2 Synthesis and Analysis of Optimal Sensor Placement
Techniques for Leak/Burst Detection and Localisation
The amount of information on a leak/burst event occurrence in a pressure or flow
signal from a DMA is a function of the number and types of sensors and their
locations, as well as the DMA structure and event location, among the others. As
such, measurements at some locations can include more information regarding an
event than measurements at other locations. The main aim of optimal sensor
placement for leaks/burst detection and localisation techniques is therefore to place
the minimum number of sensors in a DMA to capture the event “effects” no matter
where in a DMA the event occurs and then effectively use this information to
provide detection alarms and accurately identify the approximate event’s location.
Model-based leak/burst detection and localisation techniques, using pressure and
flow measurements and hydraulic models of WDSs, have been studied for approximately two decades, since the paper by Pudar and Liggett [28], which formulates the
leak detection and localisation problem as an indirect (see [29]) least-squares
parameters estimation problem. However, the estimation of the parameters describing a WDS model is a difficult task since these models are non-linear. This said, with
the papers by Farley et al. [30] and Pérez et al. [31], the last decade has seen a large
number of papers published on this subject that attempt to use direct (see [29])
methods to solve the leak/burst detection and localisation problem. Almost all these
studies work by running multiple hydraulic model simulations of various leak/burst
scenarios and then evaluating the sensitivity of different monitoring points to the
imposed ‘fault’ conditions. Because of this, many of these studies are inspired by the
model-based fault diagnosis theory (see, e.g. [32]), the main objectives of which are
maximising fault detectability (i.e. ability to identify a fault occurrence in a system)
and fault isolability (i.e. ability to distinguish between two possible fault
occurrences – as, if the effects of different faults are similar, they may result in
similar sensors’ measurements). However, different approaches have also been
proposed.
Farley et al. [30] introduced an approach which simulates, for an idealised 24 h
period, leaks/bursts at all possible locations in a DMA (i.e. as an emitter at all the
nodes of the relevant hydraulic model) and subsequently builds a matrix with rows
corresponding to the possible leak/burst points and column corresponding to possible monitoring points. Each element of this matrix contains the sum, ∑X
2 (over the
24 h period), of instantaneous chi-squared values computed as X
2
¼
P lc ÀP n
ð
Þ
2
P n
, where
P lc is the simulated pressure recorded under leak/burst conditions and P n is the
simulated pressure recorded under normal conditions. A threshold computed as the
mean of the matrix is then applied to each value in the matrix to map those values to
zeros (i.e. leak/burst undetected) and ones (i.e. leak/burst detected) by simply
checking whether the specific ∑X
2 is less or greater than the threshold, respectively.
The column with the largest number of ones is considered as the most sensitive
sensor location. The authors expanded this methodology to determine the best
combination of two sensor locations by using a complete enumeration procedure
Review of Techniques for Optimal Placement of Pressure and Flow Sensors. . .
31
Techniques for Leak/Burst Detection and Localisation
The amount of information on a leak/burst event occurrence in a pressure or flow
signal from a DMA is a function of the number and types of sensors and their
locations, as well as the DMA structure and event location, among the others. As
such, measurements at some locations can include more information regarding an
event than measurements at other locations. The main aim of optimal sensor
placement for leaks/burst detection and localisation techniques is therefore to place
the minimum number of sensors in a DMA to capture the event “effects” no matter
where in a DMA the event occurs and then effectively use this information to
provide detection alarms and accurately identify the approximate event’s location.
Model-based leak/burst detection and localisation techniques, using pressure and
flow measurements and hydraulic models of WDSs, have been studied for approximately two decades, since the paper by Pudar and Liggett [28], which formulates the
leak detection and localisation problem as an indirect (see [29]) least-squares
parameters estimation problem. However, the estimation of the parameters describing a WDS model is a difficult task since these models are non-linear. This said, with
the papers by Farley et al. [30] and Pérez et al. [31], the last decade has seen a large
number of papers published on this subject that attempt to use direct (see [29])
methods to solve the leak/burst detection and localisation problem. Almost all these
studies work by running multiple hydraulic model simulations of various leak/burst
scenarios and then evaluating the sensitivity of different monitoring points to the
imposed ‘fault’ conditions. Because of this, many of these studies are inspired by the
model-based fault diagnosis theory (see, e.g. [32]), the main objectives of which are
maximising fault detectability (i.e. ability to identify a fault occurrence in a system)
and fault isolability (i.e. ability to distinguish between two possible fault
occurrences – as, if the effects of different faults are similar, they may result in
similar sensors’ measurements). However, different approaches have also been
proposed.
Farley et al. [30] introduced an approach which simulates, for an idealised 24 h
period, leaks/bursts at all possible locations in a DMA (i.e. as an emitter at all the
nodes of the relevant hydraulic model) and subsequently builds a matrix with rows
corresponding to the possible leak/burst points and column corresponding to possible monitoring points. Each element of this matrix contains the sum, ∑X
2 (over the
24 h period), of instantaneous chi-squared values computed as X
2
¼
P lc ÀP n
ð
Þ
2
P n
, where
P lc is the simulated pressure recorded under leak/burst conditions and P n is the
simulated pressure recorded under normal conditions. A threshold computed as the
mean of the matrix is then applied to each value in the matrix to map those values to
zeros (i.e. leak/burst undetected) and ones (i.e. leak/burst detected) by simply
checking whether the specific ∑X
2 is less or greater than the threshold, respectively.
The column with the largest number of ones is considered as the most sensitive
sensor location. The authors expanded this methodology to determine the best
combination of two sensor locations by using a complete enumeration procedure
Review of Techniques for Optimal Placement of Pressure and Flow Sensors. . .
31