The principal partition of a pair of graphs and its applications

Ozawa, Takao

doi:10.1016/0166-218x(87)90011-4

Cited by 7 publications

(5 citation statements)

References 9 publications

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“…from demands of branched portions of the WDN), are removed from the system of Equation (1) since Q y is no longer unknown. The reason is the same as in the previous section and the choice is also supported by works of Ozawa (1986) and Carpentier & Cohen (1991, 1993 since it corresponds to the arc deletion used while studying topological observability.…”

Section: Some Q Y Are Knownmentioning

confidence: 70%

“…The scheme for the calibra- with graph manipulations adopted to study topological observability (Ozawa 1986;Carpentier & Cohen 1991, 1993; potential decomposition of the network into sub-systems that can be separately simulated with a further reduction of the simulation problem size; analysis of topological observability of the resulting components which can also be useful to draw recommendations on sampling design, consistent with the need of separately analyzing each connected graph (i.e. a single component) as in Ozawa (1986) and Carpentier & Cohen (1991, 1993.…”

Section: Wdn Model Calibration Formulationmentioning

confidence: 99%

“…Finally, Ozawa (1986), Carpentier & Cohen (1991, 1993 and Todini (1999) Ozawa (1986) and Carpentier & Cohen (1991, 1993.…”

mentioning

confidence: 99%

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Water distribution network calibration using enhanced GGA and topological analysis

Giustolisi

Berardi

2010

Journal of Hydroinformatics

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The calibration of hydraulic models of water distribution networks (WDN) is of preeminent importance for their analysis and management. 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.

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Section: Some Q Y Are Knownmentioning

confidence: 70%

Section: Wdn Model Calibration Formulationmentioning

confidence: 99%

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Water distribution network calibration using enhanced GGA and topological analysis

Giustolisi

Berardi

2010

Journal of Hydroinformatics

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“…This challenge has two dimensions: clustering of calibration data and construction of an equivalent reduced-size system for performing the calibration tasks. To accomplish meaningful calibration (i.e., determine pipe roughness coefficients and valve states) and avoid unnecessary simulations for large water distribution systems, a study of topological observability is considered to be necessary (Ozawa 1987;Carpentier and Cohen 1993;Giustolisi and Berardi 2011). In particular, a preliminary analysis of network observability (i.e., pipes, nodes, and segments), according to the available measurements, can significantly reduce the search space (roughness and valve states) while reducing the network simulation problem and, consequently, the required computational time.…”

Section: Future Research Directionsmentioning

confidence: 99%

Battle of the Water Calibration Networks

Ostfeld

Salomons²,

Ormsbee

et al. 2012

J. Water Resour. Plann. Manage.

149

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

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“…Pérez [2003] classified the identifiability as static and dynamic. Carpentier and Cohen [1991] performed the study of identifiability for the static problem using graph analysis based on Ozawa [1987]. The idea is that some operations in graphs are equivalent to operation on equations.…”

Section: Identifiabilitymentioning

confidence: 99%

Demand modeling for water networks calibration and leak localization

Sanz Estapé

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The success in the application of any model-based methodology (e.g. design, control, supervision) highly depends on the availability of a well calibrated model. There is no best or unique solution for the calibration problem as the methodologies are developed depending on which parameters have to be calibrated and the final use of the model. The main objective in this thesis is to develop an adaptive water distribution network model which both calibrates its demands online and discerns between faults and system evolution. The calibration is focused on demands due to their daily variability and continuous evolution. The singular value decomposition is a powerful tool for solving the optimization problem. Additionally, the deep understanding of this tool allows to redefine the demand model. A novel demand model is proposed, where each individual demand is defined as a combination of demand components. These demand components are calibrated demand multipliers that represent the behavior of nodes in a determined geographical zone. The membership of each nodal demand to every demand component is produced naturally through the analysis of the singular value decomposition of the sensitivity matrix. The same analysis is also used to define the location of sensors for the calibration. The calibration in water distribution networks needs to be performed online due to the continuous evolution of demands. During the calibration process, background leakages or bursts can be unintentionally incorporated to the demand model and treated as a system evolution (change in demands). To solve that, a leak detection and localization approach to be coupled with the calibration methodology that identifies geographically distributed parameters is proposed. The approach consists in comparing the calibrated parameters with their historical values to assess if changes in these parameters are caused by a system evolution or by the effect of leakage. The geographical distribution allows to associate an unexpected behavior of the calibrated parameters (e.g. abrupt changes, trends, etc.) to a specific zone in the network. The set of methods proposed are exemplified through an academic dummy network to help the reader completely understand their fundamentals. Furthermore, three real water distribution networks situated in Barcelona and Castelldefels are used to evaluate the performance of the whole method with real systems and real data. The good results obtained show the potential of the developed method and the viability of the real-time calibration and leak detection and localization processes. L'èxit en l'aplicació de qualsevol metodologia basada en models (p. ex. disseny, control, supervisió) depèn, en gran part, de la disponibilitat d'un model ben calibrat. No hi ha una solució única o global per aquest problema, ja que les metodologies es desenvolupen en funció de l'ús final del model. L'objectiu principal d'aquesta tesi és desenvolupar un model adaptatiu per xarxes de distribució d'aigua que calibri les seves demandes de forma online mentre distingeix entre fallades i evolució del sistema. La calibració es centra en les demandes degut a la seva variabilitat diària i a la seva evolució continua. La descomposició en valors singulars és una eina molt potent per resoldre problemes d'optimització. Addicionalment, la comprensió detallada d'aquesta eina permet redefinir el model de demandes. Es proposa un model de demandes innovador, on cada demanda individual es defineix com una combinació de components de demanda. Aquests components de demanda són multiplicadors de demanda que han estat calibrats, i que representen el comportament dels nodes en una zona geográfica determinada. La pertinença de cada demanda nodal a cadascun dels components de demanda es produeix de forma natural mitjanant l'anàlisi de la descomposició en valors singulars de la matriu de sensibilitat. El mateix anàlisi també s'utilitza per definir la localització dels sensors per la calibració. La calibració en xarxes de distribució d'aigua s'ha de realitzar en línia, ja que les demandes evolucionen contínuament. Durant el procés de calibració, les fuites latents o espontànies poden ser incorporades involuntàriament al model de demanda, i ser tractades com una evolució del sistema (canvi en les demandes). Per solucionar-ho, es proposa un mètode de detecció i localització de fuites que s'acobla a la metodologia de calibració que identifica components de demanda geogràfics. El mètode proposat consisteix en comparar els paràmetres calibrats amb els seus valors històrics per valorar si els canvis en aquests paràmetres es deuen a una evolució del sistema, o a l'efecte de les fuites. La distribució geogràfica permet associar un comportament no esperat dels paràmetres calibrats (p. ex. canvis sobtats, tendències, etc.) a una zona específica de la xarxa. El conjunt de mètodes proposats s'ha exemplificat mitjanant una xarxa acadèmica molt simple per ajudar al lector a entendre completament els seus fonaments. A més a més, s'han utilitzat tres xarxes de distribució d'aigua situades a Barcelona i Castelldefels per avaluar el funcionament del mètode complet amb sistemes i dades reals. Els bons resultats obtinguts mostren el potencial de la metodologia desenvolupada i la viabilitat de la calibració de demandes i detecció i localització de fuites en temps real.

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The principal partition of a pair of graphs and its applications

Cited by 7 publications

References 9 publications

Water distribution network calibration using enhanced GGA and topological analysis

Water distribution network calibration using enhanced GGA and topological analysis

Battle of the Water Calibration Networks

Demand modeling for water networks calibration and leak localization

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