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T1. Data are preprocessed;
T2. The Wavelet analysis is used, to re
ne the data, with a level of detail L which
is chosen by Eq. ( 38 );
T3. Normalize mean and standard deviation of detail and approximation matrices
and apply PCA to the approximation matrix A L , of order L, and to the L detail
matrices D j , where j
L;
T4. The PCA transformation matrix P and the signal covariance matrix S are
computed for each approximation and detail matrices;
T5. The X i signals (Eq. 13 ) are computed, for each wavelet matrix;
T6. The
ΒΌ
1
; ...
d i thresholds are computed, for each detail matrix and for the approxi-
mation matrix of order L, using the KDE algorithm (Eq. 18 ) and a con
dence
bound
a
;
In the second step, the model previously obtained is on-line compared with the
new data and a statistical index of failure is calculated. MSPCA diagnosis steps are
summarized below:
D1. The previous steps, except the threshold computation step (T6), are repeated
for each new dataset, the data are standardized as in the training step (T3) and
the PCA and X i signals are computed using the P and S matrices, obtained in
the training step;
D2. If any of the X i
d i , the fault is detected and the
isolation is performed by the contributions, else the next data set is analysed
[return to (D1)];
D3. Compute all the residual contributions, for each sensor, for all details and
approximation matrices and isolate and diagnose the fault type.
signals is over the thresholds
The next Section introduces the FDD experimental results in order to show the
MSPCA algorithm performances. Tests are carried out on real induction motors
with different fault severity.
5 Electric Motor FDD by MVSA: Results
The diagnosis algorithm has been tested on the vibration signals provided by the
Case Western Reserve University Bearing Data Center ( 2014 ). Experiments were
conducted using a 2 hp Reliance Electric motor, and acceleration data was mea-
sured at locations near to and remote from the motor bearings. Motor bearings were
seeded with faults using electro-discharge machining (EDM). Faults ranging from
0.007 in. to 0.040 in. of diameter were introduced separately at the inner raceway,
rolling element (i.e. ball) and outer raceway. Faulty bearings were reinstalled into
the test motor and vibration data was recorded for motor loads of 0
-
3 hp (motor
speeds of 1,797
clock
position at both the drive end and fan end of the motor housing. Digital data was
-
1,720 RPM). Accelerometers were placed at
the 12 o
'
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