Optimal Determination of Grab Sample Locations and Source Inversion in Large-Scale Water Distribution Systems

Abstract

We present a mixed-integer linear programming formulation to determine optimal locations for manual grab sampling after the detection of contaminants in a water distribution system. The formulation selects optimal manual grab sample locations that maximize the total pair-wise distinguishability of candidate contamination events. Given an initial contaminant detection location, a source inversion is performed that will eliminate unlikely events resulting in a much smaller set of candidate contamination events. We then propose a cyclical process where optimal grab samples locations are determined and manual grab samples taken. Relying only on YES/NO indicators of the presence of contaminant, source inversion is performed to reduce the set of candidate contamination events. The process is repeated until the number of candidate events is sufficiently small. Case studies testing this process are presented using water network models ranging from 4 to approximately 13000 nodes. The results demonstrate that the contamination event can be identified within a remarkably small number of sampling cycles using very few sampling teams. Furthermore, solution times were reasonable making this formulation suitable for real-time settings.