The covariance-driven continuous wavelet transform incorporated with singular value decomposition is proposed in the paper to identify the operational modal parameters of structures. The covariance of operational measurements is converted into the time-scale domain using a continuous wavelet transform. Then, by performing singular value decomposition (SVD) on the covariance matrix of multi-measurements, the ridges of the covariance wavelet coefficient are decomposed. The obtained wavelet ridges of the covariance wavelet coefficient that represent the structural modal features are used to estimate the operational natural frequencies and damping ratios. The ratio of cross-covariance wavelet coefficients to auto-covariance wavelet coefficients is proposed to estimate mode shapes. A numerically simulated frame structure and a full-size bridge tested in the field under operational conditions are studied to verify the proposed technique and to demonstrate its accuracy. It has been shown that the proposed technique is reliable and efficient to identify the dynamic characteristics of full-size structures under operational conditions, especially the damping ratios and mode shapes. It has been shown that the proposed covariance-driven continuous wavelet transform method is capable of identifying the dynamic characteristics of full-size structures under operational conditions.
AndersenP.BrinckerR. and KirkegaardP.H. (1996). “Theory of covariance equivalent ARMAV models of civil engineering structures”, Proceedings of IMAC14, Dearborn, MI, USA, pp. 518–524.
2.
ArgoulP. and LeT.P. (2003). “Instantaneous indicators of structural behavior based on continuous Cauchy wavelet transform”, Mechanical Systems and Signal Processing, Vol. 17, pp. 243–250.
3.
BendatJ.S. and PiersolA.G. (1993). Engineering Applications of Correlation and Spectral Analysis, 2nd Edition, John Wiley & Sons, New York, USA.
4.
BrinkerR.ZhangL. and AndersenP. (2001). “Modal identification of output-only systems using frequency domain decomposition”, Smart Materials and Structures, Vol. 10, No. 3, pp. 441–455.
5.
CarmonaR.HwangW.L. and TorresaniB. (1998). Practical Time-Frequency Analysis, Academic Press, San Diego, USA.
6.
ChiuJ.K.JackE.C. and ChouL.S. (2007). “Random decrement based method for modal parameter identification of a dynamic system using acceleration responses”, Journal of Wind Engineering and Industrial Aerodynamics, Vol. 95, No. 6, pp. 389–410.
7.
DaubechiesI. (1992). Ten Lectures on Wavelets, Society for Industrial and Applied Mathematics, Philadelphia, Pennsylvania, USA.
8.
DevriendtC. and GuillaumeP. (2008). “Identification of modal parameters from transmissibility measurements”, Journal of Sound and Vibration, Vol. 314, No. 1–2, pp. 343–356.
9.
GouttebrozeS. and LardiesJ. (2001). “On using the wavelet transform in modal analysis”, Mechanics Research Communications, Vol. 28, No. 5, pp. 561–569.
10.
HuangN.E.ShenZ.LongS.R.WuM.C. and ShihH.H. (1998). “The empirical mode decomposition and Hilbert spectrum for nonlinear and nonstationary time series analysis”, Proceedings of the Royal Society of London, Vol. 454, pp. 903–995.
11.
HuangC.S. and SuW.C. (2007). “Identification of modal parameters of a time invariant linear system by continuous wavelet transformation”, Mechanical Systems and Signal Processing, Vol. 21, No. 4, pp. 1642–1664.
12.
HuangC.S.HungS.L.LinC.J. and SuW.C. (2005). “A wavelet-based approach to identifying structural modal parameters from seismic response and free vibration data”, Computer-Aided Civil and Infrastructure Engineering, Vol. 20, No. 6, pp. 408–423.
13.
IbrahimS.R. (1977). “Random decrement technique for modal identification structures”, Journal of Spacecraft and Rockets, Vol. 14, No. 11, pp. 696.
14.
IbrahimS.R. and MikulcikE.C. (1977). “A method for the direct identification of vibration parameters from the free response”, Shock and Vibration Bulletin, Vol. 47, No. 4, pp. 183–198.
15.
JaishiB. and RenW.X. (2005). “Structural finite element model updating using ambient vibration test results”, Journal of Structural Engineering, ASCE, Vol. 131, No. 4, pp. 617–628.
16.
JaishiB. and RenW.X. (2006). “Damage detection by finite element model updating using modal flexibility residual”, Journal of Sound and Vibration, Vol. 290, No. 1–2, pp. 369–387.
17.
JamesG.H.IIICarneT.G. and LaufferJ.P. (1995). “The natural excitation technique (NExT) for modal parameter extraction from operating structures”, International Journal of Analytical and Experimental Modal Analysis, Vol. 10, No. 4, pp. 260–277.
18.
JuangJ.N. (1994). Applied System Identification, Prentice-Hall Inc., Englewood Cliffs, New Jersey, USA.
19.
LardiesJ. and GouttebrozeS. (2002). “Identification of modal parameters using the wavelet transform”, International Journal of Mechanical Sciences, Vol. 44, No. 11, pp. 2263–2283.
20.
LeT.P. and ArgoulP. (2004). “Continuous wavelet transform for modal identification using free decay response”, Journal of Sound and Vibration, Vol. 277, No. 1–2, pp. 73–100.
21.
MaiaN.M.M. and SilvaJ.M.M. (1997). Theoretical and Experimental Modal Analysis, Research Studies Press Ltd., Somerset, England.
22.
PeetersB. and De RoeckG. (2000). “Reference based stochastic subspace identification in civil engineering”, Inverse Problems in Engineering, Vol. 8, No. 1, pp. 47–74.
23.
RenW.X. and De RoeckG. (2002a). “Structural damage identification using modal data. I: Simulation verification”, Journal of Structural Engineering, ASCE, Vol. 128, No. 1, pp. 87–95.
24.
RenW.X. and De RoeckG. (2002a). “Structural damage identification using modal data. II: Test verification”, Journal of Structural Engineering, ASCE, Vol. 128, No. 1, pp. 96–104.
25.
RenW.X. and ZongZ.H. (2004). “Output-only modal parameter identification of civil engineering structures”, Structural Engineering and Mechanics, Vol. 17, No. 3–4, pp. 429–444.
26.
RenW.X. and SunZ.S. (2008). “Structural damage identification by using wavelet entropy”, Engineering Structures, Vol. 30, No. 10, pp. 2840–2849.
27.
RuzzeneM.FasanaA.GaribaldiL. and PiomboB. (1997). “Natural frequencies and dampings identification using wavelet transform: Application to real data”, Mechanical Systems and Signal Processing, Vol. 11, No. 2, pp. 207–218.
28.
StaszewskiW.J. (1997). “Identification of damping in m.d.o.f systems using time-scale decomposition”, Journal of Sound and Vibration, Vol. 203, No. 2, pp. 283–305.
29.
UhlT. (2005). “Identification of modal parameters for non-stationary mechanical systems”, Archive of Applied Mechanics, Vol. 74, No. 11–12, pp. 878–889.
30.
Van OverscheeP. and De MoorB. (1996). Subspace Identification for Linear Systems: Theory, Implementation and Applications, Kluwer Academic Publishers, Dordrecht, Netherlands.
31.
YanB.F.MiyamotoA. and BruhwilerE.G. (2006). “Wavelet transform-based modal parameter identification considering uncertainty”, Journal of Sound and Vibration, Vol. 291, No. 1–2, pp. 285–301.
32.
YanW.J. and RenW.X. (2012a). “Statistic structural damage detection based on the closed-form of element modal strain energy sensitivity”, Mechanical System and Signal Processing, Vol. 28, pp. 183–194.
33.
YanW.J. and RenW.X. (2012b). “Operational modal parameter identification from power spectrum density transmissibility”, Computer-Aided Civil and Infrastructure Engineering, Vol. 27, No. 3, pp. 202–217.
34.
ZongZ.H.JaishiB.GeJ.P. and RenW.X. (2005). “Dynamic analysis of a half-through concrete-filled steel tubular arch bridge”, Engineering Structures, 27, No. 1, pp. 3–15.
