Keywords: real-time demands, water distribution system, optimization.

The aim of the investigation, described in this paper, is to estimate real-time demands in a water distribution system (WDS) on the basis of the pressure measurements. The investigation is useful in the case of deliberate or accidental chemical or biological threats because demands in such a case are definitely not typical because many customers will stop consumption of water after an alarm. This will lead to a situation where real-time demands will differ drastically from any typical fluxes. The task has been formulated as an optimization procedure which finds water fluxes that minimize differences between measured and modelled pressures. The Levenberg-Marquardt algorithm (LMA) and a genetic algorithm (GA) have been tested to solve the problem. Both software (the LMA and the GA) have been developed by the Argonne National Laboratory (University of Chicago), but software using the LMA has been modified by Tallinn University of Technology [1]. Comparison showed that both the LMA and the GA give the same results if the number of parameters is low (for example 4) but even in this case the GA works several hundreds times slower. Other disadvantages of the GA is that it cannot find the same solution as the LMA if the number of parameters is 13 or greater and it was incapable of finding an acceptable solution at all if the number of parameters was 19 or greater. Again even if the number of parameters was relatively low (7 for example) it was necessary to accomplish several series of calculations to find the solution using the GA that the LMA finds at a first attempt. Therefore the use of the GA is problematic for the determination of the propagation rate of the contaminated zones in the case of deliberate or accidental chemical or biological threats within an acceptable time (when short calculation time is vitally important). The LMA works very fast and can be used for this task. The investigation showed also that estimation of the real-time water demands on the basis of pressure measurements depends on the precision of the pressure sensors and on the current demands on the water distribution system. Calculations for different weekdays and years showed that space and time differences in real-time water demands in ordinary situations contain both typical and random constituents. All the calculations have been accomplished using measurements executed in an operational WDS for different years and for different days of the week using the TOOLKIT developed by Rossman [2] for the EPANET2.

1

T. Koppel, A. Vassiljev, "Calibration of a model of an operational water distribution system containing pipes of different age", Advances in Engineering Software, 40(8), 659-664, 2009. doi:10.1016/j.advengsoft.2008.11.015

2

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

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