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.
Water distribution systems (WDS) are complex pipe networks with looped and branching topologies that often comprise of thousands to tens of thousands of links and nodes. This work presents a generic framework for improved analysis and management of WDS by partitioning the system into smaller (almost) independent sub-systems with balanced loads and minimal number of interconnection. This paper compares the performance of three classes of unsupervised learning algorithms from graph theory for practical sub-zoning of WDS: (1) Global clustering -a bottom-up algorithm for clustering n objects with respect to a similarity function, (2) Community structure -a bottom-up algorithm based on network modularity property, which is a measure of the quality of network partition to clusters versus randomly generated graph with respect to the same nodal degree, and (3) Graph partitioning -a flat partitioning algorithm for dividing a network with n nodes into k clusters, such that the total weight of edges crossing between clusters is minimized and the loads of all the clusters are balanced. The algorithms are adapted to WDS to provide a practical decision support tool for water utilities. Visual qualitative and quantitative measures are proposed to evaluate models' performance. The proposed methods are applied and results are evaluated and compared for two large-scale water distribution systems serving heavily populated areas in Singapore.
This paper focuses on the optimal sensor placement problem for the identification of pipe failure locations in large-scale urban water systems. The problem involves selecting the minimum number of sensors such that every pipe failure can be uniquely localized. This problem can be viewed as a minimum test cover (MTC) problem, which is NP-hard. We consider two approaches to obtain approximate solutions to this problem. In the first approach, we transform the MTC problem to a minimum set cover (MSC) problem and use the greedy algorithm that exploits the submodularity property of the MSC problem to compute the solution to the MTC problem. In the second approach, we develop a new augmented greedy algorithm for solving the MTC problem. This approach does not require the transformation of the MTC to MSC. Our augmented greedy algorithm provides in a significant computational improvement while guaranteeing the same approximation ratio as the first approach. We propose several metrics to evaluate the performance of the sensor placement designs. Finally, we present detailed computational experiments for a number of real water distribution networks.
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