## 4 Results
### Tests with Three Classification Classes  
The first tests were conducted with only three classification classes: healthy (baseline), faulty with generalized roughness Step 1, and faulty with generalized roughness Step 2. The number of images was 80 for the baseline and 40 for each of the cases Step 1 and Step 2. The transformation used was the CWT with a filter bank; the sampling frequency imposed was 120 kHz and the voices per octave were 12. The MATLAB function used to create the filter bank was \"cwtfilterbank\". By default, the filters are normalized so that the peak magnitudes for all passbands are approximately equal to 2. The highest frequency passband is designed so that the amplitude falls to half the peak value at the Nyquist frequency. For the objective of this work, where several similar signals were analyzed in time-frequency, the filter bank was precomputed at the beginning and then passed as input for the \"wt\" function that returns the coefficients of the CWT. As implemented, the CWT uses L1 normalization. With L1 normalization, equal amplitude oscillatory components at different scales have equal magnitude in the CWT. Moreover, L1 normalization gives a more accurate representation of the signal. The mag \begin{table}
\begin{tabular}{c c c} \hline \hline
**Type of Fault** & **Denotation** &
\begin{tabular}{c} **Number of Images** \\ **Generated** \\ \end{tabular} \\ \hline Baseline & Bas & 80 \\ Generalized roughness step 1 & BF Step 1 & 40 \\ Generalized roughness step 2 & BF Step 2 & 40 \\ Crack at hour 12 & H12 & 60 \\ Crack at hour 3 & H3 & 60 \\ Crack at hour 4.5 & H45 & 60 \\ Crack at hour 6 & H6 & 60 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Denotation and number of images generated for each faulty condition (in the Denotation column, BF means Bearing Fault). nitudes of the oscillatory components agree with the magnitudes of the corresponding wavelet coefficients. With a real value signal, \"wt\" returns a 2D matrix of coefficients, in which each row corresponds to one scale, while the columns represent the time instants and every column has the same length as the signal considered. The final matrices from which the scalogram images were derived were obtained by computing the absolute value of the wavelet coefficients. To convert from indexed images (the coefficient matrices) to RGB images, the \"ind2 rgb\" function was used (it outputs the three RGB channels with pixel values in the range 0-1). The chosen color map was \"jet\", with 128 colors. Every image was generated with the \"imwrite\" function and had a size of 224 \(\times\) 224 pixels. To ensure that the generated scalogram had this exact size in order to be fed to the input layer of the network, the \"imresize\" function was used. By default, this function uses the bicubic interpolation, where the output pixel value is a weighted average of the pixels in the nearest 4-by-4 neighborhood. The images were generated using the first 100,000 samples of each acquisition. With a sampling frequency of 120 kHz, this resulted in an interval of 833 ms. This time interval was considered to be long enough, as it contained approximately 41 fundamental cycles (all the tests were carried out with a 50 Hz fundamental frequency imposed by the inverter). In the cases in which more than 40 images were generated for each class, in addition to the first 100,000 sample segments of each acquisition, other consecutive segments of 100,000 samples were taken from the same 22 sample acquisitions. Moreover, a data augmentation was used to increase the number of images in the training dataset, whereby a random reflection over the x-axis was executed and a random translation on the x and y axis of max 30 pixels was also carried out. The hyper-parameter set for the modified GoogLeNet had a \"minibatch size\" of 6 and a maximum number of epochs of 9. The other modifications made to accommodate the transfer learning technique are described in Section 2.2.