1 Introduction
The problem of leak and pipe burst events in water distribution systems (WDSs) is a compelling issue for water companies worldwide. Leak and pipe burst events not only cause economic losses to water companies [1] but also represent an environmental issue (i.e. waste of water and energy) and a potential risk to public health [2]. Furthermore, they have a negative impact on water companies’ operational performance, customer service and reputation. Currently, a wide range of leak/burst event detection and location techniques exists that are based on various principles [3–7]. However, none is ideal, and the number of techniques currently practised by water companies is limited. In many cases, pipe bursts are brought to the attention of a water company only when someone calls in to report a visible event. Water companies embracing modern leakage management technologies devote considerable manpower and resources to proactive detecting and localising leaks and pipe bursts by utilising techniques that make use of highly specialised hardware equipment (e.g. leak noise correlators, acoustic sensors mounted on inline pipeline inspection gauges, ground penetrating radars, etc.). Despite some of these techniques being the most accurate ones used today [6], they are also costly, labour-intensive and slow to run. Consequently, much research has been focused on finding inexpensive (i.e. numerical) techniques that can help the water companies significantly reducing the leaks/bursts’ lifecycle by making them aware of the occurrence of these events much faster and guiding the water company personnel straight to the problem areas.
In the above scenario (and bearing in mind that in the last decade the importance of a proactive approach to network management and near real-time assets monitoring have become apparent as water companies have had to deal with tightening regulatory and budgetary constraints), it is clear that instrumentation and analytics can play a vital role in addressing the aforementioned issues. In the UK, and as recommended internationally by the International Water Association (IWA), WDSs are divided into District Metered Areas (DMAs), which may consist of approximately 300–5,000 properties. The current UK industry practice is to install a flow sensor (and sometimes a pressure sensor as well) at the inlet of a DMA and any outlet (e.g. to another DMA or to a large industrial user) and a (supplementary) pressure sensor at the so-called critical monitoring point within the DMA (i.e. the point located either at the point of highest elevation or alternatively at a location farthest away from the inlet). With recent improvements in sensor technology and communication technologies (such as GSM, GPRS and, more recently, LORAWAN, Sigfox, NB-IoT and 5G), data can now be transferred via wireless systems, and batteries last much longer, meaning that sensors can be placed in less accessible areas and data from these devices can be received in near real time (e.g. every 15 min). Furthermore, it is becoming more feasible to deploy larger numbers of instruments per DMA, as the cost of both pressure and flow instrumentation (and their maintenance) has been reduced considerably. As a result, a vast amount of pressure and flow data originating from the many DMAs that typically form a UK WDS is now frequently available and expected to quickly grow over time. This data can give insights into the operation and current/future status of water networks and support many water loss-related activities, such as estimating background leakage levels, establishing and maintaining hydraulic models of water systems and detecting and localising new leaks and bursts as they occur. With regard to the latter, data-driven techniques utilising machine learning and advanced statistical tools have been developed that automatically manage and analyse in an on-line fashion increasing numbers of near real-time data streams aiming at enabling the detection and (in certain instances) the approximate location of leaks, bursts and other similar network events (e.g. [8–18]). These techniques can complement traditional leak/burst localisation methods such as acoustic surveys, which can then be used for accurately determining the exact leak/burst position (i.e. pinpointing). The value of the information that can be derived through analysis of sensor data and hence the success of the aforementioned methods (especially for localisation), however, is critically linked to the number and types of sensors deployed and their locations. As previously mentioned, it is envisaged that in the near future higher numbers of sensors (especially pressure, for their lower cost and easier installation and maintenance when compared to flow sensors) will be used to monitor WDSs. However, due to the financial constraints placed on water companies, the costs of increased instrumentation in WDSs (both capital and ongoing maintenance) must be weighed against the operational and other cost savings which can be made by improving network operations and management. It is therefore desirable to limit the number of additional instruments to be deployed by selecting the optimal number and location of sensors in a DMA.
This chapter provides a critical state-of-the-art literature review on the subject of optimal sensor placement in WDSs for leak/burst detection and localisation. It provides details of a number of existing sensor macro-location design methodologies intended to facilitate the efficient collection of relevant measurements in WDSs for that specific purpose. Generally speaking, the optimal placement of a limited number of sensors within a WDS (‘ideal’ locations at which measurements of selected quantities should be taken) is a necessary step in the application of intelligent and cost-effective monitoring for current and prospective WDSs. The definition of an “optimised” sensor network is dependent on the intended purpose of the sampling scheme and the resulting sensor data. Design methodologies in the literature are typically catered towards one of a number of distinct agendas, and the field is consequently segmented into a range of subsidiary groups – i.e. methods to determine optimal placement schemes for effective contaminant detection (e.g. [19–25]), methods to determine optimal placement schemes for model calibration (both hydraulic, e.g. [26], and water quality, e.g. [27]) and methods for leak and burst detection, each formulation of which may be largely irrelevant outside of its own context. Although a large amount of methods that consider how to identify the optimal placement of both pressure and flow instrumentation within WDSs at the DMA level for leak/burst detection and localisation can be found in the sampling design literature, a comprehensive review of their capabilities, limitations and other aspects important for assessing the potential of these techniques to be beneficially utilised by water companies has not yet been presented in any review paper.
As only a limited number of sensors can be installed in WDSs due to budget constraints and since improper selection of their location may seriously hamper leak/burst detection and localisation performance, the development of optimal sensor placement strategies has become an important research issue in recent years. This chapter aims at rationalising the relevant published works in the field and is organised as follows. After this introduction, Sect. 2 presents a synthesis and analysis of the relevant published works aimed at (1) providing insight and awareness of differing arguments, theories and approaches, (2) highlighting their capabilities and limitations and (3) identifying the state of the art in their development. Section 3 focuses on specific issues encountered when developing techniques for the optimal placement of sensors for leak/burst detection and localisation that researchers in this field have tried to address (e.g. model and measurements uncertainties, simultaneous use of pressure and flow sensors, etc.) and provides insight and awareness of differing approaches that have been proposed in those contexts. Section 4 presents considerations regarding, inter alia, the potential of the proposed techniques to help water companies minimising the leaks/bursts’ runtime by effectively detecting and localising these events as they occur in a DMA and the gaps in the current research. Finally, a summary of the chapter containing the main conclusions and highlighting the key considerations made is given in Sect. 5 in order to promote further developments in this important field of research.
The desired outcome of this chapter is to serve as a useful resource for researchers and practitioners involved in sensor network design for leak/burst detection and localisation and in the development/adoption of leak/burst detection and localisation techniques.
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, ∑X2 (over the 24 h period), of instantaneous chi-squared values computed as 
, where Plc is the simulated pressure recorded under leak/burst conditions and Pn 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 ∑X2 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 of all possible pairings of locations. They tested their method on two UK DMAs with different geometries assuming a perfect model and no measurements noise. Through comparison with the leak/burst detection performance of already installed instrumentation (according to UK standard practices), they demonstrated that the optimal location(s) identified using their method enable detecting a higher percentage of simulated leak/burst events. The authors noted however that the threshold selection is cause of concern as, if obtained from the simulation of large leaks/bursts, smaller events may not be detected. Of particular importance is the fact that, in a later study [33], the authors conducted a set of field trials to evaluate their approach. These field trials simulated five different leak/burst events through the opening of fire hydrants within a selected DMA. By installing pressure instrumentation at different locations in the DMA, an understanding of how accurately the model methodology can determine sensitivity of instrument location was obtained. Indeed, the results showed that pressure instrumentation location is crucial to sensitivity and that their modelling methodology was able to predict instrument location sensitivity to leak/burst events reasonably well.
Farley et al. [11, 34] built on the work carried out in [30, 33] and proposed to search the sensitivity matrix to achieve selective sensitivity to events in different network areas. By doing this, their approach enabled providing useful leak/burst localisation information by subdividing a DMA in smaller detection zones. The main differences from the work presented in Farley et al. [30, 33] are that a genetic algorithm (GA – see, e.g. [35]) is used to improve the search efficiency when identifying the best sensor locations and an uncertainty band is applied to either side of the threshold to (somehow) account for a certain degree of model/measurements uncertainty. The single objective function of the GA search aims to identify combinations of instruments that provide an even division of the DMA and to minimise the number of nodes within the penalty zone (i.e. a zone whereby a response within the uncertainty band is produced at one or more instruments). The authors presented results from field tests using hydrant flushing to simulate leak/burst events in real DMAs. The field tests’ results demonstrated the practical applicability of the method, showing that by combining quantification of differential sensitivities with event detection techniques for data analysis (i.e. [12, 13]), events can effectively be localised using a small number of instruments (i.e. taking into account existing instrumentation and one or two additional pressure sensors). However, it was noted that the effectiveness of the localisation method was dependent on where in a DMA a leak/burst event occurs (e.g. event near a DMA inlet are likely to be missed) and, most importantly, that the method only works if all the considered instruments are working and the event detections from all the sensors’ data agree with what the model expects to happen (i.e. an incorrect or uncertain detection even at a single sensor location would cause the method to indicate an incorrect leak/burst search area).
![$$ S(k)=\left[\begin{array}{ccc}\frac{p_1^{f_1}(k)-{p}_1(k)}{f_1}& \cdots & \frac{p_1^{f_m}(k)-{p}_1(k)}{f_m}\\ {}\vdots & \ddots & \vdots \\ {}\frac{p_n^{f_1}(k)-{p}_n(k)}{f_1}& \cdots & \frac{p_n^{f_m}(k)-{p}_n(k)}{f_m}\end{array}\right] $$](../images/369945_1_En_405_Chapter/369945_1_En_405_Chapter_TeX_Equ1.png)
is the pressure of sensor i at the time instant k when a leak/burst with constant flow, fj, is present at node j, m is the number of nodes in the network (possible leak/burst locations – if leaks and burst are assumed as occurring at nodes), n is the number of sensors in the network and pi(k) represents the pressure of sensor i at the time instant k without the presence of a leak/burst in the network. The candidate leaks/bursts are those whose effect matches the best (when compared using some metric) with the observed residuals. In this study the authors proposed to normalise (i.e. divide each row by the maximum value of that row that corresponds to the leak/burst most important for that node) and then binarise the sensitivity matrix in order to be used as a leak/burst signature matrix (i.e. set of all the leak/burst signatures). The threshold used to evaluate the residuals and to binarise the sensitivity matrix was identified by looking at the trade-off between the number of unique signatures present in the binarised sensitivity matrix and the number of leaks/bursts with the same signature. The authors used a GA-based optimisation to find the location of sensors that minimises the maximum number of possible leaks/bursts with a particular signature (i.e. maximise isolability) for a pre-specified number of sensors. This method was tested using the hydraulic model of a real WDS, Placa del Diamant, in the Barcelona WDS. Here the authors simulated leaks/bursts as a single, constant demand that can appear in any node, considered a single time step k, assumed the availability of a perfect hydraulic model (e.g. no model uncertainty) and did not account for measurements noise. Subsequently, however, Pérez et al. [37] repeated their experiments considering multiple time steps (i.e. a particular time step during the night-time period for 15 days – they introduced a voting mechanism to then assign a leak/burst to a particular group of nodes) and uncertainty in the nodal demands. The authors found that, independently by the presence (or absence) of the added uncertainty, their approach required to recalculate new sensitivity matrices every day – because these matrices are strongly affected by the changing boundary conditions and total consumption. Furthermore, they found that localisation performance strongly decreases when nodal demand uncertainty is introduced, in addition 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 distance-based 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 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 [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 real-life 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 shorter average detection time is more favourable) detection efficiency indicator. With specific regard to the issue of false alarms, the authors found that maximising the rate of correct event detections and minimising the rate of false alarms are contradictory goals and the best detection locations are not likely to be the best locations for minimising the rate of false alarms. Furthermore, they found that, as the number of sensors in the DMA increases, both the rate of correct event detections and the rate of false alarms increase.
Huang et al. [57] developed a clustering-based pressure sensor placement method for pipe burst detection. They used a fuzzy self-organising map neural network (see – e.g. [58]) due to its capability to classify the inputs without knowing the number of clusters in advance and, hence, with the capability of enabling to determine the optimal number of pressure sensors required. In this method, the nodes in a WDS/DMA are grouped according to their similarity in responding to the change of node demands due to leaks/bursts. A small real-world network was used to demonstrate the effectiveness of the method. Here, the authors simulated leaks/bursts as a single, constant demand, considered a single time step (i.e. the hour of maximum daily water consumption), assumed the availability of a perfect hydraulic model and did not account for measurements noise. Because of the limited verification of the methodology carried out in this study, it is difficult to assess the value of the proposed method. Bearing this in mind, it is also important to stress that the authors stated that setting the parameters of the self-organising map neural network properly is not a trivial task and further investigations into this issue are required if this method is to be used by water companies.
Candelieri et al. [59] proposed a method that makes use of (1) a graph-based, spectral clustering procedure (see – e.g. [60]) of similar variations in pressure and flow induced by leaks/bursts simulated using a hydraulic model and (2) support vector machines classification (see – e.g. [61]) to learn the relationship between the variations in pressure and flow at the deployed sensor locations and the most probable set of pipes affected by a leak/burst (i.e. to learn to approximate the non-linear mapping performed by the spectral clustering procedure and estimate the most probable cluster which an “actual” vector of variations in pressure and flow would belong to). They run several leak/burst scenarios by varying leak/burst location and magnitude, assuming the availability of a perfect model and perfect sensors’ measurements. They proposed to use a “localisation index” measure [62] and a novel “quality of localisation” measure to evaluate the quality of the identified clusters. The authors looked at the simultaneous deployment of pressure and flow sensors by introducing a simple measure of cost (i.e. the cost of a flow sensor is ten times the cost of a pressure sensor). They demonstrated the capabilities of their method by applying it to the study of the optimal sensor locations for a real-life DMA in Timisoara, Romania.
Boatwright et al. [63] proposed a novel combined sensor placement – leak/burst localisation methodology based upon a spatially constrained version of the inverse distance weighted geospatial interpolation technique (see [64]) that aims at ensuring that optimal sensor locations (with respect to the leak/burst localisation technique used) are selected. The proposed methodology makes use of the 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.
This section is organised as follows. Firstly, the issue of model uncertainties and sensitivity to the leak/burst size assumed for hydraulic simulations is considered in Sect. 3.1. Then, Sect. 3.2 focuses on the issue of uncertainties in the sensors’ measurements. Once this is done, Sect. 3.3 deals with the issues of sensor/communication failures in sensor networks. Section 3.4 examines the topic of the simultaneous use of pressure and flow sensors. Finally, Sect. 3.5 focuses on the issue of accounting for risk when developing optimal sensor placement techniques for leak/burst detection and localisation.
3.1 Model Uncertainties and Sensitivity to the Leak/Burst Size Assumed for Hydraulic Simulations
Almost all the sensor placement algorithms for leak/burst detection and localisation in a DMA rely on modelling a large number of leak/burst scenarios. A number of reliable, readily available hydraulic solver packages exist (e.g. EPANET (see [67]); PICCOLO (see [68]); AQUIS (see [69]); WaterGEMS (see [70]); OOPNET (see [71]); etc.), which allow leaks/bursts to be modelled relatively easily. Many of the sensor placement studies for leak/burst detection and localisation found in the literature assume a perfect model (i.e. that reflects reality at all times). Such a perfect model is assumed to contain up-to-date estimates of nodal demands, background (i.e. not burst type) leaks, pipe friction factors, statuses and characteristics of valves, pumps and other devices and any other model parameter/input values (e.g. heads in service reservoirs) that may affect its predictions of network pressures and flows. However, it is well known that a perfect model does not exist. In this context, demand allocation in a hydraulic model, which requires a good characterisation of consumers, is considered as one of the most critical issues. In addition to all this, leaks and bursts in WDSs have a stochastic nature. The size, location, timing and nature/type of a leak/burst event are generally unknown. However, a nominal leak/burst size is assumed in many of the sensor placement methodologies that can be found in the literature. This section presents a selection of studies that have attempted to deal with these issues.
Blesa et al. [72] studied the robustness of the methodology introduced by Sarrate et al. [47] against sensitivity matrix uncertainties by taking into account different leak/burst magnitudes on the one hand and several operating points (although only inflows variations were considered in this study) on the other hand. The authors introduced a “robustness percentage” index, which is based on the “leak locatability” index (see [47]), to assess the robustness of the selected sensor placement methodology. Additionally, they made use of an extended sensitivity matrix that considers all possible leak/burst scenarios and operating point scenarios in their clustering analysis to reduce the number of candidate sensor locations. The authors illustrated their robustness studies by means of a simple synthetic network (note, however, that the clustering analysis was not deemed necessary there) and the same DMA in the Barcelona WDS used in previous studies by the authors (i.e. [42, 44, 47]). The main result was that the identified sensor positions are relatively insensitive to the size of the leaks/bursts. However, variation of the “leak locatability” index can be significant when different operating point scenarios are considered. Bearing this in mind, aiming at accounting for this variation and ensure robust performance, Blesa et al. [73] extended the optimal sensor placement method by Sarrate et al. [47] by formulating a multi-objective optimisation strategy to place sensors. This strategy has the following objectives: (1) to maximise the mean “leak locatability” index and (2) to maximise the worst “leak locatability” index. Optimisation was carried out by using their two-step hybrid methodology that combines clustering techniques (note that the extended sensitivity matrix considered there encompass all possible operating point scenarios only) with an exhaustive search procedure, resulting in an approximation of the entire Pareto front. The authors utilised again the simple synthetic network (without clustering analysis) and the DMA in the Barcelona WDS used in Blesa et al. [72] to test their strategy. Through comparison of the results achieved in the Barcelona DMA with and without the use of the proposed robust sensor placement methodology, the authors demonstrated that not to account for different operating point scenarios leads to solutions that are not Pareto optimal.
As mentioned in Sect. 2, Casillas et al. [39] attempted to mitigate the effect of model uncertainties and of the unknown leak/burst size by incorporating in their method an extended-horizon analysis of pressure sensitivities/residuals and by considering sets of sensitivities and residuals computed using different leak/burst sizes. However, in Casillas et al. [74, 75], the authors proposed a different sensor placement method inspired by the leak signature space-based leak/burst localisation technique presented in Casillas et al. [76]. The leak signature space analysis enables a specific signature to be associated to each leak/burst location that is minimally affected by the leak/burst size. It considers a linear model approximation of the relationship between pressure residuals and leaks/bursts to perform a transformation that allows representing leak/burst locations by means of points in the leak signature space that are not dependent on the leaks/bursts magnitude. The authors introduced the concept of a domain of influence for a particular leak signature and solved the sensor placement optimisation problem by attempting to minimise the overlapping between domains of influence considering the signatures of all network nodes. A time horizon analysis was also considered by looking at the mean number of overlaps along the time horizon analysed. A GA and a particle swarm optimisation (i.e. PSO – see [77]) algorithm were separately used to perform the optimisation. The capabilities of the proposed methodology (i.e. efficiency, in terms of the percentage of leaks correctly localised) were evaluated on the same two networks, Hanoi and Limassol, considered in a previous study by the authors (i.e. [39]), assuming perfect models but accounting for measurements uncertainties by adding Gaussian white noise. The result obtained demonstrated that efficiencies of 100% and up to about 85% could be achieved using a small number of sensors (up to 4 and 3, respectively) on the Hanoi and Limassol networks, respectively. They also emphasised, similarly to what is found in Casillas et al. [39], the benefits of the time horizon analysis. Worth of note, here, are also the results from the GA/PSO comparison that the authors detailed in these studies. They found that, generally speaking, PSO works faster than the GA (being very effective for small networks or few sensors) but, when the problem complexity increases (e.g. when more sensors are considered), the GA tends to find placements with higher efficiency. In this regard, the authors observed that PSO may tend to be trapped in a local suboptimum, probably because it has memory of past successes and therefore tends to explore around those recorded configurations; whereas when it is necessary to leap from one region of the search space to a distant other region, crossover operations like those in a GA are probably more effective. Finally, the authors stressed that, although relatively small networks were used in their studies, trying to find optimal placements for larger numbers of sensors than those detailed in their papers would be prohibitive in terms of computational time required to obtain a solution.
Steffelbauer and Fuchs-Hanusch [78] extended the work by Steffelbauer et al. [79] in which the effect of demand uncertainty on modelled predictions of pressure was incorporated in the optimal sensor placement problem (solved by using the method proposed by Casillas et al. [9, 10] but adapted in order to penalise potential sensor locations with high uncertainties) by using Monte Carlo simulation to calculate pressures for multiple realisations of nodal demands. In Steffelbauer and Fuchs-Hanusch [78], the authors solved the problem for different numbers of sensors ranging from two to ten (the study by Steffelbauer et al. [79] was limited to four sensors) taking into account different strengths of uncertainties. One of the main findings was that incorporating uncertainties leads to very different optimal placements than without uncertainties. Indeed, without uncertainties the algorithm tended to place sensors in regions with high demand uncertainties spread over the whole system. With high strength uncertainty, on the other hand, the sensors tended to be clustered “too much” in regions with low demand uncertainties, thus indicating that points which are sensitive to leaks/bursts are also likely to be points which are most sensitive to demand variations and, hence, not ideal locations to place sensors at. Worth of note in this study is also the fact that the authors derived a cost-benefit function to describe the relation between the number of sensors and the leak/burst localisation quality. The main reason for this was to provide water companies with a methodology to answer the question of how many sensors are needed to identify a specific number of leak/burst scenarios correctly. They found that the simple cost-benefit function they derived follows a power law. That is to say, for a linear improvement of the localisation quality, the number of sensors has to double. Furthermore they observed that the power law behaviour still applies even if demand uncertainties are accounted for. The only difference to simulations without uncertainties is that the localisation quality for a placement with a particular number of sensors decreases as the strength of the uncertainty increases.
A further interesting investigation into the issue of demand uncertainty can be found in Puleo et al. [80]. In this study, the authors proposed an “identifiability analysis” [81] method that makes use of the Fisher information matrix to select points that are sensitive to leaks/bursts and also provide less correlated measurements under uncertain demands. They performed Monte Carlo simulations whereby demand was randomly drawn from a normal distribution and, through limited tests on a small synthetic network (i.e. Apulian – see [82]), found that their method was not affected by the demand uncertainties.
3.2 Measurement Uncertainties
Pressure and flow sensors are the primary devices to monitor WDSs, and data coming from these devices can potentially enable timely and reliable leak/burst event detection and localisation. However, these sensors are subject to measurement errors associated with any measuring device. Differences between measured and expected data are at the core of many optimal sensor placement techniques. As uncertainties in using measured values due to the possible range of errors for these devices exist, the difference between measured and expected data must exceed the measurement error to be considered an “anomaly”. In this context, “anomalies” caused by small leaks/bursts may be difficult to identify. Furthermore, as leaks/bursts may occur at any location in a network, a leak/burst occurring farther away from a sensor may result in small variations in the signal recorded by that sensor. In view of all this, it is important to investigate if sensor placements obtained using assumptions of perfect sensors’ measurements would perform suboptimally when implemented in real-life WDSs.
A small number of studies found in the literature have considered the sensors’ accuracy as a key component of their methodology. For example, Wu and Song [49] and Forconi et al. [83] used the sensors’ accuracy as a threshold to discriminate between detections and non-detections. A few other studies have attempted to build robustness to measurements uncertainties by accounting for noisy measurements in their optimal sensor placement frameworks (e.g. [39, 75]). The work by Raei et al. [84], on the other hand, attempted to investigate this issue as its primary aim. The authors proposed to solve the sensor placement problem by using a multi-objective optimisation framework. They explored the effect of measurements uncertainty on the selection of sensor locations by identifying alternative non-dominated fronts for different values of sensor accuracy and then selected the final sensor placement from those non-dominated fronts. The sensor placement problem formulation presented in this study is based on sensitivity to leaks/bursts that are simulated at all potential nodes in a network (note that the absolute error is used in this study) and solved using the Non-dominated Sorting Genetic Algorithm-II (NSGA-II – see [85, 86]) to explore trade-offs between the minimisation of the number of sensors to be deployed and the detection time (i.e. from leak/burst start time to the time at which one sensor out of the set of sensors registers a pressure difference that is larger than an error threshold) objectives. The authors tested their approach on the C-town (see [87]) synthetic network considering a perfect model. The result obtained showed that the detection times increase as the sensor accuracy decreases. However, the sensor uncertainties did not seem to greatly affect the placement of the sensors. Worth of note in this study is also the fact that the authors proposed to simulate leaks/bursts that start at different times during the day by discretising the demand patterns into four clusters. Bearing in mind that the authors stressed that this discretisation was only necessary to mitigate the computational burden that would be faced if leaks/bursts were allowed to start at every time step of a hydraulic simulation, their attempt to account for more realistic leak/burst modelling assumptions is valuable and highlights a further source of uncertainty that has been somehow neglected by optimal sensor placement studies.
3.3 Sensor and Communication Failures
Sensor networks are exposed to failure conditions, such as sensor malfunctions and communication system failures. In the current hyperconnected world, for example, cyberattacks are now a major risk for sensor and communication malfunctions/failures [88]. Therefore, a sensor network’s robustness should be considered for the reliable provision of informative sensor data. A sensor network’s robustness should be considered at the design stage because the overall information gain and, hence, the effectiveness of the sensor network should be assessed as a whole. Despite the information gain varies for different locations, information gains from data collected at some locations can compensate for those at other locations [89].
The vast majority of optimal sensor placement methods that can be found in the literature have assumed that all sensors perform without any failure. However, this assumption is not realistic and may result in the design of a sensor network that performs poorly when the network is partially impaired (e.g. a sensor fails).
In the above context, Jung and Kim [89] proposed a leak/burst detection approach similar to that proposed by Hagos et al. [52] but that builds on that work by (1) using the NSGA-II for multi-objective optimal sensor placement and, most significantly, by (2) introducing a further criterion in that optimisation, namely, the maximisation of the robustness of a sensor network given a predefined number of sensors. The authors defined the sensor network’s robustness as its ability to consistently provide quality data in the event of sensor failure. Individual sensor failures were considered in that study, and a coefficient of variation of the rate of correct detections in the event of a sensor failure was used to assess the variation in performances of the subsets of a given set of sensors. The authors tested this method on the same synthetic network used in Hagos et al. [52], performed experiments with very similar settings and considered a similar number of pressure and flow sensors to be independently deployed. By accounting for robustness of a sensor network, quite different sensor placements were proposed, thereby confirming that a sensor network’s robustness should be considered at the sensor network’s design stage.
3.4 Use of Flow Sensors
While pressure sensors are still cheaper than flow sensors, the price difference has considerably lowered over the past years. For example, collecting flow data is now possible via insertion sensors using through bore hydrants (which, however, typically have lower accuracy than the full bore electromagnetic flow sensors normally used at a DMA inlet). Through the use of insertion sensors, the costs for excavation, pipe cut-out, installation of valves, backfilling and pavement work and the potential need to temporary decommission parts of the WDS can be avoided. Bearing this in mind, flow and pressure sensors in WDS work differently. Flow measurements are sensitive to all downstream changes, while pressure measurements are sensitive to additional head loss on the flow route to them – thus generally more sensitive to events local to the instrument, both up and down stream of the instrument. Flow data is also generally via pulse counting systems providing an average value over a time period (e.g. 15 min) generating smoothed data with good confidence, while pressure data is generally an instantaneous value including noise and variability [14, 90]. Therefore, using additional flow instrumentation should hypothetically improve the performance of optimal sensor placement methods that only use additional pressure sensors. However, in the literature there has been less analysis of the simultaneous optimisation of the locations of both pressure and flow sensors for leak/burst event detection and localisation.
In the above context, worth of mention is the work by Imschoot et al. [91]. The authors utilised an approach very similar to that presented in Farley et al. [30, 33] for event detection and in Farley et al. [11, 34] for achieving selective sensitivity. However, they incorporated data from not only pressure but also flow sensors to detect and localise leaks/bursts. The authors populated two sensitivity matrices, one for flow and one for pressure, used an absolute error rather than a chi-squared formulation (as the latter is not applicable to simulated flow measurements that could be null or negative) and considered a more conservative (than using an uncertainty band) safety factor that simply shifts the threshold (the mean of the values in each sensitivity matrix) used to binarise the matrices to a higher limit. They then performed a complete enumeration search of these matrices using a fitness function that aims at finding optimal solutions for the placement of one or two additional sensors that results in similarly sized subdivided areas. The authors tested their method on two UK DMAs assuming a perfect model and no measurements uncertainty and found that (as a general tendency) placing optimal flow sensors plus the inlet flow sensor seems to provide better results than the flow sensor at the DMA inlet with optimally placed pressure sensors.
Findings similar to those reported by Imschoot et al. [91] have also been recently presented in Raei et al. [92] whereby the authors observed that, despite the use of pressure sensors having clear benefits in improving leak/burst detection rates, the impact of pressure sensors in improving those rates diminishes quickly as the number of flow sensors increases. Overall, these initial findings seem to suggest that further development of sensor placement methods that attempt to simultaneously use pressure and flow sensors for leak/burst detection and, most importantly, localisation is needed. However, despite what stated at the beginning of this section with regard to costs, these methods could/should be further developed to also account for the differences in costs and budget constraints. Bearing this in mind, accounting for differences in costs has been attempted in studies such as those presented in Candelieri et al. [59] and Jung and Kim [93], for example, but a more thorough analysis framework for dealing with these issues would be beneficial to water companies.
3.5 Accounting for Risk
A potential drawback of all the optimal sensor placement approaches reviewed so far is that they tend to treat all leaks/bursts in the network equally – i.e. without considering the potential impact they may have on customers, for example. In real-life circumstances, a water company may decide to favour sensor placements that ensure quick detection and localisation of events that may have a major impact on nearby customers (e.g. cause local road or property damage) and especially if the customers in question are sensitive/critical (e.g. hospitals).
In Forconi et al. [83], three different risk-based functions were used to derive optimal placements of a given number of sensors in a WDS: a simple function based on likelihood of leak/burst non-detection and two other risk-based functions, where impact and exposure/vulnerability are combined with the leak/burst detection likelihood. The impact is measured by the effects of a leak/burst occurrence on the demands (i.e. volume of undelivered water), while the exposure/vulnerability is measured by the intrinsic importance of the elements that can be damaged (by assigning higher weights to certain nodes). This method therefore enables to take into account social, economic and/or safety considerations. The results obtained showed that accounting for risk can lead to significantly different sensor placements. In this context, the methodology proposed in this study can represent a useful tool for the WDS’s managers for placing sensors in the network in order to not only detect and localise leaks/bursts but to also comply with hydraulic, social and economic requirements.
Venkateswaran et al. [94] presented a good example of work that focus on refining the means of estimating the likelihood and impact components of risk (i.e. one of the most important issues in risk-based approaches). In that study, the authors proposed an approach to model and quantify the real-world impact of a leak/burst event on a community using various geospatial, infrastructural and societal factors. Specifically, they modelled the vulnerability of a community to flooding by simulating the propagation of water from a leak/burst along the surrounding terrain using a hydrodynamic flood simulation algorithm. They also partitioned the community into regions (driven by flood maps, which depend on the terrain) and determined the relative criticality of these regions by assigning scores based on the population density as well as the critical infrastructure (e.g. healthcare, transportation, government facilities, educational, etc.) present within each region. The sensor placement algorithms they developed, however, are greedy type (i.e. algorithms that solve the problem by placing one sensor and find the next sensor position through incorporation of the previous one), which have been shown to be likely to fail in finding optimal sensor placements [26, 78].
4 Discussion
Main characteristics of selected publications – primary objective (i.e. leak/burst detection or leak/burst detection and localisation) and problem formulation/solution
Detection/localisation | Problem formulation/solution | |
|---|---|---|
Farley et al. [30] | Detection | Threshold applied to the chi-squared matrix + complete enumeration (only two additional pressure sensors considered) |
Farley et al. [11] | Detection and localisation | Threshold and uncertainty band applied to the chi-squared matrix + optimisation using a GA |
Pérez et al. [31] | Detection and localisation | Threshold applied to the leak/burst sensitivity matrix + optimisation using a GA |
Casillas et al. [39] | Detection and localisation | Angle method to analyse the leak/burst sensitivity matrix + optimisation using a semi-exhaustive search/GA |
Sarrate et al. [42] | Detection and localisation | Structural model of a DMA + depth-first branch and bound search algorithm |
Sarrate et al. [44] | Detection and localisation | Structural model of a DMA + k-means clustering + depth-first branch and bound search algorithm |
Wu and Song [49] | Detection | Threshold based on the accuracy of sensors + optimisation using a GA in the Darwin optimization framework |
Hagos et al. [52] | Detection | Statistical process control + linear programming for the optimisation |
Huang et al. [57] | Detection | Influence coefficient matrix + fuzzy self-organising map neural network clustering |
Candelieri et al. [59] | Detection and localisation | Spectral clustering + support vector machines classification |
Boatwright et al. [63] | Detection and localisation | Spatially constrained version of the inverse distance weighted geospatial interpolation technique + optimisation using the GALAXY multi-objective evolutionary algorithm |
Blesa et al. [73] | Detection and localisation | Projections calculated from the extended sensitivity matrix + two-step hybrid methodology combining evidential c-means clustering algorithm and an exhaustive search |
Casillas et al. [75] | Detection and localisation | Leak signature space method + optimisation using a GA/PSO |
Steffelbauer and Fuchs-Hanusch [78] | Detection and localisation | Angle method between the general sensitivity of potential measurement points with respect to all possible leak scenarios and residual vectors + optimisation using a GA |
Puleo et al. [80] | Detection | Identifiability analysis |
Raei et al. [84] | Detection | Threshold based on the accuracy of sensors and ranking applied to the absolute error matrix + optimisation using the Non-dominated Sorting Genetic Algorithm-II |
Forconi et al. [83] | Detection | Threshold based on the accuracy of sensors + ranking using the Max-Sum method [95] |
Main characteristics of selected publications – hydraulic solver used, demand-/pressure-driven formulation, use of single/extended period simulations and choice of leak/burst simulation method
Hydraulic solver used | Demand-/pressure-driven | Single/extended period | Leak/burst simulation method | |
|---|---|---|---|---|
Farley et al. [30] | AQUIS | Not mentioneda | Extended period | Emitter at nodes |
Farley et al. [11] | AQUIS | Not mentioneda | Extended period | Emitter at nodes |
Pérez et al. [31] | PICCOLO | Demand-driven | Single period | Additional demand at nodes |
Casillas et al. [39] | EPANET | Not mentioneda | Extended period | Emitter at nodes |
Sarrate et al. [42] | N/A | N/A | N/A | Not mentionedb |
Sarrate et al. [44] | EPANET | Not mentioneda | Single period | Not mentionedb |
Wu and Song [49] | WaterGEMS | Not mentioneda | Not mentionedc | Emitter at nodes |
Hagos et al. [52] | EPANET | Not mentioneda | Extended period | Emitter at nodes |
Huang et al. [57] | Not mentioned | Not mentioneda | Single period | Additional demand at nodes |
Candelieri et al. [59] | EPANET | Pressure-driven [96] | Not mentionedc | Emitter on pipes [96] |
Boatwright et al. [63] | EPANET | Demand-driven | Single period | Emitter at nodes |
Blesa et al. [73] | EPANET | Not mentioneda | Not mentionedc | Emitter at nodes |
Casillas et al. [75] | EPANET | Not mentioneda | Extended period | Emitter at nodes |
Steffelbauer and Fuchs-Hanusch [78] | OOPNET | Not mentioneda | Not mentionedc | Emitter at nodes |
Puleo et al. [80] | EPANET | Not mentioneda | Not mentionedc | Emitter in the middle of pipes |
Raei et al. [84] | EPANET | Demand-driven | Extended period | Emitter at nodes |
Forconi et al. [83] | EPANET | Pressure-driven | Extended period | Emitter in the middle of pipes |
Main characteristics of selected publications – accounting for model uncertainty, measurements uncertainty and choice of using a single leak/burst size or multiple leak/burst sizes in the proposed optimal sensor placement frameworks
Model uncertainty | Measurements uncertainty | Leak/burst magnitude – single/multiple | |
|---|---|---|---|
Farley et al. [30] | No | No | Multiple – but one at a time |
Farley et al. [11] | No | No | Single |
Pérez et al. [31] | No | No | Single |
Casillas et al. [39] | No | Yes – incorporated in the placement method | Multiple – incorporated in the placement method |
Sarrate et al. [42] | No | No | Single |
Sarrate et al. [44] | No | No | Single |
Wu and Song [49] | No | No | Multiple – performed Monte Carlo simulations |
Hagos et al. [52] | Yes – demand uncertainty; introduced as random noise | No | Multiple – considered the emitter discharge coefficient as a random variable |
Huang et al. [57] | No | No | Single |
Candelieri et al. [59] | No | No | Multiple – varying in a given range |
Boatwright et al. [63] | No | No | Single |
Blesa et al. [73] | Yes – inflows variations; incorporated in the extended sensitivity matrix | No | Multiple – varying in a given range |
Casillas et al. [75] | No | Yes – incorporated in the placement method | Multiple – incorporated in the placement method |
Steffelbauer and Fuchs-Hanusch [78] | Yes – demand uncertainty; performed Monte Carlo simulations and used 4 different strength of uncertainty | No | Single |
Puleo et al. [80] | Yes – demand uncertainty; performed Monte Carlo simulations | No | Single |
Raei et al. [84] | No | Yes – incorporated in the placement method | Multiple – varying in a given range |
Forconi et al. [83] | No | No | Single |
Main characteristics of selected publications – details of the case study network(s) and methodology validation through field trials
Case study network(s) | Field validation | |
|---|---|---|
Farley et al. [30] | 2 × real-life: Dendritic UK DMA – 260 nodes Looped UK DMA – 86 nodes | No |
Farley et al. [11] | 14 × real-life: UK DMAs – 204–1,091 nodes; ~6.3–36 km of pipes | Yes – simulated bursts in 3 DMAs |
Pérez et al. [31] | Real-life: Placa del Diamant, Barcelona WDS, Spain – 1,600 nodes; ~41 km of pipes | No |
Casillas et al. [39] | Synthetic: Hanoi, Vietnam – 31 nodes; 34 pipes Real-life: Limassol, Cyprus – 197 nodes; 239 pipes | No |
Sarrate et al. [42] | Real-life: DMA, Barcelona WDS, Spain – 883 nodes (31 considered as possible sensor locations); 927 pipes; ~17.4 km of pipes | No |
Sarrate et al. [44] | Real-life: DMA, Barcelona WDS, Spain – 883 nodes (311 considered as possible sensor locations, 31 clusters); 927 pipes; ~17.4 km of pipes | No |
Wu and Song [49] | 2 × real-life: UK DMA – 1,321 pipes United Arab Emirates – 86 pipes | No |
Hagos et al. [52] | Synthetic: modified Austin – 125 nodes; 90 pipes | No |
Huang et al. [57] | Real-life: DMA – 77 nodes; 108 pipes | No |
Candelieri et al. [59] | Real-life: Timisoara, Romania – 335 nodes; ~4 km of pipes | No |
Boatwright et al. [63] | Synthetic: Bakryan – 35 nodes; 58 pipes; ~102 km of pipes | No |
Blesa et al. [73] | Synthetic: small benchmark – 12 nodes; 17 pipes; ~102 km of pipes Real-life: DMA, Barcelona WDS, Spain – 883 nodes (311 considered as possible sensor locations, 25 clusters); 927 pipes; ~17.4 km of pipes | No |
Casillas et al. [75] | Synthetic: Hanoi, Vietnam – 31 nodes; 34 pipes Real-life: Limassol, Cyprus – 197 nodes; 239 pipes | No |
Steffelbauer and Fuchs-Hanusch [78] | Real-life: DMA – 392 nodes; 452 pipes; ~37 km of pipes | No |
Puleo et al. [80] | Synthetic: Apulian – 23 nodes; 34 pipes | No |
Raei et al. [84] | Synthetic: C-town – 388 nodes; 429 pipes | No |
Forconi et al. [83] | Real-life: E023 DMA, Harrogate, Yorkshire, UK – 448 nodes (291 considered as possible sensor locations); 468 pipes; ~16 km of pipes | No |
By scrutinising these tables and in the light of the literature review carried out in Sects. 2 and 3, a number of considerations regarding, inter alia, the state of the art of optimal sensor placement techniques, the potential of these techniques to help water companies minimising the leaks/bursts’ runtime by effectively detecting and localising these events as they occur in a DMA and the gaps in the current research can be made. These considerations are detailed below.
Notwithstanding the individual contributions to the body of knowledge in the field made by studies that have focused on optimal placement of pressure sensors for leak/burst detection only, it is possible to observe that such studies have limited value for water companies when considering the aim of minimising the leaks/bursts’ runtime. Indeed, studies such as Hagos et al. [52] noted that the majority of optimally located pressure sensors in a network tend to detect the same set of leaks/bursts and, thus, they provide little information on where a leak/burst may be located. Furthermore, Farley et al. [11] noted that if pressure sensors were to be used solely to detect leak/burst events, the issue of false alarms would be of concern. In that study, the authors observed that false alarms are more common when using pressure time-series values for detection, as pressure fluctuates much more than the flow in the system. Similar/related observations have been made by a number of other researchers. For example, as already mentioned in Sects. 2 and 3, Hagos et al. [52] observed that the best pressure sensor locations for detection are not likely to be the best locations for minimising the rate of false alarms and that, as the number of pressure sensors in the DMA increases, the rate of false alarms increases, thus exacerbating the problem; Steffelbauer and Fuchs-Hanusch [78] stated that pressure sensor locations that are sensitive to leaks/bursts are also likely to be locations that are most sensitive to demand variations and, hence, not ideal locations to place sensors at. Mounce et al. [14] also reported that flow signals are much more reliable for leak/burst event detection than pressure signals. In view of this, it is envisaged that future optimal sensor placement studies should focus on simultaneously considering the possibility of detecting and, most importantly, localising leaks/bursts. In this scenario, flow measurements (usually available at the inlet of DMAs already) can be used first to determine detection, and the pressure instruments can then be used to determine location in addition to provide further confidence in the detection alarms (see – e.g. [16]) and to provide information useful for root-cause identification (e.g. a flow increase and a simultaneous pressure decrease can indicate a leak/burst in a DMA, whereas a simultaneous flow and pressure increase can indicate a different issue such as a pressure reducing valve failure).
With regard to the problem formulation and with specific focus on the use of hydraulic simulation packages, it is possible to state that using hydraulic models to simulate a large number of leak/burst scenarios and then (somehow) analysing the differences between the simulated pressures under leak/burst conditions and the simulated pressures recorded under normal conditions are common practices among researchers and, possibly, the only way forward. Methods that have attempted to avoid using hydraulic models such as the structural model-based approach proposed by Sarrate et al. [42, 44] have intrinsic limitations (see Sect. 2) that make their use difficult for effectively solving the optimal sensor placement for leak/burst detection and localisation problem. Therefore, it is clear that numerical models are instrumental to the future of cost-effective monitoring of WDSs for leak/burst detection and localisation purposes. Unfortunately, the numerous sources of uncertainty associated with such an approach remain a key concern. Temporarily ignoring these issues here together with issues related to increasing the complexity of the problem formulation (and, hence, the computational burden), as they will be discussed in further detail below, it is envisaged that more realistic modelling practices should be taken into consideration during the development of optimal sensor placement methodologies in the future. For example, it may be beneficial to use pressure-driven modelling rather than demand-driven modelling as leaks and bursts may induce pressure-deficient conditions in a network under certain circumstances. Additionally, better leak/burst localisation performance may be achieved by more realistically simulating leaks and bursts, which may occur at any point along the pipe (and not at nodes, as commonly done) and start at any time during the day.
With specific focus on the analysis of the differences between the simulated pressures under leak/burst conditions and the simulated pressures recorded under normal conditions, it is possible to observe that the development of different approaches for performing this particular task has attracted the attention of a large number of researchers. Generally speaking, binarisation of the residuals/sensitivity matrix (e.g. [11, 30, 31, 49]) has been recognised as leading to a loss of information [38]; therefore methods that make full use of the hydraulic simulation results (e.g. [39, 63, 73, 75, 78]) should be preferred. Many of the latter methods have been developed with the aim of addressing issues related to model, measurements and leak/burst size uncertainties, and they are very valuable for future research. The main findings from these studies have shown that different operating point scenarios and demand uncertainties may significantly affect the performance of “optimal” sensor placements if these factors are not carefully accounted for in the sensor placement methodologies. On the other hand, measurements uncertainties and uncertainties related to the leak/burst size have a much lesser impact on the optimal sensor placements. Having said this, it is envisaged that the influence of other model uncertainties such as uncertain pipe friction factors and other model-reality divergences on optimal sensor locations should be explored further.
With specific focus on the methods used to solve the optimal sensor placement problem, it can be observed that the optimal sensor placement problem has been often solved through optimisation. Complete enumeration techniques (see – e.g. [30]) or semi-exhaustive search routines utilising a lazy evaluation mechanisms to reduce the computational cost (see – e.g. [39]) have clearly shown not to scale up well as the number of sensors to be deployed, the size of the studied network and the complexity of the problem formulation, among the others, increase. GA, on the other hand, has shown the potential to be efficiently used to solve carefully formulated problems in small- to medium-sized networks. They have also been shown to outperform algorithms such as PSO in terms of quality of the sensor placements obtained (see [74, 75]). However, given the extremely large solution spaces which are typically present when real-life networks and assumptions are considered, their limitations in terms of the computational time required to obtain a solution (by not just exploring a small part of the total solution space) have also been highlighted by several researchers (see – e.g. [74, 75, 78]). Notwithstanding the fact that several researchers have attempted to reduce the size of the solution spaces/complexity of the optimisation problem using clustering techniques (as discussed in further detail below), it is envisaged that experiments with other, potentially more efficient, optimisation techniques should be carried out. Having said this, another relevant issue highlighted by researchers is the need for accurate tuning of the GA algorithms’ parameters. Therefore, the use of algorithms that are able to automatically adjust their hyper-parameters such as the hybrid GALAXY multi-objective evolutionary algorithm used by Boatwright et al. [63] may be beneficial. In addition to all this, investigations into the possibility of using parallel computing in a multi-core processor framework and high performance computing should be carried out to effectively enable considering real-life networks and assumptions and obtain a solution in a reasonable (bearing in mind that identifying an optimal sensor placement is a task that, in general, needs to be only carried out at the sensor network’s design stage) time.
With regard to the use of clustering algorithms and as briefly anticipated in the previous paragraph, several researchers have experimented with such methods with the aim to reduce the size of the solution space/complexity of the optimisation problem (e.g. [44, 73]). Valuable contributions were demonstrated in this respect, and, thus, further investigations into the potential of such methods to help solve the optimal sensor placement problem in an efficient and effective way should be carried out. Bearing this in mind, clustering algorithms have also been proposed by some researchers (e.g. [57, 59]) for solving the sensor placement problem on their own (i.e. without coupling clustering algorithms with GAs/semi-exhaustive search routines/etc.). Such an approach has been criticised by Sarrate et al. [44, 47] who argue that it may lead to suboptimal results. However, it should not be possible to deprecate the use of this approach based on that critique alone. Having said this, a further concern relevant to the use of clustering algorithms on their own may be the fact that the majority of optimally located pressure sensors in a network tend to detect the same set of leaks/bursts (i.e. the observation by [52], already mentioned above). In this regard, it could be argued that clustering algorithms, if used on their own, may struggle to provide information useful for enabling efficient leak/burst localisation.
Some of the optimal sensor placement methods that can be found in the literature utilise a different method for determining the instrumentation locations and for localising leaks/bursts (e.g. [11, 34, 91]). It is clear that this approach implies that the resulting sensor placements will not be optimised for the chosen method of leak/burst localisation. Therefore, it is envisaged that tightly coupled optimal sensor placement and leak/burst localisation frameworks should be developed by researchers in the future. Leak/burst localisation and sensor placement should be considered together since the best placement depends on the method that is used to localise the potential leaks/bursts and the efficiency of the leak/burst localisation depends on the sensor placement.
Much greater attention should be paid in the future to the issue of sensor/communication failures as this is of critical importance for the effectiveness of optimal sensor placements for leak/burst detection and localisation. In Sect. 2, it was noted that the use of the method proposed by Farley et al. [11, 34] would make the task of correctly localising a leak/burst impossible if a single sensor is not working or data are not timely received. Bearing this in mind, similar considerations could be made for the majority of the reviewed optimal sensor placement methods for leak/burst detection and localisation as they have been developed under the unrealistic assumption that all the sensors perform without any failure at all times. In this context, the methodology proposed by Boatwright et al. [63] may offer a potentially appealing way to mitigate the issue under scrutiny. Indeed, geostatistical interpolation techniques are less reliant on the availability of data from all the optimally deployed sensors when performing leak/burst localisation than methods that are based on assessing the similarities between the observed residuals and the results of hydraulic simulations, for example. Based on similar arguments, it may be possible to state that the use of geostatistical interpolation techniques could also be beneficial for mitigating some of the issues that arise because of model and measurements uncertainties. Indeed, a resulting interpolation surface created by using observed pressure measurements (which provides inferred values of pressure at every point in a network) attempts to mimic the results of a hydraulic simulation but without the reliance on an accurate hydraulic model/good measurements fed into a hydraulic model.
Methods for the optimal placement of pressure and flow sensors simultaneously should also be the focus of further research and development in the future. This is because early studies (e.g. [91]) have indicated that using additional flow instrumentation can improve the leak/burst detection and localisation performance of optimal sensor placement methods that only use additional pressure sensors. Due to the higher costs associated with obtaining flow measurements, however, these methods could/should also account for the differences in costs and budget constraints and balance all this with the additional benefits that could be realised.
It is envisaged that optimal sensor placement methods should also account for risk as, while detecting and localising all leaks/bursts is important, not all leaks/bursts are equally impactful. Nowadays, the resulting potential unplanned interruptions to the water supply and the damaging consequences of the leak/burst events are tolerated to a lesser extent, and water companies are increasingly judged by the public (and the regulatory agencies alike, where applicable) based on how well (or otherwise) they manage contingency situations. In this context, future work on this subject should focus on further refining the means of estimating the likelihood and impact components of risk.
The literature review carried out in this chapter has highlighted that different methods, the inclusion of different objectives in similar methods and even slightly changing specific settings within the same method (e.g. incorporating different strengths of uncertainty) lead to significantly different sensor placements. Despite measures for the assessment of performance being found in the literature, the majority of these measures are tailored to the particular method being proposed. All this makes the task of assessing whether a sensor placement is better that another sensor placement almost impossible. Bearing this in mind, optimal sensor placement research is pressingly in need for field trials and validation, which are the only way to understand the real value and practicality of a proposed approach. In the relevant literature, only the studies by Farley et al. [11, 33, 34] and Fuchs-Hanusch and Steffelbauer [97] report the results of field trials and validations. The main findings from the field trials carried out in the studies by Farley et al. [11, 33, 34] have been detailed in Sect. 2. These findings demonstrated the practical applicability of the methods proposed in those studies. On the other hand, in Fuchs-Hanusch and Steffelbauer [97], a comparison of several methods including the methods proposed by Pérez et al. [31], Casillas et al. [39] and Steffelbauer and Fuchs-Hanusch [78] was carried out by opening fire hydrants to simulate different leak/burst scenarios in a real network and then assessing the leak/burst localisation capabilities of the different methods by calculating the distance between the suggested leak/burst locations and the opened fire hydrants. The results from the limited tests carried out in that study showed that for different leak/burst positions, different sensor sets, mainly those with sensors close to the leak/burst position, led to the best performance. These quite disappointing findings cast a shadow on the real value of the various “optimal” sensor placement methods that have been proposed so far and demonstrated using numerical simulations only, therefore stressing even more the need for any future optimal sensor placement study to be thoroughly field validated in real-life networks. It is envisaged that, as a bare minimum, future optimal sensor placement studies should include an assessment of their underlying capabilities using a set of common quantitative metrics which may include/take inspiration by those recently proposed by Qi et al. [98]. In this context, the use by researchers in the field of a common set of benchmark models that cover a range of network layouts/sizes/etc. and a common set of leak/burst scenarios could also be beneficial.
5 Conclusions
Future optimal placement of pressure sensors studies should focus on simultaneously considering the possibility of detecting and, most importantly, localising leaks/bursts.
Hydraulic models are instrumental to the future development of cost-effective sensor placement techniques for leak/burst detection and localisation purposes. Adoption of more realistic hydraulic modelling practices such as considering pressure-driven modelling, for example, is envisaged.
Sensor placement methods that make full use of the hydraulic simulation results, as opposed to methods that involve binarisation of the residuals/sensitivity matrix, should be preferred. Further development of these methods to more effectively deal with the various sources of uncertainties is envisaged, especially for model-reality divergences that have not been considered by researchers so far.
Research into the use of other (as opposed to the techniques used so far), potentially more efficient, optimisation techniques to solve the sensor placement for leak/burst detection and localisation problem should be carried out. This research should favourably look into algorithms that are able to automatically adjust their hyper-parameters and into the possibility of using parallel and high performance computing.
Further investigations into the potential of using clustering algorithms coupled with optimisation techniques (as opposed to clustering algorithms used on their own) to reduce the size of the solution space/complexity of the sensor placement problem should be carried out.
Tightly coupled optimal sensor placement and leak/burst localisation frameworks should be developed by researchers in the future as an optimal placement depends on the method that is used to localise the potential leaks/bursts and the efficiency of the leak/burst localisation depends on the sensor placement.
Much greater attention should be paid by researchers in the future to the issue of sensor/communication failures as this is of critical importance for the effectiveness of optimal sensor placements for leak/burst detection and localisation. Research into the use of artificial intelligence-type and (geo)statistical techniques with the potential to mitigate this issue and issues related to the use of imperfect hydraulic models should also be carried out.
Methods for the optimal placement of pressure and flow sensors simultaneously should also be the focus of further research and development in the future as using additional flow instrumentation can improve the leak/burst detection and localisation performance. In this context, the developed methods should carefully account for cost-benefit considerations as, because of the higher costs associated with obtaining flow measurements, including such considerations becomes even more important than it currently is.
Future optimal sensor placement methods should also account for risk in order to be of even more value to water companies. Further research into refining the means of estimating the likelihood and impact components of risk should be carried out.
Future optimal sensor placement studies should strive to incorporate results from field demonstrations as this is the only way to ultimately assess the actual capabilities of a proposed approach. Where this is not possible, future studies should at least include an assessment of their underlying capabilities using a set of common quantitative metrics, benchmark models and leak/burst scenarios.
Although optimal sampling design for leak/burst detection and localisation has been the focus of this review, researchers and practitioners interested in this topic should also look at macro-location of sensors in the wider context of WDSs management (i.e. look at optimal sampling design techniques developed for the numerous other optimisation agendas such as detection of contamination events). Indeed, elements of research conducted for other sampling design purposes are conceptually applicable to frameworks aimed specifically at optimal sampling design for leak/burst detection and localisation. Most notably, the optimisation approaches and algorithms developed for (or merely implemented in) the wider sampling design literature are distinct from the objectives to which they are applied.
In addition to all of the above, it is also worth highlighting the fact that with the rise of easy-to-use and low-cost sensing devices, Internet of Things (IoT) technologies and edge analytics an increase in the density of heterogeneous sensors deployed in WDSs may be expected in the near future. In this scenario, pressure and flow devices will be part of a much wider network of sensors. Therefore, considerations regarding issues that have been the focus of research in the broader wireless sensor networks’ literature, such as reliable communications, efficient routing protocols, power management and computation/communication overhead, to mention just a few, will need to be accounted for when developing optimal sensor placement techniques for leak/burst detection and localisation in WDSs [99].
Finally, it must be noted that in this review the requirements for additional instrumentation have been looked at in the context of WDSs subdivided in DMAs. The rationale for this is that many of the optimal sampling design techniques for leak/burst detection and localisation found in the literature have been developed and tested under the “DMAs existence” assumption. This, in turn, is probably due to the fact that DMAs are seen as ground zero data-wise on the water companies’ journey towards operating smart water networks [100]. As evidenced by the fact that, over the past two decades, a number of technology vendors have aligned their business models based on the data flows captured or technologies required by a DMA approach, many water consultancies have implemented their DMA-dependent water balance methodologies around the world, and major industrial players have tailored products for managing sectorised networks [100]. Having said all this, however, the “DMA model” (led by UK water companies) only proliferates in Europe while gradually been adopted in countries such as Singapore, Chile, Brazil and Australia. The “non-DMA model”, on the other hand, represents the bulk of the world’s WDSs, and it proliferates in the USA as well as Germany and most of the developing world [100]. From the “non-DMA model” perspective, it may not be cost-effective or even practical to subdivide a WDS into DMAs. Therefore, the development of further optimal sampling design techniques for leak/burst detection and localisation should bear the global situation in mind and be pursued independently by the existence (or otherwise) of DMAs, which does not seem to be a strict requirement for this task. Furthermore, it is worth mentioning that this task may perhaps also be facilitated by the fact that, in recent years, the Virtual DMAs (V-DMAs) concept has started to come to fruition as data from a suite of technologies such as insertion, ultrasonic and acoustic flow metering and smart customer meters has started to be leveraged on a larger scale.