## 4 Case Study
### Feature Extraction from Motor Control Signal  
In order to extract good features representing faults in the motor control signal in operation, WPD is conducted to the current and velocity signal, in which Daubechies 6 (db6) and three levels are taken for the wavelet function and decomposition, respectively. These selections are based on similar studies by [28; 29], in which the WPD and the Daubechies mother wavelet family are used to detect faults in an AC motor or components connected to the motor using the motor current signal. Since our aim is the same, namely, the fault diagnosis of components connected to the AC motor, the Daubechies family is employed. Regarding the level of decomposition, it is generally selected to adequately capture the fault characteristics in the frequency domain of the fault signals. To this end, the FFTs are performed to all the fault conditions of different severities, and the results are given in Figure 8, which shows each spectrum in superposition. The legend of the figure represents HD \(Lv\) and TB \(Lv\). In this figure, differences are captured in specific frequency bands depending on the fault. Based on this observation, it follows that the three levels, namely, the eight bands (W0 to W7) with the length of 62.5 Hz, are enough to identify the difference between each fault condition. The bands are divided by the black dotted lines in the figure. The wavelet coefficients in each band for the four conditions are shown for the current signal in Figure 9, which exhibits a clear difference between the HD and TB faults: comparing the HD \(Lv_{2}\) fault in Figure 9 to the normal in Figure 9a, the coefficient increases in the low-frequency bands W1, W2, and W3. On the other hand, in the TB \(Lv_{3}\) fault in Figure 9c, the coefficient increases in the high-frequency bands W5, W6, and W7. In both the HD and TB with \(Lv_{2}\) faults in Figure 9d, the coefficients increase in both the low- and high-frequency bands. In order to make a more quantitative comparison, wavelet energy (WE) is calculated by using Equation (4) using the coefficients at each frequency band, which are repeated for all the fault conditions. The results are plotted in Figure 10, where black, blue, green, and red dots indicate \(Lv_{0}\), \(Lv_{1}\), \(Lv_{2}\), and \(Lv_{3}\) in TB faults, respectively, whereas HD faults are divided by vertical dotted lines. A similar observation is found, which is that the WE increases in the low-frequency bands W1 and W3 when the HD fault level increases. In the case of the TB, the WE increases in the high-frequency bands W5, 6, and 7 as the TB fault increases from \(Lv_{0}\) to \(Lv_{3}\), although the increase is significant only at \(Lv_{3}\). Figure 8: Frequency spectrum for each of the 11 fault conditions. In addition to the WE, 13 statistical time-domain features commonly used in the fault diagnosis, as shown in Table 1[19], are extracted for each of the eight frequency bands of the current signal. Applying the same process to the velocity signal, a total number of \(2\times 14\times 8=224\) features are obtained for a single operation condition. The score as defined in Equation (11) is calculated for the 224 features, which accounts for the two metrics: _corr_ for a consistent trend with respect to the fault severity and \(FDR\) for the separability of each fault. After a parametric study to determine the weight parameter \(\alpha\), the value 0.8 is found to be the most appropriate to meet both requirements. Since the calculation is performed for the components HD and TB, respectively, 224 scores are available for the features of each component. Note that the values are normalized so that they vary between 0 and 1. For these sets of scores, the RPN formula as described in Section 2.2 is applied to estimate the threshold and select the most significant features in a more logical manner. The resulting thresholds are shown in Figure 11a,b by the horizontal lines, which indicate the scores of all the features in descending order.