A convex optimization approach for automated water and energy end use disaggregation

A detailed knowledge of water consumption at an end-use level is an essential requirement to design and evaluate the efficiency of water saving policies. In the last years, this has led to the development of automated tools to disaggregate high resolution water consumption data at the household level into end use categories. In this work, a new disaggregation algorithm is presented. The proposed algorithm is based on the assumption that the disaggregated signals to be identified are piecewise constant over the time and it exploits the information on the time-of-day probability in which a specific water use event might occur. The disaggregation problem is formulated as a convex optimization problem, whose solution can be efficiently computed through numerical solvers. Specifically, the disaggregation problem is treated as a least-square error minimization problem, with an additional (convex) penalty term aiming at enforcing the disaggregate signals to be piece-wise constant over the time. The proposed disaggregation algorithm has been initially tested against household electricity data available in the literature. The obtained results look promising and similar results are expected to be obtained for water data.