Sampling significant contamination events for optimal sensor placement in water distribution systems

This paper presents a procedure for sampling the most representative contamination events in the framework of optimal sensor placement with two objective functions to be minimized, namely, sensor redundancy and contaminated population. Compared to other sampling methods present in the scientific literature, it is based on practical considerations of network topology and operation. This aspect confers upon the procedure lightness from a computational viewpoint. Sampling was carried out on four variables, namely, injection location, starting time, mass rate, and duration. The injection location was sampled as a function of distance from the source based on network connectivity. A single starting time was selected inside each network operating phase, during which pipe-water discharges were quite constant. One single mass rate was selected as significant, considering the linearity of the contaminant advection-reaction equation under specific conditions. In fact, owing to this linearity, the results of quality simulations associated with a generic mass rate can be easily derived from those associated with the selected mass rate. Finally, a single (small) duration was sampled. In fact, a long duration event can be simply regarded as the sum of various short-duration events. The procedure was tested in two case studies of different complexity. As evidence of the sampling effectiveness, the results of the optimal sensor placement did not vary significantly when the sampled contamination events were used inside the optimization, instead of the totality of possible contamination events.