Issue 49

S. Djaballah et alii, Frattura ed Integrità Strutturale, 49 (2019) 291-301; DOI: 10.3221/IGF-ESIS.49.29 298 Wavelet db1 db2 db3 db6 db7 db8 Performance % 98.95 98.95 99.21 99.47 98.69 99.21 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 2 8 1 2 8 3 3 3 3 3 3 v F E E E K K K        (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 2 3 4 7 8 1 2 8 3 3 3 3 3 3 3 3 3 vr F E E E E E E K K K       (7) Figure 8 : Energy of each sub-band for the four states of the bearing: (a) no fault, (b) defect in the inner race, (c) defect in the outer race, (d) defect in the ball. 1 2 3 4 5 6 7 8 0 0.5 1 1.5 2 2.5 3 x 10 4 The frequency bands Energy per frequency band (a) 1 2 3 4 5 6 7 8 0 0.5 1 1.5 2 2.5 3 x 10 5 The frequency bands Energy per frequency band (b) 1 2 3 4 5 6 7 8 0 0.5 1 1.5 2 2.5 3 x 10 5 The frequency bands Energy per frequency band (c) 1 2 3 4 5 6 7 8 0 0.5 1 1.5 2 2.5 3 x 10 5 The frequency bands Energy per frequency band (d)