**4. Case Analysis**

In this section, the data of the wind turbine transmission platform are used to verify our model. The wind turbine transmission platform is shown in Figure 5. It consists of a drive motor, a stator gearbox, a planetary gearbox, and a load device to simulate the vibration state under various gear faults.

The number of teeth of each gear in the drive system is shown in Figure 6. The stator gearbox consists of four gears in a two-stage drive with three shafts. The fault occurred in the intermediate shaft gear. Piezoelectric sensors are placed on the bearing seat at the right end of the intermediate shaft. This paper simulates the multiple faults of a wind turbine gearbox under variable operating conditions. Six fault modes in the stator gearbox are adopted, including normal, cracked, chipped, missing teeth, wear, and eccentricity. The data available is shown in Table 2. The data consists of six categories, with one health category and five fault categories. The first three categories contain data for four operating speeds (38 Hz, 40 Hz, 43 Hz, 45 Hz) and the last three categories only have data for 43 Hz and 45 Hz. The speed is of the driver motor. The data is sampled at a frequency of 8192 Hz; 256 data are available in each category for each working condition.

**Figure 5.** Transmission platform of wind turbine.

**Figure 6.** General structure of the gear system.



The data description of the training dataset and testing dataset is shown in Table 3. There are 256 data in each category for each speed. For each class of data under each speed, the first 160 are taken as the training set and all data are testing data. The trained percentages are 62.5%. This case addresses the problem of unbalanced data from the wind turbine transmission platform, generating missing data and improving diagnostic accuracy. Therefore, in this case, the data in categories 3, 4, and 5 where the speed is 38 Hz and 40 Hz are set missing and are not included in the training set.


**Table 3.** Data description of the training dataset and testing dataset.

For the TL-CVAE-GAN and classifier model, the update function is Adam, the training epochs for the update are 400, and the batch size is 32.

Figures 7–9 show the missing data, *XT*<sup>2</sup> , generated by the generator CVAE-GAN2. It can be seen that the generator effectively generates data for the unknown operating conditions (38 Hz, 40 Hz).

**Figure 7.** The generated data and its corresponding real data for fault 3 at 38 Hz and 40 Hz.

**Figure 8.** The generated data and its corresponding real data for fault 4 at 38 Hz and 40 Hz.

**Figure 9.** *Cont*.

**Figure 9.** The generated data and its corresponding real data for fault 5 at 38 Hz and 40 Hz.

In this case, it is the pinion of the intermediate shaft that has failed. Therefore, the rotational frequency is given in Equation (14) and the meshing frequency is given in Equation (15).

$$f\_r = speed \times 29 / 100\tag{14}$$

$$f\_m = f\_I \times \text{36} \tag{15}$$

When the operating condition is 38 Hz, the rotational frequency is 397 Hz and the meshing frequency is 11 Hz. When the operating condition is 40 Hz, the rotational frequency is 418 Hz and the meshing frequency is 12 Hz. The rotational and meshing frequency characteristics are evident in both the real data and the generated data. At the same time, there are differences in the frequency spectrum of missing, wear, and eccentric faults.

Figure 7 shows a missing fault. When a gear has a broken tooth, there is a strong shock at the broken tooth for every week the gear rotates, so there are distinct rotational and meshing frequencies present in the frequency spectrum. It is clearly modulated by the rotational frequency throughout the frequency band. The edge band is characterized by a large number of edge frequencies, a wide range, and a uniform and relatively flat distribution. It can be seen that the generated data effectively exhibits these characteristics.

Figure 8 shows a wear fault. The gears are uniformly worn, with a high amplitude sideband at the engagement frequency and its harmonics. The amplitude of the higher harmonics of the meshing frequency is large. In this data, the wear is more severe and the amplitude of the second harmonic has exceeded the amplitude of the fundamental wave of the meshing frequency. It can be seen that the generated data effectively exhibits these characteristics.

Figure 9 shows an eccentric fault. This data has only eccentricity, no faulty gears, so there are no sidebands at the meshing frequency. It can be seen that the generated data effectively exhibits these characteristics.

The generated data for the unknown working conditions are trained together with the known data for the classifier. We compared the classification accuracy of the trained model using only the training set and the training set with the generated unknown data. For better comparison, the same classifier, the same number of training epochs, and the same learning rate were used for both cases. The obtained fault classification accuracy and t-SNE is shown in Figure 10. The comparison of classification accuracy with and without the addition of generated data is shown in Table 4. It can be seen that after the data generated by TL-CVAE-GAN with unknown working conditions were added to the training set, the test accuracy of the trained classifier was improved by 21.3%.

**Figure 10.** The t-SNE of the classify using only the training set and the training set with the generated unknown data.

**Table 4.** Comparison of classification accuracy with and without the addition of generated data.

