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To increase the performance, quality and reliability of water distribution systems, implementing efficient computational and algorithmic techniques, has become a major tasks in hydraulic modelling. Examples can be found in online condition monitoring, real time control applications, or model based leakage detection and location approaches, etc. All these techniques require extensive hydraulic simulations. Well known and trusted hydraulic simulation tools like EPANET, etc. are deployed within the individual task specific code using provided interface routines. The flow dependent friction models of hydraulic systems require an iterative solution strategy to solve the problem. Although this is done efficiently using Newton-Raphson methods, the simulation output provided by those tools is limited to raw information (i.e. flow and head). Yet the superior algorithms often require more information than the raw output. I.e. gradient based optimization methods rely on derivative information. In this paper we report on a hydraulic small signal model which can be directly derived from the output of the hydraulic simulation tool itself. The model provides cheap computational access to internal information like gradients, sensitivity, etc. of the hydraulic simulation. The ATCA equilibrium structure of the model is numerically suitable and provides properties like a positive definite stiffness matrix enabling the efficient use of direct solvers like Cholesky decomposition. Further, the symmetry provides the property of self adjointness which enables the efficient use of Greens functions. We will present how the model can be assembled from the raw simulator output and present how to use it as linear approximation, for the computation of search directions in gradient based optimization schemes, for sensitivity analysis, as well as for the computation of covariance propagation due to uncertain demands.


Session S1-03, Special Symposium: Real-time State Estimation in Urban Water Systems



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