## 4 Data Generation in Machine Fault Detection
### Fault Diagnosis Using Generated Signal  
Based on both the original and generated data, we evaluated the final results using the three approaches described in Section 3. Keeping the same testing data, we simulated the actual situation of the AI model in real life. In contrast, the training data is a mix of the real data and the generated data. The ratio of the real data over generated data is 100%, 80%, 60%, 40%, 20%, and 0%. With this testing condition, different signal processing approaches, and AI model, the generated data will be evaluated comprehensively if it can satisfy the data augmentation requirement in a fault machine detection application. To verify the similarity between original data and generated data, we conducted the Kolmogorov-Smirnov test using Python version 3.7.4 [34]. The statistic value is 0.059, while the \(p\)-value is 0.336, so we can accept the hypothesis that signals are drawn from the same distribution. Figure 12 illustrates the relationship among all statistical elements between an original broken machine signal and a generated signal. The generated signal has a larger data variation distribution with taller boxed, which shows the variations during the generation phase. In Figure 13, by continuing to break down the relationship between the maximum and kurtosis values of the original and generated broken FFT of the signals, we can see high variations in the generated values. The linear regression test [35] is conducted to verify the correlation between the maximum and kurtosis values. The coefficient of determination is calculated and shown in Table 7. With the high value of Coefficient of Determination in all dimension \(g\_x,g\_y,g\_z\), and \(g\_t\), we can conclude that the maximum and kurtosis has a high correlation in fault signal. Compared with the original signal, the generated signal has a lower Coefficient of Determination, indicating that it has higher variation and less dependent on each other. This variation is good for the training phase because it can improve the machine learning models with different input patterns. Figure 11: FFT of generated vibration data for the broken machine. Figure 12: Statistical elements of the original and generated broken FFT of the signals. Table 8 shows the accuracies of ANN, K-mean clustering, and SVM with different approaches based on the FFT of the vibration signal. With the full FFT of the signal approach, the data augmentation with the original data larger than 40% worked well under the testing condition with 100% accuracy (ANN). This result is better than the 0% original data set, which has the accuracy of 89.4% (ANN), 60.2% (K-mean clustering), and 93.1% (SVM). The classification algorithms worked much better in the case where 20% original data were used, which achieve the accuracy of 95.1% (ANN), 61.3% (K-mean clustering), and 95.3% (SVM). In the case of using PCA transform for the FFT signal, the data augmentation with the original data larger than 40% worked well under the testing condition with 98.1% accuracy (ANN). This result is better than the 0% original data set, which has the accuracy of 87.2% (ANN), 55.3% (K-mean clustering), and 91.0% (SVM). The classification algorithms worked much better in the case where 20% original data were used, which achieve the accuracy of 93.1% (ANN), 65.2% (K-mean clustering), and 94.7% (SVM). In the last approach, the statistical analysis of the FFT of the signal, the ANN provides almost 100% accuracy with more than 20% original data. The accuracy of the ANN algorithm decreases to 79.41% when there is 0% original data; this is much better than the traditional augmentation method in Section 3. In this approach, the K-mean clustering and SVM have poor performance as compared with ANN. The SVM has high accuracy and stable with different test sets, so it is strong enough to be considered in real-life scenarios. In contrast, the K-mean clustering is not stable and requires more accuracy to be considered as a reliable classification approach.