Dual Model for Leak Detection and Localization

International audience; In this work, we employ a hierarchical approach for leak diagnosis, where time series analysis of AMR data, demand models and measured flows is first used for demand calibration. In the next step, efficient mathematical optimisation is used to calibrate the pipe roughnesses and valve statuses and update the network data. Finally, the calibrated water network model is employed to first build a dual hydraulic network representation for the combined sensor & water systems, simulation of which provide a first estimate for the leak's size and location. This dual network is then used to (i) detect the start time of the leaks as well as (ii) to compute analytical sensitivities and the Pearson correlation for pressure residuals, which allow further localisation of leaks. This whole process of leak diagnosis and localisation scales well as the dual network size is of the same order as the original network, analytical derivations are used for computing sensitivities, and a fast and stable least squares method is used for calibration and valve status assessment. Demand calibration Data from the 82 AMRs in Area C was used to develop a demand model for the unmeasured customers within the L-town network. Additionally, a virtual inflow measurement of Area C has been constructed from the pump flow measurements and the tank's water level. This virtual inflow was used to (i) validate the demand model and to (ii) estimate the leak outflow in Area C. Various time series models were tested on the AMRs aiming to extract daily and weekly seasonalities and trend components for the different customer types (Residential, Commercial). For both customer types, best performance was achieved with a rather simple model, consisting of a multiplicative superposition of weekly seasonalities (S(t)), a time varying trend (T(t)) and a random component (R(t)) accounting for stochastic variations and measurement noise: where " is the base demand for the corresponding customer type at the measurement node. Subsequently, the time varying demand at each unmeasured location is inferred with this model according to the base demand in the EPANET file. The seasonal and the trend components are shown in Figure 1.