Linear Model and Regularization for Transient Wave–Based Pipeline-Condition Assessment
Publication: Journal of Water Resources Planning and Management
Volume 146, Issue 5
Abstract
Condition assessment or defect detection of a pipeline is a difficult inverse problem. This paper proposes a general linear model framework that can approximately describe a wide range of pipeline condition assessment and defect detection problems. More specifically, the system response is governed by a linear function of a pipe property at discrete locations along a pipe, such that the pipe property can be reconstructed via a least-squares fit to the measured response. Real pipe systems in general involve a large number of uncertain pipe characteristics, limited data, and a very high level of noise, such that the inverse problem is ill-posed. The well-known Tikhonov regularization scheme is employed on the linear model to provide a general solution for the ill-posed inverse problem. The optimal regularization parameter, which is crucial and problem-dependent such that no universal approach always generates satisfactory results, are decided via the generalized cross validation (GCV) and L-curve approaches. The proposed general linear model and inverse problem methodologies are illustrated via two application examples: time-domain impulse response function extraction using least-squares deconvolution and leakage detection based on a frequency-domain linearized model. In both examples, numerical and experimental results demonstrate the significance of the regularization parameter and the merits of the GCV and L-curve methods in the pipeline condition assessment problems.
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Data Availability Statement
All data, models, or code generated or used during the study are available from the corresponding author by request.
Acknowledgments
This work has been supported by research grants from the Research Grant Council of the Hong Kong SAR, China (Project T21-602/15R).
References
Allen, D. M. 1974. “The relationship between variable selection and data agumentation and a method for prediction.” Technometrics 16 (1): 125–127. https://doi.org/10.1080/00401706.1974.10489157.
Bauer, F., and M. A. Lukas. 2011. “Comparing parameter choice methods for regularization of ill-posed problems.” Math. Comput. Simul. 81 (9): 1795–1841. https://doi.org/10.1016/j.matcom.2011.01.016.
Beck, S. B., M. D. Curren, N. D. Sims, and R. Stanway. 2005. “Pipeline network features and leak detection by cross-correlation analysis of reflected waves.” J. Hydraul. Eng. 131 (8): 715–723. https://doi.org/10.1061/(ASCE)0733-9429(2005)131:8(715).
Brunone, B. 1999. “Transient test-based technique for leak detection in outfall pipes.” J. Water Resour. Plann. Manage. 125 (5): 302–306. https://doi.org/10.1061/(ASCE)0733-9496(1999)125:5(302).
Chaudhry, M. H. 2014. Applied hydraulic transients. 3rd ed. New York: Springer.
Colombo, A. F., P. J. Lee, and B. W. Karney. 2009. “A selective literature review of transient-based leak detection methods.” J. Hydro-environ. Res. 2 (4): 212–227. https://doi.org/10.1016/j.jher.2009.02.003.
Contractor, D. N. 1965. “The reflection of waterhammer pressure waves from minor losses.” J. Basic Eng. 87 (2): 445–451. https://doi.org/10.1115/1.3650568.
Duan, H.-F., P. J. Lee, M. S. Ghidaoui, and Y.-K. Tung. 2010. “Essential system response information for transient-based leak detection methods.” J. Hydraul. Res. 48 (5): 650–657. https://doi.org/10.1080/00221686.2010.507014.
Duan, H.-F., P. J. Lee, M. S. Ghidaoui, and Y.-K. Tung. 2011. “Leak detection in complex series pipelines by using the system frequency response method.” J. Hydraul. Res. 49 (2): 213–221. https://doi.org/10.1080/00221686.2011.553486.
Ferrante, M., B. Brunone, and S. Meniconi. 2007. “Wavelets for the analysis of transient pressure signals for leak detection.” J. Hydraul. Eng. 133 (11): 1274–1282. https://doi.org/10.1061/(ASCE)0733-9429(2007)133:11(1274).
Ghidaoui, M. S. 2004. “On the fundamental equations of water hammer.” Urban Water J. 1 (2): 71–83. https://doi.org/10.1080/15730620412331290001.
Ghidaoui, M. S., M. Zhao, D. A. McInnis, and D. H. Axworthy. 2005. “A review of water hammer theory and practice.” Appl. Mech. Rev. 58 (1): 49–76. https://doi.org/10.1115/1.1828050.
Golub, G. H., M. Heath, and G. Wahba. 1979. “Generalized cross-validation as a method for choosing a good ridge parameter.” Technometrics 21 (2): 215–223. https://doi.org/10.1080/00401706.1979.10489751.
Gong, J., A. R. Simpson, M. F. Lambert, and A. C. Zecchin. 2013. “Determination of the linear frequency response of single pipelines using persistent transient excitation: A numerical investigation.” J. Hydraul. Res. 51 (6): 728–734. https://doi.org/10.1080/00221686.2013.818582.
Hanke, M. 1996. “Limitations of the L-curve method in ill-posed problems.” BIT Numer. Math. 36 (2): 287–301. https://doi.org/10.1007/BF01731984.
Hansen, P. C. 1990. “Truncated singular value decomposition solutions to discrete ill-posed problems with ill-determined numerical rank.” SIAM J. Sci. Stat. Comput. 11 (3): 503–518. https://doi.org/10.1137/0911028.
Hansen, P. C. 1992. “Analysis of discrete ill-posed problems by means of the L-curve.” SIAM Rev. 34 (4): 561–580. https://doi.org/10.1137/1034115.
Hansen, P. C., and D. P. O’Leary. 1993. “The use of the L-curve in the regularization of discrete ill-posed problems.” SIAM J. Sci. Comput. 14 (6): 1487–1503. https://doi.org/10.1137/0914086.
Jing, L., Z. Li, W. Wang, A. Dubey, P. Lee, S. Meniconi, B. Brunone, and R. D. Murch. 2018. “An approximate inverse scattering technique for reconstructing blockage profiles in water pipelines using acoustic transients.” J. Acoust. Soc. Am. 143 (5): EL322–EL327. https://doi.org/10.1121/1.5036957.
Kashima, A., P. J. Lee, M. S. Ghidaoui, and M. Davidson. 2013. “Experimental verification of the kinetic differential pressure method for flow measurements.” J. Hydraul. Res. 51 (6): 634–644. https://doi.org/10.1080/00221686.2013.818583.
Kashima, A., P. J. Lee, and R. Nokes. 2012. “Numerical errors in discharge measurements using the KDP method.” J. Hydraul. Res. 50 (1): 98–104. https://doi.org/10.1080/00221686.2011.638211.
Keramat, A., M. S. Ghidaoui, X. Wang, and M. Louati. 2019a. “Cramer-Rao lower bound for performance analysis of leak detection.” J. Hydraul. Eng. 145 (6): 04019018. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001603.
Keramat, A., X. Wang, M. Louati, S. Meniconi, B. Brunone, and M. S. Ghidaoui. 2019b. “Objective functions for transient-based pipeline leakage detection in a noisy environment: Least square and matched-filter.” J. Water Resour. Plann. Manage. 145 (10): 04019042. https://doi.org/10.1061/(ASCE)WR.1943-5452.0001108.
Lee, P. J. 2005. “Using system response functions of liquid pipelines for leak and blockage detection.” Ph.D. thesis, School of Civil and Environmental Engineering, Univ. of Adelaide.
Lee, P. J. 2013. “Energy analysis for the illustration of inaccuracies in the linear modelling of pipe fluid transients.” J. Hydraul. Res. 51 (2): 133–144. https://doi.org/10.1080/00221686.2012.734861.
Lee, P. J., M. F. Lambert, A. R. Simpson, J. P. Vítkovskỳ, and J. Liggett. 2006. “Experimental verification of the frequency response method for pipeline leak detection.” J. Hydraul. Res. 44 (5): 693–707. https://doi.org/10.1080/00221686.2006.9521718.
Lee, P. J., and J. P. Vítkovskỳ. 2010. “Quantifying linearization error when modeling fluid pipeline transients using the frequency response method.” J. Hydraul. Eng. 136 (10): 831–836. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000246.
Lee, P. J., J. P. Vítkovskỳ, M. F. Lambert, and A. R. Simpson. 2008a. “Valve design for extracting response functions from hydraulic systems using pseudorandom binary signals.” J. Hydraul. Eng. 134 (6): 858–864. https://doi.org/10.1061/(ASCE)0733-9429(2008)134:6(858).
Lee, P. J., J. P. Vítkovskỳ, M. F. Lambert, A. R. Simpson, and J. A. Liggett. 2005a. “Leak location using the pattern of the frequency response diagram in pipelines: A numerical study.” J. Sound Vib. 284 (3): 1051–1073. https://doi.org/10.1016/j.jsv.2004.07.023.
Lee, P. J., J. P. Vítkovskỳ, M. F. Lambert, A. R. Simpson, and J. A. Liggett. 2005b. “Frequency domain analysis for detecting pipeline leaks.” J. Hydraul. Eng. 131 (7): 596–604. https://doi.org/10.1061/(ASCE)0733-9429(2005)131:7(596).
Lee, P. J., J. P. Vítkovskỳ, M. F. Lambert, A. R. Simpson, and J. Liggett. 2007. “Leak location in pipelines using the impulse response function.” J. Hydraul. Res. 45 (5): 643–652. https://doi.org/10.1080/00221686.2007.9521800.
Lee, P. J., J. P. Vítkovskỳ, M. F. Lambert, A. R. Simpson, and J. A. Liggett. 2008b. “Discrete blockage detection in pipelines using the frequency response diagram: Numerical study.” J. Hydraul. Eng. 134 (5): 658–663. https://doi.org/10.1061/(ASCE)0733-9429(2008)134:5(658).
Liggett, J. A., and L.-C. Chen. 1994. “Inverse transient analysis in pipe networks.” J. Hydraul. Eng. 120 (8): 934–955. https://doi.org/10.1061/(ASCE)0733-9429(1994)120:8(934).
Lin, J., X. Wang, and M. Ghidaoui. 2019. “Theoretical investigation of leak’s impact on normal modes of a water–filled pipe: Small to large leak impedance.” J. Hydraul. Eng. 145 (6): 04019017. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001606.
Liou, C. P. 1998. “Pipeline leak detection by impulse response extraction.” J. Fluids Eng. 120 (4): 833–838. https://doi.org/10.1115/1.2820746.
Meniconi, S., B. Brunone, M. Ferrante, and C. Capponi. 2016. “Mechanism of interaction of pressure waves at a discrete partial blockage.” J. Fluids Struct. 62 (Apr): 33–45. https://doi.org/10.1016/j.jfluidstructs.2015.12.010.
Meniconi, S., B. Brunone, M. Ferrante, C. Capponi, C. A. Carrettini, C. Chiesa, D. Segalini, and E. A. Lanfranchi. 2015. “Anomaly pre-localization in distribution–transmission mains by pump trip: Preliminary field tests in the milan pipe system.” J. Hydroinf. 17 (3): 377–389. https://doi.org/10.2166/hydro.2014.038.
Meniconi, S., B. Brunone, M. Ferrante, and C. Massari. 2010. “Potential of transient tests to diagnose real supply pipe systems: What can be done with a single extemporary test.” J. Water Resour. Plann. Manage. 137 (2): 238–241. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000098.
Meniconi, S., B. Brunone, M. Ferrante, and C. Massari. 2011. “Transient tests for locating and sizing illegal branches in pipe systems.” J. Hydroinf. 13 (3): 334–345. https://doi.org/10.2166/hydro.2011.012.
Meniconi, S., H. F. Duan, P. J. Lee, B. Brunone, M. S. Ghidaoui, and M. Ferrante. 2013. “Experimental investigation of coupled frequency and time-domain transient test–based techniques for partial blockage detection in pipelines.” J. Hydraul. Eng. 139 (10): 1033–1040. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000768.
Mpesha, W., S. L. Gassman, and M. H. Chaudhry. 2001. “Leak detection in pipes by frequency response method.” J. Hydraul. Eng. 127 (2): 134–147. https://doi.org/10.1061/(ASCE)0733-9429(2001)127:2(134).
Newland, D. E. 2012. An introduction to random vibrations, spectral and wavelet analysis. North Chelmsford, MA: Courier Corporation.
Nguyen, S. T. N., J. Gong, M. F. Lambert, A. C. Zecchin, and A. R. Simpson. 2018. “Least squares deconvolution for leak detection with a pseudo random binary sequence excitation.” Mech. Syst. Sig. Process. 99 (Jan): 846–858. https://doi.org/10.1016/j.ymssp.2017.07.003.
Rubio Scola, I., G. Besançon, and D. Georges. 2016. “Blockage and leak detection and location in pipelines using frequency response optimization.” J. Hydraul. Eng. 143 (1): 04016074. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001222.
Tikhonov, A. N. 1963. “Solution of incorrectly formulated problems and the regularization method.” Soviet Meth. Dokl. 4: 1035–1038.
Vitkovskỳ, J. P., P. J. Lee, M. L. Stephens, M. F. Lambert, A. R. Simpson, and J. A. Liggett. 2003. “Leak and blockage detection in pipelines via an impulse response method.” In Vol. 1 of Proc., Pumps, Electromechanical Devices and Systems Applied to Urban Water Management, 423–430. Valencia, Spain: A.A. Balkema.
Vítkovskỳ, J. P., A. R. Simpson, and M. F. Lambert. 2000. “Leak detection and calibration using transients and genetic algorithms.” J. Water Resour. Plann. Manage. 126 (4): 262–265. https://doi.org/10.1061/(ASCE)0733-9496(2000)126:4(262).
Wang, X., M. Ghidaoui, and P. J. Lee. 2018. “Regularization for pipeline impulse response extraction with least square deconvolution.” In Proc., 13th Int. Conf. on Pressure Surges, 795–804. Bordeaux, France: BHR Group.
Wang, X., and M. S. Ghidaoui. 2018a. “Identification of multiple leaks in pipeline: Linearized model, maximum likelihood, and super-resolution localization.” Mech. Syst. Sig. Process. 107 (Jul): 529–548. https://doi.org/10.1016/j.ymssp.2018.01.042.
Wang, X., and M. S. Ghidaoui. 2018b. “Pipeline leak detection using the matched-field processing method.” J. Hydraul. Eng. 144 (6): 04018030. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001476.
Wang, X., and M. S. Ghidaoui. 2019. “Identification of multiple leaks in pipeline II: Iterative beamforming and leak number estimation.” Mech. Syst. Sig. Process. 119 (Mar): 346–362. https://doi.org/10.1016/j.ymssp.2018.09.020.
Wang, X., M. S. Ghidaoui, and J. Lin. 2019a. “Identification of multiple leaks in pipeline III: Experimental results.” Mech. Syst. Sig. Process. 130 (Sep): 395–408. https://doi.org/10.1016/j.ymssp.2019.05.015.
Wang, X., J. Lin, A. Keramat, M. S. Ghidaoui, S. Meniconi, and B. Brunone. 2019b. “Matched-field processing for leak localization in a viscoelastic pipe: An experimental study.” Mech. Syst. Sig. Process. 124 (Jun): 459–478. https://doi.org/10.1016/j.ymssp.2019.02.004.
Wang, X., D. P. Palomar, L. Zhao, M. S. Ghidaoui, and R. D. Murch. 2019c. “Spectral-based methods for pipeline leakage localization.” J. Hydraul. Eng. 145 (3): 04018089. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001572.
Zeng, W., J. Gong, A. C. Zecchin, M. F. Lambert, A. R. Simpson, and B. S. Cazzolato. 2018. “Condition assessment of water pipelines using a modified layer-peeling method.” J. Hydraul. Eng. 144 (12): 04018076. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001547.
Zhou, B., A. Liu, X. Wang, Y. She, and V. Lau. 2018. “Compressive sensing-based multiple-leak identification for smart water supply systems.” IEEE Internet Things J. 5 (2): 1228–1241. https://doi.org/10.1109/JIOT.2018.2812163.
Zouari, F., X. Wang, M. Louati, and M. Ghidaoui. 2017. “Single extended blockage identification using a model-based matched-field processing approach.” In Proc., 37th IAHR World Congress. Kuala Lumpur, Malaysia: International Association for Hydro-Environment Engineering and Research.
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Journal of Water Resources Planning and Management
Volume 146 • Issue 5 • May 2020
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©2020 American Society of Civil Engineers.
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Received: Mar 5, 2019
Accepted: Dec 4, 2019
Published online: Mar 13, 2020
Published in print: May 1, 2020
Discussion open until: Aug 13, 2020
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