Iterative Methods for Looped Network Pipeline Calculation

Since the value of the hydraulic resistance depends on flow rate, problem of flow distribution per pipes in a gas or water distributive looped pipelines has to be solved using iterative procedure. A number of iterative methods for determining of hydraulic solution of pipeline networks, such as, Hardy Cross, Modified Hardy Cross, Node-Loop method, Modified Node method and M.M. Andrijašev method are shown in this paper. Convergence properties are compared and discussed using a simple network with three loops. In a municipal gas pipeline, natural gas can be treated as incompressible fluid. Even under this circumstance, calculation of water pipelines cannot be literary copied and applied for calculation of gas pipelines. Some diferences in calculations of networks for distribution of these two fluids, i.e. water apropos natural gas are also noted.     

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.     

Multi-Objective Optimization Model Based on Localized Loops for the Rehabilitation of Gravity-fed Pressurized Irrigation Networks

Nowadays, some of the existing irrigation distribution networks (IDNs) are facing hydraulic performance problems, due partly to the ageing of pipe networks, initial design flaws, improper management or/and the increase in water demand. Rehabilitation of these networks may become an inevitable need to provide the best services to farmers. To this end, a comprehensive computer model was developed to assist planners and decision makers in the determination of the most cost-effective strategy for the rehabilitation of irrigation networks. This model incorporates an innovative algorithm for the automatic search of the best looping positions in the network. Two multi-objective optimizations were applied for the rehabilitation of a real medium-size network operating on-demand and by gravity, one included the looping option while the other excluded this option. The two Pareto fronts, associated with each optimization, clearly indicated that it is imperative to consider the localized loops option during the rehabilitation process as it provided superior cost-effective solutions. The comparison between two selected cases from each front showed that even though the two solutions offered the same magnitude of improvement to the network, a cost saving of about 77% is obtained by choosing the case with the looping option. The model developed in the framework of this work represents a powerful optimization tool for cost-effective rehabilitation of irrigation networks.     

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 coupled 1-D and 2-D channel network mathematical model used for flow calculations in the middle reaches of the yangtze river

A coupled one-dimensional (1-D) and two-dimensional (2-D) channel network mathematical model is proposed for flow calculations at nodes in a channel network system in this article.For the 1-D model, the finite difference method is used to discretize the Saint-Venant equations in all channels of a looped network.The Alternating Direction Implicit (ADI) method is adopted for the 2-D model at the nodes.In the coupled model, the 1-D model provides a good approximation with small computational effort, while the 2-D model is applied for complex topography to achieve a high accuracy.An Artificial Neural Network (ANN) method is used for the data exchange and the connectivity between the 1-D and 2-D models.The coupled model is applied to the Jingjiang-Dongting Lake region, to simulate the tremendous looped channel network system, and the results are compared with field data.The good agreement shows that the coupled hydraulic model is more effective than the conventional 1-D model.     

Accuracy and Sensitivity Evaluation of TFR Method for Leak Detection in Multiple-Pipeline Water Supply Systems

The transient frequency response (TFR) based pipe leak detection method has been developed and applied to water pipeline systems with different connection complexities such as branched and looped pipe networks. Previous development and preliminary applications have demonstrated the advantages of high efficiency and non-intrusion for this TFR method. Despite of the successful validations through extensive numerical applications in the literature, this type of method has not yet been examined systematically for its inherent characteristics and application accuracy under different system and flow conditions. This paper investigates the influences of the analytical approximations and assumptions originated from the method development process and the impacts of different uncertainty factors in practical application systems on the accuracy and applicability of the TFR method. The influence factors considered for the analysis contain system properties, derivation approximations and data measurement, and the pipeline systems used for the investigation include simple branched and looped multi-pipe networks. The methods of analytical analysis and numerical simulations are adopted for the investigation. The accuracy and sensitivity of the TFR method is evaluated for different factors and system conditions in this study. The results and findings are useful to understand the validity range and sensitivity of the TFR-based method, so as to better apply this efficient and non-intrusive method in practical pipeline systems.     

Hybrid Genetic Algorithm and Linear Programming Method for Least-Cost Design of Water Distribution Systems

The problems involved in the optimal design of water distribution networks belong to a class of large combinatorial optimization problems. Various heuristic and deterministic algorithms have been developed in the past two decades for solving optimization problems and applied to the design of water distribution systems. Nevertheless, there is still some uncertainty about finding a generally trustworthy method that can consistently find solutions which are really close to the global optimum of this problem. The paper proposes a combined genetic algorithm (GA) and linear programming (LP) method, named GALP for solving water distribution system design problems. It was investigated that the proposed method provides results that are more stable in terms of closeness to a global minimum. The main idea is that linear programming is more dependable than heuristic methods in finding the global optimum, but because it is suitable only for solving branched networks, the GA method is used in the proposed algorithm for decomposing a complex looped network into a group of branched networks. Linear programming is then applied for optimizing every branch network produced by GA from the original looped network. The proposed method was tested on three benchmark least-cost design problems and compared with other methods; the results suggest that the GALP consistently provides better solutions. The method is intended for use in the design and rehabilitation of drinking water systems and pressurized irrigation systems as well.     

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.     

用聚类算法及Hopfield神经网络布置环状管网

为了降低供水管网的工程投资,提出了一种环状给水管网优化设计的方法,把环状管网布置问题用K-Means算法分解成许多小规模的环状问题,对于每一个小规模的环状管网用Hopfiled连续型神经网络求解环状的最短距离,然后把各个基环当成一个点,再用Hopfield神经网络以较大的概率求出最优路径。对某小区58个供水点进行了供水管网实例计算,结果表明:该供水管网的质心间最短距离为2.893 7 km,能量函数为递减状态且最终的能量函数值为1.447,再连接相邻聚类中的最接近的两个点就形成供水管网的环状布置。     

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.     

城市供水管网瞬态水力模型的建立和应用

以上海市北自来水公司供水管网为例,阐述了在"稳态模型"的基础上自动建立"瞬态模型"的系统方法:首先,根据管网情况对瞬变流需求分析进行权值计算;其次,根据统计模型确定计算范围并对管网进行自动标志;然后确定边界条件和其他系统参数,并用特征线法对"瞬态模型"进行计算;最后根据现场实测数据对模型进行校验.与传统方法相比较,该方法在建立供水管网动态水力模型的过程中将"稳态模型"和"瞬态模型"有机地结合起来,拓展了其应用的范围,能有效地帮助管理者预防管网事故的发生.     

截流式合流制排水管网设计新思路

提出了一种以溢流井为分界线,将截流式合流制排水管网分解为一系列小型完全合流制排水管网的设计新思路,并以管网关联矩阵和节点连接特性矩阵为基础,以节点平衡原理和节点递归算法为核心,实现完全合流制排水管网的流量计算和水力计算.该方法能有效减小管网计算模型的规模,降低程序设计难度,提高程序的实用性.     

Artificial Neural Network (ANN) Based Modeling for Karstic Groundwater Level Simulation

A relatively new method of addressing different hydrological problems is the use of artificial neural networks (ANN). In groundwater management ANNs are usually used to predict the hydraulic head at a well location. ANNs can prove to be very useful because, unlike numerical groundwater models, they are very easy to implement in karstic regions without the need of explicit knowledge of the exact flow conduit geometry and they avoid the creation of extremely complex models in the rare cases when all the necessary information is available. With hydrological parameters like rainfall and temperature, as well as with hydrogeological parameters like pumping rates from nearby wells as input, the ANN applies a black box approach and yields the simulated hydraulic head. During the calibration process the network is trained using a set of available field data and its performance is evaluated with a different set. Available measured data from Edward??s aquifer in Texas, USA are used in this work to train and evaluate the proposed ANN. The Edwards Aquifer is a unique groundwater system and one of the most prolific artesian aquifers in the world. The present work focuses on simulation of hydraulic head change at an observation well in the area. The adopted ANN is a classic fully connected multilayer perceptron, with two hidden layers. All input parameters are directly or indirectly connected to the aquatic equilibrium and the ANN is treated as a sophisticated analogue to empirical models of the past. A correlation analysis of the measured data is used to determine the time lag between the current day and the day used for input of the measured rainfall levels. After the calibration process the testing data were used in order to check the ability of the ANN to interpolate or extrapolate in other regions, not used in the training procedure. The results show that there is a need for exact knowledge of pumping from each well in karstic aquifers as it is difficult to simulate the sudden drops and rises, which in this case can be more than 6 ft (approx. 2 m). That aside, the ANN is still a useful way to simulate karstic aquifers that are difficult to be simulated by numerical groundwater models.     

WASP5水质模型在平原河网区的应用

以平原河网区水环境为研究对象,选择了WASP5系统作为平原河网水质模拟的基本工具,针对WASP5系统自带的DYNHYD5水动力模型功能的局限性,以及平原河网水力调控系统复杂的特征,选择了具有产汇流模拟、闸坝控制模拟及河网水流模拟等功能的三级联解平原河网水动力模型。通过利用C++语言编程,实现了三级联解平原河网水动力模型与WASP5水质模型的耦合,使之可以应用于平原河网水环境的模拟。并把研究成果运用到实际引调水工程中去,模拟引调水工程中不同实施方案下的环境效益,为引调水工程实施方案的确定提供了理论依据。     

Noniterative Implementation of Pressure-Dependent Demands Using the Hydraulic Analysis Engine of EPANET 2

To analyze water distribution networks under pressure-deficient conditions, most of the available hydraulic simulators, including EPANET 2, must be either modified by embedding pressure-dependent demands in the governing network equations or run repeatedly with successive adjustments made to specific parameters until a sufficient hydraulic consistency is obtained. This paper presents and discusses a simple technique that implements the square root relationship between the nodal demand and the nodal pressure using EPANET 2 tools and allows a water distribution network with pressure-dependent demands to be solved in a single run of the unmodified snapshot hydraulic analysis engine of EPANET 2. In this technique, artificial strings made up of a flow control valve, a pipe with a check valve, and a reservoir are connected to the demand nodes before running the engine, and the pressure-dependent demands are determined as the flows in the strings. The resistance of the artificial pipes is chosen such that the demands are satisfied in full at a desired nodal pressure. The proposed technique shows reasonable convergence as evidenced by its testing on example 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.     

Application of Several Meta-Heuristic Techniques to the Optimization of Real Looped Water Distribution Networks

The optimization of looped water distribution systems is a complex problem as the pipe flows are unknown variables. Although many researchers have reported algorithms for minimizing the network cost applying a large variety of techniques, such as linear programming, non-linear programming, global optimization methods and meta-heuristic approaches, a totally satisfactory and efficient method is not available as yet. Many works have assessed the performance of these techniques using small or medium-sized benchmark networks proposed in the literature, but few of them have tested these methods with large-scale real networks. The aim of this paper is to evaluate the performance of several meta-heuristic techniques: genetic algorithms, simulated annealing, tabu search, and iterated local search. These techniques were first validated and compared by applying them to a medium-sized benchmark network previously reported in the literature. They were then applied to a large irrigation water distribution network that has been proposed in a previous work to assess their performance in a practical application. All the methods tested performed adequately well, compared with the results found in previous works. Genetic algorithm was more efficient when dealing with a medium-sized network, but other methods outperformed it when dealing with a real complex one.     

供水管网事故时关阀优化及影响区分析

随着城市供水行业信息化的发展,发生爆管等事故后多采用广度优先算法(BFS)得出初步的关阀方案,经进一步分析剔除多余被关闭的阀门,最终实现对关阀方案的优化。基于管网信息化的数据支持,分别考虑复杂管网树状和环状系统,避免了BFS的弊端,能够直接得到优化的关阀方案。采用水压变化程度来定义事故影响百分数,通过对事故关阀前后的管网系统进行平差计算,得出各节点水压和各管段流向的变化,由此确定关阀动作引起的事故影响区和危险控制点。     

Evolutionary Testing of Hydraulic Simulator Functionality

A method for automatic functional testing of hydraulic simulators is proposed. The method is based on using genetic algorithms to search for network parameter values at which the simulator under test computes solutions that do not satisfy the governing network equations. The search is made by maximizing the residual of the governing equations. The application of the method to the latest version of the EPANET hydraulic simulator demonstrates its efficiency in detecting incorrect results. The results of quantitative assessment of the functional adequacy of the EPANET solver by random testing are presented. The paper provides examples of hydraulic networks and of parameter value combinations for which incorrect results occur. An example of the use of automatic functional testing together with automatic convergence testing in a comprehensive study of the flow control valve model of the EPANET solver is given.     

GPS控制网设计在水利工程控制测量中的应用

简述GPS控制网设计的基本原理,阐明在水利工程控制测量中选择合适的GPS控制网对于提高观测质量和精度,减少外业观测工作量等方面具有重要意义。通过对水利工程施工中布设的GPS控制网点连式、边连式、边点混连式控制网进行技术、经济、可靠性对比分析,得出合理的GPS控制网布设方案。