Tank Simulation for the Optimization of Water Distribution Networks

In this paper an original approach to the simulation of floating-on-the-system tanks as decision variables for water distribution system design optimization is presented, aiming to bridge the gap between traditional engineering practice and mathematical considerations needed for genetic algorithms (GAs). The paper includes a systematic and detailed critical overview of various mathematical approaches in literature, as well as a novel, more “engineering oriented” approach to the simulation of tanks as decision variables for water distribution system design optimization, describing in detail assumptions and impacts to the evaluation of potential solutions. Tank simulation is based on two decision variables: capacity and minimum normal operational level, omitting risers. Shape and ratio between emergency/total capacities are taken into consideration as design parameters. Assessment of tank performance is carried out by four criteria for the normal daily operational cycle, differentiating between operational and filling capacity, as well as two further criteria for emergency flows. The original design and operational mathematical assumptions are implemented in a fuzzy multiobjective GA model, which is applied to the well-known example from literature “Anytown” water distribution network to benchmark the results.     

Adjusting Nodal Demands in SCADA Constrained Real-Time Water Distribution Network Models

This paper describes the proportional demand method and the target demand method, two techniques for adjusting estimated demands in hydraulic models of water distribution networks to produce solutions that are consistent with available supervisory control and data acquisition (SCADA) data. The two techniques assume that pipe resistances and SCADA data are accurate and that the combination of SCADA data and demand estimates produce overdetermined problems. Nodal demands are regarded as stochastic variables which fluctuate about an estimated mean value. The method of weighted least squares is used to obtain solutions that satisfy all of the constraints imposed by SCADA data with adjusted nodal demands that most closely resemble the estimates. The methods are intended for use in real-time modeling but are limited to quasi-steady state flow. The paper demonstrates the methods on two example problems.     

Considering Actual Pipe Connections in Water Distribution Network Analysis

The classical assumption of representing total demand along a pipe as two lumped withdrawals at its terminal nodes is hitherto common. It is a simplification of the network topology which is useful in order to drastically reduce the number of nodes during network simulation. Conversely, this simplification does not preserve energy balance equation of pipes and, for this reason, it is an approximation that could generate significant head loss errors. This paper presents a modification of the global gradient algorithm (GGA) which entails an enhancing of GGA (EGGA) permitting the effective introduction of the lumped nodal demands, without forfeiting correctness of energy balance, by means of a pipe hydraulic resistance correction. The robustness and convergence properties of the algorithm are compared with those of the classical GGA. Furthermore, the effectiveness of EGGA is demonstrated by computing the network pressure status under different configurations of the connections along the pipes of a test network.     

Optimal Sampling Design Methodologies for Water Distribution Model Calibration

Sampling design (SD) for water distribution systems (WDS) is an important issue, previously addressed by various researchers and practitioners. Generally, SD has one of several purposes. The aim of the methodologies developed and presented here is to find the optimal set of network locations for pressure loggers, which will be used to collect data for the calibration of a WDS model. First, existing SD approaches for WDS are reviewed. Then SD is formulated as a multiobjective optimization problem. Two SD models are developed to solve this problem, both using genetic algorithms (GA) as search engines. The first model is based on a single-objective GA (SOGA) approach in which two objectives are combined into one using appropriate weights. The second model uses a multiobjective GA (MOGA) approach based on Pareto ranking. Both SD models are applied to two case studies (literature and real-life problems). The results show several advantages and one disadvantage of the MOGA model when compared to SOGA. A comparison of the MOGA SD model solution to the results of several published SD models shows that the Pareto optimal front obtained using MOGA acts as an envelope to the Pareto fronts obtained using previously published SD models.     

Real-Time Connectivity Modeling of Water Distribution Networks to Predict Contamination Spread

This paper presents a new approach to analyzing water distribution networks during a contamination event. Previous computer models for predicting the extent of contamination spread in water distribution networks are demand-driven models. The new approach makes use of supervisory control and data acquisition (SCADA) data to create connectivity matrices, which encapsulate the worst-case projection of the potential spread of contamination obtained by combining the effects of all possible scenarios. Two methods for creating connectivity matrices are described, the first based on operating modes, and the second on fundamental paths. Both methods produce identical results, although the method of fundamental paths is more efficient computationally. The connectivity- and hydraulic-based approaches are compared using an example problem.     

Water Distribution System Analysis: Newton-Raphson Method Revisited

Looped water distribution systems are conventionally analyzed using iterative methods such as Cross, Linear, Newton-Raphson, and Gradient algorithm methods. Depending on the unknown (hydraulic head or discharge), the methods are characterized as h or Q methods. This paper focuses on the h-Newton-Raphson method, which uses the Darcy-Weisbach head loss equation. The paper presents a procedure for improving the h-Newton-Raphson iterative procedure by directly calculating the discharge of each branch by using the Swamee and Jain equation. The proposed procedure leads to a simplified algorithm and more accurate determination of the Jacobian matrix, which accelerates the convergence of the algorithm.     

Pressure-Driven Demand and Leakage Simulation for Water Distribution Networks

Increasingly, water loss via leakage is acknowledged as one of the main challenges facing water distribution system operations. The consideration of water loss over time, as systems age, physical networks grow, and consumption patterns mature, should form an integral part of effective asset management, rendering any simulation model capable of quantifying pressure-driven leakage indispensable. To this end, a novel steady-state network simulation model that fully integrates into a classical hydraulic representation, pressure-driven demand and leakage at the pipe level is developed and presented here. After presenting a brief literature review about leakage modeling, the importance of a more realistic simulation model allowing for leakage analysis is demonstrated. The algorithm is then tested from a numerical standpoint and subjected to a convergence analysis. These analyses are performed on a case study involving two networks derived from real systems. Experimentally observed convergence/error statistics demonstrate the high robustness of the proposed pressure-driven demand and leakage simulation model.     

Novel Cellular Automata Approach to Optimal Water Distribution Network Design

This paper proposes a novel heuristic-based and cellular automata-inspired approach to the optimal design of water distribution networks. The design of water distribution networks is of central importance to the water industry, but many networks cannot be optimally designed by traditional techniques due to their complexity. Genetic algorithms have become a state-of-the-art technique for this purpose but are hampered by the fact that they are population based and require a large number of model evaluations to achieve good solutions. The proposed approach uses a parallel, localist, heuristic-based algorithm to optimally design water distribution networks requiring only a limited number of model evaluations. The algorithm is applied to a well-known simple test network and two real water distribution systems in the U.K. The results indicate that the proposed cellular approach is a viable alternative to genetic algorithm approaches while using only a fraction of the computational time required by its evolutionary counterpart.     

Calibration of Water Distribution Hydraulic Models Using a Bayesian-Type Procedure

Estimating model parameters is a difficult, yet critical step in the use of water distribution system models. Most of the optimization-based approaches developed so far concentrate primarily on efficient and effective ways of obtaining optimal calibration parameter values. At the same time, very little effort has been made to determine the uncertainties (i.e., errors) associated with those values (and related model predictions). So far, this has typically been done using the first-order second moment (FOSM) method. Even though reasonably computationally efficient, the FOSM approach relies on several restrictive assumptions and requires computationally demanding calculation of derivatives. To overcome these limitations, the recently developed shuffled complex evolution metropolis (SCEM-UA) global optimization algorithm is linked to the Epanet2 hydraulic model and used to solve a least-squares-type calibration problem. The methodology is tested and verified on the Anytown literature case study. The main advantage of the SCEM-UA algorithm over existing approaches is that both calibration parameter values and associated uncertainties can be determined in a single optimization model run. In addition, no model linearity or parameter normality assumptions have to be made nor any derivatives calculated. The main drawback of the SCEM-UA methodology is that it could, potentially, be computationally demanding, although this is not envisaged as a major problem with current computers.     

Valve Distribution and Impact Analysis in Water Distribution Systems

In water distribution systems, valves play a crucial role in system reliability and security by providing a shutoff function when it is necessary to isolate subsystems. In this paper failure of shutoff valves to close is considered. The failure impact is quantified in terms of the expanding subnetwork and the increased number of customers out of service. To evaluate a system-wide valve failure impact, three methods are suggested: segment–valve matrix, decision tree analysis, and simulation. The segment–valve matrix shows the propagation of failure through the network as valves fail to close. The decision tree enumerates all possible valve failure combinations and corresponding event probabilities. Because the complete enumeration can be unwieldy, simulation procedures are offered that approximate the enumeration results closely. The details of the methods are illustrated with the aid of an example.     

Optimization of Water Distribution Networks Using Integer Linear Programming

In this study optimum design of municipal water distribution networks for a single loading condition is determined by the branch and bound integer linear programming technique. The hydraulic and optimization analyses are linked through an iterative procedure. This procedure enables us to design a water distribution system that satisfies all required constraints with a minimum total cost. The constraints include pipe sizes, which are limited to the commercially available sizes, reservoir levels, pipe flow velocities, and nodal pressures. Accuracy of the developed model has been assessed using a network with limited solution alternatives, the optimal solution of which can be determined without employing optimization techniques. The proposed model has also been applied to a network solved by others. Comparison of the results indicates that the accuracy and convergence of the proposed method is quite satisfactory.     

Algorithm for Automatic Detection of Topological Changes in Water Distribution Networks

Topological and pressure-driven analyses are an integral part of reliability/risk considerations for a water distribution system. For example, it is often necessary to identify which parts of the distribution network are isolated from water sources after the valves have been closed in response to a mechanical pipe failure. Pressure-driven analysis is then necessary to ascertain the consequences of pipe failures in terms of the performance of the functioning subsystem while pipe breaks are being fixed in the isolated area. Therefore, it is extremely useful to have an algorithm for the automatic identification of nodes/pipes disconnected from the water source(s). However, this is a complex problem because valves sometimes significantly modify the network topology. Furthermore, the use of isolation valves can cause a demand shortage to some customers (due to pressure reduction) during the abnormal operating conditions in the system. Thus, pressure-driven simulation of the network behavior is required. For these reasons, a novel algorithm capable of automatic detection of topological network changes is coupled with a robust pressure-driven simulation model. This algorithm is tested on two case studies involving a small artificial water distribution system and a larger, real-life network. The results obtained clearly demonstrate the robustness of the algorithm developed.     

Eulerian–Lagrangian Method for Constituent Transport in Water Distribution Networks

The transport and mixing of contaminants in conduits is governed by advection, dispersion, and decay. Several models are available to trace the transport of such constituents and most assume that the principal mechanisms for transport are advection and reaction only. However in pipes where low velocities prevail, longitudinal dispersion is significant and models that neglect the dispersion effects fail to properly simulate the observed concentrations in low velocity pipes. This work presents a method for simulating the advection-dispersion-reaction process of constituent transport in water networks. A Eulerian–Lagrangian method is employed whereby the dispersion term in the governing equation is approximated using finite differences and the resulting first-order partial differential equation is then integrated using the method of characteristics. Analytical solutions of the transport equation are also derived to quantify the effect of neglecting dispersion at pipe junctions and to assess the accuracy of the proposed method. The Eulerian-Lagrangian method is tested on benchmark networks and on the field study at the Cherry Hill/Brushy Plains network. Results show that the model developed is capable of simulating transport with equal accuracy for low and high velocity flows with and without significant dispersion effects. It also performs better than other models because of the nonuniform grid distribution and the interpolation schemes used.     

Two-Point Linearization Method for the Analysis of Pipe Networks

This note proposes a new method for snapshot analysis of water distribution systems based on the commonly used gradient method. The proposed method uses a secant (intersecting the head-loss function in two points) instead of a tangent to approximate the pipe head-loss function. A theoretical model is developed for the flow range in which the secant approximates the head-loss function without exceeding a given allowable error. This scheme allows a tradeoff to be made between the allowable error and the number of iterations required to achieve convergence. The proposed method is applied to an example network to illustrate its application and benefits. It is argued that the number of iterations required to find a solution can be reduced significantly in both snapshot and extended-period simulations.     

Steady-State Water Quality Analysis for Pipe Network Systems

In 1993 P. F. Boulos and T. Altman developed an efficient explicit scheme for determining steady state water quality in a distribution system for conservative and zero-order reacting constituents. This approach is extended here to first- and second-order reactions and a general reaction relationship is discussed. Mass balance relationships and nonconservative reaction kinetics lead to a general matrix for constituent analysis. The directed graph that results in steady flow conditions permits single equations to be solved sequentially providing the water quality distribution throughout the system. The method can be used to solve for linear and nonlinear conditions and is demonstrated for first-order decay and growth and second-order decay on a 13-pipe system.     

Water Distribution Network Design Using Heuristics-Based Algorithm

Water distribution network that includes supply reservoirs, overhead tanks, consumer demand nodes, interconnecting pipes, lifting pumps, and control valves is the main mode of water supply for majority of the communities especially in urban areas. Supply of required quantity of water and at right time is the primary objective of water distribution network analysis. The analysis of water distribution networks can be broadly classified into design and operation problems and both problems have been the focus of many researchers over the past three decades. In the water distribution network design problems, the target is attaining the cost effective configuration that satisfies the minimum hydraulic head requirement at the demand nodes. In this paper, a new algorithm for design of water distribution network namely “heuristics-based algorithm” which completely utilizes the implicit information associated with the water distribution network to be designed has been proposed and validated with two water distribution networks. It is found that the proposed algorithm performs well for the least-cost design of water distribution networks.     

Optimal Design of Pressurized Irrigation Subunit

A linear programming (LP) model is presented for optimal design of the pressurized irrigation system subunit. The objective function of the LP is to minimize the equivalent annual fixed cost of pipe network of the irrigation system and its annual operating energy cost. The hydraulic characteristics in the irrigation subunit are ensured by using the length, energy conservation, and pressure head constraints. The input data are the system layout, segment-wise cost and hydraulic gradients in all the alternative pipe diameters, and energy cost per unit head of pumping water through the pipeline network. The output data are: segment-wise lengths of different diameters, operating inlet pressure head, and equivalent annual cost of the pipeline network. The explicit optimal design is demonstrated with design examples on lateral and submain or manifold of pressurized irrigation systems. The effect of the equations for friction head loss calculation on optimization procedure is investigated through the design example for microirrigation manifold. The performance evaluation of the proposed model in comparison with the analytical methods, graphical methods, numerical solutions, and dynamic programming optimization model reveals the good performance of the proposed model. The verification of operating inlet pressure head obtained by the proposed model with accurate numerical step-by-step method suggested that it is mostly accurate.     

Pipe Index Vector: A Method to Improve Genetic-Algorithm-Based Pipe Optimization

This paper proposes a methodology for the optimal design of water distribution systems based on genetic algorithms. The objective of the optimization is to minimize the capital cost, subject to ensuring adequate pressures at all nodes during peak demands. The proposed method is novel in that it involves the use of a pipe index vector to control the genetic algorithm search. The pipe index vector is a measure of the relative importance of pipes in a network in terms of their impact on the hydraulic performance of the network. By using the pipe index vector it is possible to exclude regions of the search space where impractical and infeasible solutions exist. By reducing the search space it is possible to generate feasible solutions more quickly and hence process much healthier populations than would be the case in a standard genetic algorithm. This results in optimal solutions being found in a fewer number of generations resulting in a substantial saving in terms of computational time. The method has been tested on several networks, including networks used for benchmark testing least cost design algorithms, and has been shown to be efficient and robust.     

Water Distribution Network Analysis Using Excel

The analysis of water distribution networks has been and will continue to be a core component of civil engineering water resources curricula. Since its introduction in 1936, the Hardy Cross method has been used in virtually every water resources engineering text to introduce students to network analysis. The technique gained widespread popularity primarily because it is amenable to manual calculation techniques. However, the same subtle elegance that facilitates manual calculations often obscures the primary engineering and physical principles of water distribution systems relative to the nuances of algorithm implementation. Herein, the authors illustrate the application of commonly available spreadsheet software (MicroSoft Excel) to more concisely and effectively solve typical undergraduate network distribution problems using linear theory. Application development is much more efficient and straightforward than the corresponding Hardy Cross implementation enabling students to concentrate upon the engineering system and relevant design issues. The technique presented utilizes commonly available technology and is presented as a supplement to alternatives discussed in recent literature.     

Demand Forecasting for Irrigation Water Distribution Systems

One of the main problems in the management of large water supply and distribution systems is the forecasting of daily demand in order to schedule pumping effort and minimize costs. This paper examines methodologies for consumer demand modeling and prediction in a real-time environment for an on-demand irrigation water distribution system. Approaches based on linear multiple regression, univariate time series models (exponential smoothing and ARIMA models), and computational neural networks (CNNs) are developed to predict the total daily volume demand. A set of templates is then applied to the daily demand to produce the diurnal demand profile. The models are established using actual data from an irrigation water distribution system in southern Spain. The input variables used in various CNN and multiple regression models are (1) water demands from previous days; (2) climatic data from previous days (maximum temperature, minimum temperature, average temperature, precipitation, relative humidity, wind speed, and sunshine duration); (3) crop data (surfaces and crop coefficients); and (4) water demands and climatic and crop data. In CNN models, the training method used is a standard back-propagation variation known as extended-delta-bar-delta. Different neural architectures are compared whose learning is carried out by controlling several threshold determination coefficients. The nonlinear CNN model approach is shown to provide a better prediction of daily water demand than linear multiple regression and univariate time series analysis. The best results were obtained when water demand and maximum temperature variables from the two previous days were used as input data.