Pipe Index Vector: A Method to Improve Genetic-Algorithm-Based Pipe Optimization

This paper proposes a methodology for the optimal design of water distribution systems based on genetic algorithms. The objective of the optimization is to minimize the capital cost, subject to ensuring adequate pressures at all nodes during peak demands. The proposed method is novel in that it involves the use of a pipe index vector to control the genetic algorithm search. The pipe index vector is a measure of the relative importance of pipes in a network in terms of their impact on the hydraulic performance of the network. By using the pipe index vector it is possible to exclude regions of the search space where impractical and infeasible solutions exist. By reducing the search space it is possible to generate feasible solutions more quickly and hence process much healthier populations than would be the case in a standard genetic algorithm. This results in optimal solutions being found in a fewer number of generations resulting in a substantial saving in terms of computational time. The method has been tested on several networks, including networks used for benchmark testing least cost design algorithms, and has been shown to be efficient and robust.     

Novel Cellular Automata Approach to Optimal Water Distribution Network Design

This paper proposes a novel heuristic-based and cellular automata-inspired approach to the optimal design of water distribution networks. The design of water distribution networks is of central importance to the water industry, but many networks cannot be optimally designed by traditional techniques due to their complexity. Genetic algorithms have become a state-of-the-art technique for this purpose but are hampered by the fact that they are population based and require a large number of model evaluations to achieve good solutions. The proposed approach uses a parallel, localist, heuristic-based algorithm to optimally design water distribution networks requiring only a limited number of model evaluations. The algorithm is applied to a well-known simple test network and two real water distribution systems in the U.K. The results indicate that the proposed cellular approach is a viable alternative to genetic algorithm approaches while using only a fraction of the computational time required by its evolutionary counterpart.     

Decomposition Model of a General Water Supply Network Graph

A new decomposition concept of the network graph according to its connectivity properties is introduced in this paper that allows various applications in the field of systems analysis of water supply networks. In this case, the network graph consists of two main components. The outer branched component of the network is called a forest. The inner complement is denoted as the core of the network. A forest consists of a number of trees, while the core network is composed of distinct biconnected blocks that are connected by bridges. Forest and core components of the network overlap at the so-called root nodes. Calculations for the simulation or the optimization of the single components can be done, independently, thus decreasing matrix sizes and calculation time. Control actions that are necessary to efficiently operate a water supply system result in changes of the connectivity of the network graph. By using the proposed decomposition approach the in-time identification of the different supply areas according to the actual state of the network is straightforward. It also includes measures of network vulnerability and several stages of network simplification that are able to enhance the understanding of the single network components and their interaction. The simplified network model can be applied, for instance, to the development of strategies for efficient operation and control of a water distribution network.     

Pressure-Driven Demand and Leakage Simulation for Water Distribution Networks

Increasingly, water loss via leakage is acknowledged as one of the main challenges facing water distribution system operations. The consideration of water loss over time, as systems age, physical networks grow, and consumption patterns mature, should form an integral part of effective asset management, rendering any simulation model capable of quantifying pressure-driven leakage indispensable. To this end, a novel steady-state network simulation model that fully integrates into a classical hydraulic representation, pressure-driven demand and leakage at the pipe level is developed and presented here. After presenting a brief literature review about leakage modeling, the importance of a more realistic simulation model allowing for leakage analysis is demonstrated. The algorithm is then tested from a numerical standpoint and subjected to a convergence analysis. These analyses are performed on a case study involving two networks derived from real systems. Experimentally observed convergence/error statistics demonstrate the high robustness of the proposed pressure-driven demand and leakage simulation model.     

Optimal Design of Level 1 Redundant Water Distribution Networks Considering Nodal Storage

A water distribution network (WDN) is designed to meet time-varying demands with sufficient pressure, taking into consideration an appropriate demand during peak hours. Therefore, a network has inherent redundancy in the sense that under abnormal conditions such as those arising due to pipe breaks or pump failures, deficiency in supply during peak hours can be met through additional supply during off-peak periods. However, this necessitates a storage facility at the consumer end of the network, which is normally available in the form of a sump or an overhead tank in developing countries. Such a storage enables the consumer to store water during the off-peak period and then use it during the peak period. Reliability of a WDN is assessed herein considering nodal storage, and an iterative method is proposed for the optimal design of Level 1 redundant WDNs, i.e., networks that can sustain a single pipe failure without affecting consumer services either in part or in full. The method is illustrated through an example and the designs of a network with and without storage are compared. Provision of a nodal storage is found to reduce the total cost of the network.     

Self-Adaptive Fitness Formulation for Evolutionary Constrained Optimization of Water Systems

In design of water distribution networks, there are several constraints that need to be satisfied; supplying water at an adequate pressure being the main one. In this paper, a self-adaptive fitness formulation is presented for solving constrained optimization of water distribution networks. The method has been formulated to ensure that slightly infeasible solutions with a low objective function value remain fit. This is seen as a benefit in solving highly constrained problems that have solutions on one or more of the constraint bounds. In contrast, solutions well outside the constraint bounds are seen as containing little genetic information that is of use and are therefore penalized. In this method, the dimensionality of the problem is reduced by representing the constraint violations by a single infeasibility measure. The infeasibility measure is used to form a two-stage penalty that is applied to infeasible solutions. The performance of the method has been examined by its application to two water distribution networks from literature. The results have been compared with previously published results. It is shown that the method is able to find optimum solutions with less computational effort. The proposed method is easy to implement, requires no parameter tuning, and can be used as a fitness evaluator with any evolutionary algorithm. The approach is also robust in its handling of both linear and nonlinear equality and inequality constraint functions. Furthermore, the method does not require an initial feasible solution, this being an advantage in real-world applications having many optimization variables.     

Optimization of Water Distribution Networks Using Integer Linear Programming

In this study optimum design of municipal water distribution networks for a single loading condition is determined by the branch and bound integer linear programming technique. The hydraulic and optimization analyses are linked through an iterative procedure. This procedure enables us to design a water distribution system that satisfies all required constraints with a minimum total cost. The constraints include pipe sizes, which are limited to the commercially available sizes, reservoir levels, pipe flow velocities, and nodal pressures. Accuracy of the developed model has been assessed using a network with limited solution alternatives, the optimal solution of which can be determined without employing optimization techniques. The proposed model has also been applied to a network solved by others. Comparison of the results indicates that the accuracy and convergence of the proposed method is quite satisfactory.     

Water Distribution Network Analysis Using Excel

The analysis of water distribution networks has been and will continue to be a core component of civil engineering water resources curricula. Since its introduction in 1936, the Hardy Cross method has been used in virtually every water resources engineering text to introduce students to network analysis. The technique gained widespread popularity primarily because it is amenable to manual calculation techniques. However, the same subtle elegance that facilitates manual calculations often obscures the primary engineering and physical principles of water distribution systems relative to the nuances of algorithm implementation. Herein, the authors illustrate the application of commonly available spreadsheet software (MicroSoft Excel) to more concisely and effectively solve typical undergraduate network distribution problems using linear theory. Application development is much more efficient and straightforward than the corresponding Hardy Cross implementation enabling students to concentrate upon the engineering system and relevant design issues. The technique presented utilizes commonly available technology and is presented as a supplement to alternatives discussed in recent literature.     

Algorithm for Automatic Detection of Topological Changes in Water Distribution Networks

Topological and pressure-driven analyses are an integral part of reliability/risk considerations for a water distribution system. For example, it is often necessary to identify which parts of the distribution network are isolated from water sources after the valves have been closed in response to a mechanical pipe failure. Pressure-driven analysis is then necessary to ascertain the consequences of pipe failures in terms of the performance of the functioning subsystem while pipe breaks are being fixed in the isolated area. Therefore, it is extremely useful to have an algorithm for the automatic identification of nodes/pipes disconnected from the water source(s). However, this is a complex problem because valves sometimes significantly modify the network topology. Furthermore, the use of isolation valves can cause a demand shortage to some customers (due to pressure reduction) during the abnormal operating conditions in the system. Thus, pressure-driven simulation of the network behavior is required. For these reasons, a novel algorithm capable of automatic detection of topological network changes is coupled with a robust pressure-driven simulation model. This algorithm is tested on two case studies involving a small artificial water distribution system and a larger, real-life network. The results obtained clearly demonstrate the robustness of the algorithm developed.     

Quality Modeling of Water Distribution Systems Using Sensitivity Equations

In this paper, unsteady water quality modeling and the associated sensitivity equations are solved for water distribution systems. A new solution algorithm is proposed, designed for slow varying velocity and based on a time splitting method to separate and solve efficiently each phenomenon such as advection and chemical reaction. This numerical approach allows simultaneous solution of both the direct problem and the sensitivity equations. Special attention is given to the treatment of advection, which is handled with a total variation diminishing scheme. The general model presented in this study permits global sensitivity analysis of the system to be performed and its efficiency is illustrated on two pipe networks. The importance of the sensitivity analysis is shown as part of the calibration process on a real network.     

Demand Forecasting for Irrigation Water Distribution Systems

One of the main problems in the management of large water supply and distribution systems is the forecasting of daily demand in order to schedule pumping effort and minimize costs. This paper examines methodologies for consumer demand modeling and prediction in a real-time environment for an on-demand irrigation water distribution system. Approaches based on linear multiple regression, univariate time series models (exponential smoothing and ARIMA models), and computational neural networks (CNNs) are developed to predict the total daily volume demand. A set of templates is then applied to the daily demand to produce the diurnal demand profile. The models are established using actual data from an irrigation water distribution system in southern Spain. The input variables used in various CNN and multiple regression models are (1) water demands from previous days; (2) climatic data from previous days (maximum temperature, minimum temperature, average temperature, precipitation, relative humidity, wind speed, and sunshine duration); (3) crop data (surfaces and crop coefficients); and (4) water demands and climatic and crop data. In CNN models, the training method used is a standard back-propagation variation known as extended-delta-bar-delta. Different neural architectures are compared whose learning is carried out by controlling several threshold determination coefficients. The nonlinear CNN model approach is shown to provide a better prediction of daily water demand than linear multiple regression and univariate time series analysis. The best results were obtained when water demand and maximum temperature variables from the two previous days were used as input data.     

Integrated Reservoir-Based Canal Irrigation Model. I: Description

The success of irrigation system operation and planning depends on the quantification of supply and demand and equitable distribution of supply to meet the demand if possible, or to minimize the gap between the supply and demand. Most of the irrigation literature mainly focuses on the demand and distribution aspects only. In addition, irrigation projects that receive water from a reservoir can be challenging to manage as annual fluctuations in runoff from the reservoir’s catchment can have considerable impact on the irrigation management strategy. This study focuses on the development of an integrated reservoir-based canal irrigation model (IRCIM) that includes catchment hydrologic modeling, reservoir water balance, command hydrologic modeling, and a rotational canal irrigation management system. The front end of the IRCIM is developed in Visual Basic 6.0, whereas the back-end coding is done in C language. The graphical user interface is the most important feature of the model, as it provides a better interaction between the model and its user. The IRCIM has a modular structure that consists of three modules, viz., catchment module, reservoir module, and crop water demand module. The catchment module predicts daily runoff from the catchment that inflows to the reservoir. Depending on the data availability, this module is provided with the flexibility of choosing between the Soil Conservation Service’s curve number method combined with the Muskingum routing technique, and an artificial neural network technique using the Levenberg–Marquardt algorithm. The reservoir module is based on conservation of mass approach, and results in daily reservoir storage. The crop water demand module is comprised of water-balance models for both paddy and field crops. The irrigation management system serves as the program flow controller for the model and runs the required module when needed. For postseason evaluation of the irrigation system, performance indicators such as adequacy, efficiency, equity, and dependability are used. In a companion paper, the model is applied for Kangsabati Irrigation Project, West Bengal, India.     

Regional Water Management Modeling for Decision Support in Irrigated Agriculture

Efficient water management is one of the key elements in successful operation of irrigation schemes in arid and semiarid regions. An integrated water management model was developed by combining an unsaturated flow model and a groundwater simulation model. These combined models serve as a tool for decision making in irrigation water management to maintain the water tables at a safe depth. The integrated model was applied on a regional scale in Sirsa Irrigation Circle, covering about a 0.42 million ha area in the northwestern part of Haryana, India, which is faced with serious waterlogging and salinity problems in areas underlain with saline ground irrigated by the canal network. The model was calibrated using the agrohydrologic data for the period 1977–1981 and validated for the period 1982–1990 by keeping the calibrating parameters unchanged. The model was used to study the long-term impact of two water management interventions related to the canal irrigation system—change in pricing system of irrigation water, and water supply according to demand—on the extent of waterlogging risk. Both of these strategies, if implemented, would considerably reduce aquifer recharge and consequently waterlogging risk, compared to the existing practice. The water supply according to demand strategy was slightly more effective in reducing aquifer recharge than the water pricing intervention. The implementation of the proposed water pricing policy would pose no problem in fitting into the existing irrigation system, and thus it would be easier to implement, compared to the water supply according to demand strategy, when taking technical, financial, and social considerations into account.     

分簇无线传感器网络中提高网络连通性的协作算法

针对分簇无线传感器网络提出了一种基于虚拟天线阵列的协作算法.该算法通过节点间的协作来提高网络连通性,所有节点均按照泊松Voronoj网格模型进行分簇,簇首根据通信链路决定是否激活节点协作;若节点协作算法被激活,簇首从其成员中选择适合的节点作为协作节点共同组成虚拟天线阵列.通过协作,可扩展簇间的通信范围从而与远方节点直接通信以避免出现通信覆盖盲区,或者可补偿信道增益以防止由于信道深衰落所导致的传输失败.仿真结果表明,协作算法在通信过程中具有更好的连通性及能量效率,可有效降低接收端的丢包率,维持网络的连通性,从而延长网络的工作时间.     

Modeling Residual Chlorine Response to a Microbial Contamination Event in Drinking Water Distribution Systems

Changes in chlorine residual concentrations in water distribution systems could be used as an indicator of microbial contamination. Consideration is given on how to model the behavior of chlorine within the distribution system following a microbial contamination event. Existing multispecies models require knowledge of specific reaction kinetics that are unlikely to be known. A method to parameterize a rate expression describing microbially induced chlorine decay over a wide range of conditions based on a limited number of batch experiments is described. This method is integrated into EPANET-MSX using the programmer’s toolkit. The model was used to simulate a series of microbial contamination events in a small community distribution system. Results of these simulations showed that changes in chlorine induced by microbial contaminants can be observed throughout a network at nodes downstream from and distant to the contaminated node. Some factors that promote or inhibit the transport of these chlorine demand signals are species-specific reaction kinetics, the chlorine concentration at the time and location of contamination, and the system’s unique demand patterns and architecture.     

Competent Genetic-Evolutionary Optimization of Water Distribution Systems

A genetic algorithm has been applied to the optimal design and rehabilitation of a water distribution system. Many of the previous applications have been limited to small water distribution systems, where the computer time used for solving the problem has been relatively small. In order to apply genetic and evolutionary optimization technique to a large-scale water distribution system, this paper employs one of competent genetic-evolutionary algorithms—a messy genetic algorithm to enhance the efficiency of an optimization procedure. A maximum flexibility is ensured by the formulation of a string and solution representation scheme, a fitness definition, and the integration of a well-developed hydraulic network solver that facilitate the application of a genetic algorithm to the optimization of a water distribution system. Two benchmark problems of water pipeline design and a real water distribution system are presented to demonstrate the application of the improved technique. The results obtained show that the number of the design trials required by the messy genetic algorithm is consistently fewer than the other genetic algorithms.     

Optimum Design and Management of Pressurized Branched Irrigation Networks

The scarcity of water resources is the driving force behind modernizing irrigation systems in order to guarantee equal rights to all beneficiaries and to save water. Traditional distribution systems have the common shortcoming that water must be distributed through some rotational criteria. This type of distribution is necessary to spread the benefits of scarce resources. Irrigation systems based on on-demand delivery scheduling offer flexibility to farmers and greater potential profit than other types of irrigation schedules. However, in this type of irrigation system, the network design has to be adequate for delivering the demand during the peak period whilst satisfying minimum pressure constraints along with minimum and maximum velocity constraints at the farm delivery points (hydrants) and in the pipes, respectively. In this paper, optimum design and management of pressurized irrigation systems are considered to be based on rotation and on-demand delivery scheduling using a genetic algorithm. Comparison is made between the two scheduling techniques by application to two real irrigation systems. Performance criteria are formulated for the optimum design of a new irrigation system and better management of an existing irrigation system. The design and management problems are highly constrained optimization problems. Special operators are developed for handling the large number of constraints in the representation and fitness evaluation stages of the genetic algorithm. The performance of the developed genetic algorithm is assessed in comparison to traditional optimization techniques. It is shown that the methodology developed performs better than the linear programming method and that solutions generated by the modified genetic algorithm show an improvement in capital cost. The method is also shown to perform better in satisfying the constraints. Comparison between on-demand and rotation delivery scheduling shows that a greater than 50% saving can be achieved in total cost at the cost of reducing flexibility in the irrigation time. Finally, it is shown that minimizing standard deviation of flow in pipes does not result in the best distribution, and therefore minimum cost, neither for systems with uniform flows or those with large variations in discharge at hydrants.     

Improved Control of Pressure Reducing Valves in Water Distribution Networks

The behavior of transients in water pipe networks is well understood but the influence of modulating control valves on this behavior is less well known. Experimental work on networks supplied through pressure reducing valves (PRVs) has demonstrated that, in certain conditions, undesirable phenomena such as sustained or slowly decaying oscillation and large pressure overshoot can occur. This paper presents results from modeling studies to investigate interaction between PRVs and water network transients. Transient pipe network models incorporating random demand are combined with a behavioral PRV model to demonstrate how the response of the system to changes in demand can produce large or persistent pressure variations, similar to those seen in practical experiments. A proportional-integral-derivative (PID) control mechanism, to replace the existing PRV hydraulic controller, is proposed and this alternative controller is shown to significantly improve the network response. PID controllers are commonly used in industrial settings and the methods described are easy to implement in practice.