Digital Signal Processing Reference
In-Depth Information
rence of strong vibrations at twice the natural frequency [70] [95], although rotating machi‐
nery can excite vibration harmonics from twice to ten harmonics depending on the signal
pickup locations and directions [53].
Faults do not have a unique nature and most of the time, problems on a smaller scale are linked,
e.g. in the case of misalignment, when an angular misalignment is studied, parallel misalign‐
ment (minor fault) needs to be take into account. Al-Hussain and Redmond reported vibra‐
tions for parallel misalignment at the natural frequency from experimental investigations [4].
To facilitate the diagnosis in rolling elements, some companies and researchers tabulate the
most common failure modes in the frequency domain, so that the analysis can be carried out
easier. Thus, the appearance of different frequency peaks determines the existence of devel‐
oping problems such as gaps, unbalances or misalignments among other circumstances
[31].The great advantage of these tables is that the value of the frequency peak is not a par‐
ticular value and may be adapted to any situation where the natural frequency (or the rota‐
tional speed) is known.
Wavelet transform is a time-frequency technique similar to Short Time Fourier Transform
although it is more effective when the signal is not stationary. Wavelet transform decom‐
pose an input signal into a set of levels at different frequencies [77]. Wavelet transforms
have been applied to the fault detection and diagnosis in various wind turbine parts.
A hidden Markov model is a statistical model in which the system being modelled is as‐
sumed to be a Markov process with hidden states. A hidden Markov model can be consid‐
ered as the simplest dynamic Bayesian network [8]. Ocak and Loparo presented the
application for the bearing fault detection [57].
They are used when a statistical study is required. In these cases, common statistical, i.e. the
root mean square or peak amplitude; to diagnose faults are employed. Other parameters can
be maximum or minimum values, means, standard deviations to energy ratios or kurtosis.
Moreover, trend analysis refers to the collection of information in order to find a trend.
There are many methods that, as happened with the techniques available for CM, are very
specific and therefore they are used for very specific situations. Filtering methods, for exam‐
ple, are designed to remove any redundant information, eliminating unnecessary overloads
in the process. Analysis in time domain will be a way of monitoring wind turbine faults as
inductive imbalances o turn-to-turn faults. Other methodology, the power cepstrum, de‐
fined as the inverse Fourier Transform of the logarithmic power spectrum [92], reports the
occurrence of deterioration through the study of the sidebands. Time synchronous averag‐
ing, amplitude demodulation and order analysis are other signal processing methodologies
used in wind turbines.
2. Wavelet transform
The wavelet transform is a method of analysis capable of identifying the local characteristics
of a signal in the time and frequency domain. It is suitable for large time intervals, where
