*3.1. Experimental Test Rig and Data Collection*

The laboratory's wind turbine drivetrain fault test rig is shown in Figure 3, which consists of a control panel cabinet and an experimental test bench to simulate doubly-fed induction generator (DFIG) wind turbine shaft misalignment (between the gearbox and the generator) and broken gear tooth faulty conditions. In Figure 3a, the speed of the motor of the experimental test bench on the right side is decelerated by a planetary gear reducer to simulate the wind blowing blade speed, then it is accelerated by a planetary gear accelerator and a gearbox to drive the generator. The maximum speed of the driving motor is 720 r/min, the speed of the generator is 500 r/min. The left gearbox can be adjusted by the handle to select a normal gear or a broken gear. The generator can be adjusted by the support to create offset or angular misalignment. The control panel cabinet shown in Figure 3b can set and display the motor speed, showing the angle between the generator and the gearbox and other electrical parameters.

**Figure 3.** Wind turbine drivetrain fault experimental test rig: (**a**) experimental test bench; (**b**) control panel cabine.

The vibration signals in normal, misalignment, broken tooth and combined fault (misalignment and tooth broken) conditions were collected from the test rig. Set two measuring point, at the vertical and horizontal direction of the gearbox high-speed output shaft side, with a sampling frequency of 1 kHz and a sample time of 20 s. In the normal and broken tooth conditions, 18 sets of data were collected at the motor speed from 200 r/min to 720 r/min respectively. In misalignment condition, 26 sets of data were collected at the motor speed from 200 r/min to 680 r/min. In combined fault condition, 10 sets of data were collected at the motor speed from 200 r/min to 520 r/min. After preliminary frequency domain analysis of the signals, only the vertical direction signal is used for diagnosis in this paper. With non-overlapping 10,000 points of the signal, the samples in different conditions are shown in Figure 4, from which it can be seen that the presence of broken tooth is easy to distinguish, while the presence of misalignment is not.

### *3.2. LPFEWT and Comparison with Other Approaches*

Employ LPFEWT to extract features from the signal. The cut-off frequency of the low-pass filter is 50 Hz, about 6 times the rated rotating frequency of the generator. The magnitude and phase responses of the designed 40th-order Hamming Window FIR lowpass filter are shown in Figure 5. The filtered signal is decomposed by EWT and the number of EWT Fourier spectrum segments is set to 6. The EWT decomposition results of a combined fault signal are shown in Figure 6, obtained 6 empirical mode components

from low frequency to high frequency. Discard the highest frequency component (the 6th mode) and calculate features of the left 5 empirical modes.

**Figure 4.** Samples of vibration signals in different conditions: (**a**) normal; (**b**) misalignment; (**c**) broken tooth; (**d**) combined fault.

**Figure 5.** The magnitude and phase responses of the designed FIR low-pass filter.

We choose energies of the components as features, that is, the sum of the squares of the amplitude. There are 20 combined fault samples, 27 broken tooth samples, 26 misalignment samples and 27 normal samples, 100 samples in total. Shuffle the dataset and save. Take 14 combined fault samples, 18 broken tooth samples, 18 misalignment samples and 18 normal as training set. The remaining 32 samples of the dataset is testing set. We use LIBSVM Version 3.24 package for SVM classification under MATLAB 2018b. Train the SVM classification model for fault diagnosis, using GWO algorithm search the optimum values of penalty term *C* and RBF kernel parameter *γ* in the range of [0.01, 100]. The average accuracy of 3-fold cross-validation of the training set is used as the fitness of the agents. The grey wolf population is set as 100 and the iteration is set as 50. Empirical modal decomposition (EMD) which is similar to EWT is chosen for comparison. Energies of components obtained by different approaches are inputs of the SVM model. Figure 7 shows the confusion matrix obtained by inputting the components energies of different methods into the SVM model. The horizontal direction represents the predicted class, and the vertical direction represents the true class. The 4 × 4 matrix is the number of samples of each type, and the percentage includes the prediction accuracy rate, false alarm rate and missing alarm rate of each type. Comparison of results are shown in Table 1. Different approaches with 'LPF' prefix use the same FIR low-pass. All approaches use same amounts of components of the signals.

**Figure 7.** Confusion matrix charts of fault diagnosis results with features obtained by different approaches: (**a**) EWT; (**b**) LPFEWT; (**c**) EMD high frequency components; (**d**) LPFEMD high frequency components; (**e**) EMD low frequency components; (**f**) LPFEMD low frequency components.


**Table 1.** Comparison of Fault Diagnosis Results with Different Feature Extraction Approaches.

From Figure 7 and Table 1 we can see, the testing set accuracy of using EWT directly is low, only 53.125%, and there is a lot of conditions confusions. Using LPFEWT to extract time-frequency domain features, the testing set accuracy is highly improved, reaching 100%. In addition, using EWT directly has high false alarm rate, while LPFEWT solves this problem. Among approaches based on EMD, EMD low frequency components has the highest accuracy and the lowest false alarm rate and missing alarm rate, which is 75%, but there are confusions between combined fault and broken tooth or misalignment and normal condition. LPFEMD low frequency components can only identify combined fault and broken tooth correctly. Both with or without the low-pass filter, EMD low frequency components has lower false alarm rate than the high frequency components. Both using high and low frequency components, the accuracy of LPFEMD is lower than that of EMD, and the false alarm rate is higher. The use of low-pass filter in diagnosis with approaches based on EMD will decrease the accuracy instead of increase that, and increase the false alarm rate. Among the six approaches of feature extraction, LPFEWT has the best performance.

We also tried SVM with linear kernel, the accuracy of training set and testing set are 82.4% and 87.5% respectively. So the classification of the dataset is a nonlinear problem, using RBF kernel is proper.
