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.

A new view for the analytical formulation of torsional ultimate strength for reinforced concrete (RC) beams by experimental data is explored by using a new hybrid regression method termed Evolutionary Polynomial Regression (EPR). In the case of torsion in RC elements, the poor assumptions in physical models often result into poor agreement with experimental results. Nonetheless, existing models have simple and compact mathematical expressions since they are used by practitioners as building codes provisions. EPR combines the best features of conventional numerical regression techniques with the effectiveness of genetic programming for constructing symbolic expressions of regression models. The EPR modeling paradigm allows to figure out existing patterns in recorded data in terms of compact mathematical expressions, according to the available physical knowledge on the phenomenon (if any). The procedure output is represented by different formulae to predict torsional strength of RC beam. The multi-objective search paradigm used by EPR allows developing a set of formulae showing different complexity of mathematical expressions as resulting into different agreement with experimental data. The efficiency of such approach is tested using experimental data of 64 rectangular RC beams reported in technical literature. The input parameters affecting the torsional strength were selected as cross-sectional area of beams, cross-sectional area of one-leg of closed stirrup, spacing of stirrups, area of longitudinal reinforcement, yield strength of stirrup and longitudinal reinforcement, concrete compressive strength. Those results are finally compared with previous studies and existing building codes for a complete comparison considering formulation complexity and experimental data fitting. © 2011 Elsevier Ltd. All rights reserved.

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.