Estimating “True” Variability of Traffic Speed Deflectometer Deflection Slope Measurements
Publication: Journal of Transportation Engineering
Volume 141, Issue 1
Abstract
In this paper, the difference sequence method is used to decompose traffic speed deflectometer (TSD) deflection slope measurements variability into “true” spatial variability that is due to pavement structural changes and noise variability. A robust method to evaluate the noise standard deviation is presented and the difference sequence method is validated using simulated examples. The difference sequence method is then used to calculate the noise standard deviation and “true” spatial variability of TSD deflection slope measurements. The evaluated noise standard deviation is also used to determine the optimal smoothing of TSD deflection slope measurements using an unbiased measure of the risk. This method is compared with the generalized cross validation (GCV) criterion to determine the optimal smoothing. Results suggest the unbiased risk criterion performs better than the GCV criterion. This gives an objective method, which is currently lacking, to average TSD measurements, and more generally any continuous deflection device measurements. Finally, the results in this paper are presented under the reproducible research paradigm; a MATLAB implementation is made available that can be downloaded and used to reproduce all figures and tables presented in this paper.
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Acknowledgments
TSD measurements were obtained during the Second Strategic Highway Research Program (SHRP 2) Project R06(F); we would like to thank the UK HA for access to the HA TSD measurements and Simon Nell formerly from the Transportation Research Laboratory (TRL) for the collection of TSD measurements.
References
Altman, D. G., and Bland, J. M. (1983). “Measurement in medicine: The analysis of method comparison studies.” Statistician, 32(3), 307–317.
Bland, J. M., and Altman, D. G. (1986). “Statistical methods for assessing agreement between two methods of clinical measurement.” Lancet, 327(8476), 307–310.
Brown, L. D., and Levine, M. (2007). “Variance estimation in nonparametric regression via the difference sequence method.” Ann. Stat., 35(5), 2219–2232.
Bryce, J., Katicha, S., Flintsch, G. W., and Ferne, B. (2012). “Analyzing repeatability of continuous deflectometer measurements.”, Transportation Research Board Meeting, Transportation Research Board of the National Academies, Washington, DC.
Dette, H., Munk, A., and Wagner, T. (1998). “Estimating the variance in nonparametric regression—What is a reasonable choice?” J. Roy. Stat. Soc. Ser. B Stat. Method., 60(4), 751–764.
Flintsch, G. W., Ferne, B., Katicha, S., Bryce, J., and Nell, S. (2012). “Evaluation of traffic-speed deflectometers.” Transp. Res. Rec. J. Transp. Res. Board, 2304, 37–46.
Flintsch, G. W., and McGhee, K. K. (2009). “Managing the quality of pavement data collection.” NCHRP Synthesis of Highway Practice 39-01, Transportation Research Board, Washington, DC.
Flintsch, G. W., et al. (2013). Assessment of continuous pavement deflection measuring technologies, Second Strategic Highway Research Program (SHRP2), The National Academies, Washington, DC.
Gasser, T., Sroka, L., and Jennen-Steinmetz, C. (1986). “Residual variance and residual pattern in nonlinear regression.” Biometrika, 73(3), 625–633.
Hall, P., Kay, J., and Titterington, D. (1990). “Asymptotically optimal difference-based estimation of variance in nonparametric regression.” Biometrika, 77(3), 521–528.
Katicha, S. W., Flintsch, G. W., and Ferne, B. (2013). “Optimal averaging and localized weak spots identification for TSD deflection slope measurements.” Transp. Res. Rec., 2367(1), 43–52.
Katicha, S. W., Flintsch, G. W., Ferne, B., and Bryce, J. (2014a). “Limits of agreement (LOA) method for comparing TSD and FWD measurements.” Int. J. Pavement Eng., 15(6), 532–541.
Katicha, S. W., Flintsch, G. W., Bryce, J., and Ferne, B. (2014b). “Wavelet denoising of TSD deflection slope measurements for improved pavement structural evaluation.” Comput. Aided Civ. Infrastruct. Eng., 29(6), 399–415.
Katicha, S. W., Flintsch, G. W., and Ferne, B. W. (2012). “Estimation of pavement TSD slope measurements repeatability from a single measurement series.”, Transportation Research Board of the National Academies, Washington, DC.
MATLAB version 8.0 [Computer software]. The MathWorks, Natick, MA.
Munk, A., Bissantz, N., Wagner, T., and Freitag, G. (2005). “On difference-based variance estimation in nonparametric regression when the covariate is high dimensional.” J. Roy. Stat. Soc. B, 67(1), 19–41.
Rada, G. R., and Nazarian, S. (2011). “The state-of-the-technology of moving pavement deflection testing.”, U.S. Dept. of Transportation, Washington, DC.
Rice, J. (1984). “Bandwidth choice for nonparametric regression.” Ann. Stat., 12(4), 1215–1230.
von Neumann, J., Kent, R. H., Bellinson, H. R., and Hart, B. I. (1941). “The mean square successive difference.” Ann. Math. Stat., 12(2), 153–162.
Wahba, G. (1983). “Bayesian confidence intervals for the cross-validated spline.” J. Roy. Stat. Soc. Ser. B, 45(1), 133–150.
Weinert, H. L. (2007). “Efficient computation for Whittaker-Henderson smoothing.” Comput. Stat. Data Anal., 52, 959–974.
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Information
Published In
Journal of Transportation Engineering
Volume 141 • Issue 1 • January 2015
Copyright
© 2014 American Society of Civil Engineers.
History
Received: May 15, 2013
Accepted: May 1, 2014
Published online: Jul 28, 2014
Discussion open until: Dec 28, 2014
Published in print: Jan 1, 2015
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