**1. Introduction**

Early fault detection always plays a key role in the field of bearing prognostics and health management (PHM). In most recent years, the quick development of sensor techniques and artificial intelligence gave rise to a new problem: early fault online detection [1]. Compared with the traditional fault detection and diagnosis problems [2–4], early fault online detection is essentially a problem of anomaly detection with streaming data, that is the monitoring data of the target bearing arrive sequentially, and fault detection is conducted within a sampling interval. This new detection mode can evaluate the change of the working status of bearings in a very short time, avoiding economic losses caused by system halt. Obviously, early fault online detection should not only be sensitive to an early fault, but also be robust enough to avoid false alarms that are usually caused by running-in, lubrication, and so on. Especially, a false alarm can cause unplanned equipment shutdown, so online detection should pay more attention to avoiding false alarms rather than missing alarms. Such characteristics and requirements present a new challenge to the online detection method.

**Citation:** Mao, W.; Sun, B.; Wang, L. A New Deep Dual Temporal Domain Adaptation Method for Online Detection of Bearings Early Fault. *Entropy* **2021**, *23*, 162. https:// doi.org/10.3390/e23020162

Received: 9 January 2021 Accepted: 25 January 2021 Published: 29 January 2021

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This paper mainly tackles early fault online detection in unsupervised mode, i.e., with no available state information for whole-life degradation data. For online scenarios, a straightforward solution is using the initial part of online data (regarded as the normal state) to construct a one-class classification model. However, a trustful model can usually be built waiting for a long enough time to get sufficient data for model training, especially for a deep neural network. One can certainly accumulate enough whole-life degradation data in an offline environment, e.g., a laboratory. However, the distribution drift between offline data and online data is inevitable due to the change of working conditions. In this scenario, the offline trained model cannot be directly applied to the online task. Therefore, how to transfer fault information (e.g., detection rules) between different working conditions has become a key issue to improve the accuracy and robustness of early fault online detection.

Presently, most traditional fault detection methods heavily rely on the fault features [5] extracted from vibration signals, such as wavelet features [6] and envelop spectrum features [7]. These features are then fed into a classification model such as support vector machine (SVM) [5], naive Bayesian [8], Fisher discrimination analysis [9], artificial neural network [10], and support vector data description (SVDD) [11]. In the past decade, deep learning techniques have been successfully introduced to bearing PHM due to their superior capability of end-to-end feature extraction. As the process of deep feature extraction is self-adaptive with no human intervention, various deep learning techniques have been successfully applied to the fault detection and diagnosis of different rotating machinery [12–15]. However, neither traditional machine learning methods, nor deep learning techniques can effectively solve the problem of distribution drift. Therefore, these methods are not applicable to online detection. According to the authors' literature survey, very few works were found to conduct online anomaly detection. For instance, Lu et al. [16] utilized merely the initial part of online data to build a long short-term memory (LSTM) network and then recognized anomalies by calculating the residual error between real data and the LSTM prediction. Mao et al. [17] utilized semi-supervised SVM and a deep auto-encoder network to sequentially update the classification model for online detection. However, as this method merely used a small amount of normal state data to train the initial model, the extracted deep features are easily biased and then cause a false alarm.

From the discussion above, the most vital challenge to improve the performance of online detection is the effective transfer of fault knowledge between offline and online working conditions. As one of the research hotspots in machine learning, transfer learning aims to improve the predictive performance in one domain (called the target domain) by using the prior information contained in the data of another related, but different domain (called the source domain) [18]. As a kind of transfer learning technique, domain adaptation [19] focuses on the across-domain transfer of domain information. Domain adaptation can be realized well on deep neural networks by adaptively extracting domain-invariant feature representation [20]. Especially in the recent 2–3 years, deep domain adaptation has been applied to fault diagnosis [21–23] and remaining useful life prediction [24,25]. According to our literature survey, there are some preliminary research works [26] in the field of early fault detection. In these works, the role of deep domain adaptation is to learn fault information by leveraging the data from different working conditions. However, there still are some shortcomings: (1) most of these works need labeled data to train a classification model, which is not easy to realize in real-world applications; (2) most of these works mainly focus on anomalous samples rather than the temporal relationship between consecutive samples. As a result, the fault information cannot be sufficiently extracted, which may cause false alarms and reduce detection accuracy.

To solve such shortcomings, this paper proposes a new online detection method of bearing early fault based on deep transfer learning techniques. Specifically, this method contains an offline stage and an online stage. In the offline stage, a new state assessment method is firstly proposed by integrating the Hilbert–Huang transform (HHT) and support vector data description (SVDD) to determine the period of the normal state and the degradation state. The assessment results can provide the corrected data label for further domain

adaptation. Furthermore, a new deep dual temporal domain adaptation (DTDA) model is proposed to extract temporal common fault information between different working conditions. In the online stage, the sequentially collected monitoring signals are directly fed into the DTDA model to recognize if a fault occurs. This process does not need a re-training model, since the domain-invariant feature representation has been extracted by the DTDA model. Finally, a set of comparative experiments is conducted on the IEEE PHM Challenge 2012 bearing dataset, and the results demonstrate the effectiveness of the proposed method.

The main contributions of this paper can be summarized as follows:


This paper is organized as follows. In Section 2, a brief summary about TCN and DANN is provided. In Section 3, the details of the proposed method are elaborated. Section 4 is devoted to showing the experimental results on a widely-used bearing dataset, the IEEE PHM Challenge 2012 dataset, followed by the conclusion of this paper in the last section.
