First- and Higher-Order Correlation Detection Using Wavelet Transforms
Publication: Journal of Engineering Mechanics
Volume 129, Issue 2
Abstract
In order to detect intermittent first- and higher-order correlation between a pair of signals in both time and frequency, a wavelet-based coherence and bicoherence technique was developed. Due to the limited averaging in a time-frequency coherence estimate, spurious correlated pockets were detected due to statistical variance. The introduction of multiresolution, localized integration windows was shown to minimize this effect. A coarse ridge extraction scheme utilizing hard thresholding was then applied to extract meaningful coherence. This thresholding scheme was further enhanced through the use of “smart” thresholding maps, which represent the likely statistical noise between uncorrelated simulated signals bearing the same power spectral density and probability-density function as the measured signals. It was demonstrated that the resulting filtered wavelet coherence and bicoherence maps were capable of capturing low levels of first- and higher-order correlation over short time spans despite the presence of ubiquitous leakage and variance errors. Immediate applications of these correlation detection analysis schemes can be found in the areas of bluff body aerodynamics, wave-structure interactions, and seismic response of structures where intermittent correlation between linear and nonlinear processes is of interest.
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References
Burrus, C. S., Gopinath, R. A., and Guo, H. (1998). Introduction to wavelets and wavelet transforms: A primer, Prentice-Hall, Englewood Cliffs, N.J.
Carmona, R., Hwang, W. L., and Torresani, B. (1998). Practical time-frequency analysis, Academic, San Diego.
Chui, C. K. (1992). Wavelet analysis and applications: An introduction to wavelets, Vol. 1, Academic, San Diego.
Daubechies, I.(1988). “Orthonormal basis of compactly supported wavelets.” Commun. Pure Appl. Math., 41, 909–96.
Daubechies, I. (1992). Ten lectures on wavelets, Society of Industrial and Applied Mathematics, Philadelphia.
Dunyak, J., Gilliam, X., Peterson, R., and Smith, D. (1997). “Coherent gust detection by wavelet transform.” Proc., 8th U.S. National Conference on Wind Engineering (CD-ROM), Johns Hopkins Univ., Baltimore.
Farge, M.(1992). “Wavelet transforms and their applications to turbulence.” Annu. Rev. Fluid Mech., 24, 395–457.
Gabor, D.(1946). “Theory of communication.” Proc. IEEE, 93(III), 429–457.
Grossman, A., and Morlet, J. (1985). “Decompositions of functions into wavelets of constant shape and related transforms.” Mathematics and physics, lecture on recent results, L. Streit, ed., World Scientific, Singapore, 135–165.
Gurley, K., and Kareem, A.(1997a). “Analysis, interpretation, modeling and simulation of unsteady wind and pressure data.” J. Wind. Eng. Ind. Aerodyn., 69–71, 657–669.
Gurley, K., and Kareem, A. (1997b). “Modeling PDFs of non-Gaussian system response.” Proc., 7th Int. Conf. on Structural Safety and Reliability (ICOSSAR), Kyoto, Japan.
Gurley, K., and Kareem, A.(1999a). “Application of wavelet transforms in earthquake, wind, and ocean engineering.” Eng. Struct., 21, 149–167.
Gurley, K., and Kareem, A. (1999b). “Higher order velocity/pressure correlation detection using wavelet transforms.” Wind engineering into the 21st Century, Proc., 10th Int. Conf. on Wind Engineering, Copenhagen, Denmark, Vol. 1, Larsen, Larose and Livesey, eds., Balkema Press, Rotterdam, The Netherlands, 431–436.
Gurley, K., Tognarelli, M., and Kareem, A.(1997). “Analysis and simulation tools for wind engineering.” Probab. Eng. Mech., 12(1), 9–31.
Hangan, H., Kopp, G. A., Vernet, A., and Martinuzzi, R.(2001). “A wavelet pattern recognition technique for identifying flow structures in cylinder generated wakes.” J. Wind. Eng. Ind. Aerodyn., 89, 1001–1015.
Kijewski, T., and Kareem, A. (2002a). “Wavelet transforms for system identification: Considerations for civil engineering applications.” Comput.-Aided Civ. Infrastruct. Eng., in press.
Kijewski, T., and Kareem, A. (2002b). “On the presence of end effects and associated remedies for wavelet-based analysis.” J. Sound Vib., in press.
Liu, P. C. (1994). “Wavelet spectrum analysis and ocean wind waves.” Wavelets in geophysics, E. Foufoula-Georgiou and P. Kumar, eds., Academic, San Diego, 151–166.
Mallat, S. (1998). A wavelet tour of signal processing, Academic, San Diego.
Nikias, C. L., and Petropulu, A. P. (1993). Higher-order spectral analysis, a nonlinear signal processing framework, PTR Prentice-Hall, Englewood Cliffs, N.J.
Powers, E. J., Park, S. I., Mehta, S., and Yi, E. J. (1997). “Higher-order statistics and extreme waves.” IEEE Signal Processing Workshop on Higher Order Statistics, Alberta, Canada, 98–102.
Shin, Y. J., Powers, E. J., and Yi, E. J. (1999). “Comparison of time-frequency representations of random wave elevation data.” Proc., 9th Int. Offshore and Polar Engineering Conf., Brest, France, 34–40.
Strang, G., and Nguyen, T. (1996). Wavelets and filter banks, Wellesley-Cambridge Press, Wellesley, Mass.
Tognarelli, M., Zhao, J., Rao, K. B., and Kareem, A.(1997). “Equivalent statistical quadratization and cubicization for nonlinear systems.” J. Eng. Mech., 123(5), 512–523.
Torrence, C., and Compo, G. P.(1998). “A practical guide to wavelet analysis.” Bull. Am. Meteorol. Soc., 79, 61–78.
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Copyright © 2003 American Society of Civil Engineers.
History
Received: Mar 1, 2002
Accepted: Jul 8, 2002
Published online: Jan 15, 2003
Published in print: Feb 2003
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