The Colebrook-White formulation of friction factor is implicit and requires some iterations to be solved given a correct initial search value and a target accuracy. Some new explicit formulations that more efficiently calculate the friction factor compared with Colebrook-White are presented herein. The aim of this investigation is twofold: to preserve accuracy of estimates while reducing the computational burden (i.e. speed). On one hand, the computational effectiveness is important when the intensive calculation of the friction factor (e.g. large size water distribution networks (WDN) in optimization problems, flooding software etc.) is required together with its derivative. On the other hand, the accuracy of the developing formula should be realistically chosen considering the remaining uncertainties surrounding the model where the friction factor is used. In the following, 3 strategies for friction factor mapping are proposed which were computed by using the Evolutionary Polynomial Regression (EPR). The result is the encapsulation of some pieces of the friction factor implicit formulae within pseudo-polynomial structures. The term “pseudo-polynomial” is referred herein to a class of formulas obtained by adding a number of terms, all based on the same base structure, but not necessarily having integer exponents.

The calibration of hydraulic models of water distribution networks (WDN) is of preeminent importance for their analysis and anagement. It is usually achieved by solving a constrained optimization problem based on some priors on decision variables and the demand-driven simulation of the entire network, given the observations of some hydraulic status variables (i.e. typically nodal heads and sometimes pipe flows). This paper presents a framework to perform the calibration of pipe hydraulic resistances considering two main issues: (i) the enhancements of WDN simulation models allowing us to simplify network topology with respect to serial nodes/trunks and/or to account for a more realistic representation of distributed demands and (ii) a different formulation of the calibration problem itself. Depending on the available measurements, the proposed calibration strategy reduces the hydraulic simulation model size and can permit the decomposition of the network. On the one hand, such a procedure allows for numerical and computational advantages, especially for large size networks. On the other hand, it allows a prompt analysis of observability of calibration decision variables based on actual observations and might help identifying those pipes (i.e. hydraulic resistances) which are more important for the whole network behaviour.

The pumping energy is a relevant element of WDN operational costs. If tanks are used to store water, pumping optimization generally results into a less number of working pumps during the daylight hours when the electricity tariff is generally higher. Nevertheless, optimal solutions should also account for leakage component of demand which increases with pressure. In addition, the optimization of water distribution networks sometimes may require also resizing/upgrading of existing asset elements including pipes, tanks and pumps. Starting from the Battle for Water Networks II problem, this contribution presents a practical decision support tool for WDN operational optimization as new tailored function in the WDNetXL system (www.hydroinformatics.it). Capital cost and/or operational cost and/or non-revenue water can be simultaneously minimized accounting for different decision variables like controls for pumps, pipe diameters, tank sizes and pumping stations. The WDNetXL system also facilitate analysis and successive refinement of solutions according to engineering expertise.

In the developed countries the majority of water distribution networks (WDNs) were built in the last century and today the principal task is to manage those hydraulic systems for different socio-economic and environmental purposes. Thus, there is a need for building WDN models to predict the system behaviour and support decision of water managers. For this reason once built a WDN model using field information, one problem is to estimate some boundary conditions (e.g. pipe hydraulic resistances, nodal demands) which cannot be directly measured. This procedure is also called model calibration and requires the availability of observations of the hydraulic system. These observations are generally pressure measurements because cheaply available. The related devices need to be properly located and distributed in the system. The selection of the location of observations and their number is named sampling design and plays an important and sometimes decisive role in order to achieve an accurate calibration, then a good predictive model. This paper proposes a sampling design method based on a topological analysis in order to reduce the size of the mathematical inverse problem related to model calibration and to achieve better pre-conditions for the observability of the hydraulic system

Hydraulic modelling of Water Distribution Network (WDN) is crucial for design, operation and management purposes. WDN models should pursue correct representation of hydraulic behaviour, flexibility to accommodate any WDN topological change and computational efficiency. An effective preliminary analysis of WDN topology might be valuable in terms of resizing of the simulation problem, analysis of WDN functioning, correct statement of calibration problem and understanding of results. This contribution presents the key features of a tool which incorporates some recent outcomes on preliminary topological analysis of WDN. They include different kinds of skeletonization, automatic detection of network components and identification of pipe segments associate with deployed isolation valves. All these utilities for manipulation of WDN topology take advantage from the simplification of network topology with respect of serial nodes. In the case of hydraulic simulation such a simplification can be performed while preserving the correctness of the energy and mass balances as in Giustolisi and Todini (2009) who proposed the Enhanced Global Gradient Algorithm (EGGA). The paper also presents the adopted input data structure which is conceived to accommodate, besides other data, hydraulic and topological information about removed serial nodes, valves, pumps, pipe unitary hydraulic resistance, minor head losses, leakage parameters. Although it does not significantly differ from more widely adopted data structures (e.g. in EPANET) it easily accommodate tabular data formats (e.g. from MS-Excel spreadsheets), thus facilitating its integration with other software applications. The final part of the paper shows some strategies to accomplish demand-driven and pressure-driven analysis on the simplified WDN which reflect different types of approximations in network representation.

This work presents a modification to steady-state Water Distribution Network (WDN) simulation models in order to account for directional devices such as check valves and flow control valves. These devices, allowing water flow control in a definite direction, are important in order to manage the hydraulic system functioning over time by considering the variation of some boundary conditions as for example required demands and tank levels. However, the simulation models are built on the assumption that water can flow in both directions of each pipe in the hydraulic system and the information on directionality of some devices is not automatically allowed. Thus, in WDN models those devices are currently modeled using a heuristic approach, intermixed with solving the problem of steady-state WDN analysis. For this reason, a different approach using content and co-content theory was recently proposed in order to define the conditions that guarantee the existence and uniqueness of the solution. The alternative proposed here presents an adjustment of the energy balance equations to account for flow control valves. Check valves are treated as a special case of flow control valves, while the directionality of pumps, which are equipped with a check valve to avoid reverse flow, is modeled by means of their implicit check valve. Once the status of such directional devices is identified, a topological analysis of the network is performed. The methodology is applied to the demand-driven and pressure-driven analysis of a WDN solved by means of the global gradient algorithm, although it could be easily extended to other algorithms.

The advent of information technology and geographical information systems in water industry allows a detailed description of Water Distribution Network (WDN) topology and its boundary conditions. However, the complexity of network analysis and the mathematical problem size related to the hydraulic simulation considerably increase, especially for large WDN. The present paper introduces a network simplification strategy based on a correction paradigm adopted by Giustolisi and Todini in the Enhanced Global Gradient Algorithm (EGGA). Starting from the original topology of the analyzed WDN, the proposed strategy identifies the serial nodes/sections (i.e. those adjacent to two nodes/pipes only) which are iteratively removed from network topological representation. Therefore, the new network topology contains only those nodes joining three or more pipes or the terminal nodes of branched sections. Such a topological simplification results into a lower dimension of the topological matrices underlying the hydraulic simulation model. This way the WDN analysis can be performed using the EGGA formulation increasing computational efficiency, especially for large-size networks, without forfeiting energy and mass balances of the original hydraulic system. The paper reports the general formulation of EGGA and the strategy is tested on two large-size networks (of 1,461 and 12,513 internal nodes). The results are compared with those obtained using the original WDN topology and the classic Global Gradient Algorithm (GGA). Thus, it has been demonstrated that the EGGA strategy of simplification allows achieving a computational efficiency while correctly representing the hydraulic behaviour of the network.

This manuscript compares demand-driven and pressure-driven hydraulic network simulation models for assessing hydraulic capacity under uncertain scenarios. A stochastic approach is implemented assuming possible alteration of boundary conditions due to climate and socio-economic changes (i.e., the increase of peaks of customers demands), and system deterioration (i.e., the increase of pipe internal hydraulic resistances and background leakages). Two real WDNs located in Southern Italy are used for analyses. Results show that demand-driven analysis underestimates the hydraulic network capacity with respect to pressure-driven analysis. In fact, pressure-driven analysis assumes the component of model demands (human-based and leakage-based) as dependent on pressure status of the system, and thus returns a more reasonable number and location of critical nodes than demand-driven analysis. Furthermore, demand-driven analysis does not predict the water demand that can be realistically supplied to customers under pressure-deficient system functioning. Therefore, the use of pressure-driven analysis is advisable to support water managers to allocate budgets for planning rehabilitation works in order to increase the hydraulic capacity of the networks.

Nowadays it is crucial to align technical research closely with its intended recipients. These recipients are the practitioners who could use new optimal solutions for management purposes in the short term to increase their effectiveness from socio-economic and environmental standpoints. In addition, recipients can be students at any level as in the medium-term they will bring the new management methods and will need to carry out specific technical analyses. The need to transfer and disseminate technological knowledge as soon as it is available is, furthermore, exacerbated by the quick changes that information technology is bringing to the world. Thus, this paper introduces the idea of a collection of MS-Excel add-ins for Water Distribution Network (WDN) analysis. The development of an MS-Excel add-in for WDN analysis makes any technical advance readily usable via a well-known environment. MS-Excel is a friendly environment for users where several add-ins entailing WDN analyses based on classic and recently developed methods can be made available. WDNetXL is a collection of these add-ins. The use of the MS-Excel environment allows the user to personalize their WDNetXL add-in collection and to work easily on input and output of analysed data.

This paper is part of the Battle of the Water Calibration Networks (BWCN) organised during the 12th annual Water Distribution Systems Analysis conference (WDSA 2010) in Tucson, Arizona. The BWCN calibration problem is formulated and solved as a multiobjective optimisation problem with the objectives being the minimisation of different types of absolute relative errors. The implicit constraints are comprised of mass and energy balance equations written for the extended period simulation model of the analysed system and the five fire flow steady-state conditions. Calibration parameters are the grouped pipe roughness coefficients, two valve coefficients for one DMA, and a speed factor for one pump. Prior to calibration, the analysis of the pipe network topology has been performed. The hydraulic system results are spatially decomposed and simplified leading to substantial computational savings (without loss of accuracy) and enabling an easier analysis of results. The above calibration problem is solved using a multiobjective genetic algorithm. The results obtained on the BWCN case study demonstrate good agreement between the predicted and observed values.

In water distribution network (WDN) steady-state modelling, tanks and reservoirs are modelled as nodes with known heads. As a result, the tank levels are upgraded after every steady-state simulation (snapshot) using external mass balance equations in extended period simulation (EPS). This approach can give rise to numerical instabilities, especially when tanks are in close proximity. In order to obtain a stable EPS model, an unsteady formulation of the WDN model has recently introduced. This work presents an extension of the steady-state WDN model, both for demand-driven and pressure-driven analyses, allowing the direct prediction of head variation of tank nodes with respect to an initial state. Head variations at those nodes are introduced as internal unknowns in the model, the variation of tank levels can be analyzed in the single steady-state simulation and EPS can be performed as a sequence of simulations without the need for external mass balances. The extension of mass balance at tank nodes allows the analysis of some technically relevant demand components. Furthermore, inlet and outlet head losses at tank nodes are introduced and large cross-sectional tank areas are allowed by the model and reservoirs become a special case of tanks. The solution algorithm is the generalized GGA (G-GGA), although the proposed WDN model generalization is universal.

Water distribution network (WDN) models account for customer-demands as water withdrawals concentrated in nodes. Customer-demands can be assumed constant or varying with nodal head/pressure entailing demand-driven or pressure-driven simulation, respectively. In both cases, the direct connection of customer properties to the hydraulic system is implicitly assumed. Nonetheless, in many technical situations, the service pipe fills a local private storage (e.g. a roof tank or a basement tank) from which the water is actually delivered to customers by gravity or pumping systems. In such contexts, the service pipe fills the local tank by means of a top orifice. Consequently, what is really connected to the hydraulic system is a tank, which is subject to a filling/emptying process while supplying water to customers. Therefore, since modeling this technical situation in WDN analyses is necessary, the paper develops a formulation for nodal water withdrawals in WDN models accounting for the filling/emptying process of inline tanks between the hydraulic network and customers. The formulation is also introduced in a widely used method for steady-state WDN modeling, the Global Gradient Algorithm, and its effectiveness to increase the hydraulic accuracy of results is discussed using a simple case study and a small network.

Management efficiency of water distribution networks (WDNs) is of relevant interest for the water industry and operational optimization plays an important role. The energy to pump water is a significant element of operational costs and depends on electricity tariffs varying over time. As a result pumping optimization accounting for electricity costs and relevant boundary conditions of a WDN, e.g. demands, is of practical interest. When the electricity tariffs are lower, as for example in the night hours, optimization generally results in pumping more water during those hours, if the presence of tanks which are internal to the hydraulic system allows for water storage. Nevertheless, the pressure and, therefore, water leakage of the network greatly vary from night to daylight hours. Pressure and leakage generally increase in the night because of a lower level of demands and a greater level of pressures. Previous studies rarely account for this. This work investigates pumping optimization background leaks, i.e. the non-revenue water cost besides the energy cost. It is shown and discussed that the reduction of background leaks conflict with, and generally dominate, energy cost.

The availability of large environmental datasets and increased computational capability has motivated researchers to propose innovative techniques to mine information from data. The Evolutionary Polynomial Regression (EPR) is a hybrid data-driven technique that combines genetic algorithms and numerical regression for developing easily interpretable mathematical model expressions. EPR is a multi-objective search paradigm for producing multiple models by simultaneously optimizing accuracy and parsimony of resulting expressions. The EPR MOGA-XL is an MS-Excel add-in that allows the user to launch an EPR run as a function in MS-Excel, thereby exploiting a familiar environment to perform data-driven modeling. Inputs and outputs can be easily selected from a spreadsheet, while a separate sheet containing all EPR modeling options can be modified and retrieved for future analyses. The expression(s) of model(s) obtained, the model predictions and fitness indicators are stored in a separate Excel file, allowing subsequent multiple analyses. An application of EPR-MOGA-XL is presented and discussed.

An analysis of runoff generation through ephemeral streams in karst semi-arid areas is here presented. The analysis is based on a full 2D approach, integrating the hydrological and hydraulic models, in order to account first for the dynamic of catchment response to rainfall and activation of the streams, and then for the hydraulic behavior of the streams. This analysis entails the simulation of extreme events corresponding to low, medium and high return periods, in order to identify the event, which presumably activate the ephemeral streams. The analysis focuses on a case study located in southeast Italy.

Understanding mechanical vulnerability of water distribution networks (WDN) is of direct relevance for water utilities since it entails two different purposes. On the one hand, it might support the identification of severe failure scenarios due to external causes (e.g., natural or intentional events) which result into the most critical consequences on WDN supply capacity. On the other hand, it aims at figure out the WDN portions which are more prone to be affected by asset disruptions. The complexity of such analysis stems from the number of possible scenarios with single and multiple simultaneous shutdowns of asset elements leading to modifications of network topology and insufficient water supply to customers. In this work, the search for the most disruptive combinations of multiple asset failure events is formulated and solved as a multiobjective optimization problem. The higher vulnerability failure scenarios are detected as those causing the lower supplied demand due to the lower number of simultaneous failures. The automatic detection of WDN topology, subsequent to the detachments of failed elements, is combined with pressure-driven analysis. The methodology is demonstrated on a real water distribution network. Results show that, besides the failures causing the detachment of reservoirs, tanks, or pumps, there are other different topological modifications which may cause severe WDN service disruptions. Such information is of direct relevance to support planning asset enhancement works and improve the preparedness to extreme events.

The hydraulic system functioning is determined by the boundary conditions (e.g. network topology, pipe resistances/diameters, tank levels, status of control devices, status of pumps, etc.). Shutdown of isolation valves, in order to detach a portion of the hydraulic network for planned or unplanned works, generates abnormal working conditions due to the induced topological modification of the network, which may reduce the hydraulic capacity of the water system with respect to the portions still connected. Thus, a challenge for network design is to optimize diameters versus system management under abnormal working conditions, i.e. accounting for the isolation valve system. To this purpose, a methodology for optimal system design accounting for valve shutdowns is herein presented. As the optimization asks for the evaluation of network configurations that can be generated by the isolation valve system, a strategy to reduce the computational burden is required. In fact, the analysis of a large number of network configurations could be required in real-world applications. A strategy to evaluate only the critical configurations, i.e. those ones for which the hydraulic capacity becomes insufficient to satisfy water requests in the still connected network, and dominating configurations, i.e. those ones which are the most critical, is presented. The optimization procedure is explained and discussed using a small size network and the computational efficiency is demonstrated using a large size network.

The delimitation of flood-prone areas is of crucial importance for assessing the risk associated with extreme natural events and for planning/regulating the development of a given territory. This work undertakes the floodplain delineation problem for some ephemeral streams known as “lame” located in Apulia region (Southern Italy). This territory is characterized by a rather flat morphology and absence of base flow along the main waterways, except for rare and exceptionally severe rainfall events. In such particular context, traditional synthetic hydrologic models can be hardly used due to the lack of monitored rainfall-runoff data and the unpredictable runoff propagation over the peculiar catchment morphology. This paper presents the results of a “full-2D” model which simulates the runoff generation and propagation over the entire catchment (both inside and outside the ephemeral streams), once infiltration, surface roughness and rainfall event conditions are defined into every cells of the bi-dimensional domain. A sensitivity analysis of the model considering different values of ground infiltration and surface roughness parameters is presented. The results show that different prior assumptions lead to quite different peak discharge values predicted in few control sections even when such complex “full-2D” rainfall-runoff model is used.

Steady-state Water Distribution Network (WDN) modelling, which is normally performed as part of hydraulic system simulation, computes pipe flow rates and nodal heads for a given set of boundary conditions (i.e., tank levels, nodal demands, pipe hydraulic resistances, pump curves, minor losses, etc.). The problem is nonlinear based on solution of energy and mass conservation laws. The mathematical solution to such a problem is generally found by using global linearization techniques involving the simultaneous solution of all the system’s equations. The related algorithms use successive approximations in order to iteratively reach the solution of the original nonlinear mathematical system. This requires the solution of a linear system of equations at each iteration. The matrix of coefficient of that linear system is generally sparse, symmetric and positive definite, as for example in the global gradient algorithm (GGA). Thus, the robust and fast solution of such a linear problem is an important issue in order to achieve computational efficiency with respect to large size hydraulic systems. This work will study the two main strategies of linear system solvers, the direct and iterative methods, together with the most reliable and efficient ordering, factorization and pre-conditioning strategies in the context of steady-state WDN modelling. The results show that exists a direct method based on a specialized decomposition which is superior to all the other alternatives.

The simulation of flood events is essential for risk prevention and land regulation purposes. Traditionally it is performed by decoupling the prediction of hydrograph(s) at some section(s) of the waterway(s) from the delineation of downstream flooded areas by using synthetic hydrologic models and hydraulic inundation models respectively. In the case of Apulian ephemeral streams (Southern Italy) the application of such an approach is prevented by the lack of monitored rainfall-runoff data and the discrepancy of some key underlying hypotheses. Thus, the application suitability of an integrated (hydrologic-hydraulic) a full-2D models is investigated here by assuming the rainfall as the only forcing external term into each element of the bi-dimensional domain where the shallow water equations are integrated. This permits to reproduce runoff generation, propagation and, eventually, flooding at any point of the catchment. Several model runs under many combinations of hydrological losses and surface roughness parameters demonstrate that the full-2D approach realistically reproduce catchment hydraulic behaviour and predicted inundated areas of Apulian ephemeral streams, thus being of direct relevance for basin management purposes.

The traditional approach for delimitation of flood-prone areas is based on some conceptual assumptions which mainly involve the uncoupling of the hydrological modeling for flood wave prediction from the hydraulic modeling of floodplain inundation. Although the adoption of lumped parameters hydrologic models is acceptable in a number of real contexts, in other areas it is prevented due to the peculiar morphology and the lack of data for their calibration. In such circumstances the integrated simulation of surface runoff generation process on the ground with the propagation over the catchment is essential to reproduce the actual catchment behavior. After presenting the study area, that pertains some ephemeral streams located in Southern Italy, the paper discusses the features of a full 2D hydraulic model to be used to reproduce the rainfall-runoff generation and flood propagation over the entire catchment. Simulation results are discussed in terms of predicted hydraulic behavior and flooded areas.

The availability of large environmental datasets and increased computational capability has motivated researchers to propose innovative techniques to mine information from data. The Evolutionary Polynomial Regression (EPR) is a hybrid data-driven technique that combines genetic algorithms and numerical regression for developing easily interpretable mathematical model expressions. EPR is a multiobjective search paradigm for producing multiple models by simultaneously optimizing accuracy and parsimony of resulting expressions. Here the EPR MOGAXL v.1 is presented. It is an MS-Excel add-in that allows the user to launch an EPR run as a function in MS-Excel, thereby exploiting a familiar environment to perform data-driven modeling. Inputs and outputs can be easily selected from a spreadsheet, while a separate sheet containing all EPR modeling options can be modified and retrieved for future analyses. The expression(s) of model(s) obtained, the model predictions and fitness indicators are stored in a separate Excel file, allowing subsequent multiple analyses. An application of EPR-MOGA-XL is presented and discussed.

Ephemeral streams are morphological elements of karstic low-relief areas, characterised by relatively large and flat transects, which occasionally drains runoff, in particular when generated by extraordinary or extreme rainfall events. The main problem related to this streams and affecting the analysis and prediction of flood events in karst semi-arid regions is the almost complete absence of discharge time-series. Floods are relatively rare events for semi-arid karst regions, however they can be really severe and disruptive, causing serious damages to people and infrastructures. This work presents an analysis of the response to rainfall of ephemeral streamsin a karst semi-arid regions of south-east of Italy by an innovative approach. The analysis is based on a 2D simulation model of the behavior of a network of ephemeral streams. The used approach integrates the hydrological and hydraulic models, in order to account first for the dynamic of catchment response to rainfall and activation of the streams, and then for the hydraulic behavior of the streams. Results shows the slow response of ephemeral streams to the rainfall, whereas more extreme rainfall events generate quick and high discharge responses of the ephemeral streams. In addition, modeling results emphasize the non-linearity of runoff generation, in particular for some flow paths, which are biased by the local morphology as well as by the intensity of the rainfall event.

The study of aquifers dynamics is a fundamental issue for the analysis of groundwater resources. However, the modeling of aquifer dynamics by means of physically based models is geneally not simple and cheap since a lot of information is necessary in order to define the model. For this reason the use of data-driven modeling approaches, able to return explicit models starting from measured reasonably low cost data, could be a solution to this issue. Thus, this work introduces the use of an evolutionary modeling technique, namely Evolutionary Polynomial Regression (EPR), aimed at the prediction of water table levels for two aquifers located in the same area of south east of Italy. These aquifers are hydrogeologically different, even if located in the same area. The earlier is a surficial porous aquifer, while the latter is a coastal karst aquifer. Even if subject to the same climate conditions, they show different hydrogeological behaviours, in term of different dynamics and responses to rainfall. EPR is used herein to predict groundwater levels for both the aquifers as well as returning equation structures which are consistent with their different dynamics. The obtained results show how EPR is able to correctly interpretate different hydrogeological situations.

Complex and/or large size water distribution networks (WDNs) require the division of the hydraulic system into modules in order to simplify the analysis and the management tasks. In the modern science of networks, the modularity index has been proposed in order to detect communities, i.e., groups/clusters of nodes characterized by stronger inter-connections. The modularity index is a measure of the strength of the network division into communities and it is maximized in order to identify them. Therefore, the division into modules of WDNs, also named segmentation, could be performed by using the modularity index as metric in order to identify cluster of nodes. Nevertheless, modularity index needs to be revised considering the specificity of the hydraulic systems, which are infrastructure networks. In fact, the division into modules for infrastructure networks, although it can be based on the identification of clusters of nodes, is not aimed at investigating network features. Differently, the aim is the practical issue of simplifying system analysis, planning and management; therefore, the division is constrained by the technical needs. Accordingly, in the present work the classic modularity index is firstly presented. Successively, it is tailored and modified for WDNs. Furthermore, a multi-objective strategy for optimal segmentation is presented and discussed also using a real test network. The optimization framework is based on the maximization of the WDN-oriented modularity-based index versus the minimization of the cost of newly installed devices in order to obtain network segments. Those are a set of optimal divisions into modules of the hydraulic system which are the basis for an integrated, dynamical planning.

While there is no question about the fact that demands in a water distribution system can be dependent on pressure, the importance of considering pressure based demands in modeling has been widely discussed. This discussion often centres on whether demands are pressure or volume based. This, however, is the wrong question. Demands are BOTH pressure and volume based and demands are really a sum of several difference components of demand including volume based demand, controlled pressure based demand, uncontrolled pressure based demand and leakage. Each of these components is described in the paper with some special consideration of the case where pressure approaches zero and the implications of considering these components.

The search for suitable segmentations is a challenging and urgent issue for the analysis, planning and management of complex water distribution networks (WDNs). In fact, complex and large size hydraulic systems require the division into modules in order to simplify the analysis and the management tasks. In the complex network theory, modularity index has been proposed as a measure of the strength of the network division into modules and its maximization is used in order to identify community of nodes (i.e., modules) which are characterized by strong interconnections. Nevertheless, modularity index needs to be revised considering the specificity of the hydraulic systems as infrastructure systems. To this aim, the classic modularity index has been recently modified and tailored for WDNs. Nevertheless, the WDN-oriented modularity is affected by the resolution limit stemming from classic modularity index. Such a limit hampers the identification/design of small modules and this is a major drawback for technical tasks requiring a detailed resolution of the network segmentation. In order to get over this problem, we propose a novel infrastructure modularity index that is not affected by the resolution limit of the classic one. The rationale and good features of the proposed index are theoretically demonstrated and discussed using two real hydraulic networks.

Information, data and maps required to analyze water distribution networks are commonly available nowadays. Furthermore, the use of information technology and geographical information systems has become part of normal mapping and management tasks in the water industry. In particular, improved descriptions of both network topology (number and position of the property connections along water mains) and its boundary conditions (e.g. demands, leakage, etc.) permit a more detailed analysis for different management purposes. These facts increase considerably the complexity of the network analysis and the size of the system hydraulic models and related mathematical problems. For example, the mathematical description of the actual demand pattern along a water main could be potentially achieved by adding one interior node for each connection point, but this will normally increase the size of the hydraulic model by more than one order of magnitude. Thus, simplification of the network model is vital for achieving an acceptable computational efficiency level that allows effective investigation. In this paper, network simplification is achieved by using the recently developed Enhanced Global Gradient Algorithm (EGGA). EGGA simplifies the network topology by automatically removing interior/serial nodes, which are those adjacent to two nodes only, thus reducing the total number of demand nodes and pipes in the analyzed hydraulic model whilst preserving original mass and energy balance. The EGGA formulation shows clearly that the sensitivity of the algorithm results to the uncertainties of the boundary conditions is unchanged with respect to classical GGA. Thus, this paper analyses two simplification strategies based on EGGA and applying them to a case study.

Solving water distribution network hydraulics depends to a great extent on demand representation in the related simulation models. The classical approach of simulation models for water distribution networks (WDNs) is described as demand-driven. The demands are fixed a priori in the model as an assumption or from field observations. Recently a more realist approach to predict the hydraulic system behavior, described as head/pressure-driven, better accounts for the fact that the demands depend in some ways on head status of the network. Thus, this paper presents a comprehensive view of demands in the enhanced WDN simulation models including considerations of human-based, volume-based, uncontrolled orifice-based and leakage-based demands as distinct types of network outflows. The paper proposes and discusses the representation of each type of demand in a comprehensive framework which is consistent with the hydraulic principles and the specific working condition.

Steady-state Water Distribution Network models compute pipe flows and nodal heads for assumed nodal demands, pipe hydraulic resistances, etc. The nonlinear mathematical problem is based on energy and mass conservation laws which is solved by using global linearization techniques, such as global gradient algorithm (GGA). The matrix of coefficients of the linear system inside GGA belongs to the class of sparse, symmetric and positive definite. Therefore a fast solver for the linear system is important in order to achieve the computational efficiency, especially when multiple runs are required. This work aims at testing three main strategies for the solution of linear systems inside GGA. The tests are performed on eight real networks by sampling nodal demands, considering the pressure-driven and demand-driven modelling to evaluate the robustness of solvers. The results show that there exists a robust specialized direct method which is superior to all the other alternatives. Furthermore, it is found that the number of times the linear system is solved inside the GGA does not depend on the specific solver, if a small regularization to the linear problem is applied, and that pressure-driven modelling requires a greater number which depends on the size and topology of the network and not only on the level of pressure deficiency.

One of the most important objectives for water distribution networks is to provide safe and reliable water supply also changing system boundary conditions. This can be compromised by inadequate configuration of the system, unforeseen high water consumption and high leakages. Large water networks are complex and analysis of hydraulic performance requires computer models. In Oslo municipality, Water and Wastewater Department, is currently estimating the reliability of the water distribution system including the level of robustness, redundancy and preparedness of the system under today and future demand. First analyses indicate that closure of certain pipes may have relevant consequences as loss of water supply and reduction of pressure for a significant number of customers. Therefore, a major ongoing project on revision and safeguarding of Oslo water supply system also includes further analysis of the hydraulic system reliability. WDNetXL model system has been applied to this purpose.

Some simplification strategy for water distribution network simulation models are presented herein. They are achieved by using the recently developed Enhanced Global Gradient Algorithm (EGGA). EGGA allows to simulate the hydraulic system after removing interior/serial nodes, which are those adjacent to two nodes only, without forfeiting both the energy and the mass balance equations in the system model. Thus, the total number of demand nodes and pipes in the model topology results reduced. Furthermore, EGGA formulation shows clearly that its sensitivity to the uncertainties of the boundary conditions results unchanged with respect to classical GGA. Then, this paper analyses two simplification strategies based on EGGA applying them to a real large size water network. The results show significant computational efficiency gains without sacrificing accuracy of the results.

Purpose – Using discarded tyre rubber as concrete aggregate is an effective solution to the environmental problems associated with disposal of this waste material. However, adding rubber as aggregate in concrete mixture changes, the mechanical properties of concrete, depending mainly on the type and amount of rubber used. An appropriate model is required to describe the behaviour of rubber concrete in engineering applications. The purpose of this paper is to show how a new evolutionary data mining technique, evolutionary polynomial regression (EPR), is used to predict the mechanical properties of rubber concrete. Design/methodology/approach – EPR is a data-driven method based on evolutionary computing, aimed to search for polynomial structures representing a system. In this technique, a combination of the genetic algorithm and the least square method is used to find feasible structures and the appropriate constants for those structures. Findings – Data from 70 cases of experiments on rubber concrete are used for development and validation of the EPR models. Three models are developed relating compressive strength, splitting tensile strength, and elastic modulus to a number of physical parameters that are known to contribute to the mechanical behaviour of rubber concrete. The most outstanding characteristic of the proposed technique is that it provides a transparent, structured, and accurate representation of the behaviour of the material in the form of a polynomial function, giving insight to the user about the contributions of different parameters involved. The proposed model shows excellent agreement with experimental results, and provides an efficient method for estimation of mechanical properties of rubber concrete. Originality/value – In this paper, a new evolutionary data mining approach is presented for the analysis of mechanical behaviour of rubber concrete. The new approach overcomes the shortcomings of the traditional and artificial neural network-based methods presented in the literature for the analysis of slopes. EPR provides a viable tool to find a structured representation of the system, which allows the user to gain additional information on how the system performs.

Nowadays, unprecedented computing power of desktop personal computers and efficient computational methodologies, such as the global gradient algorithm (GGA), make large water distribution system modeling feasible. However, many network analysis applications, such as optimization models, require running numerous hydraulic simulations with modified input parameters. Therefore, a methodology that could reduce the computational burden of network analysis, and still provide the required model accuracy, is needed. This paper presents a matrix transformation approach to convert the classic GGA, which is implemented within the widely available freeware EPANET2, into a more computationally efficient enhanced global gradient algorithm (EGGA). The latter achieves the improved efficiency by reducing the size of the mathematical problem through the transformed topological representation of the original network model. By removing serial nodes and serial pipe-sections from the original topological representation, whilst preserving those elements both in energy and mass balance equations, EGGA provides a significant improvement to the model’s computational efficiency without forfeiting the hydraulic accuracy of the model. The computational efficiency and effectiveness of the EGGA approach is demonstrated on four examples of different real-life networks. Results show that the computational burden of the EGGA model is significantly lower than for its GGA counterpart particularly as the size of the network and/or number of service connections increases.

Calibration is a process of comparing model results with field data and making the appropriate adjustments so that both results agree. Calibration methods can involve formal optimization methods or manual methods where the modeler informally examines alternative model parameters. The development of a calibration framework typically involves: (1) definition of the model variables, coefficients, and equations, (2) selection of an objective function to measure the quality of the calibration, (3) selection of the set of data to be used for the calibration process, and (4) selection of an optimization/manual scheme for altering the coefficient values in the direction of reducing the objective function. Hydraulic calibration usually involves the modification of system demands, fine-tuning the roughness values of pipes, altering pump operation characteristics, and adjusting other model attributes that affect simulation results, and in particular those that have significant uncertainty associated with their values. From the above steps it is clear that model calibration is neither unique nor a straightforward technical task. The success of a calibration process depends on the modeler's experience and intuition, as well as on the mathematical model and procedures adopted for the calibration process. This paper provides a summary of the Battle of the Water Calibration Networks (BWCN), the goal of which was to objectively compare the solutions of different approaches to the calibration of water distribution systems through application to a real water distribution system. Fourteen teams from academia, water utilities, and private consultants participated. The BWCN outcomes were presented and assessed at the 12th Water Distribution Systems Analysis (WDSA 2010) conference in Tucson, Arizona, September 2010. This manuscript summarizes the BWCN exercise and suggests future research directions for water distribution systems calibration.

Researchers extensively studied external loads since they are widely recognized as significant contributors to water pipe failures. Physical phenomena that affect pipe bursts, such as pipe-environment interactions, are very complex and only partially understood. This paper analyses the possible link between pipe bursts and climate-related factors. Many water utilities observed consistent occurrence of peaks in pipe bursts in some periods of the year, during winter or summer. The paper investigates the relationships between climate data (i.e., temperature and precipitation-related covariates) and pipe bursts recorded during a 24-year period in Scarborough (Ontario, Canada). The Evolutionary Polynomial Regression modelling paradigm is used here. This approach is broader than statistical modelling, implementing a multi-modelling approach, where a multi-objective genetic algorithm is used to get optimal models in terms of parsimony of mathematical expressions vs. fitting to data. The analyses yielded interesting results, in particular for cold seasons, where the discerned models show good accuracy and the most influential explanatory variables are clearly identified. The models discerned for warm seasons show lower accuracy, possibly implying that the overall phenomena that underlay the generation of pipe bursts during warm seasons cannot be thoroughly explained by the available climate-related covariates.

Pressure-driven analysis of water distribution networks (WDNs) can realistically reproduce the actual behavior of the hydraulic system, especially with reference to leakages, which are not under human control, and, sometimes to demands in pressure-deficient conditions. Classical WDN models represent the demand and leakage outflows in terms of either prior fixed nodal discharges, in classical demand-driven analysis, or dependent on actual nodal pressures, in pressure-driven analysis. This work presents a WDN pressure-driven algorithm that allows accounting for actual leakage and demand patterns along pipes or, as a complementary feature, for network topological simplification. It is on the basis of the enhanced global gradient algorithm (EGGA) and has been introduced and discussed in comparison to classical pressure-driven GGA. Three test networks have been used to study the convergence issue of the newly proposed algorithm, and the largest network has been used to discuss its computational efficiency.

A methodology to analyze the vulnerability of water distribution networks (WDNs) to earthquakes by means of risk assessment is presented. The consequences of multiple pipe failures due to earthquakes are investigated in terms of unsupplied demand to customers. To this aim the steady-state WDN analysis is performed considering system topology changes due to closing isolation valves in order to separate the network segments where failures occur. The pipe failure probability is calculated using fragility curves from the American Lifelines Association (ALA). The identification of the worst pipe failure scenarios as trade-offs between unsupplied demand and probability of occurring is formulated as a multiobjective combinatorial problem and solved using a multiobjective genetic algorithm as optimization strategy. The methodology is applied to the Exnet network. Results show that WDN seismic vulnerability depends also on network segmentation due to the existing isolation valve system. The methodology allows analyzing and ranking the worst scenarios, being a valuable decision support for improving WDN preparedness to earthquakes and allowing planning appropriate asset enhancements and mitigation measures to improve system resilience.

Local scour modelling is an important issue in environmental engineering in order to prevent degradation of river bed and safe the stability of grade control structures. Many empirical formulations can be retrieved from literature to predict the equilibrium scour depth, which is usually assumed as representative of the phenomenon. These empirical equations have been mostly constructed in some ways by leveraging regression procedures on experimental data, usually laboratory observations (thus from small/medium scale experiments). Laboratory data are more accurate measurements but generally not completely representative of the actual conditions in real-world cases, that are often much more complex than those schematized by the laboratory equipment. This is the main reason why some of the literature expressions were not adequate when used for practical applications in large-scale examples,. This work deals with the application of an evolutionary modelling paradigm, named Evolutionary Polynomial Regression (EPR), to such problem. Such a technique was originally presented as a classical approach, used to achieve a single model for each analysis, and has been recently updated by implementing a multi-modelling approach (i.e. to obtain a set of optimal candidate solutions/models) where a multi-objective genetic algorithm is used to get optimal models in terms of parsimony of mathematical expressions vs. fitting to data. A wide database of field and laboratory observations is used for predicting the equilibrium scour depth as a function of a set of variables characterizing the flow, the sediments and the dimension of the grade control structure. Results are discussed considering two regressive models available in literature that have been trained on the same data used for EPR. The proposed modelling paradigm proved to be a useful tool for data analysis and, in the particular case study, able to find feasible explicit models featured by an appreciable generalization performance.