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.     

Effects of Pipe Roughness Uncertainty on Water Distribution Network Performance During its Operational Period

The design of new water distribution networks (WDNs) is an important social problem. Failures during an operational period provoke deficits in consumption nodes thus decreasing the performance of the network. WDN performance can be defined as the ability to sufficiently secure demand and desirable pressure in nodes based on changes in design parameters. This paper focuses on the evaluation of network performance during an operational period, taking into account pipe roughness uncertainty. A network analysis is performed by generating probabilistic series of pipe roughness using Monte Carlo simulation (MCS) in the operational period of the Two-loop WDN. Results show that an increase in pipe roughness uncertainty causes a decrease in network performance in the operational period. Furthermore, the network has a desirable efficiency only in the first 10 years. Thus, the proposed design methodology that considers the uncertainty of design variables is an effective procedure to evaluate network performance.     

A Superposed Model for the Pipe Failure Assessment of Water Distribution Networks and Uncertainty Analysis: A Case Study

Pipe failure often occurs in water distribution networks (WDNs) and results in high levels of water loss and socio-economic damage. Physical-based, statistical and data-driven models have been developed to estimate pipe failure rates (failures per km of pipe per year) to efficiently manage water losses from WDNs and to ensure safe operations. Due to the complexities of pipe failure patterns, we develop a superposed statistical model to depict the relationship between pipe failure rate and pipe age. The model’s level of uncertainty was then quantified by simulating pipe failures as Poisson numbers. Part of Beijing’s WDN is taken as a study case, and pipe failure data for a 4-year period, as well as pipe properties, are collected to develop the pipe failure model. The case study results show that the pipe failure rates vary with time in a non-monotonic manner and that the proposed model captures pipe failure behaviour with an R² value of 0.95. A 95% confidence interval of modelled pipe failures for each pipe age group is used to describe the uncertainty level of the model. We find that 88% of the observations fall under the 95% confidence interval. The established model could be applied to prioritize pipes with higher failure rates to optimize pipe replacement/rehabilitation strategies. Our uncertainty analysis of this model can help utility managers understand the model’s reliability and formulate reasonable WDN management plans.     

HydroGen: an Artificial Water Distribution Network Generator

Many (metaheuristic) techniques for water distribution network (WDN) design optimisation already have been developed. Despite of the aforementioned scientific attention, only few, high-quality benchmark networks are available for algorithm testing, which, in turn, hinders profound algorithm testing, sensitivity analysis and comparison of the developed techniques. This absence of high-quality benchmark networks motivated us to develop a tool to algorithmically generate close-to-reality virtual WDNs. The tool, called HydroGen, can generate WDNs of arbitrary size and varying characteristics in EPANET or GraphML format. The generated WDNs are compared to (and shown to closely resemble) real WDNs in an analysis based on graph-theoretical indices. HydroGen is used to generate an extensive library of realistic test networks on which (metaheuristic) methods for the optimisation of WDN design can be tested, allowing researchers in this area to run sensitivity analyses and to draw conclusions on the robustness and performance of their methods.     

Energy Production in Water Distribution Networks: A PAT Design Strategy

Pump operating as turbine (PAT) is an effective source of reducing the equipment cost in small hydropower plants. However, the manufacturers provide poor information on the PAT performance thus representing a limit for its wider diffusion. Additional implementation difficulties arise under variable operating conditions, characteristic of water distribution networks (WDNs). WDNs allow to obtain widespread and globally significant amount of produced energy by exploiting the head drop due to the network pressure control strategy for leak reductions. Thus a design procedure is proposed that couples a parallel hydraulic circuit with an overall plant efficiency criteria for the market pump selection within a WDN. The proposed design method allows to identify the performance curves of the PAT that maximizes the produced energy for an assigned flow and pressure-head distribution pattern. Finally, computational fluid dynamics (CFD) is shown as a suitable alternative for performance curve assessment covering the limited number of experimental data.     

Water Quality Sensor Placement: A Multi-Objective and Multi-Criteria Approach

To satisfy their main goal, namely providing quality water to consumers, water distribution networks (WDNs) need to be suitably monitored. Only well designed and reliable monitoring data enables WDN managers to make sound decisions on their systems. In this belief, water utilities worldwide have invested in monitoring and data acquisition systems. However, good monitoring needs optimal sensor placement and presents a multi-objective problem where cost and quality are conflicting objectives (among others). In this paper, we address the solution to this multi-objective problem by integrating quality simulations using EPANET-MSX, with two optimization techniques. First, multi-objective optimization is used to build a Pareto front of non-dominated solutions relating contamination detection time and detection probability with cost. To assist decision makers with the selection of an optimal solution that provides the best trade-off for their utility, a multi-criteria decision-making technique is then used with a twofold objective: 1) to cluster Pareto solutions according to network sensitivity and entropy as evaluation parameters; and 2) to rank the solutions within each cluster to provide deeper insight into the problem when considering the utility perspectives.The clustering process, which considers features related to water utility needs and available information, helps decision makers select reliable and useful solutions from the Pareto front. Thus, while several works on sensor placement stop at multi-objective optimization, this work goes a step further and provides a reduced and simplified Pareto front where optimal solutions are highlighted. The proposed methodology uses the NSGA-II algorithm to solve the optimization problem, and clustering is performed through ELECTRE TRI. The developed methodology is applied to a very well-known benchmarking WDN, for which the usefulness of the approach is shown. The final results, which correspond to four optimal solution clusters, are useful for decision makers during the planning and development of projects on networks of quality sensors. The obtained clusters exhibit distinctive features, opening ways for a final project to prioritize the most convenient solution, with the assurance of implementing a Pareto-optimal solution.

     

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.     

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.     

Heuristic Optimization Model for the Optimal Layout and Pipe Design of Sewer Systems

The design of urban stormwater systems and sanitary sewer systems consists of solving two problems: generating a layout of the system and the pipe design which includes the crown elevations, slopes and commercial pipe sizes. A heuristic model for determining the optimal (minimum cost) layout and pipe design of a storm sewer network is presented. The hierarchical procedure combines a sewer layout model formulated as a mixed-integer nonlinear programming (MINLP) problem which is solved using the General Algebraic Modeling System (GAMS) and a simulated annealing optimization procedure for the pipe design of a generated layout was developed in Excel. The GAMS and simulated annealing models are interfaced through linkage of Excel and GAMS. The pipe design model is based upon the simulated annealing method to optimize the crown elevations and diameter of pipe segments in a storm sewer network using layouts generated using GAMS. A sample scenario demonstrates that using these methods may allow for significant costs saving while simultaneously reducing the time typically required to design and compare multiple storm sewer networks.     

Pressure Management Through Optimal Location and Setting of Valves in Water Distribution Networks Using a Music-Inspired Approach

Pressure management through Pressure Reducing Valves (PRVs) is probably the most used approach related to the leakage management in Water Distribution Networks (WDNs). Its effectiveness in reducing the amount of water losses in existing networks has been highlighted in many papers. In this study, the topic is addressed with particular reference to meta-heuristic optimization techniques, that have proved to be very effective in producing good results with reduced use of computational resources. In particular, the application of the Harmony-Search (HS) method to the location and setting of a pre-fixed number of PRVs is proposed and discussed. A single objective optimization problem is defined which aims at the leakage reduction through the minimization of the water pressures. A double harmonic component is adopted for taking into account both the location and the setting of each PRV. The hydraulic constraints handled by a simulation software are considered as well. The approach is applied to a couple of WDNs: one is the Jowitt and Xu well-known literature test case and the other is a real WDN in Naples, called Napoli Est. The methodology has showed very good results compared to those obtained by using classical Genetic Algorithm techniques both in terms of leakage reduction and computation time.     

Pipe Break Rate Assessment While Considering Physical and Operational Factors: A Methodology based on Global Positioning System and Data-Driven Techniques

An accurate prediction of pipes failure rate plays a substantial role in the management of Water Distribution Networks (WDNs). In this study, a field study was conducted to register pipes break and relevant causes in the WDN of Yazd City, Iran. In this way, 851 water pipes were incepted and localized by the Global Positioning System (GPS) apparatus. Then, 1033 failure cases were reported in the eight zones of understudy WDN during March-December 2014. Pipes break rate (BR_P) was calculated using the depth of pipe installation (h_P), number of failures (N_P), the pressure of water pipes in operation (P), and age of pipe (A_P). After completing a pipe break database, robust Artificial Intelligence models, namely Multivariate Adaptive Regression Spline (MARS), Gene-Expression Programming (GEP), and M5 Model Tree were employed to extract precise formulation for the pipes break rate estimation. Results of the proposed relationships demonstrated that the MARS model with Coefficient of Correlation (R) of 0.981 and Root Mean Square Error (RMSE) of 0.544 provided more satisfying efficiency than the M5 model (R?=?0.888 and RMSE?=?1.096). Furthermore, statistical results indicated that MARS and GEP models had comparatively at the same accuracy level. Explicit equations by Artificial Intelligence (AI) models were satisfactorily comparable with those obtained by literature review in terms of various conditions: physical, operational, and environmental factors and complexity of AI models. Through a probabilistic framework for the pipes break rate, the results of first-order reliability analysis indicated that the MARS technique had a highly satisfying performance when MARS-extracted-equation was assigned as a limit state function.

     

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.

     

Decision support system to divide a large network into suitable District Metered Areas

This paper presents a new approach to divide large Water Distribution Networks (WDN) into suitable District Metered Areas (DMAs). It uses a hydraulic simulator and two operational models to identify the optimal number of DMAs, their entry points and boundary valves, and the network reinforcement/replacement needs throughout the project plan. The first model divides the WDN into suitable DMAs based on graph theory concepts and some user-defined criteria. The second model uses a simulated annealing algorithm to identify the optimal number and location of entry points and boundary valves, and the pipes reinforcement/replacement, necessary to meet the velocity and pressure requirements. The objective function is the difference between the economic benefits in terms of water loss reduction (arising from the average pressure reduction) and the cost of implementing the DMAs. To illustrate the proposed methodology, the results from a hypothetical case study are presented and discussed.     

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.

     

Vulnerability of Urban Water Distribution Networks under Intermittent Water Supply Operations

The work presented herein investigates the effects of intermittent water supply (IWS) on the condition and breakage rate of urban water distribution piping networks (WDN), by studying the change in the rate of occurrence of failures before, during and after IWS periods, using statistical and survival analyses. The analyses, based on a seven-year dataset (2003–2010) from a major urban center of about 300,000 residents, take into account information related with breakage incidents and with operating system parameters, as well as external factors and vulnerability assessments of the network’s key components. The results show an increase in the number of waterloss incidents during and immediately after the periods during which IWS practices were implemented, and they reinforce the belief that IWS practices negatively affect the vulnerability of WDNs.     

Decomposition based Multi Objective Evolutionary Algorithms for Design of Large-Scale Water Distribution Networks

In last two decades, multiobjective evolutionary algorithms (MOEAs) have shown their merit for solving different optimization problems within the context of water resources and environmental engineering. MOEAs mainly use the concept of Pareto dominance for obtaining the trade-off solutions considering different criteria. A new alternative method for solving multiobjective problems is multiobjective evolutionary algorithm based on decomposition (MOEA/D) which uses scalarizing the objective functions. In this paper, decomposition strategies are developed for the large-scale water distribution network (WDN) design problems by integrating the concepts of harmony search (HS) and genetic algorithm (GA) within the MOEA/D framework. The proposed algorithms are then compared with two well-known non-dominance based MOEAs: NSGA2 and SPEA2 across four different WDN design problems. Experimental results show that MOEA/D outperform the Pareto dominance methods in terms of both non-domination and diversity criteria. MOEA/D-HS in particular could provide very high quality solutions with a uniform distribution along the Pareto front preserving the diversity and dominating the solutions of the other algorithms. It suggests that decomposition based multiobjective evolutionary algorithms are very promising in dealing with complicated large-scale WDN design problems.     

Optimization Models for Layout and Pipe Design for Storm Sewer Systems

Optimization models are developed for simultaneously determining the pipe layout and the pipe design for storm sewer systems. The pipe design process includes computation of commercial diameters, slopes, and crown elevations for the storm sewer pipes. The optimization models aim to minimize the total costs of the layout and the pipe design for most of system elements. The optimization models are formulated as a 0–1 Integer Nonlinear Programming problem and solved using the General Algebraic Modeling System without the use of heuristic models which were characteristic of all previous models for the simultaneous determine of the pipe layout and pipe design of sewer networks. The models are based upon two different optimization approaches: (1) considers one or more commercial diameters of pipe connecting two manholes and (2) considers only one commercial diameter in a pipe connecting two manholes. The commercial diameters, pipe slopes, crown elevations, and total costs of the storm sewer system were compared for the two approaches using an example that illustrates the savings in cost by allowing multiple pipe sizes. The two new optimization modeling approaches developed herein can simultaneously determine the minimum cost pipe design (commercial diameters, slopes, and crown elevations) and pipe layout of storm sewer systems and satisfy all design constraints.

     

Evaluation of Reliability Indicators for WDNs with Demand-Driven and Pressure-Driven Models

Reliability of water distribution networks (WDNs) has received much attention in recent years due to progressive aging of infrastructures and climate change. Several reliability indicators, focusing on hydraulic aspects rather than water quality, have been proposed in literature. Reliability is generally assessed resorting to well established methods coupling hydraulic simulations and stochastic techniques that describe the WDNs hydraulic performance and component availability respectively. Two main algorithms are employed to simulate WDNs: the demand driven approach (DDA) that disregards the physical relationship between actual water demand and nodal pressure, and the pressure driven approach (PDA) that explicitly incorporates it. In this paper, we show how the choice of hydraulic solver may affect reliability indicators. We modify existing quantitative indicators at nodal and network level, and define novel indicators to consider water quality aspects. These indicators are evaluated for three example WDNs; discrepancies between results obtained with the two approaches depend on network size, feeding scheme and skeletonization. Results suggest to use with caution the DDA for reliability assessment at both local and global level.     

Multi- Objective Optimal Design of on- Demand Pressurized Irrigation Networks

In the context of water as an economic good, from the use of water, one can derive a value, which can be affected by the reliability of supply. On-demand irrigation systems provide valuable water to skilled farmers who have the capacity to maximize economic value of water. In this study, simultaneous optimization of on-demand irrigation network layout and pipe sizes is considered taking into account both investment and annual energy costs. The optimization problem is formulated as a problem of searching for the upstream head value, which minimizes the total cost (investment and energy costs) of the system. The investment and annual energy costs are obtained in two separate phases. Max–Min ant system (MMAS) algorithm is used to obtain the minimum cost design considering layout and pipe diameters of the network simultaneously. Clement methodology is used to determine flow rates of pipelines at the peak period of irrigation requirements. The applicability of the proposed method is showed by re-designing a real world example from literature.     

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.