Study of Cubic Splines and Fourier Series as Interpolation Techniques for Filling in Short Periods of Missing Building Energy Use and Weather Data

A study of cubic splines and Fourier series as interpolation techniques for filling in missing data in energy and meteorological time series is presented. The followed procedure created artificially missing points (pseudo-gaps) in measured data sets and was based on the local behavior of the data set around those pseudo-gaps. Five variants of the cubic spline technique and 12 variants of Fourier series were tested and compared with linear interpolation, for filling in gaps of 1 to 6 hours of data in 20 samples of energy use and weather data. Each of the samples is at least one year in length. The analysis showed that linear interpolation is superior to the spline and Fourier series techniques for filling in 1–6 hour gaps in time series dry bulb and dew point temperature data. For filling 1–6 hour gaps in building cooling and heating use, the Fourier series approach with 24 data points before and after each gap and six constants was found to be the most suitable. In cases where there are insufficient data points for the application of this approach, simple linear interpolation is recommended.Copyright © 2002 by ASME

[1]  Mark S. Martinez,et al.  International performance measurement & verification protocol: Concepts and options for determining energy and water savings , 2001 .

[2]  Dennis M. Driscoll,et al.  A Mathematical Model for the Generation of Hourly Temperatures , 1977 .

[3]  Saad Bennis,et al.  Improving single-variable and multivariable techniques for estimating missing hydrological data , 1997 .

[4]  David E. Claridge,et al.  Procedures for Filling Short Gaps in Energy Use and Weather Data , 2000 .

[5]  G. Cowan.  Statistical data analysis , 1998 .

[6]  Richard S Gates,et al.  Determination of the 1%, 2.5%, and 5% occurrences of extreme dew-point temperatures and mean coincident dry-bulb temperatures , 1995 .

[7]  Morris H. McCutchan,et al.  Determining the Diurnal Variation of Surface Temperature in Mountainous Terrain. , 1979 .

[8]  Shuichi Hokoi,et al.  Stochastic models of solar radiation and outdoor temperature , 1990 .

[9]  Ross Sparks,et al.  Patching rainfall data using regression methods. , 1997 .

[10]  David E. Claridge,et al.  Baseline calculations for measurement and verification of energy and demand savings in a revolving loan program in Texas , 1998 .

[11]  David E. Claridge,et al.  Restoration of Short Periods of Missing Energy Use and Weather Data Using Cubic Spline and Fourier Series Approaches: Qualitative Analysis , 2002 .

[12]  Hui Chen.  Rehabilitating missing energy use and weather data when determining retrofit energy savings in commercial buildings , 1999 .

[13]  W. Y. Tang,et al.  Comparative studies of various missing data treatment methods - Malaysian experience , 1996 .