improvements, requiring a post-treatment analysis to tackle such a problem, whereas
considering the improvements enabled them to avoid any post-treatment analysis.
Sarrate et al. [42] proposed a sensor placement method based on an extension of
the work done, although not focusing on WDSs specifically, in Rosich et al.
[43]. This method takes into account maximum diagnosability (i.e. leak/burst
isolability and detectability maximisation) specifications for a specific number of
sensors to be installed. The strategy is based on the structural model of a WDS. A
structural model is a coarse model description, based on a graph representation of the
analytical model structure whereby only the relationship between variables and
equations is taken into account, while the mathematical expression of this relationship is neglected. Because of this an efficient graph-based method (i.e. depth-first
branch and bound search algorithm) was applied to solve the sensor placement
problem. Bearing this in mind, it is important to stress that, due to the coarse nature
of a structural model, the diagnosis performance obtained using such a model cannot
be guaranteed for the real WDS. Considering only a small subset of nodes as
potential sensor locations, the authors applied their method to a DMA in the
Barcelona WDS and demonstrated the feasibility of their approach. However, in a
later study [44], the author stated that, because of the size and the complexity of the
optimal sensor placement problem in real-life WDSs, the applicability of the method
proposed in Sarrate et al. [42] is limited to small-/medium-sized networks. Therefore, they attempted to reduce the size and complexity of the problem by combining
their structural model-based method with clustering techniques. Clustering techniques enable the unsupervised classification of patterns (observations, data items or
feature vectors) into groups (clusters) and have been used to solve various
problems in different domains [45]. Specifically, a k-means clustering technique
(see – e.g. [46]) was used in that study as a pre-processing step to reduce the number
of candidate sensor locations before solving the sensor placement problem proposed
by Sarrate et al. [42]. Aiming at grouping together nodes that respond in a similar
manner to leak/burst events, the authors built a fault sensitivity matrix as done in
Pérez et al. [31]. However, they did not binarise that matrix but used the cosine
distance on the residuals for the k-means algorithm. As a result, the number of
candidate sensor locations to be used in the depth-first branch and bound search
algorithm was reduced by selecting only one candidate sensor location (i.e. the
nearest to the cluster centroid) from each cluster. In this study, the authors tested
their method on the same DMA used in Sarrate et al. [42], simulated leaks/bursts as a
single, constant demand that can appear at selected (in order to limit problem
complexity) nodes, assumed the availability of a perfect hydraulic model and did
not account for measurements noise. Of particular note in this study is the fact that
the authors stated that although it might seem appealing (in order to reduce computational efforts) to skip the branch and bound step and directly apply the clustering
step to obtain the final sensor configuration, such an approach may lead to
suboptimal results as “only a reduced set of directional residuals (the primary
residuals) are represented in the fault sensitivity matrix according to the simulation
method used”. That statement was then validated in a following study by the authors
Review of Techniques for Optimal Placement of Pressure and Flow Sensors. . .
35
considering the improvements enabled them to avoid any post-treatment analysis.
Sarrate et al. [42] proposed a sensor placement method based on an extension of
the work done, although not focusing on WDSs specifically, in Rosich et al.
[43]. This method takes into account maximum diagnosability (i.e. leak/burst
isolability and detectability maximisation) specifications for a specific number of
sensors to be installed. The strategy is based on the structural model of a WDS. A
structural model is a coarse model description, based on a graph representation of the
analytical model structure whereby only the relationship between variables and
equations is taken into account, while the mathematical expression of this relationship is neglected. Because of this an efficient graph-based method (i.e. depth-first
branch and bound search algorithm) was applied to solve the sensor placement
problem. Bearing this in mind, it is important to stress that, due to the coarse nature
of a structural model, the diagnosis performance obtained using such a model cannot
be guaranteed for the real WDS. Considering only a small subset of nodes as
potential sensor locations, the authors applied their method to a DMA in the
Barcelona WDS and demonstrated the feasibility of their approach. However, in a
later study [44], the author stated that, because of the size and the complexity of the
optimal sensor placement problem in real-life WDSs, the applicability of the method
proposed in Sarrate et al. [42] is limited to small-/medium-sized networks. Therefore, they attempted to reduce the size and complexity of the problem by combining
their structural model-based method with clustering techniques. Clustering techniques enable the unsupervised classification of patterns (observations, data items or
feature vectors) into groups (clusters) and have been used to solve various
problems in different domains [45]. Specifically, a k-means clustering technique
(see – e.g. [46]) was used in that study as a pre-processing step to reduce the number
of candidate sensor locations before solving the sensor placement problem proposed
by Sarrate et al. [42]. Aiming at grouping together nodes that respond in a similar
manner to leak/burst events, the authors built a fault sensitivity matrix as done in
Pérez et al. [31]. However, they did not binarise that matrix but used the cosine
distance on the residuals for the k-means algorithm. As a result, the number of
candidate sensor locations to be used in the depth-first branch and bound search
algorithm was reduced by selecting only one candidate sensor location (i.e. the
nearest to the cluster centroid) from each cluster. In this study, the authors tested
their method on the same DMA used in Sarrate et al. [42], simulated leaks/bursts as a
single, constant demand that can appear at selected (in order to limit problem
complexity) nodes, assumed the availability of a perfect hydraulic model and did
not account for measurements noise. Of particular note in this study is the fact that
the authors stated that although it might seem appealing (in order to reduce computational efforts) to skip the branch and bound step and directly apply the clustering
step to obtain the final sensor configuration, such an approach may lead to
suboptimal results as “only a reduced set of directional residuals (the primary
residuals) are represented in the fault sensitivity matrix according to the simulation
method used”. That statement was then validated in a following study by the authors
Review of Techniques for Optimal Placement of Pressure and Flow Sensors. . .
35