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Auto Spectrum

This calculates the auto-spectral density (frequency spectrum) of a signal.

Click the Select... button to define the signal to be processed. If you have selected multiple channels you will be able to specify a number of load cases and variables to be processed in a single calculation, and the results for each load case will then be stored as additional outputs of that load case, and/or accumulated over the turbine lifetime.

Options for spectral analysis

All calculations involving spectral analysis use a Fast Fourier Transform technique with ensemble averaging. To perform the spectral analysis, the signal is divided into a number of segments of equal length, each of which contains a number of points which must be a power of 2. The segments need not be distinct, but may overlap. Each segment is then shaped by multiplying by a ‘window’ function which tapers the segment to zero at each end. This improves the spectrum particularly at high frequencies. A choice of windowing functions is available. Optionally, each segment may have a linear trend removed before windowing, which can improve the spectral estimation at low frequencies. The final spectrum is obtained by averaging together the resulting spectra from each segment.

The information required is therefore as follows:

  • Number of points: the number of datapoints per segment. Must be a power of 2, maximum 4096. More points will give better frequency resolution, which may be important especially at low frequencies. However, choosing fewer points may result in a smoother spectrum because there will be more segments. If in doubt, 512 is a good starting point.

  • Percentage overlap: the overlap between the segments. Must be less than 100%. 50% is often satisfactory, although 0% may be more appropriate if a rectangular window is used.

  • Window: Some function \(G(f)\) where f is the fractional position along the segment (0 at the start, 1 at the end). A Hanning, Hamming or welch window is recommended. The window options are:

    • Rectangular \(G(f) = 1\) (equivalent to not using a window).
    • Triangular \(G(f) = 1 - |2f-1|\)
    • Hanning \(G(f) = (1-\cos (2 \pi f))/2\)
    • Hamming \(G(f) = 0.54 - 0.46 \cos (2 \pi f)\)
    • Welch \(G(f) = 1- (2f - 1)^2\)

  • Trend removal: If checked, a linear trend is calculated for each segment and removed from it before windowing, this is usually desirable. If left unchecked, the mean is calculated instead for each segment and removed from it before windowing.

Last updated 05-08-2024