Extended Abstract (120K)P3.11
Estimation of the integral time scale with time series models
Stijn de Waele, Delft University of Technology, Delft, Netherlands; and A. van Dijk, P. Broersen, and P. G. Duynkerke
The integral time scale Ti is a characteristic time scale for the dynamics of measured quantities in a turbulent flow such as temperature, wind velocity and humidity. It is defined as the sum of the squared autocorrelation function r(n). Ti is a measure for the correlation length of a process. The subject of the paper is the estimation of the integral time scale from a given signal.
A procedure for the estimation of the integral time scale is to estimate the autocorrelation function as the sum of lagged products of the observations x[n]x[n-m]. These estimates are then squared and summed. However, for a lag n where the true autocorrelation r(n) is zero, the estimate for the autocorrelation will deviate from zero due to statistical estimation uncertainty. As a result, the estimate of Ti obtained in this manner will be greater than the true Ti.
A better approach is to describe the statistical properties of the signal using a parametric model. The estimate of the integral time scale is calculated from the model parameters that have been estimated from the data. Simple (low-order) autoregressive models have been used successfully to obtain an accurate estimate of the integral time scale.
However, low-order models can lead to biased estimates of the integral time scale when the model cannot capture the significant characteristics of the process. In this paper it will be shown how considering higher-order model as well can solve this problem. Using statistical order selection, an optimal model order can be selected from the data.
Estimation of the integral time scale has been studied using both simulated and experimental turbulence data. The experimental data are wind velocity signals obtained from boundary layer turbulence. In the simulations the estimates are compared to the true integral time scale. For the experimental data the estimates are related to the dimensionless Richardson number.
Supplementary URL: http://www.tn.tudelft.nl/mmr
Poster Session 3, Fundamental Studies
Tuesday, 16 July 2002, 2:00 PM-2:00 PM
Previous paper Next paper