Identification of Water Demand Models From Noisy Data

摘要

The identification of a proper water demand model when all the variables are noisy is one of the major problems in the planning process. So far, this problem has been overlooked, and generally, regression or time series models have been used. It has been suggested that the existing methods to include noisy variables are fraught with problems such as nonidentifiability and unboundedness. An alternative procedure is proposed to identify a water demand model from a set of noisy data using noisy realization theory. A mathematical programming‐based solution algorithm is developed to identify a first‐order lag dynamical model for this noisy problem. This algorithm gives bounds on both the model parameters and on the noise covariance matrix. The unboundedness problem is addressed by using prior information about the upper bound on the noise covariance matrix. The monthly municipal water demand of Tucson, Arizona, from 1974 to 1977 is modeled as an example. The model assumes 10–30 noise in the variables and then correspondingly gives a range for each model para