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An interval estimator for chlorine monitoring in drinking water distribution systems under uncertain system dynamics, inputs and chlorine concentration measurement errors

Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The design of an interval observer for estimation of unmeasured state variables with application to drinking water distribution systems is described. In particular, the design process of such an observer is considered for estimation of the water quality described by the concentration of free chlorine. The interval observer is derived to produce the robust interval bounds on the estimated water quality state variables. The stability and robustness of the interval observer are investigated under uncertainty in system dynamics, inputs, initial conditions and measurement errors. The bounds on the estimated variables are generated by solving two systems of first-order ordinary differential equations. For that reason, despite a large scale of the systems, the numerical efficiency is sufficient for the on-line monitoring of the water quality. Finally, in order to validate the performance of the observer, it is applied to the model of a real water distribution network.
Rocznik
Strony
309--322
Opis fizyczny
Bibliogr. 34 poz., rys., wykr.
Twórcy
  • Department of Control Systems Engineering, Gdańsk University of Technology, G. Narutowicza 11/12, 80-233 Gdańsk, Poland, rafal.langowski1@pg.gda.pl
autor
  • Department of Control Systems Engineering, Gdańsk University of Technology, G. Narutowicza 11/12, 80-233 Gdańsk, Poland; School of Electronic, Electrical and Computer Engineering, College of Engineering and Physical Sciences, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK
Bibliografia
  • [1] Al-Omari, A.S. and Chaudhry, M.H. (2001). Unsteady-state inverse chlorine modeling in pipe networks, Journal of Hydraulic Engineering 127(8): 669–677.
  • [2] Alcaraz-González, V., Harmand, J., Rapaport, A., Steyer, J.P., González-Alvarez, V. and Ortiz, C.P. (2005). Application of a robust interval observer to an anaerobic digestion process, Developments in Chemical Engineering and Mineral Processing 13(3–4): 267–278.
  • [3] Amairi, M. (2016). Recursive set membership estimation for output-error fractional models with unknown-but-bounded errors, International Journal of Applied Mathematics and Computer Science 26(3): 543–553, DOI: 10.1515/amcs-2016-0038.
  • [4] Arminski, K. and Brdys, M.A. (2013). Robust monitoring of water quality in drinking water distribution system, Proceedings of the 13th IFAC Symposium on Large Scale Complex Systems: Theory and Applications, Shanghai, China, Vol. 46, pp. 105–110.
  • [5] Arminski, K., Zubowicz, T. and Brdys, M.A. (2013). A biochemical multi-species quality model of a drinking water distribution system for simulation and design, International Journal of Applied Mathematics and Computer Science 23(3): 571–585, DOI: 10.2478/amcs-2013-0043.
  • [6] Boccelli, D.L., Tryby, M.E., Uber, J.G. and Summers, R.S. (2003). A reactive species model for chlorine decay and THM formation under rechlorination conditions, Water Research 37(11): 2654–2666.
  • [7] Boulos, P.F., Lansey, K.E. and Karney, B.W. (2004). Comprehensive Water Distribution Systems Analysis Handbook, MWH Soft, Inc., Pasadena, CA.
  • [8] Brdys, M.A. and Chen, K. (1995). Joint estimation of state and parameters in quantity models of water supply and distribution systems, Automatisierungstechnik 43(2): 77–84.
  • [9] Brdys, M.A. and Chen, K. (1996). Joint estimation of states and parameters of integrated quantity and quality models of dynamic water supply and distribution systems, Proceedings of the 13th IFAC World Congress, San Francisco, CA, Vol. 1, pp. 759–762.
  • [10] Brdys, M.A. and Łangowski, R. (2008). Interval estimator for chlorine monitoring in drinking water distribution systems under uncertain system dynamics, inputs and state measurement errors, Proceedings of the 11th IFAC/IFORS/IMACS/IFIP Symposium on Large Scale Systems: Theory and Applications, Gdańsk, Poland, Vol. 11, pp. 85–90.
  • [11] Brdys, M.A., Puta, H., Arnold, E., Chen, K. and Hopfgarten, S. (1995). Operational control of integrated quality and quantity in water systems, Proceedings of the IFAC/IFORS/IMACS Symposium on Large Scale Systems, London, UK, Vol. 2, pp. 715–719.
  • [12] Brdys, M.A. and Ulanicki, B. (1994). Operational Control of Water Systems: Structures, Algorithms and Applications, New York, NY.
  • [13] Chen, K. (1997). Set Membership Estimation of State and Parameters and Operational Control of Integrated Quantity and Quality Models of Water Supply and Distribution Systems, PhD thesis, University of Birmingham, Birmingham.
  • [14] Clark, R.M., Abdesaken, F., Boulos, P.F. and Mau, R.E. (1996). Mixing in distribution system storage tanks: Its effect on water quality, Journal of Environmental Engineering 122(9): 814–821.
  • [15] Duzinkiewicz, K. (2006). Set membership estimation of parameters and variables in dynamic networks by recursive algorithms with a moving measurement window, International Journal of Applied Mathematics and Computer Science 16(2): 209–217.
  • [16] Efimov, D. and Raissi, T. (2016). Design of interval observers for uncertain dynamical systems, Automation and Remote Control 77(2): 191–225.
  • [17] EU Cost Action IC0806—IntelliCIS (2008). Memorandum of Understanding, 7th Framework Program, http://www.intellicis.eu.
  • [18] Gouzé, J.L., Rapaport, A. and Hadj-Sadok, M.Z. (2000). Interval observers for uncertain biological systems, Ecological Modelling 133(1–2): 45–56.
  • [19] Hadj-Sadok, M. Z. and Gouzé, J. L. (2001). Estimating of uncertain models of activated sludge process with interval observers, Journal of Process Control 11(3): 299–310.
  • [20] Jauberthie, C., Travé-Massuyès, L. and Verdière, N. (2016). Set-membership identifiability of nonlinear models and related parameter estimation properties, International Journal of Applied Mathematics and Computer Science 26(4): 803–813, DOI: 10.1515/amcs-2016-0057.
  • [21] Łangowski, R. (2015). Algorithms of Allocating Quality Sensors for Monitoring Quality in Drinking Water Distributions Systems, PhD thesis, Gdańsk University of Technology, Gdańsk, (in Polish).
  • [22] Łangowski, R. and Brdys, M.A. (2006). Interval asymptotic estimator for chlorine monitoring in drinking water distribution systems, Proceedings of the 1st IFAC Workshop on Applications of Large Scale Industrial Systems, Helsinki, Finland, Vol. 39, pp. 35–40.
  • [23] Łangowski, R. and Brdys, M.A. (2007). Monitoring of chlorine concentration in drinking water distribution systems using interval estimator, International Journal of Applied Mathematics and Computer Science 17(2): 199–216, DOI: 10.2478/v10006-007-0019-y.
  • [24] Males, R.M., Grayman,W.M. and Clark, R.M. (1988). Modeling water quality in distribution systems, Journal of Water Resources Planning and Management 114(2): 197–209.
  • [25] Mau, R.E., Boulos, P.F., Clark, R.M., Grayman, W.M., Tekippe, R.J. and Trussell, R.R. (1995). Explicit mathematical models of distribution storage water quality, Journal of Hydraulic Engineering 121(10): 699–709.
  • [26] Mitchel, A.R. and Griffiths, D.F. (1980). The Finite Difference Method in Partial Differential Equations, Wiley, Chichester.
  • [27] Nowicki, A., Grochowski, M. and Duzinkiewicz, K. (2012). Data-driven models for fault detection using kernel PCA: A water distribution system case study, International Journal of Applied Mathematics and Computer Science 22(4): 939–949, DOI: 10.2478/v10006-012-0070-1.
  • [28] Park, K. and Kuo, A.Y. (1996). A multi-step computation scheme: Decoupling kinetic processes from physical transport in water quality models, Water Research 30(10): 2255–2264.
  • [29] Propato,M., Uber, J.G., Shang, F. and Polycarpou, M.M. (2001). Integrated control and booster system design for residual maintenance in water distribution systems, Proceedings of the World Water and Environmental Resources Congress, Orlando, FL, USA, Vol. 111, pp. 1–10.
  • [30] Rapaport, A. and Dochain, D. (2005). Interval observers for biochemical processes with uncertain kinetics and inputs, Mathematical Biosciences 193(2): 235–253.
  • [31] Rossman, L.A. and Boulos, P.F. (1996). Numerical methods for modeling water quality in distribution systems: A comparison, Journal of Water Resources Planning and Management 122(2): 137–146.
  • [32] Rossman, L.A., Boulos, P.F. and Altman, T. (1993). Discrete volume-element method for network water-quality models, Journal of Water Resources Planning and Management 119(5): 505–517.
  • [33] Rossman, L.A., Clark, R.M. and Grayman, W.M. (1994). Modeling chlorine residuals in drinking water distribution systems, Journal of Environmental Engineering 120(4): 803–820.
  • [34] Smith, H.L. (1995). Monotone Dynamical Systems. An Introduction to the Theory of Competitive and Cooperative Systems, AMS, Providence, RI.
Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-f8ac1f0f-3da2-4b7b-acfe-a73d7236a47b
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