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.     

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.     

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.     

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.     

Optimal Design of Pipe Networks Accounting for Future Demands and Phased Expansion using Integrated Dynamic Programming and Differential Evolution Approach

The water distribution network (WDN) design comprises determining optimal pipe sizes to achieve minimum cost pipe network to meet the required demands and performance levels. However, with time, the water demand for any region changes due to population, migration, and lifestyles, so interventions need to be made to the existing WDNs. Therefore, the capacity expansion problem consists of determining the suitable interventions at various stages such that the required demands are met at minimum cost. The present study proposed a novel methodology for planning such interventions based on Dynamic Programming (DP) formulation and presented a combined Self-Adaptive Differential Evolution and DP (SADE-DP) methodology for solving the WDN expansion problems considering life cycle costs. The methodology is applied and tested on three benchmark WDNs, namely New York Tunnel (NYT), Two loop (TL), and Blacksburg (BLA) networks, and also for a real case study of the Badlapur WDN in Maharashtra, India. The proposed model solutions are validated by comparing them with other WDN expansion methods taken from the literature. The results indicate that the proposed SADE-DP approach is computationally efficient and provides cost-effective solutions by meeting desired performance levels at various stages, and can serve as a potential alternative for solving real-world WDN expansion problems.

     

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 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.

     

Water Distribution Networks Resilience Analysis: a Comparison between Graph Theory-Based Approaches and Global Resilience Analysis

Water Resources Management - The structure and connectivity of infrastructure systems such as water distribution networks (WDNs) affect their reliability, efficiency and resilience. Suitable...     

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.     

Extending EPANET hydraulic solver capacity with rigid water column global gradient algorithm

EPANET is one of the most commonly used open-source programs in hydraulic modelling water distribution networks (WDNs), based on steady-state and extended period simulation approaches. These approaches effectively estimate flow capacity and average pressures in networks; however, EPANET is not yet fully effective in modelling incompressible unsteady flows in WDNs. In this study, the hydraulic solver capacity of EPANET 3 is extended with the Rigid Water Column Global Gradient Algorithm (RWC-GGA) to model incompressible unsteady flow hydraulics in WDNs. Moreover, we incorporated dynamically more accurate valve expressions than the existing ones in the default EPANET code and introduced a new global convergence algorithm, Convergence Tracking Control Method (CTCM), in the solver code. The RWC-GGA, CTCM, and valve expressions are tested and validated in three different WDNs varying from simple to sophisticated set-ups. The results show that incompressible unsteady flows can be modelled with RWC-CGA and dynamic valve representations. Finally, the convergence problem due to the valve motion and the pressure-dependent algorithm (PDA) is solved by the implemented global convergence algorithm, i.e. CTCM.     

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.     

Design of a Pumping Main Considering Pipeline Failure

Cost and reliability are two diametrically opposite objectives in a pumping main design as the objective of an uninterrupted supply of water will increase the system cost. In this investigation, a methodology for pumping main design is presented by considering the costs of pumping main and pipeline breakage. Although it has been found that there is no clear-cut optimum point in such a design objective, there is however, a set of non-dominated points called Pareto-optimal front which can be used to optimize pipe diameter. It is hoped that this methodology will be useful to design engineers engaged in the design of pumping mains and will also result in the cost savings to water service providers.     

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.     

Application of Parameter-Less Rao Algorithm in Optimization of Water Distribution Networks Through Pressure-Driven Analysis

Water Resources Management - Water distribution networks (WDNs) connect consumers to the source of water. The primary goal of optimizing WDNs is to minimize the network costs as WDNs entail high...     

Design of Water Distribution Network for Equitable Supply

Water shortage is experienced in different parts of the world in different magnitude. In certain countries, water deficit is a regular phenomenon and in some other countries it happens for a short duration, due to failure of any component in the system. Shortage of water at source can be best tackled by distributing the available water equally among the consumers. This paper deals with the design of water distribution network capable of equitable supply during shortage in addition to the satisfactory performance under non-deficit condition. Performance of a typical water distribution network, with shortage of water at source is illustrated in detail. Head dependent outflow analysis with extended period simulation, is used to determine the actual supply from each node to consumers. Relationship between duration of supply and volume available at source as well as supply from each node are established for understanding the behaviour of network under low supply situation. A term “inequity” which is the maximum difference in supply demand ratio among different consumers is presented. This is based on the actual performance of the network instead of surrogate measures, generally used for reliability. It is illustrated that the maximum “inequity” in supply in a network during the entire duration of supply can be estimated with single analysis. Design of a water distribution network, duly considering equity in addition to the cost minimization and minimum head requirement is presented. Genetic Algorithm is used for solving this multi objective problem. The solution technique is illustrated using two benchmark problems, namely two loop network and Hanoi network. Results show that considerable improvement in equitable supply can be achieved with additional investment on pipes above the least cost solution. Hence it is better to design networks duly considering deficit condition for better reliability. It is also illustrated that it will be difficult to improve equity beyond a limit for a given network, through selection of different pipe diameters.     

考虑水质与水价影响的城市再生水需求研究

再生水是城市的“第二水源”,加强再生水配置利用对优化供水结构、增加水资源供给、缓解水量供需矛盾以及保障水生态安全具有重要意义。科学预测城市再生水需求是提高污水资源化利用水平的重要基础。在区域水资源需求分析基础上,充分考虑工业生产、城市杂用、河道补水、农林灌溉等4大领域的水量和水质需求特点,提出考虑水质与水价的分领域再生水需求预测技术框架。首先考虑水质影响,引入再生水可替代率指标,分析水资源需求总量中可由再生水供给的水量;其次,考虑自主定价模式下再生水价格对用户需求的影响,建立“补贴-价格-需求”模型,计算不同补贴情景下区域再生水的需求量;最后,应用于宿迁市中心城市。结果表明：在规划年2025和2030年的再生水利用率目标要求下,采用中等补贴情景能在有效推广再生水利用的同时兼顾政府财政压力,再生水需求量分别可达10 095×10⁴和13 387×10⁴ m³。本研究进一步拓展了城市再生水需求量预测的理论方法,也为宿迁市再生水利用配置提供了科学依据。     

Optimal Design of Pressurized Irrigation Networks to Minimize the Operational Cost under Different Management Scenarios

The adoption of measures leading to higher efficiencies in the use of both water and energy in water distribution networks is strongly demanded. The methodology proposed combines a multi-objective approach and a financial analysis to determine de optimal design of pressurized irrigation networks which entails the minimization of both the investment cost and operational cost under three operating scenarios that incorporate energy saving strategies: 1- all hydrants operate simultaneously; 2- hydrants are grouped into sectors and irrigation turns are established; 3- the on-demand operation of the network is assumed. This methodology has been applied in a real irrigation network located in Southern Spain showing that the lowest overall design cost (investment and operational costs) is achieved in scenario 2. The comparison of the selected solutions in the three proposed scenarios with the current network design considering the total fulfillment of irrigation requirements showed that operational cost savings between 65% and 76% could be achieved.     

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.     

Equity in Domestic Water Rates Design

Water rates seek at once to fund the service, to distribute the cost among users and to allocate water based on demand. Therefore, rates design is frequently subject to normative criteria such as full cost recovery, efficiency, equity and simplicity. This paper, proposes a method of ensuring the operational effectiveness of the equity criterion. Specifically, the objective is to resolve the problem of equity caused by pricing systems involving stepwise increments in the cost of aggregate household consumption. The problem is that it is more costly to meet basic individual water needs, the larger the household concerned. This paper analyses the water rates applied in the city of Zaragoza (Spain) and proposes a new rates design based on the normative criteria referred to above, which is applicable to any city and, therefore, may be of general interest. The authors are grateful for the financial support received from the Spanish Ministry of Education and Science via research project SEC2005-06069/ECON and from the City Council of Zaragoza under the Agreement for water research made with the University of Zaragoza.     

TWO-PROCEDURE OF MODEL RELIABILITY-BASED OPTIMIZATION FOR WATER DISTRIBUTION SYSTEMS

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