# Bearing Fault Diagnosis Using Grad-CAM and Acoustic Emission Signals
## 5 Conclusions  
In this paper, we proposed NBCC, which contains bearing characteristic frequencies for training CNNs when used for the task of rolling element bearing fault diagnosis. In addition, we analyzed  
Figure 11: Confusion matrix of the classification result.  
Figure 12: Importance-weights for each bearing failure.  
the feature representation of the trained CNN for the bearing fault diagnosis using the Grad-CAM technique. In the experiment, a custom simulator was used to imitate bearing faults. Using the bearing fault simulator, AE signals were measured for healthy state of the bearing and three different types of bearing faults such as the outer race way, inner race way, and rolling element with a crack on their surface. In the experimental result, the CNN achieved 99% accuracy when trained with the proposed NBCC. The result also demonstrated that the low frequency components were important for classifying healthy state of the bearing, whereas bearing characteristic frequencies were essential for diagnosing various types of bearing faults. This result indicates that CNN trained with the proposed NBCC properly understood the valuable features of the envelop power spectrum for each bearing condition used in this work. For the application of CNNs in real environment, the proposed approach can be utilized to verify whether CNN learns inappropriate feature representation or not.  
All of the authors contributed equally to the conception of the idea, the design of experiments, the analysis and interpretation of results, as well as the writing of the manuscript. Writing--original draft preparation, J.K. and J.-M.K.; writing--review and editing, J.K. and J.-M.K. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) and the Ministry of Trade, Industry and Energy (MOTIE) of the Republic of Korea (No. 20181510102160). This work was also supported by the Technology Infrastructure Program funded by the Ministry of SMEs and Startups (MSS, Korea).  
The authors declare no conflict of interest.  
The following nomenclatures are used in this manuscript  
\(A_{k}\)\(k\)-th output of a convolutional layer  
\(BCC\) bearing characteristic components  
\(Bd\) the diameter of the rolling element of bearing  
\(BPFO\) ball pass frequency on the outer race of bearing  
\(BPFI\) ball pass frequency on the inner race of bearing  
\(BSF\) ball spin frequency of bearing  
\(e(t)\) a sample of envelope signal at the time, \(t\)  
\(F_{max}\) the maximum frequency covering bearing characteristic  
\(f(\omega)\) the magnitude of envelope spectrum at the frequency, \(\omega\)  
\(f_{side}\) The sideband of bearing characteristic frequency  
\(M_{c}\) the importance-weight for the input data, \(NBCC\)  
\(n\) the number of harmonics of bearing characteristic  
\(n\) frequencies used in the proposed method  
\(Nb\) the number of rolling elements  
\(NBCC\) normalized bearing characteristic components  
\(P_{k}^{c}\) importance weight vector of k-th filter of a convolutional  
\(Pd\) the pitch diameter of rolling element bearing  
\(S\) shaft rotating speed  
\(x(t)\) a sample of signal at the time, \(t\)  
\(\hat{x}(t)\) a sample of Hilbert-transformed signal at time, t  
\(y_{c}\) the score of classification for class, \(c\)  
\(z(t)\) a sample of analytical signal at the time, t  
\(\theta\) the contact angle of rolling element