A novel rolling bearing fault diagnosis method for limited data

Abstract

The ability of deep learning based bearing fault diagnosis methods is developing rapidly. However, it is difficult to obtain sufficient and comprehensive fault data in industrial applications, and changes in vibration signals caused by machine operating conditions can also hinder the accuracy of the model. The problem of limited data and frequent changes in operating conditions can seriously affect the effectiveness of deep learning methods. To tackle these challenges, a novel transformer model named the Differential Window Transformer (Dwin Transformer), which employs a new differential window self-attention mechanism, is presented in this paper. Meanwhile, the model introduces a hierarchical structure and a new patch merging to further improve performance. Furthermore, a new fault diagnosis model dealing with limited training data is proposed, which combines the Auxiliary Classifier Generative Adversarial Network with the Dwin Transformer(DT-ACGAN). The DT-ACGAN model can generate high-quality fake samples to facilitate training with limited data, significantly improving diagnostic capabilities. The proposed model can achieve excellent results under the dual challenges of limited data and variable working conditions by combining Dwin Transformer with GAN. The DT-ACGAN owns superior diagnostic accuracy and generalization performance under limited sample data and varying working environments when compared with other existing models. A comparative test about cross-domain ability is conducted on the Case Western Reserve University dataset and Jiang Nan University dataset. The results show that the proposed method achieves an average accuracy of 11.3% and 3.76% higher than other existing methods with limited data respectively.

Keywords

Transformer generative adversarial network cross-domains limited data fault diagnosis

1 Introduction

As technologies develop and the demand for machinery grows, the mechanical structure becomes increasingly complex. Rolling bearings have been widely applied and played a crucial role in rotating machinery for high efficiency and easy installation. The health of the rolling bearings impacts the status of the mechanical equipment. Bearing failure can cause equipment failure and significant economic loss or personnel casualties. Therefore, monitoring and diagnosing the health of rolling bearings through their vibration signal is essential for ensuring expected production for enterprises [1–3].

Models based on deep learning have end-to-end capabilities and are widely used in various industrial scenarios [4–6]. Convolutional Neural Networks (CNNs) are widely researched in bearing fault diagnosis due to their precise diagnostic capabilities [7, 8]. Xu et al. [9] proposed a novel CNN called a Collaborative Fusion Convolutional Neural Network (CFCNN), which considers intrinsic correlations and the distribution gap between different signals. Ruan et al. [10] proposed a novel physics-guided CNN (PGCNN), which explores the physics-guided design for CNN’s parameters based on signal analysis, including the input size and convolution kernel size. However, it is difficult for CNN to effectively capture the global features of the data, which can lead to overfitting in the model. Overfitting of the model will intensify when the training data is limited, which can lead to a significant decrease in the model’s performance.

Compared to CNN, Long Short-Term Memory(LSTM) exhibit robust capabilities in extracting global features and capturing temporal relationships between data [11]. Fan et al. [12] proposed a novel method based on One-Layer Wide Convolutional and Long-Short Term Memory network(1LWCNNLSTM), which has better load generalization capability and noise immunity for the vibration data coming from the complex working environments. However, LSTM has a large computational load and performs poorly when the sequence length is too long. Therefore, LSTM lacks good performance when the data sequence is too long or requires high real-time performance. Another model that can effectively extract global features is the Transformer, which utilizes multi-head self-attention and parallel training mechanisms to capture global features and long-range information of the time-series signals. However, the transformer encounters challenges such as high computational requirements stemming from the global attention mechanism and limited local feature extraction capability. Liu et al. [13] made enhancements to the ViT model to tackle this issue by proposing the Shifted Window Transformer model (Swin Transformer). The improvements included constructing a hierarchical structure based on Transformer and the window self-attention mechanism instead of the global self-attention mechanism. Moreover, the shifted window mechanism captured the lost data relationship between different windows. However, the performance of this model is poor when confronted with noisy training samples and varying working conditions because its architecture is so deep, and the shifted window mechanism cannot effectively capture vibration signal features.

Most of the previously mentioned studies necessitate substantial and comprehensive training data. These models performance notably declines when confronted with limited training samples. Currently, prevalent methods that enhance model performance with limited samples include data augmentation or few-shot learning. Generative Adversarial Networks (GAN) [14] is a typical method of data augmentation, which can generate data that closely approximates the real data distribution. Fu et al. [15] proposed a fault diagnosis method by combining GAN and a stacked denoising auto-encoder (SDAE), which boosted SDAE’s fault diagnosis performance on limited training data by augmenting the real measured data. Huang et al. [16] proposed an improved label-noise robust auxiliary classifier generative adversarial network (rAC-GAN) driven by limited data, which learns shallow fault features in advance based on real bearing fault data to obtain input signals. Consequently, the model’s performance notably advanced when confronted with limited data. Data augmentation can improve the model’s performance with limited data by amplifying the sample count. However, these methods cannot adapt to changing working conditions. Moreover, inappropriate data augmentation can lead to model overfitting, which results in good performance on training data but is unreliable on real data [17].

Presently, the predominant technique in few-shot learning involves metric-based meta-learning. The fundamental idea of meta-learning is to ’learn to learn’. Meta-learning algorithms train models across multiple tasks to acquire versatile learning strategies. These strategies enable the model to adapt quickly with limited data. Classic methods include Siamese Networks [18], Matching Networks [19], and Prototypical Networks [20], among others. Zhang et al. [21] proposed Siamese CNN by combining CNN with the Siamese network, which achieved significant performance improvement with limited samples. Wang et al. [22] proposed a Feature Space Metric-based Meta-learning Model (FSM3) by extending Matching Networks and Prototypical Networks. The model diagnoses fault by using sample attributes and cluster similarity data. However, Siamese networks and Matching networks demand high-quality training data. In addition, the attention mechanism may be challenging to converge in some cases.

It is worth noting that the lack of samples and frequent changes in working conditions often coexist in the actual production process. However, existing models often can only solve one type of problem, and rarely can they simultaneously solve this dual challenge well [23]. The problem of limited data and frequent changes in operating conditions can seriously affect the effectiveness of deep learning models. A model that can simultaneously address these two challenges is necessary to improve the safety of actual production activities.

This paper enhances the Swin Transformer to address this gap and proposes a new fault diagnosis model called the Differential Window Transformer (Dwin Transformer). The model used a novel window attention mechanism and feature fusion method according to the data distribution characteristics of one-dimensional vibration signals. In addition, applying a hierarchical structure enhances enhances the feature extraction ability of the model. Then, we replace the discriminator of ACGAN with the Dwin Transformer to improve the diagnostic ability of this model under limited fault samples. This paper proposed an Auxiliary Classification Generative Adversarial Network based on the Dwin transformer (DT-ACGAN). The model can accurately extract features, complete the classification task under limited samples, and effectively deal with the challenge of changing working conditions. The contributions of this study are as follows:

(1)A new differential window multi-head self-attention mechanism was proposed. Furthermore, a new Transformer named Dwin Transformer was proposed based on differential window multi-head self-attention. The model significantly reduced computational effort and enhanced generalization to vibration signals under variable working conditions.

(2)The paper explored and found the most suitable combination between Dwin Transformer and GAN. The DT-ACGAN was presented by substituting the discriminator with the Dwin Transformer. The model notably improves the performance of the discriminator, thereby enhancing the quality of generated samples and the diagnostic capabilities of the model.

(3)DT-ACGAN still has excellent fault diagnosis performance with limited data. It also inherits the remarkable cross-domain generalization ability of the Dwin Transformer. Therefore, it solved two challenges simultaneously of limited training data and different working conditions.

The rest of this paper is organized as follows. Section 2 details the related methods of DT-ACGAN. Section 3 describes the DT-ACGAN model’s architecture and clarifies the model’s principle. In Section 4, the model is comprehensively analyzed through experiments, including the Case Western Reserve University (CWRU) dataset [24] and the JangNan University (JUN) dataset [25]. Different working conditions are included in the dataset. Section 5 describes the research conclusions, highlights the cross-domain generalization ability of the proposed model with limited data, and discusses future research work.

2 Methodology

2.1 Swin Transformer

The Swin Transformer model consists of 3 parts: Patch partition, Patch merging, and Swin Transformer block. The model is described in detail below.

2.1.1 Overall architecture

Figure 1 illustrates the complete architecture of the Swin Transformer. The input data is first divided into patches of uniform size in Patch Partition, and each patch is flattened in the channel direction. Then, the processed data is sent to the Swin Transformer block for computation. The output is then sent to the patch merging layer. The data is further expanded in the channel dimension while reducing its width and height to create a hierarchy and reduce the amount of data. The data is then fed to the second Swin Transformer block, and the final output is obtained after two iterations.

Fig. 1

Structure of the Swin Transformer.

2.1.2 Swin Transformer Bolck

The Swin Transformer block is the core component of the proposed model. It introduces a window self-attention mechanism to reduce the amount of computation significantly. The feature map is divided into multiple Windows in the window self-attention algorithm. The self-attention computation is performed independently for each window. The self-attention computation process consists of the following steps [26].

Attention (Q, K, V) = SoftMax (\frac{Q K^{T}}{\sqrt{d}} + B) V

(1)

Where Q, K, and V are query, key, and value matrices, respectively; d is the dimension of query/key, and B is the bias matrix. Moreover, the computational quantities of these two attention mechanisms are shown as follows [13].

Ω (MSA) = 4 hw C^{2} + 2 {(hw)}^{2} C

(2)

Ω (W - MSA) = 4 hw C^{2} + 2 MN hwC

(3)

where hw represents the number of patches, C represents the depth of the channel dimension, and MN represents the size of each window. When MN is fixed, the latter computation grows linearly as the feature map size increases. When hw is relatively large, the computation required for global self-attention computation is usually unaffordable, while window-based self-attention requires much less computation. However, the window self-attention mechanism may lead to a loss of global information interaction. The Shifted Windows Multi-Head Self-Attention module is introduced to overcome this limitation. Figure 2 illustrates the functioning of this module.

Fig. 2

The illustration of the shifted window approach for computing self-attention.

After the window moved, the previously unreachable window reestablished contact. This method solves the problem of interacting with information between different windows [13].

2.2 Generative adversarial network

GAN expand the dataset by generating fake data [14]. The generator’s goal is to generate data similar to real data, while the discriminator initially acts as a classifier to distinguish between real data and generated data. These networks iteratively compete with each other to enhance their capabilities until they reach equilibrium. In an ideal state, the generator can generate data that matches the distribution of real data, while the discriminator cannot distinguish between real and synthetic data. The objective function T (D, G) of GAN can be expressed using the formula as follows [14].

\begin{matrix} \min_{G} \max_{D} V (D, G) = E_{x p (x)} [logD (x)] + \\ E_{z p (z)} [log (1 - D (G (Z)))] . \end{matrix}

(4)

Where E represents mathematical expectation, p (x) and p (z) correspond to the probability distributions of the real and noisy samples, respectively. The training objective aims to maximize logD (x) and minimize log (1 - D (G (z))).

Auxiliary Classifier GAN(AC-GAN) enables discriminators to distinguish the authenticity and category of input samples [27]. To achieve this, the Softmax was introduced into the discriminator. The Softmax calculates the probability value for each classification. Furthermore, ACGAN used a new objective function. The objective function has two parts: [27]:

\begin{matrix} L_{S} = E [logP (S = real | X_{real})] + \\ E [logP (S = fake | X_{fake})] \end{matrix}

(5)

\begin{matrix} L_{C} = E [logP (C = c | X_{real})] \\ + E [logP (C = c | X_{fake})] \end{matrix}

(6)

The L_S is the adversarial loss responsible for adjusting the generator’s ability to generate fake samples and the discriminator’s ability to identify fake samples. The L_C is the auxiliary classification loss responsible for classifying the generated samples. The missions of the discriminator is to maximize L_S + L_C, and the mission of the generator is to maximize L_C - L_S.

3 Model structure

3.1 Dwin Transformer

This article first normalizes the vibration signal and folds it into two dimensions. Then, convert the data into images to match the structure of the proposed model [28]. However, it is worth noting that the converted image differs from the typical image. The pixels in the transformed data have a stronger correlation with their adjacent pixels on the left and right rather than the top and bottom. Given this unique feature, we apply the rectangular window partitioning mode to Windows Multi Head Self Attention (W-MSA) and adopt Differential Window Multi Head Self Attention (DW-MSA) to facilitate information exchange between these windows. Figure 3 describes the structure of DW-MSA, where we select two windows of different sizes for self-attention to minimize data loss caused by window attention mechanisms while ensuring that computation speed is not affected.

Fig. 3

The illustration of the different window approaches for computing self-attention.

Inspired by CNN, the hierarchical structure is more conducive to feature extraction. The model consists of two blocks containing two multi-head self-attention mechanisms with different window sizes. The model’s structure is shown in Fig. 4.

Fig. 4

Structure of the Dwin Transformer.

We set the patch size to 1x4 to match our data input format and propose a patch merging method to reduce the data volume. The proposed method groups pixels in each unit with identical relative positions and then merges these groups in the channel dimension. Figure 5 demonstrates the specific steps of our implementation.

Fig. 5

Patch Merging.

The Dwin Transformer Block is the core part of the Dwin Transformer model, and its structure is shown in Fig. 6.

Fig. 6

Two Successive Dwin Transformer Blocks.

The Dwin Transformer Block is calculated as the following equation [13].

{\bar{z}}^{l} = W - MSA (LN (z^{l - 1})) + z^{l - 1}

(7)

z^{l} = MLP (LN ({\bar{z}}^{l})) + {\bar{z}}^{l}

(8)

{\bar{z}}^{l + 1} = DW - MSA (LN (z^{l})) + z^{l}

(9)

z^{l + 1} = MLP (LN ({\bar{z}}^{l + 1})) + {\bar{z}}^{l + 1}

(10)

Where

\bar{z}

denote the output of attention, and z denote the output of the Multilayer Perceptron(MLP). l denotes the number of blocks. The LayerNorm (LN) layer is applied before the MSA module and the MLP block. Then, the Dwin transformer’s pseudocode is provided to improve the readability of the paper. This pseudocode uses two algorithm blocks, one representing the overall Dwin Transformer process and the other representing a basic module (block) in the Dwin Transformer.

3.2 DT-ACGAN

Although Dwin Transformer has excellent cross-domain generalization ability, it typically requires much training data. However, without sufficient training samples, using the Dwin Transformer for fault diagnosis tasks may lead to performance degradation and failure to demonstrate its powerful cross-domain generalization ability. A feasible solution to this problem is to use GAN to increase training samples.

Based on this idea, we propose an improved model by replacing ACGAN’s discriminator with the Dwin Transformer. This modification enhances the recognition and classification capabilities of the discriminator, thereby improving the network’s overall performance in fault diagnosis tasks. The increase in sample size dramatically enhances the Transformer’s capabilities. At the same time, we introduced Differentiable Augmentation to make the data distribution more consistent with real data [29]. The improved model can effectively utilize limited training samples to improve the performance of the fault diagnosis model.The model structure diagram is shown in Fig. 7. Then, the DT-ACGAN’s pseudocode is provided as Algorithm 3 to improve the readability of the paper.In the Algorithm 3, the discriminator consists of the Dwin Transformer.

Fig. 7

Structure of the DT-ACGAN model.

This improved model architecture not only solves the problem of insufficient training samples but also fully utilizes the cross-domain generalization ability of the Dwin Transformer. We generated more training samples by combining GANs and Transformer, which improved the diagnostic accuracy and generalization ability of the Transformer model. Moreover, this method balances the discriminator and generator’s capabilities, improving the performance of the entire fault diagnosis system.

In summary, we significantly improved the diagnostic ability of the model by using the Dwin Transformer and integrating GANs to expand the training samples. This method solves the challenge of limited training samples and inherits the advantages of the Dwin Transformer in cross-domain generalization. The construction process of the model is summarized as follows:

1.Divide the original signal into datasets corresponding to different operating conditions.

2.Perform overlapping sampling using sliding windows on the dataset.

3.Initialize the model parameters.

4.Input Gaussian noise into the generator to generate synthetic samples.

5.Merge the synthetic and real samples to create a mixed dataset and feed it into the discriminator.

6.Iteratively adjust the parameters through forward and backward propagation until the diagnostic accuracy on the validation dataset satisfies the practical requirements.

7.Validate the trained model using the test dataset and evaluate its diagnostic capability.

4 Experiment results and analysis

4.1 Case Study 1: CWRU dataset

4.1.1 Description of experimental data

PyTorch was used as a machine learning framework in the experiment in this study. This program runs on a computer with 32GB RAM, NVIDIA GeForce RTX 3090 GPU, Intel i7-13700K CPU, and the operating system Windows 11. The dataset in the experiment is from the CWRU Bearing Data Center.

The experimental equipment was shown in Fig. 8. The bearing used is an SKF6205. The damage to the bearing is achieved using the Electro-Discharge Machining (EDM) technique.

Fig. 8

Motor driving mechanical system used by CWRU.

The entire dataset is divided into four types: A, B, C, and D, where datasets A, B, and C represent data with loads of 1HP, 2HP, and 3HP, respectively. Dataset D includes all data. The data length of each data sample is 2500. The Table 1 summarizes the dataset used in this article.

Table 1

Description of the CWRU dataset

Fault Location		Ball			Inner race			Outer race			Normal	Load(HP)
Damage diameter (inches)		0.007	0.014	0.021	0.007	0.014	0.021	0.007	0.014	0.021	0
Label		1	2	3	4	5	6	7	8	9	0
Dataset A	Train	700	700	700	700	700	700	700	700	700	700	1
	Validation	100	100	100	100	100	100	100	100	100	100
	Test	200	200	200	200	200	200	200	200	200	200
Dataset B	Train	700	700	700	700	700	700	700	700	700	700	2
	Validation	100	100	100	100	100	100	100	100	100	100
	Test	200	200	200	200	200	200	200	200	200	200
Dataset C	Train	700	700	700	700	700	700	700	700	700	700	3
	Validation	100	100	100	100	100	100	100	100	100	100
	Test	200	200	200	200	200	200	200	200	200	200
Dataset D	Train	2100	2100	2100	2100	2100	2100	2100	2100	2100	2100	1,2,3
	Validation	300	300	300	300	300	300	300	300	300	300
	Test	600	600	600	600	600	600	600	600	600	600

4.1.2 Performance of the Dwin Transformer

Comparative experiments were conducted to evaluate the cross domain generalization ability of the Dwin converter. The experimental content includes training the model on one dataset and testing it using data from other datasets after training, for example, A → B refers to training on dataset A and testing on dataset B. All of which have a training period of 20. the comparison results of the generalization experiments are shown in Fig. 9.

Fig. 9

Migration and generalization performance comparison of different models.

This figure shows the performance of various models. The Dwin Transformer achieving achieved the highest accuracy, which confirm that the Dwin Transformer exhibits excellent cross-domain generalization ability when sufficient training samples are provided. It is worth mentioning that the Swin Transformer is prone to overfitting when dealing with the vibration signal, which results in low test set accuracy. The Dwin Transformer achieved stronger performance than the Swin Transformer in processing one-dimensional vibration signals. This can also prove that our improvement of Swin Transformer is effective.

To illustrate the help of the window attention mechanism in reducing computational complexity, we compared the running times of the Vision Transformer, Swin Transformer, and Dwin Transformer. The results are shown in the Table 2. The results show that the W-MSA can effectively reduce computational complexity compared to the global MSA. Furthermore, the structure of the Dwin Transformer is more straightforward and more suitable for one-dimensional vibration signals. Therefore, it has less computational complexity and better fault diagnosis performance.

Table 2

The running times of different models

Models	Epochs	Train time	Test time
Vision Transformer	20	823s	52s
Swin Transformer	20	724s	39s
Dwin Transformer	20	524s	23s

4.1.3 Performance of the DT-ACGAN

To verify the effectiveness of the proposed model, we conducted comparative experiments using ACGAN and Dwin Transformer instead of generators, discriminators, or both. The experimental results are shown in the Table 3.

Table 3
Comparison of different structures of ACGAN with 60 samples

Generator Discriminator 1HP 2HP 3HP

ACGAN ACGAN 0.451 0.419 0.534

Dwin Transformer ACGAN 0.658 0.785 0.742

ACGAN Dwin Transformer 0.917 0.921 0.904

Dwin Transformer Dwin Transformer 0.846 0.915 0.876

Generator	Discriminator	1HP	2HP	3HP
ACGAN	ACGAN	0.451	0.419	0.534
Dwin Transformer	ACGAN	0.658	0.785	0.742
ACGAN	Dwin Transformer	0.917	0.921	0.904
Dwin Transformer	Dwin Transformer	0.846	0.915	0.876

The Table 3 indicates that the model performs best when the discriminator is replaced separately. We believe this is because the imbalance between the discriminator and generator hinders training when using vibration signals as samples. The addition of Dwin transformers effectively corrected this imbalance.

In order to comprehensively evaluate the fault diagnosis ability of the proposed model under limited training samples, we conducted comparative experiments using the same experimental setup described earlier. The experimental results are depicted in Fig. 10.

Fig. 10

Comparison of diagnostic results for different samples.

The figure indicates that the proposed model exhibits a significant advantage in scenarios with a small sample size. Therefore, the proposed model reduces the dependence on the number of training samples and can effectively handle rolling bearing fault diagnosis tasks with limited samples. Then, a comparative experiment was designed to evaluate the cross-domain generalization ability of the proposed model under limited samples. The data volume for this experiment is 60, and all models are trained on one dataset. Data from other datasets is used for testing after training is completed. The experimental results are presented in Fig. 11.

Fig. 11

Migration and generalization performance comparison of diffrent models with 60 samples.

The results in the figure indicate that although the training samples are limited, the proposed model achieves the highest diagnostic accuracy and exhibits excellent cross-domain generalization performance. In order to increase the persuasiveness of the experiment, we will conduct in-depth analysis of task cases. Then, we selected the precision, the recall,and the F1 score to evaluate the performance of the proposed model. Given the relatively poor performance of the cross-domain task B→C, we have chosen it as our case study. Tables 4–6 respectively represent the precision, recall, and F1 score for this task. We employ a confusion matrix to visualize the model’s classification for each fault category, as depicted in Fig. 12. To ensure the accuracy and stability of the test results, we have re selected 2000 new samples from the dataset as the test dataset. The experimental results show that the proposed model performs poorly in the third type of task, but exhibits excellent performance in other tasks. It must be emphasized that this task represents the worst performance of the proposed model, which will perform better in other tasks. In addition, compared to other models, the advantages are more pronounced. The results indicate that DT-ACGAN outperforms all other models.

Fig. 12

Confusion matrix of DT-ACGAN with 60 samples.

Table 4

Precision (%) comparison for cross-domain task B→C with 60 samples

	Class1	Class2	Class3	Class4	Class5	Class6	Class7	Class8	Class9	Class0
WDCNN	65.22	61.71	61.48	62.04	62.13	61.67	67.29	58.62	61.11	60.21
Siamese CNN	67.51	67.23	63.63	70.37	64.73	71.91	67.84	64.74	68.52	68.96
FSM3	73.21	73.26	78.39	72.18	76.82	73.42	73.14	72.45	75.51	76.95
1DCNN-LSTM	67.23	62.87	67.59	65.41	63.33	63.72	67.14	65.94	66.45	62.06
CRNN	63.58	65.21	67.99	67.76	62.45	66.87	67.84	61.12	68.92	65.83
GAN-SDAE	75.42	73.98	73.12	72.06	76.79	74.33	71.67	74.89	70.62	72.55
Dwin Transformer	87.35	75.52	22.56	83.67	88.54	85.18	87.54	87.35	86.47	82.39
Siamese ViT	80.34	77.91	78.15	82.62	85.18	84.36	81.07	78.29	85.72	84.62
1LWCNNLSTM	78.37	76.54	77.62	79.58	80.14	74.57	78.66	72.13	76.58	79.31
DT-ACGAN	100	78.57	19.48	98.54	99.13	100	100	92.54	98.15	100

Table 5

Recall (%) comparison for cross-domain task B→C with 60 samples

	Class1	Class2	Class3	Class4	Class5	Class6	Class7	Class8	Class9	Class0
WDCNN	63.88	56.21	63.54	62.74	62.61	61.82	59.67	64.92	65.53	57.12
Siamese CNN	68.23	61.89	61.75	61.02	61.45	63.11	66.34	62.84	64.01	63.96
FSM3	79.73	77.96	78.91	70.04	78.94	79.51	79.72	70.57	78.45	70.38
1DCNN-LSTM	66.89	70.43	66.57	68.21	69.78	66.34	67.89	65.98	71.01	67.45
CRNN	65.12	68.45	71.23	66.89	65.43	67.56	69.78	72.09	66.77	70.88
GAN-SDAE	75.34	70.89	69.76	72.45	76.12	78.97	71.23	76.78	73.56	77.45
Dwin Transformer	53.12	97.26	54.63	86.24	85.34	87.71	85.24	86.37	92.76	86.18
Siamese ViT	78.37	82.34	77.89	83.25	81.39	79.26	82.16	79.66	83.38	81.02
1LWCNNLSTM	78.59	73.42	71.54	78.35	79.62	75.31	77.21	76.20	71.03	72.64
DT-ACGAN	52.37	100.00	55.11	98.54	98.17	97.14	99.51	100.00	100.00	100.00

Table 6

F1 score (%) comparison for cross-domain task B→C with 60 samples

	Class1	Class2	Class3	Class4	Class5	Class6	Class7	Class8	Class9	Class0
WDCNN	64.54	58.85	64.49	62.39	62.37	61.47	63.26	61.67	63.27	58.63
Siamese CNN	67.87	64.46	62.67	65.42	63.06	67.22	67.08	63.78	66.18	66.39
FSM3	76.37	75.56	78.65	71.09	77.87	76.39	76.33	71.5	76.94	73.57
1DCNN-LSTM	67.06	66.54	67.08	66.79	66.43	65.99	67.02	65.96	68.68	64.66
CRNN	64.34	66.8	69.57	67.32	63.9	67.21	68.8	66.28	67.83	68.27
GAN-SDAE	75.38	72.41	71.4	72.26	76.46	76.57	71.45	75.82	72.06	75.92
Dwin Transformer	65.83	85.02	32.04	84.93	86.91	86.43	86.38	86.86	89.51	84.24
Siamese ViT	79.34	80.06	78.02	82.93	83.25	81.72	81.61	78.97	84.53	82.79
1LWCNNLSTM	78.48	74.95	74.48	78.96	79.88	74.93	77.93	74.11	73.71	75.87
DT-ACGAN	68.57	88.00	28.87	98.54	98.65	98.55	99.75	96.11	99.06	100.00

4.2 Case Study 2: JNU dataset

4.2.1 Description of experimental data

To further evaluate the stability and performance of the model, we conducted additional comparative experiments using the JNU bearing fault dataset. The experimental setup used to collect this dataset is illustrated in Fig. 13.

Fig. 13

The acquisition equipment of JNU dataset.

The dataset is divided into four types: A, B, C, and D. Datasets A, B, and C represent data collected at different speeds, while dataset D includes all data. The bearing model used in the dataset is ER-12K, and the sampling frequency is 50 kHz. The experimental setup is the same as the Study 1. The length of each data sample is 2500. The Table 7 summarizes the dataset used in this article.

Table 7

Description of the JNU dataset

Fault Location		Inner race	Ball	Outer race	Normal	Rotational
label		1	2	3	0	Speed(rpm)
	Train	700	700	700	700	600
Dataset A	Validation	100	100	100	100
	Test	200	200	200	200
	Train	700	700	700	700	800
Dataset B	Validation	100	100	100	100
	Test	200	200	200	200
	Train	700	700	700	700	1000
Dataset C	Validation	100	100	100	100
	Test	200	200	200	200
	Train	700	700	700	700	600
Dataset D	Validation	100	100	100	100	800
	Test	200	200	200	200	1000

4.2.2 Results and analysis

To evaluate the fault diagnosis ability of the proposed model under limited data conditions, we randomly selected 80, 240, 480, 720, 1000, and 4000 samples from dataset D. At the same time, we selected the same comparative model as in Case Study 1 for comparative experiments. The experimental results are depicted in Fig. 14.

Fig. 14

Comparison of diagnostic results for different samples.

The results in the figure clearly indicate that the overall performance of the JUN dataset is worse than that of the CWRU dataset. This result indicates that the JUN dataset is more complex than CWRU. Nevertheless, the proposed model still achieved the best results. To further demonstrate the cross-domain generalization ability of the proposed model under limited data, we conducted experiments using the same approach as in Case Study 1. The experimental results are illustrated in Fig. 15. The figure indicates that our method consistently performs best across all scenarios.

Fig. 15

Migration and generalization performance comparison of diffrent models with 80 samples.

Furthermore, we selected the task C→B for detailed analysis for the same reasons as in Case Study 1. Tables 8 –10 present precision, recall, and F1 score for this task. The data in these tables clearly demonstrate the excellent cross-domain generalization ability of the proposed model under limited data.

Table 8

Precision (%) comparison for cross-domain task C→B with 80 samples

	Class 1	Class 2	Class 3	Class 0
WDCNN	50.78	49.53	53.49	47.89
Siamese CNN	61.73	62.48	63.12	61.88
FSM3	65.89	66.54	71.16	72.58
1DCNN-LSTM	53.68	60.74	59.81	54.16
CRNN	45.78	50.94	52.34	51.61
GAN-SDAE	64.24	66.71	68.18	70.48
Siamese ViT	62.37	66.52	63.49	67.81
1LWCNNLSTM	63.26	67.54	65.21	68.92
Dwin Transformer	54.84	59.18	57.04	58.66
DT-ACGAN	71.48	75.62	72.65	74.58

Table 9

Recall (%) comparison for cross-domain task C→B with 80 samples

	Class 1	Class 2	Class 3	Class 0
WDCNN	51.26	47.61	54.81	46.57
Siamese CNN	63.15	59.62	64.95	62.34
FSM3	67.84	64.02	72.31	71.83
1DCNN-LSTM	51.07	59.84	62.08	53.64
CRNN	47.67	49.87	56.24	50.62
GAN-SDAE	62.37	68.58	67.64	69.86
Siamese ViT	61.29	68.21	69.54	67.29
1LWCNNLSTM	65.75	69.34	68.27	65.84
Dwin Transformer	55.15	60.57	55.28	57.96
DT-ACGAN	69.53	76.82	71.59	72.31

Table 10

F1 score (%) comparison for cross-domain task C→B with 80 samples

	Class 1	Class 2	Class 3	Class 0
WDCNN	51.02	48.56	54.14	47.22
Siamese CNN	62.43	61.03	64.03	62.11
FSM3	66.85	65.26	71.73	72.20
1DCNN-LSTM	52.36	60.29	60.92	53.90
CRNN	46.71	50.40	54.22	51.11
GAN-SDAE	63.29	67.63	67.91	70.17
Siamese ViT	61.82	67.35	66.38	67.54
1LWCNNLSTM	64.48	68.42	66.71	67.36
Dwin Transformer	55.00	59.87	56.15	58.31
DT-ACGAN	70.50	76.22	72.11	73.43

4.3 Performance in noisy environment

The Gaussian white noise with different Signal-to-Noise Ratios (SNR) was added to the samples in the CWRU dataset to evaluate the noise resistance of the proposed model. SNR represents the ratio of signal power to noise power and is typically expressed in decibels (dB). The smaller the SNR value, the stronger the noise and an SNR of 0 indicates that the signal and noise power are equal. This experiment used samples with SNR values of 0dB, 2dB, 4dB, 6dB, and 8dB to simulate vibration signals containing noise. The specific experimental results are shown in the Fig. 16.

Fig. 16

Results of different models in a noise environment with 60 samples.

The figure indicates that DT-ACGAN consistently outperforms other models under limited sample conditions. Although this result does not necessarily indicate that the proposed model has the most substantial anti-interference ability, it demonstrates its excellent diagnostic ability in noisy environments.

5 Conclusion

The two major challenges faced by rolling bearing fault diagnosis based on vibration signals are limited data and changes in operating conditions. A novel Transformer based GAN is proposed in this article to address these issues. This article first designs a new window self-attention mechanism and then proposes the Dwin Transformer based on this mechanism to effectively extract the features of vibration signals. The Dwin Transformer can effectively adapt to changes in operating conditions. In addition, we have combined Dwin Transformer with ACGAN to propose DT-ACGAN to address the challenge of limited data. We present the experimental results showing that our method has better generalization ability in the limited data and cross-domain tasks compared with the existing approaches.

However, the proposed model still has some limitations. For example, the model’s input only uses one type of vibration signal in the time domain. We think that multimodality fusion is the future direction for the diagnosis of rolling bearing faults. We will combine different forms and types of signals for further research in the future.

References

Sun

Zhao

, Fault diagnosis for bearing based on 1dcnn andlstm, Shock and Vibration2021 (2021).

Baydar

Ball

, Detection of gear failures via vibration andacoustic signals using wavelet transform, Mechanical Systemsand Signal Processing17(4) (2003), 787–804.

Glowacz

, Ventilation diagnosis of angle grinder using thermalimaging, Sensors21(8) (2021), 2853.

Zhang

Tian

Alcaide

A.M.

Leon

J.I.

Vazquez

Franquelo,

L.G.

Luo

Yin

, Lifetime extension approach based onthe levenberg-marquardt neural network and power routing of dc-dcconverters, IEEE Transactions on Power Electronics38(8) (2023), 10 280–10 291.

Zhang

Huang

Chow

M.-Y.

Tian

Luo

Yin

, Adata-model interactive remaining useful life prediction approach oflithium-ion batteries based on pf-bigru-tsam, IEEE Transactionson Industrial Informatics (2023), 1–11.

Zhang

Tian

Alcaide

A.M.

Leon

J.I.

Vazquez

, Franquelo,

L.G.

Luo

Yin,

Lifetime extension approach based on levenberg-marquardt neural network and power routing of dc–dc converters, IEEE Transactions on Power Electronics, 2023.

Lihui

Jingwei

Chunbao

, Research on fault location ofbp neural network based on artificial fish swarm optimization, in, 2021 4th International Conference on Advanced ElectronicMaterials, Computers and Software Engineering (AEMCSE)IEEE (2021), 768–772.

Ince

Kiranyaz

Eren

Askar

Gabbouj

, Real-timemotor fault detection by 1-d convolutional neural networks, IEEE Transactions on Industrial Electronics63(11) (2016), 7067–7075.

Feng

Yan

Sun

Lei

Zhang

Liu

, Cfcnn: A novel convolutional fusion framework forcollaborative fault identification of rotating machinery, Information Fusion95 (2023), 1–16.

10.

Ruan

Wang

Yan

Gühmann

, Cnn parameter design based on fault signal analysis and its application in bearing fault diagnosis, Advanced Engineering Informatics55 (2023), 101877. [Online]. Available: https://www-sciencedirect-com-443.web.bisu.edu.cn/science/article/pii/S1474034623000058.

11.

Khorram

Khalooei

Rezghi

, End-to-end cnn+ lstm deeplearning approach for bearing fault diagnosis, AppliedIntelligence51 (2021), 736–751.

12.

Sun

Fan

, Fault diagnosis of rolling bearings based on cnnand lstm networks under mixed load and noise, Multimedia Toolsand Applications (2023), 1–25.

13.

Liu

Lin

Cao

Wei

Zhang

Lin

Guo

Swin transformer: Hierarchical vision transformer using shifted windows, in Proceedings of the IEEE/CVF International Conference on Computer Vision (2021), 10 012–10 022.

14.

Goodfellow

Pouget-Abadie

Mirza

Warde-Farley

, Ozair,

Courville

Bengio,

, Generative adversarial nets, Advances in Neural Information Processing Systems27(2014).

15.

Wang

, A novel deep learning system with dataaugmentation for machine fault diagnosis from vibration signals, Applied Sciences10(17) (2020), 5765.

16.

Huang

Chen

Cai

Zhang

Zhao

, Faultdiagnosis of bearing in wind turbine gearbox under actual operatingconditions driven by limited data with noise labels, IEEETransactions on Instrumentation and Measurement70 (2020), 1–10.

17.

Lin

Shao

Min

Luo

Xiao

Yan

Zhou

, Cross-domain fault diagnosis of bearing using improved semi-supervised meta-learning towards interference of out-of-distribution samples, Knowledge-Based Systems252 (2022), 109493. [Online]. Available: https://www-sciencedirect-com-443.web.bisu.edu.cn/science/article/pii/S095070512200747X.

18.

Koch

Zemel

Salakhutdinov

, et al. Siamese neural networksfor one-shot image recognition, in, ICML Deep Learning Workshop2(1), Lille, 2015.

19.

Vinyals

Blundell

Lillicrap

Wierstra

, et al. Matchingnetworks for one shot learning, Advances in Neural InformationProcessing Systems29, 2016.

20.

Snell

Swersky

Zemel

, Prototypical networks forfew-shot learning, Advances in Neural Information ProcessingSystems30 (2017).

21.

Zhang

Cui

Yang

Dong

, Limited datarolling bearing fault diagnosis with few-shot learning, IEEEAccess7 (2019), 110 895–110 904.

22.

Wang

Zhang

Yang

Zhang

, Metric-based meta-learning model for few-shot fault diagnosis under multiple limited data conditions, Mechanical Systems and Signal Processing155 (2021), 107510.

23.

Chen

Cao

Zhang

Chen

Blaabjerg

, Ameta-learning method for electric machine bearing fault diagnosisunder varying working conditions with limited data, IEEETransactions on Industrial Informatics19(3) (2023), 2552–2564.

24.

Smith

W.A.

Randall

R.B.

, Rolling element bearing diagnostics using the case western reserve university data: A benchmark study, Mechanical Systems and Signal Processing64-65 (2015), 100–131. [Online]. Available:https://www-sciencedirect-com-443.web.bisu.edu.cn/science/article/pii/S0888327015002034.

25.

ClarkGableWang. JNU-Bearing-Dataset. [Online]. Available: https://github.com/ClarkGableWang/JNU-Bearing-Dataset (2023).

26.

Dosovitskiy

Beyer

Kolesnikov

Weissenborn

Zhai

, Unterthiner,

Dehghani,

Minderer,

, Heigold,

Gelly

, et al. An image is worth 16x16 words: Transformers for image recognition at scale, arXiv preprint arXiv:2010.11929, 2020.

27.

Odena

Olah

Shlens

, Conditional image synthesis withauxiliary classifier gans, in PMLR, International Conference onMachine Learning (2017), 2642–2651.

28.

Kumar

Hati

A.S.

, Deep convolutional neural network based onadaptive gradient optimizer for fault detection in scim, ISATransactions111 (2021), 350–359.

29.

Zhao

Liu

Lin

Zhu

J.-Y.

Han

, Differentiableaugmentation for data-efficient gan training, Advances inNeural Information Processing Systems33 (2020), 7559–7570.

A novel rolling bearing fault diagnosis method for limited data

Abstract

Keywords

1 Introduction

2 Methodology

2.1 Swin Transformer

2.1.1 Overall architecture

3.1 Dwin Transformer

4.1 Case Study 1: CWRU dataset

4.1.1 Description of experimental data

Table 3 Comparison of different structures of ACGAN with 60 samples Generator Discriminator 1HP 2HP 3HP ACGAN ACGAN 0.451 0.419 0.534 Dwin Transformer ACGAN 0.658 0.785 0.742 ACGAN Dwin Transformer 0.917 0.921 0.904 Dwin Transformer Dwin Transformer 0.846 0.915 0.876

4.2.1 Description of experimental data

References

Table 3
Comparison of different structures of ACGAN with 60 samples

Generator Discriminator 1HP 2HP 3HP

ACGAN ACGAN 0.451 0.419 0.534

Dwin Transformer ACGAN 0.658 0.785 0.742

ACGAN Dwin Transformer 0.917 0.921 0.904

Dwin Transformer Dwin Transformer 0.846 0.915 0.876