*3.1. Experimental Dataset Description*

The intelligent fault diagnosis methods trained with the labeled data are required to classify the unlabeled data accurately to validate the effectiveness of this method in universal domain transfer learning. Therefore, as discussed in this section, the datasets acquired from two dedicated rotating part workbenches are used for bearing fault diagnosis experiments.

*CWRU***:** The Case Western Reserve University (CWRU) bearing dataset was collected from an experimental platform provided by the CWRU [27]. The CWRU workbench collected sample data of four health conditions at the 6 o'clock position (orthogonal area of applied load) of the deep groove ball bearing on the drive end of the motor housing. The four health conditions were normal condition (NC), inner race failure (IF), outer race failure (OF), and ball failure (BF). The sampling frequency at the time of data collection is set to 48 kHz, and each fault type was run with varying degrees of damage (0.007-, 0.014-, and 0.021-inch fault diameters). Each type of fault data was collected by the test motor running at three different motor speeds (i.e., 1772, 1750, and 1730 rpm) for fault diagnosis. The CWRU dataset information is shown in Table 1.


**Table 1.** Information of the two datasets.

*SDUST***:** The Shandong University of Science and Technology (SDUST) bearing dataset was collected from a diagnostic test bench specially designed for bearing faults. The timedomain signal of bearings at different speeds of the motor is collected. Figure 4a shows that the bearing fault test bench is composed of a motor, a rotor, a brake, a bearing seat, and two shaft couplings. The cylindrical roller bearing faults in the SDUST dataset contains three single types of fault and a type of composite fault, which are: OF, roller fault (RF), IF, and roller and outer race fault (ROF). Figure 4 is a schematic diagram of the three single types of fault bearings. The collected bearing signals of each type of fault are divided into two fault severity levels: crack 0.2 mm and crack 0.4 mm. The NC time-domain signal was added to the SDUST dataset to obtain nine types of faults as shown in Table 1. Each acceleration sensor was respectively installed in different parts of the bearing seat, and the sampling frequency was set at 25.6 kHz. The motor speed was set to 1500 r/min, 1800 r/min, and 2000 r/min during data collection, and a total of 200 samples were collected for each fault health status at different motor speeds, and each time-domain sample contained 6400 data points.

**Figure 4.** (**a**) Bearing fault test rig and (**b**) three single types of fault bearings.

#### *3.2. Compared Methods Description*

The proposed method shares the same experimental configuration and test dataset with all the following comparison methods to evaluate the diagnostic advantages of the proposed model.:

**Baseline:** First, a baseline method without a special technique is proposed to diagnose the UDA problem [28]. The feature extractor and classifier are trained under supervision, and the network is used directly for the fault diagnosis of the target domain dataset.

**L1/2-SF:** The L1/2-SF (L1/2 regularized sparse filtering) approach [29] is widely used as an excellent method for bearing and gear fault diagnosis. This method follows the traditional unsupervised machine learning model, thus providing a benchmark for the proposed method.

**WD-MCD:** The Wasserstein Distance—Maximum Classifier Discrepancy (WD–MCD) approach maximizes the output discrepancy of the classifier and combines marginal probability distribution adaptation to focus on the diagnosis of the transfer model [20]. This model is compared with the proposed model because it is a popular transfer learning method.

**BN–SAE:** As a popular method, the Batch Normalization—Stacked AutoEncoders (BNSAE) approach [30] is an adaptive reparametrization algorithm that aims not to optimize but to regularize the model. The effect of the healthy data classification scheme can thus be examined.

#### *3.3. Experimental Results Display*

As reported in this section, the UDA problem is experimentally verified. The model parameters during the experiment are shown in Table 2 and are mainly determined in accordance with the verification results of the diagnostic task.



The detailed task information is shown in Table 3. This information randomly selects the fault type for fault diagnosis in the two datasets. In order to verify the fault diagnosis performance of the framework under variable speed conditions, the experiment sets the fault type diagnosis in the phase of gradually increasing bearing speed and the fault type diagnosis in the phase of gradually decreasing speed. The "source classes" represent the fault type of the source domain training sample, the type of fault marked red represents the private type of the source domain (the category does not appear in the target domain fault sample), and the "unknown class" represents the fault type that has not been learned during source domain training. A total of 100 labeled samples under each machine condition are randomly selected as source domain data for model training, and 100 unlabeled samples are used as target domain samples for experimental verification. An average of 10 experiments for each group of results is performed to reduce the effect of randomness.


**Table 3.** Universal domain transfer learning task information.

3.3.1. CWRU Task Set Result Analysis

Table 4 shows the fault diagnosis results of the proposed model using the CWRU dataset for different universal domain tasks. The selected comparison approaches are currently the highly popular domain adaptive and transfer learning methods. The stable diagnostic performance presented by the proposed method in the CWRU dataset task group shows its superiority in solving universal domain adaptation. Furthermore, the proposed method generally obtains smaller standard deviations than other models when performing different tasks, indicating that it has good convergence in the experimental process.

**Table 4.** Means of the testing accuracies in different tasks with the CWRU dataset (%).


The L1/2-SF, the WD-MCD, and the DA-BNSAE methods achieve relatively ideal accuracy rates in the tasks with the CWRU dataset compared with the baseline method, and their accuracy in some tasks is as high as 80 or more. These methods generally have good feature recognition capabilities in the diagnosis of minor faults. However, in serious fault diagnosis, the proposed model has superior feature recognition and diagnosis performance. Typical task cases are represented by tasks A3 and A7. The accuracy of the proposed method is as high as over 90%, and high accuracy is also obtained in the process of solving task 9. Task 4 is specially set as the task benchmark, which has no unknown fault type and belongs to pure rotation speed transfer. It can be seen that the proposed method can still guarantee high diagnostic accuracy. Comparing the standard deviation of each method reveals that the proposed method exhibits relatively stable performance in multiple tasks, further verifying its convergence performance. Although the performance in minor fault diagnosis shown by the proposed method is not as good as that of the three comparison methods, the superiority of the modified model can be seen in the overall task performance comparison. Moreover, the proposed model is more suitable for fault diagnosis problems in the universal domain than other comparison methods.

The t-distributed Stochastic Neighbor Embedding (t-SNE) method [31] is widely used in the display of various fault diagnosis results. This approach can reduce the dimensionality of the output of the high-dimensional features by the model and provide visualization processing. The A1 task based on the CWRU dataset is selected as the demonstration experiment for t-SNE dimensionality reduction processing for visually displaying the fault diagnosis performance of each network as shown in Figure 5.

**Figure 5.** Feature visualization of the t-SNE results for the CWRU dataset in the A1 task.

The baseline approach exhibits poor fault diagnosis performance as illustrated in Figure 5a. It not only fails to aggregate various types of faults completely, but it also clusters BF14 faults and BF7 faults together. As can be seen in Figure 5b,d, the L1/2-SF, and the DA-BNSAE approach incorrectly classify the BF14 fault as the BF7 fault, and the L1/2-SF approach also shows that the target domain and the source domain samples of the OF7 fault are not clustered. As presented in Figure 5c, although the WD-MCD approach has a better fault clustering effect than the previous three methods, a situation wherein the fault type BF14 is mistakenly classified as a healthy sample exists. The clustering dimensionality reduction graph of the proposed method is shown in Figure 5e. Although a small number of IF14 fault samples are close to the BF14 fault in the proposed method, the target domain and the source domain samples of various types of faults have obvious domain boundaries and show a good fault classification effect.

Figure 6 depicts that the training accuracy and testing accuracy of the method tends to stabilize as the training progresses, and feature and distance losses in the model gradually decrease as accuracy increases.

**Figure 6.** Accuracy and training loss of the proposed method in the A1 task.

#### 3.3.2. SDUST Task Set Result Analysis

The experimental accuracy for the SDUST dataset is shown in Table 5. Given that this dataset has more drastic speed changes, diagnostic performance with this dataset is worse than that with the CWRU dataset. It can be seen that the three comparison methods show good diagnostic performance in individual tasks. However, the proposed method is more convincing in terms of overall fault classification effect and stability. The model still provides superior fault diagnosis accuracy under variable speed conditions that further validates its robustness and superiority for UDA problems.


**Average** 48.37 72.12 74.29 69.80 84.68

**Table 5.** Means of the testing accuracies in different tasks with the SDUST dataset (%).

Considering that the experimental task is too heavy, the B1 task based on the SDUST dataset is selected as the demonstration experiment for t-SNE dimensionality reduction processing for visually displaying the fault diagnosis performance of each network (Figure 7). Although the baseline approach provides a good clustering of the source domain fault types, it shows a small amount of confusion between the fault type 3 (NC) and the fault type 8 (ROF0.2), as well as between the fault type 8 (ROF0.2) and the fault type 1 (IF0.2) in the target domain. The baseline approach mistakenly classifies the target domain fault type 8 (ROF0.2) sample as the fault RF0.2 as shown in Figure 7a. As can be seen from Figure 7c, the WD-MCD approach incorrectly classifies the NC samples at 1800 speed as the OF0.2 fault, and some samples as the fault type 8 (ROF0.2) in the target domain are mixed with the fault RF0.2. The DA-BNSAE network, one of the approaches used for comparison, confuses the fault type boundaries of IF0.2, RF0.2, and ROF0.2 faults as presented in Figure 7d. Comparing the proposed method with the L1/2-SF approach, it is found that although the L1/2-SF method has a good clustering effect on the source domain samples, there are still a small number of OF0.2, RF0.2, and ROF0.2 fault samples that are misclassified. The proposed network not only has a more obvious clustering effect on samples of various fault types but also has obvious separation between samples of different fault types, as shown in Figure 7b,e.

**Figure 7.** Feature visualization of the t-SNE results for the SDUST dataset in the B1 task.

Therefore, the proposed model can diagnose the samples of the unknown fault types more effectively than other networks.

#### **4. Conclusions**

This paper presents a new UDA method for bearing fault diagnosis under different working conditions, which breaks the assumption that the traditional domain adaptive network shares the label space and attempts to solve the unknown scale domain by using a universal label domain method. The proposed method was compared with the current popular domain adaptation methods in the experimental verification stage. Under the premise of sharing the experimental configuration and dataset, we set up multiple sets of experimental tasks for different actual work needs. Through multiple experimental verifications, it is concluded that the proposed method has higher classification accuracy and robustness than the comparison methods in diagnosing bearing datasets under variable conditions, and it can still guarantee high diagnostic performance even in the presence of bearing samples of unknown fault types. Therefore, the proposed method is more suitable for actual working conditions that change from time to time.

**Author Contributions:** Conceptualization, Z.Y. and J.W.; methodology, Z.Y.; software, H.B.; validation, Z.Z., X.Z., and B.H.; formal analysis, Z.Y.; investigation, Z.Y.; resources, J.W.; data curation, Z.Y.; writing-original draft preparation, Z.Y.; writing-review and editing, Z.Y.; visualization, Z.Y.; supervision, J.W.; project administration, G.L.; funding acquisition, J.W. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported by the National Natural Science Foundation of China, grant number 52005303, the Project of China Postdoctoral Science Foundation, grant number 2019M662399, and the Natural Science Foundation of Shandong Province, grant number ZR202020QE157.

**Data Availability Statement:** The data used to support the findings of this study are available from the corresponding author upon request.

**Acknowledgments:** This research was supported by special funds and experimental equipment from the Shandong University of Science and Technology.

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

#### **Notations**


