# A Deep-Learning-Based Bearing Fault Diagnosis Using Defect Signature Wavelet Image Visualization
## 4 Methodology Evaluation Results
### Performance Evaluation of DSWI Compared to Vibration Image and Conventional Wavelet Spectrogram  
The same sample signals are used to create 2-D representations with the vibration image method and the conventional wavelet spectrogram. The vibration image is constructed by segmenting the raw signal in the time-domain into smaller samples and the segments are stacked one by one to generate the 2-D matrix. Then the values of the matrix are normalized in range \([0,255]\) and converted to a grayscale image. This method is also used in [10,11] to generate the 2-D image from the vibration signal. The second method to compare with the proposed method is the conventional wavelet spectrogram. The AE signal is directly analyzed with the continuous wavelet transform without envelope analysis and the information of the damage frequency band is used to create the wavelet spectrogram. The detailed visualization of vibration image, wavelet spectrogram, and the DSWI for different types of faults in bearings and the normal case is shown in Figure 6. The proposed method with DSWI shows the pattern differences more distinctly between different types of signals compared to other 2-D representations. The other patterns do not show clearly separate visualizations from the different bearing status AE signals. Moreover, the pattern of DSWI illustrates a correlation to the damage frequencies as ascertained in Section 3. Since the AE-based method becomes more sensitive to low energy emissions from the bearing, gathering separate visual information associated with the energy distribution through low amplitudes can supply useful knowledge to further analyze. The DSWI with time-frequency-domain analysis can catch these small changes in signal form of the image by highlighting the powerful energy bands. Therefore, the DSWI includes low energy information in the field of time-frequency-domain. These kinds of images are provided as the input to the DCNN to indirectly evaluate the performance of the proposed approach through the classification accuracy. The classification accuracy performance is detailed by the confusion matrices as illustrated in Figure 7. The confusion matrix indicates the class distinguishing performance by calculating the actual versus predicted deviation. For validating the diagnostic result, the metrics of sensitivity score (SS) and mean per class of sensitivity score are used. The sensitivity score formula is presented as follows:  
\[SS=\frac{\#true\_pos}{\#true\_pos+\#false\_neg}\times 100\% \tag{7}\]  
Here, the term \(\#true\_pos\) depicts the number of correctly predicted data samples from the provided test dataset which are used to validate the model at each iteration, and the term \(\#false\_neg\) refers to the number of data samples from a class that are wrongly classified. Hence, the average sensitivity can be obtained by \(avgSS=(\sum SS)/\#class\), where \(\sum SS\) represents a summation of the class-wise sensitivity score for all the test dataset. Then, the averages of all the accuracies and losses are collected to observe the accuracy values and loss values during the training stage. The DCNN model hit an accuracy of 98.79% on average with the scenario of using the DSWI as the input, while the other scenarios of using the vibration image and conventional wavelet spectrogram had average accuracies of 83.06% and 93.15%, respectively, as described in Figure 7. Other devices such as motors and the noisy factory environment create  
Figure 6: The generated image of bearing fault signal from different methods: (**a**) Vibration image (**b**) Conventional Wavelet spectrogram image (**c**) DSWI. impulses or random fluctuation peaks in the AE signal making the time-domain or frequency-domain analysis inefficient for this kind of AE signal. Processing the AE signal with DWSI can, however, partly alleviate the noisy random fluctuations and environmental stimulation in the AE signal.