Modeling Multi-Level Power Usage with Latent States and Smooth Functions

• Activity Number: 180
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Camila Pedroso Estevam de Souza* and Nancy Heckman
• Companies: The University of British Columbia and The University of British Columbia
• Keywords: Nonparametric regression ; Latent variables ; Building power usage data ; Functional data analysis ; Switching nonparametric regression model ; Machine learning

Abstract

We develop and apply a new approach for analyzing a building's business day power usage. We treat each business day as a replicate and model power usage as arising from two smooth functions, one function giving power usage when the cooling system is off, the other function giving power usage when the cooling system is on. The condition "chiller on"/"chiller off" at any particular time cannot be observed directly, thus forming a latent process. In general, our method can be applied to multi-curve data where each curve is driven by a latent state process. The state at any particular point determines a smooth function. Thus each curve follows what we call a switching nonparametric regression model. We develop an EM algorithm to estimate the parameters of the latent process and the function corresponding to each state. We also obtain standard errors for the parameter estimates of the state process. Simulations studies show the frequentist properties of our estimates.