Barcelona WDS used in previous studies by the authors (i.e. [42, 44, 47]). The main
result was that the identified sensor positions are relatively insensitive to the size of
the leaks/bursts. However, variation of the “leak locatability” index can be significant when different operating point scenarios are considered. Bearing this in mind,
aiming at accounting for this variation and ensure robust performance, Blesa et al.
[73] extended the optimal sensor placement method by Sarrate et al. [47] by
formulating a multi-objective optimisation strategy to place sensors. This strategy
has the following objectives: (1) to maximise the mean “leak locatability” index and
(2) to maximise the worst “leak locatability” index. Optimisation was carried out by
using their two-step hybrid methodology that combines clustering techniques (note
that the extended sensitivity matrix considered there encompass all possible operating point scenarios only) with an exhaustive search procedure, resulting in an
approximation of the entire Pareto front. The authors utilised again the simple
synthetic network (without clustering analysis) and the DMA in the Barcelona
WDS used in Blesa et al. [72] to test their strategy. Through comparison of the
results achieved in the Barcelona DMA with and without the use of the proposed
robust sensor placement methodology, the authors demonstrated that not to account
for different operating point scenarios leads to solutions that are not Pareto optimal.
As mentioned in Sect. 2, Casillas et al. [39] attempted to mitigate the effect of
model uncertainties and of the unknown leak/burst size by incorporating in their
method an extended-horizon analysis of pressure sensitivities/residuals and by
considering sets of sensitivities and residuals computed using different leak/burst
sizes. However, in Casillas et al. [74, 75], the authors proposed a different sensor
placement method inspired by the leak signature space-based leak/burst localisation
technique presented in Casillas et al. [76]. The leak signature space analysis enables
a specific signature to be associated to each leak/burst location that is minimally
affected by the leak/burst size. It considers a linear model approximation of the
relationship between pressure residuals and leaks/bursts to perform a transformation
that allows representing leak/burst locations by means of points in the leak signature
space that are not dependent on the leaks/bursts magnitude. The authors introduced
the concept of a domain of influence for a particular leak signature and solved the
sensor placement optimisation problem by attempting to minimise the overlapping
between domains of influence considering the signatures of all network nodes.
A time horizon analysis was also considered by looking at the mean number of
overlaps along the time horizon analysed. A GA and a particle swarm optimisation
(i.e. PSO – see [77]) algorithm were separately used to perform the optimisation. The
capabilities of the proposed methodology (i.e. efficiency, in terms of the percentage
of leaks correctly localised) were evaluated on the same two networks, Hanoi and
Limassol, considered in a previous study by the authors (i.e. [39]), assuming perfect
models but accounting for measurements uncertainties by adding Gaussian white
noise. The result obtained demonstrated that efficiencies of 100% and up to about
85% could be achieved using a small number of sensors (up to 4 and 3, respectively)
on the Hanoi and Limassol networks, respectively. They also emphasised, similarly
to what is found in Casillas et al. [39], the benefits of the time horizon analysis.
Worth of note, here, are also the results from the GA/PSO comparison that the
40
M. Romano
result was that the identified sensor positions are relatively insensitive to the size of
the leaks/bursts. However, variation of the “leak locatability” index can be significant when different operating point scenarios are considered. Bearing this in mind,
aiming at accounting for this variation and ensure robust performance, Blesa et al.
[73] extended the optimal sensor placement method by Sarrate et al. [47] by
formulating a multi-objective optimisation strategy to place sensors. This strategy
has the following objectives: (1) to maximise the mean “leak locatability” index and
(2) to maximise the worst “leak locatability” index. Optimisation was carried out by
using their two-step hybrid methodology that combines clustering techniques (note
that the extended sensitivity matrix considered there encompass all possible operating point scenarios only) with an exhaustive search procedure, resulting in an
approximation of the entire Pareto front. The authors utilised again the simple
synthetic network (without clustering analysis) and the DMA in the Barcelona
WDS used in Blesa et al. [72] to test their strategy. Through comparison of the
results achieved in the Barcelona DMA with and without the use of the proposed
robust sensor placement methodology, the authors demonstrated that not to account
for different operating point scenarios leads to solutions that are not Pareto optimal.
As mentioned in Sect. 2, Casillas et al. [39] attempted to mitigate the effect of
model uncertainties and of the unknown leak/burst size by incorporating in their
method an extended-horizon analysis of pressure sensitivities/residuals and by
considering sets of sensitivities and residuals computed using different leak/burst
sizes. However, in Casillas et al. [74, 75], the authors proposed a different sensor
placement method inspired by the leak signature space-based leak/burst localisation
technique presented in Casillas et al. [76]. The leak signature space analysis enables
a specific signature to be associated to each leak/burst location that is minimally
affected by the leak/burst size. It considers a linear model approximation of the
relationship between pressure residuals and leaks/bursts to perform a transformation
that allows representing leak/burst locations by means of points in the leak signature
space that are not dependent on the leaks/bursts magnitude. The authors introduced
the concept of a domain of influence for a particular leak signature and solved the
sensor placement optimisation problem by attempting to minimise the overlapping
between domains of influence considering the signatures of all network nodes.
A time horizon analysis was also considered by looking at the mean number of
overlaps along the time horizon analysed. A GA and a particle swarm optimisation
(i.e. PSO – see [77]) algorithm were separately used to perform the optimisation. The
capabilities of the proposed methodology (i.e. efficiency, in terms of the percentage
of leaks correctly localised) were evaluated on the same two networks, Hanoi and
Limassol, considered in a previous study by the authors (i.e. [39]), assuming perfect
models but accounting for measurements uncertainties by adding Gaussian white
noise. The result obtained demonstrated that efficiencies of 100% and up to about
85% could be achieved using a small number of sensors (up to 4 and 3, respectively)
on the Hanoi and Limassol networks, respectively. They also emphasised, similarly
to what is found in Casillas et al. [39], the benefits of the time horizon analysis.
Worth of note, here, are also the results from the GA/PSO comparison that the
40
M. Romano