Digital Signal Processing Reference
In-Depth Information
From point 2, the peak at frequencies as 2X and 3X becomes more significant and sometimes
exceed the amplitude of the natural frequency.
The results for experiment 8 are also remarkable. The rigid coupling added causes a severe
looseness and vibration. The growth of a frequency at 4X and a constant noise over the spec‐
trum is observed. Although it is usual to find sidebands, peaks below 1X and high frequen‐
cy peaks for all this type of experiments, this feature is unique to this last experiment.
Initially, a similar diagnosis for cases 1, 4 and 8 was expected, but the behavior has been
slightly different for this reason.
3.4. Wavelet transform processing approach and results
Wavelet transforms were employed to analyse the sound signals. As for the Fast Fourier Trans‐
form, an algorithm has been written with Matlab. This program plots and compares two sig‐
nals. Data has been transformed in 5 decompositions named
a
4
,
d
4
,
d
3
,
d
2
and
d
1
, where each of
them has an energy rate associated from the original signal (Figure 16). The algorithm also re‐
turns a percentage value per decomposition. These values of energy, the decomposition levels
attached and the peak amplitudes are examined in order to look for patterns.
Functions in the time domain can be represented as a linear combination of all frequency
components present in a signal, where the coefficients are the amount of energy provided by
each frequency component to the original signal. The main decomposition is associated with
a
4
(
main
or
mother wavelet
) that usually has the highest energy, though it is not always neces‐
sarily the case. It has a similar pattern to the original signal. The first (
d
4
), second (
d
3
), third
(
d
2
) and fourth (
d
1
) transformed signals have decreasing energy rates, being
s
the original
signal. Usually
a
4
is the low frequency component of the original signal while
d
i
is the high
frequency component, having
d
1
the biggest value.
It is necessary to verify that the experiments performed at 1500 rpm can be extrapolated to
other speeds. In the case of wind turbines, most of the engines rotate at speeds close to 3000
rpm. A certain number of tests were done varying from 500 to 3000 rpm (at intervals of 500
rpm) in order to ensure the existence of the proportional pattern.
The results showed that regardless of the speeds or the points of study, all the graphical rep‐
resentations for the different decompositions of energy had the same patterns. Figure 17 in‐
dicates the existence of a similar behavior where only changes the numerical value. The
biggest ones will correspond to the
main
signals, while the results for decompositions
d
1
and
d
2
are similar.
Data can be studied according to the evolution of a single point along the different experi‐
ments or analysing the evolution of the set points for all the experiment. Each row in Figure
18 contains two graphics, one with the amplitude peaks (left) and the other one with the en‐
ergy distribution of the sound signal (right). The first two graphics correspond to the engine
end (point 1). The following two graphics are the closest to the coupling (point 2). The third
row belongs to the points of the generator next to the coupling (point 3), and finally, the last
two graphics are for the end of the generator (point 4).
