Information Technology Reference
In-Depth Information
collected at 12,000 samples per second. Experiments were conducted for both fan
and drive end bearings with outer raceway faults located at 3 o
'
clock (directly in the
load zone), at 6 o
'
clock (orthogonal to the load zone), and at 12 o
'
clock.
5.1 Results and Discussion
The proposed approach described in Sect.
4.2
has been tested using a Daubechies
mother wavelet of order 15, de
in
Sect.
4.1.2
). Since the motor rotation frequency is 30 Hz and the sampling fre-
quency is 12 kHz, applying Eq. (
38
), the level of detail obtained is L
ned db15 mother wavelet (de
ned kernel
/
¼
7. The
dimension of principal component subspace d, chosen by the Kaiser
'
is rule, is
described in Jolliffe (
2002
).
Incoming batch data samples are then fed into the MSPCA model and the PCA
residual contributions are computed for the matrices D
j
, j
¼
1
; ...;
L, A
L
. In the
following, these matrices are de
ned scale matrices, and they are compared with
the respective thresholds. When, at any scale, the number of residual contribution
samples over the thresholds is greater than
a c
, where
a
is the signi
cance level
used for the threshold
d
i
calculation (stated in Sect.
4.2
) and
c
is a corrective index
(
(fixed equal to 2), a fault is detected and the motor is considered faulty.
Once a fault is detected, the isolation and diagnosis tests are performed. At this
step the PCA contributions are computed for each scale matrix. Fault isolation
allows to detect which sensors are involved in the fault. By using several scales for
the DWT analysis, it is possible to cluster the residual contributions of each scale
and de
ne a unique signature of the motor fault, as in a MVSA approach. More in
detail, the signature of each fault is given by the contributions of each variable for
each scale. The results are the average of 1,000 Monte Carlo simulations where the
training and testing data sets are randomly changed.
Figures
6
and
7
show the residuals of the first accelerometer (i.e. placed at the
drive end) for drive end bearing faults estimated by Eq. (
16
). The thresholds, drawn
in dashed red line, are estimated by KDE (Eq.
18
). While Fig.
6
a shows the
residuals for healthy motor, Fig.
6
b, c show the residuals of rolling element and
inner raceway faults respectively at the detail scales D
1
and D
4
, which are, among
all scales, the most affected by the faults.
Figures
7
a
-
c show the residuals of outer raceway faults located at 3, 6, 12
o
clock respectively at the detail scales D
1
, D
2
and D
4
, which are, among all scales,
the most affected by the faults. It can be noticed how the residuals are related to the
fault type and so they can be exploited as signatures of the rotating electrical
machine conditions.
Figures
8
and
9
show the contribution plots of each accelerometer at different
scales for drive end bearing fault, particularly Figs.
8
a
'
c show the contribution
plots of healthy motor, rolling element and inner raceway faults while Figs.
9
a
-
-
c
Search WWH ::
Custom Search