on a small synthetic network (i.e. Apulian – see [82]), found that their method was
not affected by the demand uncertainties.
3.2 Measurement Uncertainties
Pressure and flow sensors are the primary devices to monitor WDSs, and data
coming from these devices can potentially enable timely and reliable leak/burst
event detection and localisation. However, these sensors are subject to measurement
errors associated with any measuring device. Differences between measured and
expected data are at the core of many optimal sensor placement techniques. As
uncertainties in using measured values due to the possible range of errors for these
devices exist, the difference between measured and expected data must exceed the
measurement error to be considered an “anomaly”. In this context, “anomalies”
caused by small leaks/bursts may be difficult to identify. Furthermore, as leaks/
bursts may occur at any location in a network, a leak/burst occurring farther away
from a sensor may result in small variations in the signal recorded by that sensor. In
view of all this, it is important to investigate if sensor placements obtained using
assumptions of perfect sensors’ measurements would perform suboptimally when
implemented in real-life WDSs.
A small number of studies found in the literature have considered the sensors’
accuracy as a key component of their methodology. For example, Wu and Song [49]
and Forconi et al. [83] used the sensors’ accuracy as a threshold to discriminate
between detections and non-detections. A few other studies have attempted to build
robustness to measurements uncertainties by accounting for noisy measurements in
their optimal sensor placement frameworks (e.g. [39, 75]). The work by Raei et al.
[84], on the other hand, attempted to investigate this issue as its primary aim. The
authors proposed to solve the sensor placement problem by using a multi-objective
optimisation framework. They explored the effect of measurements uncertainty on
the selection of sensor locations by identifying alternative non-dominated fronts for
different values of sensor accuracy and then selected the final sensor placement from
those non-dominated fronts. The sensor placement problem formulation presented in
this study is based on sensitivity to leaks/bursts that are simulated at all potential
nodes in a network (note that the absolute error is used in this study) and solved
using the Non-dominated Sorting Genetic Algorithm-II (NSGA-II – see [85, 86]) to
explore trade-offs between the minimisation of the number of sensors to be deployed
and the detection time (i.e. from leak/burst start time to the time at which one sensor
out of the set of sensors registers a pressure difference that is larger than an error
threshold) objectives. The authors tested their approach on the C-town (see [87])
synthetic network considering a perfect model. The result obtained showed that the
detection times increase as the sensor accuracy decreases. However, the sensor
42
M. Romano
not affected by the demand uncertainties.
3.2 Measurement Uncertainties
Pressure and flow sensors are the primary devices to monitor WDSs, and data
coming from these devices can potentially enable timely and reliable leak/burst
event detection and localisation. However, these sensors are subject to measurement
errors associated with any measuring device. Differences between measured and
expected data are at the core of many optimal sensor placement techniques. As
uncertainties in using measured values due to the possible range of errors for these
devices exist, the difference between measured and expected data must exceed the
measurement error to be considered an “anomaly”. In this context, “anomalies”
caused by small leaks/bursts may be difficult to identify. Furthermore, as leaks/
bursts may occur at any location in a network, a leak/burst occurring farther away
from a sensor may result in small variations in the signal recorded by that sensor. In
view of all this, it is important to investigate if sensor placements obtained using
assumptions of perfect sensors’ measurements would perform suboptimally when
implemented in real-life WDSs.
A small number of studies found in the literature have considered the sensors’
accuracy as a key component of their methodology. For example, Wu and Song [49]
and Forconi et al. [83] used the sensors’ accuracy as a threshold to discriminate
between detections and non-detections. A few other studies have attempted to build
robustness to measurements uncertainties by accounting for noisy measurements in
their optimal sensor placement frameworks (e.g. [39, 75]). The work by Raei et al.
[84], on the other hand, attempted to investigate this issue as its primary aim. The
authors proposed to solve the sensor placement problem by using a multi-objective
optimisation framework. They explored the effect of measurements uncertainty on
the selection of sensor locations by identifying alternative non-dominated fronts for
different values of sensor accuracy and then selected the final sensor placement from
those non-dominated fronts. The sensor placement problem formulation presented in
this study is based on sensitivity to leaks/bursts that are simulated at all potential
nodes in a network (note that the absolute error is used in this study) and solved
using the Non-dominated Sorting Genetic Algorithm-II (NSGA-II – see [85, 86]) to
explore trade-offs between the minimisation of the number of sensors to be deployed
and the detection time (i.e. from leak/burst start time to the time at which one sensor
out of the set of sensors registers a pressure difference that is larger than an error
threshold) objectives. The authors tested their approach on the C-town (see [87])
synthetic network considering a perfect model. The result obtained showed that the
detection times increase as the sensor accuracy decreases. However, the sensor
42
M. Romano