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Hydrological Sciences-J'ournal-des Sciences Hydrologiques, 42(4) August 1997 549

Evolving sustainable water networks

D. A. SAVIC & G. A. WALTERS School of Engineering, University of Exeter, North Park Road, Exeter EX4 4QF, UK

Abstract The need for efficient pipe networks for urban water supply and drainage is introduced and discussed in the context of global sustainable development. The role of computer based analysis and design tools in the planning and operation of such systems is described, with the way in which these tools can help to minimize use of resources, energy and water losses being explained. In particular, numerical techniques such as Genetic Algorithms, which are based on the principles of natural evolution, are found to be particularly effective in dealing with the large, complex systems that typify urban water distribution networks. These evolutionary techniques are introduced and discussed, and several applications of the techniques to the development of efficient water systems are described. A case study on the use of these techniques in the calibration of an accurate mathematical model of an urban water distribution system is included.

Elaboration de réseaux hydrauliques durables Résumé Le besoin de réseaux de canalisations efficaces pour l'alimentation en eau et l'assainissement est présenté et analysé dans le contexte d'un aménagement global durable. Le rôle des analyses informatiques et des outils de conception utilisés pour l'élaboration et la gestion de tels systèmes est décrit. La manière dont ces outils peuvent minimiser les besoins et les pertes d'énergie et d'eau est également expliquée. On s'aperçoit en particulier que les techniques numériques telles que les algorithmes génétiques, fondés sur la théorie de l'évolution par la sélection naturelle, sont particulièrement efficaces pour traiter les systèmes vastes et complexes que sont les réseaux urbains de distribution d'eau. Ces techniques, fondées sur la théorie de l'évolution, sont présentées et analysées et plusieurs applications de ces techniques à l'aménagement de systèmes hydrauliques efficaces sont décrites. Une étude de cas concernant l'utilisation de ces techniques pour caler un modèle mathématique précis d'un réseau de distribution d'eau urbain est incluse.

INTRODUCTION

Since the Earth Summit in Rio de Janeiro in 1992 it has become obvious that there can be no global sustainable development without sustainable settlement. However, today the issue of urban environmental sustainability is becoming critical because urbanisation and its associated environmental impacts are occurring at an unprecedented rate (Girardet, 1995). Urbanization brings increased demand for energy, raw materials and results in pollution and production of waste. The key activities of modern cities—transport, electricity supply, water supply, waste disposal, heating, service activities, manufacturing, etc.—are all characterized by the aforementioned problems.

Nowadays pipelines are the most common means for transporting water (potable and waste water), gases and oils necessary for everyday life in modern cities. The

Open for discussion until 1 February 1998

550 D. A. Savic & G. A. Walters

design, construction, operation and maintenance of millions of kilometres of these pipelines represent an immense challenge for engineers around the world. This paper concentrates on water networks as an element of urban settlement, on issues associated with sustainable development of water distribution networks in England and Wales in particular, and on the development and use of evolution-based techniques for the design of new networks (developing countries) and transforming existing networks (developed countries) into sustainable ones.

WATER DISTRIBUTION NETWORKS, SUSTAINABILITY AND MODELLING

A water supply network capable of supplying a sufficient quantity of potable water, together with drainage and waste water systems, is a necessity for a modern city. This system is usually referred to as "clean water system" as opposed to "dirty water systems" associated with drainage and waste water networks. It typically consists of a system of interconnected pipes, pumps, valves and reservoirs with external supplies from boreholes, rivers and lakes. It may be argued that there are many factors affecting sustainability of water networks but the key ones are: (a) use of energy; and (b) use of water as a resource.

These factors basically mean that sustainable water supply systems must be designed and operated so as to: minimize energy use; limit leakage and not-accoun-ted-for water; minimize the number and consequences of pipe failures; make most effective use of the existing assets; and still meet customers' needs (both present and future) in terms of water quality and quantity. The two key factors are closely related to economic, legislative, social, environmental and other pressures on organizations/institutions in charge of operating water supply networks.

A water utility, be it privately or publicly owned, is in charge of operating a system, planning for its future and providing a certain level of service to the community. In England and Wales the actions of privatized water utilities are influenced by different forces (Rees et ai, 1996). These have been classified as external and internal forces. External forces include the regulatory regime (economic, water quality and environmental regulators) and the requirements of the owners of the businesses. These forces are the key to sustainability as they provide permanent guidance on how the water utilities function. Although less important for sustainability, internal forces may play a role in defining elements in the sustainability equation. These include pressures from staff, the aspirations of the senior management of the businesses, and the pressures which the businesses themselves generate in response to the external forces.

Having described in general terms what the key factors of sustainable water networks are and what are the key forces in the decision-making process within water utilities, it is now necessary to identify basic modelling tools for analysing pipe networks and making decisions for efficient planning, design and operation. The basic one is network analysis (simulation) which allows complex water supply and distribution networks to be examined under a variety of current and future operating

Evolving sustainable water networks 5 5 ]

conditions. Models capable of performing steady-state, extended period and water quality simulations have improved considerably during the past decade (Coulbeck, 1993). Nowadays, it is widely acknowledged that the design and operation of pressurized network systems depend critically on the efficiency and accuracy of mathematical models utilized to model the systems' behaviour. In conjunction with simulation models, the use of Evolution Programs (EPs) and other similar evolution-based computing techniques has caught the imagination of researchers and engineers in the field. Evolution Programs are general artificial-evolution search methods based on natural selection and mechanisms of population genetics (Michalewicz, 1992). They emulate nature's very effective optimization techniques of evolution which are based on preferential survival and reproduction of the fittest members of the population, the maintenance of a population with diverse members, the inheritance of genetic information from parents, and the occasional mutation of genes. After reported successes in many problem domains (Goldberg, 1989), water resources systems optimization has started to benefit from the use of EPs. The next sections will introduce Genetic Algorithms and present a few of the applications where these techniques have been used to evolve solutions for water distribution networks. A case study involving calibration of a water network model is given in more detail as an illustration of the technique and its effectiveness. It is argued that such an application represents a step closer to better understanding and ultimately lead to the design and development of sustainable networks.

GENETIC ALGORITHMS

The Genetic Algorithm is probably the best known type of Evolution Program (Michalewicz, 1992), this being a biologically motivated adaptive system based on natural selection and genetic recombination. Genetic Algorithms (GAs) are also referred to as stochastic optimization techniques because the solution space is examined by generating candidate solutions with the aid of a pseudo-random number generator. As the run proceeds, the probability distribution by which new candidate solutions are generated may change, based on the results of trials earlier in the run. Because of their stochastic nature there is no guarantee that the global optimum will be found using GAs although the number of applications suggests a good rate of success in identifying good solutions for complex systems where classical optimization methods have failed.

There are many forms of GA but the following description includes most of the important features. An algorithmic model of Darwinian evolution is established by the creation of a set of solutions called a population of individuals. Each individual in a population is represented by a set of parameter values which completely define a solution. Computer encoding of candidate solutions is done via so-called chromosomes, which are sets of strings analogous to the chromosomes found in DNA. Standard GAs use a binary alphabet (characters may be 0 or 1) to form chromosomes. For example a two-parameter solution x = (x,, x2) may be represented as an 8-bit binary chromosome: 1001 0011 (i.e. 4 bits per parameter, JC, = 1001,


x2 = 0011). It should be noted that not all EPs restrict representation to the binary alphabet which makes them more flexible and applicable to a variety of decision making problems.

The initial population of solutions is usually chosen randomly. The chromosomes are then allowed to evolve over a number of generations. This is accomplished by the recombination operation, which is generally referred to as crossover because of the way that genetic material crosses over from one chromosome to another. For example, if two chromosomes are x = (xu x2) = 1111 1111 and y = (yu y2) = 0000 0000, the two offspring may be z = 1100 0000 and w = 0011 1111.

The probability that a chromosome from the original population will be selected to produce offspring for the new generation is dependent on its fitness value (a measure of how well a chromosome optimizes the objective function). Due to this selective pressure applied through a number of generations, the overall trend is toward higher fitness solutions. A further mechanism called mutation also plays a role in the reproduction phase, though it is not the dominant role, as is popularly believed, in the process of evolution (Goldberg, 1989). A GA handles mutation by flipping a binary digit (also called gene) from 0 to 1 or vice versa. For example, if the original chromosome is x = (Xj, x2) = 1111 1111, the same chromosome after mutation may be x ' = 1110 1111. If the probability of mutation is set too high, the search degenerates into a random process. This should not be allowed as a properly-tuned GA is not a random search for a solution to a problem. As a simulation of a genetic process a GA uses stochastic mechanisms, but the result is distinctly better than random.

GENETIC ALGORITHM APPLICATIONS TO DESIGN AND MANAGEMENT OF WATER NETWORKS

Early work using GAs in the design and management of water networks centred on the design of layout and pipe sizing of water distribution networks (Cembrowicz & Krauter, 1977; Walters & Lohbeck, 1993) with the use of similar algorithms for the design of sewer systems. The implementation of these methods in the design of new water supply and sewerage networks for a number of cities in developing countries is described by Cembrowicz (1992). Most recent work on GAs in the areas of water networks has been on aspects of water distribution network optimization, including new design, rehabilitation, modelling and operation (Walters & Savic, 1996).

Design of water distribution networks is often viewed as a least-cost optimization problem with pipe diameters being decision variables. Even that, somewhat restricted, formulation of the optimal network design represents a difficult problem to solve because the optimization problem is nonlinear due to energy conservation constraints and because pipes for water supply are manufactured in a set of discrete-sized diameters. In order to solve this NP-hard problem* exactly it is suggested that only

* The term "NP-hard problem" denotes a set of practical (integer optimization) problems that are intractable.

Evolving sustainable water networks 553

explicit enumeration or an implicit enumeration technique, such as dynamic programming, can guarantee the optimal solution. Simpson et al. (1994) and Savic & Walters (1994, 1997) used a binary GA to solve several example problems from the literature. They found that G A solutions compared favourably in terms of cost and minimum head requirements to those obtained by several other techniques. Namely, consistently better discrete-diameter results were obtained, while they were up to 3% more costly than the continuous-diameter or split-pipe solutions from the literature.

However, sustainable water networks cannot be achieved without models being able to deal with environmental issues and resources that are not priced in the market place, that are variable and uncertain, and involve major costs now but major benefits only far into the future. An attempt to overcome that problem for rehabilitation/design of water networks was presented by Halhal et al. (1997). Their work uses a multi-objective approach combined with a specially developed Structured Messy Genetic Algorithm (SMGA). In contrast to the binary GA where the length of the chromosome is fixed, the SMGA approaches the problem in a progressive way, starting with short strings of one digit length and increasing them during the process until reaching their maximum length. This parallels the natural process in which complex life-forms evolve from single cell structures. With a limited fund, the problem was to determine the set of improvements which will maximize the benefit to a water distribution system, in terms of reducing supply shortfall, inadequate pressure, leakage, breakages, etc., while minimizing costs. The final optimal results of the SMGA are all non-dominated solutions, known as Pareto-optimal solutions, which are neither inferior nor superior to one another with respect to all the objectives. The results obtained for a real water distribution network in Morocco showed that the SMGA method is greatly superior to the binary GA for this large problem (Halhal et al., 1997).

One of the operational aspects of water supply systems that has been tackled by optimization is that of minimizing the cost of pumping water. Classical optimization methods, such as linear and dynamic programming, may become inadequate when there are more than two reservoirs in the system or even for one-reservoir systems which have several different pump combinations or complicated system constraints. Genetic Algorithms treat discrete values used in pump scheduling models naturally and thus they seem well suited to this kind of optimization. An attempt was made to investigate the use of a simple (binary) GA for pump scheduling by Mackle et al. (1995) by minimizing pumping costs of a simple system with four different pumps (16 pump combinations) delivering water to a single reservoir. Further work incorporating a multiobjective approach was carried out by Schwab et al. (1996) where not only the cost of electricity was considered, but also the pump switching. This additional objective was introduced to discourage schedules involving numerous changes to a pump's status (pump switches) as well as undesirable complex operation decisions. A hybrid model was also developed which combines a G A and a hill-climbing (local search) technique. The best solutions identified by the G A show, as expected, that as much of the water as possible should be pumped using the cheap night-time tariff. The water distribution reservoir is consequently as full as possible at the end of the cheap period and as empty as allowed at the end of the expensive


period (Schwab et ah, 1996). In addition to the above problems, EPs have been successfully applied to network

layout optimization and pressure regulation. Detailed descriptions of the two problems and solution approaches are given in Walters & Lohbeck (1993), Savic & Walters (1995, 1997) and Walters & Smith (1995).

GENETIC ALGORITHM TECHNIQUES FOR CALIBRATING WATER DISTRIBUTION NETWORK MODELS

It has already been said that the design and operation of water distribution systems depend critically on the efficiency and accuracy of the mathematical models utilized to model the behaviour of a system under a variety of conditions. Before a model is used, it must be adjusted to ensure that it will predict, with reasonable accuracy, the behaviour of the system it models, i.e. it must be calibrated. This is widely acknowledged by the research community and several studies on the calibration of network models have been published in the past two decades (Rahal et al, 1980; Walski, 1983; Lansey & Basnet, 1991; Data & Sridharan, 1994). The problem of model calibration, even if only for water quantity (pressures and flows), is highly complex due to the large number of parameters examined and nonlinear due to the flow equations. Several researchers have addressed this problem, developing methods to minimize the difference between the values of the observed data and those computed by the network simulation model. These methods are based on the use of analytical equations (Walski, 1983), simulation models (Rahal et al, 1980), or optimization techniques (Lansey & Basnet, 1991). Techniques based on analytical models may be applied to very small networks or may alternatively require a large network to be simplified by considering only the skeleton network. Simulation techniques can handle larger networks but are generally restricted to a single loading condition. The most promising calibration procedures are based on optimization. However, the success of current methods usually depends on linearizing assumptions or the unrealistic calculation of partial derivatives. In addition, they are generally local optimization procedures which tend to become entrapped in local minima or suffer from numerical instabilities associated with matrix inversion.

Since models capable of simulating the hydraulic behaviour of pipe networks are complex in terms of size, nonlinearity, and discrete nature, the use of analytical methods or classical optimization techniques requires many simplifications. These in turn may cause unsatisfactory or unrealistic results. On the other hand, Genetic Algorithms, which are capable of dealing with complex, multi-modal and discontinuous functions, have the required robustness and efficiency as well as conceptual simplicity to handle the aforementioned problems. The research described in this section combines theoretical and practical work in modelling (simulation) and Genetic Algorithms (optimization) to develop novel, efficient and robust calibration procedures and tools. It is believed that the availability of these tools and an increased understanding of the data requirements for reliable model construction have great potential benefits. These include improved operation and more purposeful


monitoring of water supply systems, increased quality of supply and ultimately less wastage of energy and water resources.

Mathematical formulation

A distribution network may be viewed as a connected graph with arcs representing pipes and nodes representing network elements like valves, pumps, reservoirs, demand points, etc. Two hydraulic variables are associated with network elements, namely flows and heads (pressures). The following mathematical statement of the problem is presented for a general water distribution network. The equations of the network express flow conservation at nodes and relationships between head losses and heads for arcs:

S qit =c, (1) je.I(i) J

Milj=hl-h) (2)

where /(/) is a set of nodes adjacent to node i, c( is the consumption at node /, qjt is the flow from node 7" to node i, Ahy is the head loss in the pipe connecting i and j and hj is the head at node /. The head loss to friction Ahy associated with flow through a pipe can be expressed in a general form as:

where Rtj and n (n > 1) depend on the flow resistance law selected. In this work the Colebrook-White formula is used to calculate the resistance coefficient Ry as a function of the friction factor ftj, the diameter dtj of the pipe connecting i and j , the flow qtj and the pipe length Ly

^ = ( p ( / t f , ^ ^ , A j ) (4)

The friction factor / is a function of the roughness of the pipe k, the diameter d, the flow q through the pipe and the viscosity of the fluid (which is for this work considered constant).

For specified pipe characteristics, demand patterns and reservoir heads the system of nonlinear equations (l)-(4) has a unique solution defined by the flows and heads in the whole network. There are several iterative techniques available for solving the above system (Jeppson, 1983) which are incorporated into modern simulation tools (Wood, 1980; WRc, 1989; Rossman, 1993). These tools allow network analysts to concentrate solely on building realistic representation of the water distribution network thus enabling easier development of models. If input data for the model are correct, then predicted pressures and flows will match observed values. However, two main sources of problem are associated with data collection for real networks: (a) not all input parameters are measured directly because of the expense of data collection; and (b) even if it is possible to measure all parameters a certain amount of inaccuracy will still be associated with readings in the field.


Standard calibration procedures

Techniques and procedures for constructing a WDS model may vary but in the UK they are summarized by the Water Research Centre (WRc pic) into the following activities (WRc, 1989): (i) inspection of supply, distribution and consumer records and maps; (ii) site inspection of plant and equipment; (iii) preliminary field measurement; (iv) field measurement exercise; (v) entry of network data for a computer analysis; and (vi) calibration of the network model.

The basic aim of the inspection of supply and distribution records and maps is to select network data which can justifiably be included in the model. For example, pipes which are below a certain size are either ignored or grouped together and replaced by equivalent pipes. Since the demand for water is modelled to take place at nodes, consumer records and maps are inspected in order to enable allocation of the total demand to network demand zones and finally to nodes. The demand allocation is aided by the field measurement exercise which involves flow measurement of significant demands, transfers to and from the network and from source works, pump stations and reservoirs. The key to meaningful calibration is having field measurements corresponding to more than one flow rate. In addition to flows the exercise also entails pressure logging at as many key sites as possible, e.g. at pump stations, in known problem areas, at large diameter pipes, etc.

Calibration performed using modern simulation packages commences when input data including an initial estimate of the roughness values of all pipes is entered into the model. The model is then analysed and the results compared with the field test measurements. Calibrations of this type normally proceed based on a time-consuming trial-and-error procedure where the parameter values are adjusted based on the hydraulic results and the hydraulic analysis is repeated. This iterative process continues until some stated operating specifications are satisfied or no viable change in input parameters which improves agreement between observed and predicted values can be found. In the latter case, the possibility of modelling anomalies, such as reduced pipe diameter due to internal corrosion, an incorrectly modelled open/closed valve, etc., should be investigated.

The calibration procedure presented above is extremely tedious and, even assuming enough time and resources are given for model building, depends critically on the skills of the analyst and on his/her understanding of the water distribution system being studied. Often this procedure will result in a less than accurate model and may not be effective when a large number of variables and operating conditions are investigated.

Genetic algorithms for calibration

In recent years, many researchers have begun to investigate the use of evolution based computer methods for the calibration of various hydraulic/hydrological


models. Wang (1991) investigated the use of GAs combined with fine-tuning by a local search method for the calibration of a conceptual rainfall-runoff model. Models were calibrated by minimizing the residual variance defined as the sum of the squares of differences between computed and observed discharges. Duan et al. (1994) introduced the Shuffled Complex evolution method for a similar problem by hybridizing a GA with the Simplex search method. The objective function used was the mean daily square root of the difference between the observed flows and simulated flows. Babovic et al. (1994) used GA and the hydrodynamic MOUSE package to fit Manning resistance values to pipes while Mohan & Loucks (1995) reported on the use of GAs for estimating parameter values of some linear and nonlinear flow routing and water quality prediction models.

Most of those studies used the GA formulation with binary representation requiring an additional decoding procedure from bit-strings to the real-valued parameters being calibrated. This representation has several advantages over other encodings (Davis, 1991). It is simple to create and manipulate, it is theoretically tractable, and it is widely applicable since very many problems can be encoded in binary strings. The mapping from a binary string to a parameter can be accomplished in many different ways but the precision of the mapping is limited to:

where xmin and xmax are the lower and upper bounds on parameter x and n is the length of the bit-string representing parameter x. To construct a multi-parameter coding one can concatenate several bit-strings into a single chromosome representing a set of parameters. However, when dealing with a large number of parameters requiring high accuracy representation, a solution chromosome becomes increasingly long and the power of the GA search diminishes.

Instead of working with binary coding and applying problem-independent genetic operators, the size of water distribution model calibration problems dictates direct representation of decision variables. This simply means that bit-strings of a binary GA are replaced with real numbers. The change simplifies the algorithm in that no additional mapping is necessary since these numbers represent unknown parameters of the model. However, other alterations to the binary GA are required. Firstly, random binary initialisation is replaced with random real number initialisation. This is simply achieved by generating lists of real numbers that fall within parameter limits (xrain, xmax).

The standard GA crossover operator may also be used for real number chromosomes since it does not depend on the representation scheme. Similarly to the standard GA recombination, genetic material crosses over from one chromosome to another. Let x = (xu ..., x„) and y = (y,, ..., y„) be the parent chromosomes. Then the offspring z = (zu ..., z„) may be computed by:

z, = [x,} or [y, ) (6)

where xt or y, are chosen with some probability of crossover pc. In addition to this, an operator suitable for continuous parameter optimization may be used, namely the


average crossover (Davis, 1991) which takes two chromosomes and produces one offspring that is the result of averaging the corresponding parameters of two parental chromosomes:

Other crossover operators such as extended intermediate recombination and extended line recombination (Miihlenbein & Schlierkamp-Voosen, 1993) can also be used.

The mutation operator has been investigated for binary domains by many authors (Goldberg, 1989) and there have been many suggestions on how often it should be applied to a chromosome. The authors are of the opinion that the mutation rate should be inversely proportional to the number of bits in the chromosome as suggested by Miihlenbein & Schlierkamp-Voosen (1993). However, an operator analogous to binary mutation, but suitable for continuous parameter optimization must be used since simple bit inversion is not possible with a floating-point representation. An obvious way to mutate a real-valued parameter x is to randomly select a number that falls within parameter limits xm e [xmin, xmaJ. Alternatively, the new parameter may be given by:

xm =x + z (8)

where z is a number in the mutation range interval. This range can be a constant value throughout the evolution process or it may be a function of the generation number. By exploiting an analogy with annealing processes the range should become smaller with the evolution process approaching its final stages.

Case study

The proposed algorithm is used to provide a calibrated network model for the Danes Castle Zone of Exeter City (Devon, UK). This network was chosen for the study because it provides a complex calibration problem to solve and because the necessary input and output data were readily available, the network model for this zone having already been built in 1991 (Ewan Associates, 1991). The original model was based on the supply arrangement by which water is drawn from the River Exe and after treatment pumped via a dedicated 457 mm (18") main directly to the Danes Castle service reservoir and via a 305 mm (12") pumping main directly into distribution However, the reservoir was known to be in poor condition and was reconstructed in 1992/93. Later, the Dunsford Hill reservoir was constructed and connected to the existing network. In addition to the new pumping main, this also involved changing the setting of some valves in the network to improve the management of the distribution zones.

The present Danes Castle zone is supplied from Pynes Water Treatment Works (Fig. 1). After treatment, water is pumped into two service reservoirs and from there fed by gravity into distribution. The skeleton of the network is given in Fig. 1, while the full network used in this study consists of 256 nodes and 301 elements (including


DANES CASTLE PUMPS

i—a— I 500mm delivery \main

DUNSFORD HILL SERVICE RESERVOIR

distribution

PYNES WATER TREATMENT WORKS

DANES CASTLE SERVICE RESERVOIR

Legend _j- j_ meter

{ \ waste K-'\.' district

Fig. 1 Supply and distribution arrangements for Danes Castle.

284 pipes, 2 pumps and 15 valves). Of the 256 nodes, one is a fixed-head reservoir (at the treatment works) and two are the service reservoirs. In order to monitor leakage, five waste districts have been set up as shown in Fig. 1. These zones are serving between 1500 and 4500 properties each. Information obtained from these zones were used for demand calculations.

An attempt to use GAs for calibration of the original (1991) Danes Castle network model is reported by Savic & Walters (1995). The study showed that the network calibration can be handled effectively by a GA, with considerable improvement in the accuracy of the ensuing model compared with the traditional trial-and-error approach. However, due to changes in the network topology a new model calibration was necessary together with new measurements. A 24-h field test was undertaken on 29 January 1996. Flows were monitored into or within the system at 19 locations while pressures were monitored at 10 locations including the water level variation at the service reservoirs.


Manual calibration was then performed based on the procedure used in the original model building (Ewan Associates, 1991) which comprised the following tasks: (1) match the total system flows; (2) assess the predicted and observed total pressures for selected demand loading

cases and make reasoned adjustments to pipe roughness coefficients; and (3) report model anomalies.

Initially roughness values taken from standard hydraulic tables (HR Wallingford, 1983) were adopted for various materials as in Table 1. Steps (2) and (3) were carried out through a trial-and-error procedure based on experience and knowledge of the system. The quality of the solution was judged based on the three typical loading conditions considered in the analysis: (a) peak daily demand—at 10:00 h on 29 January; (b) average daily demand—at 16:00 h on 29 January; and (c) minimum (night) demand—at 03:00 h on 29 January. The same loading conditions were used for the GA calibration. The results of both the GA and trial-and-error calibrations, in terms of absolute pressure head prediction errors for eight logged nodes, are presented in Fig. 2.

Table 1 Initial estimates of pipe roughness coefficients.

Material type

Cast iron Asbestos cement Ductile iron PVC Relined mains

k value (mm)

6.00 0.15 0.15 0.10 0.15

Assumed pipe condition

80 years of moderate attack Good Good Good Good

Although the number of parameters to be estimated cannot exceed the number of total observations available for all the loading conditions, the solutions obtained using the GA technique are based on fitting friction factor values to each of the pipes. This assumption was used for several reasons: - to demonstrate model capabilities to deal with a large number of variables; - to obtain an initial grouping of pipes in the absence of detailed knowledge of the

age and the service condition of pipes; and - to investigate how different and unrealistic solutions can result from attempting

to acquire more information from collected data than is available. Once consistent results have been obtained, groups of pipes with similar friction

values can be identified and the G A can be restarted. Starting from an initial grouping of pipes based only on nominal pipe diameters may introduce initial bias and prevent realistic solutions from being found.

The objective function used in this work is:

mmf(H,Q) = PlZ(H:-Hn2 + pJLiQ] -Qf)2 (9) k i j

where pi2 are normalizing coefficients, H" and if/1 are the observed and predicted


lc)

4.50 —

4.00 —

3.50 —

O 2.00 tn J3 < 1-50-H

Dtnai-and-error HGA

1 , -1 • • 1 •H 1

m , r-i \ F i '

1.00

0.50

3060 7011 BU3M2 BLDM1 ALDM STDM2 DCCM1 4010

Node Fig. 2 Absolute pressure head prediction errors (a) for the minimum loading condition; (b) for the average loading condition; and (c) for the maximum loading condition.


heads at node z, respectively, and Q° and gj'are the observed and predicted flows

through pipe j . Since information regarding the internal condition of the mains was not available,

the initial values for calibration parameters were initially restricted to k<kmm = 20 mm. Results obtained in the original study (Ewan Associates, 1991) and the GA results obtained by Savic & Walters (1995) indicate that better calibration results could be obtained if higher roughness values were used. However, £max = 20 mm is considered to be sufficiently high to enable meaningful results to be obtained.

The results in Figs 2(a), (b) and (c) show a noticeable dominance of GA calibration over the trial-and-error procedure. As expected the improvement achieved by the GA solution is largest for the maximum loading condition for which the system is stretched to its full capability. In terms of decision variables, i.e. k values, out of 284 pipes 85 were found to require k ~ kmiX = 20 mm, while in the manual solution 64 had k>20 mm (ranging up to kmx =120 mm). This indicates that significant throttling is occurring within the network which warrants further system investigation work.

CONCLUSIONS

Global sustainable development is not possible without sustainable settlement, and water supply systems play an important role in achieving the ultimate goal of sustainability. Sustainable water supply systems must be designed and operated so as to: minimize energy use, maximize efficient use of water as a resource and limit or even decrease associated environmental impacts. Achieving this for present and future generations may be possible if adequate modelling tools are available to facilitate decision support for design, planning and operation of these systems.

This paper introduces Genetic Algorithms (GAs) and their recent applications to illustrate the possible improvements to water systems design brought by these evolution-based optimization techniques. They represent an efficient search method for nonlinear optimization problems that is gaining in acceptance among water systems researchers and managers/planners. These algorithms share the favourable attributes of Monte Carlo techniques over local optimization methods in that they require neither linearizing assumptions nor the calculation of partial derivatives; also they avoid numerical instabilities associated with matrix inversion. In addition, their sampling is global, rather than local, thus increasing the tendency of converging onto the global optimum and avoiding dependency on a starting point. The applications presented include pipe sizing, water network rehabilitation, pump scheduling and pressure regulation.

A calibration method was successfully developed based on a Genetic Algorithm, introduced here by the authors, and was compared in approach and efficiency with a trial-and-error procedure widely used by the industry. The results obtained by applying the developed model to the Danes Castle network (Exeter, Devon, UK)


show noticeable dominance of GA calibration over the trial-and-error procedures used to match hydraulic model output with observed data sets. In addition, with respect to other optimization or analytical models, the GA-based calibration tool: (a) is easier to use because it does not need complex mathematical apparatus to evaluate partial derivatives or to invert matrices; (b) can handle larger networks, several loading conditions and a larger number of calibration parameters; and (c) permits easy incorporation of additional parameter types (pipe diameters, demands, etc) and constraints into the optimization process.

It can be anticipated that the number of applications in water systems design will steadily grow since GAs are not only effective, but also are easily realizable due to the conceptual simplicity of the basic mechanisms. Their potential is even greater when parallel forms of the algorithms can be developed and executed in low-cost multiprocessor computing systems.

Acknowledgement This work was supported by the UK Engineering and Physical Sciences Research Council, grant GR/J09796.

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