A proposal of optimal sampling design using a modularity strategy

Real water distribution networks (WDNs) are composed of thousands nodes and optimal placement of pressure and flow observations is a relevant issue for different management tasks. The monitoring system of WDNs has been traditionally conceived as a mean to ensure model calibration of hydraulic networks in terms of assessing pipe hydraulic resistances. Nowadays, water utilities are mostly interested in system monitoring, allocating budget for planning system observations aimed at calibrating the model also with respect to background leakages, detection of anomalies and leakages, etc. The planning of pressure observations in terms of spatial distribution and number is named sampling design and it was faced considering model calibration. In recent years, the optimal location of flow observations is an emerging issue, related to design of optimal district metering areas (DMAs) and leakage management purposes. Optimal network segmentation is the basis to identify network modules by means of optimal conceptual cuts, which are the candidate locations of closed gates or flow meters creating the DMAs. Giustolisi and Ridolfi (2014) recently proposed the modularity index as a metric for WDN segmentation and a multi-objective strategy for optimal segment design. The original modularity was transformed to be WDN-oriented and they proposed a novel metric, named infrastructure modularity index, in order to overcome the resolution limit of the original modularity. This paper proposes a new way to perform the sampling design, i.e. the optimal location of pressure meters, using newly developed sampling-oriented modularity-based metrics. The strategy optimizes the pressure monitoring system mainly based on network topology and weights assigned to pipes according to the specific technical tasks. A multi-objective optimization minimizes the cost of pressure meters while maximizing the sampling-oriented modularity index. The methodology is presented and discussed using the Apulian and Exnet networks.