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case the K
es the fault. By Monte Carlo simula-
tions, all fault types are diagnosed with accuracy reported in Table
2
. It can be
noticed how the classi
-
L divergence detects and identi
cation accuracy in the case of healthy motor is always
100 %, therefore the algorithm is able to detect if motors are healthy or if there are
some faults or defects. In Figs.
5
b and c the blue lines of motors with cracked and
wrong rotor are never overlapped to the blue lines of healthy motors so, in these
tests, the algorithm never confuses the cases of healthy motors from those not
healthy.
The next Section describes the well-known MSPCA algorithm for fault detection
and isolation based on vibration signals.
4 Electric Motor FDD by MVSA
In electric motors, faults and defects are often correlated to the vibration signals,
which can be processed to model the motor behaviours by patterns that represent
the normal and abnormal motor conditions. Vibration analysis is widely accepted as
a tool to detect faults of a rotating machine since it is reliable, not destructive and it
permits continuous monitoring without stopping the machine. A brief literature
review is given by: Fan and Zheng (
2007
), Immovilli et al. (
2010
), Sawalhi and
Randall (
2008a
,
b
), Tran et al. (
2009
), Yang and Kim (
2006
). In particular, it is
possible to detect different faults by analysing the vibration power spectrum. Most
common faults are unbalance and misalignment. Unbalance may be caused by poor
balancing, shaft in
ection (i.e. thermal expansion) and rotor distortion by magnetic
forces (a well known problem in high power electrical machines). Misalignment
may be caused by misaligned couplings, misaligned bearings or crooked shaft.
In order to model the vibration signals, MSPCA is taken into account, as pre-
sented in Bakshi (
1998
). MSPCA deals with processes that operate at different
scales, and have contributions from:
fl
events occurring at different localizations in time and frequency;
stochastic processes whose energy or power spectrum changes over time and/or
frequency;
variables measured at different sampling rate or containing missing data.
MSPCA transforms the process data information at different scales by WT. The
information of each different scale is captured by PCA modelling. These patterns,
which represent the process conditions, can be used to identify each fault and
defect.
To detect the defects, a KDE algorithm is used on the PCA residuals, and the
thresholds are computed for each sensors signal. It allows to identify if, for each
wavelet scale, the signals are involved in the fault or not. When Gaussian
assumption is not recognized, KDE method is a robust methodology to estimate
numerically the PDF, by Odiowei and Cao (
2010
). Fault isolation is carried out by
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