Testing Stationarity with Wavelet-Based Surrogates
This article has a reply.
VIEW THE REPLYThis article has a reply.
VIEW THE REPLYPublication: Journal of Engineering Mechanics
Volume 139, Issue 2
Abstract
Traditional methods of using surrogate data to test for linearity of time-series data can be extended into the time-frequency domain to test for stationarity. Surrogates are time series that are created directly from the original dataset through manipulation and seek to replicate important properties of the original dataset. By comparing the original signal to the surrogates, additional structure in the original dataset not explained by the replicated properties may be revealed. The surrogates used for the purpose of testing stationarity are stationarized versions of an original signal that have the same Fourier amplitudes, but have randomized phases. Wavelet analysis is used in this method to transform the signals into the time-frequency domain and wavelet scalograms are used to quantitatively compare the original signal to the stationarized surrogate signals. Methods introduced in previous research compare the local and global spectral features of the surrogate signals with the local and global spectral features of the original signal to evaluate the stationarity of the signal as a whole. These methods are compared with a perceived new method, introduced here, that uses the surrogate-signal scalograms, which should contain no meaningful nonstationarity, to filter-out stationary portions of the original signal and noise, revealing where nonstationarity may be occurring within the signal. The methods are tested on a diverse set of generated signals as well as data from windstorms such as hurricanes and thunderstorms/downbursts, which may contain strong nonstationary features characterized by rapid changes in wind speed and direction. While several of the methods presented in previous research show good results with specific types of nonstationarity present, it is shown that the new technique of filtering out stationarity is better able to evaluate signals that contain many sources of nonstationarity.
Get full access to this article
View all available purchase options and get full access to this article.
References
Beck, T. W., et al. (2006). “An examination of the runs test, reverse arrangements test, and modified reverse arrangements test for assessing surface EMG signal stationarity.” J. Neurosci. Methods, 156(1–2), 242–248.
Bendat, J. S., and Piersol, A. G. (2010). Random data: Analysis and measurement procedures, 4th Ed., Wiley, Hoboken, NJ.
Borgnat, P., and Flandrin, P. (2009). “Stationarization via surrogates.” J. Stat. Mech., 2009(01), P01001–14.
Borgnat, P., Flandrin, P., Honeine, P., Richard, C., and Xiao, J. (2010). “Testing stationarity with surrogates: A time-frequency approach.” IEEE Trans. Signal Process., 58(7), 3459–3470.
Canu, S., Grandvalet, Y., Guigue, V., and Rakotomamonjy, A. (2005). “SVM and kernel methods MATLAB Toolbox,” Perception Systèmes et Information, INSA de Rouen, Rouen, France. 〈http://asi.insa-rouen.fr/enseignants/∼arakoto/toolbox/index.html〉
Cappa, P., Silvestri, S., and Sciuto, S. A. (2001). “On the robust utilization of non-parametric tests for evaluation of combined cyclical and monotonic drift.” Meas. Sci. Technol., 12(9), 1439–1444.
Cieslak, D., and Chawla, N. (2009). “A framework for monitoring classifiers’ performance: When and why failure occurs.” Knowl. Inf. Syst., 18(1), 83–109.
Efron, B. (1982). The jackknife, the bootstrap and other resampling plans, SIAM, Philadelphia.
Efron, B., and Tribshirani, R. J. (1993). An introduction to the bootstrap, Chapman and Hall, New York.
FCMP (2011). “Florida Coastal Monitoring Program.” 〈http://fcmp.ce.ufl.edu〉.
Gast, K. D., and Schroeder, J. L. (2003). “Supercell rear-flank downdraft as sampled in the 2002 thunderstorm outflow experiment.” Proc., 11th Int. Conf. on Wind Engineering (ICWE11), International Association for Wind Engineering, Lubbock, TX.
Gurley, K. R., and Kareem, A. (1999). “Applications of wavelet transforms in earthquake, wind and ocean engineering.” Eng. Structures, 21(2), 149–167.
Gurley, K. R., Kijewski, T., and Kareem, A. (2003). “First- and higher-order correlation detection using wavelet transforms.” J. Eng. Mech., 129(2), 188–201.
Kijewski-Correa, T., and Kareem, A. (2007). “Performance of wavelet transform and empirical mode decomposition in extracting signals embedded in noise.” J. Eng. Mech., 133(7), 849–852.
Kijewski, T., and Kareem, A. (2003). “Wavelet transforms for system identification in civil engineering.” Comput. Aided Civ. Infrastruct. Eng., 18(5), 339–355.
MATLAB 8 [Computer software]. Natick, MA, MathWorks.
Orwig-Gast, K. D., and Schroeder, J. L. (2005). “Extreme wind events observed in the 2002 thunderstorm outflow experiment.” Proc., 10th Americas Conf. on Wind Engineering, International Association for Wind Engineering, Baton Rouge, LA.
Richard, C., Ferrari, A., Amoud, H., Honeine, P., Flandrin, P., and Borgnat, P. (2010). “Statistical hypothesis testing with time-frequency surrogates to check signal stationarity.” Proc., IEEE Int. Conf. on Acoustics, Speech and Signal Processing (ICASSP 2010), Institute for Electrical and Electronics Engineers (IEEE), Dallas, 3666–3669.
Schölkopf, B., Bartlett, P., Smola, A., and Williamson, R. (1999). “Shrinking the tube: A new support vector regression algorithm.” Proc., Conf. Advances in Neural Information Processing Systems 11, M. S. Kearns, S. A. Solla, and D. A. Cohn, eds., MIT Press, Cambridge, MA.
Schreiber, T., and Schmitz, A. (1996). “Improved surrogate data for nonlinearity tests.” Phys. Rev. Lett., 77(4), 635–638.
Schreiber, T., and Schmitz, A. (1997). “Discrimination power of measures for nonlinearity in a time series.” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics, 55(5), 5443–5447.
Schreiber, T., and Schmitz, A. (2000). “Surrogate time series.” Physica D, 142, 346–382.
Shinozuka, M. (1971). “Simulation of multivariate and multidimensional random processes.” J. Acoust. Soc. Am., 49(1B), 357–367.
Theiler, J., Eubank, S., Longtin, A., Galdrikian, B., and Doyne Farmer, J. (1992). “Testing for nonlinearity in time series: The method of surrogate data.” Physica D, 58(1–4), 77–94.
Witten, I. H., and Frank, E. (2005). Data mining: Practical machine learning tools and techniques, Elsevier, San Francisco.
Wittig, L. E., and Sinha, A. K. (1975). “Simulation of multicorrelated random processes using the FFT algorithm.” J. Acoust. Soc. Am., 58(3), 630–634.
Xiao, J., Borgnat, P., and Flandrin, P. (2007a). “Testing stationarity with time-frequency surrogates.” Proc., 15th European Signal Processing Conf. (EUSIPCO 2007), European Association for Signal Processing, Poznan, Poland, 2020–2024.
Xiao, J., Borgnat, P., Flandrin, P., and Richard, C. (2007b). “Testing stationarity with surrogates—A one-class SVM approach.” Proc., IEEE Stat. Sig. Proc. Workshop SSP07, Institute for Electrical and Electronics Engineers (IEEE), Madison, WI.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 139 • Issue 2 • February 2013
Pages: 200 - 209
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Jan 17, 2012
Accepted: May 29, 2012
Published online: Jul 26, 2012
Published in print: Feb 1, 2013
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.