Modeling automatic meter reading water demands as nonhomogeneous point processes

In this paper, an overview of a strategy for automatic meter reading (AMR) data interpretation and aggregation is presented along with the proposed stochastic models adequate for representing the intrinsic characteristics of the data. Water demand measurements from single user accounts are obtained from an AMR system that continuously monitors consumption in different zones of Cincinnati, Ohio. The data represent volumetric measurements characterized by fixed increments, which depend on the sensitivity of the instruments used and occur at irregular times due to the polling method of the AMR system. Given the nature of the data, a nonhomogeneous Poisson process is proposed to model the arrivals of the increments within a selected time interval of 350 days. An exponential-polynomial-trigonometric rate function with multiple periodicities (EPTMP) is assumed to describe both trends and periodicities in the observed data. A specific methodology for estimating the parameters of the EPTMP rate function is presented, based on the method of maximum likelihood. In order to evaluate the estimation technique, a performance evaluation is carried out on synthetic data generated in simulation. Finally, the estimation method is applied and tested on samples of the complete AMR data set, which is obtained from aggregating randomly selected subsets of different magnitude. The results provide significant evidence of the numerical stability and accuracy of the modeling procedure and encourage the use in simulation and prediction of water demands at network nodes from available AMR data.