NEW CONCEPTS AND TOOLS FOR PIPE NETWORK DESIGN

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1 Proceedings of the 10 th Annual Water Distribution Systems Analysis Conference WDSA2008, Van Zyl, J.E., Ilemobade, A.A., Jacobs, H.E. (eds.), August 17-20, 2008, Kruger National Park, South Africa. NEW CONCEPTS AND TOOLS FOR PIPE NETWORK DESIGN D. Laucelli 1, O. Giustolisi 1 and E. Todini 2 1 Technical University of Bari, Engineering Faculty of Taranto, Dept. of Civil and Environmental Engineering, via Turismo, 8, 74100, Taranto, Italy, phone , d.laucelli@poliba.it; o.giustolisi@poliba.it 2 University of Bologna, Department of Earth and Geo-Environmental Sciences, Via Zamboni, 67, Bologna, Italy ezio.todini@unibo.it Abstract Water Distribution Network design has been traditionally approached as a cost minimization problem, constrained by some additional restrictions intended to ensure an acceptable level of customer service. Although the ideas have existed for same time, it was only recently that various researchers developed new network optimization approaches trying to address the minimization of design costs, while maximizing the benefits through some other performance indicators assessment in a risk-based scenario. Unfortunately, network simulation is still performed within a demand-driven context, even when reliability is considered among the benefits, and leakages are given as a constant percentage of nodal demands instead of being computed as a function of pipe pressure. This article introduces a more realistic approach to network design and simulation, performed using pressure-driven leakages employing a recently developed simulation model. Thus, the design procedure is conceived as multiobjective optimization, performed considering the minimization of pipe cost and together with total network leakage flow. The approach was tested on a small-size Italian real network which supplies an industrial area, and on a simpler network that yielded some interesting observations about the proposed paradigm. 1. INTRODUCTION The risk-based approach to Water Distribution Networks (WDN) management leads water utilities to recognize reliability assessment as a useful tool for achieving effective management of new and existing networks. Walski (2001) stressed the need for developing new network design strategies, not only for addressing the minimization of pipe costs, but also the maximization of network reliability. In recent years, many studies have been conducted in order to find optimal design solutions for WDN looking at minimizing cost while maximizing some benefits, such as network reliability (Tung, 1985; Wagner et al., 1988; Lansey and Mays, 1989; Goulter, 1992; Gupta and Bhave, 1996; Fujiwara and Li, 1998; Xu and Goulter, 1999; Todini, 2000; Tolson et al., 2004; Babayan et al., 2005; Kapelan et al., 2005; Giustolisi and Laucelli, 2007). Undoubtedly, most of the above contributions focus on some performance indicators in order to evaluate the level of network reliability of the proposed solutions, typically the satisfaction of either nodal pressure or nodal flow demands. This work offers a different approach to optimal pipe sizing looking at improving the natural attitude of the network to have a low total leakage flow. Thus, the performance indicator used as a measure of network level of service during its operational life is the total amount of water loss due to leakages in the system and the concept of reliability/benefit with respect to leakage flow is introduced. In fact, the ageing of a WDN involves as a natural consequence the growth of water loss because of the occurrence of new pipe failures of various nature and size. Some of these breaks, usually named as leakages, remain unreported to water utilities or they are difficult to observe due to their small size, thus affecting overall

2 system reliability. Moreover, leakage can be considered as a major water resource for utilities, since it may vary from 15% in the best cases to 60-65% in the worst cases. For these reasons, water losses via leakages constitute a major challenge to the effective operation of municipal WDN since they represent not only diminished revenue for utilities, but also undermined service quality (Almandoz et al., 2005) and wasted energy resources (Colombo and Karney, 2002). Nonetheless, it must be recognized that pressure management, which implies the subdivision of a WDN into districts, could be more effective if the design of the network was made by aiming at a more even spatial distribution of the water pressure field, thus reducing average pressure (Araque and Saldarriaga, 2006). Hence, in order to conduct more accurate analysis of a WDN, such as a better estimate of flow through the network (with respect to both satisfied demand and losses through leakage), a hydraulic model capable of accounting for pressure-driven (also known as head-driven) demand and leakage flow at the pipe level should prove invaluable. Several models have been developed to incorporate pressure-driven demand analysis into water network simulation (Reddy and Elango; 1989; Chandapillai, 1991; Gupta and Bhave, 1996; Fujiwara and Li, 1998; Ackley et al., 2001; Kalungi & Tanyimboh, 2003; Todini, 2003; Giustolisi et al., 2008a) and only in these last years the problem of leakage characterization within network hydraulic simulation has been posed as focal point for the more realistic simulation of WDN (Doglioni et al., 2007; Giustolisi and Laucelli, 2007; Giustolisi et al., 2008b). The optimal sizing strategy is here conceived in a multi-objective framework, in which capital costs and total network water loss are traded off. The innovative aspect, if compared with most of the above cited works, is that every network configuration along with the multi-objective optimization is hydraulically simulated by means of the novel network simulator. It was recently presented in Giustolisi et al. (2008b), which uses the framework of Todini s simulation model (Todini, 2003) in order to account for pressuredriven leakage at the pipe level, while assuming the representation of (pressure-driven) leakages as proposed in Germanopoulos (1985). 2. SIMULATION MODEL AND PRESSURE-DRIVEN LEAKAGES Network designs obtained from demand-driven analysis assume leakage proportional to demand at each node, but independent of network nodal pressure, leading to unrealistic nodal leakage estimates (Giustolisi et al., 2008b). For example, two obvious and significant drawbacks of the unrealistic assumption of a constant leakage percentage normally employed with demand-driven simulation (when combined with optimization for network design) are: (i) the resultant low leakage flows for nodes experiencing low demand, even if they experience high pressure (e.g., are close to a tank); (ii) the fact that two nodes having equal demand will have equal leakage flow rates despite their actual positions in the network (pressure levels) related to elevations, tank and pump locations, etc. For these reasons, to ensure a more accurate hydraulic simulation of WDN accounting for leakages and nodal demands, it is mandatory to apply a pressure-driven simulator. In order to perform this task, the article makes use of an improved hydraulic simulation model that integrates pressure-driven nodal demand analysis and leakage simulation according to pipe deterioration (Giustolisi et al., 2008b). This model starts from the paradigm introduced by Todini (2003), that describes the pressure-driven simulation of a network comprising n p pipes with unknown discharges (i.e., flow rates), n n nodes with unknown heads (junctions), and n 0 nodes with known heads (tank levels) by the following system of equations based on energy and mass balance conservation: App Apn Q Ap0H0 = Anp Ann H 0 (1)

3 where the diagonal matrix A pp of order n p is equal to R k Q k n-1, being R k = hydraulic resistance of pipe that is a function of a pipe s roughness, diameter, and length, while n = exponent that takes into account the actual flow regime and the head loss relationship used (1.85 for the Hazen-Williams and 2 for the Darcy- Weisbach models); Q = [Q 1,Q 2,...,Q np ] T = [n p, 1] is a column vector of unknown pipe flow rates; H = [H 1, H 2,..., H nn ] T = [n n, 1] is a column vector of unknown nodal heads; H 0 = [H 01, H 02,..., H 0n0 ] T = [n 0,1 ] is a column vector of known nodal heads. In the system of Eq. (1), A pn = A np T and A p0 are topological incidence sub-matrices of size [n p, n n ] and [n p, n 0 ], respectively, derived from the general topological matrix as defined in Todini (2003). In order to account for leakage flow rates in model (1), A nn can be cast as a diagonal matrix whose elements are the scalar product (q act + q l )H 1, where q act (H) is a column vector of pressure-driven nodal demands, and q l is a column vector of nodal leakage flow rates (assuming a positive sign for node outflow), see Giustolisi et al., (2008b). Actually, leakage occurs at pipe level and is only reported at the nodes as will be explained subsequently. In the system of Eq. (1), q act characterizes demand-pressure dependence whose elements are defined for the i th node of the network by the function q i act (P i ), which is here derived from those proposed in Wagner et al. (1988) (Giustolisi et al., 2008b). Moreover, for reasons of simplicity, and while still preserving generality, elements such as pumps, valves, and other dissipation devices have not been considered in the simulation model (1). At the scale of individual pipes, the pressure-leakage relationship is defined in q l, whose elements are nodal leakages q i leak that are computed from the pipe leakage model q k leak. In order to avoid confusion among variables, the index i will be used for nodal-level variables and k for pipe-level variables. Thus, assuming a uniform distribution of leakage q k leak along pipe k, the background leakage model can be expressed as (Germanopoulos, 1985) q k leak αk ( ) if 0 βklk Pk Pk > = 0 ifpk 0 (2) where P k = average pressure in the pipe computed as the mean of the pressure values at the end nodes i and j of the k th pipe; and l k = length of that pipe. Variables α k and β k are two leakage model parameters, that can be explained as follows (Giustolisi et al., 2008b) d k αk = αk, m k 1 k n sk β = β age, d, s, m, pr,... 1 k n ( ) k k k k k k k p p (3) where m = the pipe material; pr = number of properties supplied (or connections on the main); d k = diameter of the k th pipe; and s = pipe wall thickness. From Eq. (3) arise that β depends, in general, on both pipe characteristics and various external factors (e.g., environmental conditions, traffic loading, external stress and corrosion, etc.). In contrast, α is a function of pipe characteristics only (material m and rigidity d/s). Clearly, the change in β over the years is related to average pressure (Lambert, 2001). The average pressure vector P pipes can be computed from the general topological matrix and nodal pressure as dependent from the pressure vector of unknown nodal heads (P nodes ), from the pressure vector of known nodal heads (P nodes 0 ) and from the absolute value of the topological matrix ( A pn ), see Giustolisi et al., (2008b) for more details. The allocation of leakage to the two end nodes can be performed in a number of ways (Ainola et al., 2000; Giustolisi and Todini, 2008). Here the nodal leakage flow q i leak is computed as the sum of q k leak flows of all pipes connected to node i as follows: q 1 1 αk i leak= = β ( ) k k leak k k k k 2 q 2 l P (4)

4 where P k = (P i +P j )/2. Thus, the elements of the vector q l can be computed from a topological matrix as follows: q l = 1 2 A np q K q K q 1 leak k leak np leak where A np is the absolute value of the topological matrix and q k leak comes from Eq. (2). The solution to the system of Eq. (1) for the pressure-driven demands defined as defined in Wagner et al., (1988) was first given by Todini (2003) and successively expanded by Giustolisi et al. (2008b). (5) 3. CASE STUDIES: NETWORK DESIGN WITH LEAKAGE CONSIDERATIONS The article considered three different case studies aimed at analyzing the proposed approach for the optimal sizing of water distribution pipes. The design procedure is conceived as a multi-objective optimization, which is performed considering the minimization of pipe cost and leakage within the candidate network configurations. The first two analyzed network layouts are shown in Figure 1. Figure 1. Layout of NET_1 (left) and NET_2 (right) They are simple networks that have been conceived in order to test the proposed approach on a simple case, since this usually facilitates highlighting the main advantages and drawbacks of a certain methodology. For this reason, the first network (NET_1) is an open network, with one reservoir, while the second example (NET_2) is a looped network which has the same pipes of NET_1 but one which is the pipe that closes the loop, linking the reservoir to the last node (pipe number 21). In NET_1 and NET_2 each trunk is 500 meters long, each node delivers 20 l/s and has an elevation above a datum (HL i ) equal to zero, while the reservoir has a total available head of 30 m. The third considered network (NET_3) is a real planned network designed for an industrial area in Apulian town (Southern Italy). The network layout is shown in Figure 2 and the corresponding data are provided in Giustolisi et al. (2008a). For both the case studies the least-cost optimization were performed using as design constraint a minimum nodal pressure of 10 m.

5 Figure 2. Layout of the Apulian Network (NET_3) With respect to the leakages, they have been assumed as pressure-driven (see Equation 2) since they are implemented in the pressure-driven network simulation model as above described (Giustolisi et al., 2008b). In particular, for NET_1 and NET_2, the leakage model parameter β has been set equal to and α was assumed equal to 1.5 while, for NET_3, the parameter β = and α = 1.2, as reported in Giustolisi et al. (2008b) for that particular network. The multi-objective design procedure As explained above, the paradigm for optimal WDN design here proposed is conceived as a Multi- Objective (MO) optimization in which the first objective function (f 1 ) is the minimization of capital cost for pipe installation and the second function (f 2 ) is the minimization of the total water loss in the network. Actually, every network configuration along with the optimization can be coupled with its proper cost (f 1 ) and with the value of total water losses that have been evaluated by means of the hydraulic simulation model expressed in Eqs.(1). The optimization is Genetic Algorithm-based (Giustolisi et al., 2008b), and the evolution through all the generations is ruled by the Pareto dominance criterion (Pareto, 1896). Therefore, the formal expression for this optimization problem can be articulated as follows: { R( d,, l γ )} App A pn Q Ap0H0 = Anp Ann H 0 np min { f1( d1, d2,..., dn )} = min C( d, ) p k lk k = 1 min,,, min min { f2 ( αk βk Pk lk )} = { qk leak} = { Qleak} ( ) H HL + P > 0 i = 1,2, K, n i i i ser n k (6) where P k is the average pressure assigned to the k th pipe, evaluated as the mean value between the pressure values of its node [P k = (P i +P j )/2], Q leak is the total value of leakage flows in the network, while the last formulation in system (6) is a design constraint, that forces every solution to satisfy the minimum

6 required nodal pressure. Given a fixed layout, the solution of the optimization problem as expressed in Equation 6 returns a Pareto front of optimal network configurations which are able to supply the required nodal demands (thus satisfying the constraint on nodal service pressure) having a low value of capital costs and, simultaneously, a diameter range that allows for an average value of nodal pressure as low as possible. In this way, assuming a certain value for the leakage parameters (α and β), the water losses due to leakages from the network, here evaluated by Eq. (2), can be reduced. 4. RESULTS The results of applying the sizing strategy given the layout of NET_1 are reported in Figure 3, that has on the x-axis the capital costs increasing (in percentage) of each optimal solution with respect to the least expensive network configuration (that with the highest level of water losses), and on the y-axis, the total water loss evaluated for each network, expressed as percentage with respect to total amount of nodal demands supplied by the network. First of all, it is remarkable that NET_1 (and also its companion network NET_2) are completely flat, given that its nodes are at an elevation above a datum (HL i ) equal to zero. This assumption eschews the influence of network topography from the results returned by the application of the design strategy to this network layout. The Pareto front in Figure 3 shows that with a capital cost increase of 13%, with respect to the least expensive network, it is possible to reduce the total amount of water loss by more than 6% (from 19% to 13%). Moreover, Figure 3 confirms the value of a MO strategy, for optimal design purposes in this case, based on the Pareto front dominance criterion, since more expensive solutions, that basically admit the same level of water savings, can be easily highlighted. Figure 3. Pareto front for optimal networks (NET_1) Figure 4. Average nodal pressure and total water loss trends (NET_1)

7 Figures 4 and 5 can be useful for visualizing the differences among candidate solutions in Figure 3. In fact, Figure 4 shows that the average pressure in each network is strictly correlated to water losses and, given the values of the leakage parameters (α and β), its reduction of about 4 meters leads to a water loss reduction of 7% along with the set of optimal solutions in Figure 3. Figure 5. Diameter values for the pipes close to the reservoirs (NET_1) Figure 5 highlights that the network configurations characterized by smaller losses, higher costs and a lower average value of nodal pressure (those on the left part of the x-axis in Figures 4 and 5) generally presents smaller diameters for the closest pipes to the reservoir. Moreover, Figure 5 reports the diameter values in every optimal configuration on the Pareto front for the last pipe in NET_1 (pipe number 1). It is clear that this pipe, like mostly all the other pipes in the network, increase its diameter with the decreasing of total water loss. In summary, on the one hand, the results show that the network configuration that can be considered as optimal only from the perspective of investment minimization (solution number 28 in Figures 4 and 5) is coupled with a higher level of leakage due to its higher average value of nodal pressure and, on the other hand, that a lower level of total water loss can be obtained by reducing the diameter of the pipes next to the reservoir and enlarging the diameter for the downstream pipes. For the second case study, which basically consists of closing the layout of NET_1 and obtaining a single loop, by looking at the Pareto front in Figure 6, the first relevant observation can be that the same water saving of NET_1 (6%, evaluated as difference between 20% and 14%) is obtained with a lower extra expense (10%) and thus, reaching a network cost increase of 30%, it is possible to gain a water saving of 9%. From a hydraulic perspective, the nature of the NET_2 layout relative to that of NET_1 (looped vs. branched), can justify the higher water losses for the worst solutions in the second case (those on the right on x-axis in Figure 7), since an even distribution of nodal pressure (as a consequence of their looped nature) can lead to more leakage, because of their strict correlation (see Equation 2 and Figure 7). Conversely, the looped nature of these networks can facilitate the design procedure in returning optimal solutions that are able to avoid the same loss of water (in percentage) with lower cost increase than branched network.

8 Figure 6. Pareto front of optimal networks (NET_2) Figure 7. Average nodal pressure and total water loss trends (NET_2) The trend of cross-section size for the closest pipes to the reservoirs for NET_2, see Figure 8, confirms that going toward well performing solutions causes pipe diameter reduction near the source of water and energy (see pipes number 20 and 21 in Figure 8), while the downstream pipes (pipes number 19 and 1, which are immediately after pipes number 20 and 21, see Figure 1) increase their diameters in order to preserve pressure head for the next trunks. Moreover, the looped layout seems to allow for smaller diameters (and diameter reductions) than those typical of branched networks, due to the different pathways available for flow, thus admitting some costs extra-savings.

9 Figure 8. Diameter values for the pipes close to the reservoirs (NET_2) The observation pertaining to the last example proposed in this work (NET_3) is reported in Figure 9, where the variables reported on the x-axis and on the y-axis have been already described. Looking at the diagram in Figure 9, it is clear that, with a 23% increase of pipe capital cost over the least expensive network, it is possible to reduce the total amount of water loss by more than 5% (from 24% to 19%). Bearing in mind this is a real network, this is undoubtedly an interesting result, also considering that the system is located in a flat area (e.g., little variations of HL i along with the network). Moreover, the higher design cost of the best performing configuration could be reasonably offset by the management expense and the environmental cost due to the lost water. Figure 9. Pareto front of optimal networks (NET_3) Therefore, Figures 10 and 11 can explain the differences among the networks shown in Figure 9. Figure 10 again validates the strict correlation between the average pressure in each network and water losses, while showing once again that the looped network, having a more uniform pressure distribution, can loose more water (for NET_3 the worst solution lost the 24% of the total supplied water with a lower average pressure than NET_1 and NET_2). Moreover, Figure 11 confirms what was already observed in the other case study about the closest pipes to the reservoir, in particular for pipe number 34, due to the layout of NET_3.

10 Figure 10. Average nodal pressure and total water loss trends (NET_3) Figure 11. Diameter values for the pipes close to the reservoirs (NET_3) Therefore, in order to design a network with a low level of total predicted leakages (i.e., higher reliability from the water loss perspective), it seems necessary to perform pipe sizing looking at the reduction of the average value of nodal pressure in all the operating conditions of a WDN. With regard to the classical pipe sizing procedure, this could be obtained by reducing the diameter of those mains which are closest to the reservoir (thus dissipating energy upstream) and, conversely, ensuring higher diameters for the downstream pipes. This different approach can permit lower friction losses in the downstream part of the network, in order to satisfy the required nodal pressure (i.e., the last formulation in Equation 6. However, this exigency leads to an increase of network cost. Finally, it is worth noting that upstream diameter reduction could be surrogated by the location of Pressure Reducing Valves (PRVs), or other design solutions aimed at avoiding the operational problems connected with diameter reduction, such as excessive velocity. This last concern can be considered as equivalent to the use of PRVs during the daily peak within networks that have big pipe diameters (low velocity), while it is not comparable to their use for leakage reduction during nighttime. 5. CONCLUSIONS The present work introduces a different approach to the optimal pipe sizing of a WDN looking at minimization of total water loss. The design paradigm is conceived as a multi-objective optimization between costs and leakage reduction. The procedure makes use of an innovative pressure-driven hydraulic simulation model that is able to account for water losses, thus leading to a more accurate simulation of the operating condition of a network (Giustolisi et al., 2008b). In summary, the case studies show that with a

11 reasonable increase in network cost, with respect to the least-cost solution, it is possible to significantly reduce the total amount of water loss. This basically leads to diameter reduction for the pipes that are adjacent to the reservoir (overall pressure reduction), while the mains that are more distant from the sources need to have wider cross-sections in order to satisfy the minimum nodal pressure requirements. Hence, taking into account the results indicated by these applications, water losses can be considered as management (and environmental) costs to be reduced within the traditional design paradigm. Moreover, once again the value of the assumed network deterioration (by means of the leakage parameter β) can be perceived as a key management element in order to plan water loss control and system rehabilitation within a whole-life costing paradigm. 6. ACKNOWLEDGEMENTS The study is part of the Optimization of information-intensive processes: applications to the ICT and environment sectors (PROPT) project, supported by the Italian Government and by the Regional Government of Puglia (Accordo di programma quadro in materia di ricerca scientifica 2008). 7. REFERENCES Ackley, J.R.L., Tanyimboh, T.T., Tahar, B., and Templeman, A.B. (2001) Head-driven analysis of water distribution systems. Proceedings of CCWI, Water software systems: theory and applications, Ulanicki, B.(ed.), Research Studies Press, England, vol. 1, Ainola, L., Koppel, T., Tiiter, T., and Vassiljev, A. (2000) Water network model calibration based on grouping pipes with similar leakage and roughness estimates. Proc., Joint Conf. on Water Resource Engineering and Water Resource Planning and Management (EWRI) (CD-ROM). Almandoz, J., Cabrera, E.M., Arregui, F., Cabrera, E.Jr., and Cobacho, R. (2005) Leakage Assessment through Water Distribution Network Simulation. J. Water Resour. Plan. and Manage., 131(6), Araque, D., and Saldarriaga, J.G. (2006) Water Distribution Network Operational Optimization by Maximizing the Pressure Uniformity at Service Nodes. Proceedings of the 8 th Annual Water Distribution Systems Analysis Symposium WDSA2006, Buchberger, S.G. (ed.), August 27-30, Cincinnati, Ohio. Babayan, A.V, Kapelan, Z., Savic, D.A., and Walters, G.A. (2005) Least Cost Design of Robust Water Distribution Networks Under Demand Uncertainty. J. Water Resour. Plan. and Manage., 131(5), Chandapillai, J. (1991) Realistic simulation of water distribution system. J. of Transportation Eng., 117(2), Colombo, A.F., and Karney, B.W. (2002) Energy and costs of leaky pipes: Toward a comprehensive Picture. J. Water Resour. Plan. Manage., 128(6), Doglioni, A., Primativo, F., Savic, D., and Giustolisi, O., (2007) Possible scenarios of contaminant diffusion in water distribution systems: which is the best moment to place a strike? Proceedings of Computer and Control in Water Industry (CCWI) - Water Management Challenges in Global Changes, Ulaniki et al. (eds), Taylor & Francis Group, London, Fujiwara, O., and Li, J. (1998) Reliability analysis of water distribution networks in consideration of equity, redistribution, and pressure-dependent demand. Water Res. Research, 34(7), Germanopoulos, G. (1985) A technical note on the inclusion of pressure dependent demand and leakage terms in water supply network models. Civil Engineering Systems, 2(9), Giustolisi O., and Todini E., (2008) On the Approximation of Distributed Demands as Nodal Demands in WDN calibration. Urban Water, special issue on WDS Model Calibration, (submitted).

12 Giustolisi, O., and Laucelli, D. (2007) More realistic water distribution network design using pressuredriven demands and leakages. Proceedings of Computer and Control in Water Industry (CCWI) - Water Management Challenges in Global Changes, Ulaniki B., et al. (eds), Taylor & Francis Group, London, Giustolisi, O., Kapelan, Z., and Savic, D.A., (2008a) An Algorithm for Automatic Detection of Topological Changes in Water Distribution Networks. J. Hydr. Eng., 134(4), Giustolisi, O., Savic, D.A., Kapelan, Z. (2008b) Pressure-driven demand and leakage simulation for water distribution networks. Journal of Hydraulic Engineering, 134 (5), Goulter, I.C. (1992) Assessing the reliability of water distribution network using entropy based measures of network redundancy. Entropy and energy dissipation in water resources, V.P. Singh & M. Florentino (eds), Kluwer, Gupta, R., and Bhave, P.R., (1996) Comparison of Methods for Predicting Deficient-Network Performance. J. Water Resour. Plan. and Manage., 122(3), Kalungi, P., and Tanyimboh, T. (2003) Redundancy model for water distribution systems. Reliability Engineering & System Safety, 82(3), Kapelan, Z.S., Savic, D.A. and Walters, G.A. (2005) Multiobjective design of water distribution systems under uncertainty. Water Resour. Res., 41(11). Lambert, A.O. (2001) What do we know about Pressure: Leakage Relationships in Distribution Systems? IWA Conference on System Approach to Leakage Control and Water Distribution Systems Management, Brno, Vol. 1, Lansey, K. E., and Mays, L. W. (1989) Optimization model for water distribution network design. J. Hydraul. Eng., 115(10), Pareto, V. (1896) Cours D Economie Politique. Rouge and Cic, Lausanne, Switzerland. Reddy, L., and Elango, R. (1989) Analysis of water distribution networks with head-dependent outlets. Civ. Eng. Syst., 6(3), Todini, E. (2000) Looped water distribution networks design using a resilience index based heuristic approach. Urban Water, 2(3), Todini, E. (2003) A more realistic approach to the extended period simulation of water distribution networks. Advances in Water Supply Management, Maksimovic, C., Butler, D., and Memon, F.A. (eds), Balkema, Lisse, The Netherlands, Tolson, B.A., H.R. Maier, A.R. Simpson, and B.J. Lence (2004) Genetic algorithms for reliability-based optimisation of water distribution systems. J. Water Resour. Plan. and Manage., 130(1), Tung, Y.K. (1985) Evaluation of water distribution network reliability. Hydraulics and hydrology in the small computer age, W.R. Waldrop (ed.) ASCE, New York, Wagner, J.M., Shamir, U., and Marks, D.H. (1988) Water distribution reliability: simulation methods. J. Water Resour. Plan. and Manage., 114(3), Walski, T.M. (2001) Editorial: The wrong paradigm why water distribution optimization doesn t work. J. Water Resour. Plng. and Mgmt., 127(4), Xu, C., and Goulter, I.C. (1999) Reliability-Based Optimal Design of Water Distribution Network. J. Water Resour. Plan. and Manage., 125(6),

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