**1. Introduction**

As an indispensable element of rotating machinery, the rolling bearing plays an effective and crucial role in real industries, whose operation status profoundly influences the performance of rotating machinery equipment. If faults occur in critical bearings, it may cause costly downtime and catastrophic accidents. Therefore, having an effective and accurate fault diagnosis of bearings is critical to improving the reliability and safety of rotating machinery equipment.

During the past decades, the fault detection and diagnosis of roller bearings have been receiving increasing attention and have been a research hotspot. Due to the distinctive characteristics of the vibration signals produced by a faulty bearing, such as its periodicity and sensitivity to faults, grea<sup>t</sup> efforts have been made to develop a bearing fault diagnosis based on vibration-based methods. Model-based methods are devoted to revealing the fault generation mechanism and finding the fault-related information according to the map from inputs to responses [1,2]. Meanwhile, a few model-based methods have also been applied for degradation data analysis and the remaining useful life estimation and prediction [3,4]. In addition, numerous signal processing methods have been used to reduce the noise and extract and highlight the fault-related features in vibration signals to achieve an accurate fault diagnosis [5,6]. These methods can be classed into three categories on the basis of the

**Citation:** Qian, L.; Pan, Q.; Lv, Y.; Zhao, X. Fault Detection of Bearing by Resnet Classifier with Model-Based Data Augmentation. *Machines* **2022**, *10*, 521. https:// doi.org/10.3390/machines10070521

Academic Editors: Hongtian Chen, Kai Zhong, Guangtao Ran and Chao Cheng

Received: 28 May 2022 Accepted: 24 June 2022 Published: 27 June 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

fundamentals of signal processing methods. The first is time-domain analysis [7], such as the peak value, standard deviation and kurtosis, and so on. Frequency domain analysis, typified by fast Fourier frequency transform (FFT) [8], is the second category. The third kind is time-frequency domain analysis, including short-time Fourier transform (STFT) [9], wavelet transform [10,11] and empirical mode decomposition (EMD) [12], and so forth. However, most of the available traditional signal-based methods presently require human intervention and sufficient expert knowledge on the diagnosis of an object and signal processing, which limits their industrial application to mechanical equipment fault diagnosis. In this regard, alternative methods should be developed for a bearing fault diagnosis.

To overcome the limitations of demands of prior expertise based on the signal-based methods and achieve higher performance, machine learning techniques have already been widely applied in mechanical fault diagnoses [13]. Based on the machine learning techniques, fault diagnosis is regarded as a classification problem. In the traditional machine learning methods, representative features are first extracted from the raw signals, based on which pattern of recognition technology is applied to classify the health conditions of the equipment, for instance, support vector machines (SVM) [14], clustering algorithms [15] and artificial neural networks (ANN) [16,17] and so on. Shi et al. [18] applied linear discriminant analysis and gray wolf optimizer to improve the SVM algorithm and enhance the performance of fault classification. Zhang et al. [19] applied the BP neural network algorithm, which was based on the transfer component analysis, to detect the bearing fault states. In spite of the success achieved by these methods of fault diagnosis in the past years, it is still a challenge to ensure fault diagnosis accuracy with highly complex nonlinear signals. Due to the high performance in dealing with nonstationary signals, the deep learning method has recently been developed for feature extraction and pattern recognition [20]. Lei et al. [21] presented a framework for intelligent fault diagnosis, where a two-layer neural network with sparse filtering was constructed to learn the features from raw mechanical signals directly. Additionally, based on these learned features, the mechanical faults were identified by the classifier. Kolar et al. [22] propose a multi-channel deep convolutional neural network configuration for a rotary-machinery state classification. Janssens et al. [23] proposed a feature learning model for the bearings condition monitoring, based on convolutional neural networks, which removed the need for expert knowledge related to feature extraction compared with the classical statistical feature analysis. Mao et al. [24] proposed a multiple-fault diagnosis method that was based on deep output kernel learning, in which the depth features were extracted adaptively by an auto encoder neural network and thus, by means of solving the objective function constructed by the output kernel regularizer, the fault classifier was constructed. Due to the powerful capacity for classification and excellent convergence behaviors, deep learning methods can learn the deep features of different data and distinguish them automatically. However, deep learning methods require a large number of datasets to achieve a high accuracy of classification [25]. The industrial applications are limited by the requirement of in-service data under a wide range of operating conditions, which is generally an expensive and timeconsuming practice to carry out dozens of experiments, especially for the key components in large machinery and equipment.

To deal with this issue, researchers have started to focus on the data augmentation method to extend the amount of available data with limited in-service data. Data augmentation is first applied in the field of two-dimensional images, and then the available images are transformed into new images by various means [26,27]. To solve the problem of the paucity of data, some approaches were developed based on data augmentation to deal with one-dimensional signals. To achieve the engineering prognostics, Kim et al. [28] proposed a run-to-fail (RTF) data augmentation method based on the dynamic time warping (DTW) technique, where a neural network was trained for the remaining useful life prediction of the current system by using the other system's RTF data. A semi-supervised learning (SSL) approach, based on data augmentation and metric learning, was proposed by Yu et al. [29]. Seven data augmentation strategies were applied to expand the feature space with limited

labeled data. However, the data augmentation was realized by transforming the available signals into new signals in these studies, which led to limited distribution and feature space of the dataset. To overcome this barrier, simulation-driven machine learning methods were studied to create the training data, including a variety of operating conditions, which can be combined with available in-service fault data for the fault diagnosis. A data simulation by resampling (DSR) method was proposed by Hu et al. [30] to generate various working conditions of data for fault diagnoses. Lu et al. [31] proposed a vibration-based classification approach using model-based data augmentation for light-weight robotic-drilling-condition identification, where a dynamic model for a robotic drilling system was built to generate signals for the training data augmentation. Sobie et al. [32] generated training data by using information gained from high-resolution roller bearing dynamics simulations. Then, the machine learning algorithms were trained with the simulated data to classify the bearing faults. However, the roller bearing dynamics in this study are considered as a linear system, in which the race defect is modeled with a prescribed force, and the interaction between each element caused by faults is neglected. There exist certain differences with the actual situation.

Motivated by the aforementioned studies, we developed a fault detection approach based on data augmentation for roller bearing in this paper, which integrated a model-based method and deep learning method. To be specific, a dynamic model of a roller bearing was first established to reflect the correspondence between the bearing states and vibration signals. Then, the data augmentation was achieved by the simulated signals generated by the dynamic model, and based on this, a fault classifier was trained by a deep learning algorithm. Moreover, the envelop signals were used instead of the original signals in the training process to reduce the gap between the simulated data and the real data. Finally, the operation states of the roller bearings could be identified by the trained fault classifier by inputting the vibration signals to be classified.

The remainder of the paper is organized as follows: Section 2 introduces the framework of the proposed method in detail, including the model-based data augmentation and deep residual network classification. The experimental study will be presented and discussed in Section 3. Finally, some conclusions are given in Section 4.

### **2. Methodology of Data Augmentation**

Model-based methods and data-driven methods have demonstrated the effectiveness and performance of fault diagnosis of machines [1,33,34]. Model-based methods show advantages in providing the map from inputs to responses and revealing the fault generation mechanism. However, it is less effective in dealing with data at a low signal-to-noise ratio (SNR). By contrast, intelligent fault diagnosis methods can achieve reliable diagnostic results with complex signals. However, massive datasets are required to ensure classification accuracy, which brings about a high cost of data collection and training. To detect the bearing state with less real data, a fault detection method for bearings based on data augmentation is proposed in this paper, which integrates the model-based methods and data-driven methods. To this end, based on the physics knowledge and failure mechanism of the bearings, a dynamic model was constructed to generate the vibration signals of the bearing to alleviate the problem of data acquisition. Then, the generated dataset was used to realize the data augmentation, and the deep learning algorithm was applied to train the fault classifier. Moreover, the envelop signals were used instead of the raw signals in the training process to reduce the gap between the simulated data and the real data. Finally, a reliable fault classifier insensitive to noise signals was obtained. The operation states of the rolling bearings can be delivered by the fault classifier by inputting the vibration signals to be classified. The framework of the proposed method is shown in Figure 1.

**Figure 1.** Framework of the fault detection by Resnet classifier with model-based data augmentation.
