to different sensor placement configurations being identified as “optimal” despite
using the same number of sensors.
One of the main issues in the work presented in Pérez et al. [31, 37] is the
threshold selection. Furthermore, even with an optimal threshold selection,
binarising the sensitivity matrix leads to a loss of information [38]. Therefore,
aiming at circumventing these issues, Casillas et al. [39] formulated the optimal
sensor placement problem as an integer optimisation problem based on projections
from a non-binarised leak/burst sensitivity matrix solved with a semi-exhaustive
search or a GA. The projection-based method used in this study (i.e. angle method) is
based on evaluating the angle between the vector of the “actual” residuals and every
column (i.e. possible leak/burst nodes) of the leak/burst sensitivity matrix. The
“actual” leak/burst node is then identified by looking at the column (sensitivity
matrix vector) that presents the smallest angle with the residual vector. This method
was first proposed by Casillas et al. [29] for the sole purpose of leaks/bursts
localisation. It was then compared in that study and in Casillas et al. [9, 10] against
other ways of using the leak/burst sensitivity matrix to isolate/localise a leak/burst
(including the binarisation method proposed by [31] and the correlation method
presented in [38] and in [40]), and, through tests on small synthetic networks and on
a real-life network (i.e. Nova Icaria, in the Barcelona WDS), it was found to offer
better localisation performance than the other tested methods. With specific regard to
the method used for solving the integer optimisation problem, the authors evaluated
the performance of a semi-exhaustive search, which uses a lazy evaluation mechanisms to reduce the computation cost by discarding potential sensor configurations
as soon as it is found that they cannot be candidates for the optimum solution, against
the performance of a GA on the Hanoi network (see [41]) and on a relatively small
real-life network in Limassol, Cyprus. They found that the semi-exhaustive search
would not scale up well to bigger networks, whereas the GA allowed the finding of
good near-optimal solutions in a computationally efficient manner. Bearing all this
in mind, it is important to stress that Casillas et al. [39] also proposed improving the
robustness of their sensor placement methodology by (1) carrying out a time horizon
analysis (which, by performing an extended-horizon analysis of pressure sensitivities and residuals and then looking at the mean projection, can reduce the sensitivity
to demand changes and noise in the measurements observed when using methods
that consider a time instant evaluation only – see, e.g. [9, 10]), (2) using a distancebased scoring during the optimisation process (which, by accounting for the topological distance between the “actual” leak/burst node and the node indicated by the
projection-based method, attempts to retain more information than the traditional
binary scoring process would in the case of leaks/bursts incorrectly localised – as all
the incorrectly localised leaks/bursts are treated in the same way), (3) incorporating
sets of sensitivities and residuals in their evaluation function that are computed
considering different leak/burst sizes and (4) adding noise to the model pressures
before computing the residuals to simulate measurements noise. Through comparison of the results obtained on the Limassol network with and without considering
the proposed improvements, the authors found that leak magnitude changes
were impacting the resulting optimal sensor placement found in the case of no
34
M. Romano
using the same number of sensors.
One of the main issues in the work presented in Pérez et al. [31, 37] is the
threshold selection. Furthermore, even with an optimal threshold selection,
binarising the sensitivity matrix leads to a loss of information [38]. Therefore,
aiming at circumventing these issues, Casillas et al. [39] formulated the optimal
sensor placement problem as an integer optimisation problem based on projections
from a non-binarised leak/burst sensitivity matrix solved with a semi-exhaustive
search or a GA. The projection-based method used in this study (i.e. angle method) is
based on evaluating the angle between the vector of the “actual” residuals and every
column (i.e. possible leak/burst nodes) of the leak/burst sensitivity matrix. The
“actual” leak/burst node is then identified by looking at the column (sensitivity
matrix vector) that presents the smallest angle with the residual vector. This method
was first proposed by Casillas et al. [29] for the sole purpose of leaks/bursts
localisation. It was then compared in that study and in Casillas et al. [9, 10] against
other ways of using the leak/burst sensitivity matrix to isolate/localise a leak/burst
(including the binarisation method proposed by [31] and the correlation method
presented in [38] and in [40]), and, through tests on small synthetic networks and on
a real-life network (i.e. Nova Icaria, in the Barcelona WDS), it was found to offer
better localisation performance than the other tested methods. With specific regard to
the method used for solving the integer optimisation problem, the authors evaluated
the performance of a semi-exhaustive search, which uses a lazy evaluation mechanisms to reduce the computation cost by discarding potential sensor configurations
as soon as it is found that they cannot be candidates for the optimum solution, against
the performance of a GA on the Hanoi network (see [41]) and on a relatively small
real-life network in Limassol, Cyprus. They found that the semi-exhaustive search
would not scale up well to bigger networks, whereas the GA allowed the finding of
good near-optimal solutions in a computationally efficient manner. Bearing all this
in mind, it is important to stress that Casillas et al. [39] also proposed improving the
robustness of their sensor placement methodology by (1) carrying out a time horizon
analysis (which, by performing an extended-horizon analysis of pressure sensitivities and residuals and then looking at the mean projection, can reduce the sensitivity
to demand changes and noise in the measurements observed when using methods
that consider a time instant evaluation only – see, e.g. [9, 10]), (2) using a distancebased scoring during the optimisation process (which, by accounting for the topological distance between the “actual” leak/burst node and the node indicated by the
projection-based method, attempts to retain more information than the traditional
binary scoring process would in the case of leaks/bursts incorrectly localised – as all
the incorrectly localised leaks/bursts are treated in the same way), (3) incorporating
sets of sensitivities and residuals in their evaluation function that are computed
considering different leak/burst sizes and (4) adding noise to the model pressures
before computing the residuals to simulate measurements noise. Through comparison of the results obtained on the Limassol network with and without considering
the proposed improvements, the authors found that leak magnitude changes
were impacting the resulting optimal sensor placement found in the case of no
34
M. Romano