Abstract
Robust methods for time-frequency analysis of time series, which provide local information of signals, allow earthquake engineers to study both the input and output of dynamic time history analysis with more reliability. Moreover, time-frequency representations (TFRs) have a major role in the analysis of non-stationary seismic signals exhibiting significant time variation of frequency content. S-Transform (ST) is a modern TFR, which can measure local characteristics of a signal such as amplitude, frequency, and phase at any time instant. This paper presents a new method for decomposition of ground motion signals. A modified version of ST-based technique, originally employed to decompose signals of gearbox vibration, is introduced and applied to the extraction and characterization of pulse-like part of near-fault velocity records, which is contributed to the directivity effects. In addition, a new definition based on ST analysis is used to identify pulse period. The results of implementation of proposed procedure on a database of pulse-like ground motion recordings belonging to the different ranges of magnitude demonstrate the efficiency of proposed method compared with other available approaches. The results, also, indicate that simple approximation of distinct pulses using single-period waveforms, unlike the extracted pulses, cannot represent the impulsive nature of real records adequately.
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10518-013-9581-x/MediaObjects/10518_2013_9581_Fig1_HTML.gif)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10518-013-9581-x/MediaObjects/10518_2013_9581_Fig2_HTML.gif)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10518-013-9581-x/MediaObjects/10518_2013_9581_Fig3_HTML.gif)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10518-013-9581-x/MediaObjects/10518_2013_9581_Fig4_HTML.gif)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10518-013-9581-x/MediaObjects/10518_2013_9581_Fig5_HTML.gif)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10518-013-9581-x/MediaObjects/10518_2013_9581_Fig6_HTML.gif)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10518-013-9581-x/MediaObjects/10518_2013_9581_Fig7_HTML.gif)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10518-013-9581-x/MediaObjects/10518_2013_9581_Fig8_HTML.gif)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10518-013-9581-x/MediaObjects/10518_2013_9581_Fig9_HTML.gif)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10518-013-9581-x/MediaObjects/10518_2013_9581_Fig10_HTML.gif)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10518-013-9581-x/MediaObjects/10518_2013_9581_Fig11a_HTML.gif)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10518-013-9581-x/MediaObjects/10518_2013_9581_Fig11b_HTML.gif)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10518-013-9581-x/MediaObjects/10518_2013_9581_Fig11c_HTML.gif)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10518-013-9581-x/MediaObjects/10518_2013_9581_Fig12_HTML.gif)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10518-013-9581-x/MediaObjects/10518_2013_9581_Fig13_HTML.gif)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10518-013-9581-x/MediaObjects/10518_2013_9581_Fig14_HTML.gif)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10518-013-9581-x/MediaObjects/10518_2013_9581_Fig15_HTML.gif)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10518-013-9581-x/MediaObjects/10518_2013_9581_Fig16_HTML.gif)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10518-013-9581-x/MediaObjects/10518_2013_9581_Fig17_HTML.gif)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10518-013-9581-x/MediaObjects/10518_2013_9581_Fig18_HTML.gif)
Similar content being viewed by others
References
Agrawal A, He W (2002) A closed-form approximation of near-fault ground motion pulses for flexible structures. Paper presented at the 15th ASCE Engineering Mechanics Conference, Columbia University, New York, NY, June 2–5, 2002
Akkar S, Yazgan U, Gülkan P (2005) Drift estimates in frame buildings subjected to near-fault ground motions. J Struct eng 131(7):1014–1024. doi:10.1061/(ASCE)0733-9445(2005)131:7(1014)
Alavi B, Krawinkler H (2001) Effects of near-fault ground motions on frame structures. The John A. Blume earthquake engineering center. Stanford University, Stanford
Baker JW (2007) Quantitative classification of near-fault ground motions using wavelet analysis. Bull Seismol Soc Am 97(5):1486–1501. doi:10.1785/0120060255
Baker JW, Cornell CA (2008) Vector-valued intensity measures for pulse-likenear-fault ground motions. Eng Struct 30(4):1048–1057. doi:10.1016/j.engstruct.2007.07.009
Bray JD, Rodriguez-Marek A (2004) Characterization of forward-directivity ground motions in the near-faul tregion. Soil Dyn Earthq Eng 24(11):815–828. doi:10.1016/j.soildyn.2004.05.001
Campos-Costa A, Pinto AV (1999) European seismic hazard scenarios—an approach to the definition of input motions for testing and reliability assessment of civil engineering structures. Joint Research Center Special Publication, Ispra
Chopra AK, Chintanapakdee C (2001) Comparing response of SDF systems to near-fault and far-fault earthquake motions in the context of spectral regions. Earthq Eng Struct Dyn 30(12):1769–1789. doi:10.1002/eqe.92
Cohen L (1995) Time-frequency analysis: theory and applications. Prentice-Hall, Upper Saddle River
Dickinson BW, Gavin HP (2011) Parametric statistical generalization of uniform-hazard earthquake ground motions. J Struct Eng 137(3):410–422. doi:10.1061/(ASCE)ST.1943-541X.0000330
Ditommaso R, Mucciarelli M, Ponzo F (2010) S-Transform based filter applied to the analysis of nonlinear dynamic behaviour of soil and buildings. Paper presented at the 14th European conference on earthquake engineering, Ohrid, Republic of Macedonia, August 30 to September 3
Djurovića I, Sejdićb E, Jiang J (2008) Frequency-based window width optimization for S-transform. AEU Int J Electron Commun 62(4):245–250. doi:10.1016/j.aeue.2007.03.014
Elnashai AS, DiSarno L (2008) Fundamentals of earthquake engineering. Wiley, New York. doi:10.1002/9780470024867
Fajfar P, Vidic T, Fischinger M (1990) A measure of earthquake motion capacity to damage medium-period structures. Soil Dyn Earthq Eng 9(5):236–242. doi:10.1016/S0267-7261(05)80002-8
George N (2009) S Transform: time frequency analysis and filtering. Dissertation, National Institute of technology, Rourkela
Ghahari SF, Jahankhah H, Ghannad MA (2010) Study on elastic response of structures to near-faul tground motions through record decomposition. Soil Dyn Earthq Eng 30(7):536–546. doi:10.1016/j.soildyn.2010.01.009
Ghahari SF, Khaloo AR (2010) Considering rupture directivity effects, which structures should be named ‘long-period buildings’? Struct Des Tall Special Build early view. doi:10.1002/tal.667
Gurley K, Kareem A (1999) Applications of wavelet transforms in earthquake, wind and ocean engineering. Eng Struct 21(2):149–167
He W-L, Agrawal AK (2008) Analytical model of ground motion pulses for the design and assessment of seismic protective systems. J Struct Eng 134(7):1177–1188. doi:10.1061/(ASCE)0733-9445(2008)134:7(1177)
Jangid RS, Kelly JM (2001) Base isolation for near-fault motions. Earthq Eng Struct Dyn 30(5):691–707. doi:10.1002/eqe.31
Kalkan E, Kunnath SK (2006) Effects of fling step and forward directivity on seismic response of buildings. Earthq Spectr 22(2):367–390. doi:10.1193/1.2192560
Kalkan E, Kunnath SK (2008) Relevance of absolute and relative energy content in seismic evaluation of structures. Adv Struct Eng 11(1):17–34. doi:10.1260/136943308784069469
Kramer SL (1996) Geotechnical earthquake engineering. Prentice-Hall, Upper Saddle River
Liao W-I, Loh C-H, Wan S (2001) Earthquake responses of RC moment frames subjected to near-fault ground motions. Struct Des Tall Special Build 10(3):219–229. doi:10.1002/tal.178
Loh C-H, Wu T-C, Huang NE (2001) Application of the empirical mode decomposition-hilbert spectrum method to identify near-fault ground-motion characteristics and structural responses. Bull Seismol Soc Am 91(5):1339–1357. doi:10.1785/0120000715
MacRae GA, Mattheis J (2000) Three-dimensional steel building response to near-fault motions. J Struct Eng 126(1):117–126. doi:10.1061/(ASCE)0733-9445(2000)126:1(117)
MacRae GA, Morrow DV, Roeder CW (2001) Near-fault ground motion effects on simple structures. J Struct Eng 127(9):996–1004. doi:10.1061/(ASCE)0733-9445(2001)127:9(996)
Makris N, Black CJ (2004) Evaluation of peak ground velocity as a “good” intensity measure for near-source ground motions. J Eng Mech 130(9):1032–1044. doi:10.1061/(ASCE)0733-9399(2004)130:9(1032)
Malhotra PK (1999) Response of buildings to near-field pulse-like ground motions. Earthq Eng Struct Dyn 28(11):1309–1326. doi:10.1002/(SICI)1096-9845(199911)28:11<1309:AID-EQE868>3.0.CO;2-U
Manfredi G (2001) Evaluation of seismic energy demand. Earthq Eng Struct Dyn 30(4):485–499. doi:10.1002/eqe.17
Mavroeidis G (2004) Modeling and simulation of near-fault strong ground motions for earthquake engineering applications. Dissertation, The State University of New York, Buffalo, New York
Mavroeidis GP, Papageorgiou AS (2003) A mathematical representation of near-fault ground motions. Bull Seismol Soc Am 93(3):1099–1131. doi:10.1785/0120020100
McFadden PD, Cook JG, Forster LM (1999) Decomposition of gear vibration signals by the generalized S-transform. Mech Syst Sig Process 13(5):691–707. doi:10.1006/mssp.1999.1233
Mollaioli F, Bosi A (2012) Wavelet analysis for the characterization of forward-directivity pulse-like ground motions on energy basis. Meccanica 47(1):203–219. doi:10.1007/s11012-011-9433-1
Mollaioli F, Bruno S, Decanini LD, Panza GF (2006) Characterization of the dynamic response of structures to damaging pulse-type near-fault ground motions. Meccanica 41(1):23–46. doi:10.1007/s11012-005-7965-y
Mukherjee S, Gupta VK (2002) Wavelet-based characterization of design ground motions. Earthq Eng Struct Dyn 31(5):1173–1190. doi:10.1002/eqe.155
Pinnegar C (2001) The generalized S-transform and TT-transform, in one and two dimensions, Dissertation. The University of Western Ontario, London, Ontario
Pinnegar CR (2006) A new subclass of complex-valued S-transform windows. Signal Process 86(8):2051–2055. doi:10.1016/j.sigpro.2005.10.013
Pinnegar CR, Mansinha L (2003a) The Bi-Gaussian S-Transform. SIAM J Sci Comput 24(5):1678–1692. doi:10.1137/S1064827500369803
Pinnegar CR, Mansinha L (2003b) The S-transform with windows of arbitrary and varying shape. Geophysics 68(1):381–385. doi:10.1190/1.1543223
Pinnegar CR, Mansinha L (2004) Time-local Fourier analysis with ascalable, phase-modulated analyzing function: the S-transform with a complex window. Signal Process 84(7):1167–1176. doi:10.1016/j.sigpro.2004.03.015
Puglia R, Ditommaso R, Pacor F, Mucciarelli M, Luzi L, Bianca M (2011) Frequency variation in site response as observed from strong motion data of the L’Aquila (2009) seismic sequence. Bull Earthq Eng 9(3):869–892. doi:10.1007/s10518-011-9266-2
Rodriguez-Marek A (2000) Near-fault site response, Dissertation. University of California, Berkeley
Rodriguez-Marek A, Cofer W (2009) Incorporation of forward-directivity into seismic hazard analysis. Washington University State, Seattle
Rupakhety R, Halldorsson B, Sigbjörnsson R (2010) Estimating coseismic deformations from near source strong motion records: methods and case studies. Bull Earthq Eng 8(4):787–811. doi:10.1007/s10518-009-9167-9
Rupakhety R, Sigbjörnsson R (2011) Can simple pulses adequately represent near-fault ground motions? J Earthq Eng 15(8):1260–1272. doi:10.1080/13632469.2011.565863
Rupakhety R, Sigurdsson SU, Papageorgiou AS, Sigbjörnsson R (2011) Quantification of ground-motion parameters and response spectra in the near-fault region. Bull Earthq Eng 9(4):893–930. doi:10.1007/s10518-011-9255-5
Samantaraya SRDP, Panda G (2006) Fault classification and location using HS-transform and radial basis function neural network Electr Pow. Syst Res 76(9–10):897–905. doi:10.1016/j.epsr.2005.11.003
Sarkara I, SriRamb V, Hamzehlooc H, Khattri KN (2005) Subevent analysis for the Tabas earthquake of September 16, 1978, using near field accelerograms. Phys Earth Planet Int 151(1–2):53–76. doi:10.1016/j.pepi.2005.01.004
Sehhati R, Rodriguez-Marek A, ElGawady M, Cofe WF (2011) Effects of near-fault ground motions and equivalent pulses on multi-story structures. Eng Struct 33(3):767–779. doi:10.1016/j.engstruct.2010.11.032
Somerville PG (1998) Development of an improved ground motion representation for near fault ground motions. Paper presented at the proceedings of SMIP98 seminar on utilization of strong-motion data, Oakland, CA, September
Somerville PG (2003) Magnitude scaling of the near fault rupture directivity pulse. Phys Earth Planet Int 137(1–4):201–212. doi:10.1016/S0031-9201(03)00015-3
Somerville PG, Smith N, Graves R, Abrahamson N (1997) Modification of empirical strong ground motion attenuation relations to include the amplitude and duration effects of rupture directivity. Seismol Res Lett 68(1):180–203. doi:10.1785/gssrl.68.1.199
Stockwell RG (2007a) A basis for efficient representation of the S-transform. Digit Signal Process 17(1):371–393. doi:10.1016/j.dsp.2006.04.006
Stockwell RG (2007b) Why use the S-transforms? In: Rodino L, Schulze B-W, Wong MW (eds) AMS Pseudo-differential operators: partial differential equations and time-frequency analysis, vol 52. Co-publication of the AMS and Fields Institute, Toronto, pp 279–309
Stockwell RG, Mansinha L, Lowe RP (1996) Localization of the complex spectrum: the S transform. IEEE Trans Signal Process 44(4):998–1001. doi:10.1109/78.492555
Tana P, Agrawal AK, Pan Y (2005) Near-field effects on seismically excited highway bridge equipped with nonlinear viscous dampers. Bridge Struct 1(3):307–318. doi:10.1080/15732480500272718
Tian Y-j, Yang Q-s, Lu M-q (2007) Simulation method of near-fault pulse-type ground motion. Acta Seismol Sin 20(1):80–87. doi:10.1007/s11589-007-0080-5
Todorovska MI, Meidani H, Trifunac MD (2009) Wavelet approximation of earthquake strongground motion-goodness of fit for a database in terms of predicting nonlinear structural response. Soil Dyn Earthq Eng 29(4):742–751. doi:10.1016/j.soildyn.2008.08.001
Tothong P, Cornell CA, Baker JW (2007) Explicit directivity-pulse inclusion in probabilistic seismic hazard analysis. Earthq Spectr 23(4):867–891. doi:10.1193/1.2790487
Trifunac MD (2008) Energy of strong motion at earthquake source. Soil Dyn Earthq Eng 28(1):1–6. doi:10.1016/j.soildyn.2007.06.009
Uang C-M, Bertero VV (1990) Evaluation of seismic energy in structures. Earthq Eng Struct Dyn 19(1):77–90. doi:10.1002/eqe.4290190108
**e L, Xu L, Adrian R-M (2005) Representation of near-fault pulse-type ground motions. Earthq Eng Eng Vib 4(2):191–199. doi:10.1007/s11803-005-0002-2
Xu L, Rodriguez-Marek A, **e L (2006) Design spectra including effect of rupture directivity in near-fault region. Earthq Eng Eng Vib 5(2):159–170. doi:10.1007/s11803-006-0636-8
Yaghmaei-Sabegh S (2010) Detection of pulse-like ground motions based on continues wavelet transform. J Seismol 14(4):715–726. doi:10.1007/s10950-010-9193-8
Yang D, Pan J, Li G (2009) Non-structure-specific intensity measure parameters and characteristic period of near-fault ground motions. Earthq Eng Struct Dyn 38(11):1257–1280. doi:10.1002/eqe.889
Zhang Y, Hu Y, Zhao F, Liang J, Yang C (2005) Identification of acceleration pulses in near-fault ground motion using the EMD method. Earthq Eng Eng Vib 4(2):201–212. doi:10.1007/s11803-005-0003-1
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Amiri, G.G., Moghaddam, S.A. Extraction of forward-directivity velocity pulses using S-Transform-based signal decomposition technique. Bull Earthquake Eng 12, 1583–1614 (2014). https://doi.org/10.1007/s10518-013-9581-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10518-013-9581-x