Abstract
The monitoring of the evolution of structural dynamic response under transient loads must be carried out to understand the physical behaviour of building subjected to earthquake ground motion, as well as to calibrate numerical models simulating their dynamic behaviour. Fourier analysis is one of the most used tools for estimating the dynamic characteristics of a system. However, the intrinsic assumption of stationarity of the signal imposes severe limitations upon its application to transient earthquake signals or when the dynamic characteristics of systems change over time (e.g., when the frequency of vibration of a structure decreases due to damage). Some of these limitations could be overcome by using the Short Time Fourier Transform (STFT). However, the width of the moving window adopted for the analysis has to be fixed as a function of the minimum frequency of interest, using the best compromise between resolution in both the time and frequency domains. Several other techniques for time-frequency analysis of seismic signals recorded in buildings have been recently proposed. These techniques are more suitable than the STFT for the application described above, although they also present drawbacks that should be taken into account while interpreting the results. In this study, we characterize the dynamic behaviour of the Falkenhof Tower (Potsdam, Germany) while forced by ambient noise and vibrations produced by an explosion. We compare the results obtained by standard frequency domain analysis with those derived by different time-frequency methods. In particular, the results obtained by the standard Transfer Function method, Horizontal to Vertical Spectral Ratio (HVSR), Short Time Fourier Transform (STFT), Empirical Mode Decomposition (EMD) and S-Transform are discussed while most of the techniques provide similar results, the EMD analyses suffer some problems derived from the mode mixing in most of the Intrinsic Mode Functions (IMFs).
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References
Addison PS (2002) The illustrated wavelet transform handbook. Institute of Physics. ISBN 0750306920
Assous S, Humeau A, Tartas M, Abraham P, L’Huillier JP (2005) Physiological effects of indomethacin and celecobix: an S-transform laser Doppler flowmetry signal analysis. Phys Med Biol 50: 1951. doi:10.1088/0031-9155/50/9/002
Battista BM, Knapp C, McGee T, Goebel V (2007) Application of the empirical mode decomposition and Hilbert-Huang transform to seismic reflection data. Geophysics 72(2): H29–H37. doi:10.1190/1.2437700
Bindi D, Parolai S, Cara F, Di Giulio G, Ferretti G, Luzi L, Monachesi G, Pacor F, Rovelli A (2009) Site amplifications observed in the Gubbio basin, Central Italy: hints for lateral propagation effects. Bull Seismol Soc Am 99: 741–760
Bin Altaf MU, Gautama T, Tanaka T, Mandic DP (2007) Rotation invariant complex empirical mode decomposition. In: Proceedings of ICASSP 2007, pp 1009–1012
Chopra AK (1995) Dynamic of structures—theory and applications to earthquake engineering. Prentice Hall, Englewood Cliffs
Cohen L (1989) Time-frequency distributions—a review. Proc IEEE 77(7): 941–981
Dehghani MJ (2009) Comparison of S-transform and wavelet transform in power quality analysis. World Acad Sci Eng Technol 50: 395–398
Ditommaso R, Parolai S, Mucciarelli M, Eggert S, Sobiesiak M, Zschau J (2010a) Monitoring the response and the back-radiated energy of a building subjected to ambient vibration and impulsive action: the Falkenhof Tower (Potsdam, Germany). Bull Earthquake Eng 8(3): 705–722. doi:10.1007/s10518-009-9151-4
Ditommaso R, Mucciarelli M, Ponzo FC (2010b) S-Transform based filters applied to the analysis of nonlinear dynamic behaviour of soil and buildings. In: Proceedings of the 14th European conference on earthquake engineering. Ohrid
Ditommaso R, Mucciarelli M, Ponzo FC (2012) Analysis of non-stationary structural systems by using a band-variable filter. Bull Earthquake Eng. doi:10.1007/s10518-012-9338-y
Faisal MF, Mohamed A, Hussain A, Nizam M (2009) Support vector regression based S-transform for prediction of single and multiple power quality disturbances. Eur J Sci Res 34(2):237–251. ISSN 1450-216X
Flandrin P, Gonçalvès P, Rilling G (2005) EMD equivalent filter banks, from interpretation to applications. In: Huang NE, Shen SSP (eds) hilbert-huang transform : introduction and applications, World Scientific, Singapore, pp 67–87, 360 p
Gabor D (1946) Theory of communication. J Inst Elect Eng 93(3): 429–457
Gallego TS, Staszewski WJ, Worden K (2010) Vibration analysis of simulated mdof time-variant systems using the Hilbert-Huang transform. In: Fifth world conference on structural control and monitoring, Shinjuku
Huang JW, Milkereit B (2009) Empirical mode decomposition based instantaneus spectral analysis and its applications to heterogeneous petrophysical model construction. In: Proceedings of volume 2009 CSPG CSEG CWLS Convention, Calgary
Huang NE, Shen Z, Long SR, Wu MC, Shih HH, Zheng Q, Yen N-C, Tung CC, Liu HH (1998) The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc R Soc Lond Ser A 454: 903–995
Jena G, Singh RB, Prasad GMV (2006) Study of S transform & its application in digital signal processing. National, Conference Recent trends in Intelligent Computing (RTIC06), Kalyani Govt. Engg. College, Kalyani, pp 45–50
Jones KA, Porjesz B, Chorlian D, Rangaswamy M, Kamarajan C, Padmanabhapillai A, Stimus A, Begleiter H (2006) S-transform time-frequency analysis of P300 reveals deficits in individuals diagnosed with alcoholism. Clin Neurophysiol 117(10):2128–2143. Epub 2006 Aug 22
Mucciarelli M (1998) Reliability and appllicability of Nakamura’s technique using microtremors: an experimental approach. J Earthq Eng 2(4): 625–638
Mucciarelli M, Bianca M, Ditommaso R, Gallipoli MR, Masi A, Milkereit C, Parolai S, Picozzi M, Vona M (2010) Far field damage on RC buildings: the case study of Navelli during the L’Aquila (Italy) seismic sequence, 2009. Bull Earthquake Eng. doi:10.1007/s10518-010-9201-y
Pakrashi V, Ghosh B (2009) Application of S transform in structural health monitoring. NDTCE’09, non-destructive testing in civil engineering Nantes, France
Parolai S (2009) Denoising of seismograms using the S-transform. Bull Seismol Soc Am 99(1): 226–234
Picozzi M, Parolai S, Mucciarelli M, Milkereit C, Bindi D, Ditommaso R, Vona M, Gallipoli MR, Zschau J (2011) Interferometric analysis of strong ground motion for structural health monitoring: the example of the L’Aquila, Italy, seismic sequence of 2009. Bull Seismol Soc Am 101(2): 635–651. doi:10.1785/0120100070
Pinnegar CR, Eaton DE (2003) Application of the S-transform to prestack noise attenuation filtering. J Geophys Res 108(B9): 2422. doi:10.1029/2002JB00002258
Poon CW, Chang CC (2007) Identification of nonlinear elastic structures using empirical mode decomposition and nonlinear normal modes. Smart Struct Syst 3(2): 000–000
Portnyagin YI, Merzlyakov EG, Jacobi C, Mitchell NJ, Muller HG, Manson AH, Singer W, Hoffmann P, Fachrutdinova AN (1999) Some results of S-transform analysis of the transient planetary-scale wind oscillations in the lower thermosphere. Earth Planets Space 51: 711–717
Puglia R, Ditommaso R, Pacor F, Mucciarelli M, Luzi L, Bianca M (2011) Frequency variation in site response over long and short time scales, as observed from strong motion data of the L’Aquila (2009) seismic sequence. Bull Earthquake Eng. doi:10.1007/s10518-011-9266-2
Pulkkinen A, Kataoka R (2006) S-transform view of geomagnetically induced currents during geomagnetic superstorms. Geophys Res Lett 33: L12108. doi:10.1029/2006GL025822
Rehman N, Mandic DP (2010) Multivariate empirical mode decomposition. Proc R Soc A 466(2117): 1291–1302
Rehman N, Mandic DP (2011) Filter bank property of multivariate empirical mode decomposition. IEEE Trans Signal Process 59(tba):tba
Rezaei D, Taheri F (2010) Health monitoring of pipeline girth weld using empirical mode decomposition. Smart Mater Struct 19: 055016. doi:10.1088/0964-1726/19/5/055016
Ruthner MP, de Oliveira AS, Petrobras SA, Gattass M, TecGraf PUC-Rio (2005) Application of S transform in the spectral decomposition of seismic data. In: 9th international congress of the Brazilian Geophysical Society
Schimmel M, Gallart J (2005) The inverse S-transform in filters with time-frequency localization. Signal Process IEEE Trans 53(11):4417–4422. ISSN: 1053-587X. doi:10.1109/TSP.2005.857065
Smith T, Ditommaso R, Carradine D, Ponzo FC, Pampanin S (2012) Seismic performance of a post-tensioned LVL building subjected to the Canterbury earthquake sequence. NZSEE Annual Technical Conference & AGM, 13–15 April 2012, Christchurch. Paper number 126
Stockwell RG, Mansinha L, Lowe RP (1996) Localization of the complex spectrum: the S-Transform. IEEE Trans Signal Process 44: 998–1001
Young RK (1993) Wavelet theory and its applications. Kluwer Academic Publishers, Dordrecht
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Ditommaso, R., Mucciarelli, M., Parolai, S. et al. Monitoring the structural dynamic response of a masonry tower: comparing classical and time-frequency analyses. Bull Earthquake Eng 10, 1221–1235 (2012). https://doi.org/10.1007/s10518-012-9347-x
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DOI: https://doi.org/10.1007/s10518-012-9347-x