# Generative Oversampling Method for Imbalanced Data on Bearing Fault Detection and Diagnosis
## 5 Conclusions  
In this study, we developed a novel generative oversampling method to address the data imbalance issue for bearing FDD. In short, because the volume of faulty condition data is much lower than that of normal condition data, a lower recognition accuracy of the fault condition results. Before introducing the oversampling method, the proposed method was used to transform time-series data into the image domain via the NSP method; bearing faults in the induction motor were classified using designed CNNs. The classification accuracy was 2.4 to 25% points higher than that of previous work; furthermore, our approach provided around 90% accuracy even when the imbalance ratio was weak (50:1); the accuracy declined to 80% when the imbalance ratio increased to 1000:1. To overcome the data imbalance problem, we generated fault images using DCWGAN-GP. Experiments demonstrated that the proposed method improves accuracy by 7.2 and 4.27% points on average and gives maximum values with 5.97 and 3.57% points higher accuracy than the previously developed DCGAN approach. Additionally, the accuracy of the proposed method was close to that under data imbalance ratio conditions of 20:1 and 40:1 without oversampling. As future work, we will consider accuracy improvement in generative oversampling methods. Even though the proposed DCWGAN-GP improved the FDD accuracy in the given imbalanced data conditions, there is less than a 2% gap compared to the weak imbalanced data conditions. Furthermore, comparing to the DNN with HHT [11] and the CNN with CWTS [17,18], CBFD with BF-NSP takes at least twice training and testing time. We will optimize the classification network and reduce computational time. In addition, we plan to apply the proposed methods to other data-imbalanced conditions in FDD. conceptualization, J.J. and Y.O.L. ; methodology, S.S. and H.L. ; software, S.S., H.L., and J.J.; validation, S.S. and H.L. ; formal analysis, S.S.; investigation, S.S. and H.L. ; resources, Y.O.L. ; data curation, J.J. and Y.O.L. ; writing--original draft preparation, S.S.; writing--review and editing, H.L., J.J., P.L. and Y.O.L. ; visualization, S.S.; supervision, P.L. and Y.O.L. ; project administration, Y.O.L. ; funding acquisition, Y.O.L. This research was supported by KIST Europe Institutional Program [Project No. 11806]. We thank [PERSON] and [PERSON] in ISEA of RWTH Aachen University for discussion on data collection and synthetic fault data generation. We also thank [PERSON] of Hanyang University, who conducted the fault classification experiments as an intern in KIST Europe. The authors declare no conflict of interest. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & \multicolumn{5}{c}{**A-NFR**} \\  & & 20:1 & 10:1 & 4:1 & 2:1 & 1:1 \\ \hline \multirow{6}{*}{DCGAN} & (a) & 91.05\% & 91.13\% & 92.51\% & 94.24\% & 93.89\% \\  & (b) & 95.20\% & 95.79\% & 96.23\% & 97.03\% & 97.05\% \\  & (c) & 93.54\% & 94.10\% & 94.88\% & 95.59\% & 95.63\% \\  & (d) & 96.39\% & 96.68\% & 97.15\% & 97.42\% & 97.52\% \\ \hline \multirow{6}{*}{DCWGAN-GP} & (a) & 97.02\% & 97.10\% & 97.63\% & 97.88\% & 98.05\% \\  & (b) & 98.77\% & 98.78\% & 98.98\% & 98.98\% & 99.30\% \\ \cline{1-1}  & (c) & 97.58\% & 97.81\% & 98.21\% & 98.30\% & 98.41\% \\ \cline{1-1}  & (d) & 99.15\% & 99.16\% & 99.50\% & 99.16\% & 99.50\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Accuracy of original data and oversampled data using the deep convolution generative adversarial network (DCGAN) and the proposed Wasserstein generative adversarial networks with gradient penalty (WGAN-GP) on DCGAN architecture model (DCWGAN-GP) method. (a) Normal-to-fault ratio (NFR) = 200:1 with 10,000 normal data; lower bound = 90.77% at NFR=200:1, upper bound = 98.99% at NFR = 20:1. (b) NFR = 100:1 with 10,000 normal data; lower bound = 94.63% at NFR=100:1, upper bound = 98.99% at NFR = 20:1. (c) NFR = 400:1 with 20,000 normal data; lower bound = 91.30% at NFR=400:1, upper bound = 99.42% at NFR = 40:1.