**1. Introduction**

Existing deep neural networks have shown superior performance in various diagnostic tasks for rotating component faults due to their impressive feature learning capabilities [1–3]. Such networks include the convolutional neural network [4,5], recurrent neural network [6], and restricted Boltzmann machine [7]. The outstanding performances of these networks heavily depend on the pretraining of deep diagnostic networks with real sample data from the same domain as the test data [8]. However, under actual operating conditions, the dataset is often time-varying and unknowable. Improving the generalization capability of a model under variable working conditions has been regarded as a potential solution for solve unknown working conditions.

Domain discrepancy causes the model based on the previous training data to perform poorly with the new test data set [9,10]. The typical solution to this problem is to pre-train the model and fine-tune the diagnostic network trained from the source domain with the feature distribution of the target domain [11], and the method for the marginal distribution alignment of feature spaces is widely used to narrow the distance between two different domains [12]. Li et al. [13] proposed a fault diagnosis model based on multi-scale permutation entropy (MPE) and multi-channel fusion convolutional neural networks (MCFCNN), which constructs a feature vector set by permuting entropy so that the high accuracy and stability of fault diagnosis are realized. Guo et al. [14] reported a new transfer learning network, which gradually realized the multi-module operation of automatic features

**Citation:** Yan, Z.; Liu, G.; Wang, J.; Bao, H.; Zhang, Z.; Zhang, X.; Han, B. A New Universal Domain Adaptive Method for Diagnosing Unknown Bearing Faults. *Entropy* **2021**, *23*, 1052. https://doi.org/10.3390/e23081052

Academic Editor: Fengshou Gu

Received: 22 July 2021 Accepted: 9 August 2021 Published: 16 August 2021

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learning and machine health status recognition through a one-dimensional convolutional network. Singh et al. [15] presented a deep convolution model to diagnose the type of the gearbox fault under the obvious change of speed. The model minimizes the cross-entropy loss of the source domain and the maximum mean discrepancy loss between the two domains to obtain superior diagnostic performance. Hasan et al. [16] proposed a transfer diagnosis framework based on high-order spectral analysis and multitask learning, which can diagnose non-stationary and non-linear rolling bearing signals in combination with different modes of a given fault type. As can be seen from the above-mentioned networks, solving the problem of domain discrepancies has become a tacit prerequisite for current fault diagnosis.

Traditional diagnostic networks usually assume that the label space of the fault samples in the target domain and the source domain is consistent. However, in actual engineering practice, the fault type of the target domain is often difficult to predict, and the fault type label space is often smaller than the source domain fault label space. Therefore, Cao et al. [17] proposed the use of selective weighting to maximize the positive migration of shared tag space data; this approach can achieve the purpose of per-class adversarial distribution matching. Zhang et al. [18] established an importance weighted adversarial network. This network is especially suitable for partial domain adaptation where the number of fault types in the target domain is less than the number of fault types in the source domain, and can effectively reduce the distribution difference to realize knowledge migration and the fault diagnosis of the target sample. Li et al. [19] suggested applying unsupervised prediction consistency schemes and conditional data alignment for partial domain adaptation. This method effectively solves the partial domain adaptation problem that the target domain data under unsupervised training cannot cover the entire healthy label space. Jia et al. [20] proposed a weighted subdomain adaptation network (WSAN), and a weighted local maximum-mean-discrepancy (WLMMD) is introduced to obtain the transferable information and weight of the sample to realize the diagnosis of the fault type. The research on partial domain adaptation pushes the field of intelligent fault diagnosis into a practical setting.

However, only a very small number of networks can cope with the identification and diagnosis of sudden unknown fault types in the existing fault diagnosis models. We cannot know that the fault type of the target samples must belong to the source domain label space when providing unlabeled target samples. Therefore, open set recognition is an urgent problem faced by transfer learning to broaden practical application scenarios. Busto et al. [21] were the first to suggest marking the shared classes of the source and target domains as general classes and constructed an iterative method to solve the labeling problem. Saito et al. [22] modified the description of open set domain adaptation, which allows only the target domain to contain the private label set. His team also added a boundary between the source domain and the target domain to facilitate the separation of unknown fault samples from known fault samples. This method has been widely evaluated in the field. You et al. [23] provided a concept of universal domain in the field of image recognition which allows intersection between source and target domains and provides a benchmark for future related research.

Considering that the current domain transfer methods often assume that the fault type of the test data is the same as the training data set, while ignores that the specific working conditions and label types of the target domain samples are often unpredictable. It is impossible to diagnose the fault type by directly comparing the distribution of the source domain and the target domain. Thus, we propose a new universal domain adaptation (UDA) method for fault diagnosis under the changing conditions of bearing speed. As shown in Figure 1, the model allows different types of faults to exist between data sets and generates a feature center belonging to each fault type for fault diagnosis by learning the fault features of each fault sample. In order to solve the problem of negative model transfer caused by the input of unknown samples into the network, the model proposes three optimization goals, and train the network gradually by optimizing the objective function to alleviate the phenomenon of negative network transfer. The main contributions of this model are as follows:

**Figure 1.** Universal domain adaptation setting (unshaded shapes indicate shared labels).


In this paper, a new transfer learning model based on universal domain adaptation is proposed and the proposed model is described in detail. The specific article structure is organized as follows. The details of the proposed method for fault diagnosis under changing speed conditions are provided in Section 2. The fault diagnosis experiment with two sets of bearing data is presented in Section 3. Finally, the conclusions are provided in Section 4.
