A consistency regularization based semi-supervised learning approach for intelligent fault diagnosis of rolling bearing

Highlights

• A SSL method for intelligent fault diagnosis of rolling bearing is proposed.

• Data augmentation is the basic foundation of the proposed method.

• Two consistency terms make the trained network less sensitive to the extra perturbations.

• The proposed method achieves excellent performance on the experimental study.

Abstract

Deep learning has been widely used nowadays to achieve an automated fault diagnosis of rolling bearings. However, most of deep learning based bearing fault diagnosis methods are based on the assumption that the recorded samples are labeled data, though most of field data are recorded without label information. To address this issue, an effective semi-supervised learning method based on the principle of consistency regularization is proposed in this study. The principle of consistency regularization underlines that the model predictions should be less sensitive to the extra perturbation imposed on the input samples. In the proposed method, a data augmentation method is proposed to serve as the extra perturbation, which is imposed on both the labeled and unlabeled samples to enrich the data library. Meanwhile, a label predicting process is formulated to estimate the appreciable label distribution for the unlabeled sample. Correspondingly, two consistency loss terms are introduced to regularize the model predictions for both the labeled and unlabeled samples to be invariant to the extra perturbation, among which a supervised loss term is adopted to enforce the model predictions for augmented labeled samples to be consistent with its true label information and an unsupervised loss is proposed to minimize the discrepancy between label distributions for the original unlabeled samples and its appreciable label distributions. The analysis result on an experimental bearing fault dataset demonstrates that the proposed method can provide an excellent identification performance under limited labeled samples situation.

Introduction

Rolling bearing is one of the most important mechanical components, which has been widely used in rotating machinery. Since the rolling bearing usually carries a large dynamic load in its service life, it is easy to cause an unattended failure on its surface [1], [2], [3], [4]. Their failure will directly affect the performance of the whole production line and further lead to a huge economic loss. It is thus essential to propose a bearing fault diagnosis method to accurately detect a bearing defect at the first hand [5], [6], [7].

Data-driven fault diagnosis methods are becoming a current research trend due to their high automatic level and fast implement rate [8], [9], [10]. Several data-driven bearing fault diagnosis methods have been proposed which can be generally classified into two categories, (1) shallow learning based diagnostic methods [11], [12], and (2) deep learning based diagnostic methods [13], [14], [15]. Shallow learning based diagnostic methods used none or just a couple hidden layers in the network structure which lack capacities in handling complicated fault classification cases. Moreover, a feature extraction step is essential in shallow learning based diagnostic methods, which increases the computational complexity and reduces the automatic level of these techniques [11], [12]. On the other hand, deep learning based diagnostic methods integrate the feature extraction and fault classification into an ensemble form to increase the accuracy in the fault diagnosis task, which can greatly address the issues in shallow learning based diagnostic methods and significantly improve the performance of the deep learning algorithms. Various deep architectures have been proposed in literatures to achieve the fault diagnostic applications [16], [17], [18], [19], [20], [21]. For examples, Kong et al. [16] integrated the multiple deep auto-encoder architectures into the ensemble learning framework to achieve the bearing fault diagnosis. Jing et al. [17] proposed a convolutional neural network (CNN) to directly extract the discriminative features from the Fourier data and realize the automatic gearbox fault diagnosis. Jiao et al. [18] proposed a deep coupled CNN architecture to fuse the feature streams from various information sources. Lei et al. [19] proposed a long short-term memory (LSTM) network to extract discriminative features from the multivariate time series with considering the long-term dependencies, and effectively achieve the fault diagnosis of wind turbine. An et al. [20] adopted an LSTM network to eliminate the effect of the nonstationary characteristic of the vibration data on learning performance.

Deep learning based diagnostic methods can effectively classify the fault conditions from the recorded data samples without the need of manual interventions. However, most of existing deep learning based diagnostic methods were established on the assumption that the recorded samples are labeled samples, which ignore the fact that there exist no label information for most of the recorded samples on account of that labeling a sample will takes more manpower and resources in industrial fields. Semi-supervised learning (SSL) methods which can make use of both labeled and unlabeled samples appear to be a powerful approach to address this issue. A series of SSL approaches have been proposed recently to address the limited labeled samples in industrial fields [22], [23], [24], [25], [26], [27]. For example, Zhang et al. [22] proposed a deep semi-supervised method of multiple association layers networks on the basis of the ladder network to achieve the fault diagnosis of planetary gearbox. Jiang et al. [23] tried to achieve the process monitoring with both limited labeled data and sufficient unlabeled data in a two-step manner. Razavi-Far et al. [24] integrated the statistic features from multiple sensory streams into a semi-supervised deep ladder network to achieve the gearbox fault diagnosis. A semi-supervised smooth alpha layering algorithm is proposed in Ref. [25] to realize the bearing fault identification under limited labeled samples situation. Li. et al. [26] proposed a semi-supervised gear fault diagnosis method using a combination of both augmented auto-encoder and augmented monitoring data. Liang et al. [27] transformed the one-dimensional monitoring data into two-dimensional time–frequency image and then put them into the semi-supervised generative adversarial network to achieve the fault diagnosis of rotating machinery. Though the above mentioned methods can improve the identification ability in addressing the SSL task, the tedious procedures adopted in the above mentioned methods make it unavailable to achieve the fault diagnosis task with a high efficiency.

Data augmentation (DA) is an effective approach to enrich the data library for the recorded data and it has been widely used in the fields of object recognition and image processing [28]. The basic idea of the data augmentation is to change the partial structure of the recorded data to generate more variant versions, whilst the label information for the recorded data remains unchanged [29], [30]. When the augmented data are introduced to update the parameters of the network, it can be viewed as an extra perturbation imposed on the current network. However, on account of the fact that the label information for the augmented data remains unchanged, the trained network is expected to be less sensitive to the deformation of the recorded data. This idea is an effective approach to improve the generalization ability of the network and also coincide with the principle of consistency regularization based SSL methods. In consistency regularization based SSL methods, an extra perturbation is firstly imposed on the input samples or the hidden states of the network architecture, and then a regularization term is introduced to make the model predictions invariant to the extra perturbation. Various SSL techniques have been proposed under this framework, such as virtual adversarial training (VAT) [31], MixMatch [32], unsupervised data augmentation (UDA) [33], ladder network [34] and mean teacher [35]. Among them, the main difference is how and where the extra perturbation is imposed. In VAT [31], an additive perturbation which can maximally change the output distribution is imposed on the input samples and the model prediction is enforced to be less sensitive to the imposed perturbation. In MixMatch [32], the random horizontal flips and crops are initially imposed on the input image data and then a MixUp is used to further mix the labeled and unlabeled samples. Corresponding, two consistency costs are designed for the labeled data and unlabeled data to regularize the model. In UDA [33], a consistency regularization framework is firstly proposed and then the effectiveness of various perturbation strategies is investigated. In ladder network [34], two parallel encoders are built for labeled and unlabeled data simultaneously. The encoder for labeled data is corrupted by adding isotropic Gaussian noise on its hidden states and the encoder for unlabeled data is noise free, a regularization term is formulated to enforce the consistency between the hidden states of these two encoders. In mean teacher [35], though various perturbations are imposed on the input samples, the output distributions from student model and teacher model are assumed to be consistent. In these literatures, most of the extra perturbations were designed for two-dimensional image data and cannot be adopted to achieve the bearing fault diagnosis task on account of that the bearing condition monitoring data is typically one-dimensional data. To address this issue, a new SSL method based on the principle of consistency regularization is proposed in this study to achieve the bearing fault diagnosis task under the limited labeled samples situation. In the proposed method, a DA method (DAM) designed for one-dimensional bearing fault data is proposed to impose the extra perturbation on the original samples, which can effectively enrich the data library for both labeled samples and unlabeled samples. Then, an appreciable label distribution for the unlabeled samples is formulated by using the model predictions for the augmented unlabeled samples. After that, two consistency loss terms are formulated to regularize the model predictions to be invariant to the extra perturbations. Among them, a supervised cross entropy loss is adopted to enforce the model predictions for augmented labeled samples to be consistent with the true label information for original labeled samples and an unsupervised consistency loss is formulated to minimize the discrepancy between label distributions for the original unlabeled sample and its appreciable label distributions. A schematic illustration of the proposed method is given in Fig. 1. In the proposed method, the proposed DAM can greatly improve the diversity of the original samples, which can lead to a high identification performance under limited labeled samples. Moreover, the consistency regularization principle on the unlabeled samples can help the classifier better detect the membership for unlabeled sample, which is beneficial to push the decision boundary far away from the high-density region of the marginal data distribution. The classification result on an experimental bearing dataset demonstrates that the proposed method can provide an accurate bearing fault diagnosis under the limited labeled samples situation.

The main contributions of this study are highlighted as follows:

• In this study, an effective SSL method based on the principle of consistency regularization is proposed for automatic bearing fault diagnosis under limited labeled samples situation. In the proposed method, a DAM designed for one-dimensional vibration data can be viewed as the extra perturbations imposed on the samples. Correspondingly, two consistency loss terms targeted for the labeled samples and the unlabeled samples are used to regularize the model predictions to be invariant to the extra perturbations. The effectiveness and necessity of the proposed two consistency manners are validated in the experimental study.

• Though the labeled samples are limited in the SSL task, the proposed data augmentation strategies conducted on the labeled samples can greatly improve its diversity. Meanwhile, considering that the label information for the labeled samples still maintains, a standard cross entropy conducted on augmented labeled samples can greatly improve the identification performance in addressing the SSL task.

• The appreciable label information for the unlabeled samples is estimated by conducting the average and highlight on the one-hot labels for the augmented unlabeled samples. Then, an unsupervised consistency loss is formulated to minimize the discrepancy between the label distributions for the original unlabeled samples and its appreciable label distributions. The experimental result illustrates that this regularization method can also further improve the identification performance to a certain extent.

The rest of this paper is organized as follows: Firstly, the principle of the proposed method are given in Section 2. Then, an experimental case study is presented in Section 3 to validate the effectiveness of the proposed method. Finally, conclusions are drawn in Section 4.