Nodal Demands Research Articles

Pressure Zoning Approach for Leak Detection in Water Distribution Systems Based on a Multi Objective Ant Colony Optimization

Leakages result in considerable loss of water in water pipe networks. Therefore it is an important issue to detect leakage amount and its approximate location. Leakages in water distribution system are directly related to the operating pressure. In the current study, a new model is proposed for leakage amount and location detection and it is applied into two benchmark water distribution networks. In the proposed method, the water distribution networks are divided into three pressure zones in order to consider the leakage differences in different operating pressures. Then, nodal pressures and demands are calibrated using a new multi objective ant colony based optimization model. In this method, leaks are simulated as extra nodal demands. For determining the nodes where leakage happens, a probability based scheme is used. The leakage occurrence probability varies depending on the pressure zone that each node is located. The results illustrate the applicability of the proposed model for detecting the leakages in water distribution systems.

Using DFP Algorithm for Nodal Demand Estimation of Water Distribution Networks

Nodal demand estimation of a Water Distribution Network (WDN) means calculating the estimated values of nodal demands with some measured parameter values through mathematical methods. The most existing methods are based on an constrained weighted least-squares model and repeated computation of Jacobian matrix for optimal solutions. In this paper a new nonlinear model combined with pseudo-measurements and pressure constraints was developed for solution uniqueness. Davidon-Fletcher-Powell (DFP) algorithm was proposed to search for the solution by one dimensional optimization and scale matrix calculation, which was easier than Jacobian matrix computation. Two cases, including a real-life WDN of X city in northwest China, were used to show the performance of the proposed algorithm. Encouraging results showed that the proposed method was effective and feasible macroscopically, and it had potential for practical applications of WDNs.

Process of hydraulic models calibration

Mathematical modelling of the water supply systems (WSS) and water quality changes in the system is a complex and difficult task to solve, it requires an interdisciplinary approach to considering the determinants of WSS work. Prognosis models of the WSS in relation to hydraulic quantities are well known and there are many packages that implement these models. These packages allow you to calculate the flow and pressure in the water distribution system under certain operating conditions. However, to make a hydraulic model a useful tool in the management of water supply systems, a calibration process is required. This process involves estimating model parameters to minimize the difference between model results and actual observations. This is a complex and multi-stage process where the network graph and parameters such as roughness coefficient, pump characteristics, or nodal demands are checked and corrected. The following work contains a complex process of calibration of the actual WSS that supplies water to the customers of the selected part of the Silesian agglomeration.

Reliability-based design of Water Distribution Networks using Self-Adaptive Differential Evolution algorithm

This paper presents the application of Self-Adaptive Differential Evolution (SADE) algorithm for reliability-based design of Water Distribution Networks (WDNs). The algorithm is first applied and tested for deterministic design of various benchmark WDNs. Reliability-based design is then performed on the benchmark WDNs as well as real WDN in India by employing the SADE algorithm considering the uncertainty in nodal water demands. Monte Carlo simulation approach is used to incorporate the uncertainty in nodal demands; and pressure driven analysis is adopted for simulating the distribution of flows and pressures in pipe networks with the help of EPANET toolkit. A thorough comparison is made between the performance of SADE and DE methods. The results illustrate that SADE performs much better than DE since SADE converges faster with a higher success rate, making it a more preferable option for WDN design problem. The results of the study also illustrate that the optimal cost increases with increasing uncertainty level, but the percentage increase in cost is problem specific, which requires a robust tool for handling such complexities. The consistent results obtained by the application of SADE algorithm makes it a preferable option for reliability-based design of large WDNs including real world problems.

Exploring Numerically the Benefits of Water Discharge Prediction for the Remote RTC of WDNs

This paper explores numerically the benefits of water discharge prediction in the real time control (RTC) of water distribution networks (WDNs). An algorithm aimed at controlling the settings of control valves and variable speed pumps, as a function of pressure head signals from remote nodes in the network, is used. Two variants of the algorithm are considered, based on the measured water discharge in the device at the current time and on the prediction of this variable at the new time, respectively. As a result of the prediction, carried out using a polynomial with coefficients determined through linear regression, the RTC algorithm attempts to correct the expected deviation of the controlled pressure head from the set point, rather than the currently measured deviation. The applications concerned the numerical simulation of RTC in a WDN, in which the nodal demands are reconstructed stochastically through the bottom-up approach. The results prove that RTC benefits from the implementation of the prediction, in terms of the closeness of the controlled variable to the set point and of total variations of the device setting. The benefits are more evident when the water discharge features contained random fluctuations and large hourly variations.

Optimal Design of Water Distribution Networks with Incorporation of Uncertainties and Energy Nexus

The reliability of water distribution networks is susceptible to large impacts resulting from uncertainties. Several factors may contribute to such uncertainties. These include nodal demands, reservoir/tank levels, and availability of system components. Additional sources of uncertainties arise when water-energy nexus is considered. For instance, when water desalination systems that are coupled with power plants are incorporated in the water distribution networks, uncertainties in energy demand influence the design of the water network system. In this work, a multi-objective optimization framework is developed for the design of water networks that involve dual-purpose power plants for simultaneous water desalination and power generation. The multi-objective model accounts for sustainability goals through environmental, economic, and societal metrics such as greenhouse gas emissions, net profit, and number of jobs created, respectively. Fossil fuels, as well as renewable biofuels and solar power, are considered as candidate sources of energy. Water resources include multiple systems such as dams, lakes, rivers, aquifers, and artificial storage lakes. Demands from agricultural, industrial as well as domestic needs in the region are considered. In order to incorporate uncertainty in the proposed approach, a stochastic optimization model is formulated with a probabilistic objective function and constraints. The network has multiple sources as well as demands with varied distributions. In order to find an overall distribution for probability density estimation, a decomposition scheme is applied where each scenario is solved separately as a sub-problem. The solution from sub-problem is used to find the probability using kernel density estimator. The modified model equations lead to a stochastic MINLP problem. The proposed framework and optimization formulations are applied to a case study in the Mexican state of Sonora. From the demand and natural resource distribution, 12 scenarios have been identified and the model is weighted by their probability of occurrence. The results are compared with the deterministic solution to obtain the cost associated with uncertainty.

Impact of Climate Change on Hydraulic Performance in Water Distribution Networks

The Intergovernmental Panel on Climate Change (IPCC) has forecast higher mean air temperatures for the mid-latitude region of North America. Studies have shown a strong positive correlation between temperature and municipal water demand. Warmer air temperatures in the future have the potential to increase municipal water demand above levels forecast without climate change considerations. The predicted increase in mean temperature and the onset of hotter and dryer summer weather may create challenges for water providers in the future. Without appropriate network upgrades, higher water demands may degrade the hydraulic performance of existing systems. This creates a need to characterize the impact of higher temperatures on peak water demands and on the hydraulic performance in water distribution networks. The aim of the research is to begin to understand the impact of higher temperatures on nodal demands and pressures in water distribution networks. The sensitivity of municipal water demand to an increase in air temperature is established through previous climate adaptation research completed for the geographical region of central Canada. Results indicate that without adaptation, a 2-4 °C temperature increase causes mean pressure head to fall below the acceptable minimum and produces large uncertainties in pressure head under maximum hour demand (MHD) and maximum day demand (MDD) + fire design conditions in the Anytown network. The combination of low mean pressure head and a high coefficient of variation of pressure head increases the probability of hydraulic failure in the Anytown network. Adaptation strategies are presented as ways to hedge the effects of a warming climate in the Anytown network

Roughness and Demand Estimation in Water Distribution Networks Using Head Loss Adjustment

AbstractTo estimate pipe roughness and nodal demand parameters in water distribution networks, a method based on head loss adjustment is proposed. By using weighted least squares (WLS), model-simul...

Estimation of Water Demand in Water Distribution Systems Using Particle Swarm Optimization

Demand estimation in a water distribution network provides crucial data for monitoring and controlling systems. Because of budgetary and physical constraints, there is a need to estimate water demand from a limited number of sensor measurements. The demand estimation problem is underdetermined because of the limited sensor data and the implicit relationships between nodal demands and pressure heads. A simulation optimization technique using the water distribution network hydraulic model and an evolutionary algorithm is a potential solution to the demand estimation problem. This paper presents a detailed process simulation model for water demand estimation using the particle swarm optimization (PSO) algorithm. Nodal water demands and pipe flows are estimated when the number of estimated parameters is more than the number of measured values. The water demand at each node is determined by using the PSO algorithm to identify a corresponding demand multiplier. The demand multipliers are encoded with varying step sizes and the optimization algorithm particles are also discretized in order to improve the computation time. The sensitivity of the estimated water demand to uncertainty in demand multiplier discrete values and uncertainty in measured parameters is investigated. The sensor placement locations are selected using an analysis of the sensitivity of measured nodal heads and pipe flows to the change in the water demand. The results show that nodal demands and pipe flows can be accurately determined from a limited number of sensors.

Calibration Model for Water Distribution Network Using Pressures Estimated by Artificial Neural Networks

The success of hydraulic simulation models of water distribution networks is associated with the ability of these models to represent real systems accurately. To achieve this, the calibration phase is essential. Current calibration methods are based on minimizing the error between measured and simulated values of pressure and flow. This minimization is based on a search of parameter values to be calibrated, including pipe roughness, nodal demand, and leakage flow. The resulting hydraulic problem contains several variables. In addition, a limited set of known monitored pressure and flow values creates an indeterminate problem with more variables than equations. Seeking to address the lack of monitored data for the calibration of Water Distribution Networks (WDNs), this paper uses a meta-model based on an Artificial Neural Network (ANN) to estimate pressure on all nodes of a network. The calibration of pipe roughness applies a metaheuristic search method called Particle Swarm Optimization (PSO) to minimize the objective function represented by the difference between simulated and forecasted pressure values. The proposed method is evaluated at steady state and over an extended period for a real District Metering Area (DMA), named Campos do Conde II, and the hypothetical network named C-town, which is used as a benchmark for calibration studies.

Probabilistic Analysis and Evaluation of Nodal Demand Effect on Transient Analysis in Urban Water Distribution Systems

AbstractThe implementation of nodal demands in current transient modeling and analysis in the urban water distribution system (WDS) is usually based on steady-state conditions or empirical-based ap...

Informational Entropy: a Failure Tolerance and Reliability Surrogate for Water Distribution Networks

Evolutionary algorithms are used widely in optimization studies on water distribution networks. The optimization algorithms use simulation models that analyse the networks under various operating conditions. The solution process typically involves cost minimization along with reliability constraints that ensure reasonably satisfactory performance under abnormal operating conditions also. Flow entropy has been employed previously as a surrogate reliability measure. While a body of work exists for a single operating condition under steady state conditions, the effectiveness of flow entropy for systems with multiple operating conditions has received very little attention. This paper describes a multi-objective genetic algorithm that maximizes the flow entropy under multiple operating conditions for any given network. The new methodology proposed is consistent with the maximum entropy formalism that requires active consideration of all the relevant information. Furthermore, an alternative but equivalent flow entropy model that emphasizes the relative uniformity of the nodal demands is described. The flow entropy of water distribution networks under multiple operating conditions is discussed with reference to the joint entropy of multiple probability spaces, which provides the theoretical foundation for the optimization methodology proposed. Besides the rationale, results are included that show that the most robust or failure-tolerant solutions are achieved by maximizing the sum of the entropies.

Multiobjective Optimization of Pressure Dependent Dynamic Design for Water Distribution Networks

Optimal design and rehabilitation scheduling of water distribution networks (WDNs) have been often dealt separately over the past few decades. However initial design (which is named as static design in this paper) has indubitable influence on the operational condition and rehabilitation scheduling of network. This paper introduces an approach for simultaneous optimization of initial design and rehabilitation scheduling of WDNs during their life cycle. In this approach which is named as dynamic design, pipe diameters in the first year and their rehabilitation/replacement in the next years of the expected life of the network are determined considering the nodal demands growth and increase in pipes’ roughness. The proposed model consists of a multiobjective ant colony optimization engine linked to a pressure dependent analysis model and a pipe break prediction model. This paper introduces the following contributions: (1) it implements dynamic design based on the pressure dependent analysis with considering leakage; (2) a support vector machine based sub model is used for pipe break prediction. Then pipe breaks and their repair costs are considered in dynamic design process; (3) a new reliability index is used as one of the objective functions. Two networks are used to investigate the impact of static and dynamic designs on the reliability and total cost of design and rehabilitation of WDNs during their life cycle. The results show that the dynamic design produces more reliable and lower cost networks in comparison to the ones resulted from either static design or rehabilitation scheduling separately.

Hydraulic Model of District Metered Areas for Leakage Reduction in Ghana Water Company Limited: A Case Study of Dansoman DMA in Accra, Ghana

Water distribution network models are used by water utilities extensively. A promising model is required for increasing reliability of water provision. The main intention of the study was to develop a well calibrated and validated hydraulic model and also determine the level of leakage in the DMA. It presents a hydraulic model for Dansoman District Metered Area (DMA) pipe network in Accra, which is part of the supply network operated by Ghana Water Company Limited (GWCL). The DMA serves a population of approximately 16,390 people and it covers an area of 363 hectares. Bulk flow readings were taken at inlet points. Nodal demands were allocated by calculating average uniform demand per connection. Variation in spatial distribution of population was accounted by computing the nodal influence areas by Theison polygon principle in Arc-GIS. Minimum Night Flow (MNF) measurements were taken by night flow loggers at sample points for leakage computation. The model was developed by using EPANET 2.0 and calibration of the model performed at critical moments produced a well calibrated and validated hydraulic model that presents quite closer measured and computed values with correlation coefficients between 0.66-0.98. The developed model can be used for both operations and management of water supply in the DMA. The study also found that leakage (physical water loss) in the DMA was 30.6% of the total water supplied. Therefore, the result of this study informs GWCL to implement a full scale leakage reduction action by showing how much of the water produced is being lost which could have increased the coverage and efficiency of the utility.

Analytical Solution of Jacobian Matrices of WDS Models

The Jacobian matrices of water distribution system (WDS) models contain the gradient information of input parameters to observations, which are the key to construct gradient vectors for model calibration via gradient-based methods. In existing studies, the perturbation method is most often applied to approximate Jacobian matrices, however it is computation expensive for larger WDSs. Besides, although other methods have also been presented to compute the analytical solution of Jacobian matrices directly, they fail to provide the explicit expressions of Jacobian matrices leading to the difficulty in application. This paper presents a novel matrix analysis method to deduce the analytical solution of Jacobian matrices of WDS models, including the nodal demand, pipe roughness and pipe diameter to nodal pressure and pipe flow, respectively. All solutions are expressed in a concise matrix form with advantages of being easy to understand. A numerical case is used to detail the construction of the involved matrices.

Sensitivity Analysis of Topological Subgraphs within Water Distribution Systems

Sensitivity analysis of the actual hydraulic state of water distribution systems is a valuable tool with number of applications in hydraulic systems analysis. Sensitivity matrices include the information of the response of the hydraulic state variables (flows, pressures) to changes in model parameters (e.g. demands, roughness, control parameters) for a specific hydraulic state of the system. For calculation, there exists in addition to finite difference approximations also exact solutions that include the inversion of the system matrix (the Schur Complement of the Jacobian of the hydraulic network equations). In combination with hydraulic network simulations, the factorization (for example Cholesky matrix decomposition) of the matrix that has already been done by the hydraulic solver in the computation process can be used for the efficient calculation of the inverse matrix. However, for large realworld networks the sensitivity calculation is a time and memory consuming process because the inverse of the system matrix of a connected network has no zero elements. In this paper a new method is presented that allows for the exact calculation of sensitivities of a particular subgraph of interest, the topological minor or supergraph within a water distribution system network graph. Supernodes are the most important nodes in terms of connectivity redundancy within the network graph. Superlinks replace all pipes (links) in series between two supernodes. It will be shown that the sensitivities that are calculated for the subgraph deliver exactly the same results as the inversion of the entire system matrix reduced to supernodes. This paper focuses on the derivation of the equations for the reduced system matrix inversion of the topological subgraph. In addition, the paper includes the proof of equivalence of the matrix inverses for the topological minor subgraph. This inverse represents the fundamental sensitivities of nodal heads and pipe flows with respect to nodal demands in demand driven analysis. The results presented can be extended to other sensitivities, since the matrix inverse in question is included in all other derived parameter sensitivities.

Emergency Management of Water Distribution Systems: The Nodal Demand Control

During emergency situations (e.g., due to pipe bursts or other network failures), appropriate management of Water Distribution Systems (WDS) is required. Critical events often cause service failures, because the pressure head in some nodes of the network become inadequate to deliver required demand. In this paper, a new methodology is developed based on the nodal demand control. with the aim to increase the pressure head, and hence the flow rate actually delivered at critical nodes (i.e., hospitals, vulnerable customers, etc.). This is done to avoid or minimize service interruptions between the failure and the repair times. Furthermore, a pipe burst can cause isolation of a portion of the network such that the flow along pipes changes and this causes the reduction of head in some nodes. The proposed methodology is manages the delivered flow rate using a Pressure Driven Analysis (PDA) approach. This is based on operating control of valves and by identifying the nodes where the pressure control should be implemented. Those control nodes are chosen by the analysis of sensitivity matrices and the Max-Sum Method (Bush and Uber, 1998; Fiorini Morosini et al., 2014). The methodology is demonstrated on a case study for a real network of Cosenza, a town in the South of Italy.

State Estimation for Water Distribution Networks in the Presence of Control Devices with Switching Behavior

In process monitoring and control, state estimation is the fundamental tool for processing redundant and noise-corrupted measurements in order to provide reliable estimates of the state of a system. In the context of water distribution networks (WDNs), state estimation has been proposed as the core technology which can enable various applications ranging from real-time monitoring and control to anomaly diagnosis, such as leak detection and localization. Measurements are typically available from sparse and often scarce telemetry sensors, such as flow at the inlet of a district metered area (DMA) and pressure at some nodes, or from utility estimates, for example prior estimates of the nodal demands. The problem consists of using the available measurements to reconstruct an estimate of the state variables and is solved iteratively by minimizing the weighted least squares (WLS) of the differences between the measurements and model predictions, typically with gradient methods. WDN state estimation in the presence of control devices, such as pressure reducing valves, remains an open problem due to the complexity in modeling efficiently their switching behavior. Control elements prevent from obtaining an explicit function of the measurements with respect to the state variables for all possible switching statuses. In this paper, an extension to traditional state estimation methods is proposed, which only requires a minor modification of existing WLS solvers based on gradient methods. Based on residual analysis, conditions are given in order to verify correct convergence at the end of a state estimation or to identify changes in connectivity due to opening/closing of control elements before proceeding to a new run. The method does not require including explicit binary variables to model the state of control elements, which would require complex heuristic-based solvers and would present scalability challenges for large networks with many such elements. Results on a real-world test case with two PRVs are reported to demonstrate the effectiveness and of the proposed method.

Verifying Pressure Dependent Demand Modeling

While most water distribution system models are demand driven, there are situations where the ability to model pressure dependent demands (PDD) is essential. These models incorporate some function relating nodal demand to pressure. While the underlying logic behind PDD is sound, there has not been a study to verify PDD modeling.In this study, a laboratory scale water distribution system was constructed where orifice opening and flow could be accurately controlled and measured. Data were collected over a wide range of flow patterns, orifice opening and source heads. In all 109 runs were made with multiple readings for each run.These data were compared with a calibrated hydraulic model of PDD and the results showed that the lab model and computer model agreed well with the average orifice exponent just slightly greater than the theoretically expected value of 0.5. The study showed that for correctly calibrated orifices in steady conditions, PDD modeling is accurate.

Uncertainty Analysis of Pipe-Network Hydraulics Using a Many-Objective Particle Swarm Optimization

AbstractIn water-supply pipe networks, inherent uncertainties in the analysis parameters, including nodal demands, pipe friction factors, reservoir heads, etc., lead to imprecise hydraulic responses. This study introduces a methodology based on fuzzy set theory to analyze network hydraulics under uncertainty. The fuzzy approach results in a complex optimization problem that is neither single nor common multiobjective. To solve the problem efficiently to find extreme values of nodal pressures and pipe velocities, a novel many-objective particle swarm optimization (MO-PSO) model is developed and coupled to a network hydraulic simulation model from the literature. The coupled model is applied against a benchmark example and a real pipe network from the literature and the results are compared with those from the previous methods. The examples manifest that the proposed fuzzy MO-PSO is computationally efficient and reliable. Analyzing the real pipe network shows that, for instance, ±15% uncertainty in the pipe...