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==Background==
[[Analysis]] of the loads on a [[wind turbine]] can be 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>Remote sensing: models and methods for image processing, R. a. 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 the signal processing sense, the autocovariance can be related to the [[autocorrelation]] function.
==Deterministic processes==
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===Power spectral density functions===
====Drivetrain components====
The [[drivetrain]] of a wind turbine comprises the hub, the low speed shaft, the [[Transmission (mechanical device)|gearbox]], the high speed shaft, and the generator. The torque at the hub is strongly influenced by the rotor dynamics. The instantaneous hub torque is found by summing all the torques from all the blades of the wind turbine at any instant in time.
Consider an <math>n</math> bladed wind turbine. Each [[blade]] is separated angularly from a neighbouring blade by <math>360/n</math> degrees. That is, for a 3-bladed wind turbine, the blades are 120 degrees apart.
The torque acting on the blade is defined as the z-component of <math>\textbf{r}\times\mathbf{F}</math>, where '''r''' is the radius from the axis of rotation (in this case the hub), and '''F''' is the force acting on the blade. If the torque is defined as the z-component of this cross product, then the torque is simply ''rF''<sub>perp</sub> where ''F''<sub>perp</sub> is the force perpendicular to the radius vector, or tangential to the instantaneous velocity of the blade (See figure below)
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