DOI QR코드

DOI QR Code

Direct identification of modal parameters using the continuous wavelet transform, case of forced vibration

  • Bedaoui, Safia (Laboratoire Navier (ENPC/IFSTTAR/CNRS), Ecole des ponts Paris Tech, Universite Paris Est) ;
  • Afra, Hamid (National Center for Studies and Building Research (CNERIB)) ;
  • Argoul, Pierre (Laboratoire Navier (ENPC/IFSTTAR/CNRS), Ecole des ponts Paris Tech, Universite Paris Est)
  • Received : 2012.12.30
  • Accepted : 2014.01.02
  • Published : 2014.04.30

Abstract

In this paper, a direct identification of modal parameters using the continuous wavelet transform is proposed. The purpose of this method is to transform the differential equations of motion into a system of algebraic linear equations whose unknown coefficients are modal parameters. The efficiency of the present method is confirmed by numerical data, without and with noise contamination, simulated from a discrete forced system with four degrees-of-freedom (4DOF) proportionally damped.

Keywords

modal identification;dynamics of structures;forced vibration;continuous wavelet transform

References

  1. Argoul, P. and Erlicher, S. (2005), "On the use of continuous wavelet analysis for modal identification", Mechanical Modelling and Computational Issues in Civil Engineering, Lecture Notes in Applied and Computational Mechanics, Volume 23, 359-368.
  2. Argoul, P., Erlicher, S. and Nguyen, T.M. (2005), "Free oscillations of a beam with a local non- linearity: comparison of mechanical modeling and experiments by means of wavelet analysis", ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conferences, Long Beach, California, USA, 24th- 28th September.
  3. Argoul, P. and Le, T.P. (2003), "Instantaneous indicators of structural behaviour based on continuous Cauchy wavelet transform", Mech. Syst. Signal Pr., 17(1), 243-250. https://doi.org/10.1006/mssp.2002.1557
  4. Carmona, R., Hwang, W.L. and Torresani, B. (1998), Practical time-frequency analysis, Academic Press, New York, USA.
  5. Carmona, R., Hwang, W.L. and Torresani, B. (1999), "Multiridge detection and time-frequency reconstructions", IEEE T. Signal Proces., 47(2), 480-492. https://doi.org/10.1109/78.740131
  6. Kougioumtzoglou, I.A. and Spanos, P.D. (2013), "An identification approach for linear and nonlinear time-variant structural via harmonic wavelet", Mech. Syst. Signal Pr., 37(1-2), 338-352. https://doi.org/10.1016/j.ymssp.2013.01.011
  7. Chakraborty, A., Basua, B. and Mitra, M. (2006), "Identification of modal parameters of a mdof system by modified Littlewood-Paley wavelet packets", J. Sound Vib., 295(3-5), 827-837. https://doi.org/10.1016/j.jsv.2006.01.037
  8. Erlicher, S. and Argoul, P. (2007), "Modal identification of linear non-proportionally damped systems by wavelet transform", Mech. Syst. Signal Pr., 21(3), 1386-1421. https://doi.org/10.1016/j.ymssp.2006.03.010
  9. Grossmann, A. and Morlet, J. (1984), "Decomposition of hardy functions into square integrable wavelets of constant shapes", SIAM J. Math. Anal., 15(4), 723-736. https://doi.org/10.1137/0515056
  10. Lardies, J. (2002), "Identification of modal parameters using the wavelet transform", Int. J. Mech. Sci., 44(11), 2263-2283. https://doi.org/10.1016/S0020-7403(02)00175-3
  11. Lardies, J. and Ta, M.N. (2005), "A wavelet based approach for the identification of damping in non-linear oscillators", Int. J. Mech. Sci., 47(8), 1262-1281. https://doi.org/10.1016/j.ijmecsci.2005.04.010
  12. Le, T.P. and Argoul, P. (2004), "Continuous wavelet transform for modal identification using free decay response", J. Sound Vib., 277(1-2), 73-100. https://doi.org/10.1016/j.jsv.2003.08.049
  13. Maia, N.M.M., Silva, J.M.M., He, N.J., Lieven, N.A.J., Lin, R.M., Skingle, G.W., To, W.M. and Urgueira, A.P.V. (1998), Theoretical and experimental modal analysis, Research Studies Press Ltd., Hertfordshire, England.
  14. Mallat, S. (1999), A wavelet tour of signal processing, Elsevier Academic Press, Sang Diego.
  15. Marchesiello, S., Bedaoui, S., Garibaldi, L. and Argoul, P. (2009), "Time-dependent identification of a bridge-like structure with crossing loads", Mech. Syst. Signal Pr., 23(6), 2019-2028. https://doi.org/10.1016/j.ymssp.2009.01.010
  16. Mensler, M. (1999), "Analyse et etude comparative de methodes d'identification des systemes a representation continue : developpement d'une boite a outils logicielle Universite Henri Poincare"-Nancy, France. ("Analysis and comparative study of continuous-time system identification techniques. Development of the CONTSID toolbox", PhD thesis, Henri Poincare University, Nancy 1, French)
  17. Pacheco, R.P. and Steffen, V.Jr. (2002), "Using orthogonal functions for identification and sensitivity analysis of mechanical systems", J. Vib. Control, 8(7), 993-1021. https://doi.org/10.1177/107754602029583
  18. Remond, D., Neyrand, J., Aridon, G. and Dufour, R. (2008), "On the improved use of Chebyshev expansion for mechanical system identification", Mech. Syst. Signal Pr., 22(2), 390-407. https://doi.org/10.1016/j.ymssp.2007.07.011
  19. Rouby, C., Remond, D. and Argoul, P. (2010), "Orthogonal polynomials or wavelet analysis for mechanical system direct identification", Ann. Solid Struct. Mech., 1(1), 41-58. https://doi.org/10.1007/s12356-009-0005-1
  20. Slavic, J., Simonovski, I. and Boltezar, M. (2003), "Damping identification using a continuous wavelet transform: application to real data", J. Sound Vib., 262(2), 291-307. https://doi.org/10.1016/S0022-460X(02)01032-5
  21. Staszewski, W.J. (1997), "Identification of damping in MDoF systems using time-scale decomposition", J. Sound Vib., 203(2), 283-305. https://doi.org/10.1006/jsvi.1996.0864
  22. Staszewski, W.J. (1998), "Identification of nonlinear systems using multi-scale ridges and skeletons of the wavelet transform", J. Sound Vib., 214(4), 639-658. https://doi.org/10.1006/jsvi.1998.1616
  23. Tan, J.B., Liu, Y., Wang, L. and Yang, W.G. (2007), "Identification of modal parameters of a system with high damping and closely spaced modes by combining continuous wavelet transform with pattern search", Mech. Syst. Signal Pr., 22(5), 1055-1060.
  24. U lker-Kaustell, M. and Karoumi, R. (2011), "Application of the continuous wavelet transform on the free vibration of a steel-concrete composite railway bridge", Eng. Struct., 33(3), 911-919. https://doi.org/10.1016/j.engstruct.2010.12.012

Cited by

  1. Effect of higher modes and multi-directional seismic excitations on power plant liquid storage pools vol.8, pp.3, 2015, https://doi.org/10.12989/eas.2015.8.3.779