Source Location Inversion and the Effect of Stochastically Varying Demand

In recent years, significant advances have been made in the development of gradientbased optimization algorithms and their application to inverse problems in water distribution systems. We apply a gradient-based optimization procedure to the problem of identifying the location of a contaminant injected into a distribution system based on data collected at a finite number of sensors. The solution of this problem is complicated by uncertainty in the instantaneous water demands occurring at nodes throughout the distribution system. We characterize the effect of this demand uncertainty on the ability of the inversion algorithm to accurately and precisely identify the correct source location by varying the time step at which the variable demands are aggregated from 30 minutes to 24 hours. These calculations determine the effect of demand aggregation on the inversion results by comparing the results across time step sizes to the results achieved at the smallest time scale (30 minutes). In a distribution system the true water demands at any time step are unknown and represent irreducible uncertainty. We show how large of an effect this irreducible uncertainty has on our ability to locate the source location of contaminants within a distribution system. The calculations are done on a moderately sized distribution system network and the stochastic demands are generated using a recently developed Poisson Rectangular Pulse (PRP) demand generator. The contaminant is simulated with tracer transport using EPANET. Results for the example problem examined herein using 100 sensors show that the inverse approach is capable of identifying the correct source node at all time step aggregations.