Rotational sampling in wind turbines: Difference between revisions

Revision as of 09:04, 26 May 2013

Revision as of 16:18, 26 May 2013

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== Background ==

Analysis of the loads on a wind turbine are usually carried out through use of power spectra. A power spectrum is defined as the power spectral density function of a signal plotted against frequency. The power spectral density function of a plot is defined as the Fourier transform of the covariance function.<ref>httpRemote sensing://books models and methods for image processing, R.google a.co.uk/books?id=T0pOaju7eWkC&pg=PA148&lpg=PA148&dq=covariance+function+power+spectral+density+fourier+transform&source=bl&ots=5pzAA95zbW&sig=h1M05rSiMpJGPB0IhqtWcIuT7is&hl=en&sa=X&ei=6dygUfDjHcSm0wWWxIDIDw&ved=0CEEQ6AEwAg#v=onepage&q=covariance%20function%20power%20spectral%20density%20fourier%20transform&f=false Schowengerdt</ref><ref>Remote Sensing: Models and Methods for Image Processing, Robert A. Schowengerd</ref> Regarding analysis of loads, the analysis involves time series, in which case the covariance function becomes the autocovariance function.

In [[statistics]], given a real [[stochastic process]] ''Z''(''t''), the '''autocovariance''' is the [[covariance]] of the variable against a time-shifted version of itself. If the process has the [[mean]] <math>E[Z_t] = \mu_t</math>, then the autocovariance is given by