Application of Hilbert-Huang Transform Method for Analyzing Toxic Concentrations in the Niagara River
Publication: Journal of Hydrologic Engineering
Volume 15, Issue 2
Abstract
A novel application of the Hilbert-Huang transform (HHT) method for the analysis of nonstationary and nonlinear time series is proposed in this paper. The HHT is introduced to the field of water quality analysis both to evaluate trends and to assess the cause-effects relationship between the system under study and external physical factors. The HHT combines two distinct analytical methods: the empirical mode decomposition (EMD) to decompose observed series into independent intrinsic mode functions and the Hilbert transform to transform these time-dependent functions into time-frequency functions. A practical application of the HHT method for data analysis is presented herein for four time series in the Niagara River: flow, water temperature, and incoming concentrations of two polycyclic aromatic hydrocarbons. It is shown that the EMD improves the spectral representation of the original time series, enabling a better detection of periodic trends and dominant time scales. It is concluded that the ability of the HHT of decomposing the signal based on the data and transforming it into the frequency-time domain provides insights into time series characteristics that could improve the modeling effort on the Niagara River.
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Acknowledgments
The financial support from National Science Foundation Graduate Fellowship, the Civil, Structural, and Environmental Engineering Department, and the Environment and Society Institute at the State University of New York at Buffalo to the first writer is highly appreciated. The writers also thank Donald J. Williams and the Aquatic Sciences and Reporting Ecosystem Health Division Environment Conservation Branch of the Ontario region in Canada, for providing essential information for this study and Professor S. Ping Ho at National Taiwan University for his useful suggestions on the HHT method.
References
Benaouda, D., Murtagh, F., Starck, J. L., and Renaud, O. (2006). “Wavelet-based nonlinear multiscale decomposition model for electricity load forecasting.” Neurocomputing, 70(1–3), 139–154.
Coulibaly, P. (2006). “Spatial and temporal variability of Canadian seasonal precipitation (1900–2000).” Adv. Water Res., 29(12), 1846–1865.
Dohan, K., and Whitfield, P. H. (1997). “Identification and characterization of water quality transients using wavelet analysis. I. Wavelet analysis methodology.” Water Sci. Technol., 36(5), 325–335.
Flandrin, P. (2004). HHT toolbox for Matlab 7, Matlab Routines, Lyon, France.
Franceschini, S. (2007). “Development of a framework to account for uncertainty sources in modeling toxic concentrations in the Niagara River.” Ph.D. dissertation, SUNY at Buffalo, Buffalo, N.Y.
Gaucherel, C. (2002). “Use of wavelet transform for temporal characterisation of remote watersheds.” J. Hydrol., 269(3–4), 101–121.
Gu, P., and Wen, Y. K. (2005). “Simulation of nonstationary random processes using instantaneous frequency and amplitude from Hilbert-Huang transform.” The Hilbert-Huang transform in engineering, N. E. Huang and N. O. Attoh-Okine, eds., Taylor and Francis, London, 191–212.
Guadagnini, A., and Franzetti, S. (1999). “Time-related capture zones for contaminants in randomly heterogeneous formations.” Ground Water, 37(2), 253–260.
Huang, H., and Pan, J. Q. (2006). “Speech pitch determination based on Hilbert-Huang transform.” Signal Process., 86(4), 792–803.
Huang, N. E., et al. (1998). “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis.” Proc. R. Soc. London, A454, 903–995.
Huang, N. E., and Attoh-Okine, N. O. (2005). The Hilbert-Huang transform in engineering, Taylor & Francis, Boca Raton, Fla.
Huang, N. E., and Shen, S. S. P. (2006). Hilbert-Huang transform and its applications interdisciplinary mathematical sciences, Vol. 5, World Scientific, River Edge, N.J.
Huang, W., Shen, Z., Huang, N. E., and Fung, Y. C. (1999). “Nonlinear indicial response of complex nonstationary oscillations as pulmonary hypertension responding to step hypoxia.” Proc. Natl. Acad. Sci. U.S.A., 96(5), 1834–1839.
Kwon, H. -H., Lall, U., Moon, Y. -I., Khalil, A. F., and Ahn, H. (2006). “Episodic interannual climate oscillations and their influence on seasonal rainfall in the Everglades National Park.” Water Resour. Res., 42(11), W11404.
Labat, D. (2008). “Wavelet analysis of the annual discharge records of the world’s largest rivers.” Adv. Water Resour., 31(1), 109–117.
Mattavelli, M., Vesin, J. M., Amaldi, E., and Gruter, R. (1996). “A new approach to piecewise linear modeling of time series.” Digital Signal Processing Workshop Proc., 1996, IEEE, Loen, Norway, 502–505.
Peng, Z. K., Tse, P. W., and Chu, F. L. (2005a). “A comparison study of improved Hilbert-Huang transform and wavelet transform: Application to fault diagnosis for rolling bearing.” Mech. Syst. Signal Process., 19(5), 974–988.
Peng, Z. K., Tse, P. W., and Chu, F. L. (2005b). “An improved Hilbert-Huang transform and its application in vibration signal analysis.” J. Sound Vib., 286(1–2), 187–205.
Samara, F., Tsai, C. W., and Aga, D. S. (2006). “Determination of potential sources of PCBs and PBDEs in sediments of the Niagara River.” Environ. Pollut., 139(3), 489–497.
Schaefli, B., Maraun, D., and Holschneider, M. (2007). “What drives high flow events in the Swiss Alps? Recent developments in wavelet spectral analysis and their application to hydrology.” Adv. Water Resour., 30(12), 2511–2525.
Sparr, T. M., and Schaezler, D. J. (1975). “Spectral analysis techniques for evaluating historical water quality records.” Proc., Int. Seminar and Exposition on Water Resources Instrumentation, Vol. II, Ann Arbor, Sci. Publishers, Chicago, 271–297.
Tsai, C. N., Adrian, D. D., and Singh, V. P. (2001). “Finite Fourier probability distribution and applications.” J. Hydrol. Eng., 6(6), 460–471.
Tyagi, V., Wellekens, C., and Bourlard, H. (2006). “A variable-scale piecewise stationary spectral analysis technique applied to ASR.” Proc., Machine Learning for Multimodal Interaction: 2nd Int. Workshop, MLMI 2005, Vol. 3869, Springer, New York, 274–284.
USEPA and NYSDEC. (2003). “Niagara River toxic management plan (NRTMP)—Progress report and work plan.” ⟨http://www.epa.gov/glnpo/lakeont/nrtmp/pr_wp_2003.pdf⟩.
Xie, H. B., and Wang, Z. Z. (2006). “Mean frequency derived via Hilbert-Huang transform with application to fatigue EMG signal analysis.” Comput. Methods Programs Biomed., 82(2), 114–120.
Yang, J. N., Lei, Y., Lin, S., and Huang, N. (2004). “Identification of natural frequencies and dampings of in situ tall buildings using ambient wind vibration data.” J. Eng. Mech., 130(5), 570–577.
Zetterqvist, L. (1991). “Statistical estimation and interpretation of trends in water quality time series.” Water Resour. Res., 27(7), 1637–1648.
Information & Authors
Information
Published In
Journal of Hydrologic Engineering
Volume 15 • Issue 2 • February 2010
Pages: 90 - 96
Copyright
© 2010 ASCE.
History
Received: Jun 5, 2007
Accepted: Jun 9, 2009
Published online: Jan 15, 2010
Published in print: Feb 2010
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