A simple forecast technique for estimating the statistical
characteristics of water consumption
József Bene, Dávid Bóka, Csaba Ho ˝ s and Varga Roxána
ABSTRACT
The forecast water consumption values are the most critical input data in the pump schedule
optimization of water distribution systems. The aim of this paper is to present a simple technique
which is able to estimate the mean consumption and its distribution for a given demand zone with an
hourly resolution. Simplicity (low computational cost) is advantageous since the forecast model
needs to be run for any optimization computation. The proposed technique uses a recorded hourly
consumption database and consists of two steps. First, the database content is automatically
grouped based on the similarity of the elements (more precisely, their normality). This step is time-
consuming but is performed only once for a given database independently of optimization. The
second step – which is quick but has to be performed before the actual optimization – makes use of
this grouping for forecasting mean value and standard deviation. The proposed technique provides
hourly water consumption predictions independently; that is, the neighbouring hours do not effect
each other, which prevents the accumulation of prediction errors. The daily overall consumption is
computed a posteriori. The test results presented in this paper prove the applicability of the
technique for real-life problems. Moreover, it is demonstrated that the confidence interval provided
by the technique includes the actual measured data.
József Bene (corresponding author)
Dávid Bóka
Csaba Ho ˝ s
Varga Roxána
Department of Hydrodynamic Systems,
Budapest University of Technology and Economics,
H-1521 Budapest,
P.O. Box 91,
Hungary
E-mail: bene@hds.bme.hu
József Bene
Systems Engineering Laboratory,
Department of Process and Environmental
Technology,
University of Oulu,
FIN-90014 Oulu,
P.O. Box 4300,
Finland
Key words | forecast technique, normality test, pump schedule optimization, water consumption
INTRODUCTION
Pump schedule optimization problems of water distribution
systems have inspired many scientific studies resulting in a
rich literature, see for example, Mays (), Nicklow et al.
() and Ormsbee & Lansey (). These optimization
methods are based either on heuristic (e.g. genetic algor-
ithms) or deterministic (e.g. dynamic programming)
methods; they can take into account full hydraulics or use
simple flow-only models (Cembrano et al. ). Neverthe-
less, even though the modelling and the solution technique
of these methods are different, the aim is the same: to deter-
mine the pump schedule for a given time horizon (typically
for the next 24 h) which satisfies the complex constraint
system of the optimization problem and offers the lowest
possible energy cost or energy consumption. All of these
methods require ‘forecast’ water consumption values as
input data. The authors’ experience showed that the
accuracy of the consumption is the bottleneck of the pro-
blem: weak and unreliable forecast consumption results in
such a significant difference between the forecast and the
measured values, that the computed ‘optimal’ schedule is
far from being optimal, or, even worse, it might not even
satisfy the constraint system.
Consumption can be involved in the computations as
deterministic or stochastic data. In the first case, when the
water demands are assumed to be deterministic (Certainty
Equivalent Control; Bertsekas ), they are usually deter-
mined a priori from statistics or by some forecasting
approach (Alvisi et al. ; Adamowski ; Bárdossy
et al. ). When the stochastic behaviour is taken expli-
citly into account, the consumptions are described by a
priori determined distributions (Cervellera et al. ;
Ikonen & Bene , ; Selek et al. ).
593 © IWA Publishing 2014 Water Science & Technology: Water Supply | 14.4 | 2014
doi: 10.2166/ws.2014.013