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shown in Tables 1 and 2 . The tests are also performed for both cases using the
asymmetric K
L divergence (Eq. 9 ). The results are comparable to those achieved
with the symmetric K
-
-
L divergence described in the next subsections.
3.1.1 Broken Rotor Bars and Connectors Diagnosis
Figures 2 a
c depict the patterns of a healthy motor, one broken bar and one broken
connector conditions, respectively; these
-
figures show how the PDFs, estimated by
KDE in the principal component space, are used as the speci
c patterns for the
motor conditions. The simulation results, given in Figs. 3 a
c, show the faults
diagnosis for broken rotor bars and connectors, setting n grid ¼
-
64 and the
current signals acquisition time in steady-state condition is equal to 0.3 s. Figure 3
(a) shows the K
64
L divergence among the PDFs, estimated by KDE, of all motor
conditions (i.e. healthy, from one to ten broken rotor bars and from one to ten
broken connectors) and the PDF estimated by KDE from stator current signals of
healthy motor. The results show as the minimum K
-
-
L distance is exactly the
healthy condition. Figure 3 b shows the K
L divergence among all PDFs and the
PDF estimated from stator current signals affected by one broken rotor bar. In this
case the graph shows as the minimum K
-
L distance is exactly the broken bar
condition. The last graph, Fig. 3 c, shows the one broken connector diagnosis. Even
in this case the K
-
es the fault, that is one broken
connector. By Monte Carlo simulations, all fault types are diagnosed with 100 %
accuracy hence the K
-
L divergence detects and identi
-
L divergence
figures for the other faults are not reported.
Moreover the classi
cation accuracy is 100 % with acquisition time above 0.3 s
for each fault, while below 0.3 s, the classi
cation accuracy decreases as shown
in Table 1 .
3.1.2 Real Induction Motors Diagnosis
Figures 4 a
-
c depict the patterns of three real motors: healthy, cracked and wrong
rotor; these
figures show as the PDFs, estimated by KDE in the principal compo-
nent space, are different and therefore can be used as speci
c patterns for each
motor condition. Experimental results given in Figs. 5 a
-
c show the fault diagnosis
for cracked and wrong rotors, setting n grid ¼
64 and the current signals
acquisition time in steady-state is equal to 0.7 s. Figure 5 a shows the K
64
L diver-
gence among the PDFs, estimated by KDE, of all motor conditions (i.e. healthy,
cracked and wrong rotors) and the PDF estimated by KDE from stator current
signals of healthy motor. The results show as the minimum K
-
-
L distance is exactly
the healthy condition. Figure 5 b shows the K
L divergence among all PDFs and the
PDF estimated from stator current signals where cracked rotors are diagnosed. In
this case the graph shows as the minimum K
-
L distance is exactly the cracked rotor
condition. The last graph, Fig. 5 c, shows the wrong rotor diagnosis. Even in this
-
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