Time-Frequency Localization of Earthquake Record by Continuous Wavelet Transforms

Document Type : Original Article

Authors

1 Department of Civil Engineering, Islamic Azad University Shahrekord Branch, Shahrekord, Iran

2 Department of Civil Engineering, Shahrekord University, Shahrekord, Iran

3 Researcher, Charmahal and Bakhtiari Water and Wastewater Company, Ministry of Energy, Iran

Abstract

Wavelet analysis is a new mathematical method and has been increasingly applied in engineering in recent years. Unlike Fourier transform, this method is particularly appropriate for non-stationary processes. Exceptional localization can be allowed using wavelet transform, both in time and frequency domains. Wavelet transform has been rarely used in earthquake engineering. A preliminary study of continuous wavelet transforms (CWTs) was conducted in this paper. As a rather novel technique, CWT application has generated enormous interest in recent years. It has been successfully employed in many fields, including the theories of communication and ordinary, partial differential equations, signal and image processing, and numerical analysis. As evidenced, exceptional localizations of time-frequency domains have become possible through CWTs. In this paper, CWT capability of providing a full time-frequency representation of an earthquake record was demonstrated. The Morlet mother wavelet was utilized to calculate the time-frequency localization of the desired earthquake records. In this method, the time series of the earthquake records, which were broken in a wave flume, demonstrated the ability of the wavelet transform technique in detecting the complex variabilities of signals in the time-frequency domain. In this investigation, various spectral representations resulting from the CWTs were discussed and their applications for earthquake records were shown.

Highlights

Google Scholar

Keywords

Main Subjects

References

[1]      Lafrenière M, Sharp M. Wavelet analysis of inter-annual variability in the runoff regimes of glacial and nival stream catchments, BowLake, Alberta. Hydrol Process 2003;17:1093–118. doi:10.1002/hyp.1187.
[2]      Naga P, Eatherton MR. Analyzing the effect of moving resonance on seismic response of structures using wavelet transforms. Earthq Eng Struct Dyn 2014;43:759–68. doi:10.1002/eqe.2370.
[3]      Smyrou E, Bal İE, Tasiopoulou P, Gazetas G. Wavelet analysis for relating soil amplification and liquefaction effects with seismic performance of precast structures. Earthq Eng Struct Dyn 2016;45:1169–83. doi:10.1002/eqe.2701.
[4]      Yaghmaei-Sabegh S. Wavelet-based analysis for pulse period of earthquake ground-motions 2013.
[5]      Gholizadeh S, Samavati OA. Structural optimization by wavelet transforms and neural networks. Appl Math Model 2011;35:915–29.
[6]      Kaveh A, Mahdavi VR. A new method for modification of ground motions using wavelet transform and enhanced colliding bodies optimization. Appl Soft Comput 2016;47:357–69.
[7]      Sharbati R, Khoshnoudian F, Ramazi HR, Amindavar HR. Stochastic modeling and simulation of ground motions using complex discrete wavelet transform and Gaussian mixture model. Soil Dyn Earthq Eng 2018;114:267–80. doi:10.1016/j.soildyn.2018.07.003.
[8]      Huang D, Wang G. Energy-compatible and spectrum-compatible (ECSC) ground motion simulation using wavelet packets. Earthq Eng Struct Dyn 2017;46:1855–73. doi:10.1002/eqe.2887.
[9]      Heidari A, Raeisi J, Kamgar R. The application of wavelet theory with denoising to estimate the parameters of earthquake. Sci Iran 2019:0–0. doi:10.24200/sci.2019.50675.1815.
[10]    Raeisi J. Investigation of strong ground motion using a wavelet theory for hydraulic structure in far fault. MSc Thesis, Department of Civil Engineering, Shahrekord University, Iran. Shahrekord, Iran. 2017.
[11]     Heidari A, Raeisi J. A new method for calculating earthquake characteristics and nonlinear spectra using wavelet theory. J Rehabil Civ Eng 2020;8:50–62.
[12]    R. P. The Wavelet Tutorial, http://www.public.iastate.edu/~rpolikar/WAVELETS/ wave letindex html 1996.
[13]    Chen W-K. The circuits and filters handbook. CRC Press; 2002.
[14]    Strang G, Nguyen T. Wavelets and filter banks. SIAM; 1996.
[15]    J.B.T.M. R. Wavelets for Signal and Image Processing. Lecture notes, Department of Computing Science, Rijksuniversiteit Groningen, NL 1993.
[16]    Alonso RJ, Noori M, Saadat S, Masuda A, Hou Z. Effects of excitation frequency on detection accuracy of orthogonal wavelet decomposition for structural health monitoring. Earthq Eng Eng Vib 2004;3:101–6.
[17]    Yaghmaei-Sabegh S. Detection of pulse-like ground motions based on continues wavelet transform. J Seismol 2010;14:715–26.
[18]    Nagarajaiah S, Basu B. Output only modal identification and structural damage detection using time frequency & wavelet techniques. Earthq Eng Eng Vib 2009;8:583–605. doi:10.1007/s11803-009-9120-6.
[19]    Pioldi F, Rizzi E. A refined Frequency Domain Decomposition tool for structural modal monitoring in earthquake engineering. Earthq Eng Eng Vib 2017;16:627–48. doi:10.1007/s11803-017-0394-9.
[20]    Ansari A, Noorzad A, Zafarani H, Vahidifard H. Correction of highly noisy strong motion records using a modified wavelet de-noising method. Soil Dyn Earthq Eng 2010;30:1168–81. doi:10.1016/j.soildyn.2010.04.025.
[21]    Todorovska MI, Meidani H, Trifunac MD. Wavelet approximation of earthquake strong ground motion-goodness of fit for a database in terms of predicting nonlinear structural response. Soil Dyn Earthq Eng 2009;29:742–51. doi:10.1016/j.soildyn.2008.08.001.
[22]    Pnevmatikos NG, Hatzigeorgiou GD. Damage detection of framed structures subjected to earthquake excitation using discrete wavelet analysis. Bull Earthq Eng 2017;15:227–48.
[23]    Salajegheh E, Heidari A. Approximate dynamic analysis of structures for earthquake loading using FWT. Int J Eng 2007;20:37–47.
[24]    Heidari A, Pahlavan sadegh S, Raeisi J. Investigating the Effect of Soil Type on Non-linear Response Spectrum Using Wavelet Theory. Int J Civ Eng 2019;17:1909–18. doi:10.1007/s40999-019-00394-6.
[25]    Salajegheh E, HEYDARI A. Dynamic analysis of structures against earthquake by combined wavelet transform and fast Fourier transform 2002.
[26]    Salajegheh E, Heidari A. Time history dynamic analysis of structures using filter banks and wavelet transforms. Comput Struct 2005;83:53–68. doi:10.1016/j.compstruc.2004.08.008.
[27]    Salajegheh E, Heidari A. Optimum design of structures against earthquake by wavelet neural network and filter banks. Earthq Eng Struct Dyn 2005;34:67–82. doi:10.1002/eqe.417.
[28]    Heidari A, Raeisi J. Optimum Design of Structures Against earthquake by Simulated Annealing Using Wavelet Transform. J Soft Comput Civ Eng 2018;2:23–33.
[29]    Heidari A, Raeisi J, Kamgar R. Application of wavelet theory in determining of strong ground motion parameters. Iran Univ Sci Technol 2018;8:103–15.
[30]    Bakhshi H, Khosravi H, Ghoddusi M. Evaluation of Seismic Behavior of Steel Shear Wall by Time History Analysis. Comput Eng Phys Model 2019;2:38–55. doi:10.22115/cepm.2019.160278.1055.
[31]    Torkian H, Keshavarz Z. Determining the drift in reinforced concrete building using ANFIS soft computing modeling. Comput Eng Phys Model 2018;1:1–11.
[32]    Bracewell RN, Bracewell RN. The Fourier transform and its applications (Vol. 31999). New York: McGraw-Hill 1986.
[33]    Sejdić E, Djurović I, Jiang J. Time–frequency feature representation using energy concentration: An overview of recent advances. Digit Signal Process 2009;19:153–83. doi:10.1016/j.dsp.2007.12.004.
[34]    Griffin D, Lim J. Signal estimation from modified short-time Fourier transform. IEEE Trans Acoust 1984;32:236–43.
[35]    Grossmann A, Kronland-Martinet R, Morlet. Reading and understanding continuous wavelet transforms. Wavelets Springer, Berlin, Heidelb 1990:2–20.
[36]    Daubechies I. The wavelet transform, time-frequency localization and signal analysis. IEEE Trans Inf Theory 1990;36:961–1005. doi:10.1109/18.57199.
[37]    Shyh-Jier Huang, Cheng-Tao Hsieh. High-impedance fault detection utilizing a Morlet wavelet transform approach. IEEE Trans Power Deliv 1999;14:1401–10. doi:10.1109/61.796234.
[38]    Torrence C, Compo GP. A Practical Guide to Wavelet Analysis. Bull Am Meteorol Soc 1998;79:61–78. doi:10.1175/1520-0477(1998)0792.0.CO;2.
[39]    Farge M. Wavelet transforms and their applications to turbulence. Annu Rev Fluid Mech 1992;24:395–458.
[40]    PERCIVAL DP. On estimation of the wavelet variance. Biometrika 1995;82:619–31. doi:10.1093/biomet/82.3.619.
[41]    Heidari A, Salajegheh E. Wavelet analysis for processing of earthquake records 2008.

Files

History

  • Receive Date: 06 July 2019
  • Revise Date: 12 November 2019
  • Accept Date: 13 November 2019

Share

How to cite

Statistics