A new tool to assess water pipe networks vulnerability and robustness

The safety of a population also relies on the safety of the water pipe network systems. Good quality water supplying is required. A failure of these types of systems may have a huge social impact. The theory of vulnerability of water pipe networks intends to give a contribution in this context by tracing the vulnerable parts of the system and, consequently, giving guidance to increase its robustness. This theory is described in brief and supported on three water pipe networks examples.     

Leakage detection in water pipe networks using a Bayesian probabilistic framework

A Bayesian system identification methodology is proposed for leakage detection in water pipe networks. The methodology properly handles the unavoidable uncertainties in measurement and modeling errors. Based on information from flow test data, it provides estimates of the most probable leakage events (magnitude and location of leakage) and the uncertainties in such estimates. The effectiveness of the proposed framework is illustrated by applying the leakage detection approach to a specific water pipe network. Several important issues are addressed, including the role of modeling error, measurement noise, leakage severity and sensor configuration (location and type of sensors) on the reliability of the leakage detection methodology. The present algorithm may be incorporated into an integrated maintenance network strategy plan based on computer-aided decision-making tools.     

Some new insights on informational entropy for water distribution networks

Several researchers have studied the use of informational entropy as a surrogate measure for the reliability of water distribution networks. The hypothesis is that the numerical value of network entropy in some way reflects the reliability of water distribution networks, and this appears to be supported by the analysis of some example water distribution networks. However, the precise relationship between the entropy value and some measures of reliability has not been formally established. The primary objective in this paper is to present an alternative methodology to calculate the informational entropy of water distribution networks. This methodology is termed as the Path Entropy Method (PEM), which provides some insights into the entropy of branching-tree networks and maximum-entropy flows of single-source networks. In addition, a quick method of computing the maximum-entropy value of single-source networks is presented and termed as the Simplified Path Entropy Method (SPEM).     

The decay of suddenly blocked flow in a curved pipe

Pressure-driven viscous flow through a rigid curved pipe of uniform circular cross-section which is suddenly stopped, for example through the instantaneous closure of a valve, is considered here. The profile of the flow at early times after the stoppage is analysed asymptotically, by matching diffusive boundary layers to a core flow that is driven by an axial pressure gradient. This pressure gradient is unknown a priori and, furthermore, exhibits singular behaviour immediately after the stoppage. This analysis therefore provides the flow information at small but finite times that is required for numerical determination of the flow at later times. The limiting case of weak curvature is also considered, where linearization of the governing flow equations is possible. The results illustrate some novel features of the flow which result solely from the pipe’s curvature and the consequences for the flow’s rate of decay are discussed.     

Optimal cost design of water distribution networks using a decomposition approach

Water distribution network decomposition, which is an engineering approach, is adopted to increase the efficiency of obtaining the optimal cost design of a water distribution network using an optimization algorithm. This study applied the source tracing tool in EPANET, which is a hydraulic and water quality analysis model, to the decomposition of a network to improve the efficiency of the optimal design process. The proposed approach was tested by carrying out the optimal cost design of two water distribution networks, and the results were compared with other optimal cost designs derived from previously proposed optimization algorithms. The proposed decomposition approach using the source tracing technique enables the efficient decomposition of an actual large-scale network, and the results can be combined with the optimal cost design process using an optimization algorithm. This proves that the final design in this study is better than those obtained with other previously proposed optimization algorithms.     

Optimal design of water distribution networks by a discrete state transition algorithm

In this study it is demonstrated that, with respect to model formulation, the number of linear and nonlinear equations involved in water distribution networks can be reduced to the number of closed simple loops. Regarding the optimization technique, a discrete state transition algorithm (STA) is introduced to solve several cases of water distribution networks. Firstly, the focus is on a parametric study of the ‘restoration probability and risk probability’ in the dynamic STA. To deal effectively with head pressure constraints, the influence is then investigated of the penalty coefficient and search enforcement on the performance of the algorithm. Based on the experience gained from training the Two-Loop network problem, a discrete STA has successfully achieved the best known solutions for the Hanoi, triple Hanoi and New York network problems.     

On the optimal design of water distribution networks: a practical MINLP approach

We propose a practical solution method for real-world instances of a water-network optimization problem with fixed topology using a nonconvex continuous NLP (NonLinear Programming) relaxation and a MINLP (Mixed Integer NonLinear Programming) search. Our approach employs a relatively simple and accurate model that pays some attention to the requirements of the solvers that we employ. Our view is that in doing so, with the goal of calculating only good feasible solutions, complicated algorithmics can be confined to the MINLP solver. We report successful computational experience using available open-source MINLP software on problems from the literature and on difficult real-world instances. An important contribution of this paper is that the solutions obtained, besides being low cost, are immediately usable in practice because they are characterized by an allocation of diameters to pipes that leads to a correct hydraulic operation of the network. This is not the case for most of the other methods presented in the literature.     

Statistical models for the analysis of water distribution system pipe break data

The deterioration of pipes leading to pipe breaks and leaks in urban water distribution systems is of concern to water utilities throughout the world. Pipe breaks and leaks may result in reduction in the water-carrying capacity of the pipes and contamination of water in the distribution systems. Water utilities incur large expenses in the replacement and rehabilitation of water mains, making it critical to evaluate the current and future condition of the system for maintenance decision-making. This paper compares different statistical regression models proposed in the literature for estimating the reliability of pipes in a water distribution system on the basis of short time histories. The goals of these models are to estimate the likelihood of pipe breaks in the future and determine the parameters that most affect the likelihood of pipe breaks. The data set used for the analysis comes from a major US city, and these data include approximately 85,000 pipe segments with nearly 2500 breaks from 2000 through 2005. The results show that the set of statistical models previously proposed for this problem do not provide good estimates with the test data set. However, logistic generalized linear models do provide good estimates of pipe reliability and can be useful for water utilities in planning pipe inspection and maintenance.     

Optimal cost design of water distribution networks using harmony search

This study presents a cost minimization model for the design of water distribution networks. The model uses a recently developed harmony search optimization algorithm while satisfying all the design constraints. The harmony search algorithm mimics a jazz improvisation process in order to find better design solutions, in this case pipe diameters in a water distribution network. The model also interfaces with a popular hydraulic simulator, EPANET, to check the hydraulic constraints. If the design solution vector violates the hydraulic constraints, the amount of violation is considered in the cost function as a penalty. The model was applied to five water distribution networks, and obtained designs that were either the same or cost 0.28–10.26% less than those of competitive meta-heuristic algorithms, such as the genetic algorithm, simulated annealing and tabu search under similar or less favorable conditions. The results show that the harmony search-based model is suitable for water network design.     

Scatter search heuristic for least-cost design of water distribution networks

The optimization problems of water distribution networks are complex, multi-modal and discrete-variable problems that cannot be easily solved with conventional optimization algorithms. Heuristic algorithms such as genetic algorithms, simulated annealing, tabu search and ant colony optimization have been extensively employed over the last decade. This article proposed an optimization procedure based on the scatter search (SS) framework, which is also a heuristic algorithm, to obtain the least-cost designs of three well-known looped water distribution networks (two-loop, Hanoi and New York networks). The computational results obtained with the three benchmark instances indicate that SS is able to find solutions comparable to those provided by some of the most competitive algorithms published in the literature.     

A contaminant detection system for early warning in water distribution networks

Water distribution systems are spatially diverse. As such, they are inherently vulnerable to accidental or deliberate physical, chemical, or biological threats. Efficient water quality monitoring is one of the most important tools to guarantee a reliable potable water supply. A methodology and two example applications for finding the optimal layout of a detection system, taking explicitly into account the dilution and decay properties of the water quality constituents as distributed with flow, as well as the ability of the monitoring equipment to detect contaminant concentrations, are formulated and demonstrated. The detection system outcome is aimed at capturing contaminant entries within a pre-specified level of service (LOS) defined as the maximum volume of polluted water exposure to the public at a concentration higher than a minimum hazard level. The proposed methodology couples hydraulic simulations with graph theory techniques to identify a minimum set of monitoring stations that ‘covers’ the entire network for a given LOS, at a maximum degree of system invulnerability. The model developed extends a previous work of the authors through explicitly considering the deterioration and dilution of water quality as distributed with flow, and by taking into account the monitoring equipment capabilities to detect pollutant concentrations. The methodology is demonstrated using two example applications.     

幂律流体圆管紊流新速度分布式

从牛顿流体在圆管中的层流流动的力平衡方程出发,通过引入参考窦国仁的紊流随机理论和普朗特的混合长度理论,推导出牛顿流体在圆管中的紊流流动的力平衡方程.然后,将幂律流体本构方程带入到该力平衡方程中,通过求解该方程推导出幂律流体在圆管中紊流流动的新的速度分布式,该新的分布式的速度分布由幂律流体的流性指数、稠度系数、密度即流体本身特性决定,可以从该式分析幂律流体的本身特性相关参数与其流动情况之间的关系,计算结果与实验对照比较吻合.     

Joint layout,pipe size and hydraulic reliability optimization of water distribution systems

A multicriteria maximum-entropy approach to the joint layout, pipe size and reliability optimization of water distribution systems is presented. The capital cost of the system is taken as the principal criterion, and so the trade-offs between cost, entropy, reliability and redundancy are examined sequentially in a large population of optimal solutions. The novelty of the method stems from the use of the maximum-entropy value as a preliminary filter, which screens out a large proportion of the candidate layouts at an early stage of the process before the designs and their reliability values are actually obtained. This technique, which is based on the notion that the entropy is potentially a robust hydraulic reliability measure, contributes greatly to the efficiency of the proposed method. The use of head-dependent modelling for simulating pipe failure conditions in the reliability calculations also complements the method in locating the Pareto-optimal front. The computational efficiency, robustness, accuracy and other advantages of the proposed method are demonstrated by application to a sample network.     

Characteristics of corrosion sales and biofilm in aged pipe distribution systems with switching water source

Red water has occasionally been observed in the water distribution system of Beijing following a change in the city's water source. Aged cast iron pipes from both affected and unaffected areas were used to establish experimental drinking water distribution systems under different disinfection conditions. The scale deposits formed under different conditions were characterized by X-ray diffraction and scanning electron microscopy, and the bacterial characteristics of the corrosion scales were determined using several molecular methods. The water quality changed less in pipe samples from the unaffected areas than pipes from the affected areas. The pipe samples from the unaffected area included predominantly α-FeOOH, Fe₃O₄, and γ-FeOOH, and 24.2% nitrate-reducing bacteria (NRB) were predominant with fewer iron-oxidizing bacteria (IOB) being observed. The composition of corrosion products did not exhibit large variation over time although their crystallinity exhibited a slight decrease throughout the duration of the experiment. In contrast, in the pipe samples from the affected, α-FeOOH was the main compound with less γ-FeOOH and Fe₃O₄, and 3.3% IOB and 12% NRB with few IRB were observed. However, after transporting surface water containing disinfectants, the Fe₃O₄ and dense corrosion layer formed, inhibiting the release of iron. Moreover, IRB and NRB became dominant. 22.6% and 34.3% NRB appeared in the pipes after chlorination and chloramination, respectively. The synergistic interaction of IRB and NRB with the corrosion layer played a large role in the release of iron from a cast iron pipe following changes in water quality.     

分子筛包嵌Ag团簇新型双功能材料用于水体杀菌

为了有效杀死水体中大肠杆菌并同时吸附其死亡过程中释放的内毒素,采用原位合成法首次合成了X型分子筛包嵌Ag纳米团簇的新型双功能材料(Ag@NaX),高倍透射电镜和扫描透射电镜分析结果表明该材料中Ag纳米团簇分布均一、平均尺寸在1.03 nm,且大部分Ag纳米团簇位于分子筛的孔道中。将材料用于水体中大肠杆菌的去除,该材料表现出非常优异的杀菌性能,当杀菌时间保持在20 min,2.5 mg/100 mL的材料使用量(Ag的负载量质量分数约为1.07wt%)就可以完全杀死水体中的大肠杆菌,并且分子筛可以快速高效地吸附大肠杆菌死亡过程中释放的内毒素,使水体中内毒素的含量能够保持在8×10?9g/100 mL,低于相关饮用水规定中内毒素含量的安全标准。在Ag纳米粒子与分子筛的密切协同下该复合材料同时具备优异的杀菌和吸附的双重功能。分子筛骨架可以有效地阻碍Ag纳米团簇的流失,使材料具有非常优异的稳定性,在多次使用后,材料的杀菌性能仍然能够得到较好的保持。      

Self-adaptive multi-objective harmony search for optimal design of water distribution networks

In multi-objective optimization computing, it is important to assign suitable parameters to each optimization problem to obtain better solutions. In this study, a self-adaptive multi-objective harmony search (SaMOHS) algorithm is developed to apply the parameter-setting-free technique, which is an example of a self-adaptive methodology. The SaMOHS algorithm attempts to remove some of the inconvenience from parameter setting and selects the most adaptive parameters during the iterative solution search process. To verify the proposed algorithm, an optimal least cost water distribution network design problem is applied to three different target networks. The results are compared with other well-known algorithms such as multi-objective harmony search and the non-dominated sorting genetic algorithm-II. The efficiency of the proposed algorithm is quantified by suitable performance indices. The results indicate that SaMOHS can be efficiently applied to the search for Pareto-optimal solutions in a multi-objective solution space.     

Optimal long-term design,rehabilitation and upgrading of water distribution networks

Given a limited budget, the choice of the best water distribution network upgrading strategy is a complex optimization problem. A model for the optimal long-term design and upgrading of new and existing water distribution networks is presented. A key strength of the methodology is the use of maximum entropy flows, which reduces the size of the problem and enables the application of linear programming for pipe size optimization. It also ensures the reliability level is high. The capital and maintenance costs and hydraulic performance are considered simultaneously for a predefined design horizon. The timing of upgrading over the entire planning horizon is obtained by dynamic programming. The deterioration over time of the structural integrity and hydraulic capacity of every pipe are explicitly considered. The upgrading options considered include pipe paralleling and replacement. The effectiveness of the model is demonstrated using the water supply network of Wobulenzi town in Uganda.     

Some observations on energy loss and network entropy in water distribution networks

The design of water distribution networks has been extensively studied with the aid of computers, and the focus has shifted from merely satisfying the hydraulic requirements to fulfilling the need for reliability. One of the interesting research areas recently is the use of informational entropy as a surrogate measure for reliability. The actual meaning of the informational entropy for water distribution network has not been fully elucidated, and it was hypothesed that reliability is in some way proportional to the numerical value of network entropy. The purpose of this paper is to explore the relationship between energy loss and network entropy. The investigation approach used is to take a simple looped network and individually vary the pipe diameters from zero to infinity, and calculate the corresponding network entropy and energy loss for the water distribution network. The results revealed many interesting observations in the variation of network entropy with pipe resistance coefficient K _i , and the revelation of local maximum and minimum points.