Issue 49

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S. Djaballah et alii, Frattura ed Integrità Strutturale, 49 (2019) 291-301; DOI: 10.3221/IGF-ESIS.49.29

Wavelet

db1

db2

db3

db6

db7

db8

Performance %

98.95

99.21

98.69

99.21

99.47

Table 4: Classification rate with decomposition level N = 3

We conclude that the optimal wavelet most appropriate to fault diagnosis of bearings is the Daubechies wavelet of order 6 "db6" with a level of decomposition, N = 3, has proven its performance in several works dealing with the diagnosis of defects [14,15,16]. Reduction of the vector of indicators The application of the wavelet packet transform (DWPT) to the vibratory signal, using the wavelet db6 with decomposition level N = 3, generates 2 3 = 8 frequency sub-bands. Recall that the 16 indicators used in this work are based on energy and kurtosis calculated for each frequency sub-band and are given by:

1 v F E E E K K K        2 8 1 2 8 3 3 3 3 3 3

(6)

In order to see which of the 16 indicators are sensitive to the state of rotation, the diagrams representing the energies and kurtosis of each sub-band are plotted and shown in Fig. 8 and 9 respectively. From Fig. 8, we can easily see that the two indicators, in this case, 5 6 3 3 and E E are almost invariant. For kurtosis, represented by Fig. 9, we can note that the 8 indicators 1 2 3 4 5 6 7 8 3 3 3 3 3 3 3 3 , , , , , , ,and K K K K K K K K are sensitive to changing the state of the bearing. As a result, we have maintained the 14 most relevant indicators for the classification of bearing defects that are given by:

1 vr F E E E E E E K K K       2 3 4 7 8 1 2 8 3 3 3 3 3 3 3 3 3

(7)

x 10 5

(a)

(b)

x 10

0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3

frequency band

Energy per

1 2 3 4 5 6 7 8

The frequency bands