Pressure sensor placement for water distribution network calibration based on graph-theoretic approaches

The optimal location of pressure sensors is typicallysolved using heuristic algorithms. Non-dominated Sorting Genetic Algorithm II (NSGA-II) is one of the most used algorithms in the water industry, requiring a preliminary parameter tuning process. The lack of guidelines on how to tune model parameters generally limits the use of these algorithms by researchers or practitioners and, as such, fails to be used in real-life problems. The current paper explores different NSGA-II parameterizations for the optimal location of pressure sensors by using a multi-objective optimization methodology applied to a real distribution network. Results show that (i) both the uniform and simulated binary crossover operators (depending on the internal parameters) produce the best results, being the former recommended since it does not require further parameter tuning; (ii) polynomial mutation with lower probability value should be chosen; and (iii) the distribution indices of polynomial mutation have a minor effect on NSGA-II performance.

This study addresses complex multi‐objective optimization challenges in large‐scale, real‐world water distribution networks (WDNs). The primary objectives are to improve a water quality index (water age) and network resilience by optimizing pipe diameters and network topology as decision variables. The proposed approaches leverage the non‐dominated sorting genetic algorithm II (NSGA‐II) producing Pareto optimal alternatives for water utility decision‐makers. To enhance computational convergence runtime and solution quality of optimization, novel techniques are employed. These include advanced NSGA‐II constraint handling, search space reduction, graph theory‐based formulation of decision variables, constraints, and objective functions, as well as multi‐stage and hydraulic‐free optimization strategies. Furthermore, soft constraints are relaxed and integrated into Pareto decision‐making spaces to provide a comprehensive, multi‐criteria decision‐making framework. The approaches are applied to a real case study, and the results demonstrate optimization performance improvements, with efficiency increasing by approximately 20% (in terms of convergence speed). Additionally, water age is reduced by 52% while achieving favorable results in the hydraulic and topological criteria. These findings highlight the effectiveness of the proposed methodologies in addressing WDN optimization challenges.

Water distribution networks (WDN) model optimization is an important part of smart water systems to achieve optimal strategies. WDN optimization focuses on the nonlinearity of the discharge head loss equation, the availability of discrete properties of pipe sizes, and the conservation of constraints. Multi-objective evolutionary algorithms (MOEAs) have been proposed and successfully applied in the field of WDN design optimization. Previous studies have focused on comparing the optimization effects of algorithms in water distribution networks, ignoring the problems of unbalanced pressure distribution and water hammer at the nodes of the pipe network caused by the complex terrain in mountainous areas. In this paper, a multi-objective water supply optimization model that integrated cost, reliability, and water quality was established for a mountainous WDN in real engineering. The method of traversing the nodes to solve the water age was introduced to find a more scientific and practical water age solution model, with setting the weight function to evaluate the water age of the water supply model comprehensively. Strength Pareto Evolutionary Algorithm II (SPEA-II) and Non-dominated Sorting Genetic Algorithm II (NSGA-II) were adopted to optimize the WDN design model in the mountainous complex terrain. The significance levels of the number of Pareto solutions (NOPS) and running time are 0.029 and 0.001, respectively, indicating that the two algorithms have significant differences. Compared to NSGA-II, SPEA-II has a better convergence rate and running time in multi-objective water supply optimization design. The solution set distribution of SPEA-II is more concentrated than that of NSGA-II, also the numerical value is better. The number of SPEA-II optimization schemes is larger and the scheme is more effective. Among them, the Pareto solution set of SPEA-II can obtain more desirable optimization results on cost, reliability index (RI) and water age. In summary, the study provides valuable information for decision makers in WDN with complex terrain.

In this paper, a pragmatic approach for leakage detection and localization is presented to solve the problem introduced within the framework of the Battle of the Leakage Detection and Isolation Methods (BattLeDIM). The method is based on the application of the hydraulic model of the water distribution network and the comparison of simulated pressures against the corresponding values observed in field. In particular, it consists of two phases: (1) calibration of the hydraulic model of the network; (2) detection and localization of the leakages affecting the water distribution network through the application of engineering judgment and the adoption of an enumerative procedure. The method was applied to the case-study network of L-Town, enabling 16 of 23 leakages to be efficiently detected and 11 of these also accurately localized. The proposed method is simple and transparent and can aid water utilities in water leakage management.

Leakages in the water distribution networks (WDNs) are real problems for utilities and other governmental agencies. Timely leak detection and location identification have been challenges. In this paper, an integrated approach to geospatial and infrared image processing was used for robust leak detection. The method combines drops in flow, pressure, and chlorine residuals to determine potential water leakage locations in the WDN using Geographic Information System (GIS) techniques. GIS layers were created from the hourly values of these three parameters for the city of Sharjah provided by the Sharjah Electricity, Water, and Gas Authority (SEWA). These layers are then analyzed for locations with dropped values of each of the parameters and are overlaid with each other. In the case where there were no overlaying locations between flow and pressure, further water quality analysis was avoided, assuming no potential leak. In the case where there are locations with drops in flow and pressure layers, these overlaying locations are then examined for drops in chlorine values. If overlaying locations are found, then these regions are considered potential leak locations. Once potential leak locations are identified, a specialized remote sensing technique can be used to pinpoint the leak location. This study also demonstrated the suitability of using an infrared camera for leak detection in a laboratory-based setup. This paper concludes that the following methodology can help water utility companies in the timely detection of leaks, saving money, time, and effort.

In the first place, this paper presents an examination of the effects of missing cadastral information on the modeling and calibration of water distribution networks (WDN). For this purpose, cadastral errors were artificially introduced to the hydraulic models of the WDN of three cities of the province of Valle del Cauca (Colombia), with population in the range of 15,000–30,000 inhabitants. The cadastral errors were introduced by eliminating some pipes from the unaltered models using the resilience index as selection criterion. From this examination, typical responses observed during the calibration process were associated to specific topological and hydraulic errors and it was also noted that there is a direct relation between the resilience index and the effect of the removal of a certain pipe on the hydraulic performance of the model. In the second place, after identifying the effects of missing and erroneous cadastral and hydraulic information on the calibration of WDN models, the inverse procedure was carried out: the calibration process was used as a tool for detecting missing and erroneous cadastral and hydraulic information. This methodology was successfully applied to the WDN of Sector Estadio (250,000 inhabitants), which is a complex area of the city of Bucaramanga (Colombia); through the calibration of this WDN, errors such as failing water meters, pipes and valves that existed in the real system but were not in the model, significant errors in pipe diameters in the model, among others, were identified.

Given a water distribution network, where should we place sensors toquickly detect contaminants? Or, which blogs should we read to avoid missing important stories?.These seemingly different problems share common structure: Outbreak detection can be modeled as selecting nodes (sensor locations, blogs) in a network, in order to detect the spreading of a virus or information asquickly as possible. We present a general methodology for near optimal sensor placement in these and related problems. We demonstrate that many realistic outbreak detection objectives (e.g., detection likelihood, population affected) exhibit the property of submodularity. We exploit submodularity to develop an efficient algorithm that scales to large problems, achieving near optimal placements, while being 700 times faster than a simple greedy algorithm. We also derive online bounds on the quality of the placements obtained by any algorithm. Our algorithms and bounds also handle cases where nodes (sensor locations, blogs) have different costs.We evaluate our approach on several large real-world problems,including a model of a water distribution network from the EPA, andreal blog data. The obtained sensor placements are provably near optimal, providing a constant fraction of the optimal solution. We show that the approach scales, achieving speedups and savings in storage of several orders of magnitude. We also show how the approach leads to deeper insights in both applications, answering multicriteria trade-off, cost-sensitivity and generalization questions.

Various leakage detection algorithms have been proposed in the literature to pursue prompt leakage identification in water distribution networks using sensor data. Some use stochastic process control (SPC) methods, where the leak identification is considered an anomaly detection problem. However, several practical challenges emerge from SPC in leakage detection, including outliers, random fluctuations, and non-normally distributed and autocorrelated data. Here, we contribute a comparative analysis of seven advanced SPC techniques based on cumulative sum for leakage identification in water distribution networks, selected based on an extensive literature review of approximately 100 publications. We test their usability for leakage detection by integrating them into a state-of-the-art data-driven detection method and demonstrating them on the L-Town benchmark network. Ultimately, this study offers actionable recommendations to guide the selection of change point detection methods for leakage detection: our results indicate that transformations are best combined with robust statistics. Nonparametric and adaptive methods are suited to retrieve reliable alarms under heterogeneous conditions. Lastly, incorporating a decorrelation step improves the detection performance if irregular water demand patterns occur in the network.

The American infrastructure report card in 2013 rated the US water system infrastructure with grade of ‘D’. The Canadian infrastructure report card in 2012 stated that around 15.4% of Canada’s water infrastructure has a condition of fair to very poor. Thus, there is a critical need to develop efficient inspection, maintenance and rehabilitation plans for water distribution networks. However, such plans require an assessment tool to evaluate the performance and condition of water distribution networks. Therefore, the main purpose of this paper is to develop an integrated performance assessment model for water distribution networks. Two modules were developed to assess the performance of water pipelines and accessories, respectively. A third module was developed to assess the performance of water segments that includes pipelines and accessories. Moreover, a fourth module was built to assess the performance of each sub-network and the entire network based on the segments’ connection type using a reliability-based approach. To assess the performance of the water distribution network, the critical factors affecting its pipelines and accessories were identified and studied. The fuzzy analytic network process technique was used to obtain the importance weights of the identified factors.

Water distribution networks (WDNs) are a critical component of modern society, responsible for delivering water to local communities and industries while maintaining continuous, stable flow within the system, which carries low-grade hydropower potential. These systems are vulnerable to disruptive events, such as pipeline failures and water contamination. To mitigate the risk of disruption events, recent EU policies have focused on the digitalisation of critical infrastructure, including WDNs and wastewater treatment plants (WWTPs), through the integration of Internet of Things (IoT) technologies. Digitalisation enables system operators to collect real-time data and perform predictive maintenance, thereby improving resilience and operational efficiency. Thus, system electricity requirements will increase to support IoT and digitalisation retrofitting.This creates an opportunity to deploy energy-harvesting (EH) devices within WDNs and WWTP infrastructure that harness and utilise the resonant and kinetic energy inherent in water flow. Although the benefits of EH devices are often considered minimal and their energy outputs are low, EH devices are considered a viable power source for low-power sensors, such as pressure, contamination, and temperature sensors.This study proposes and applies a feasibility assessment framework to evaluate EH devices as an alternative, decentralised power source for IoT-enabled monitoring in WDNs. The framework includes technical performance analysis, economic viability, and environmental impact assessments, combined with probability-based resilience modelling. It uses case-specific hydraulic, operational, design, and economic data to quantify EH power outputs, assess the costs of design and deployment, evaluate the environmental footprint of the devices, determine sensor energy requirements, and assess system resilience across different deployment scenarios.Results demonstrate that the EH device has a mechanical power-generation capacity potential ranging from 0.049 to 36 watts, depending on the study location, flow conditions, and design characteristics. This EH generation capacity is sufficient to power pressure, contamination, and temperature sensors. The resilience modelling indicates that the detection probability of WDNs exhibits the most significant gains from adding sensors at low deployment levels. Thus, most of the improvement in detection levels occurs between deploying the first five to ten sensors; beyond this threshold, adding more sensors exhibits diminishing marginal returns to detection probability and system resilience. In addition, adding more sensors can significantly reduce system resilience by increasing power requirements, thereby placing excessive load on the power supply of the EH devices. Thus, it increases the risk of failure rather than enhancing resilience.Overall, the results underscore the importance of strategic sensor allocation over high-density deployment and of balancing monitoring coverage with energy availability. Furthermore, the results show that EH devices are suitable power-generation technologies for supporting the digitalisation of WDNs and informing the design of new monitoring systems and sensor placement to enhance system reliability, enable cost-effective monitoring, and maximise mitigation benefits. In addition, the proposed framework provides decision-makers with a structured approach to assessing EH integration applications for digitalised WDNs, focusing on enhancing resilience through monitoring, conducting technical performance and cost-benefit analyses, assessing environmental trade-offs, and designing monitoring strategies aligned with sustainability and resilience objectives.

Leaks in water distribution networks are estimated to account for up to 30% of the total distributed water; moreover, the increasing demand and the skyrocketing energy cost have made leak localization and adoption ever more important to water utilities. Each leak scenario is run on a simulation model to compute the resulting values of pressure and flows over the whole network. The values recorded by the sensors are seen as features of one leak scenario and can be considered as the signature of the leak. The key distinguishing element in this paper is to consider the entire distribution of data, representing a leak as a probability distribution. In this representation, the similarity between leaks can be captured by the Wasserstein distance. This choice matches the physics of the system as follows: the equations modeling the generation of flow and pressure data are non-linear. The signatures obtained through the simulation of a set of leak scenarios are non-linearly clustered in the Wasserstein space using Wasserstein barycenters as centroids. As a new set of measurements arrives, its signature is associated with the cluster with the closest barycenter. The location of the simulated leaks belonging to that cluster are the possible locations of the observed leak. This new framework allows a richer representation of pressure and flow data embedding both the modeling and the computational modules in a space whose elements are discrete probability distribution endowed with the Wasserstein distance. Experiments on benchmark and real-world networks confirm the feasibility of the proposed approach.

Detecting and mitigating leaks in water distribution networks are vital for water conservation. Machine-learning-based (ML) acoustic leak detection models were introduced as effective alternatives for leak management. However, ML model training requires sufficient labeled data, which hinders related development. To address this challenge, this study employed contrastive learning (CL) for leak detection using limited labeled signals. Experimental results indicate that flip-x and amplitude scaling are optimal combinations for contrastive learning. Besides, ablation and t-distributed stochastic neighbor embedding (t-SNE) results reveal that increasing the model depth does not always yield performance improvement, and five convolutional blocks are more suitable for the leak detection problem in this study. Comparison experiments demonstrate that contrastive learning outperforms supervised learning (SL) when trained with insufficient labeled data. The out-of-sample validation results indicate that the proposed leak detection model is robust and effective in unexplored pipelines. The proposed framework significantly advances ML-based leak detection research and supports sustainable water management practices.

The positioning of quality detection points as well as the frequency of sampling is a crucial aspect for the implementation of Water Safety Plans (WSPs), which have been proposed worldwide to ensure water quality and to minimize the risk from contamination in water distribution networks (WDNs). In this regard, some international legislations and best practices about quality of drinking water suggest very fine sampling frequencies, but they do not specify where the detection points should be located in a WDN. In this paper, three different approaches, based on empiricism, optimization and topology, respectively, were applied to locate detection quality points in a WDN. The comparison highlighted that empirical approach commonly adopted by water utility practitioners is unsatisfactory. The optimization-based approach, although performing significantly better, is difficult to apply, since it requires a calibrated hydraulic model. The topological approach, based on the use of the betweenness centrality and not requiring any hydraulic information and simulation, proves to be effective, and it can be easily adopted by water utilities to identify the location for quality detection points, due to its simplicity compared with the optimization-based approach.

Data-driven leak localization in WDN using pressure sensor and hydraulic information

Many Machine Learning models are vulnerable to adversarial attacks: There exist methodologies that add a small (imperceptible) perturbation to an input such that the model comes up with a wrong prediction. Better understanding of such attacks is crucial in particular for models used in security-critical domains, such as monitoring of water distribution networks, in order to devise counter-measures enhancing model robustness and trustworthiness. We propose a taxonomy for adversarial attacks against machine learning based leakage detectors in water distribution networks. Following up on this, we focus on a particular type of attack: an adversary searching the least sensitive point, that is, the location in the water network where the largest possible undetected leak could occur. Based on a mathematical formalization of the least sensitive point problem, we use three different algorithmic approaches to find a solution. Results are evaluated on two benchmark water distribution networks.