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...     

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.     

A Graph-Theoretic Framework for Assessing the Resilience of Sectorised Water Distribution Networks

Water utilities face a challenge in maintaining a good quality of service under a wide range of operational management and failure conditions. Tools for assessing the resilience of water distribution networks are therefore essential for both operational and maintenance optimization. In this paper, a novel graph-theoretic approach for the assessment of resilience for large scale water distribution networks is presented. This is of great importance for the management of large scale water distribution systems, most models containing up to hundreds of thousands of pipes and nodes. The proposed framework is mainly based on quantifying the redundancy and capacity of all possible routes from demand nodes to their supply sources. This approach works well with large network sizes since it does not rely on precise hydraulic simulations, which require complex calibration processes and computation, while remaining meaningful from a physical and a topological point of view. The proposal is also tailored for the analysis of sectorised networks through a novel multiscale method for analysing connectivity, which is successfully tested in operational utility network models made of more than 100,000 nodes and 110,000 pipes.     

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.     

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 Prioritization Model for Rehabilitation of Water Distribution Networks Using GIS

Decision-making for the rehabilitation of water distribution networks in the traditional procedure is based on some simple indices such as the number of incidents while several mechanical, hydraulic and qualitative factors are involved in this process. Evidently, making decision on the rehabilitation of water networks seems to be very difficult as the number of factors increases and they interact with each other. The main objective of this research is to prepare, implement and evaluate a conceptual model to prioritize the rehabilitation of pipes based on different scenarios with respect to the combination effects of basic factors in physical, hydraulic and experimental categories. In order to organize the wide range of data to be used in decision-making models, including the plans aimed for pipe replacement, it is necessary to use geographical information systems (GIS). By determining and introducing the factors involved in the rehabilitation of water networks, this research aims to provide an integrated model consisting of conceptual, GIS, hydraulic analysis and the breakage models to prioritize the rehabilitation schemes. By using the data provided from a real network, the advantages of the proposed methodology are evaluated. Based on the obtained results, age factor, among all the other physical parameters, and pressure, among the hydraulic factors, have the greatest influence in outlining the final rehabilitation scenario. The importance of the pipe length has decreased considerably as well. Furthermore, it can be concluded that rehabilitation management of pipe networks can be optimized by using this methodology.     

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.     

A Branch-and-Bound Algorithm for Optimal Pump Scheduling in Water Distribution Networks

Nowadays water distribution operation systems are accomplished with the aid of qualified professionals who use their experience in order to achieve a satisfactory performance of the several hydromechanical devices, which are part of the system, such as boosters and valves. In general, these operational rules are empirical and the main goal is to assure the availability of water for the population, with no special concerns about saving energy used in pumping systems. Besides, these empirical rules often disregard hours of lower energy rates. There are several research works concerning the developments of operational rules optimization applied to specific water distribution systems. However, in this work, a general optimization routine integrated with EPANET is presented, which allows the determination of strategic optimal rules of operation for any type of water distribution system. Moreover, a Branch-and-Bound algorithm is also used, where finding the global optimal solution is guaranteed, in admissible computational times. The water distribution system used in this work corresponds to a hypothetical network proposed in the specialized literature.     

Informational Entropy: a Failure Tolerance and Reliability Surrogate for Water Distribution Networks

Evolutionary algorithms are used widely in optimization studies on water distribution networks. The optimization algorithms use simulation models that analyse the networks under various operating conditions. The solution process typically involves cost minimization along with reliability constraints that ensure reasonably satisfactory performance under abnormal operating conditions also. Flow entropy has been employed previously as a surrogate reliability measure. While a body of work exists for a single operating condition under steady state conditions, the effectiveness of flow entropy for systems with multiple operating conditions has received very little attention. This paper describes a multi-objective genetic algorithm that maximizes the flow entropy under multiple operating conditions for any given network. The new methodology proposed is consistent with the maximum entropy formalism that requires active consideration of all the relevant information. Furthermore, an alternative but equivalent flow entropy model that emphasizes the relative uniformity of the nodal demands is described. The flow entropy of water distribution networks under multiple operating conditions is discussed with reference to the joint entropy of multiple probability spaces, which provides the theoretical foundation for the optimization methodology proposed. Besides the rationale, results are included that show that the most robust or failure-tolerant solutions are achieved by maximizing the sum of the entropies.     

Resilience Indexes for Water Distribution Network Design: A Performance Analysis Under Demand Uncertainty

Traditionally, the optimal design of water distrubution networks has been dealt with using single-objective constrained approaches, where the aim is to minimize the network investment cost while maintaining minimum pressure head constraints at all nodes. However, in the last decade some authors have proposed multi-objective approaches which optimize other objectives than network investment cost. In most cases, these objectives have been formulated using the concept of resilience index, which mimics the design aim of providing excess head above the minimum allowable head at the nodes and of designing reliable loops with practicable pipe diameters. Although several authors have proposed different resilience indexes for this pupose, to date there is no empirical study that analyzes the advantages and disadvantages of these proposals. This paper evaluates the performance of a well-known multi-objective evolutionary algorithm, the Strength Pareto Evolutionary Algorithm 2, using three different resilience indexes. The results obtained in two water supply networks under a large number of simulated over-demand scenarios show the advantages and disadvantages of these measures.     

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.

     

Parameter Estimation in Water Distribution Networks

Estimation of pipe roughness coefficients is an important task to be carried out before any water distribution network model is used for online applications such as monitoring and control. In this study, a combined state and parameter estimation model for water distribution networks is presented. Typically, estimation of roughness coefficient for each individual pipe is not possible due to non-availability of sufficient number of measurements. In order to address this problem, a formal procedure based on K-means clustering algorithm is proposed for grouping the pipes which are likely to have the same roughness characteristics. Also, graph-theoretic concepts are used to reduce the dimensionality of the problem and thereby achieve significant computational efficiency. The performance of the proposed model is demonstrated on a realistic urban water distribution network.     

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.     

Optimization of Investments in the Resilience of Water Distribution Systems Subject to Interruptions

In this paper, we propose an optimization model to support decisions related to the design of water distribution systems (WDS) that are subjected to interruptions caused by disruptive events, emphasizing their resilience capabilities, namely: absorption, adaptation, and recovery. Considering the exposure of WDS operation to random interruptions, we aim at minimizing the total investment considering the possibility of implementing actions that improve these capabilities, which can be put in place prior or posterior to the occurrence of a disruptive event. An application example is discussed as a way to understand the nature of the problem and to support the formulation of the proposed model. The results demonstrate the need to invest in resilient capacities adequate to each interruption probability associated to the disruptive scenarios, characterizing these considerations as of great importance to support managerial decisions, thus constituting a guideline for the allocation of investments before and/or after the occurrence of the event.

     

Reliability and Tolerance Comparison in Water Supply Networks

Urban water supply is a high priority service and so looped networks are extensively used in order to considerably reduce the number of consumers affected by a failure. Looped networks may be redundant in connectivity and capacity. The concept of reliability has been introduced in an attempt to quantitatively measure the possibility of maintaining an adequate service for a given period. Numerous researchers have considered reliability as a measure of redundancy. This concept is usually implicit, but some researchers have even stated it explicitly. This paper shows why reliability cannot be considered a measure of redundancy given that branched networks can achieve high values of reliability and this would deny the fact that a looped network is more reliable than a branched network with a similar layout and size. To this end the paper discusses two quantitative indices for measuring expected network behavior: reliability and tolerance. These indices are calculated and a comparison is made between looped, branched, and mixed networks.     

A Pipe Ranking Method for Water Distribution Network Resilience Assessment Based on Graph-Theory Metrics Aggregated Through Bayesian Belief Networks

Water Resources Management - The resilience assessment is crucial for many infrastructures, including water supply and distribution networks. In particular, the identification of the...     

用遗传算法求解给水管网系统优化改扩建模型

针对给水管网系统所面临的改扩建问题 ,建立了给水管网系统实用优化改扩建模型。采用遗传算法求解 ,一次性解决了求解管径标准化的难题 ,同时计算得到水源最优分配流量。在不影响水力模型计算精度的前提下 ,引入管网简化 ,对非改扩建区域的管网实现任意程度的简化 ,大大提高了计算速度 ,并用实例进行了验证     

Nodal Analysis of Urban Water Distribution Networks

There are three methods for analysing the flow and pressure distribution in looped water supply networks (the loop method, the node method, the pipe method), accounting for the chosen unknown hydraulic parameters. For all of these methods, the nonlinear system of equations can be solved using iterative procedures (Hardy–Cross, Newton–Raphson, linear theory). In the cases of the extension or the rehabilitation of distribution networks, the unknown parameters are the hydraulic heads at nodes, and the nodal method for network analysis is preferred. In this paper, a generalised classic model is developed for the nodal analysis of complex looped systems with non-standard network components and the solvability of new problems, along with the determination of the pressure state in the system. In addition, this paper exhibits a different approach to this problem by using the variational formulation method for the development of a new analysis model based on unconditioned optimisation techniques. This model has the advantage of using a specialised optimisation algorithm, which directly minimises an objective multivariable function without constraints, implemented in a computer program. The two proposed models are compared with the classic Hardy–Cross method, and the results indicated a good performance of these models. Finally, a study is performed regarding the implications of the long-term operation of the pipe network on energy consumption using these models. The new models can serve as guidelines to supplement existing procedures of network analysis.     

Optimal Location of Pump as Turbines (PATs) in Water Distribution Networks to Recover Energy and Reduce Leakage

Water distribution networks are high energy and low efficiency systems, where water pressure is frequently reduced by dissipation valves to limit leakage. The dissipation produced by the valves can be converted to energy production to increase the efficiency and reduce the energy impact of networks. If valves are replaced by turbines or pumps as turbines (PATs), they can both reduce pressure and produce energy. This study focuses on the optimal location of PATs within a water distribution network in order to both produce energy and reduce leakage. A new optimization model is developed consisting of several linear and non-linear constraints and a newly proposed objective function, where the turbine installation costs as well as the energy production and the economic saving due to the reduction of leakage can be accounted all together. The case study shows that the application of the mathematical model to a synthetic network ensures better results, in terms of both energy production and water saving, in comparison to other procedures.     

基于不确定性的渠系水资源优化配置

在以渠灌为主的灌区,设计合理的渠系工作制度,将水资源在渠系间进行高效配置具有重要意义。在实际灌溉中,同级渠道的灌水时间往往存在较大差异。为此,在灌区渠系建立0-1线性整数规划优化配水模型,并考虑了此过程中的不确定性,将模型运用到汾东灌区,进行求解。首先将支渠划分为两个灌溉组同时进行灌水,然后对每个灌溉组内的斗渠划分轮灌组,最后再将斗渠下的农渠划分为若干个轮灌组,实现在某次灌溉过程中的轮流输水。这样就缩短了各条渠道的输水时间,有利于提高灌水效率,且因不确定性信息的加入,结果更符合实际。通过上述优化过程,可以得到整个灌区的渠系工作制度,为决策者提供决策参考。