control for time-varying systems,” IEEE Transactions on Automatic Control, vol. 29, no. 7, pp. 638–640, 1984. View at Publisher · View at Google Scholar · View at MathSciNet
  16. Z. Li, “Discrete-time adaptive control of deterministic fast time-varying systems,” IEEE Transactions on Automatic Control, vol. 32, no. 5, pp. 444–447, 1987. View at Publisher · View at Google Scholar
  17. M. Niedzwiecki, “Recursive functional series modeling estimators for identification of time-varying plants-more bad news than good?” IEEE Transactions on Automatic Control, vol. 35, no. 5, pp. 610–616, 1990. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. M. K. Tsatsanis and G. B. Giannakis, “Modelling and equalization of rapidly fading channels,” International Journal of Adaptive Control and Signal Processing, vol. 10, no. 2-3, pp. 159–176, 1996. View at Publisher · View at Google Scholar · View at Scopus
  19. A. Joensen, H. Madsen, H. A. Nielsen, and T. S. Nielsen, “Tracking time-varying parameters with local regression,” Automatica, vol. 36, no. 8, pp. 1199–1204, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. M. Niedzwiecki and T. Kłaput, “Fast recursive basis function estimators for identification of time-varying processes,” IEEE Transactions on Signal Processing, vol. 50, no. 8, pp. 1925–1934, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. G. G. Walter, Wavelets and Other Orthogonal Systems with Applications, Taylor & Francis, Boca Raton, Fla, USA, 1994.
  22. H. Lütkepohl, Handbook of Matrices, John Wiley & Sons, New York, NY, USA, 1996. View at MathSciNet
  23. S. Yang, Y. Wu, and J. Xuan, Time Series Analysis in Engineering Application, Huazhong University of Science and Technology Press, Wuhan, China, 2nd edition, 2007.
  24. C. M. Bishop, Pattern Recognition and Machine Learning, Springer, New York, NY, USA, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  25. C. E. Rasmussen and C. K. Williams, Gaussian processes for machine learning, Adaptive Computation and Machine Learning, MIT Press, Cambridge, Massachusetts, USA, 2006. View at MathSciNet
  26. W. Liu, J. C. Príncipe, and S. Haykin, Kernel Adaptive Filtering: A Comprehensive Introduction, John Wiley & Sons, New Jersey, NJ, USA, 2010.
  27. S. Van Vaerenbergh, J. Via, and I. Santamaría, “Nonlinear system identification using a new sliding-window Kernel RLS algorithm,” Journal of Communications, vol. 2, no. 3, pp. 1–8, 2007. View at Google Scholar · View at Scopus
  28. J. A. K. Suykens, M. Signoretto, and A. Argyriou, Regularization, Optimization, Kernels, and Support Vector Machines, CRC Press, Boca Raton, Fla, USA, 2014.
  29. N. Aronszajn, “Theory of reproducing kernels,” Transactions of the American Mathematical Society, vol. 68, pp. 337–404, 1950. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  30. A. Poulimenos, M. Spiridonakos, and S. Fassois, “Parametric time-domain methods for non-stationary random vibration identification and analysis: an overview and comparison,” in Proceedings of the International Conference on Noise and Vibration Engineering (ISMA '06), pp. 2885–2905, Leuven, Belgium, 2006.
  31. Z.-S. Ma, L. Liu, S.-D. Zhou, and W. Yang, “Modal parameter estimation of the coupled moving-mass and beam time-varying system,” in Proceedings of the International Conference on Noise and Vibration Engineering (ISMA '14), pp. 587–596, Leuven, Belgium, 2014.