Abstract
Conservative chemicals (such as sodium chloride) have been utilized to perform tracer studies within drinking water distribution systems. The resulting signals from a tracer study can provide significant quantitative information to assess the ability of a given network model to represent the underlying hydraulic and transport characteristics of the network. Often, however, the resulting observed water quality time-series data are simply visually inspected to assess the ability of the network model to accurately predict water quality transport. The use of standard quantitative metrics, such as arrival times, sum of squared errors (SSE), and correlation analysis at different time lags to assess the differences between the observed and predicted time-series, can provide some useful information but are not sufficient for paired data signals. In this study, the use of dynamic time warping (DTW)—an approach for estimating the similarity between two time series of data—is presented as a method for quantitative analysis of observed and model-predicted conservative chemical time-series data. DTW uses dynamic programming to match the elements of two time series, in a sequential approach, to minimize the SSE of the two signals. Whereas the SSE provides one goodness-of-fit metric, the resulting length of the warping path also provides additional information as to the degree of the alignment between the two data streams.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This work was supported through a contract from the National Institute of Hometown Security: HSHQDC-07-3-00005 “Studying Distribution System Hydraulics and Flow Dynamics to Improve Water Utility Operational Decision Making.”
Disclaimer
This paper has been subjected to the USEPA’s review and has been approved for publication. The views expressed in this paper are those of the authors and approval does not signify that the contents necessarily reflect the views of the Agency. Mention of trade names, products, or services does not convey official EPA approval, endorsement, or recommendation.
References
Berndt, D. J., and J. Clifford. 1994. Using dynamic time warping to find patterns in time-series. Palo Alta, CA: Association for the Advancement of Artificial Intelligence.
Bertsekas, D. P. 2005. Dynamic programming and optimal control. Belmont, MA: Athena Scientific.
Boccelli, D. L., F. Shang, J. G. Uber, A. Orcevic, D. Moll, S. Hooper, M. Maslia, J. Sautner, B. Blount, and F. Cardinali. 2004. “Tracer tests for network model calibration.” In Proc., World Water and Environmental Resources Congress 2004, 449–449. Reston, VA: ASCE.
Boyle, D. P., H. V. Gupta, and S. Sorooshian. 2000. “Toward improved calibration of hydrologic models: Combining the strengths of manual and automatic methods.” Water Resour. Res. 36 (12): 3663–3674. https://doi.org/10.1029/2000WR900207.
Clark, R. M., and W. M. Grayman. 1998. Modeling water quality in drinking water distribution systems. Denver: American Water Works Association.
Clark, R. M., W. M. Grayman, J. A. Goodrich, R. A. Deininger, and A. F. Hess. 1991. “Field-testing distribution water-quality models.” J. Am. Water Works Assoc. 83 (7): 67–75. https://doi.org/10.1002/j.1551-8833.1991.tb07181.x.
DiGiano, F. A., W. Zhang, and A. Travaglia. 2005. “Calculation of the mean residence time in distribution systems from tracer studies and models.” J. Water Supply Res. Technol. AQUA 54 (1): 1–14. https://doi.org/10.2166/aqua.2005.0001.
Felty, T. 2005. “Dynamic time warping.” Accessed August 2, 2019. https://www.mathworks.com/matlabcentral/fileexchange/6516-dynamic-time-warping.
Itakura, F. 1975. “Minimum prediction residual principle applied to speech recognition.” IEEE Trans. Acoust. Speech Signal Process. 23 (1): 67–72. https://doi.org/10.1109/TASSP.1975.1162641.
Kassidas, A., J. F. MacGregor, and P. A. Taylor. 1998. “Synchronization of batch trajectories using dynamic time warping.” AIChE J. 44 (4): 864–875. https://doi.org/10.1002/aic.690440412.
Kennedy, M. S., S. Sarikelle, and K. Suravallop. 1991. “Calibrating hydraulic analyses of distribution systems using fluoride tracer studies.” J. Am. Water Works Assn. 83 (7): 54–59. https://doi.org/10.1002/j.1551-8833.1991.tb07179.x.
Keogh, E., and C. A. Ratanamahatana. 2004. “Exact indexing of dynamic time warping.” Knowl. Inf. Syst. 7 (3): 358–386. https://doi.org/10.1007/s10115-004-0154-9.
Keogh, E. J., and M. J. Pazzani. 2001. “Derivative dynamic time warping.” In Proc., 2001 SIAM Int. Conf. on Data Mining. Philadelphia: Society for Industrial and Applied Mathematics.
Krause, P., D. P. Boyle, and F. Bäse. 2005. “Comparison of different efficiency criteria for hydrological model assessment.” Adv. Geosci. 5: 89–97. https://doi.org/10.5194/adgeo-5-89-2005.
Legates, D. R., and G. J. McCabe. 1999. “Evaluating the use of ‘goodness-of-fit’ measures in hydrologic and hydroclimatic model validation.” Water Resour. Res. 35 (1): 233–241. https://doi.org/10.1029/1998WR900018.
Li, Q., and G. D. Clifford. 2012. “Dynamic time warping and machine learning for signal quality assessment of pulsatile signals.” Physiol. Meas. 33 (9): 1491–1501. https://doi.org/10.1088/0967-3334/33/9/1491.
Lin, J., G. Cervone, and P. Franzese. 2010. “Assessment of error in air quality models using dynamic time warping.” In Proc., 1st ACM SIGSPATIAL Int. Workshop on Data Mining for Geoinformatics, DMG 2010, 38–44. New York: ACM Press.
Moriasi, D. N., J. G. Arnold, M. W. Van Liew, R. L. Bingner, R. D. Harmel, and T. L. Veith. 2007. “Model evaluation guidelines for systematic quantification of accuracy in watershed simulations.” Trans. ASABE 50 (3): 885–900. https://doi.org/10.13031/2013.23153.
Munich, M. E., and P. Perona. 1999. “Continuous dynamic time warping for translation-invariant curve alignment with applications to signature verification.” In Vol. 1 of Proc., 7th IEEE Int. Conf. on Computer Vision, 108–115. New York: IEEE.
Myers, C., L. Rabiner, and A. E. Rosenberg. 1980. “Performance tradeoffs in dynamic time warping algorithms for isolated word recognition.” IEEE Trans. Acoust. Speech Signal Process. 28 (6): 623–635. https://doi.org/10.1109/TASSP.1980.1163491.
Nash, J. E., and J. V. Sutcliffe. 1970. “River flow forecasting through conceptual models. Part I—A discussion of principles.” J. Hydrol. 10 (3): 282–290. https://doi.org/10.1016/0022-1694(70)90255-6.
Quiroz-Centeno, A., and P. F. Parault. 2010. “Water quality calibration of New York City’s water distribution system model.” In Proc., 12th Annual Conf. on Water Distribution Systems Analysis (WDSA), 697–704. Reston, VA: ASCE.
Rabiner, L. R., and B.-H. Juang. 1993. Fundamentals of speech recognition. Upper Saddle River, NJ: Prentice Hall.
Ratanamahatana, C. A., and E. Keogh. 2004. “Making time-series classification more accurate using learned constraints.” In Proc., 2004 SIAM Int. Conf. on Data Mining, 11–22. Philadelphia: Society for Industrial and Applied Mathematics.
Rossman, L. A. 2000. EPANET 2 users manual. Washington, DC: USEPA.
Rubulis, J., S. Dejus, and R. Meksa. 2010. “Online measurement usage for predicting water age from tracer tests to validate a hydraulic model.” In Proc., 12th Annual Conf. on Water Distribution Systems Analysis (WDSA), 1488–1497. Reston, VA: ASCE.
Sakoe, H., and S. Chiba. 1978. “Dynamic programming algorithm optimization for spoken word recognition.” IEEE Trans. Acoust. Speech Signal Process. 26 (1): 43–49. https://doi.org/10.1109/TASSP.1978.1163055.
Sautner, J. B., M. L. Maslia, and C. Valenzuela. 2005. “Field testing of water-distribution systems at US Marine Corps Base, Camp Lejeune, North Carolina, in support of an epidemiologic study.” In World Environmental and Water Resources Congress 2005. Reston, VA: ASCE.
Simon, D., K. Gertig, and S. Stone. 2006. “Fluoride tracer test planning and implementation to support water distribution model calibration and IDSE compliance.” In Proc., 8th Annual Water Distribution Systems Analysis Symp. (WDSA). Reston, VA: ASCE.
USEPA. 2005. Water distribution system analysis: Field studies, modeling and management. Washington, DC: USEPA.
Vasconcelos, J. J., L. A. Rossman, W. M. Grayman, P. F. Boulos, and R. M. Clark. 1997. “Kinetics of chlorine decay.” J. Am. Water Works Assn. 89 (7): 54–65. https://doi.org/10.1002/j.1551-8833.1997.tb08259.x.
Zhang, Y., and T. F. Edgar. 2008. “A robust dynamic time warping algorithm for batch trajectory synchronization.” In Proc., American Control Conf., 2864–2869. Evanston, IL: IEEE.
Information & Authors
Information
Published In
Journal of Water Resources Planning and Management
Volume 145 • Issue 12 • December 2019
Copyright
©2019 American Society of Civil Engineers.
History
Received: Nov 24, 2017
Accepted: Mar 7, 2019
Published online: Sep 18, 2019
Published in print: Dec 1, 2019
Discussion open until: Feb 18, 2020
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.