Issue 49

S. Djaballah et alii, Frattura ed Integrità Strutturale, 49 (2019) 291-301; DOI: 10.3221/IGF-ESIS.49.29 299 D IAGNOSIS OF DEFECTS BY TRANSFORM WAVELET PACKETS he diagnosis and classification of bearing defects are performed by an artificial neural network (ANN) whose inputs are energy indicators and kurtosis calculated using coefficients derived from the decomposition level 3 transform wavelet packet ( DWPT) using the db6 wavelet. We kept the same configuration of the RNA used before. Thus, the structure of the RNA takes the form:  3-layer network: 1 single hidden layer;  10 neurons in the hidden layer;  The number of nodes at the input is equal to the number of indicators that is 14;  The number of nodes in the output layer is: - Case 1: 4 outputs (see Fig. 10) corresponding to the four bearing states. - Case 2: 10 outputs (see Fig. 11) for detecting the severity of the fault. Corresponding the different defects as well as their diameters:  Normal.  Fault in the inner race (0.007 and 0.014 and 0.021 inches ).  Fault in the inner race (0.007 and 0.014 and 0.021 inches ).  Fault in the ball (0.007 and 0.014 and 0.021 inches ). Figure 9 : Kurtosis of. each sub-band for the four states of the bearing: (a) no fault, (b) fault in the inner race, (c) fault in the outer race, (d) fault in the ball. Tab. 5 shows the RNA classification rates based on the wavelet packet transform for both the 4 and 10 output configurations. T 1 2 3 4 5 6 7 8 0 5 10 15 20 25 Frequency bands Kurtosis by frequency band (a) 1 2 3 4 5 6 7 8 0 5 10 15 20 25 Frequency bands Kurtosis by frequency band (b) 1 2 3 4 5 6 7 8 0 5 10 15 20 25 Frequency bands Kurtosis by frequency band (c) 1 2 3 4 5 6 7 8 0 5 10 15 20 25 Frequency bands Kurtosis by frequency band (d)