GALAXY multi-objective evolutionary algorithm [65] to identify the optimal
location of pressure sensors in the DMA given a specified number of sensors.
Similarly to the work presented in Farley et al. [30], the first step for solving the
optimal sensor placement problem involves hydraulic modelling of leaks/bursts at all
nodes and building a matrix containing instantaneous chi-squared values (as only a
single time step was considered in this study). These chi-squared values are then
used for building various interpolation surfaces during the optimisation step, which
aims at maximising (using an objective function also based on the spatially
constrained inverse distance weighted interpolation technique and a threshold that
defines the leak/burst search area on an interpolation surface) the localisation
performance of each configuration of sensors for every leak/burst being modelled.
After determining the optimal sensors configuration by looking at the results of the
optimisation step, the spatially constrained inverse distance weighted interpolation
technique is used again to calculate the approximate location of an “actual” leak/
burst occurring in a DMA (once a leak/burst has been identified or is suspected)
based on the “actual” pressures measured at the sensor locations. The authors
considered a perfect model and perfect sensors’ measurements and tested their
method on a small synthetic network from the literature, the Bakryan benchmark
WDS (see [66]). Despite the limited testing/validation of this method, it is worth
highlighting one of the potential benefits of the approach proposed in this work,
namely, the use of spatially constrained geostatistical techniques. Generally speaking, geostatistical techniques have the potential to limit the number of instruments
which are deployed in a DMA as they can estimate the values of parameters at
locations which are not measured based on the measurements from nearby sensors
and, hence, to enable higher leak/burst localisation performance to be achieved for a
given number of sensors. The use of geostatistical techniques for leak/burst
localisation was already proposed by Romano et al. [15] with encouraging results.
However, the use of a spatially constrained version of the inverse distance weighted
interpolation technique proposed in Boatwright et al. [63] enables the overcoming of
the obvious limitation of using the Euclidean distance instead of the pipe length
between the estimation locations and the instrument locations (i.e. not accounting for
the actual network layout of a DMA).
3 Considerations on Specific Issues Encountered When
Developing Optimal Sensor Placement Techniques
for Leak/Burst Detection and Localisation
In this section several issues that have been considered by researchers when developing sensor placement methodologies for leak/burst detection and localisation are
presented together with details of relevant research works that have aimed at
addressing these issues.
38
M. Romano
location of pressure sensors in the DMA given a specified number of sensors.
Similarly to the work presented in Farley et al. [30], the first step for solving the
optimal sensor placement problem involves hydraulic modelling of leaks/bursts at all
nodes and building a matrix containing instantaneous chi-squared values (as only a
single time step was considered in this study). These chi-squared values are then
used for building various interpolation surfaces during the optimisation step, which
aims at maximising (using an objective function also based on the spatially
constrained inverse distance weighted interpolation technique and a threshold that
defines the leak/burst search area on an interpolation surface) the localisation
performance of each configuration of sensors for every leak/burst being modelled.
After determining the optimal sensors configuration by looking at the results of the
optimisation step, the spatially constrained inverse distance weighted interpolation
technique is used again to calculate the approximate location of an “actual” leak/
burst occurring in a DMA (once a leak/burst has been identified or is suspected)
based on the “actual” pressures measured at the sensor locations. The authors
considered a perfect model and perfect sensors’ measurements and tested their
method on a small synthetic network from the literature, the Bakryan benchmark
WDS (see [66]). Despite the limited testing/validation of this method, it is worth
highlighting one of the potential benefits of the approach proposed in this work,
namely, the use of spatially constrained geostatistical techniques. Generally speaking, geostatistical techniques have the potential to limit the number of instruments
which are deployed in a DMA as they can estimate the values of parameters at
locations which are not measured based on the measurements from nearby sensors
and, hence, to enable higher leak/burst localisation performance to be achieved for a
given number of sensors. The use of geostatistical techniques for leak/burst
localisation was already proposed by Romano et al. [15] with encouraging results.
However, the use of a spatially constrained version of the inverse distance weighted
interpolation technique proposed in Boatwright et al. [63] enables the overcoming of
the obvious limitation of using the Euclidean distance instead of the pipe length
between the estimation locations and the instrument locations (i.e. not accounting for
the actual network layout of a DMA).
3 Considerations on Specific Issues Encountered When
Developing Optimal Sensor Placement Techniques
for Leak/Burst Detection and Localisation
In this section several issues that have been considered by researchers when developing sensor placement methodologies for leak/burst detection and localisation are
presented together with details of relevant research works that have aimed at
addressing these issues.
38
M. Romano