Information Technology Reference
In-Depth Information
contribution plots, which is based on quantifying the contribution of each process
variable to the single scores of the PCA. Diagnosis can be performed using the
contribution plots because they represent the signatures of the rotating electrical
machine conditions. The contributions are the inputs of a LDA classi
er, which is a
supervised machine learning algorithm used here to diagnose each motor defect.
Several simulations are carried out using a benchmark provided by the Case
Western Reserve University Bearing Data Center (
2014
).
4.1 Recalled Results
In this section authors present the algorithms used to develop the fault and defect
diagnosis procedure. It extracts patterns by vibration signals using MSPCA and
PCA contributions are used to diagnose each motor fault.
4.1.1 Principal Component Analysis
PCA is introduced in the Sect.
2.1.1
, here an improved PCA fault detection index is
described. A deviation of the new data sample X from the normal correlation could
change the projections onto the subspaces, either S
d
or S
r
. Consequently, the
magnitude of either X or X could increase over the values obtained with normal
data. The Square Prediction Error (SPE) is a statistic that measures lack of
tofa
model to data. The SPE statistic is the difference, or residual, between a sample and
its projection into the d components retained in the model. The description of the
distribution of SPE is given in Jackson (
2003
):
2
2
X
PP
T
SPE
¼
X
ð
I
Þ
:
ð
13
Þ
The process is faultless if:
2
SPE
d
ð
14
Þ
2
where
dence limit expression for SPE,
when x follows a normal distribution, is developed in Jackson and Mudholkar
(
1979
), Misra et al. (
2002
) and Rodriguez et al. (
2006
). The fault detectability
condition is given in Dunia and Joe Qin (
1998
) and recalled in the following.
De
d
is a con
dence limit for SPE. A con
ning:
X
þ
X
¼
f
N
;
ð
15
Þ
Search WWH ::
Custom Search