Smart Structures and Systems

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Modal identifiability of a cable-stayed bridge using proper orthogonal decomposition

  • Li, M. (Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University) ;
  • Ni, Y.Q. (Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University)
  • Received : 2015.06.22
  • Accepted : 2015.12.02
  • Published : 2016.03.25
⟨ Previous Next ⟩

Abstract

The recent research on proper orthogonal decomposition (POD) has revealed the linkage between proper orthogonal modes and linear normal modes. This paper presents an investigation into the modal identifiability of an instrumented cable-stayed bridge using an adapted POD technique with a band-pass filtering scheme. The band-pass POD method is applied to the datasets available for this benchmark study, aiming to identify the vibration modes of the bridge and find out the so-called deficient modes which are unidentifiable under normal excitation conditions. It turns out that the second mode of the bridge cannot be stably identified under weak wind conditions and is therefore regarded as a deficient mode. To judge if the deficient mode is due to its low contribution to the structural response under weak wind conditions, modal coordinates are derived for different modes by the band-pass POD technique and an energy participation factor is defined to evaluate the energy participation of each vibration mode under different wind excitation conditions. From the non-blind datasets, it is found that the vibration modes can be reliably identified only when the energy participation factor exceeds a certain threshold value. With the identified threshold value, modal identifiability in use of the blind datasets from the same structure is examined.

Keywords

References

  1. Bergermann, R. and Schlaich, M. (1996), "Ting Kau Bridge, Hong Kong", Struct. Eng. Int., 6(3), 152-154. https://doi.org/10.2749/101686696780495563
  2. Chelidze, D. and Zhou, W. (2006), "Smooth orthogonal decomposition-based vibration mode identification", J. Sound Vib., 292(3), 461-473. https://doi.org/10.1016/j.jsv.2005.08.006
  3. Farooq, U. and Feeny, B.F. (2008), "Smooth orthogonal decomposition for modal analysis of randomly excited systems", J. Sound Vib., 316(1), 137-146. https://doi.org/10.1016/j.jsv.2008.02.052
  4. Feeny, B.F. (2002), "On proper orthogonal co-ordinates as indicators of modal activity", J. Sound Vib., 255(5), 805-817. https://doi.org/10.1006/jsvi.2001.4120
  5. Feeny, B.F. and Kappagantu, R. (1998), "On the physical interpretation of proper orthogonal modes in vibrations", J. Sound Vib., 211(4), 607-616. https://doi.org/10.1006/jsvi.1997.1386
  6. Feeny, B.F. and Liang, Y. (2003), "Interpreting proper orthogonal modes of randomly excited vibration systems", J. Sound Vib., 265(5), 953-966. https://doi.org/10.1016/S0022-460X(02)01265-8
  7. Fukagana, K. (1972), Introduction to Statistical Pattern Recognition, Academic Press, New York.
  8. Han, S. (2000), "Linking proper orthogonal modes and normal modes of the structure", Proceedings of the IMAC 18, San Antonio, TX.
  9. Han, S. and Feeny, B.F. (2002), "Enhanced proper orthogonal decomposition for the modal analysis of homogeneous structures", J. Sound Vib., 8(1), 19-40.
  10. Han, S. and Feeny, B. (2003), "Application of proper orthogonal decomposition to structural vibration analysis", Mech. Syst. Signal Pr., 17(5), 989-1001. https://doi.org/10.1006/mssp.2002.1570
  11. Holmes, J.D. (1990), "Analysis and synthesis of pressure fluctuations on bluff bodies using eigenvectors", J. Wind. Eng. Ind. Aerod., 33(1-2), 219-230. https://doi.org/10.1016/0167-6105(90)90037-D
  12. Hotelling, H. (1933), "Analysis of a complex of statistical variables into principal components", J. Educ. Psychol., 24(6), 417-441. https://doi.org/10.1037/h0071325
  13. Jolliffe, I.T. (2002), Principal Component Analysis, 2nd Ed., Springer, New York.
  14. Kerschen, G. and Golinval, J.C. (2002), "Physical interpretation of the proper orthogonal modes using the singular value decomposition", J. Sound Vib., 249(5), 849-865. https://doi.org/10.1006/jsvi.2001.3930
  15. Kunisch, K. and Volkwein, S., (1999), "Control of the Burgers' equation by a reduced order approach using proper orthogonal decomposition", J. Optimiz. Theory App., 102, 345-371. https://doi.org/10.1023/A:1021732508059
  16. Ko, J.M. and Ni, Y.Q. (2005), "Technology developments in structural health monitoring of large-scale bridges", Eng. Struct., 27(12), 1715-1725. https://doi.org/10.1016/j.engstruct.2005.02.021
  17. Mariani, R. and Dessi, D. (2012), "Analysis of the global bending modes of a floating structure using the proper orthogonal decomposition", J. Fluid Struct., 28, 115-134. https://doi.org/10.1016/j.jfluidstructs.2011.11.009
  18. Ni, Y.Q., Wang, Y.W. and Xia, Y.X. (2015), "Investigation of mode identifiability of a cable-stayed bridge: comparison from ambient vibration responses and from typhoon-induced dynamic responses", Smart Struct. Syst., 15(2), 447-468. https://doi.org/10.12989/sss.2015.15.2.447
  19. Ni, Y.Q., Wong, K.Y. and Xia, Y. (2011), "Health checks through landmark bridges to sky-high structures", Adv. Struct. Eng., 14(1), 103-119. https://doi.org/10.1260/1369-4332.14.1.103
  20. Pearson, K. (1901), "On lines and planes of closest fit to systems of points in space", Phil. Mag., 2, 559-572. https://doi.org/10.1080/14786440109462720
  21. Wong, K.Y. (2004), "Instrumentation and health monitoring of cable-supported bridges", Struct. Control. Health Monit., 11(2), 91-124. https://doi.org/10.1002/stc.33
  22. Wong, K.Y. (2007), "Design of a structural health monitoring system for long-span bridges", Struct. Infrastruct. E., 3(2), 169-185. https://doi.org/10.1080/15732470600591117
  23. Wong, K.Y. and Ni, Y.Q. (2009), "Modular architecture of structural health monitoring system for cable-supported bridges", Encyclopedia of Structural Health Monitoring, (Eds., C. Boller, F.K. Chang and Y. Fujino), John Wiley & Sons, Chichester, UK, 5.

Cited by

  1. Human induced vibration vs. cable-stay footbridge deterioration vol.18, pp.1, 2016, https://doi.org/10.12989/sss.2016.18.1.017
  2. Dynamic Property Evaluation of a Long-Span Cable-Stayed Bridge (Sutong Bridge) by a Bayesian Method pp.1793-6764, 2018, https://doi.org/10.1142/S0219455419400108
  3. Mode identifiability of a cable-stayed bridge using modal contribution index vol.20, pp.2, 2017, https://doi.org/10.12989/sss.2017.20.2.115
  4. Fast operational modal analysis of a single-tower cable-stayed bridge by a Bayesian method vol.174, pp.None, 2021, https://doi.org/10.1016/j.measurement.2021.109048
  5. Hilbert square demodulation and error mitigation of the measured nonlinear structural dynamic response vol.160, pp.None, 2016, https://doi.org/10.1016/j.ymssp.2021.107935