Keywords: pattern, demands, water distribution system, optimization.

Demand patterns or demand dynamics are one type of uncertainty in the modelling of water distribution systems (WDS). At present researchers investigate mostly the differences in demand patterns on different weekdays, in different seasons and in different district meter areas (DMAs), or investigate the probabilistic nature of demand [1]. The real demand may differ even for consumers of the same type because of different daily plans of the residents in different parts of a DMA.

The aim of this paper is to investigate the spatial distribution of fluxes correcting demands inside a DMA using pressure measurements. The optimization methods are used to redistribute water flow fluxes in a DMA. The Levenberg-Marquardt algorithm (LMA) with the appropriate selection of the increment of parameters for the calculation of partial derivatives [2] has been used to find water fluxes correcting demands in different parts of the DMA which minimize errors in the modelled pressures. These water fluxes may be found by different approaches. One is based on the use of all points of measurement in one set of parameters. The second approach is based on the idea proposed in [3] and uses the ranking of measurements according to closeness to water source and performs calculations step by step from measurements of the lowest order to measurements of the highest order. In this case a small number of junctions (and consequently a low number of parameters) are considered in each step. The third approach uses junctions with the measurements of the first and second order in the first step of water flux correction, the junctions with the measurements of the second and third order in the second step of correction and so on. The calculations have been accomplished for an operational WDS using the TOOLKIT developed by Rossman [4] for the EPANET2. The calculations showed that the optimization procedure may be used to find the water fluxes to correct the demand patterns in the previously calibrated model and that the ranking of measurements according to the closeness of water sources decreases the calculation time significantly.

1

S. Surendran, T.T. Tanyimboh, M. Tabesh, "Peaking demand factor-based reliability analysis of water distribution systems", Advances in Engineering Software, 36, 789-796, 2005. doi:10.1016/j.advengsoft.2005.03.023

2

T. Koppel, A. Vassiljev, "Calibration of a model of an operational water distribution system containing pipes of different age", Advances in Engineering Software, 40, 659-664, 2009. doi:10.1016/j.advengsoft.2008.11.015

3

T. Koppel, A. Vassiljev, "The Use of Error Dynamics for Calibration of Water Distribution Systems", in B.H.V. Topping, L.F. Costa Neves, R.C. Barros, (Editors), "Proceedings of the Twelfth International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 247, 2009. doi:10.4203/ccp.91.247

4

L.A. Rossman, "EPANET 2 User's Manual", Water Supply and Water Resources Division, National Risk Management Research Laboratory, Cincinnati, OH 45268, September, 2002.

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