Pressure-Dependent EPANET Extension

In water distribution systems (WDSs), the available flow at a demand node is dependent on the pressure at that node. When a network is lacking in pressure, not all consumer demands will be met in full. In this context, the assumption that all demands are fully satisfied regardless of the pressure in the system becomes unreasonable and represents the main limitation of the conventional demand driven analysis (DDA) approach to WDS modelling. A realistic depiction of the network performance can only be attained by considering demands to be pressure dependent. This paper presents an extension of the renowned DDA based hydraulic simulator EPANET 2 to incorporate pressure-dependent demands. This extension is termed “EPANET-PDX” (pressure-dependent extension) herein. The utilization of a continuous nodal pressure-flow function coupled with a line search and backtracking procedure greatly enhance the algorithm’s convergence rate and robustness. Simulations of real life networks consisting of multiple sources, pipes, valves and pumps were successfully executed and results are presented herein. Excellent modelling performance was achieved for analysing both normal and pressure deficient conditions of the WDSs. Detailed computational efficiency results of EPANET-PDX with reference to EPANET 2 are included as well.     

Effect of Breakage Level One in Design of Water Distribution Networks

Design of water distribution networks (WDNs) that do not consider performance criteria would possibly lead to less cost but it could also decrease water pressure reliability in abnormal conditions such as a breakage of pipes of the network. Thus, awareness of the situation of consumption nodes, by considering water pressures and the amount of water that is being supplied, could be an effective source of information for designing high performance WDNs. In this paper, Two-loop and Hanoi networks are selected for least-cost design, considering water pressures and the amount of water supplied on each consumption node under breakage level one, using the honey-bee mating optimization (HBMO) algorithm. In each state of design, a specific pressure is defined as the minimum expected pressure under breakage level one which holds the pressure reliability in the considered range. Also, variations of some criteria such as reliabilities of pressure and demand, vulnerability of the network, and flexibility of the design are analyzed as a tool for choosing the appropriate state of design. Results show that a minor increase in the cost of design could lead to a considerable improvement in reliabilities of pressure and demand under breakage level one.     

Water Distribution Network Risk Analysis Under Simultaneous Consumption and Roughness Uncertainties

The design of water distribution networks (WDNs) is an optimization problem with minimization of pipes and their associated installation costs as the objective function. In this problem, securing the allowable minimum pressure or the allowable maximum velocity in the demand pattern is important. A reliable long-term system requires a high reliability when first designed. Thus, assessment of the network condition during the operational period, when it is first designed, can be an effective way to increase the network efficiency. In addition, consideration of uncertainty of network parameters is important. This paper develops a probabilistic model based on the Monte Carlo simulation (MCS) method to assess effects of those uncertainties simultaneously in the long-term performance of the network by considering various scenarios for variations of nodal demands and pipe roughness using different values of the coefficient of variation (CV) as the uncertainty measure. Consumption nodal demands and pipe roughness in a benchmark two-loop network are considered as uncertain variables. Calculation of a deterministic performance (failure) index (I _f ) for various generated probabilistic scenarios in the MCS method during a 30-year operational period simulation in this network show that an increase of uncertainty in each variable separately causes a decrease in the deterministically-designed network efficiency. Sensitivity of changing the average value of I _f calculations show a nodal demand deficit of 45 % and a nodal pressure deficit of 61 % during the operational period. This condition shows the necessity of considering uncertain changes of variables simultaneously during the operational period in the design of WDNs.     

Optimal Design of Water Distribution Networks Considering Fuzzy Randomness of Demands Using Cross Entropy Optimization

This paper presents cross entropy (CE) optimization for optimal design of water distribution networks (WDN) under demand uncertainty. In design of WDNs, it is desired to achieve a minimum cost WDN that provides higher reliability in meeting the demands. To achieve these goals, an optimization model is formulated for design of WDNs with an objective of minimizing the total cost of WDN subject to meeting the nodal demands at a specified system reliability, mass conservation and other physical constraints. The uncertainty in future water demands is modeled using the theory of fuzzy random variable (FRV). The water demand at each node is assumed to be following a normal distribution with a fuzzy mean, and 10 % (or 20 %) of the fuzzy mean as its standard deviation. The water demand is represented as a triangular fuzzy number with the random demand as its kernel, and the interval of ±5 % (or ±10 %) variation of the random demand as its support for two scenarios. The fuzzy random system reliability (R) of WDNs is defined on the basis of necessity measure to assess system performance under fuzzy random demands and crisp head requirements. The latin hypercube sampling method is adopted for sampling of uncertain demands. The methodology is applied to two WDNs, and optimization models are solved through cross entropy optimization for different levels of reliability, and generated tradeoffs between the cost and R. On comparing the solutions obtained with the proposed methodology with earlier reported solutions, it is noted that the proposed method is very effective in producing robust optimal solutions. On analyzing the tradeoffs between reliability and costs, the results show that negligence of uncertainty can lead to under design of the WDNs, and the cost increases steeply at higher levels of reliability. The results of the two case studies demonstrate that the presented CE based methodology is effective for fuzzy-probabilistic design of WDNs.     

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.     

Simulation of Water Distribution Network under Pressure-Deficient Condition

Pressure deficient condition occurs in the water distribution network (WDN) when the nodal demands are in excess of the design discharge as in the case of fire demand, pump failure, pipe breaks, valve failure etc. It causes either no-flow or partial-flow depending upon the available pressure head at the nodes. To evaluate the nodal flows in such condition, node flow analysis (NFA) gives reasonable results in comparison to demand-driven analysis (DDA) and head-dependent analysis (HDA). The NFA works on the predefined pressure-discharge relationship to evaluate the nodal flows. However, this approach requires human intervention and hence cannot be applied to large WDN. Recently, modified pressure-deficient network algorithm (M-PDNA) has been developed by Babu and Mohan (2012) for pressure-deficient analysis with EPANET toolkit. However, it requires modification of the source code of EPANET. In this study a relationship with the M-PDNA and node flow analysis (Gupta and Bhave 1996) has been investigated and it is found that M-PDNA is the simplified version of NFA. Further, the working principle of M-PDNA has been investigated with suitable examples of Babu and Mohan (2012). The theoretical basis of M-PDNA has not been investigated in terms of head-discharge relationship. Herein, a head-discharge relationship based on the working principal of M-PDNA is proposed. Some of the toolkits are also readily available to modify demand driven solver of EPANET 2 to suit for the pressure-driven analysis and then it can be used for analysing pressure deficient network. Also in this study, a modification in M-PDNA approach is proposed which does not require the use of EPANET toolkit which is found to be capable of simulating both pressure-sufficient and pressure-deficient conditions in a single hydraulic simulation. Using the proposed approach, pressure-deficient condition is analysed with constant and variable demand pattern.     

Modelling Water Distribution Systems with Deficient Pressure: An Improved Iterative Methodology

In the last three decades, many researchers have proposed different models for water distribution network (WDN) hydraulic analysis by head-driven analysis (HDA). By considering a pressure-discharge relationship (PDR), head-driven analysis (HDA) can avoid deviation caused by traditional demand-driven analysis (DDA) under abnormal conditions. Generally, there are three types of HDA models: 1) models achieved by embedding a PDR into DDA, 2) models using EPANET structures such as emitter or tank to take place of PDR, 3) models aiming at modifying nodal outflows to satisfy PDR based on EPANET. Among these models, modifying nodal outflows is flexible to simulate network with different PDRs and specify parameters related to PDR. Most of the models use iterative algorithms to solve HDA problems; however, present ways to ensure convergence of models are still inadequate. The purpose of this paper is to present a new way to meet the iterative convergence when modifying nodal outflows based on PDR and leakage. This new methodology has been incorporated into the hydraulic network solver EPANET and is formalized algorithmically as EPANET-IMNO. Then two typical networks are used to test EPANET-IMNO, and the results demonstrate that EPANET-IMNO can converge well and applied successfully both in static simulation and extended period simulation. Different pressure deficiency conditions are tested to further confirm the flexibility and the convergence of EPANET-IMNO. Furthermore, quality analysis results back that pressure reduction can be a practical way in contamination accident response.     

Water Distribution System Reliability Based on Minimum Cut – Set Approach and the Hydraulic Availability

Reliability analysis of water distribution systems is a complex task, as it requires both definition and calculation of several reliability measures. In this paper, a methodology for evaluating water distribution system reliability is developed and demonstrated on a simple water distribution network based on the minimum cut-set approach. In general, the definition of the minimum cut-set can arise either from the mechanical reliability or from the concept of hydraulic reliability. In the case of mechanical reliability, a new method based on graph theory is developed, in order to determine the minimum cut-set. This method is based on the counting of paths between nodes. Furthermore, the general concept of reliability is proposed, to include apart from the mechanical reliability, more generally, the pressure availability at nodes as a main hydraulic property. Based on the pressure availability, the sense of hydraulic availability can be expressed as a fuzzy set, while the combination of the water unavailability of the nodes can be achieved by using fuzzy averaging aggregator. Finally, an overall reliability index is proposed based on both the hydraulic and the mechanical reliability. An illustrative example is developed to indicate the methodology.     

Noniterative Implementation of Pressure-Dependent Demands Using the Hydraulic Analysis Engine of EPANET 2

To analyze water distribution networks under pressure-deficient conditions, most of the available hydraulic simulators, including EPANET 2, must be either modified by embedding pressure-dependent demands in the governing network equations or run repeatedly with successive adjustments made to specific parameters until a sufficient hydraulic consistency is obtained. This paper presents and discusses a simple technique that implements the square root relationship between the nodal demand and the nodal pressure using EPANET 2 tools and allows a water distribution network with pressure-dependent demands to be solved in a single run of the unmodified snapshot hydraulic analysis engine of EPANET 2. In this technique, artificial strings made up of a flow control valve, a pipe with a check valve, and a reservoir are connected to the demand nodes before running the engine, and the pressure-dependent demands are determined as the flows in the strings. The resistance of the artificial pipes is chosen such that the demands are satisfied in full at a desired nodal pressure. The proposed technique shows reasonable convergence as evidenced by its testing on example networks.     

Uniformly Distributed Demand EPANET Extension

EPANET-2 is a popular public domain package widely used to determine flow in Water Distribution Networks (WDN) in Extended Period Simulation (EPS). In its original formulation the water demand is represented as lumped withdrawals at network nodes. However, this approximation may introduce significant errors in the hydraulic head distribution, since energy balance is not respected at the level of the single edge (pipe). To overcome this drawback we propose a new implementation of EPANET-2 with the water demand uniformly distributed along the pipes. This new formulation obeys energy balance but introduces significant changes in the system of equations, which is therefore solved by introducing a proper relaxation factor in the Global Gradient Algorithm (GGA) implemented in the original version of the software. This new version of the software, we named DD-EPANET, produces an accurate representation of pressure distribution and allows to identify accurately the point of minimum head also when it is located within an edge of the network. The new scheme is suitable for long term simulations in particular for calibration and optimization of WDNs, in particular when data on water demand are scarce.     

Identification of Critical Pipes for Water Distribution Network Rehabilitation

The water distribution network needs to be rehabilitated when the network is unable to perform the desired function. In this study, a methodology is developed to identify the critical pipes in the water distribution network for its rehabilitation by using four network reliability metrics: supply shortage, pressure decline, energy loss per unit length, and the hydraulic uniformity index. These metrics consider different aspects of reliability of the water distribution network using pressure-dependent analysis to calculate the overall criticality of the pipes. In contrast to the conventional reliability index, the present study uses both the normal and abnormal conditions at nodes (fire demand) and pipe (pipe failure) and thus, provides more balance reliability metrics for the network. The literature shows that the node and pipe level metrics have been used separately, whereas in this study both the node and pipe level metrics are combined to develop the present methodology. The methodology is applied to four different water distribution networks, including one typical realistic water distribution network, the data for which is adopted from literature. The results show that the methodology can identify the critical pipes successfully to prioritize the water distribution network rehabilitation and found to be simple in implementation for practicing professionals. The results further show that the critical pipes are found to be located from the source on the paths that do not have a loop or around the nodes of higher demand. The study might also be useful for the extension plan of a water distribution network along with strengthening the deficient nodes/ pipes of the network.

     

Pressure Driven analysis of water distribution systems for preventing siphonic flow

The analysis of the water distribution network is complicated and requires several assumptions to simplify its problem definition. Demand Driven Analysis (DDA) is typically used to analyse the network assuming that all network nodes can deliver the required demand regardless of the available pressure. In the case of analysing an existing network under deficit condition such as pipe breakage or extra demand required for firefighting, assumptions used to simulate the network with DDA is not valid. Node Head Flow Relationship (NHFR) should be considered through Pressure Driven Analysis (PDA) to analyse the network. Most PDA methods assume that the networks are airtight which means that if the pressure at any demand node is negative, delivered demand will be equal to zero and the flow is permitted in the connected pipes (Siphonic flow). This assumption is hydraulically incorrect since the air is allowed to get into the connected pipes and prevent their flow leading to node isolation. In this paper, a new Pressure Driven Analysis to Prevent Siphonic Flow (PDA-SF) approach is proposed to analyze the network under deficit conditions and consider isolating the nodes that show available head less than node elevation. The PDA-SF was tested and compared to previous methods in four case studies under steady state analysis or extended period simulation. The case studies cover also different network conditions whether node isolation is needed or not. The PDA-SF was able to solve different networks where other methods failed to achieve the required demand or service pressure. The new PDA-SF method shall enable peers and modelers to better simulate and analysis water distribution networks.     

Comparison Among Resilience and Entropy Index in the Optimal Rehabilitation of Water Distribution Networks Under Limited-Budgets

The replacement of existing pipes is a strategy for the rehabilitation of water distribution networks that is frequently adopted by water companies. Usually, the optimal choice of the pipes diameter is a difficult optimization task, because limited budgets are available. In order to support the selection of a rehabilitation strategy, surrogate reliability measures are often used as an indirect measure of the water distribution system hydraulic performance. Among others, the resilience and entropy indices have attracted considerable interest because they both represent a measure of the network robustness. In the present work, a comparison between these indices is provided in the framework of the optimal rehabilitation of an existing network under limited budget constraint. The resilience and entropy indices are applied to the case of a realistic water distribution network in an extended period simulation framework. Several values of the maximum budget allocable for rehabilitation are considered, and hydraulic calculations are undertaken by means of a pressure driven approach within a modified EPANET 2 environment. The effectiveness of the two surrogate reliability measures is demonstrated by an a-posteriori reliability assessment.     

A New Optimization Approach for the Least-Cost Design of Water Distribution Networks: Improved Crow Search Algorithm

Due to large number of decision variables and several hydraulic constraints, optimal design of water distribution networks (WDNs) is considered as one of the most complex optimization problems. This paper introduces and applies a new optimization approach, improved crow search algorithm (ICSA), based on the improvement of original crow search algorithm (CSA) by adding an operator parameter. Both approaches (i.e., CSA and ICSA) were applied to two case studies (i.e., Two-Reservoir and Khorramshahr City networks) by linking the hydraulic simulator (e.g., EPANET 2.0). The proposed ICSA saved the total construction cost by 2.16% and 1.79% for the Two-Reservoir and Khorramshahr City networks compared to the original CSA based on optimal network design, respectively. Results revealed that the proposed ICSA provided outstanding design for the both WDNs compared to previous studies and original CSA.

     

Optimal Operational Scheduling of Pumps to Improve the Performance of Water Distribution Networks

Widely used software packages might still be deficient when it comes to optimal pump scheduling as they allow concurrent Variable Speed Pumps (VSPs) at low speeds and low efficiency. In this study, a new method is developed to optimize the Number of Active Pumps (NAPs) and their variable setting, not only to address the mentioned issue, but also to improve pressure reliability, leakage, and electrical power consumption in Water Distribution Networks (WDNs). For this purpose, an Active Pumps Index (API) is proposed to find the optimal NAPs at each time step and a single-objective Network Pressure Reliability Index (NPRI) is used to optimize VSP setting. Particle Swarm Optimization (PSO) algorithm is developed in MATLAB and linked with EPANET as the hydraulic simulator. The proposed method is applied to a sample and a real WDN. The results in both cases show a significant reduction in NAPs, as well as energy costs, while tangibly improving leakage and pressure reliability, especially in big pump stations with several pumps.

     

Pressure Management Model for Urban Water Distribution Networks

A technique for leakage reduction is pressure management, which considers the direct relationship between leakage and pressure. To control the hydraulic pressure in a water distribution system, water levels in the storage tanks should be maintained as much as the variations in the water demand allows. The problem is bounded by minimum and maximum allowable pressure at the demand nodes. In this study, a Genetic Algorithm (GA) based optimization model is used to develop the optimal hourly water level variations in a storage tank in different seasons in order to minimize the leakage level. Resiliency and failure indices of the system have been considered as constraints in the optimization model to achieve the minimum required performance. In the proposed model, the results of a water distribution simulation model are used to train an Artificial Neural Network (ANN) model. Outputs of the ANN model as a hydraulic pressure function is then linked to a GA based optimization model to simulate hydraulic pressure and leakage at each node of the water distribution network based on the water level in the storage tank, water consumption and elevation of each node. The proposed model is applied for pressure management of a major pressure zone with an integrated storage facility in the northwest part of Tehran Metropolitan area. The results show that network leakage can be reduced more than 30% during a year when tank water level is optimized by the proposed model.     

A New Method for Simultaneous Calibration of Demand Pattern and Hazen-Williams Coefficients in Water Distribution Systems

Water distribution systems, where flow in some pipes is not measured or storage tanks are connected together, calculation of demand pattern coefficients of the network is difficult. Since, Hazen-Williams coefficients of the network are also unknown; the problem is becoming unintelligible further. The present study proposes a new method for simultaneous calibration of demand pattern and Hazen-Williams coefficients that uses the Ant Colony Optimization (ACO) algorithms coupled with the hydraulic simulator (EPANET2) in a MATLAB code. In this paper demand pattern and Hazen-Williams coefficients are the calibration parameters and measured data consist of nodal pressure heads and pipe flows. The defined objective function minimizes the difference between the measured and simulated values. The new proposed method was tested on a two-loop test example and a real water distribution network. The results show that the new calibration model is able to calibrate demand pattern and Hazen-Williams coefficients simultaneously with high precision and accuracy.     

Optimal Design of Water Distribution Systems Based on Entropy and Topology

A new multi-objective evolutionary optimization approach for joint topology and pipe size design of water distribution systems is presented. The algorithm proposed considers simultaneously the adequacy of flow and pressure at the demand nodes; the initial construction cost; the network topology; and a measure of hydraulic capacity reliability. The optimization procedure is based on a general measure of hydraulic performance that combines statistical entropy, network connectivity and hydraulic feasibility. The topological properties of the solutions are accounted for and arbitrary assumptions regarding the quality of infeasible solutions are not applied. In other words, both feasible and infeasible solutions participate in the evolutionary processes; solutions survive and reproduce or perish strictly according to their Pareto-optimality. Removing artificial barriers in this way frees the algorithm to evolve optimal solutions quickly. Furthermore, any redundant binary codes that result from crossover or mutation are eliminated gradually in a seamless and generic way that avoids the arbitrary loss of potentially useful genetic material and preserves the quality of the information that is transmitted from one generation to the next. The approach proposed is entirely generic: we have not introduced any additional parameters that require calibration on a case-by-case basis. Detailed and extensive results for two test problems are included that suggest the approach is highly effective. In general, the frontier-optimal solutions achieved include topologies that are fully branched, partially- and fully-looped and, for networks with multiple sources, completely separate sub-networks.     

Improved Reservoir Operation Using Hybrid Genetic Algorithm and Neurofuzzy Computing

A hybrid genetic and neurofuzzy computing algorithm was developed to enhance efficiency of water management for a multipurpose reservoir system. The genetic algorithm was applied to search for the optimal input combination of a neurofuzzy system. The optimal model structure is modified using the selection index (SI) criterion expressed as the weighted combination of normalized values of root mean square error (RMSE) and maximum absolute percentage of error (MAPE). The hybrid learning algorithm combines the gradient descent and the least-square methods to train the genetic-based neurofuzzy network by adjusting the parameters of the neurofuzzy system. The applicability of this modeling approach is demonstrated through an operational study of the Pasak Jolasid Reservoir in Pasak River Basin, Thailand. The optimal reservoir releases are determined based on the reservoir inflow, storage stage, sideflow, diversion flow from the adjoining basin, and the water demand. Reliability, vulnerability and resiliency are used as indicators to evaluate the model performance in meeting objectives of satisfying water demand and maximizing flood prevention. Results of the performance evaluation indicate that the releases predicted by the genetic-based neurofuzzy model gave higher reliability for water supply and flood protection compared to the actual operation, the releases based on simulation following the current rule curve, and the predicted releases based on other approaches such as the fuzzy rule-based model and the neurofuzzy model. Also the predicted releases based on the newly developed approach result in the lowest amount of deficit and spill indicating that the developed modeling approach would assist in improved operation of Pasak Jolasid Reservoir.     

Location and Calibration of Valves in Water Distribution Networks Using a Scatter-Search Meta-heuristic Approach

Recently, there has been an increase in the use of meta-heuristic techniques addressing water distribution network design and management optimization problems. The meta-heuristic approach applied to water distribution systems has provided interesting results both for optimum pipe diameter sizing and for the location and management of network pressure control devices (i.e., pumps and valves). Regarding the insertion and calibration of pressure regulation valves, the use of meta-heuristic techniques is relatively recent. We search to strategically placing the valves in order to achieve pressure control in the network and, therefore, the valves must be calibrated in relation to water demand trends over time. In the Pressure Reference Method (PRM) described in this paper, the search for valve location is restricted to pipe-branch sets defined on the basis of hydraulic analysis and considering the range between minimum and maximum acceptable pressures in the network. In the PRM approach, the Scatter-Search (Glover and Laguna, 1997) meta-heuristic procedures are applied to obtain the optimal location and calibration of valves in the water distribution network.