Abstract
Although use of wavelet transform has significantly increased in civil engineering, selection of a proper wavelet type for a particular civil engineering application remains to be a question. The purpose of this study is to provide a guideline for the proper selection of wavelet type in civil engineering applications. A total of 64 articles were reviewed with an emphasis on the use of wavelet transform and the choice of a mother wavelet. A survey of the literature shows that wavelet transform is useful to mathematically address a range of problems, with the specific applications of the wavelet transform in civil engineering being sixfold: denoising, discontinuity detection, feature extraction, frequency identification, system modeling, and data compression. The result of the study is expected to help civil engineers to choose the right type of wavelet transform for the particular field of civil engineering.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Abdullah, S., Sahadan, S. N., Nuawi, M. Z., and Nopiah, Z. M. (2008). “Fatigue road signal denoising process using the 4th order of Daubechies wavelet transform.” Journal of Applied Sciences, Vol. 8, No. 14, pp. 2496–2509, DOI: 10.3923/jas.2008.2496.2509.
Addison, P. S., Murray, K. B., and Watson, J. N. (2001). “The wavelet transform analysis of open channel wake flows.” J. Eng. Mech., Vol. 127, No. 1, pp. 58–70, DOI: 10.1061/(ASCE)0733-9399(2001)127:1(58).
Adeli, H. and Ghosh-Dastidar, S. (2004). “Mesoscopic-wavelet freeway work zone flow and congestion feature extraction model.” J. Transp. Eng., Vol. 130, No. 1, pp. 94–103, DOI: 10.1061/(ASCE)0733-947X(2004)130:1(94).
Adeli, H. and Jiang, X. (2006). “Dynamic fuzzy wavelet neural network model for structural system identification.” J. Struct. Eng., Vol. 132, No. 1, pp. 102–111, DOI: 10.1061/(ASCE)0733-9445(2006)132:1 (102).
Adeli, H. and Karim, A. (2000). “Fuzzy-wavelet RBFNN model for freeway incident detection.” J. Transp. Eng., Vol. 126, No. 6, pp. 464–471, DOI: 10.1061/(ASCE)0733-947X(2000)126:6(464).
Adeli, H. and Kim, H. (2004). “Wavelet-hybrid feedback-least mean square algorithm for robust control of structures.” J. Struct. Eng., Vol. 130, No. 1, pp. 128–137, DOI: 10.1061/(ASCE)0733-9445 (2004)130:1(128).
AL-Qassab, M. and Nair, S. (2003). “Wavelet-Galerkin method for free vibrations of elastic cable.” J. Eng. Mech., Vol. 129, No. 3, pp. 350–357, DOI: 10.1061/(ASCE)0733-9399(2003)129:3(350).
Badrzadeh, H., Sarukkalige, R., and Jayawardena, A. W. (2015). “Hourly runoff forecasting for flood risk management: Application of various computational intelligence models.” Journal of Hydrology, Vol. 529, pp. 1633–1643, DOI: 10.1016/j.jhydrol.2015. 07.057.
Basu, B. and Gupta, V. K. (1998). “Seismic response of SDOF systems by wavelet modeling of non-stationary processes.” J. Eng. Mech., Vol. 124, No. 10, pp. 1142–1150, DOI: 10.1061/(ASCE)0733-9399(1998)124:10(1142).
Basu, B. and Nagarajaiah, S. (2010). “Multi-scale wavelet-LQR controller for linear time varying systems.” J. Eng. Mech., Vol. 136, No. 9, pp. 1143–1151, DOI: 10.1061/(ASCE)EM.1943-7889.0000162.
Chakraborty, A. and Basu, B. (2008). “Non-stationary response analysis of long span bridges under spatially varying differential support motions using continuous the wavelet transform.” J. Eng. Mech., Vol. 134, No. 2, pp. 155–162, DOI: 10.1061/(ASCE)0733-9399 (2008)134:2(155).
Chakraborty, A. and Basu, B. (2010). “Analysis of frequency nonstationarity via continuous wavelet transform in the response of primarysecondary systems.” J. Struct. Eng., Vol. 136, No. 12, pp. 1608–1612, DOI: 10.1061/(ASCE)ST.1943-541X.0000257.
Chandan, C., Sivakumar, K., Masad, E., and Fletcher, T. (2004). “Application of imaging techniques to geometry analysis of aggregate particles.” J. Comput. Civ. Eng., Vol. 18, No. 1, pp. 75–82, DOI: 10.1061/(ASCE)0887-3801(2004)18:1(75).
Daubechies, I. (1992). Ten lectures on wavelets, Dept. of Mathematics, Univ. of Lowell, MA., Society for Industrial and Applied Mathematics, Philadelphia.
Duvert, C., Jourde, H., Raiber, M., and Cox, M. E. (2015). “Correlation and spectral analyses to assess the response of a shallow aquifer to low and high frequency rainfall fluctuations.” Journal of Hydrology, Vol. 527, pp. 894–907, DOI: 10.1016/j.jhydrol.2015.05.054.
Fang, Z., Bogena, H., Kollet, S., Koch, J., and Vereecken, H. (2015). “Spatio-temporal validation of long-term 3D hydrological simulations of a forested catchment using empirical orthogonal functions and wavelet coherence analysis.” Journal of hydrology, Vol. 529, pp. 1754–1767, DOI: 10.1016/j.jhydrol.2015.08.011.
Fenton, G. A. (1999). “Estimation for stochastic soil models.” J. Geotech. And Geoenvir. Eng., Vol. 125, No. 6, pp. 470–485, DOI: 10.1061/(ASCE)1090-0241(1999)125:6(470).
Ferrante, M., Brunone, B., and Meniconi, S. (2007). “Wavelets for the analysis of transient pressure signals for leak detection.” J. Hydr. Eng., Vol. 133, No. 11, pp. 1274–1282, DOI: 10.1061/(ASCE)0733-9429(2007)133:11(1274).
Goring, D. G. (2008). “Extracting long waves from tide–gauge records.” J. Wtrwy., Port, Coast., and Oc. Eng., Vol. 134, No. 5, pp. 306–312, DOI: 10.1061/(ASCE)0733-950X(2008)134:5(306).
Grant, D. N. (2011). “Response spectral matching of two horizontal ground-motion components.” J. Struct. Eng., Vol. 137, No. 3, pp. 289–297, DOI: 10.1061/(ASCE)ST.1943-541X.0000227.
Graps, A. (1995). “An introduction to wavelets.” IEEE Computational Science and Engineering, Vol. 2, No. 2, pp. 50–61, DOI: 10.1109/99.388960.
Gurley, K., Kijewski, T., and Kareem, A. (2003). “First-and higherorder correlation detection using the wavelet transforms.” J. Eng. Mech., Vol. 129, No. 2, pp. 188–201, DOI: 10.1061/(ASCE)0733-9399(2003)129:2(188).
Hajj, M. R. (1999). “Intermittency of energy-containing scales in atmospheric surface layer.” J. Eng. Mech., Vol. 125, No. 7, pp. 797–803, DOI: 10.1061/(ASCE)0733-9399(1999)125:7(797).
Hera, A. and Hou, Z. (2004). “Application of wavelet approach for ASCE structural health monitoring benchmark studies.” J. Eng. Mech., Vol. 130, No. 1, pp. 96–104, DOI: 10.1061/(ASCE)0733-9399(2004)130:1(96).
Honda, R. and Ahmed, T. (2011). “Design input motion synthesis considering the effect of uncertainty in structural and seismic parameters by feature indexes.” J. Struct. Eng., Vol. 137, No. 3, pp. 391–400, DOI: 10.1061/(ASCE)ST.1943-541X.0000085.
Hou, Z., Noori, M., and Amand, R. St. (2000). “Wavelet-based approach for structural damage detection.” J. Eng. Mech., Vol. 126, No. 7, pp. 677–683, DOI: 10.1061/(ASCE)0733-9399(2000)126:7(677).
Hubbard, B. B. (1998). The World According to Wavelets: the Story of a Mathematical technique in the Making, A KPeters, Natick, MA,USA.
Ji, Y. F. and Chang, C. C. (2008). “Nontarget stereo vision technique for spatiotemporal response measurement of line–like structures.” J. Eng. Mech., Vol. 134, No. 6, pp. 466–474, DOI: 10.1061/(ASCE) 0733-9399(2008)134:6(466).
Jiang, X. and Adeli, H. (2005). “Dynamic wavelet neural network model for traffic flow forecasting.” J. Transp. Eng., Vol. 131, No. 10, pp. 771–779, DOI: 10.1061/(ASCE)0733-947X(2005)131:10(771).
Jiang, X. and Mahadevan, S. (2008). “Bayesian probabilistic inference for nonparametric damage detection of structures.” J. Eng. Mech., Vol. 134, No. 10, pp. 820–831, DOI: 10.1061/(ASCE)0733-9399 (2008)134:10(820).
Karim, A. and Adeli, H. (2002). “Incident detection algorithm using wavelet energy representation of traffic patterns.” J. Transp. Eng., Vol. 128, No. 3, pp. 232–233, DOI: 10.1061/(ASCE)0733-947X (2002)128:3(232).
Karim, A. and Adeli, H. (2003). “Fast automatic incident detection on urban and rural freeways using wavelet energy algorithm.” J. Transp. Eng., Vol. 129, No. 1, pp. 57–68, DOI: 10.1061/(ASCE) 0733-947X(2003)129:1(57).
Kijewski-Correa, T. and Kareem, A. (2006). “Efficacy of Hilbert and wavelet transforms for time-frequency analysis.” J. Eng. Mech., Vol. 132, No. 10, pp. 1037–1049, DOI: 10.1061/(ASCE)0733-9399(2006) 132:10(1037).
Kijewski-Correa, T. and Kareem, A. (2007). “Performance of the wavelet transform and empirical mode decomposition in extracting signals embedded in noise.” J. Eng. Mech., Vol. 133, No. 7, pp. 849–852, DOI: 10.1061/(ASCE)0733-9399(2007)133:7(849).
Kim, H., Rauch, A. F., and Haas, C. T. (2004). “Automated quality assessment of stone aggregates based on laser imaging and a neural network.” J. Comput. Civ. Eng., Vol. 18, No. 1, pp. 58–64, DOI: 10.1061/(ASCE)0887-3801(2004)18:1(58).
Kim, T. and Valdeoe, J. B. (2003). “Nonlinear model for drought forecasting based on a conjunction of the wavelet transforms and neural networks.” J. Hydrogic. Eng., Vol. 8, No. 6, pp. 319–328, DOI: 10.1061/(ASCE)1084-0699(2003)8:6(319).
Kingsbury, N. (2001). “Complex wavelets for shift invariant analysis and filtering of signals.” Applied and Computational Harmonic Analysis, Vol. 10, No. 3, pp. 234–256, DOI: 10.1006/acha.2000.0343.
Kitada, Y. (1998). “Identification of nonlinear structural dynamic systems using wavelets.” J. Eng. Mech., Vol. 124, No. 10, pp. 1059–1066, DOI: 10.1061/(ASCE)0733-9399(1998)124:10(1059).
Kii, Ö. (2009). “Neural networks and wavelet conjunction model for intermittent streamflow forecasting.” J. Hydrologic. Eng., Vol. 14, No. 8, pp. 773–782, DOI: 10.1061/(ASCE)HE.1943-5584.0000053.
Law, S. S., Li, X. Y., and Lu, Z. R. (2006). “Structural damage detection from wavelet coefficient sensitivity with model errors.” J. Eng. Mech., Vol. 132, No. 10, pp. 1077–1087, DOI: 10.1061/(ASCE) 0733-9399(2006)132:10(1077).
Liang, J., Chaudhuri, S. R., and Shinozuka, M. (2007). “Simulation of nonstationary stochastic processes by spectral representation.” J. Eng. Mech., Vol. 133, No. 6, pp. 616–627, DOI: 10.1061/(ASCE) 0733-9399(2007)133:6(616).
Liew, K. M. and Wang, Q. (1998). “Application of wavelet theory for crack identification in structures.” J. Eng. Mech., Vol. 124, No. 2, pp. 152–157, DOI: 10.1061/(ASCE)0733-9399(1998)124:2(152).
Ma, Y., Dong, G., Liu, S., Zang, J., Li, J., and Sun, Y. (2010). “Laboratory study of unidirectional focusing waves in intermediate depth water.” J. Eng. Mech., Vol. 136, No. 1, pp. 78–90, DOI: 10.1061/(ASCE)EM.1943-7889.0000076.
Mallat, S. G. (1989). “A theory for multiresolution signal decomposition: the wavelet representation.” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 11, No. 7, pp. 674–693, DOI: 10.1109/34.192463.
Marwala, T. (2000). “Damage identification using committee of neural networks.” J. Eng. Mech., Vol. 126, No. 1, pp. 43–50, DOI: 10.1061/(ASCE)0733-9399(2000)126:1(43).
Massel, S. R. (2001). “Wavelet analysis for processing of ocean surface wave records.” Ocean Engineering, Vol. 28, No. 8, pp. 957–987, DOI: 10.1016/S0029-8018(00)00044-5.
MathWorks (2010). Wavelet Toolbox for Use with MATLAB: User’s Guide Version 1, The MathWorks, Inc., Natick, MA,USA.
Melhem, H. and Kim, H. (2003). “Damage detection in concrete by Fourier and wavelet analyses.” J. Eng. Mech., Vol. 129, No. 5, pp. 571–577, DOI: 10.1061/(ASCE)0733-9399(2003)129:5(571).
Mizuno, Y., Monroig, E., and Fujino, Y. (2008). “Wavelet decompositionbased approach for fast damage detection of civil structures.” J. Infrastruct. Syst., Vol. 14, No. 1, pp. 27–32, DOI: 10.1061/(ASCE) 1076-0342(2008)14:1(27).
Mwale, D. and Gan, T. Y. (2010). “Integrating wavelet empirical orthogonal functions and statistical disaggregation for predicting weekly runoff for the upper kafue basin in zambia, africa.” J. Hydrologic. Eng., Vol. 15, No. 10, pp. 822–833, DOI: 10.1061/(ASCE)HE.1943-5584.0000231.
Mwale, D., Gan, T. Y., Devito, K. J., Silins, U., Mendoza, C., and Petrone, R. (2011). “Regionalization of runoff variability of Alberta, Canada, by wavelet, independent component, empirical orthogonal, function, and geographical information system analyses.” J. Hydrologic. Eng., Vol. 16, No. 2, pp. 93–107, DOI: 10.1061/(ASCE) HE.1943-5584.0000284.
Mwale, D., Gan, T. Y., Shen, S. S. P., Shu, T. T., and Kim, K. (2007). “Wavelet empirical orthogonal functions of space-time-frequency regimes and predictability of Southern Africa summer rainfall.” J. Hydrologic. Eng., Vol. 12, No. 5, pp. 513–523, DOI: 10.1061/(ASCE)1084-0699(2007)12:5(513).
Nourani, V., Alami, M. T., and Vousoughi, F. D. (2015). “Waveletentropy data pre-processing approach for ANN-based groundwater level modeling.” Journal of Hydrology, Vol. 524, pp. 255–269, DOI: 10.1016/j.jhydrol.2015.02.048.
Nourani, V., Baghanam, A. H., Adamowski, J., and Kisi, O. (2014). “Applications of hybrid wavelet–Artificial Intelligence models in hydrology: A review.” Journal of Hydrology, Vol. 514, pp. 358–377, DOI: 10.1016/j.jhydrol.2014.03.057.
Ogaja, C., Wang, J., and Rizos, C. (2003). “Detection of wind-induced response by the wavelet transformed GPS solutions.” J. Surv. Eng., Vol. 129, No. 3, pp. 99–104, DOI: 10.1061/(ASCE)0733-9453 (2003)129:3(99).
Park, S., Inman, D. J., Lee, J., and Yun, C. (2008). “Piezoelectric sensorbased health monitoring of railroad tracks using a two-step support vector machine classifier.” J. Infrastruct. Syst., Vol. 14, No. 1, pp. 80–88, DOI: 10.1061/(ASCE)1076-0342(2008)14:1(80).
Rao, R. M. and Bopardikar, A. S. (1998). Wavelet Transforms, Addison Wesley Longman, Inc., Reading, MA,USA.
Ren, W., Sun, Z., Xia, Y., Hao, H., and Deeks, A. J. (2008). “Damage identification of shear connectors with wavelet packet energy: Laboratory test study.” J. Struct. Eng., Vol. 134, No. 5, DOI: 10.1061/(ASCE)0733-9445(2008)134:5(832).
Rizzo, P., Scalea, F. L., Banerjee, S., and Mal, A. (2005). “Ultrasonic characterization and inspection of open cell foams.” J. Eng. Mech., Vol. 131, No. 11, pp. 1200–1208, DOI: 10.1061/(ASCE)0733-9399(2005)131:11(1200).
Satirapod, C., Wang, J., and Rizos, C. (2003). “Comparing different global positioning system data processing techniques for modeling residual systematic errors.” J. Surv. Eng., Vol. 129, No. 4, pp. 129–136, DOI: 10.1061/(ASCE)0733-9453(2003)129:4(129).
Sattar, A. M. A., Dickerson, J. R., and Chaudhry, M. H. (2009). “Wavelet-Galerkin solution to the water hammer equations.” J. Hydr. Eng., Vol. 135, No. 4, pp. 283–295, DOI: 10.1061/(ASCE)0733-9429 (2009)135:4(283).
Shin, S. and Hryciw, R. D. (2004). “Wavelet analysis of soil mass images for particle size determination.” J. Comput. Civ. Eng., Vol. 18, No. 1, pp. 19–27, DOI: 10.1061/(ASCE)0887-3801(2004)18:1(19).
Shoaib, M., Shamseldin, A. Y., Melville, B. W., and Khan, M. M. (2015). “Runoff forecasting using hybrid Wavelet Gene Expression Programming (WGEP) approach.” Journal of Hydrology, Vol. 527, pp. 326–344, DOI: 10.1016/j.jhydrol.2015.04.072.
Spanos, P. D. and Failla, G. (2004). “Evolutionary spectra estimation using wavelets.” J. Eng. Mech., Vol. 130, No. 8, pp. 952–960, DOI: 10.1061/(ASCE)0733-9399(2004)130:8(952).
Spanos, P. D. and Rao, V. R. S. (2001). “Random field representation in a biorthogonal wavelet basis.” J. Eng. Mech., Vol. 127, No. 2, pp. 195–206, DOI: 10.1061/(ASCE)0733-9399(2001)127:2(194).
Stamos, D. G. and Hajj, M. R. (2001). “Reflection and transmission of waves over submerged breakwaters.” J. Eng. Mech., Vol. 127, No. 2, pp. 99–105, DOI: 10.1061/(ASCE)0733-9399(2001)127:2(99).
Sun, Z. and Chang, C. C. (2002). “Structural damage assessment based on wavelet packet transform.” J. Struct. Eng., Vol. 128, No. 10, pp. 1354–1361, DOI: 10.1061/(ASCE)0733-9445(2002)128:10(1354).
Sun, Z. and Chang, C. C. (2004). “Statistical wavelet-based method for structural health monitoring.” J. Struct. Eng., Vol. 130, No. 7, pp. 1055–1062, DOI: 10.1061/(ASCE)0733-9445(2004)130:7(1055).
Torrence, C. and Compo, G. P. (1998). “A practical guide to wavelet analysis.” Bull. Am. Meteorol. Soc., Vol. 79, pp. 61–78, DOI: 10.1175/1520-0477(1998)079<0061:APGTWA>2.0.CO;2.
Wei, L., Fwa, T. F., and Zhe, Z. (2005). “Wavelet analysis and interpretation of road roughness.” J. Transp. Eng., Vol. 131, No. 2, pp. 120–130, DOI: 10.1061/(ASCE)0733-947X(2005)131:2(120).
Woo, S. and Liu, P. L. -F. (2004). “Finite-element model for modified Boussinesq equations. II: applications to nonlinear harbor oscillations.” J. Wtrwy., Port, Coast., and Oc. Eng., Vol. 130, No. 1, pp. 17–28, DOI: 10.1061/(ASCE)0733-950X(2004)130:1(17).
Wu, J., Amaratunga, K., and Chitradon, R. (2002). “Design of distributed interactive online geographic information system viewer using wavelets.” J. Comput. Civ. Eng., Vol. 16, No. 2, pp. 115–123, DOI: 10.1061/(ASCE)0887-3801(2002)16:2(115).
Yoon, D., Weiss, W. J., and Shah, S. P. (2000). “Assessing damage in corroded reinforced concrete using acoustic emission.” J. Eng. Mech., Vol. 126, No. 3, pp. 273–283, DOI: 10.1061/(ASCE)0733-9399(2000)126:3(273).
Yu, H. L. and Lin, Y. C. (2015). “Analysis of space–time non-stationary patterns of rainfall–groundwater interactions by integrating empirical orthogonal function and cross wavelet transform methods.” Journal of Hydrology, Vol. 525, pp. 585–597, DOI: 10.1016/j.jhydrol.2015. 03.057.
Zhang, Y. and Li, J. (2006). “Wavelet-based vibration sensor data compression technique for civil infrastructure condition monitoring.” J. Comp. Civ. Eng., Vol. 20, No. 6, pp. 390–399, DOI: 10.1061/(ASCE)0887-3801(2006)20:6(390).
Özger, M. (2011). “Investigating the multifractal properties of significant wave height time series using a wavelet–based approach.” J. Wtrwy., Port, Coast., and Oc. Eng., Vol. 137, No. 1, pp. 34–42, DOI: 10.1061/(ASCE)WW.1943-5460.0000062.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kim, B., Jeong, H., Kim, H. et al. Exploring wavelet applications in civil engineering. KSCE J Civ Eng 21, 1076–1086 (2017). https://doi.org/10.1007/s12205-016-0933-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12205-016-0933-3