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International audience; Water utilities are challenged to reduce their water losses through detecting, localizing, and repairing leaks as quickly as possible in their aging distribution systems. In this work, we solve this challenging problem by detecting multiple leaks simultaneously in a water distribution network for the Battle of the Leak Detection and Isolation Methods. The performance of leak detection and localization depends on how well the system roughness and demand are calibrated. In addition, existing leaks affect the diagnosis performance unless they are identified and explicitly represented in the model. To circumvent this chicken-and-egg dilemma, we decompose the problem into multiple levels of decision-making (a hierarchical approach) where we iteratively improve the water distribution network model and so are able to solve the multileak diagnosis problem. First, a combination of time series and cluster analysis is used on smart meter data to build patterns for demand models. Second, point and interval estimates of pipe roughnesses are retrieved using least squares to calibrate the hydraulic model, utilizing the demand models from the first step. Finally, the calibrated primal model is transformed into a dual model that intrinsically combines sensor data and network hydraulics. This dual model automatically converts small pressure deviations caused by leaks into sharp and localized signals in the form of virtual leak flows. Analytical derivations of sensitivities with respect to these virtual leak flows are calculated and used to estimate the leakage impulse responses at candidate nodes. Subsequently, we use the dual network to (1)detect the start time of the leaks, and (2)compute the Pearson correlation of pressure residuals, which allows further localization of leaks. This novel dual modeling approach resulted in the highest true-positive rates for leak isolation among all participating teams in the competition.

International audience; This paper used the fusion of an active-set method (ASM) and an interior point method (IPM), with a Newton method, to solve for the steady-state flows, heads, and outflows of a pressure-dependent water distribution system. The outflow constraints which arise from the pressure dependency are handled by an ASM, and the linkflow constraints are handled by an IPM. The authors believe that this is the first time an ASM and an IPM have been used together in this way to solve a real-world optimization problem. Including flow constraints in a network model allows a variety of flow control devices (flow control valves, check valves, pumps) to be modeled efficiently. The new method does not require damping. The separate treatment methods for the two constraint sets mean that the linear inequality constraint qualification condition cannot be violated during iteration, unlike the case in which all the constraints are handled by an ASM. The method was shown to converge quickly on nine case study networks, the largest of which had more than 157,000 links, 150,000 nodes, and 6,000 linkflow constraints. When tested on those same nine networks, an interior point optimizer software package took about 2–4 times longer than the new method for five of the networks, 7 and 9 times as long for two of the networks, and about an equal amount of time for the remaining two networks. For the largest network, the software package took 34 min, whereas the method presented here took 4 min. The generality of the method makes it applicable to network design and management, capacity analysis, and self-cleaning networks.

International audience; In this paper a new method is proposed that solves for the steady state of pressure-dependent models (PDMs) with flow control valves. Rather than model flow devices individually, the method solves the more general problem in which a water distribution system (WDS) has some link flows constrained to lie between upper and lower, or possibly equal, set limits. No heuristics are used to determine device states. The method is shown to be fast, and its effectiveness is demonstrated on PDM WDSs with up to about 20,000 links and 18,000 nodes and 60 link flow constraints, some of which prescribe a fixed flow. The method has applications in network management, network design, and flow control to deal with water distribution where there is insufficient supply.

International audience; The paper presents the results of the Battle of Postdisaster Response and Restoration (BPDRR) presented in a special session at the first International water distribution systems analysis & computing and control in the water industry (WDSA/CCWI) Joint Conference, held in Kingston, Ontario, Canada, in July 2018. The BPDRR problem focused on how to respond and restore water service after the occurrence of five earthquake scenarios that cause structural damage in a water distribution system. Participants were required to propose a prioritization schedule to fix the damages of each scenario while following restrictions on visibility/nonvisibility of damages. Each team/approach was evaluated against six performance criteria: (1)time without supply for hospital/firefighting, (2)rapidity of recovery, (3)resilience loss, (4)average time of no user service, (5)number of users without service for eight consecutive hours, and (6)water loss. Three main types of approaches were identified from the submissions: (1)general-purpose metaheuristic algorithms, (2)greedy algorithms, and (3)ranking-based prioritizations. All three approaches showed potential to solve the challenge efficiently. The results of the participants showed that for this network, the impact of a large-diameter pipe failure on the network is more significant than several smaller pipes failures. The location of isolation valves and the size of hydraulic segments influenced the resilience of the system during emergencies. On average, the interruptions to water supply (hospitals and firefighting) varied considerably among solutions and emergency scenarios, highlighting the importance of private water storage for emergencies. The effects of damages and repair work were more noticeable during the peak demand periods (morning and noontime) than during the low-flow periods; and tank storage helped to preserve functionality of the network in the first few hours after a simulated event.

[Departement_IRSTEA]Eaux [TR1_IRSTEA]GEUSI [ADD1_IRSTEA]Gestion intégrée de la ressource et des infrastructures; International audience; Water distribution networks are critical infrastructures that should ensure the reliable supply of high quality potable water to its users. Numerical models of these networks are generally governed by many parameters for which the exact value is not known. This may be due to a lack of precise knowledge like for consumer demand or due to a lack of accessibility as for the pipe roughness. For network managers, the effect of these uncertainties on the network state is important information that supports them in the decision-making process. This effect is generally evaluated by propagating the uncertainties using the mathematical model. In the past, perturbation, fuzzy and stochastic collocation methods have been used for uncertainty propagation. However, these methods are limited either in the accuracy of the results or the computational effort of the necessary calculations. This paper uses an alternative spectral approach that uses the polynomial chaos expansion and has the potential to give results of comparable accuracy to the Monte Carlo sampling through the definition of a stochastic model. This approach is applied to the hydraulic model of two real networks in order to evaluate the influence of uncertain demands on the water age.

The calculation of hydraulic state variables for a network is an important task in managing the distribution of potable water. Over the years the mathematical modeling process has been improved by numerous researchers for the utilization in new computer applications and the more realistic modeling of water distribution networks. But, in spite of these continuous advances, there are still a number of physical phenomena that cannot be tackled correctly by current models. This paper will take a closer look on the two modeling paradigms given by demand and pressure driven modeling. The basic equations are introduced and parallels are drawn to the optimization formulations from electrical engineering. These formulations guarantee existence and uniqueness of the solution. One of the central questions in the French and German research project ResiWater is the investigation of the network resilience in case of extreme events or disasters. Under such extraordinary conditions where models are pushed beyond their limits we talk of deficient network models. Examples of deficient networks are given by highly regulated flow, leakage or pipe bursts and cases where pressure falls below the vapor-pressure of water. These examples will be presented and analyzed on the solvability and physical correctness of the solution with respect to demand and pressure driven models.

Modeling of water distribution systems is fundamental for the design, analysis and operation of any water network. As with all hydraulic models, water demands are one of the most important input components in the model. However, estimation of the demand parameters is usually complicated due to the stochastic behavior of the water consumptions. Several methods have been proposed for estimating water demands. Most of them have been developed based on given frameworks where the number of unknown parameters is assumed to be equal or less than the number of measurements. The outcomes, therefore, rely on this assumption, which can lead to significant approximation errors in real water distribution systems. The approach proposed in this paper does not require the number of known inputs to be equal to the number of variables. In fact, nodes in the model could each have a different demand pattern. The genetic algorithm approach adopted here shows that the average results of multiple GA runs can estimate the demand patterns at each node. Moreover, the model can also be used to estimate the flow rates and nodal heads at non-measured locations of the water network, although the accuracy of the estimation depends on number, type and location of the measurements. Results are shown and discussed for a literature case study tested for a 24-hour time period.

Sensitivity analysis of the actual hydraulic state of water distribution systems is a valuable tool with number of applications in hydraulic systems analysis. Sensitivity matrices include the information of the response of the hydraulic state variables (flows, pressures) to changes in model parameters (e.g. demands, roughness, control parameters) for a specific hydraulic state of the system. For calculation, there exists in addition to finite difference approximations also exact solutions that include the inversion of the system matrix (the Schur Complement of the Jacobian of the hydraulic network equations). In combination with hydraulic network simulations, the factorization (for example Cholesky matrix decomposition) of the matrix that has already been done by the hydraulic solver in the computation process can be used for the efficient calculation of the inverse matrix. However, for large realworld networks the sensitivity calculation is a time and memory consuming process because the inverse of the system matrix of a connected network has no zero elements. In this paper a new method is presented that allows for the exact calculation of sensitivities of a particular subgraph of interest, the topological minor or supergraph within a water distribution system network graph. Supernodes are the most important nodes in terms of connectivity redundancy within the network graph. Superlinks replace all pipes (links) in series between two supernodes. It will be shown that the sensitivities that are calculated for the subgraph deliver exactly the same results as the inversion of the entire system matrix reduced to supernodes. This paper focuses on the derivation of the equations for the reduced system matrix inversion of the topological subgraph. In addition, the paper includes the proof of equivalence of the matrix inverses for the topological minor subgraph. This inverse represents the fundamental sensitivities of nodal heads and pipe flows with respect to nodal demands in demand driven analysis. The results presented can be extended to other sensitivities, since the matrix inverse in question is included in all other derived parameter sensitivities.

International audience; A new content-based, box-constrained, active-set projected Newton method is presented that solves for the heads, the pipe flows, and the nodal outflows of a water distribution system in which nodal outflows are pressure dependent. The new method is attractive because, by comparison with the previously published weighted least-squares energy and mass residuals (EMR) damped Newton method, (1) it typically takes fewer iterations, (2) it does not require damping, (3) it takes less wall-clock time, (4) it does not require the addition of any virtual elements, and (5) it is algorithmically easier to deal with. Various pressure-outflow relationships (PORs), which model nodal outflows, were considered and two new PORs are presented. The new method is shown, by application to eight previously published case study networks with up to about 20,000 pipes and 18,000 nodes, to be up to five times faster than the EMR method and to take between 34% and 70% fewer iterations than the EMR method.

Water distribution networks are critical infrastructures that should ensure the reliable supply of high quality potable water to its users. Numerical models of these networks are generally governed by many parameters for which the true value is unknown. This may be due to a lack of knowledge like for consumer demand or due to a lack of accessibility as for the pipe roughness. For network managers, the effect of these uncertainties on the network state is important information that supports them in the decision-making process. This effect is generally evaluated by propagating the uncertainties using the mathematical model. In the past, perturbation and stochastic collocation methods have been used for uncertainty propagation. However, these methods are limited either in the accuracy of the results or the complexity of the calculation. This paper uses an alternative spectral approach with the polynomial chaos expansion that has the potential to give comparable results to the Monte Carlo sampling through the definition of a stochastic model. This approach is applied to the model of a water distribution network in order to evaluate the influence of uncertain demands on the water age.

The reliability of a water distribution system is highly dependent on the management of its pipeline network. A pipe or a portion of the network can be isolated for inspection, maintenance,...

1st International WDSA / CCWI 2018 Joint Conference, Kingston, CAN, 23-/07/2018 - 25/07/2018; International audience; Water distribution systems (WDSs) are an essential part of the urban infrastructure, which consist of a labyrinth of networks of pipes, tanks, pumps and monitoring systems. In order to provide water of appropriate quantity, quality and pressure to customers, a WDS needs to be stable and reliable. Isolation valves, which are installed along the pipelines, are designed to provide system reliability. By closing related isolation valves, a pipe or a portion of the network can be isolated for inspection, maintenance and replacement without disrupting other parts of the system. However, these isolation valves may cause adverse operating conditions in the network if some of the valves in the system are active (partially or fully closed) while their statuses are unknown (due to poor or non-existent documentation, valves left closed inadvertently, errors in data transfer or valve mechanical failure, etc.). This can be observed by a disagreement between the measured pressure and flow values from the real system and results from its corresponding hydraulic simulation model. Calibration of these unknown valve statuses is, therefore, a necessary step that has to be implemented to ensure the reliability of the system. This paper introduces a hybrid method for the identification of unknown partially/fully closed valves in a water distribution network. An optimization problem is formulated for unknown valve statuses and solved by application of three sequentially applied methods, which include: a local sensitivity analysis, the application of genetic algorithms and the application of the Levenberg-Marquardt algorithm. In order to eliminate the valves that are unable to be localized by the measurement data, first, the sensitivity of the flow rates and nodal heads at measurement locations with respect to the change in the minor losses of the valves is computed. Following, a genetic algorithm combined with an extended period simulation is applied to preliminarily identify the locations of the partially/fully closed valves and their degree of opening of the valves. Finally, the application of the Levenberg- Marquardt algorithm has been implemented to correct the results from the GA model. A water distribution network is used to demonstrate the applicability of the proposed methodology. Results show that the model is able to provide relatively good approximation of the locations of unknown partially/fully closed valves as well as their corresponding settings.

International audience; The forest core partitioning algorithm (FCPA) and the fast graph matrix partitioning algorithm (GMPA) have been used to improve efficiency in the determination of the steady-state heads and flows of water distribution systems that have large, complex network graphs. In this paper, a single framework for the FCPA and the GMPA is used to extend their application from demand dependent models to pressure dependent models (PDMs). The PDM topological minor (TM) is characterized, important properties of its key matrices are identified, and efficient evaluation schemes for the key matrices are presented. The TM captures the network's most important characteristics: It has exactly the same number of loops as the full network, and the flows and heads of those elements not in the TM depend linearly on those of the TM. The inverse of the TM's Schur complement is shown to be the top, left block of the inverse of the full system Jacobian's Schur complement, thereby providing information about the system's essential behavior more economically than is otherwise possible. The new results are applicable to other nonlinear network problems, such as in gas, district heating, and electrical distribution.

Analysing water networks online should not be constrained to classic hydraulic simulations. Including other processes can give a much better global view of what is happening in the network. Water quality modelling [1], event detection [2] or online source identification [3], for example, are some of the processes that can be considered as part of a global water network analysis. In the context of this paper, the online analysis is understood as getting the most of the water network current state based on the information available from it. The work presented describes a system aimed to support the coordination of different processes working on the online analysis of water networks. Several aspects of Petri nets [4] are used for modelling the interaction among the processes. The system is described from a software engineering perspective but the application is focused on the benefits for running online water distribution system analysis.

Accurate modeling of water distribution systems is fundamental for planning and operating decisions in any water network. One important component that directly affects model accuracy is kno...

The automatic identification of the source of a contamination is an important component of an early warning and event management system for security enhancement of water supply networks. Whilst a number of algorithms have been published on the algorithmic development, only few information exists about the integration within a comprehensive real-time Event Detection and Management System. In the following the analytical solution and the software implementation of a real-time source identification module and its integration within a web-based Event Management System is described. The development was part of the project SAFEWATER, which was funded under FP 7 of the European Commission.

International audience; The first-order sensitivity matrices (matrices of sensitivity or influence coefficients) have application in many areas of water distribution system analysis. Finite-difference approximations, automatic differentiation, sensitivity equations, and the adjoint method have been used in the past to estimate sensitivity. In this paper new, explicit formulas for the first-order sensitivities of water distribution system (WDS) steady-state heads and flows to changes in demands, resistance factors, roughnesses, relative roughnesses, and diameters are presented. The formulas cover both pressure-dependent modeling (PDM) and demand-dependent modeling (DDM) problems in which either the Hazen-Williams or the Darcy-Weisbach head-loss models are used. Two important applications of sensitivity matrices, namely calibration and sensor placement, are discussed and illustrative examples of the use of sensitivity matrices in those applications are given. The use of sensitivity matrices in first-order confidence estimation is briefly discussed. The superior stability of the PDM formulation over DDM is established by the examination of the sensitivity matrices for the same network solved by both model paradigms. The sensitivity matrices and the key matrices in both the global gradient method for DDM problems and its counterpart for PDM problems have many elements in common. This means that the sensitivity matrices can be computed at marginal cost during the solution process with either of these methods.

[1] A novel optimization approach for water distribution network design is proposed in this paper. Using graph theory algorithms, a full water network is first decomposed into different subnetworks based on the connectivity of the network’s components. The original whole network is simplified to a directed augmented tree, in which the subnetworks are substituted by augmented nodes and directed links are created to connect them. Differential evolution (DE) is then employed to optimize each subnetwork based on the sequence specified by the assigned directed links in the augmented tree. Rather than optimizing the original network as a whole, the subnetworks are sequentially optimized by the DE algorithm. A solution choice table is established for each subnetwork (except for the subnetwork that includes a supply node) and the optimal solution of the original whole network is finally obtained by use of the solution choice tables. Furthermore, a preconditioning algorithm is applied to the subnetworks to produce an approximately optimal solution for the original whole network. This solution specifies promising regions for the final optimization algorithm to further optimize the subnetworks. Five water network case studies are used to demonstrate the effectiveness of the proposed optimization method. A standard DE algorithm (SDE) and a genetic algorithm (GA) are applied to each case study without network decomposition to enable a comparison with the proposed method. The results show that the proposed method consistently outperforms the SDE and GA (both with tuned parameters) in terms of both the solution quality and efficiency.

International audience; Hydraulic models have been widely used for design, analysis, and operation of water distribution systems. As with all hydraulic models, water demands are one of the main parameters that cause the most uncertainty to the model outputs. However, the calibration of the water demands is usually not feasible attributable to the limited quantity of available measurements in most real water networks. This paper presents an approach to calibration of the demand multiplier factors under an ill-posed condition where the number of measurements is less than the number of parameter variables. The problem is solved using a genetic algorithm (GA). The results show that not only is the GA able to match the calibrated values at measured locations, but by using multiple runs of the GA model, the flow rates and nodal heads at nonmeasured locations can be estimated. Three case studies are presented as an illustration of the problem. The first case study is a small network that demonstrates the calibration model. The second case study shows a comparison between the genetic algorithm model and a singular value decomposition model. The last case study is a large network that allows for practical considerations in applying the proposed methodology to a realistic context.

International audience; In the past, pressure dependent models (PDM) have suered from convergence diculties. In this paper conditions are established for the existence and uniqueness of solutions to the PDM problem posed as two optimization problems, one based on weighted least squares (WLS) and the other based on the co-content function. A damping scheme based on Goldstein's algorithm is used and has been found to be both reliable and robust. A critical contribution of this paper is that the Goldstein theorem conditions guarantee convergence of our new method. The new methods have been applied to a set of eight challenging case study networks, the largest of which has nearly 20,000 pipes and 18,000 nodes, and are shown to have convergence behaviour that mirrors that of the Global Gradient Algorithm on demand dependent model problems. A line search scheme based on the WLS optimization problem is proposed as the preferred option because of its smaller computational cost. Additionally, various consumption functions, including the Regularized Wagner function, are considered and four starting value schemes for the heads are proposed and compared. The wide range of challenging case study problems which the new methods quickly solve suggests that the methods proposed in this paper are likely to be suitable for a wide range of PDM problems.

In this paper a method that determines the steady-state hydraulics of a water distribution system, the graph matrix partitioning algorithm (GMPA), is presented. This method extends the technique of separating the linear and nonlinear parts of the problem and using the more time-consuming nonlinear solver only on the nonlinear parts of the problem and faster linear techniques on the linear parts of the problem. The previously developed forest-core partitioning algorithm (FCPA) used this approach to separate the network graph’s external forest from its looped core but did not address the fact that within the core of a network graph there may be many internal trees—nodes in series—for which a more economical linear process can be used. This extension of the separation process can significantly reduce the dimension of the nonlinear problem that must be solved: GMPA applied to eight case study networks with between 900 and 20,000 pipes show reductions to between 5 and 55% of the core dimension (after F...

Currently the modeling of check valves and flow control valves in water distribution systems is based on heuristics intermixed with solving the set of nonlinear equations governing flow in the network. At the beginning of a simulation, the operating status of these valves is not known and must be assumed. The system is then solved. The status of the check valves and flow control valves are then changed to try to determine their correct operating status, at times leading to incorrect solutions even for simple systems. This paper proposes an entirely different approach. Content and co-content theory is used to define conditions that guarantee the existence and uniqueness of the solution. The work here focuses solely on flow control devices with a defined head discharge versus head loss relationship. A new modeling approach for water distribution systems based on subdifferential analysis that deals with the nondifferentiable flow versus head relationships is proposed in this paper. The water distribution equations are solved as a constrained nonlinear programming problem based on the content model where the Lagrangian multipliers have important physical meanings. This new method gives correct solutions by dealing appropriately with inequality and equality constraints imposed by the presence of the flow regulating devices (check valves, flow control valves, and temporarily closed isolating valves). An example network is used to illustrate the concepts.

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

[Departement_IRSTEA]Eaux [TR1_IRSTEA]GEUSI; International audience; The vulnerability analysis of our societies to major disturbances is of outmost importance in the fields of Infrastructure Asset Management (IAM). Several methodologies have already been developed to assess the vulnerability of critical infrastructures (CIs). Supply networks (water, gas, energy…) are also critical infrastructures (called Critical Networks or CNs hereafter), and should be considered with specific care due to (a) their complexity and spatial extent, (b) their role in providing other CIs with resources. In a first part, we present our framework for vulnerability and resilience in the French-German project “ResiWater” (Innovative Secure sensor Networks and Model-based Assessment Tools for Increased Resilience of water Infrastructures), funded by ANR and BMBF. We will then illustrate the various approaches to vulnerabilities. Lastly, we will draw our conclusions, which will be the guidelines for our project.

International audience; The safety and/or security of drinking water can be threatened by natural disasters, accidents or malevolent attacks. The European FP7 project SAFEWATER aims at developing a comprehensive event detection and event management solution for drinking water security management and mitigation against major deliberate, accidental or natural CBRN related contaminations. New cost-effective C, B, and RN sensors will be developed. An innovative concept with a broad network of low-cost sensors-"domestic sensors" (complementary to a set of sensors in strategic locations) will be developed. A technology platform will be provide which is able to capture and analyze the data collected by the sensors and from other information systems and give a full overview of the crisis to the responders by means of online look-ahead simulations to efficiently manage potential crises. For testing the SAFEWATER solution it will be integrated with on utility-partners' information systems.

International audience; Water utilities have started to install water quality sensors to protect their network against intentional and accidental contamination events. In this context, for taking appropriate action, not only are early-warning detection systems important, but so is the identification of the contamination source, and knowledge of the present and future contamination extent. For the latter there is a need for reliable and updated network models. The main objective of this paper is to specify which performance criteria should be considered to place water quality and water quantity sensors for both early detection and model calibration. Firstly, a brief bibliographical review is given for optimal sensor location design. Next, formulations and objectives for early-warning detection are proposed. Problem formulations that aim to minimize the estimator variance for calibration are then specified. Finally, the method is applied on the real WDN system of the CUS water service (1,000 km, 25,000 nodes and 45,000 customers).

The proper estimation and regular update of model parameters is crucial for the actuality of a mathematical simulation model representing the hydraulics and water quality of a real physical water distribution system. Especially, when the model is running online, uncertainties in model parameters can result in large discrepancies between model predictions and behavior of the real system. Therefore, adequate techniques for data acquisition, maintenance and update of model parameters have to be developed. In what follows the “parameterization” of a hydraulic online simulation model is described including the classification of parameters regarding data source, update cycles and function in the model. The parameterization framework was developed to benefit the modeling of water critical infrastructure systems.

Many different methods have been devised to solve the nonlinear systems of equations that model water distribution networks. Probably the most popular is Todini and Pilati's global gradient algorithm (GGA). Given the GGA's success, alternative methods have not aroused much interest. One example is the co-tree method, which requires some cumbersome steps in its implementation. In this paper, a reformulated co-trees method (RCTM) is presented that simplifies the procedure by manipulating the incidence matrix into trapezoidal form: a lower triangular block at the top representing a spanning tree and rectangular block below it representing the corresponding co-tree. This reordering leads to significant efficiencies that make the RCTM competitive with the GGA in certain settings. The new method has some similarities to the loop flows corrections formulation, and it is shown, by application to a set of eight case study networks with between 932 and 19,647 pipes and between 848 and 17,971 nodes, to be between 15 and 82% faster than the GGA in a setting, such as optimization using evolutionary algorithms, where the methods are applied hundreds of thousands, or even millions, of times to networks with the same topology. It is shown that the key matrix for the RCTM can require as little as 7% of the storage requirements of the corresponding matrix for the GGA. This can allow for the solution of larger problems by the RCTM than might be possible for the GGA in the same computing environment. Unlike some alternatives to the GGA, the following features make the RCTM attractive: (1) it does not require a set of initial flows that satisfy continuity; (2) there is no need to identify independent loops or the loops incidence matrix; (3) a spanning tree and co-tree can be found from the incidence matrix without the addition of virtual loops, particularly when multiple reservoirs are present; and (4) it does not require the addition of a ground node and pseudoloops for each demand node and does not require the determination of cut sets. In contrast with the GGA, the RCTM does not require special techniques to handle zero flow problems that can occur when the head loss is modeled by the Hazen-Williams formula (a sufficient condition is given). The paper also (1) reports a comparison of the sparsity of the key RCTM and GGA matrices for the case study networks; (2) shows mathematically why the RCTM and GGA always take the same number of iterations and produce precisely the same iterates; and (3) establishes that the loop flows corrections and the nullspace methods (previously shown by Nielsen to be equivalent) are actually identical to the RCTM. Keywords: Co-tree formulation; Global gradient algorithm (GGA); Hydraulic analysis; Nullspace method; Water distribution systems

Although mathematical modeling of the hydraulics and water quality of drinking water distribution networks is widely used in network planning and management existing solvers sometimes deliver no results or even wrong results if the connectivity of the system is not correctly maintained. In this paper two major causes for deficient network connectivity are considered. In the first case, the network graph consists of several maximal connected components where some of them have no node with a fixed head source. Those deficient networks can result from errors in the reference data system (GIS) or during data transfer. In the second case, all the links and nodes of the network graph are connected. However, some links representing control devices have upper and/or lower bounds for the flows. Similar problems as in the first case can be observed if the topology of the network is reduced by removing links with active flow control devices from the graph resulting in a disconnected system. The problem is that the identification of control devices that are active (when an inequality constraint is fulfilled be equality) at a certain time step is not straight forward and depends on the actual hydraulic state of the distribution system. In this paper two preprocessing steps of the hydraulic steady-state or extended period simulations are proposed to check the solvability of the mathematical problem with respect to the flow constraints. In the first step, the connectivity of the system is analyzed and network parts without a fixed head source are identified. In the second step, a Linear Program (LP) is formulated that includes the nodal continuity conditions plus additional inequality constraints that refer to the operation of the flow controlling devices. The optimal objective value of the LP indicates if for the original problem either a) a solution exists, b) does not exist or c) exists but has redundant control constraints.

Over the last decade considerable research in water distribution network modeling has focused on the security of water supply against terrorist attacks. In this paper, specific issues of urban and regional distribution systems as to their vulnerability against terrorist attacks with CBRN (chemical, biological, radiological, nuclear) substances, detection methods and emergency plans are investigated. As a first step, a risk analysis is carried out based on topological properties of different parts of the network, classification of building developments and customers. The decomposition of the network graph enables the differentiation of network components (into treed components, blocks and bridges). Following this subdivision, the impacts and detection of attacks on various parts can be assessed. For example, looped parts (blocks) of the network are at a higher risk than branched subsystems (trees) since toxic matter can be distributed using alternate paths that depend on the particular water demand loading case whereas in a branched network only the system downstream the intrusion point is affected. The results of the risk analysis will be used for the creation of risk maps, efficient placement of sensors and the development of emergency plans. The specific differences of urban (mainly looped) and regional (mainly branched) supply networks will be demonstrated. The observation of water distribution systems with water quality sensors has been studied by researchers in detail over recent years. The application of the decomposition of the network graph to the sensor allocation problem will be demonstrated using the example network 2 of the Battle of the Water Sensor Networks (BWSN). The network is subdivided into tree, bridge and looped block components. It will turn out that tree structures should be excluded from application of sensor allocation algorithms using mathematical optimization since they are mostly responsible for non-detections. Decrease in calculation time can be further reached if separated blocks are identified in a preliminary analysis and the information is used for the solving the allocation problem. The crucial point of all sensor networks is that a full coverage of the system won’t be reachable and there will be a more or less long time to detection. An alarm is not actually generated until the toxic substance has passed a sensor. In this study another approach is proposed. The case of intrusion of the toxic substance by pumping against the pressure of the network will be considered. This event is considered as a “positive” leak. Leak detection methods that are normally used for the observation of pipelines are applied to the investigation of the water hammer event caused by the intrusion. Finally, conditions for the practical applicability of the method will be put up for discussion.

Positioning sensors in a water supply network is a NP–hard task. We propose three algorithms – one based on integer linear programming (ILP) and the other two based on the Greedy paradigm. We apply these algorithms to real case networks and com-pare the results of these algorithms with the results of an algorithm based on NSGA II, a genetic algorithm. We come to the conclusion that our algorithms outperform NSGA II in every single case. The algorithm based on linear integer programming may be applied as a competitor to the algorithm implemented in TEVA –SPOT (Ber-ry, 2009), while the first Greedy algorithm may replace the ILP algorithm in large networks due to its faster running time. The second Greedy algorithm approaches the question on finding those nodes which are the most sensitive to variations in pressure and are thereby ideal places to monitor the hydraulic state of a water distribution network. KEYWORDS Graph Theory, Sensor location layout, Greedy Algorithm, Genetic Algorithm, Integ-er Linear Programming, Sensitivity

Water supply utilities are increasingly being confronted with growing maintenance requirements in order to provide a reliable and cost efficient operation of the water distribution system in order to deliver high standard drinking water. One specific challenge is to find a satisfactory compromise between the contradictory objectives of saving investment cost and meeting the increasing expectations of customers. A valuable tool for the planner is reliability analysis of the system that for instance provides information about the importance of each particular pipe in determining the total reliability of the system. This information can be used to decide which pipes should be replaced next or potentially duplicated to reduce the risk of system isolation. Since structural (topological) reliability only considers the connectivity of the network a new approach for the calculation of structural hydraulic reliability is presented in this paper. The algorithmic implementation is based on a decomposition method of the network graph that greatly enhances both the calculation of pure structural reliability as well as structural hydraulic reliability.

Difficulties of simulation in existing hydraulic models arising from combinations of pressure and flow controlling devices in water distribution systems have been discussed in a number of previous papers. For instance, examples for non-convergence or wrong results of the hydraulic solver EPANET (version 2.00.10) were first published by Simpson in 1999. It may be shown that the problems were caused by a singularity of the equation system that appears if in an iteration two interacting control devices are active at the same time. In terms of graph theory the part of the network between the two active valves in this case is disconnected from the rest of the system leading to the singularity. In the new EPANET version 2.00.12 that has been released recently this problem is tackled by adding a virtual coefficient to all matrix columns and rows corresponding to nodes of active flow control valves. Mathematically this method is equivalent to adding a very small diameter pipe to the actual network in parallel to the FCV resulting in a nonsingular system. The examples of networks published by Simpson (1999) where EPANET 2.00.10 failed to converge or converged to wrong results now can be solved successfully. Nevertheless the latest release of EPANET still has difficulties in modeling of combinations of control devices. Whereas the former version of EPANET (version 2.00.10) often failed to calculate the correct valve states (active, closed, open) the problems of the new version consist of numerical inexactness that is caused by the addition of the virtual matrix terms for FCVs. In addition examples can be found where version 2.00.12 of EPANET still fails to converge.

Developing fast calibration algorithms is an important step towards the online simulation of hydraulic water networks. The ob- jective of this paper is to report a new demand calibration approach by using algorithms from control theory. We propose a multivariable PID control where the control parameters are identified by a system identification approach and the system matrix is decoupled. In this control approach the measured flow variables are regarded as dynamic set-points. The controllers use the demand values as manipulated variables in order to control the flow variables to the measured flow. The concept was applied successfully using a small test-network.

Unidirectional flushing is a technique for periodic cleaning of water supply pipes to remove deposits and may also be an important response to contamination of drinking water networks. For unidirectional flushing the defined flushing path is fed by clean water at an entrance point. The development of an efficient flushing strategy is not straight forward. The objective is to minimize the effort of operating staff. The flushing plan consists of a well- defined series of flushing actions in which the current flushing path is always connected to previously cleaned sections. The paper describes the software tool referred to as Flushing Planner.

1st International WDSA / CCWI 2018 Joint Conference, Kingston, CAN, 23-/07/2018 - 25/07/2018; International audience; In this manuscript, we consider the problem of optimally scheduling the restoration of a water distribution network with multiple failures after a disaster. The decisions made are the sequence of burst/broken pipes and leaks that need to be replaced or repaired, respectively, subject to constraints on workforce availability and physical hydraulic conditions. In order to sufficiently capture the objectives of the utility (\eg service levels, resilience loss and customer minutes lost without service), which are all pressure dependent, pressure driven leakage and demand models (PDM) are employed. The restoration decisions are modelled as time-dependent closure and opening of links and are simulated using a PDM in EPANET, propagating decisions as pressure-driven hydraulic constraints and computing a posteriori their impact on the multiple desired restoration objectives, some of which have trade-offs. The combination of discrete decisions with time-dependent couplings, and the presence of objectives that are conditional functions of demands met and time indices make it difficult to pose this optimal task scheduling problem as a standard numerically tractable mixed-integer programming problem. To make the problem tractable for the given large-scale water distribution system, we propose greedy heuristics that use a hierarchical decomposition of the decision space using structural properties of the network graph and hydraulics. Firstly, PDM simulations are used to sort the breaks and leaks from the biggest losses to the smallest, or determine visibility of the damages. In addition to solving the multi-criteria scheduling problem, we also use engineering principles to derive metaheuristic that can prioritise water loss reductions. The greedy algorithm is employed to iteratively schedule isolation and repairs by first stabilizing the system with the isolation of the biggest breaks; an alternative approach considers all objectives `equally'. With these we explore the trade-offs in response between water loss and resilience indicators. To enable the scheduling, we use graph decomposition techniques to identify the valves that need to be closed to isolate a hydraulic segment (\ie set of links sharing same closing valves) for replacement; this gives us a map (or look up table) that will be used in the scheduling. The map also includes information about the number of nodes isolated, unsatisfied demand when isolating each segment and the total pipe length of the segments. We also analyse the system flows, network pressures and how the depletion of tanks affects service levels. Using these, we make recommendations for improving the capacity of the system, including the improvement of pumping stations, installation of control valves and some pipe re-enforcement. The same greedy task scheduling algorithm is then used under these alternative network improvements, to show a much better response in all criteria.

[Departement_IRSTEA]Eaux [TR1_IRSTEA]GEUSI [ADD1_IRSTEA]Gestion intégrée de la ressource et des infrastructures; WP 1 aims at evaluating new sensors and secured sensor networks, self-learning monitoring tools, robust simulation models and vulnerability and resilience assessment tools by means of several realistic use cases. WP5 is focused on developing prototype of vulnerability and resilience assessment tools. The present work contributes to both work packages. First, the vulnerability and resilience is explained from a theoretical point of view. A simple model of Water Distribution System (WDS) facing a simple threat vignette (use case) is used throughout the document in order to illustrate the methodology. First subchapter explains general principles on system modelling and use cases definitions. The second one focusses on the vulnerability assessment; the third one is the resilience assessment. The fourth part is the tutorial detail for the resilience assessment. A questionnaire is presented in appendices for applying the methodology. Then, the use cases are described within the framework of the first part. For BWB there are three case studies: 1. Cut off of two waterworks by a regional power cut; 2. Contamination (non-pathogen bacteria) in south east of Berlin; 3. Cyber attack at control systems (stuxnet). For EMS also three case studies: 1. Main production unit stopped by major flood event; 2. Water quality degradation by intentional network contamination; 3. IT attack Oberhausbergen power plant stopped, event masked by false data (replicated data set). And for VEDIF four case studies: 1. Fire Hydrants operation in "Street Pooling" situation; 2. Terrorist attack on network in the situation of a major International Event (COP 21); 3. Centennial Flood; 4. Above Centennial Flood - Establishment of the major crisis emergency plan.

Water distribution systems are large, spatially distributed infrastructures that ensure the distribution of potable water of sufficient quantity and quality. Mathematical models of these systems are characterized by a large number of state variables and parameter. Two major challenges are given by the time constraints for the solution and the uncertain character of the model parameters. The main objectives of this thesis are thus the investigation of projection based reduced order modelling techniques for the time efficient solution of the hydraulic system as well as the spectral propagation of parameter uncertainties for the improved quantification of uncertainties. The thesis gives an overview of the mathematical methods that are being used. This is followed by the definition and discussion of the hydraulic network model, for which a new method for the derivation of the sensitivities is presented based on the adjoint method. The specific objectives for the development of reduced order models are the application of projection based methods, the development of more efficient adaptive sampling strategies and the use of hyper-reduction methods for the fast evaluation of non-linear residual terms. For the propagation of uncertainties spectral methods are introduced to the hydraulic model and an intrusive hydraulic model is formulated. With the objective of a more efficient analysis of the parameter uncertainties, the spectral propagation is then evaluated on the basis of the reduced model. The results show that projection based reduced order models give a considerable benefit with respect to the computational effort. While the use of adaptive sampling resulted in a more efficient use of pre-calculated system states, the use of hyper-reduction methods could not improve the computational burden and has to be explored further. The propagation of the parameter uncertainties on the basis of the spectral methods is shown to be comparable to Monte Carlo simulations in accuracy, while significantly reducing the computational effort., Les réseaux de distribution d’eau consistent en de grandes infrastructures réparties dans l’espace qui assurent la distribution d’eau potable en quantité et en qualité suffisantes. Les modèles mathématiques de ces systèmes sont caractérisés par un grand nombre de variables d’état et de paramètres dont la plupart sont incertains. Les temps de calcul peuvent s’avérer conséquents pour les réseaux de taille importante et la propagation d’incertitude par des méthodes de Monte Carlo. Par conséquent, les deux principaux objectifs de cette thèse sont l’étude des techniques de modélisation à ordre réduit par projection ainsi que la propagation spectrale des incertitudes des paramètres. La thèse donne tout d’abord un aperçu des méthodes mathématiques utilisées. Ensuite, les équations permanentes des réseaux hydrauliques sont présentées et une nouvelle méthode de calcul des sensibilités est dérivée sur la base de la méthode adjointe. Les objectifs spécifiques du développement de modèles d’ordre réduit sont l’application de méthodes basées sur la projection, le développement de stratégies d’échantillonnage adaptatives plus efficaces et l’utilisation de méthodes d’hyper-réduction pour l’évaluation rapide des termes résiduels non linéaires. Pour la propagation des incertitudes, des méthodes spectrales sont introduites dans le modèle hydraulique et un modèle hydraulique intrusif est formulé. Dans le but d’une analyse plus efficace des incertitudes des paramètres, la propagation spectrale est ensuite évaluée sur la base du modèle réduit. Les résultats montrent que les modèles d’ordre réduit basés sur des projections offrent un avantage considérable par rapport à l’effort de calcul. Bien que l’utilisation de l’échantillonnage adaptatif permette une utilisation plus efficace des états système pré-calculés, l’utilisation de méthodes d’hyper-réduction n’a pas permis d’améliorer la charge de calcul. La propagation des incertitudes des paramètres sur la base des méthodes spectrales est comparable aux simulations de Monte Carlo en termes de précision, tout en réduisant considérablement l’effort de calcul.