A genetic algorithm for demand pattern and leakage estimation in a water distribution network

Abstract

The sustainable management of water supply networks requires the control of physical pipe leakages, such as those due to junction obsolescence or pipe creeping. These leakages usually increase with the operating pressure, and their discharge is commonly assumed to scale with the power of the pressure. The same functional form is also employed to evaluate leakage occurring in the portion of the network downstream a node. The parameters involved in these relationships may be estimated from field experimental data. However, a sensible fluctuation in their values is observed, and therefore the definition of a suitable leakage law represents a major source of uncertainty in water network modeling. In the present paper, the estimation of the leakage law parameters is carried out simultaneously to the hourly demand pattern. To this aim, a hydraulic network model coupled to a genetic algorithm is employed to minimize the deviation between predicted and measured time series of pressure and flow at a small number of sites of the network.A field test case is analyzed to show the effectiveness of the proposed procedure. NOTATIONc parameter of leakage law [m 3Àγ /s] C d per-capita hourly water demand [m 3 /s/inhab.] d data vector [dimensions may vary] D node outflow [m 3 /s] G(·) symbolic operator of a generic mathematical model [dimensions may vary] L leak discharge [m 3 /s] m number of parameters [-] M parameter vector for G model [dimensions may vary] N 1 exponent of leakage law [-] n h number of hours in the time pattern [-] n mP total number of pressure stations [-] n mQ total number of flow stations [-] n u,i number of users supplied by i-th node [-] OF objective function [-] P node pressure head [m] P cross crossover probability [-] Q volumetric flow [m 3 /s] γ exponent of leakage law [-] SUPERSCRIPT k hour index SUBSCRIPTS 1 pertaining to network zone 1 2 pertaining to network zone 2 C computed i node index M measured 35

Baseline adjustment methodology in a shared water savings contract under serious drought conditions

“…Various advanced methods are also available elsewhere to estimate the water demand of consumers, including comprehensive end-use studies (Beal et al, 2011;Mayer et al, 2003;Arbon et al, 2014). Advanced algorithms such as genetic algorithms (Di Nardo et al, 2015) are available to minimise the deviation between predicted and measured timeseries data at hourly intervals.…”

Modelling the Leakage Rate and Reduction Using Minimum Night Flow Analysis in an Intermittent Supply System

“…Using the FAVAD concept in this study, leakage can be modelled at any hour during the day, assuming a fixed value for the exponent N 1 , of a linear relationship (N 1 = 1) as the network is mixed pipes, rigid and plastic [9,46]. However, estimating the relationship between the leakage exponent N 1 and the fluctuating pressure in the DMA during the day is increasingly discussed [47][48][49]. The zonal night test is used to determine the variable N 1 , which is influenced by a changing pressure in the DMA.…”

The optimization of calibration of the computer model describing the flows in the water distribution network; Study of the example

“…Therefore (but not only therefore), they are more and more often used by engineers. Regarding the issues and their resolving, which are the essence of the calibration of the model of water distribution network the best are genetic algorithms [2,5,6]. This paper will describe a computer model of flows occurring in the sample water distribution network.…”