Development of Fourier Series and Artificial Neural Network Approaches to Model Hourly Energy Use in Commercial Buildings

Abstract

This dissertation develops Fourier series and Artificial Neural Network (ANN) approaches to model hourly energy use in commercial buildings and illustrates application to data-screening. The procedure for modeling hourly energy use has two steps: (i) Day-typing and (ii) Model development. The mean diurnal energy use and the diurnal profile may be different during working weekdays, weekends, holidays and Christmas due to major changes in mode of operation. The first step, known as day-typing, is important for removing such effects. The second step is to develop models for each day-type. Fourier series analysis is eminently suitable for modeling strongly periodic data. Energy use in commercial buildings being strongly periodic, is appropriate for Fourier series treatment. Generalized Fourier Series (GFS) model equations, developed for both weather independent and weather dependent energy use, give a set of parameters involving time and/or weather variables. Stepwise regression is performed to select the important parameters and a final model for each day-type is developed using the selected parameters. There are situations when only temperature data is available. A Temperature based Fourier Series (TFS) equation for modeling heating and cooling energy use has been developed to deal with such cases. Two important advantages of TFS are that it (i)

represents nonlinear variation of energy use in a linearized functional form and (ii) can indirectly account for humidity and solar effect in the cooling energy use. ANNs with back propagation algorithms give high prediction accuracy and has been applied by many researchers to model hourly energy use in commercial buildings. However, the training of Back Propagation Network (BPN) algorithms is a long, uncertain process. ANNs with local basis functions require significantly shorter training times than conventional BPNs. A methodology has been developed to model heating and cooling energy use in commercial buildings using a one-hidden-layer ANN with two dimensional wavelet basis functions derived from cubic splines. A suitable prediction interval can be generated and used to perform data­ screening. Application of the TFS approach to data-screening is illustrated with monitored data.