*4.2. The Fault Diagnosis Results*

In this paper, "one-versus-all" is used to extend LSSVM from two classifications to multiple classifications. That is, each time, one fault is selected as one type, and the rest of the states are selected as another type. In order to produce the posterior probabilities of the four classifications in the vibration feature space, four two-class LSSVM are constructed, and each LSSVM calculates a set of *A* and *B*, and then the corresponding posterior probability is calculated according to (5) and (6). In the same way, the probability vectors of the temperature and stator current signal classifiers for the four states can be obtained as the BPA of D–S evidence fusion.

The five-dimensional feature vectors of the vibration signal after t-SNE dimensionality reduction are used as the inputs, and the four working conditions of the transmission system are used as outputs to train the LSSVM, which is optimized by the improved artificial bee colony algorithm. The parameters of the four two-classification LSSVM in the vibration feature space are shown in Table 6. Four samples are selected, such as samples 5, 44, 82, and 130, and the corresponding BPA1 calculated is shown in Table 7.


**Table 6.** Parameters in four vibration least square support vector machine (LSSVM).

**Table 7.** Basic probability assignment 1 (BPA1) of vibration LSSVM.


The two-dimensional feature vectors of the temperature signal are used as the inputs, and the four operating states of the transmission system are used as the outputs to train the optimized LSSVM. The parameters of the four binary LSSVM in the temperature feature space are shown in Table 8. The BPA2 calculated from the same four samples is shown in Table 9.

**Table 8.** Parameters in four temperature LSSVM.




The four-dimensional vectors after the dimensionality reduction of the stator current signal are used as inputs, and the four operating states of the transmission system are as outputs to train the optimized LSSVM. The parameters of the four two-class LSSVM in the stator current feature space are shown in Table 10, and the BPA3 calculated by the same four samples is shown in Table 11.

**Table 10.** Parameters in four current LSSVM.



**Table 11.** BPA3 of current LSSVM.

Then, the probability assignments are calculated after the fusion of the three BPAs. The category with the highest degree of belief is selected as belonging to the class of the fusion model. Table 12 shows the basic and the fusion probability of the three LSSVM outputs for the selected test samples. Table 13 shows the fusion and classification results of the four test samples. Figure 3 shows the test samples' diagnosis results, in which "0" indicates normal operation, "1" indicates parallel misalignment, "2" indicates angular misalignment, and "3" indicates integrated misalignment.

**Table 12.** Probability assignment of three LSSVMs and fusion.


**Table 13.** Fusion and classification results of four test samples.


**Figure 3.** The diagnosis results of the testing set.

In order to better evaluate the performance of the fault diagnosis method, three indexes are adopted: the training set classification accuracy, the testing set classification accuracy, and the fault false alarm rate. The fault false alarm rate means that the fault does not actually occur, but the fault detection alarm is given by the detection system. The false alarm rate equals the number of false alarm samples divided by the total number of actual fault-free samples. Table 14 compares the results of the sample sets diagnosed by the indexes of a single signal (vibration, temperature, or current signal) with the D–S evidence fusion.


**Table 14.** Comparison of diagnostic results.

From Table 14, it can be seen that the accuracy of D–S fusion is higher than that of any single signal, and the failure false alarm rate is equal to zero, lower than others, which proves the advantage of information fusion in the diagnosis of wind turbine misalignment fault.

#### **5. Experimental Verification of Platform**

In this paper, the 1.5 kW misalignment experimental platform is used for experimental verification. The platform is shown in Figure 4a. It includes a generator, coupling, gearbox, driving motor, and so on. The speed of the driving motor is changed by a planetary gear reducer with a transmission ratio of 1:50 to simulate the wind blowing blade speed, then it is accelerated by a planetary gear with a transmission ratio of 40:1 and a spur gear with a transmission ratio of 1.5:1 to drive the generator. The generator can be adjusted by the support to create parallel or angular misalignment.

**Figure 4.** Experiment equipment. (**a**) The platform of wind turbine; (**b**) layout of vibration sensor; (**c**) current signal acquisition card USB 4AD Plus.

The vibration signal of the gearbox is obtained using the DFT5100 dynamic data collector from the acceleration sensor (ICP type) on the experimental platform (Figure 4b). The current signal is transmitted to the USB signal acquisition and recording platform through the signal acquisition card USB 4AD Plus (Figure 4c). In this paper, the rotation speed of the motor is set to 600 rpm; the sampling time is 10 s; and the sampling frequency of vibration and current is 1 kHz and 2 kHz, respectively. In the experiments, the temperature signal is easily affected by the operation time of the unit and the ambient temperature, and it cannot reflect the actual operating temperature of the wind turbine. Therefore, when fusing different signals by D–S evidence theory, we set the temperature signal to 0, regardless of its influence. Four groups for each working condition, with a total of 16 groups, are sampled on the platform. Some characteristic indexes of vibration and current signal are shown in Tables 15 and 16. The actual classification and diagnosis results of fusion signals and individual signals are shown in Figure 5. Table 17 is the calculation of two examples.


**Table 15.** Part of the characteristic index of the vibration signal.

**Table 16.** Partial characteristic index of current signal.


**Figure 5.** Diagnostic result. (**a**) Vibration signal + current signal; (**b**) vibration signal; (**c**) current signal.


**Table 17.** Basic probability assignment of two kinds signals and probability after fusion.

It can be seen from Figure 5 that the classification accuracy of the testing set is 75%, while that of the single vibration signal is 62.5% and that of the single current signal is 62.5%, which indicates that the accuracy of the diagnosis is improved by using the D–S decision fusion method with multi-source signals as the diagnosis information. In addition, the reason the classification accuracy of the experimental results is much lower than that of the simulation results is that there is no temperature signal in the D–S evidence theory

fusion. It can be seen from Table 17 that the first sample is correctly identified using either the single signal or fusion signal, while the second sample is mistakenly diagnosed as angle misalignment using only the vibration signal, but is correctly identified by D–S fusion.

#### **6. Conclusions**

This paper proposes an integrated fault diagnosis method for wind turbine transmission system misalignment based on information decision fusion. The method uses multiple sources of signal including vibration signal, temperature signal, and stator current signal as the original source, and extracts different features from their time domain, frequency domain, and time–frequency domain. t-SNE is used to eliminate the correlation of characteristic values of the vibration signal and the stator current signal. Three posterior probability least squares support vector machines optimized using improved artificial bee colony algorithm are constructed respectively. The output probabilities of least squares support vector machines are used as the basic probability distribution of evidence fusion, and the fault diagnosis is completed by D–S synthesis and decision rules. Finally, the simulation experiments and platform verification show that the D–S evidence fusion model has higher diagnostic accuracy than the non-fusion model for the wind turbine misalignment fault.

**Author Contributions:** Conceptualization, Y.X. and Y.W.; software, Y.W.; validation, M.L.; writing original draft preparation, Y.W. and Y.X.; writing—review and editing, L.Z. and J.X.; project administration, Y.X. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China (51577008).

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

