[47] where, however, it was also noted that results from the direct application of the
clustering step were not too far from the global optimum.
Bearing in mind the above, in order to overcome the aforementioned intrinsic
limitation of their structural model-based strategy, Sarrate et al. [47] proposed a
further approach based entirely on analysis of the leak/burst sensitivity matrix. In
this study, projections are calculated from the sensitivity matrix, a “leak locatability”
index (to be maximised for the specific number of sensors to be installed) is
introduced, and a two-step hybrid methodology that combines clustering techniques
(the evidential c-means algorithm was used in that study – see [48]) with an
exhaustive search is utilised to search for the optimal sensor configuration. Again,
the authors tested their method on the same DMA used in Sarrate et al. [42] and
conducted their experiments with settings very similar to those used in that study. It
was found that their further approach enables solving the optimal sensor placement
problem in a reasonable time. However, the authors noted that despite the exhaustive
search approach providing an optimal result, “optimality” of this result over the set
of original candidate pressure locations is strongly dependent on the performance of
the clustering algorithm.
Wu and Song [49] developed a pressure sensor placement method that maximises
the number of leak/burst events that can be detected for a given number of sensors by
performing the following two steps. Firstly, a Monte Carlo method (see – e.g. [50]) is
used to generate a large number of random events with different magnitudes and that
may occur at a single location or at two locations simultaneously. In this step, the
simulated nodal pressures are compared with the baseline condition, and residuals
are stored in a matrix. Then a binary matrix is obtained from the residuals matrix
using the sensors’ accuracy (from manufacturer’s specifications) as the threshold.
That is to say, an event is considered to be detected as long as a pressure change is
greater than the pressure sensor accuracy. In the second step, the pressure sensor
locations are optimised using a GA in the Darwin optimization framework [51] for a
given number of sensors, so that the optimised sensor locations are able to cover the
maximum number of leak/burst events. The authors tested their method on two reallife networks considering a perfect model.
Hagos et al. [52] presented a method that attempts to mitigate the “arbitrary
threshold” selection issue present in many of the previous studies that convert the
sensitivity matrix to a binary matrix by promoting the use of statistical process
control tools. Specifically, the use of Shewhart control charts [53] and of the Western
Electric Company detection rules [54] was proposed in that study as the authors
deemed this detection approach more statistically robust, in addition to enabling up
to eight most recent past measurements rather than a single/current value/measurement. The method focuses on the placement of pressure and flow sensors
independently, makes use of linear programming for the optimisation (binary integer
programming problem solved by the general reduced gradient non-linear solver – see
[55]) and was demonstrated on a modified Austin network (see [56]). In this study,
the authors looked into the issue of false alarms in determining sensor placements’
detection effectiveness and made use of the average detection time as a secondary
(given placements with the same detection effectiveness, the placement with a
36
M. Romano
clustering step were not too far from the global optimum.
Bearing in mind the above, in order to overcome the aforementioned intrinsic
limitation of their structural model-based strategy, Sarrate et al. [47] proposed a
further approach based entirely on analysis of the leak/burst sensitivity matrix. In
this study, projections are calculated from the sensitivity matrix, a “leak locatability”
index (to be maximised for the specific number of sensors to be installed) is
introduced, and a two-step hybrid methodology that combines clustering techniques
(the evidential c-means algorithm was used in that study – see [48]) with an
exhaustive search is utilised to search for the optimal sensor configuration. Again,
the authors tested their method on the same DMA used in Sarrate et al. [42] and
conducted their experiments with settings very similar to those used in that study. It
was found that their further approach enables solving the optimal sensor placement
problem in a reasonable time. However, the authors noted that despite the exhaustive
search approach providing an optimal result, “optimality” of this result over the set
of original candidate pressure locations is strongly dependent on the performance of
the clustering algorithm.
Wu and Song [49] developed a pressure sensor placement method that maximises
the number of leak/burst events that can be detected for a given number of sensors by
performing the following two steps. Firstly, a Monte Carlo method (see – e.g. [50]) is
used to generate a large number of random events with different magnitudes and that
may occur at a single location or at two locations simultaneously. In this step, the
simulated nodal pressures are compared with the baseline condition, and residuals
are stored in a matrix. Then a binary matrix is obtained from the residuals matrix
using the sensors’ accuracy (from manufacturer’s specifications) as the threshold.
That is to say, an event is considered to be detected as long as a pressure change is
greater than the pressure sensor accuracy. In the second step, the pressure sensor
locations are optimised using a GA in the Darwin optimization framework [51] for a
given number of sensors, so that the optimised sensor locations are able to cover the
maximum number of leak/burst events. The authors tested their method on two reallife networks considering a perfect model.
Hagos et al. [52] presented a method that attempts to mitigate the “arbitrary
threshold” selection issue present in many of the previous studies that convert the
sensitivity matrix to a binary matrix by promoting the use of statistical process
control tools. Specifically, the use of Shewhart control charts [53] and of the Western
Electric Company detection rules [54] was proposed in that study as the authors
deemed this detection approach more statistically robust, in addition to enabling up
to eight most recent past measurements rather than a single/current value/measurement. The method focuses on the placement of pressure and flow sensors
independently, makes use of linear programming for the optimisation (binary integer
programming problem solved by the general reduced gradient non-linear solver – see
[55]) and was demonstrated on a modified Austin network (see [56]). In this study,
the authors looked into the issue of false alarms in determining sensor placements’
detection effectiveness and made use of the average detection time as a secondary
(given placements with the same detection effectiveness, the placement with a
36
M. Romano