Zur hydraulischen Systemanalyse von Wasserversorgungsnetzen [online]

Kurzfassung Städtische Wasserversorgungssysteme stellen einen komplexen Bestandteil der technischen Infrastruktur dar. In den vergangenen Jahrzehnten fand, bedingt durch die Verbreitung immer leistungsfähigerer Rechenanlagen, eine rasante Entwicklung unterschiedlicher mathematischer Modelle auf dem Gebiet der Systemanalyse städtischer Druckrohrnetze statt. Die Haupteinsatzbereiche können grob in Entwurf kostenoptimaler Netze bei Neuplanung und Erweiterung, Simulation des täglichen Betriebs und Kalibrierung der mathematischen Abbildung eingeteilt werden. Dabei lassen sich keine klaren Abgrenzungen vornehmen, besonders Methoden der beiden zuletzt genannten gehen teilweise nahtlos ineinander über. Im Rahmen dieser Arbeit steht die Simulation des stationären Fließzustandes im Mittelpunkt der Betrachtung. Beschleunigungseffekte sind wegen der geringen Fließgeschwindigkeit in städtischen Wasserversorgungssystemen zu vernachlässigen, \u27dynamische\u27 Berechnungen (Simulation des zeitabhängigen Betriebs) finden als Sequenz einzelner stationärer Simulationsrechnungen statt. Reale Wasserversorgungsnetze beinhalten eine Vielzahl unterschiedlicher Armaturen, die der Kontrolle und Steuerung dienen. Ihr Einsatz reicht von Rehabilitation defekter Netzteile über den energiesparenden Betrieb der Anlagen und Minimierung von Leckageverlusten bis zur optimierten Datenerhebung in Messkampagnen zur Mängelidentifikation und Kalibrierung. Mit Bezug auf die Durchführung stationärer Simulationsrechnungen lässt sich das hydraulische Verhalten der Anlagen drei Gruppen zuordnen: i) Hydraulisches Verhalten und Betriebszustand vor Simulation bekannt, ii) hydraulisches Verhalten bekannt, Betriebszustand vor Simulation unbekannt, iii) Betriebszustand und hydraulisches Verhalten vor Simulation unbekannt (Anlagen mit Rückkoppelung). Es werden, zunächst ohne Berücksichtigung der oben genannten Kontrollarmaturen, die zur Beschreibung des stationären Fließzustandes notwendigen Gleichgewichtsbedingungen angegeben (synthetische Methode). Danach wird eine alternative Vorgehensweise, deren Ziel die Herleitung eines äquivalenten mathematischen Modells, das zweckmäßig die Form einer Optimierungsaufgabe besitzt, besprochen (analytische Methode). Der Vorteil der zweiten Variante liegt in der Möglichkeit, Existenz- und Eindeutigkeitsaussagen treffen zu können, des Weiteren sind Sensitivitätssätze und Algorithmen aus der Optimierung auf das Problem anwendbar. Das entwickelte Modell besitzt die Gestalt einer konvexen, nichtlinearen Minimierungsaufgabe ohne Nebenbedingungen (Minimierung des System-\u27Content\u27). Es gibt den Stand der mathematischen Entwicklungen auf dem Gebiet der analytischen Methoden in der stationären Flussberechnung von vermaschten Druckrohrnetzen wieder und gestattet die Berücksichtigung von Behältern, Drosselklappen und Pumpen mit gegebener Formulierung des hydraulischen Verhaltens. Im nächsten Schritt werden Kontrollarmaturen nach Punkt i) und ii) eingeführt. Als Konsequenz kommen lineare Gleichungs- und Ungleichungsnebenbedingungen hinzu. Die mathematische Umgebung des Aufgabengebietes werden definiert und allgemeine Bedingungen an die hydraulischen Beziehungen der Systemelemente formuliert, welche hinreichend für die Konvexität der Aufgabe sind. Diese Erweiterung des mathematischen Modells gestattet die Berücksichtigung von Durchflusskontrollschiebern, Rückflussverhinderungsventilen, zeitweise geschlossenen Schiebern, aber auch die realistische Simulation unterschiedlicher Systemmängel wie druckabhängige Leckagen und unzureichende Versorgung. Die Anwendung von Sensitivitätssätzen der Nichtlinearen Programmierung liefert Aussagen über die Änderung der Systemvariablen infolge von Parameteränderungen. In realen Versorgungssystemen finden zusätzlich Armaturen nach Typ iii) Anwendung, deren hydraulisches Verhalten über Rückkoppelung zwischen Steuerparameter und Systemvariable - in der vorliegenden Anwendung über den Druck an gegebener Stelle im Netz - bestimmt ist. Bisher war kein geschlossenes mathematisches Modell bekannt, welches die Berücksichtigung dieser Anlagen gestattete. Ein rigoroser Beweis der Eindeutigkeit von Systemzuständen stand aus. Unter diese Kategorie fallen z.B. Druckminderungsventile (PRVs), die selbsttätig (ohne Fremdenergie) den Prozess über eine Sollwertfeder regeln. Das Gleichgewicht, das sich zwischen der Feder und dem Wasserdruck einstellt, wird hier als Minimierungsproblem eines hydrostatischen Potenzials formuliert. Insgesamt ist der stationäre Punkt durch die Lösungen der sich gegenseitig beeinflussenden Minimierungsprobleme des hydrostatischen Potenzials und des System-\u27Content\u27 beschrieben. Im Rahmen dieser Arbeit wird der Versuch unternommen, das sogenannte Nash-Konzept der Spieltheorie auf ein technisches Problem anzuwenden. Notwendige und hinreichende Bedingungen für die Eindeutigkeit eines Gleichgewichts werden gegeben. Die Eindeutigkeit der Lösung ermöglicht Aussagen über Parametersensitivitäten entsprechend denen der Nichtlinearen Optimierung. Schließlich werden Beispiele für Anwendungsmöglichkeiten des entwickelten Modells gegeben und der Einsatz innerhalb des Kalibrierungsprozesses zur Modelleichung oder Mängelanalyse skizziert. Abstract Water supply networks represent an important part of the urban technical infrastructure. As a consequence of the capacity increase of personal computers over the last decades, also research and development of water supply network systems analysis was enhanced. This refers, in particular, to specific areas such as Network design optimization including rehabilitation and extension, Simulation of the daily operation and Calibration of simulation models. A distinct separation of those subject areas is difficult to define, especially, the two last mentioned subjects are related and intertwine. This study is to focus upon the simulation of the steady state in reticulate water supply networks. Non-steady state hydraulics are not considered due to the existing low velocities in water supply networks. Time extended analysis is taken into account by assuming a sequence of steady state approximations. In reality, water supply networks contain a multitude of control devices. The objectives of their application vary from supporting rehabilitation of deficient network components, working towards energy-saving, helping with leak detection and control, data collection, allocation of gauging points for model calibration, etc. Three categories may be identified as to the hydraulics of those control devices: i) hydraulics and operating state are known prior to simulation ii) hydraulics are known, operating state is unknown prior to simulation iii) hydraulics and operating state are unknown prior to simulation (feedback devices). In this study, first, without referring to specific devices, the equilibrium conditions of the steady state are described for a reticulate system (synthesis approach). Second, an alternative approach is discussed representing an equivalent mathematical model formulated as an optimization problem (analysis approach). This second approach offers the advantage to answering questions as to the existence and uniqueness of the hydraulic equilibrium. Also, available optimization algorithms can be applied, sensitivity analyses can be conducted. The resulting model turns out to be a convex nonlinear minimization problem without constraints (minimization of the \u27system-content\u27). It reflects the state of the art of analytical methods with respect to the definition of sufficient and necessary conditions of the hydraulic equilibrium of reticulate pipe networks, allowing to include control devices like tanks, throttle control valves and pumps with known hydraulics. The subsequent step of this study is devoted to including control devices of type i) and ii). Thus, linear equality and inequality constraints are added to the model, and the concept of sub-gradients is introduced. The resulting mathematical framework of the problem is analyzed yielding, again, general necessary and sufficient conditions required to define convexity of the problem. This extension of the model allows to account for control valves, check valves, temporary closed valves. Simulation of certain system\u27s deficiencies, e.g. of pressure dependent leakage and intermittend supply, is made possible. Sensitivity analyses via Parametric Nonlinear Programming can be employed to assess the impact of parameter changes upon systems variables. The final section of the study treats devices of type iii) whose hydraulic behaviour is characterised by a feedback between control parameters and systems variables, the latter being, e.g., the pressure at given points of the network. So far, a mathematical approach was not available to include these devices. A rigorous proof of the uniqueness of resulting system states had not been derived. An example of this category are pressure reducing valves (PRVs) operated \u27self-acting\u27 by a set-value spring. It is shown that the equilibrium between spring force and water pressure can be formulated as a minimzation problem of a hydrostatic potential. The equilibrium point is reached by solving mutually interacting minimization problems of the hydrostatic potential and the \u27system-content\u27. The approach applies the so called Nash-concept of Game Theory to a technical system. This way, again, necessary and suÆcient conditions for uniqueness of the hydraulic equilibrium are determined. The model also delivers parameter sensitivities as a result of uniqueness of the Nash-equilibrium according methods of Parametric Nonlinear Programming. Examples of model application are presented, eventually, and special reference is given to the model\u27s capacity in the realm of network deciency analysis and network calibration

Lessons Learned In Solving The Contaminant Source Identification In An Online Context

Protection of Water Distribution Networks (WDNs) against contamination events has a paramount importance. Either deliberate or accidental contamination of these infrastructures has strong negative consequences from both social and economical point of view. The project SMaRT-OnlineWDN aimed to develop methods and software solutions 1) to detect contamination from non-specific sensors, 2) to maintain an online water quantity and water quality model that is reliable and 3) to use the past model predictions to backtrack the potential sources of contaminations. For source identification, is more reliable velocities from an historical data base a substantial advantage compared to offline velocity predictions? The aim of this paper is to answer to this question and to report the main findings in the SMaRT-OnlineWDN project for contaminant source identification in an online context. The problem of source identification consists in determining the location and duration of a contamination taking into account sensor responses. Our solution is a two-step enumeration/exploration method. Firstly, we solve the transport equation in reverse time for enumeration of the potential solutions. This is made independent of the reaction kinetics of particular substances. The known boundary conditions are the responses of sensors that count the successive contaminant fronts arriving at each sensor. In the second exploration step a probability calculation for ranking of the candidate solutions is proposed with two general stochastic methods (minimum relative entropy or least squares methods). An extensive use of simplification methods is carried on both temporally and spatially on the dynamic graph. A sensitivity analysis is made with regards to the demand uncertainty. Results on real networks in France and Germany are presented

SMaRT-OnlineWDN: A Franco-German Project For The Online Security Management Of Water Distribution Networks

Water Distribution Networks (WDNs) are critical infrastructures that are exposed to deliberate or accidental chemical, biological or radioactive contamination which need to be detected in due time. However, until now, no monitoring system is capable of protecting a WDN in real time. Powerful online sensor systems are currently developed and the prototypes are able to detect a small change in water quality. In the immediate future, water service utilities will install their networks with water quantity and water quality sensors. For taking appropriate decisions and countermeasures, WDN operators will need to dispose of: 1) a fast and reliable detection of abnormal events in the WDNs; 2) reliable online models both for the hydraulics and water quality predictions; 3) methods for contaminant source identification backtracking from the data history. Actually, in general none of these issues (1) – (3) are available at the water suppliers. Consequently, the main objective of the project SMaRT-OnlineWDN is the development of an online security management toolkit for WDNs that is based on sensor measurements of water quality as well as water quantity. Its main innovations are the detection of abnormal events with a binary classifier of high accuracy and the generation of real-time, reliable (i) flow and pressure predictions, (ii) water quality indicator predictions of the whole water network. Detailed information regarding contamination sources (localization and intensity) will be explored by means of the online running model, which is automatically calibrated to the measured sensor data. Its field of application ranges from the detection of deliberate contamination including source identification and decision support for effective countermeasures to improved operation and control of a WDN under normal and abnormal conditions (dual benefit).In this project, the technical research work is completed with a sociological, economical and management analysis

Adaptive Modeling Of Water Supply Networks For Improved Practical Applicability Of Hydraulic Online-Simulation

Online-Simulation of water distribution networks allows for estimating the current state of the entire network in near real-time. Measurement data coming from sensors at selected positions in the real network are used for driving a mathematical simulation model. Therefore the information gained from the measurements is extended and covers the whole system. As part of online monitoring or decision support systems online-simulations have multiple applications in operations and control of water supply networks. Although sensors and techniques for data transfer as well as mathematical simulation techniques are highly developed the practical applicability of online-simulations for decision support in large networks still suffers from the high time requirements for the whole cycle of measurement data updates, simulation and post-processing. One common approach to tackle this problem is the aggregation of the underlying models. However, for some applications like contaminant source identification the information that is lost can be crucial for the reliability of the decisions that are made based on the online-simulation results. In order to enhance online calculations and to improve the practical applicability of large online simulation models an adaptive calculation framework has been developed that allows for running the model with different levels of accuracy but using all one and the same data base. For each problem an adequate level of accuracy is chosen. Higher functions like source identification or optimisation algorithms that require a number of extra simulations can be focused on selected regions of the network. For the subnetwork in question detailed data are used whereas the rest of the system is omitted or, if necessary, considered with a lower level of accuracy. The framework is based on topological analysis and decomposition of the network graph. The paper describes the basic concepts and demonstrates its applicability by means of contaminant source identification

A Gradient-Type Method For Real-Time State Estimation Of Water Distribution Networks

Drinking water distribution networks risk exposure to malicious or accidental contamination. Several levels of responses are conceivable. One of them consists to install a sensor network to monitor the system on real time. Once a contamination has been detected, this is also important to take appropriate counter-measures. In the SMaRT-OnlineWDN project, this relies on modeling to predict both hydraulics and water quality. An online model use makes identification of the contaminant source and simulation of the contaminated area possible. The objective of this paper is to present SMaRT-OnlineWDN experience and research results for hydraulic state estimation with sampling frequency of few minutes. A least squares problem with bound constraints is formulated to adjust demand class coefficient to best fit the observed values at a given time. The criterion is a Huber function to limit the influence of outliers. A Tikhonov regularization is introduced for consideration of prior information on the parameter vector. Then the Levenberg-Marquardt algorithm is applied that use derivative information for limiting the number of iterations. Confidence intervals for the state prediction are also given. The results are presented and discussed on real networks in France and Germany

Modeling the Behavior of Flow Regulating Devices in Water Distribution Systems Using Constrained Nonlinear Programming

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. © 2009 ASCE.Jochen W. Deuerlein, Angus R. Simpson and Stephan Demp

Battle of Postdisaster Response and Restoration

[EN] 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. 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Kingston Canada: Open Journal Systems.Castro-Gama M. C. Quintiliani and S. Santopietro. 2018. “After earthquake post-disaster response using a many-objective approach a greedy and engineering interventions.” In Proc. 1st Int. WDSA/CCWI 2018 Joint Conf. 14. Kingston Canada: Open Journal Systems.Cimellaro, G. P., Tinebra, A., Renschler, C., & Fragiadakis, M. (2016). New Resilience Index for Urban Water Distribution Networks. Journal of Structural Engineering, 142(8). doi:10.1061/(asce)st.1943-541x.0001433Cover, T., & Hart, P. (1967). Nearest neighbor pattern classification. IEEE Transactions on Information Theory, 13(1), 21-27. doi:10.1109/tit.1967.1053964Creaco, E., Franchini, M., & Alvisi, S. (2010). Optimal Placement of Isolation Valves in Water Distribution Systems Based on Valve Cost and Weighted Average Demand Shortfall. Water Resources Management, 24(15), 4317-4338. doi:10.1007/s11269-010-9661-5Deb, K., Mohan, M., & Mishra, S. (2005). Evaluating the ε-Domination Based Multi-Objective Evolutionary Algorithm for a Quick Computation of Pareto-Optimal Solutions. Evolutionary Computation, 13(4), 501-525. doi:10.1162/106365605774666895Deuerlein J. D. Gilbert E. Abraham and O. Piller. 2018. “A greedy scheduling of post-disaster response and restoration using pressure-driven models and graph segment analysis.” In Proc. 1st Int. WDSA/CCWI 2018 Joint Conf. 14. Kingston Canada: Open Journal Systems.Deuerlein, J. W. (2008). Decomposition Model of a General Water Supply Network Graph. Journal of Hydraulic Engineering, 134(6), 822-832. doi:10.1061/(asce)0733-9429(2008)134:6(822)Di Nardo, A., Di Natale, M., Giudicianni, C., Santonastaso, G. F., & Savic, D. (2018). Simplified Approach to Water Distribution System Management via Identification of a Primary Network. Journal of Water Resources Planning and Management, 144(2), 04017089. doi:10.1061/(asce)wr.1943-5452.0000885Eliades D. G. M. Kyriakou S. Vrachimis and M. M. Polycarpou. 2016. “EPANET-MATLAB toolkit: An open-source software for interfacing EPANET with MATLAB.” In Proc. 14th Int. Conf. on Computing and Control for the Water Industry (CCWI) 8. The Hague The Netherlands: International Water Conferences. https://doi.org/10.5281/zenodo.831493.Fragiadakis, M., Christodoulou, S. E., & Vamvatsikos, D. (2013). Reliability Assessment of Urban Water Distribution Networks Under Seismic Loads. Water Resources Management, 27(10), 3739-3764. doi:10.1007/s11269-013-0378-0Gilbert, D., Abraham, E., Montalvo, I., & Piller, O. (2017). Iterative Multistage Method for a Large Water Network Sectorization into DMAs under Multiple Design Objectives. Journal of Water Resources Planning and Management, 143(11), 04017067. doi:10.1061/(asce)wr.1943-5452.0000835Hill, D., Kerkez, B., Rasekh, A., Ostfeld, A., Minsker, B., & Banks, M. K. (2014). Sensing and Cyberinfrastructure for Smarter Water Management: The Promise and Challenge of Ubiquity. 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B. 1967. “Some methods for classification and analysis of multivariate observations.” In Vol. 1 of Proc. 5th Berkeley Symp. on Mathematical Statistics and Probability 281–297. Berkeley: University of California Press.Mahmoud, H. A., Kapelan, Z., & Savić, D. (2018). Real-Time Operational Response Methodology for Reducing Failure Impacts in Water Distribution Systems. Journal of Water Resources Planning and Management, 144(7), 04018029. doi:10.1061/(asce)wr.1943-5452.0000956Meng, F., Fu, G., Farmani, R., Sweetapple, C., & Butler, D. (2018). Topological attributes of network resilience: A study in water distribution systems. Water Research, 143, 376-386. doi:10.1016/j.watres.2018.06.048Ostfeld, A., Uber, J. G., Salomons, E., Berry, J. W., Hart, W. E., Phillips, C. A., … Walski, T. (2008). The Battle of the Water Sensor Networks (BWSN): A Design Challenge for Engineers and Algorithms. Journal of Water Resources Planning and Management, 134(6), 556-568. doi:10.1061/(asce)0733-9496(2008)134:6(556)Paez D. Y. Filion and M. Hulley. 2018a. “Battle of post-disaster response and restoration (BPDRR)—Problem description and rules.” Accessed June 14 2019. https://www.queensu.ca/wdsa-ccwi2018/problem-description-and-files.Paez, D., Suribabu, C. R., & Filion, Y. (2018). Method for Extended Period Simulation of Water Distribution Networks with Pressure Driven Demands. Water Resources Management, 32(8), 2837-2846. doi:10.1007/s11269-018-1961-1Salcedo C. A. Aguilar P. Cuero S. Gonzalez S. Muñoz J. Pérez A. Posada J. Robles and K. Vargas. 2018. “Determination of the hydraulic restoration capacity of b-city involving a multi-criteria decision support model.” In Proc. 1st Int. WDSA/CCWI 2018 Joint Conf. 14. Kingston Canada: Open Journal Systems.Santonastaso G. F. E. Creaco A. Di Nardo and M. Di Natale. 2018. “Post-disaster response and restauration of B-town network based on primary network.” In Vol. 1 of Proc. 1st Int. WDSA/CCWI 2018 Joint Conf. Kingston Canada: Open Journal Systems.Sophocleous S. E. Nikoloudi H. A. Mahmoud K. Woodward and M. Romano. 2018. “Simulation-based framework for the restoration of earthquake-damaged water distribution networks using a genetic algorithm.” In Proc. 1st Int. WDSA/CCWI 2018 Joint Conf. 14. Kingston Canada: Open Journal Systems.Sweetapple C. F. Meng R. Farmani G. Fu and D. Butler. 2018. “A heuristic approach to water network post-disaster response and restoration.” In Proc. 1st Int. WDSA/CCWI 2018 Joint Conf. 14. Kingston Canada: Open Journal Systems.Tabucchi, T., Davidson, R., & Brink, S. (2010). Simulation of post-earthquake water supply system restoration. Civil Engineering and Environmental Systems, 27(4), 263-279. doi:10.1080/10286600902862615Taormina, R., Galelli, S., Tippenhauer, N. O., Salomons, E., Ostfeld, A., Eliades, D. G., … Ohar, Z. (2018). Battle of the Attack Detection Algorithms: Disclosing Cyber Attacks on Water Distribution Networks. Journal of Water Resources Planning and Management, 144(8), 04018048. doi:10.1061/(asce)wr.1943-5452.0000969Walski, T. M. (1993). Water distribution valve topology for reliability analysis. Reliability Engineering & System Safety, 42(1), 21-27. doi:10.1016/0951-8320(93)90051-yWang, Y., Au, S.-K., & Fu, Q. (2010). Seismic Risk Assessment and Mitigation of Water Supply Systems. Earthquake Spectra, 26(1), 257-274. doi:10.1193/1.3276900Yoo, D. G., Kang, D., & Kim, J. H. (2016). Optimal design of water supply networks for enhancing seismic reliability. Reliability Engineering & System Safety, 146, 79-88. doi:10.1016/j.ress.2015.10.001Zhang Q. F. Zheng K. Diao B. Ulanicki and Y. Huang. 2018. “Solving the battle of post-disaster response and restauration (BPDRR) problem with the aid of multi-phase optimization framework.” In Proc. 1st Int. WDSA/CCWI 2018 Joint Conf. 14. Kingston Canada: Open Journal Systems

SMaRT-OnlineWDN D5.3 : Concept pour la paramétrisation du modèle de simulation temps réel

The proper estimation and regular update of model parameters is crucial for the actuality of a mathematical simulation representing the hydraulics and water quality of 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 behaviour of the real system. Therefore, adequate techniques for data acquisition, maintenance and update of model parameters have to be developed. In what follows the process of choosing the parameters of the mathematical model will be called "parameterization". The parameterization consists of two steps. In the first (offline) step the components that are important for drawing a reliable picture of the real system are identified including: pipes and their characteristics, network topology, nodal elevations, control devices and pumps and their physical properties and operational modes, location of valves and hydrants and the customers including average consumption (normally retrieved from the billing system. Measurement data of the past are typically used for a first offline calibration of model parameters. In the second (online) step the model is confronted with "live" data from the SCADA system. In this context, the measurements and operational states of devices are subdivided into three groups. The first group includes operational states of devices (valves states, rpm of pumps) that can be directly transferred to the corresponding parameter of the model. The second group concerns measurements that are used as boundary conditions in the model like tank inflows and water levels. Group one and two are the driving parameters of the model. The third group consist of measurements that can be used only indirectly for the online calibration of the model (see task 4). Examples are pressure heads at nodes and zone inflows that are used for adjusting the parameters that cannot be observed directly and are subject to uncertainty like demand values. An additional differentiation between the measurements can be done by distinguishing water quality sensors from hydraulic measurements. The objective of this document is to clarify which parameters belong to which group and the impact on calculation results and calibration needs. The paper starts with an introduction where the difference between model parameters and state variables of three technical systems (race car, bridge and supply system) is discussed. In the next chapter, firstly, the mathematical model of hydraulic slow transient calculations is introduced and, secondly, the model parameters and state variables are discussed from both, a mathematical perspective as well as practical considerations like acquisition of relevant data, update cycles and integration of the processes within the utilities operative task. The third chapter describes a three-step procedure for model simplification that is based on the decomposition of the network graph. The method can assist in the implementation of a model with the most appropriate level of detail for the online simulation application. As an alternative to non-reversible aggregation the approach can be also used for adaptive modelling. That means that based on a very detailed all pipe model simplified views on the system can be derived in real-time

Rapport livrable ResiWater D4.1 : Modélisation des appareils de régulation stable et robuste

This report describes different methods for modelling of pressurized water supply networks with consideration of pressure dependent demands (PDM: Pressure Driven Modelling) in combination with flow constraints. For that purpose, the PDM model described in D 4.1 is extended by additional bounds for the link flows that refer to closed or failed links (equality conditions) and the operation of more sophisticated and automated flow control devices such as check valves and flow control valves (inequality constraints). In contrast to the pure PDM model where the proof of the Linear Constraint Qualification (LICQ) to hold was simple (only assumption is connectivity of the network) the same is not true for general flow bounded problems. A simple example is given by the case where two valves are closed in a path disconnecting at least one node from the rest of the system. If the disconnected node is a demand node then in DDM the problem would have no solution. In contrast, PDM allows to reduce the outflow to zero such that a solution exists. Adding the two flow constraints with q = 0 for the closed valves to the continuity equation results in linear dependency of the constraints, which in turn leads to a singular Jacobian. Because of the singularity, there is non-uniqueness of equation, with infinity of solutions for nodal heads and minor losses of active flow control devices (the Lagrangian multipliers associated with the problem constraints). In this report, it will be shown that almost all problems of non- convergence are related to the problem of linear dependent constraints and the resulting singularity of the system. Consequently, the central problem of the robust solver is the prevention of linear dependent constraints or the derivation of methods that deal explicitly with non-unique multipliers. The content of the deliverable is as follows. After a brief introduction that summarizes the problem of modelling disconnected systems a relevant Literature about flow and pressure control modelling in hydraulic system analysis is reviewed. In the main part the extended PDM model for flow controlled problems is derived and the appearance of non-unique pressure heads is discussed, Then, different approaches for avoiding singularities in the network equations are summarized and compared as to their robustness, efficiency and practical applicability