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.     

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.

     

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.     

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.     

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.     

Uniformly Distributed Demand EPANET Extension

EPANET-2 is a popular public domain package widely used to determine flow in Water Distribution Networks (WDN) in Extended Period Simulation (EPS). In its original formulation the water demand is represented as lumped withdrawals at network nodes. However, this approximation may introduce significant errors in the hydraulic head distribution, since energy balance is not respected at the level of the single edge (pipe). To overcome this drawback we propose a new implementation of EPANET-2 with the water demand uniformly distributed along the pipes. This new formulation obeys energy balance but introduces significant changes in the system of equations, which is therefore solved by introducing a proper relaxation factor in the Global Gradient Algorithm (GGA) implemented in the original version of the software. This new version of the software, we named DD-EPANET, produces an accurate representation of pressure distribution and allows to identify accurately the point of minimum head also when it is located within an edge of the network. The new scheme is suitable for long term simulations in particular for calibration and optimization of WDNs, in particular when data on water demand are scarce.     

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.     

Pipe Break Rate Assessment While Considering Physical and Operational Factors: A Methodology based on Global Positioning System and Data-Driven Techniques

An accurate prediction of pipes failure rate plays a substantial role in the management of Water Distribution Networks (WDNs). In this study, a field study was conducted to register pipes break and relevant causes in the WDN of Yazd City, Iran. In this way, 851 water pipes were incepted and localized by the Global Positioning System (GPS) apparatus. Then, 1033 failure cases were reported in the eight zones of understudy WDN during March-December 2014. Pipes break rate (BR_P) was calculated using the depth of pipe installation (h_P), number of failures (N_P), the pressure of water pipes in operation (P), and age of pipe (A_P). After completing a pipe break database, robust Artificial Intelligence models, namely Multivariate Adaptive Regression Spline (MARS), Gene-Expression Programming (GEP), and M5 Model Tree were employed to extract precise formulation for the pipes break rate estimation. Results of the proposed relationships demonstrated that the MARS model with Coefficient of Correlation (R) of 0.981 and Root Mean Square Error (RMSE) of 0.544 provided more satisfying efficiency than the M5 model (R?=?0.888 and RMSE?=?1.096). Furthermore, statistical results indicated that MARS and GEP models had comparatively at the same accuracy level. Explicit equations by Artificial Intelligence (AI) models were satisfactorily comparable with those obtained by literature review in terms of various conditions: physical, operational, and environmental factors and complexity of AI models. Through a probabilistic framework for the pipes break rate, the results of first-order reliability analysis indicated that the MARS technique had a highly satisfying performance when MARS-extracted-equation was assigned as a limit state function.

     

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.     

Transient Influence Zone Based Decomposition of Water Distribution Networks for Efficient Transient Analysis

Computational efficiency and accuracy of transient analysis for urban water distribution networks (WDN) become progressively important to the design and management of the system. In addition to the improvement of numerical model and computational capacity, which has been widely studied in the literature, efficient and accurate treatment of practical and complex WDN is another potential way to enhance the transient analysis. This paper aims to develop a zonal method for effective decomposition of WDN, which is mainly based on the transient sources and their influence regions in the system, in order to achieve efficient transient analysis. A concept of transient influence zone (TIZ) is firstly proposed and implemented to demonstrate the critical influence region of transient wave propagation in the system under specific design criteria. The obtained TIZ for each transient source is then mapped by introducing appropriate and equivalent boundaries so as to separate the TIZ from the entire WDN. To this end, the efficient Lagrangian model for prior-estimating pressure fluctuation extremes, the pressure fluctuation limitation for mapping TIZ borders and the quasi-reservoir condition for representing border boundaries are applied for characterizing the TIZs. A realistic network is adopted to demonstrate the applicability and accuracy of the proposed method. The application results and analysis indicate that the developed TIZ-based decomposition method provides a considerable efficiency improvement for transient analysis with sufficient modeling accuracy.     

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.     

Decision support system to divide a large network into suitable District Metered Areas

This paper presents a new approach to divide large Water Distribution Networks (WDN) into suitable District Metered Areas (DMAs). It uses a hydraulic simulator and two operational models to identify the optimal number of DMAs, their entry points and boundary valves, and the network reinforcement/replacement needs throughout the project plan. The first model divides the WDN into suitable DMAs based on graph theory concepts and some user-defined criteria. The second model uses a simulated annealing algorithm to identify the optimal number and location of entry points and boundary valves, and the pipes reinforcement/replacement, necessary to meet the velocity and pressure requirements. The objective function is the difference between the economic benefits in terms of water loss reduction (arising from the average pressure reduction) and the cost of implementing the DMAs. To illustrate the proposed methodology, the results from a hypothetical case study are presented and discussed.     

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.     

Decomposition based Multi Objective Evolutionary Algorithms for Design of Large-Scale Water Distribution Networks

In last two decades, multiobjective evolutionary algorithms (MOEAs) have shown their merit for solving different optimization problems within the context of water resources and environmental engineering. MOEAs mainly use the concept of Pareto dominance for obtaining the trade-off solutions considering different criteria. A new alternative method for solving multiobjective problems is multiobjective evolutionary algorithm based on decomposition (MOEA/D) which uses scalarizing the objective functions. In this paper, decomposition strategies are developed for the large-scale water distribution network (WDN) design problems by integrating the concepts of harmony search (HS) and genetic algorithm (GA) within the MOEA/D framework. The proposed algorithms are then compared with two well-known non-dominance based MOEAs: NSGA2 and SPEA2 across four different WDN design problems. Experimental results show that MOEA/D outperform the Pareto dominance methods in terms of both non-domination and diversity criteria. MOEA/D-HS in particular could provide very high quality solutions with a uniform distribution along the Pareto front preserving the diversity and dominating the solutions of the other algorithms. It suggests that decomposition based multiobjective evolutionary algorithms are very promising in dealing with complicated large-scale WDN design problems.     

Topological Robustness and Vulnerability Assessment of Water Distribution Networks

The reliability of a water distribution network (WDN) is a function of several time-invariant and time-dependent factors affecting its components and connectivity, most important of which have been shown to be the network’s topology, its operating pressure, the type of key components (such as the diameter, length, material and age of water pipes) and the network’s historical performance (such as the number of previously observed failures in the network). In terms of network topology, this attribute even though generally thought as time-invariant it actually is time-dependent, as the paths in a water distribution network change over time based on the hydraulics in the network (water demand and water pressure/flow alter the way water flows in the piping network). The work described herein examines the time-dependent nature of a WDN topology and by means of a betweenness centrality index (BC) method demonstrates the effect of topology on the network’s vulnerability / reliability. The importance of the betweenness centrality index is demonstrated by use of a case-study water distribution network operated under both normal and abnormal conditions. The proposed method is also coupled with spatial mapping to indicate areas of concern in the network, and with a decision support system to assist in prioritizing actions to improve on the network’s robustness and resilience.     

Comparative Study of Pressure Control Modes Impact on Water Distribution System Performance

Four pressure control modes (CMs) for water distribution systems, which are: 1) fixed control (FC); 2) time-based control (TBC); 3) reactive control (RC); and 4) ideal predictive control (IC), are compared based on their performance in terms of reduction in i) leakage rate and ii) pressure fluctuation intensity. The comparison is performed for three real Canadian distribution networks. Pressure fluctuation intensity, pressure variations distribution, and leakage rate reduction are the performance indices computed for each CM. The impact of differences in elevation and pipe roughness are also assessed. It is shown that in all cases, the active CMs (IC and RC) are more effective than the passive ones (TBC and FC). A decrease in water loss and in pressure fluctuation intensity was obtained when adopting CMs other than FC. The highest benefits were provided by IC, followed by RC and TBC (e.g. reduction in leakage rates lower than 4% for TBC and up to 26% for IC and RC, compared with the fixed control mode). The benefits of active CMs are higher when the difference in nodes elevation is lower and when the pipe roughness is greater, both cases amplifying the relative impact of pipe friction on the pressure delivered to each node in the system.

     

外河水位顶托下雨水管网排水能力变化的SWMM模拟

以沈阳市和平区雨水管网系统为例,选取芝加哥雨型为设计雨型,利用SWMM,模拟分析了不同暴雨重现期和外河设计洪水位下的雨水管网系统排涝过程。结果表明:随着降雨重现期增大,雨水管网排水能力增加,但积水程度加重;雨水管网系统有效排涝系数随着降雨重现期的增大而减小,且在高重现期时变化程度减缓;雨水管网系统总排水能力与外河水位和各节点(雨水井)的平均落差呈显著正相关,相关系数R为0.992,并呈近似线性关系;泵站排水在淹没出流地区至关重要,本例中可提升36.3%的管网系统排水能力,而对于自由出流地区,泵站对系统排水能力基本没有贡献。     

Hydraulic performance of sewer pipes with deposited sediments.

This paper investigates in-sewer sediment deposit behaviour and its influence on the hydraulic performance of sewer pipes. This evaluation is based on experimental results regarding the mobility of non-cohesive and partly cohesive deposits in a partially full circular pipe. The focus of these tests is on the development of bed forms and friction characteristics. In particular, it is investigated to what extent the bed forms from the non-cohesive and (partly) cohesive sediments affect a sewer's discharge capacity. Based on the laboratory study results and on the existing criteria for sewer design, a generic assessment of a sewer's hydraulic performance is made. The relative discharge factor for a pipe with sediment deposit is analysed in terms of the thickness and roughness of the deposit.     

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.

     

Performances of Pressure Reducing Valves in Variable Demand Conditions: Experimental Analysis and New Performance Parameters

Pressure Reducing Valves (PRV) play a critical role in Water Distribution Networks (WDN): they regulate pressure ensuring an efficient service to users and preventing damage to pipelines. In recent years, the attention of water utilities towards pressure management and leakage control led to the necessity of more flexible and responsive technologies that can guarantee a higher level of pressure control accuracy. Because of this the common performance parameters based on steady state conditions are no longer satisfactory to evaluate the effective behaviour of the devices when used in situations where demand can change. In the present paper the pressure control effectiveness of different types of PRV (electric actuated, pilot operated and direct acting) in variable demand conditions is discussed. The data used are from experimental tests, literature and field application. To assess valves’ pressure control performance, the use of new parameters, which consider the peak of pressure reached during control operations and the accuracy of target pressure regulation, has been proposed. The use of these parameters allows the comparison between different type of valves giving to WDN managers a direct overview on the valves ability to regulate pressure under variable demand conditions.