Joint Entropy Based Multi-Objective Evolutionary Optimization of Water Distribution Networks

It is essential to consider resilience when designing any water distribution network and surrogate measures of resilience are used frequently as accurate measures often impose prohibitive computational demands in optimization algorithms. Previous design optimization algorithms based on flow entropy have essentially employed a single loading condition because the flow entropy concept formally has not been extended to multiple loading conditions in water distribution networks. However, in practice, water distribution networks must satisfy multiple loading conditions. The aim of the research was to close the gap between the prevailing entropy-based design optimization approaches based on one loading condition essentially and water distribution practice that must address multiple loading conditions. A methodology was developed and applied to a real-world water distribution network in the literature, based on the concept of the joint entropy of independent probability schemes. The results demonstrated that the critical loading conditions were design specific. In other words, the critical loading and operating conditions cannot readily be determined beforehand. Consequently, maximizing the joint entropy provided the most consistently competitive solutions in terms of the balance between cost and resilience. The results were derived using a penalty-free genetic algorithm with three objectives. Compared to previous research using flow entropy based on a single loading condition and two objectives, there was a substantial increase of 274% in the number of nondominated solutions achieved.     

Self-Adaptive Solution-Space Reduction Algorithm for Multi-Objective Evolutionary Design Optimization of Water Distribution Networks

An effective way to improve the computational efficiency of evolutionary algorithms is to make the solution space of the optimization problem under consideration smaller. A new reliability-based algorithm that does this was developed for water distribution networks. The objectives considered in the formulation of the optimization problem were minimization of the initial construction cost and maximization of the flow entropy as a resilience surrogate. After achieving feasible solutions, the active solution space of the optimization problem was re-set for each pipe in each generation until the end of the optimization. The algorithm re-sets the active solution space by reducing the number of pipe diameter options for each pipe, based on the most likely flow distribution. The main components of the methodology include an optimizer, a hydraulic simulator and an algorithm that calculates the flow entropy for any given network configuration. The methodology developed is generic and self-adaptive, and prior setting of the reduced solution space is not required. A benchmark network in the literature was investigated, and the results showed that the algorithm improved the computational efficiency and quality of the solutions achieved by a considerable margin.     

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.     

Reliability Assessment of Urban Water Distribution Networks Under Seismic Loads

Presented herein is a methodology for the seismic assessment of the reliability of urban water distribution networks (UWDN) based on general seismic assessment standards, as per the American Lifelines Alliance (ALA) guidelines, and localized historical records of critical risk-of-failure metrics pertaining to the specific UWDN under assessment. The proposed methodology is applicable to UWDN under both normal or abnormal operating conditions (such as intermittent water supply), and the assessment of reliability incorporates data of past non-seismic damage, the vulnerabilities of the network components against seismic loading, and the topology of a UWDN. Historical data obtained using records of pipe burst incidents are processed to produce clustered ‘survival curves’, depicting the pipes’ estimated survival rate over time. The survival curves are then used to localize the generalized fragility values of the network components (primarily pipes), as assessed using the approach suggested by the ALA guidelines. The network reliability is subsequently assessed using Graph Theory (Djikstra’s shortest path algorithm), while the system reliability is calculated using Monte Carlo simulation. The methodology proposed is demonstrated on a simple small-scale network and on a real-scale district metered area (DMA). The proposed approach allows the estimation of the probability that a network fails to provide the desired level of service and allows for the prioritization of retrofit interventions and of capacity-upgrade actions pertaining to existing water pipe networks.     

Comparison of Surrogate Measures for the Reliability and Redundancy of Water Distribution Systems

An investigation into the effectiveness of surrogate measures for the hydraulic reliability and/or redundancy of water distribution systems is presented. The measures considered are statistical flow entropy, resilience index, network resilience and surplus power factor. Looped network designs that are maximally noncommittal to the surrogate reliability measures were considered. In other words, the networks were designed by multi-objective evolutionary optimization free of any influence from the surrogate measures. The designs were then assessed using each surrogate measure and two accurate but computationally intensive measures namely hydraulic reliability and pipe-failure tolerance. The results indicate that by utilising statistical flow entropy, the reliability of the network can be reasonably approximated, with substantial savings in computational effort. The results for the other surrogate measures were often inconsistent. Two networks in the literature were considered. One example involved a range of alternative network topologies. In the other example, based on whole-life cost accounting, alternative design and upgrading schemes for a 20-year design horizon were considered. Pressure-dependent hydraulic modelling was used to simulate pipe failures for the reliability calculations.     

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.     

Multi-Directional Maximum-Entropy Approach to the Evolutionary Design Optimization of Water Distribution Systems

A new multi-directional search approach that aims at maximizing the flow entropy of water distribution systems is investigated. The aim is to develop an efficient and practical maximum entropy based approach. The resulting optimization problem has four objectives, and the merits of objective reduction in the computational solution of the problem are investigated also. The relationship between statistical flow entropy and hydraulic reliability/failure tolerance is not monotonic. Consequently, a large number of maximum flow entropy solutions must be investigated to strike a balance between cost and hydraulic reliability. A multi-objective evolutionary optimization model is developed that generates simultaneously a wide range of maximum entropy values along with clusters of maximum and near-maximum entropy solutions. Results for a benchmark network and a real network in the literature are included that demonstrate the effectiveness of the procedure.     

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

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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.     

A Simplified Methodology for Optimal Location and Setting of Valves to Improve Equity in Intermittent Water Distribution Systems

In this paper, a simplified methodology to increase the water distribution equity in existing intermittent water distribution systems (WDSs) is presented. The methodology assumes to install valves in the water distribution network with the objective to re-arrange the flow circulation, thus allowing an improved water distribution among the network users. Valve installation in the WDS is based on the use of algorithms of sequential addition (SA). Two optimization schemes based on SA were developed and tested. The first one allows identifying locations of gate valves in order to maximize the global distribution equity of the network, irrespectively of the local impact of the valves on the supply level of the single nodes. Conversely, the second scheme aims to maximize the global equity of the network by optimizing both location and setting (opening degree) of control valves, to include the impact of the new flow circulation on the supply level of each node. The two optimization schemes were applied to a case study network subject to water shortage conditions. The software EPA Storm Water Management Model (SWMM) was used for the simulations in the wake of previous successful applications for the analysis of intermittent water distribution systems. Results of the application of the SA algorithms were also compared with those from the literature and obtained by the use of the multi-objective Non-Dominated Sorted Genetic Algorithm II (NSGA II). The results show the high performance of SA algorithms in identifying optimal position and settings of the valves in the WDS. The comparison pointed out that SA algorithms are able to perform similarly to NSGA II and, at the same time, to reduce significantly the computational effort associated to the optimization process.

     

Socially-Optimal and Nash Pareto-Based Alternatives for Water Allocation under Uncertainty: an Approach and Application

This study has proposed a methodology by enhancing an interactive algorithm to multi-objective optimization problems with interval parameters, in an attempt to reach the tradeoff between quality and reliability of the resultant optimum solutions. The earlier algorithm could turn into a prolonged procedure that deals with several players with different aspirations at different reliability, or risk, levels under non-deterministic conditions. Hence, it is not a pertinent approach to solve problems of water allocation between competing parties. The enhanced methodology aims to alleviate the burdens of the procedure and generate a unique set of solutions (i.e., near-Pareto-optimal alternatives), instead of a myriad of compromise solution sets. We have investigated a real-world hydro-environmental problem, the allocation of water between Dorudzan-Korbal irrigation networks and Bakhtegan Lake in Fars Province, Iran to assess feasibility of this methodology. In order to reach a consensus concerning the stakeholders’ individual preferences, we identified the compromise alternatives from the obtained sets of non-dominated solutions by taking advantage of various social choice rules and the Nash bargaining model. The results demonstrated that the developed methodology could incorporate the risk of system constraints violations (i.e., planning reliability under uncertainty) into the process of approximating the optimal tradeoff set of solutions. It also gave policymakers a chance to acquire perception into the potentially best compromise for land and water allocation schemes regarding the preference profiles of the involved interest groups.     

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

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

Entropy-Based Sensor Placement Optimization for Waterloss Detection in Water Distribution Networks

The work presented herein addresses the problem of sensor placement optimization in urban water distribution networks by use of an entropy-based approach, for the purpose of efficient and economically viable waterloss incident detection. The proposed method is applicable to longitudinal rather than spatial sensing, thus to devices such as acoustic, pressure, or flow sensors acting on pipe segments. The method utilizes the maximality, subadditivity and equivocation properties of entropy, coupled with a statistical definition of the probability of sensing within a pipe segment, to assign an entropy metric to each pipe segment and subsequently optimize the location of sensors in the network based on maximizing the total entropy in the network. The method proposed is a greedy-search heuristic.     

面向双保证率的水库供水能力优化计算方法研究

随着城市化进程的推进和生态文明理念的深入,水库供水任务日趋复杂,涵盖城镇供水、农业灌溉、生态保障多类目标,分析水库多目标供水能力对于工程的功能调整等决策十分必要。本文综合考虑水库供水目标的竞争性与保证率差异性,提出面向双保证率的水库供水能力双层优化计算方法,通过调度线控制和城镇供水能力区间迭代实现满足不同保证率的多目标供水能力计算。外层基于粒子群算法以城镇供水能力最大为目标对水库调度线进行优化,协调不同用户的供水关系;内层在给定规则下通过迭代计算满足双保证率要求的城镇供水能力。通过内外层嵌套计算实现对水库调度规则和供水能力的同步优化。以三亚市赤田水库为实例进行研究,在城镇供水保证率为95%、农业灌溉保证率为90%时,通过优化调度规则得出水库总供水能力为9400万m~3。设置不同农业保证率和农业需水情景作分析对比,二者均对城镇供水能力有影响,总供水能力随农业保证率降低而提高。分析表明,双层优化计算方法可以实现对调度线的优化,得出满足城镇、农业双保证率要求的供水能力,且计算方法收敛稳定性较高,优化生成的调度线年内分布合理,可为水库多目标供水能力的计算和相关决策提供参考。     

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.     

IMPLEMENTING ENVIRONMENTAL FLOWS IN COMPLEX WATER RESOURCES SYSTEMS – CASE STUDY: THE DUERO RIVER BASIN,SPAIN

European river basin authorities are responsible for the implementation of the new river basin management plans in accordance with the European Water Framework Directive. This paper presents a new methodology framework and approach to define and evaluate environmental flow regimes in the realistic complexities that exist with multiple water resource needs at a basin scale. This approach links river basin simulation models and habitat time series analysis to generate ranges of environmental flows (e‐flows), which are evaluated by using habitat, hydropower production and reliability of water supply criteria to produce best possible alternatives. With the use of these tools, the effects of the proposed e‐flows have been assessed to help in the consultation process. The possible effects analysed are impacts on water supply reliability, hydropower production and aquatic habitat. After public agreements, a heuristic optimization process was applied to maximize e‐flows and habitat indicators, while maintaining a legal level of reliability for water resource demands. The final optimal e‐flows were considered for the river basin management plans of the Duero river basin. This paper demonstrates the importance of considering quantitative hydrologic and ecological aspects of e‐flows at the basin scale in addressing complex water resource systems. This approach merges standard methods such as physical habitat simulations and time series analyses for evaluating alternatives, with recent methods to simulate and optimize water management alternatives in river networks. It can be integrated with or used to complement other frameworks for e‐flow assessments such as the In‐stream Flow Incremental Methodology and Ecological Limits of Hydrologic Alteration. Copyright © 2011 John Wiley & Sons, Ltd.     

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.

     

引江济淮工程（河南段）多目标水量优化调度

引江济淮工程（河南段）涉及河道、闸泵、管道和调蓄水库,约束条件复杂,常规的优化调度算法难以搜索可行解,求解效率低。选用受水区缺水率平均值最小、泵站总抽水量最小和受水区缺水率标准差最小作为目标函数,从供水保障、供水成本和公平性角度构建多目标水量优化调度模型。基于可行搜索思路,结合逆序演算和顺序演算过程对约束条件进行处理,引入决策系数,通过映射关系使搜索空间保持在可行域中,结合多目标非支配排序遗传算法（non-dominated sorting genetic algorithms,NSGA-II）进行求解,得到Pareto最优解集,并采用熵权法进行方案优选。结果表明,基于可行搜索的NSGA-II算法能够有效求解复杂调度系统的多目标优化问题,综合考虑多个目标的最优方案相对单目标方案更加合理,结果可为引江济淮工程（河南段）运行管理提供决策支撑。     

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.     

Technical and Environmental Sustainability Assessment of Water Distribution Systems

An environmental and technical sustainability assessment methodology is developed for both centralized and dual water distribution systems (WDSs) with and without fire flow scenarios. Technical sustainability of potable and reclaimed water networks is measured by a sustainability index (SI) assessment using reliability, resiliency, and vulnerability performance criteria. The U.S. Environmental Protection Agency EPANET software is used to simulate hydraulic (i.e. nodal pressure) and water quality (i.e. water age) analysis in a WDS. Total fresh water use and total energy intensity are considered as environmental sustainability criteria. The procedure considers two separate alternatives for meeting fire flows: (1) adding pumping to a system or (2) adding a non-potable WDS. The reclaimed system is designed using linear programming (LP) optimization. For each alternative, multi-criteria decision analysis (MCDA) is used to combine technical and environmental sustainability criteria for an urban WDS.