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In this study, a general framework integrating a data-driven estimation model with sequential probability updating is suggested for detecting quality faults in water distribution systems from multivariate water quality time series. The method utilizes artificial neural networks (ANNs) for studying the interplay between multivariate water quality parameters and detecting possible outliers. The analysis is followed by updating the probability of an event, initially assumed rare, by recursively applying Bayes' rule. The model is assessed through correlation coefficient (R(2)), mean squared error (MSE), confusion matrices, receiver operating characteristic (ROC) curves, and true and false positive rates (TPR and FPR). The product of the suggested methodology consists of alarms indicating a possible contamination event based on single and multiple water quality parameters. The methodology was developed and tested on real data attained from a water utility.

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[1] The objective of the least cost design problem of a water distribution system is to find its minimum cost with discrete diameters as decision variables and hydraulic controls as constraints. The goal of a robust least cost design is to find solutions which guarantee its feasibility independent of the data (i.e., under model uncertainty). A robust counterpart approach for linear uncertain problems is adopted in this study, which represents the uncertain stochastic problem as its deterministic equivalent. Robustness is controlled by a single parameter providing a trade-off between the probability of constraint violation and the objective cost. Two principal models are developed: uncorrelated uncertainty model with implicit design reliability, and correlated uncertainty model with explicit design reliability. The models are tested on three example applications and compared for uncertainty in consumers' demands. The main contribution of this study is the inclusion of the ability to explicitly account for different correlations between water distribution system demand nodes. In particular, it is shown that including correlation information in the design phase has a substantial advantage in seeking more efficient robust solutions.Citation: Perelman, L., M. Housh, and A. Ostfeld (2013), Robust optimization for water distribution systems least cost design, Water Resour. Res., 49,[6795][6796][6797][6798][6799][6800][6801][6802][6803][6804][6805][6806][6807][6808][6809]