Water Distribution Network Models Research Articles

Burst Diagnosis Multi-Stage Model for Water Distribution Networks Based on Deep Learning Algorithms

Pipe bursts in water distribution networks (WDNs) pose significant threats to the safety of distribution networks, driving attention to deep learning-based burst detection and localization. However, the applicability of different pressure features still needs to be compared and verified. A large number of nodes challenges deep learning with the excessive number of classification categories and low recognition accuracy. To address these problems, this paper extracts different burst pressure features, including pressure value, pressure difference, and pressure fluctuation ratio, and inputs one of these features into a Burst Diagnosis Multi-Stage Model (BDMM) based on three CS-LSTMs (a combination of the Cuckoo Search algorithm and a long short-term memory network). The first model addresses a binary classification problem, outputting labels indicating whether a pipe burst has occurred. The second one solves a multi-classification problem, outputting the label of the burst partition, and the third model also solves a multi-classification problem, outputting the ID of the bursting junction. The model is tested on a real network and outperforms ELM. For basic burst identification tasks using CS-LSTM, differences among the three features are minimal, while pressure difference and pressure fluctuation ratio exhibit superior performance to pressure value when resolving more complex problems like burst junction localization.

The Hourly Peak Coefficient of Single-Family and Multi-Family Buildings in Poland: Support for the Selection of Water Meters and the Construction of a Water Distribution System Model

Taking care of water resources and minimizing water losses in water supply networks requires a broad approach to identifying and neutralizing operational problems. The correct selection of water meters to minimize apparent losses requires knowledge of the characteristic flows that may occur in the facility to which water is supplied. The research aimed to develop tools in the form of mathematical models and water consumption curves along with hourly water consumption coefficients to facilitate the process of selecting water meters for engineers and creating computer models of water supply systems. The research involved monitoring the flow of 76 single-family and multi-family buildings in four towns in Poland, followed by data analysis and development of tools supporting the selection of water meters and the construction of computer models of water distribution networks. High correlation coefficients of the studied variables indicate the results’ usefulness. Four models were developed to determine the maximum flow values in multi-family buildings (three models) and single-family buildings (one model) in the range of water meter diameters DN15-DN40. Characteristics of the average hourly peak coefficient (HPC) values were also developed, along with the range of changes in HPC values for single-family and multi-family buildings.

A Multi-step Data Assimilation Framework to Investigate the Effect of Measurement Uncertainty in the Reduction of Water Distribution Network Model Errors

Water distribution network (WDN) models are a common decision support tool for understanding the behavior and performance of WDNs, aiding in the planning and management of WDN systems. The increasing availability of real-time data has recently promoted the exploration of Data Assimilation (DA) techniques to improve these models. However, flow, pressure and demand data are uncertain, particularly due to sensor characteristics such as precision and noise. An open question is to what extent DA can still improve hydraulic models when the data used to this end is uncertain. This paper proposes a three-step Ensemble Kalman Filter based DA approach for WDNs (3-EnKF-WDN), building on previous approaches, and advancing in two main fronts: the use of extended period simulation, and the use of pressure-dependent demand (PDD) analysis. Different scenarios considering uncertain sensor data, with varied precision and noise, are applied to two networks of different sizes, representative of real-world WDNs. The computational demand of the 3-EnKF-WDN method is also assessed. Results show that increasing sensor’s precision and decreasing the noise in state measurements reduce model error, as expected. However, we also found that model errors: 1) are reduced more effectively by using 3-EnKF-WDN than by increasing sensors’ precision; 2) are not reduced if certain noise thresholds are surpassed; 3) can be reduced without assimilating demand data if the WDNs are fully monitored with head sensors in all the nodes and flow sensors in all the links.

Improving Water Distribution Network Models with Data Assimilation: Unleashing the Power of Real-Time Improvements

Ensuring a reliable water supply in the face of changing conditions and growing demand is a critical global challenge. Water distribution networks (WDNs) are essential infrastructure, but traditional modeling methods based on historical data often struggle to adapt in real-time and integrate new information. In order to lower model errors in WDN models, this study explores the use of a Data Assimilation (DA) method that makes use of the Ensemble Kalman Filter. The study explores the effectiveness of the DA method, and a novel Greedy Algorithm (GA) for optimizing the location of sensors. The study shows that the DA method improves the WDN model and the GA is able to successfully determine optimal sensor locations. It was observed that increasing the number of sensors in the WDN increased the effectiveness of the DA method. This study highlights the potential of data assimilation to improve WDN modeling. Water utilities can gain from more precise predictions, greater system performance, and efficient decision-making for the management and maintenance of water distribution networks by allowing models to adapt and improve dynamically

A Review of Hydraulic Pressure for Water Supply Unites Considering Iraqi Geodetic Reference

The hydraulic pressure head of the flowing water (between the entrance and exit pipes) in water distribution networks depends on the length and the slope of these pipes, which can represent the head losses for each meter length, where the slope and length of the water supply network pipes are dependent on specified datum ground elevations. This ground elevation may result in a reduction in head losses with hydraulic grade pressure. As a result, the precision of the measured data used to observe ground elevations is critical to decrease the error of these losses and apply an accurate local reference. It's critical to comprehend the implications of using Geographic Information System (GIS) application technology for water distribution network models to evaluate the hydraulic grade head with Iraqi Geodetic Reference. These GIS input data are based on an analysis of the relationship between selected spatial data resolution and the precision of the expected hydraulic head for selected stations with a distribution network. This research aims to review the literature and try to track the conversion of geodetic references and datums to accurately identify the hydraulic pressure for the selected locations of the water supply network. It was found that recent researches tend to use GIS application to create novel methods to reduce head losses and error.

Application of Strength Pareto Evolutionary Algorithm II in Multi-Objective Water Supply Optimization Model Design for Mountainous Complex Terrain

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.

Shall we always use hydraulic models? A graph neural network metamodel for water system calibration and uncertainty assessment

Representing reality in a numerical model is complex. Conventionally, hydraulic models of water distribution networks are a tool for replicating water supply system behaviour through simulation by means of approximation of physical equations. A calibration process is mandatory to achieve plausible simulation results. However, calibration is affected by a set of intrinsic uncertainty sources, mainly related to the lack of system knowledge. This paper proposes a breakthrough approach for calibrating hydraulic models through a graph machine learning approach. The main idea is to create a graph neural network metamodel to estimate the network behaviour based on a limited number of monitoring sensors. Once the flows and pressures of the entire network have been estimated, a calibration is carried out to obtain the set of hydraulic parameters that best approximates the metamodel. Through this process, it is possible to estimate the uncertainty that is transferred from the few available measurements to the final hydraulic model. The paper sparks a discussion to assess under what circumstances a graph-based metamodel might be a solution for water network analysis.

A parallel computing architecture based on cellular automata for hydraulic analysis of water distribution networks

Water distribution networks (WDNs) are one of the largest infrastructures in society. Various methods for formulation and hydraulic analysis of water distribution networks, including numerical and non-numerical methods, have been previously proposed. Due to the complexity, the nonlinearity of the hydraulic equations of water distribution networks, and the need for multiple executions and uncertainties in parameters, solving the hydraulic model of water distribution networks has high time complexity. In this paper, a parallel computational architecture based on the concept of cellular automata is proposed to accelerate the numerical solution of the steady-state water distribution network model. Taylor series is proposed to solve hydraulic equations. The presented architecture was implemented as a parallel hardware platform on a field-programmable gate array. The performance of the proposed method was compared with EPANET software for networks with different complexities and topologies. The results show that the proposed parallel algorithm can accelerate the hydraulic analysis of regular water distribution networks up to 700 times and 250 times for small and large networks, respectively.

Pipe and isolation valve failure-impact analysis and prioritization model for an urban water distribution network

Abstract Pipe and isolation valve failure in an urban water distribution network (WDN) causes service interruption to the water users. It is important to identify and prioritize the maintenance of the most severe impact-causing pipes and valve failures. This study investigates the impacts of such failures in terms of the number of isolation elements, the number of affected customers, and the supply shortfall (SS). The study proposes an impact-based prioritization model for pipe and isolation valve repair/replacement in a WDN using the analytic hierarchy process (AHP). The WDN modeling, simulation, and generation of segments are carried out using the WaterGEMS software. The proposed methodology is illustrated with the help of a real-time WDN of Dire Dawa city in Ethiopia. Through the study, it is noticed that each valve/pipe failure has varied impacts and gets reduced with the increase in valve density. Further, the supply shortfall is the most important parameter for prioritizing the maintenance. The failure of the valves and pipes significantly affects the system's performance and should be repaired/replaced on priority basis. It is hoped that the proposal will help the decision-makers in the optimal utilization of limited resources available for repair/ maintenance.

MAGNets: Model Reduction and Aggregation of Water Networks

Hydraulic models of large water distribution networks can have thousands of components, and real-time simulation of these systems can be slowed down by their complexity. Several methods have been developed for which the size of the water network models can be reduced while the hydraulic performance of the reduced systems remains very similar to the original model. Model reduction allows users to model only components of interest, thus saving expensive computation time. However, while model reduction has been widely adopted for control and optimization purposes, few tools are available to reduce models on command. This paper introduces MAGNets, an open-source Python package capable of reducing and aggregating EPANET-compatible water models using the variable elimination reduction method. The package allows the user to specify the operating point around which the model will be reduced, the nodes that must remain in the network, and the maximum nodal degree of nodes removed. The reduced model preserves pressure heads of the original model with high accuracy and results in faster running times. The reduction algorithm iteratively removes nodes from the full model and updates the adjacent nodal demands and pipe properties until the final reduced model is achieved. To test the effect of the order of node removal on the size of the reduced model and computational complexity, we tested three different strategies for reduction order. Results suggest that dynamically updating reduction order greatly improves model performance compared to static and random orders. To increase usability, the Python package includes twelve benchmark networks for testing and validation. MAGNets allows for the quick and efficient reduction of hydraulic models as a way to facilitate time-sensitive tasks, such as real-time state estimation and control.

Review of Urban Drinking Water Contamination Source Identification Methods

When drinking water flows into the water distribution network from a reservoir, it is exposed to the risk of accidental or deliberate contamination. Serious drinking water pollution events can endanger public health, bring about economic losses, and be detrimental to social stability. Therefore, it is obviously crucial to research the water contamination source identification problem, for which scholars have made considerable efforts and achieved many advances. This paper provides a comprehensive review of this problem. Firstly, some basic theoretical knowledge of the problem is introduced, including the water distribution network, sensor system, and simulation model. Then, this paper puts forward a new classification method to classify water contamination source identification methods into three categories according to the algorithms or methods used: solutions with traditional methods, heuristic methods, and machine learning methods. This paper focuses on the new approaches proposed in the past 5 years and summarizes their main work and technical challenges. Lastly, this paper suggests the future development directions of this problem.

Online Edge Flow Imputation on Networks

An online algorithm for missing data imputation for networks with signals defined on the edges is presented. Leveraging the prior knowledge intrinsic to real-world networks, we propose a bi-level optimization scheme that exploits the causal dependencies and the flow conservation, respectively via <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(i)</i> a sparse line graph identification strategy based on a group-Lasso and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(ii)</i> a Kalman filtering-based signal reconstruction strategy developed using simplicial complex (SC) formulation. The advantages of this first SC-based attempt for time-varying signal imputation have been demonstrated through numerical experiments using EPANET models of both synthetic and real water distribution networks.

Port-Hamiltonian based control of water distribution networks

We design controllers for a nonlinear model of a water distribution network (WDN). Most existing approaches to the control of WDNs model the pumps as simple pressure gains. We show that a commonly used empirical model of a pump leads to a port-Hamiltonian (pH) and hence stable system. We use standard arguments to show that WDNs are incrementally pH, and show that local PI controllers preserve stability. These controllers are robust in that they do not require specific knowledge of the equilibrium input. We further show that controllers based on physical feedback that WDN operators usually rely on have merit in the pH framework. All of these controllers are shown to be useful in mitigating disturbances and tracking setpoints corresponding to assignable equilibria.

Multi-objective and risk-based optimal sensor placement for leak detection in a water distribution system

The optimal sensor placement for leak detection in a water supply network has been studied extensively. The previous studies usually assume that each node of the water distribution network has the same importance. However, this assumption does not consider the difference in the impact when a leak occurs at the different nodes on the water distribution network. When the number of sensors is limited, the detection of only leakage events that can cause serious consequences is usually prioritized. This study proposes a multi-objective optimization method for sensor placement while taking into consideration the differences in the risk of leakage for the different nodes. First, five types of risk-based leakage functions are obtained based on the impact on the water distribution network when a leakage occurs at each node. The pressure at the node drops, which causes the water demand and pipe pressure to decrease while the flow rate increases. The multi-objective optimization method is then used to obtain the Pareto front according to the various risk-based leakage functions. Finally, the multi-criteria decision analysis method is used to rank and cluster the Pareto fronts, the optimal solution for each cluster is obtained, and these solutions are compared and analyzed. This study contains a case study that is based on the example water distribution network model C-town. When the number of sensors is limited, a more reasonable optimal sensor placement scheme can be obtained by considering the different risk-based leakage functions of the nodes, with a smaller impact on the water distribution network when a leakage occurs. • A multi-objective optimization sensor placement for leak detection in water distribution system. • Five types of risk-based leakage functions are obtained based on the impact of each leakage. • The impacts of the leakage occurring at each node of the pipe network are compared.

Pulsed Demand Modeling for the Optimal Placement of Water Quality Sensors in Water Distribution Networks

AbstractThis paper deals with the issue of the consistency of water distribution network (WDN) modeling concerning the nature of demand for the optimal water quality sensor placement. In this regard, a biobjective optimization for the sensor placement is carried out by minimizing the contamination extension or the contaminated population in the trade‐off with the number of sensors installed, by considering two alternative demand modeling conditions, that is, smooth and pulsed demand, respectively. The real layout of the two Italian WDNs is considered for the application of the methodology. The results show that for a given placement of sensors, the contamination extension always increases when the pulsed demand is considered. Furthermore, optimal sensor positions are affected by the pulsed demand especially in the case of highly looped WDN layouts and when the extent of contamination is used as objective function.

Pressure-Leak Duality for Leak Detection and Localization in Water Distribution Systems

Water utilities are challenged to reduce their water losses through detecting, localizing, and repairing leaks as quickly as possible in their aging distribution systems. In this work, we solve this challenging problem by detecting multiple leaks simultaneously in a water distribution network for the Battle of the Leak Detection and Isolation Methods. The performance of leak detection and localization depends on how well the system roughness and demand are calibrated. In addition, existing leaks affect the diagnosis performance unless they are identified and explicitly represented in the model. To circumvent this chicken-and-egg dilemma, we decompose the problem into multiple levels of decision-making (a hierarchical approach) where we iteratively improve the water distribution network model and so are able to solve the multileak diagnosis problem. First, a combination of time series and cluster analysis is used on smart meter data to build patterns for demand models. Second, point and interval estimates of pipe roughnesses are retrieved using least squares to calibrate the hydraulic model, utilizing the demand models from the first step. Finally, the calibrated primal model is transformed into a dual model that intrinsically combines sensor data and network hydraulics. This dual model automatically converts small pressure deviations caused by leaks into sharp and localized signals in the form of virtual leak flows. Analytical derivations of sensitivities with respect to these virtual leak flows are calculated and used to estimate the leakage impulse responses at candidate nodes. Subsequently, we use the dual network to (1) detect the start time of the leaks, and (2) compute the Pearson correlation of pressure residuals, which allows further localization of leaks. This novel dual modeling approach resulted in the highest true-positive rates for leak isolation among all participating teams in the competition.

Improving the leak detection efficiency in water distribution networks using noise loggers

Leak detection techniques are effective ways of controlling water leakage in real water distribution networks (WDNs). Nevertheless, developing detection techniques for real WDNs has received little attention compared to the detection models developed based on laboratory simulated leaks. On the other hand, ambient noises and irregular water usage are difficult to simulate in a laboratory environment so detection models based on the laboratory simulated leaks are usually of low efficiency in practical applications. To achieve a better understanding of the detection models of real WDNs, machine learning (ML)-based leak detection models were developed in this work. This study employs wireless sensors to record acoustic signals emitted by real WDNs for the development of the leak detection models. The acquired acoustic signals are de-noised using the discrete wavelet transform. Thereafter, seventeen features are extracted from both the raw and de-noised signals using the principle of linear prediction, and the features are subsequently used for the development of the ML-based leak detection models. A thorough comparison is made for the performances of the detection models in terms of metal and non-metal WDNs, different features, and different ML algorithms, namely decision tree (DT), support vector machine (SVM), artificial neural network (ANN), and k-nearest neighbor (K−NN). Generally, the performance of the ML-based detection models developed by using the features extracted from de-noised signals has a better classification accuracy as compared to the performance of the models developed based on the features extracted from raw signals. For the de-noised signals, the accuracy, precision, and recall for the models developed based on the DT, SVM, and ANN algorithms are 100% for metal and non-metal WDNs.

Hydraulic optimization of the physical parameters of a drinking water distribution system

Drinking-water distribution systems are generally designed with methodologies based on trial-and-error tests, which generate feasible results. However, these trials are not the most economical and reliable solution since they do not consider the optimization of the network. For the present work, the hydraulic model of the drinking water distribution network of San José de Cúcuta, Colombia, was optimized by applying the concept of resilience rate and minimum cost. The development of the work consisted of the hydraulic modeling of the physical components of the network in EPANET software, as well as the application of calculations of the connectivity coefficient and the unitary power of each section. With the data obtained from the modeling and calculations, the physical parameters were optimized, and the cost-benefit ratio was estimated. It was found that the current drinking water distribution system does not have a power surplus to overcome a system failure. The optimization increased the total energy surplus of the network (261%) and the resilience rate (585%). Also, the connectivity coefficient was improved with an average value of 0.95. The hydraulic optimization methodology applied resulted in a network resilient to system failures.

A growth model for water distribution networks with loops.

Water distribution networks (WDNs) expand their service areas over time. These growth dynamics are poorly understood. One facet of WDNs is that they have loops in general, and closing loops may be a functionally important process for enhancing their robustness and efficiency. We propose a growth model for WDNs that generates networks with loops and is applicable to networks with multiple water sources. We apply the proposed model to four empirical WDNs to show that it produces networks whose structure is similar to that of the empirical WDNs. The comparison between the empirical and modelled WDNs suggests that the empirical WDNs may realize a reasonable balance between cost, efficiency and robustness in terms of the network structure. We also study the design of pipe diameters based on a biological positive feedback mechanism. Specifically, we apply a model inspired by Physarum polycephalum to find moderate positive correlations between the empirical and modelled pipe diameters. The difference between the empirical and modelled pipe diameters suggests that we may be able to improve the performance of WDNs by following organizing principles of biological flow networks.

Effects of Orifice Diameter and Retention Time of Local Tanks on the Reliability and Carbon Footprint of Water Distribution Networks

The role of private tanks is to provide excess storage to the consumer to satisfy the water demand. However, they are disregarded during the design stage, in favor of simplified network analysis. This affects the accuracy of the simulation because vital components, such as tank inlets and volume sizes, are completely ignored. Hence, the purpose of this study is to demonstrate the effectiveness of advanced modeling of water distribution networks (WDNs), encompassing the presence of local private tanks, to determine the optimum values of different parameters of private tanks by conducting time- and volume-based reliability analyses. Two network models are used to perform the analysis: a small sample network and a real network that resembles the area of Dubai Silicon Oasis, Dubai, United Arab Emirates. The results obtained from the simulation of networks indicated that the lowest orifice and volume sizes to achieve the required reliability of unity is the optimum values. Furthermore, it implied that any change in their optimum values would either result in tank failure or increase in the head loss and carbon footprint of the network.