Explicit Expressions for State Estimation Sensitivity Analysis in Water Systems
Publication: Journal of Water Resources Planning and Management
Volume 144, Issue 4
Abstract
The implementation of state estimation techniques to water systems enables the hydraulic state of a given network to be computed at any time. However, errors in both measurements and model parameters can severely affect the quality of the state estimate, thus sensitivity analysis is crucial to assess its performance. The aim of this paper is to provide general explicit expressions for the sensitivities of the objective function and the primal variables of the state estimation problem with respect to both measurements and roughness parameters based on the perturbation of the Karush-Kuhn-Tucker (KKT) conditions. Additionally, among all the possible applications of sensitivity analysis, two specific forms of such analysis for water systems are presented: identifiability of roughness parameters, and linear state estimate approximation. The merit of these applications is illustrated by means of a case study, which highlights the usefulness of compact sensitivity formulae to further understanding of state estimation solutions.
Get full access to this article
View all available purchase options and get full access to this article.
References
Andersen, J. H., Powell, R. S., and Marsh, J. F. (2001). “Constrained state estimation with applications in water distribution network monitoring.” Int. J. Syst. Sci., 32(6), 807–816.
Bargiela, A. (1985). “An algorithm for observability determination in water-system state estimation.” IEEE Proc., 132(6), 245–250.
Bargiela, A., and Hainsworth, G. D. (1989). “Pressure and flow uncertainty in water systems.” J. Water Resour. Plann. Manage., 212–229.
Brdys, M. A., and Ulanicki, B. (2002). Operational control of water systems: Structures, algorithms and applications, Prentice Hall, London.
Caro, E., Conejo, A. J., Mínguez, R., Zima, M., and Andersson, G. (2011). “Multiple bad data identification considering measurement dependencies.” IEEE Trans. Power Syst., 26(4), 1953–1961.
Caro, E., Mínguez, R., and Conejo, A. J. (2013). “Robust WLS estimator using reweighting techniques for electric energy systems.” Electr. Power Syst. Res., 104, 9–17.
Carpentier, P., and Cohen, G. (1991). “State estimation and leak detection in water distribution networks.” Civ. Eng. Syst., 8(4), 247–257.
Castillo, E., Conejo, A. J., Castillo, C., Mínguez, R., and Ortigosa, D. (2006). “Perturbation approach to sensitivity analysis in mathematical programming.” J. Optim. Theory Appl., 128(1), 49–74.
Conejo, A. J., Castillo, E., Mínguez, R., and García-Bertrand, R. (2006). Decomposition techniques in mathematical programming. Engineering and science applications, Springer, New York.
Díaz, S., González, J., and Mínguez, R. (2016a). “Observability analysis in water transport networks: Algebraic approach.” J. Water Resour. Plann. Manage., 04015071.
Díaz, S., González, J., and Mínguez, R. (2016b). “Uncertainty evaluation for constrained state estimation in water distribution systems.” J. Water Resour. Plann. Manage., 06016004.
Díaz, S., Mínguez, R., and González, J. (2016c). “Stochastic approach to observability analysis in water networks.” Ingeniería del Agua, 20(3), 139–152.
Díaz, S., Mínguez, R., and González, J. (2017). “Calibration via multi-period state estimation in water distribution systems.” Water Resour. Manage., 31(15), 4801.
Fiacco, A. V. (1983). Introduction to sensitivity and stability analysis in nonlinear programming, Academic Press, New York.
Fu, G., Kapelan, Z., and Reed, P. (2012). “Reducing the complexity of multiobjective water distribution system optimization through global sensitivity analysis.” J. Water Resour. Plann. Manage., 196–207.
Fujiwara, O., and Khang, D. B. (1990). “A two-phase decomposition method for optimal design of looped water distribution networks.” Water Resour. Res., 26(4), 539–549.
GAMS (General Algebraic Modeling System) [Computer software]. GAMS Development Corporation, Washington, DC.
Kapelan, Z. S., Savic, D. A., and Walters, G. A. (2007). “Calibration of water distribution hydraulic models using a Bayesian-type procedure.” J. Hydraul. Eng., 927–936.
Kumar, S. M., Narasimhan, S., and Bhallamudi, S. M. (2008). “State estimation in water distribution networks using graph-theoretic reduction strategy.” J. Water Resour. Plann. Manage., 395–403.
Kumar, S. M., Narasimhan, S., and Bhallamudi, S. M. (2010). “Parameter estimation in water distribution networks.” Water Resour. Manage., 24(6), 1251–1272.
Lansey, K. E., and Basnet, C. (1991). “Parameter estimation for water distribution networks.” J. Water Resour. Plann. Manage., 126–144.
Lansey, K. E., El-Shorbagy, W., Ahmed, I., Araujo, J., and Haan, C. T. (2001). “Calibration assessment and data collection for water distribution networks.” J. Hydraul. Eng., 270–279.
MATLAB version 7.12.0 [Computer software]. Mathworks, Natik, MA.
Piller, O., Elhay, S., Deuerlein, J., and Simpson, A. R. (2017). “Local sensitivity of pressure-driven modeling and demand-driven modeling steady-state solutions to variations in parameters.” J. Water Resour. Plann. Manage., 04016074.
Powell, R. S., Irving, M. R., and Sterling, M. J. H. (1988). “A comparison of three real-time state estimation methods for on-line monitoring of water distribution systems.” Computer applications in water supply, B. Coulbeck, ed., Vol. 1, Research Studies Press, Taunton, U.K., 333–348.
Saltelli, A., Tarantola, S., Campolongo, F., and Ratto, M. (2004). Sensitivity analysis in practice: A guide to assessing scientific models, Wiley, New York.
Schweppe, F. C., and Wildes, J. (1970). “Power system static-state estimation. I: Exact model.” IEEE Trans. Power Apparatus Syst., 89(1), 120–125.
Sterling, M. J. H., and Bargiela, A. (1984). “Minimum norm state estimation for computer control of water distribution systems.” IEEE Proc., 131(2), 57–63.
Vairavamoorthy, K., and Ali, M. (2005). “Pipe index vector: A method to improve genetic-algorithm-based pipe optimization.” J. Hydraul. Eng., 1117–1125.
Vrachimis, S. G., Eliades, D. G., and Polycarpou, M. M. (2017). “Real-time hydraulic interval state estimation for water transport networks: A case study.” Drink. Water Eng. Sci. Discuss., in press.
Walski, T. M. (1983). “Technique for calibrating network models.” J. Water Resour. Plann. Manage., 360–372.
Information & Authors
Information
Published In
Copyright
©2018 American Society of Civil Engineers.
History
Received: Mar 30, 2017
Accepted: Sep 27, 2017
Published online: Jan 25, 2018
Published in print: Apr 1, 2018
Discussion open until: Jun 25, 2018
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.