I'm analysing vibration data from 4 wind turbines (WTs). 8 different sensors are sampled at 25.6 kHz for 10 seconds once a day. I have data from around 400 days (intervals). The plot underneath is for one of the four WT in the time domain.

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The frequency domain from FFT of the four turbines (Gearbox HSS) in the the range 0-12kHz:

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Current plan and questions:

I want to look for faults in the gearbox, and I am suspecting that WT 4 (bottom right plot above) is most degraded. I want to apply some kind of high frequency technique for looking for early stage bearing damages in the higher frequency range, since these are not captured by FFT.

  • What approaches should can I consider here? (I have looked a bit at Hilbert transform, but I'm not exactly sure how that would help me.) I am also considering performing some kind of enveloping/wavelet transform.
  • Should I be looking at lower frequencies as well?

This is not my main study field, and I want to try building a machine learning classifier with variables obtained from the signal processing.

Plots of the lower frequency (0-2000Hz) development over the 400 intervals for all 4 turbines:

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2 Answers 2


One technique that I've seen used in determining bearing faults is using the kurtosis of the vibration signal.

You can track as a function of time what Wikipedia calls the sample excess kurtosis. This is the kurtosis that is different from the kurtosis you would see if the signal was Gaussian distributed.

The sample excess kurtosis is defined as:

$$ \frac{m_4}{m_2^2} - 3 = \frac{\frac{1}{N} \displaystyle \sum_{n=0}^{N=1} (x_n - \bar{x})^4}{\left(\frac{1}{N} \displaystyle \sum_{n=0}^{N=1} (x_n - \bar{x})^2\right)^2} - 3 $$

where $\bar{x}$ is the sample mean, $m_2$ is the sample second order moment, and $m_4$ is the sample fourth order moment.

Brüel & Kjær have a nice writeup about using kurtosis, though they use the actual kurtosis rather than the excess kurtosis.


Bearing faults tend to show up when grit or dirt or broken bearing pieces get into the rotating elements. When that happens, the vibration signals tend to be more "spiky" as the fault-inducing material gets ground against the rolling elements and bearing races.

Other approaches

You can also look at removing what you know about the harmonic content of the signals and then looking at the remainder. There's some stuff about that here. However, try something simple like kurtosis first.


(I am relatively new to this field of study as well, but here is my input which I hope is of help).

Frequency analysis techniques should be chosen that reflect the characteristics of the system you use. Fourier analysis in this way assumes that the data is stationary for each sample interval over which the data is collected. As you only take the data in 10 second time intervals this may be a good assumption (the system output is unlikely to change dramatically with time in this interval).

I want to apply some kind of high frequency technique for looking for early stage bearing damages in the higher frequency range, since these are not captured by FFT.

Why does the FFT not capture high frequency characteristics of your data? Theoretically you should only be limited by the 25.6 kHz sample frequency of your data (unless I have missed something in which case apologies).

Take a look an the Hilbert-Huang transform, which is applicable to non-linear and non-stationary data. If you use/have ever used MATLAB, then the MATLAB hht documentation has a step by step example of how to diagnose bearing fault, which might be a good starting point.

  • 1
    $\begingroup$ Thats is what I thought as well. At 18:33 in this video youtube.com/watch?v=Vj1xmze3GlE&t=1833s high frequency faults is mentioned, which is why I assumed other analysis methods than FFT have to be applied. $\endgroup$
    – meerkat
    Mar 6, 2020 at 14:46

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