Hydraulic Analysis of Water Distribution Systems Based on Fixed Point Iteration Method

Water distribution systems with complex configurations are important urban facilities and the hydraulic analysis is essential for system design, optimization and management. Hydraulic analysis involves the procedure of calculating the hydraulic parameters of nodal pressure heads and pipe flow rates under steady-state condition. The equations governing the heads and flows are nonlinear and the most popular method for solving the equations is the Newton-Raphson method, which is the basis of existing hydraulic simulator (EPANET 2). In this paper, fixed point iteration method is proposed for hydraulic analysis after transformation of the original nonlinear equations. Compared to EPANET 2, the proposed method can analyze a water distribution system without differentiation for the convergence for some problems which cannot be solved by EPANET 2. Three test networks were analyzed by the proposed method and EPANET 2. It is proved that the proposed method could get the convergence after a series of iterations, even in cases that EPANET 2 fail. And the initial values of nodal pressure heads and the specified calculation accuracy are considered to have influences on the calculation procedure.     

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 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.

     

基于机器学习的跨海管道泄漏位置预测模型

为解决跨海管道泄漏位置定位问题,利用EPANET 软件对海底管道泄漏探测进行建模,采用BP 神经网络模型和经K-CV 改进的SVR 模型进行泄漏位置预测。对BP 神经网络的隐含层数和学习函数进行优化和选择,使用K-CV 方法对SVR 算法的惩罚系数c 和核函数参数g 进行最优组合探寻。利用EPANET 软件建模数据形成训练集,随机选取测试集进行预测,同时使用均方根误差和相关系数对预测结果进行评价。实例验证结果表明:K-CV 方法能够有效提高SVR 模型预测精度;与水力学稳态方程相比,BP 神经网络模型在泄露位置预测问题中应用范围更广、预测精度更高。     

Convergence of a Hydraulic Solver with Pressure-Dependent Demands

This paper analyzes the convergence of a pressure-driven analysis (PDA) model of a water distribution network solver based on Todini’s global gradient algorithm. The PDA model is constructed by embedding a pressure?demand relationship in the EPANET simulator code. To avoid spurious convergence, a residual-based convergence error was used. The introduction of pressure-dependent demands is shown to result in a far poorer convergence. The study of solver convergence as a function of the smoothness of the pressure?demand curve has demonstrated that, statistically, a smooth pressure?demand relationship gives a somewhat better convergence. To improve convergence, use was made of a quadratic approximation of the Hazen–Williams head loss?flow relationship in the vicinity of zero and the correct implementation of the Darcy?Weisbach formula in the solver. To further improve convergence, an iteration step control technique called the line search was used. The analysis of solver convergence for different line search variants has shown that the line search in its usual form is not efficient enough and may result in poorer convergence. A necessary error decrease algorithm, whose use in the line search improves solver convergence, is proposed. It is shown that due to the convergence improvement methods the convergence of the PDA solver is somewhat better than that of the demand-driven analysis solver and sufficient for direct problems such as design, for example.     

Pressure-Dependent EPANET Extension

In water distribution systems (WDSs), the available flow at a demand node is dependent on the pressure at that node. When a network is lacking in pressure, not all consumer demands will be met in full. In this context, the assumption that all demands are fully satisfied regardless of the pressure in the system becomes unreasonable and represents the main limitation of the conventional demand driven analysis (DDA) approach to WDS modelling. A realistic depiction of the network performance can only be attained by considering demands to be pressure dependent. This paper presents an extension of the renowned DDA based hydraulic simulator EPANET 2 to incorporate pressure-dependent demands. This extension is termed “EPANET-PDX” (pressure-dependent extension) herein. The utilization of a continuous nodal pressure-flow function coupled with a line search and backtracking procedure greatly enhance the algorithm’s convergence rate and robustness. Simulations of real life networks consisting of multiple sources, pipes, valves and pumps were successfully executed and results are presented herein. Excellent modelling performance was achieved for analysing both normal and pressure deficient conditions of the WDSs. Detailed computational efficiency results of EPANET-PDX with reference to EPANET 2 are included as well.     

Modelling Water Distribution Systems with Deficient Pressure: An Improved Iterative Methodology

In the last three decades, many researchers have proposed different models for water distribution network (WDN) hydraulic analysis by head-driven analysis (HDA). By considering a pressure-discharge relationship (PDR), head-driven analysis (HDA) can avoid deviation caused by traditional demand-driven analysis (DDA) under abnormal conditions. Generally, there are three types of HDA models: 1) models achieved by embedding a PDR into DDA, 2) models using EPANET structures such as emitter or tank to take place of PDR, 3) models aiming at modifying nodal outflows to satisfy PDR based on EPANET. Among these models, modifying nodal outflows is flexible to simulate network with different PDRs and specify parameters related to PDR. Most of the models use iterative algorithms to solve HDA problems; however, present ways to ensure convergence of models are still inadequate. The purpose of this paper is to present a new way to meet the iterative convergence when modifying nodal outflows based on PDR and leakage. This new methodology has been incorporated into the hydraulic network solver EPANET and is formalized algorithmically as EPANET-IMNO. Then two typical networks are used to test EPANET-IMNO, and the results demonstrate that EPANET-IMNO can converge well and applied successfully both in static simulation and extended period simulation. Different pressure deficiency conditions are tested to further confirm the flexibility and the convergence of EPANET-IMNO. Furthermore, quality analysis results back that pressure reduction can be a practical way in contamination accident response.     

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 New Method for Simultaneous Calibration of Demand Pattern and Hazen-Williams Coefficients in Water Distribution Systems

Water distribution systems, where flow in some pipes is not measured or storage tanks are connected together, calculation of demand pattern coefficients of the network is difficult. Since, Hazen-Williams coefficients of the network are also unknown; the problem is becoming unintelligible further. The present study proposes a new method for simultaneous calibration of demand pattern and Hazen-Williams coefficients that uses the Ant Colony Optimization (ACO) algorithms coupled with the hydraulic simulator (EPANET2) in a MATLAB code. In this paper demand pattern and Hazen-Williams coefficients are the calibration parameters and measured data consist of nodal pressure heads and pipe flows. The defined objective function minimizes the difference between the measured and simulated values. The new proposed method was tested on a two-loop test example and a real water distribution network. The results show that the new calibration model is able to calibrate demand pattern and Hazen-Williams coefficients simultaneously with high precision and accuracy.     

基于GIS的给水管网动态水力计算模型的建立与应用

基于GIS和给水管网水力计算方法,采用一种新的更符合实际的节点流量分配方法,建立了给水管网动态水力计算模型,实现了模拟结果和GIS图形信息的良好结合,解决了工况结果难以在GIS中显示和输出的问题。将模型应用于天津市津南区咸水沽镇供水管网,并将计算结果与MIKENET模拟值、EPANET2.0计算值进行比较,验证了模型的实用性。     

Simulation of Water Distribution Network under Pressure-Deficient Condition

Pressure deficient condition occurs in the water distribution network (WDN) when the nodal demands are in excess of the design discharge as in the case of fire demand, pump failure, pipe breaks, valve failure etc. It causes either no-flow or partial-flow depending upon the available pressure head at the nodes. To evaluate the nodal flows in such condition, node flow analysis (NFA) gives reasonable results in comparison to demand-driven analysis (DDA) and head-dependent analysis (HDA). The NFA works on the predefined pressure-discharge relationship to evaluate the nodal flows. However, this approach requires human intervention and hence cannot be applied to large WDN. Recently, modified pressure-deficient network algorithm (M-PDNA) has been developed by Babu and Mohan (2012) for pressure-deficient analysis with EPANET toolkit. However, it requires modification of the source code of EPANET. In this study a relationship with the M-PDNA and node flow analysis (Gupta and Bhave 1996) has been investigated and it is found that M-PDNA is the simplified version of NFA. Further, the working principle of M-PDNA has been investigated with suitable examples of Babu and Mohan (2012). The theoretical basis of M-PDNA has not been investigated in terms of head-discharge relationship. Herein, a head-discharge relationship based on the working principal of M-PDNA is proposed. Some of the toolkits are also readily available to modify demand driven solver of EPANET 2 to suit for the pressure-driven analysis and then it can be used for analysing pressure deficient network. Also in this study, a modification in M-PDNA approach is proposed which does not require the use of EPANET toolkit which is found to be capable of simulating both pressure-sufficient and pressure-deficient conditions in a single hydraulic simulation. Using the proposed approach, pressure-deficient condition is analysed with constant and variable demand pattern.     

基于精细积分法的城市配水系统动态建模

基于功率键合图理论,将所研究的城市配水系统的动态结构绘制成功率键合图,从功率键合图推导出系统的非线性状态空间方程.首先通过增维法将非齐次系统方程转化成齐次方程的形式,避免了系统矩阵求逆,节省计算时间,增强了计算稳定性.模型应用精细积分法迭代求解.实例计算表明,模型计算得到的稳态值同EPANET软件的稳态计算结果一致,验证了算法的正确性.     

城市排水管网明满交替非恒定流数学模型的研究

该文针对城市排水管网系统存在的明满流共存的计算难点,从一维水流的圣维南方程组的物理意义入手,推导了适用于有压管流的方程组表达形式,提出了当量宽度的概念和计算方法,修正了Preissmann窄缝假定方法中的窄缝宽度公式,将明渠和有压管道两种情况下的方程组写成统一的形式,实现了对明满过渡流的有效数值模拟。通过数学模拟,与经验数据和SWMM模型的对比验证,揭示了当量宽度法的合理性、可行性及其实际应用价值。     

Automated Framework for Water Looped Network Equilibrium

In this paper, a novel algorithm is proposed for balancing water looped network in steady state through a fully automated general framework of hydraulic networks regardless of their topological complexity. The model is developed by combining the following two steps, firstly a set of independent loops are identified based on a graph theoretical analysis in a looped network. Further the second step is devoted to the equilibrium process by determining the flow rate distribution within the network ducts and the pressure in the delivery nodes. The above such equilibrium process gives rise to a system of non linear algebraic equations which are solved numerically using both Hardy Cross (HC) and Newton Raphson (NR) methods. In HC method, the flow correction term is modified and a generalized expression is given to consider various possibilities of independent loops selection. Some real networks topologies that were commonly used as benchmarks, for testing various independent loops selection algorithms, are taken as case studies to apply the general automatic framework for hydraulic network analysis. Such network analysis enhances proving the applicability as well as the effectiveness of the proposed approach. Also, during the equilibrium procedure, it is proved that NR method is capable of producing accurate results and it converges more rapidly comparing to the widely used HC method. Moreover, it is demonstrated that NR’s iterative process, contrary to HC’s one, converges to reliable results even with a choice of random initial flow rates which makes a NR algorithm quite simple to implement without affecting the accuracy of the results.     

Calibration Model for Water Distribution Network Using Pressures Estimated by Artificial Neural Networks

The success of hydraulic simulation models of water distribution networks is associated with the ability of these models to represent real systems accurately. To achieve this, the calibration phase is essential. Current calibration methods are based on minimizing the error between measured and simulated values of pressure and flow. This minimization is based on a search of parameter values to be calibrated, including pipe roughness, nodal demand, and leakage flow. The resulting hydraulic problem contains several variables. In addition, a limited set of known monitored pressure and flow values creates an indeterminate problem with more variables than equations. Seeking to address the lack of monitored data for the calibration of Water Distribution Networks (WDNs), this paper uses a meta-model based on an Artificial Neural Network (ANN) to estimate pressure on all nodes of a network. The calibration of pipe roughness applies a metaheuristic search method called Particle Swarm Optimization (PSO) to minimize the objective function represented by the difference between simulated and forecasted pressure values. The proposed method is evaluated at steady state and over an extended period for a real District Metering Area (DMA), named Campos do Conde II, and the hypothetical network named C-town, which is used as a benchmark for calibration studies.     

岩体裂隙网络非线性渗流分析

裂隙中水流为紊流状态时，流量与水力坡度呈非线性关系，不再满足线性的立方定律，以岩体裂隙网络中结点的水量平衡来建立岩体裂缝网络非线性渗流控制方程式，提出矩阵求解方法和迭代运算步骤，并给出应用算例与验证。算例结果表明，不能采用岩体裂隙网络线性渗流规律来代替岩体裂隙网络非线性渗流规律。     

水力平差模型在供水规划中的应用

在供水规划中,管网设计是重要的组成部分,为了降低管网建成后的漏损及运行费用,需要在规划设计阶段对管网进行水力平差计算.针对规划管网水力平差的特点,提出应用GIS的分析功能及EPANET水力计算软件构建管网的水力平差模型,进行规划管网的水力计算,并根据计算结果对管网进行调整,得到满足规划供水量及水压要求的供水管网布置方案,为供水规划管网设计提供科学的依据.     

Pressure Control for Leakage Minimisation in Water Distribution Systems Management

A model to support decision systems regarding the quantification, location and opening adjustment of control valves in a network system, with the main objective to minimise pressures and consequently leakage levels is developed. This research work aims at a solution that allows simultaneously optimising the number of valves and its location, as well as valves opening adjustments for simulation in an extended period, dependently of the system characteristics. EPANET model is used for hydraulic network analysis and two operational models are developed based on the Genetic Algorithm optimisation method for pressure control, and consequently leakage reduction, since a leak is a pressure dependent function. In these two modules, this method has guaranteed an adequate technique performance, which demands a global evaluation of the system for different scenarios. A case study is presented to show the efficiency of the system by pressure control through valves management.     

EPANET软件在区域供水管网改造设计中的应用

以天津市某区域的供水管网为例,利用EPANET软件对其进行水力计算,指明现有管网的缺陷.为了保障其安全性,根据实际调研设计管网改造方案,选取关键节点作为改造前后对比分析的依据.根据最终水力计算结果,验证改造方案的合理性,为实际的改造工程提供理论依据.     

Modelling of 2-D extended Boussinesq equations using a hybrid numerical scheme

In this paper, a hybrid finite-difference and finite-volume numerical scheme is developed to solve the 2-D Boussinesq equations. The governing equations are the extended version of Madsen and Sorensen＇s formulations. The governing equations are firstly rearranged into a conservative form. The finite volume method with the HLLC Riemann solver is used to discretize the flux term while the remaining terms are discretized by using the finite difference method. The fourth order MUSCL-TVD scheme is employed to reconstruct the variables at the left and right states of the cell interface. The time marching is performed by using the explicit second-order MUSCL-Hancock scheme with the adaptive time step. The developed model is validated against various experimental measurements for wave propagation, breaking and runup on three dimensional bathymetries.