A Novel Method of Production Line Bearing Fault Diagnosis Based on 2D Image and Cross-Domain Few-Shot Learning

Abstract

Data-driven intelligent fault diagnosis has made considerable strides. However, collecting sufficient fault information in real production data is extremely challenging. Therefore, a novel method of bearing fault diagnosis based on two-dimensional (2D) images and cross-domain few-shot learning is proposed. Initially, the approach uses multiscale morphology to convert the bearing’s one-dimensional (1D) vibration signal into a 2D image, which preserves the whole information. Second, to address the issue of limited bearing fault data, we extend a substantial amount of natural image knowledge to the converted 2D image based on the improved cross-domain few-shot learning method. A distance-based classifier is employed to prevent the problem of overfitting owing to insufficient data to improve the approach’s classification capacity with few samples. The experimental results demonstrate that, with the limited dataset provided, our method outperforms other prevalent methods and has high feasibility and certain engineering applications.

1. Introduction

Modern machinery is evolving in the direction of high performance, high precision, and intelligence as technology and industrialization continue to improve. Particularly rolling bearings are becoming more crucial in production, transportation on rails, and other areas [1]. As the primary rotating equipment component, prognostics health management (PHM) is a necessity to prevent significant financial losses and human tragedies in businesses [2]. Therefore, fault diagnosis and feature extraction, two essential PHM processes, have become important research topics in practical industrial settings.

The “big data” era has now arrived in the field of machinery health monitoring, and some of the drawbacks of earlier fault diagnosis methods have been effectively addressed [3]. Utilizing a data-driven approach will make troubleshooting intricate mechanical systems less challenging [4]. Data-driven approaches have gone through two stages: Traditional Intelligent Fault Diagnosis (TIFD) based on manual features and Modern Intelligent Fault Diagnosis (MIFD) based on deep learning. TIFD first requires feature extraction from the signal and then a classification algorithm. Frequently employed methods include Spectral Clustering (SC) [5], K-Nearest Neighbor (KNN) [6], Extreme Learning Machine (ELM) [7], and Support Vector Machine (SVM) [8]. These methods’ features, however, have a poor ability to generalize; they are unable to directly identify features on the original test data. Deep Learning (DL) has overcome these drawbacks and evolved into a potent intelligent diagnosis approach [9,10]. Different DL methods, including Restricted Boltzmann machine (RBM) [11], Auto-Encoder (AE) [12], Recurrent Neural Networks (RNN) [13], Convolutional Neural Networks (CNN) [14], etc., are utilized to tackle various diagnostic problems. An integrated depth auto-encoder was effectively employed by Shao et al. [15] in feature extraction and intelligent fault diagnosis of bearings. Khorram et al. [16] suggested a novel convolutional long-term memory recurrent neural network for fault detection. However, traditional DL methods demand a huge quantity of high-quality labeled data, as a limited sample size will cause overfitting and impair performance. It is common knowledge that equipment is not permitted to run in a fault status in real industrial settings. Therefore, it is very challenging to gather enough marker data for each failure type.

Few-shot learning has significantly improved recently at overcoming the data scarcity issue, especially in image classification [17,18]. Common model, Transfer Learning, and Few-shot learning are depicted in Figure 1 with various colors denoting various domains. Common models assume that there are enough samples, and that the train set and test set are in the same domain. Transfer Learning refers to the train set and test set being in different domains, with correlation between the domains. Fewer samples are provided in the few-shot learning training set compared to classic deep learning and transfer learning, which makes it easier to tackle issues such as conditional transfer and few-shot scenes. In order to diagnose bearings in the presence of sparse fault data, Zhang et al. [19] introduced a novel few-shot learning diagnosis. Fang et al. [20] proposed a small sample denoising fault diagnosis algorithm, which can solve the bearing fault diagnosis problem under small samples. Yu et al. [21] proposed a me-ta-learning fault diagnosis method. It attempts to obtain prior knowledge by optimizing initialization parameters. Fast and accurate bearing fault diagnosis is realized under unknown operating conditions using a small number of samples. Hu et al. [22] proposed a new diagnosis method based on less shot learning, which is applicable to the environment of data scarcity. The above methods require the source domain dataset to be pre-trained, and the correlation between the source domain and the target domain significantly affects the results. Most existing research has been constrained to same-component-same-testbed [23,24] and component-different-testbed [25,26]. A few scholars have performed cross-domain experiments of different-component-same-testbed [27], but the model has not performed well in the new field, severely restricting its application in real-world working situations.

Currently, most studies directly use 1D vibration signals for classification, while 2D images provide more information that allows the model to achieve higher recognition accuracy [28,29]. Given that the fault classification and image recognition processes are extremely similar, it is highly feasible to introduce computational methods from the field of image processing into fault diagnosis [30]. For instance, Zhu et al. [31] suggested a capsule network made by switching the starting blocks and utilizing the short-time Fourier transform (STFT) to acquire time-frequency pictures as input. Chen et al. [32] used cyclic spectral coherence to transform 1D signals into a 2D image that was integrated with CNN for fault diagnosis of bearings. A 2D convolutional structure derived from LeNet-5 was proposed by Lon et al. [33], in which segmentation folds 1D signals into a 2D image. Kunar et al. [34] performed automatic detection and damage evaluation of damaged bearing components by transforming vibration signals into a 2D grayscale image with time-frequency representation using a continuous wavelet transform. These research methods, however, are prescriptive and heavily rely on expert expertise.

This paper proposes a novel method of bearing fault diagnosis based on 2D images and cross-domain few-shot learning, taking into account the aforementioned issues. Considering that the signals estimated using multiscale morphology contain more fault information and that no artificial parameter setup is required for full-scale calculation, the 1D bearing vibration data is transformed into a 2D image. In the meanwhile, the knowledge from the natural image dataset using MiniImageNet [35] is extended to the transformed bearing images. On this basis, the feature extractor is trained and then fine-tuned using a small number of samples from the target domain. In addition, a distance-based classifier [36] was utilized rather than a fully connected layer to improve the classification capacity of the few samples. Finally, using the experiment and production line datasets, the proposed method’s effectiveness has been verified. The outcomes show that, in comparison to previous methods, our method offers more generality in addition to improved accuracy.

2. Basic Theory

2.1. Multiscale Mathematical Morphological Operators

Matheron and Serra were among the first to employ mathematical morphology in image processing, and it is currently often used in rotating machinery fault diagnosis [37]. Multiscale morphological filtering is used in the fault diagnosis of bearings in order to gain more specific information about the fault characteristics. Assuming that ε (ε = 1, 2, 3, ..., λ) is the scale of the structural element, the basic morphological operators for the four multiscale scales of dilation, erosion, opening and closing are described as follows:

Multiscale dilation operators:

$$(f\oplus \lambda g)(n)=\underset{\lambda -1}{\underbrace{f\oplus g\oplus g\oplus \cdots \oplus g}}$$

(1)

Multiscale erosion operators:

$$(f\Theta \lambda g)(n)=\underset{\lambda -1}{\underbrace{f\Theta g\Theta g\Theta \cdots \Theta g}}$$

(2)

Multiscale opening, closing operators:

$$(f\circ \lambda g)(n)=((f\Theta \lambda g)\oplus \lambda g)(n)$$

(3)

$$(f•\lambda g)(n)=((f\oplus \lambda g)\Theta \lambda g)(n)$$

(4)

where denotes ⊕ dilation operator, Θ stands for erosion operator, denotes ∘ opening operator and • stands for closing operator.

The above is based on the properties of the morphological data that the aforementioned basic operator extracted. Additionally, given that the top-hat operator can differentiate the positive from the negative pulse sequences, the 1D signal’s detailed information is improved. A new multiscale enhanced morphological top-hat filter (MEMTF) has been demonstrated by Wang et al. [38]. The expression is shown below:

$$MEMTF(f{(n)}_{\lambda g})=2\left[f(n)-\frac{(f\oplus \lambda g)(n)+(f\Theta \lambda g)(n)}{2}\right]\cdot \left[f(n)-\frac{(f•\lambda g\oplus \lambda g\Theta \lambda g)(n)+(f\circ \lambda g\Theta \lambda g\oplus \lambda g)(n)}{2}\right]$$

(5)

In order to obtain more detailed information about the fault characteristics, the signals calculated by multiscale mathematical morphology are considered to contain richer fault information, and no artificially set parameters are required for the full-scale calculation. Therefore, the MEMTF multiscale morphology is chosen to process the data. First, the one-dimensional original vibration signal to be input is separated into small windows and repeated sampling is performed. The separated windows are reconstructed using the MEMTF method, the results are analyzed by multi-scale FFT spectral analysis, and finally, the two-dimensional image feature information at the frequency scale is obtained for the next step of the study.

2.2. Few-Shot Learning

Few-shot learning is a type of machine learning problem (defined by the variables experience E, task T, and performance metric P), where experience E only contains a small number of examples and supervised data about task T [20]. The model can be well-extended to new tasks and trained with a relatively small number of samples, or “learning to learn” [39], as seen in Figure 2. The majority of the newly proposed few-shot learning techniques pull knowledge from some auxiliary sets from the source domain to train the model with a given small sample support set in the target domain.

With multiple learning experiences and many applications, it is initially trained using a variety of sample types belonging to the same or distinct categories. The input is a sample pair with the same or different classes ($x_1^i$,$x_2^i$). The output is the probability that ($x_1^i$,$x_2^i$) two input samples are the same. In contrast to conventional classification techniques, few-shot learning frequently expresses performance in terms of “K-way N-shot.” In a K-way test, given a test sample $\widehat{x}$ for classification, the support set S is shown in Equation (1), which contains K samples, each with a different label y.

$$S=\{(x_1,y_2),\dots ,(x_K,y_K)\}$$

(6)

As stated in Equation (2), the test samples are subsequently classified based on the most similar samples in the support set.

$$C\left(\widehat{x},S\right)=\underset{c}{\arg \max }(P(\widehat{x},x_c)),x_c\in S$$

(7)

In the K-way N-shot test, the model is given a support set consisting of K different classes, each with N samples (S₁, S₂, ..., S_N). The model must then determine which support set class the test samples should belong to, as shown in Equation (3).

$$C\left(\widehat{x},(S_1,\cdots ,S_N)\right)=\underset{c}{\arg \max }({\displaystyle \sum _{n=1}^{N}P(\widehat{x},x_c{}_n)}),x_c{}_n\in S_n$$

(8)

Even though few-shot learning-based methods can attain the needed accuracy based on a tiny dataset, they require base data for pre-training, and the degree of relevance of the base data to the target domain can greatly affect the outcomes. It is crucial to achieving cross-domain few-shot learning for this reason.

3. The Proposed Fault Diagnosis Method

In this section, a novel method of bearing fault diagnosis based on 2D image and cross-domain few-shot learning is proposed. The fault diagnosis framework for the proposed method is presented in Section 3.1. The structure is presented in further depth in Section 3.2.

3.1. Fault Diagnosis Framework

For intelligent fault diagnosis, a framework for the categorization of bearings with few samples that are not restricted to working conditions is built in this study. In Figure 3, the comprehensive structure is displayed.

The framework deals with the issue of poor generality caused by the requirement to locate a particular dataset as the source dataset for a few samples bearing fault diagnosis tasks. In order to achieve feature transfer, we will use MiniImageNet, a big collection of natural image datasets, and construct the Conv5 feature extraction network. Then, the 1D vibration signal in the new job is transferred to a 2D image utilizing multiscale morphology, and the transferred image is employed for feature extraction by a trained feature extractor. To eventually get at an intelligent diagnosis of a few samples of bearings, fine-tuning is then carried out using a distance-based classifier.

3.2. Learning Procedure

3.2.1. Training Feature Extractor Based on MiniImageNet

Deep neural networks can typically extract high-quality features through multilayer processing, but they also need several labelled samples and a lot of computational power [40]. However, robust multilayer neural networks cannot be trained since failure data is lacking. Due to the success of deep learning in computer vision, some research has shifted to leveraging MiniImageNet datasets to hasten training and improve the precision of mechanical defect diagnostic networks [41,42]. In order to develop a feature extraction network, this framework will conduct feature transfer using the MiniImageNet image dataset as the source dataset.

In this paper, the proposed feature extraction network structure consists of five convolutional layers, five pooling layers, and one fully connected layer. In the Conv5 architecture proposed in this paper, the input size of the image is 84 × 84, and in each convolutional layer configuration, the convolutional step is fixed at 1 pixel. The size of the convolutional kernel is set to 3 × 3 in order to capture more information, the boundary filling method is used to extend the size of the image, and the extended area is filled with zeros. Following each convolutional layer is a pooling layer with a maximum pooling span of 2 and a pooling window size of 2 × 2. Halving the image features after pooling the convolutional layers, this cuts down on computation time and model overfitting. The fully connected layer is the last layer. The Conv5 framework that is proposed in this paper is described in depth in

Table 1. Parameters of the proposed Conv5 architecture.

Layers.	Kernel Size	Kernel Number	Output Size	Activation Function
Input	/	/	84 × 84 × 3	/
Conv1	3 × 3	16	84 × 84 × 16	ReLU
Pool1	2 × 2	16	42 × 42 × 16	/
Conv2	3 × 3	32	42 × 42 × 32	ReLU
Pool2	2 × 2	32	21 × 21 × 32	/
Conv3	3 × 3	32	21 × 21 × 32	ReLU
Pool3	2 × 2	32	10 × 10 × 32	/
Conv4	3 × 3	64	10 × 10 × 64	ReLU
Pool4	2 × 2	64	5 × 5 × 64	/
Conv5	3 × 3	64	5 × 5 × 64	ReLU
Pool5	2 × 2	64	2 × 2 × 64	/
FC1	256	/	N × 1	/

.

3.2.2. Constructing Multiscale Morphological Image

Given that deep neural networks are more capable of extracting powerful features, a multiscale morphological technique is required to transform the original 1D vibration signal into a 2D image containing more feature information. In this paper, data sets are generated for each operating state using an overlapping truncation method, which takes into account the enormous number of acquired vibration signal data points [33]. A displacement interval of 512 data points is used to move the truncation window alongside the original vibration signal. In this paper, the window size is 4096 data points. Therefore, each window movement provides 4096 data samples of length 4096. The size of the signal converted into an image is set to 84 × 84. The outcomes are displayed in Figure 4.

3.2.3. Faults Diagnosis Based on Cross-Domain Few-Shot Learning

We employed the aforementioned method to convert the 1D vibration signal into a 2D image in order to obtain additional details and achieve fault diagnosis for bearings under various operating situations. The converted image data were divided into support set $S=\{\left(x_1^s,y_1^s\right),\left(x_2^s,y_2^s\right),\dots ,\left(x_{N*K}^s,y_{N*K}^s\right)$, N representing the number of categories contained in the support set, K representing the number of samples contained in each category and query set $Q=\{\left(x_1^q,y_1^q\right),\left(x_2^q,y_2^q\right),\dots ,\left(x_{N*L}^q,y_{N*L}^q\right)$, and L representing the number of samples contained in each category. When classifying the bearing fault types in the target domain, we used a different classifier from the full connection layer used in the training stage of the Conv5 model. The framework proposed in this paper uses a weight matrix $W_n\in R^{(d\times c)}$ as a classifier, which is based on the idea of cosine distance. For each of the different target domains, the weight matrix W_n was adjusted according to the image in the support set of target domain. When adjusting the weight matrix W_n, we first used the $f_{\theta }(x)$ to extract the features of the $x_i^s$ image in the support set, $f_{\theta }(x)$ is the rest of Conv5 trained in A after removing the full connection layer. The similarity score $[s_{i,1},s_{i,2},\dots ,s_{i,c}]$ is obtained by calculating the cosine similarity between $f_{\theta }(x_i^s)$ and each weight vector $[w_1,w_2,\dots ,w_c]$ in W_n Cosine similarity calculation formula is as follows:

$$s_{i,j}=\frac{f_{\theta }{(x_i)}^T{w}_j}{\Vert f_{\theta }{(x_i)}^T\Vert \Vert w_j\Vert }$$

(9)

Then, we normalized these similarity scores using softmax function to obtain the prediction probability $\left[p_{i,}{}_1,p_{i,2},\dots ,p_{i,}{}_c\right]$ of each category, and the predicted results p_i is taken from the maximum value in $\left[p_1,p_2,\dots ,p_c\right]$. Finally, we used Stochastic Gradient Descent (SGD) to fine tune W_n based on the loss value calculated from the label and predicted result of image in support set. Loss value calculation formula is as follows:

$$Loss=-\frac{1}{N*L}{\displaystyle \sum _{\mathrm{i}=1}^{N*L}{{\displaystyle y}}_i^s}*p_i$$

(10)

After adjusting the weight matrix W_n, we diagnosed the bearing fault data in the query set by calculating the cosine similarity between $f_{\theta }(x_i^q)$ and the adjusted weight matrix W_n and classified the fault types of each image in the query set based on the cosine similarity.

4. Experiment and Validation

In this study, it was possible to evaluate the proposed method by utilizing the bearing dataset from the Case Western Reserve University (CWRU) Bearing Data Center [43] and the production line dataset. Meanwhile, it was compared to three comparable methods: VGGNet [44], Conv5, and ProtoNet [45]. A brief description of the methods being compared will be provided. We performed a 10-way cross-domain diagnostic case on the CWRU dataset and a 4-way cross-domain diagnostic case on the production line real operating conditions dataset, respectively. Additionally, we displayed the outcomes using tables, graphs, confusion matrix, and visualization by t-Distributed Stochastic Neighbor Embedding (t-SNE) [46]. All of the methods used in our tests were performed in the same environment using Pytorch [47] and an NVIDIA RTX Titan GPU.

4.1. Comparison of Methods

The proposed method is compared to the other three methods (VGGNet, Conv5, and ProtoNet) in order to fully illustrate its advantages. Maxpool and ReLU functions are employed between the layers of the five convolutional layers, three fully connected layers, and one softmax output layer that make up VGGNet. This paper comprises VGG16, which has a total of 16 sublayers. Conv5 is the proposed architecture in this paper, and it consists of five convolutional layers, five pooling layers, and one fully connected layer in the superposition. The fully connected layer in Conv5 is removed as the network’s feature extraction component in the few sample methodology proposed in this paper. To achieve reasonably trustworthy comparison findings under the same conditions, it should be noted that the sample sizes of VGGNet and Conv5 are equivalent to those in Few-shot learning. Moreover, to compare the novel few-shot method proposed in this paper with the traditional few-shot method, the ProtoNet method is used in experiments on fault diagnosis. Conv5 is also used in the method’s feature extraction step to guarantee experiment fairness. Each group of experiments is run 50 times to prevent the randomness that the experiments can cause, and the average accuracy was then computed as the output of each model.

4.2. Cross-Domain Fault Diagnosis Case 1: CWRU

4.2.1. Experimental Platform and Dataset

The effectiveness of the proposed method is tested in this section using CWRU drive-end bearing failure data. Figure 5 depicts the layout of the test bench, which consists of an induction motor, a torque encoder, a dynamometer, control electronics and accelerometers.

The bearing vibration signals were collected under different load conditions, including (0HP, 1797 rpm), (1HP, 1772 rpm), (2HP, 1750 rpm), and (3HP, 1730 rpm), respectively. According to the needs of the motor load on the mechanical conditions, four sets of bearing data were collected for the investigation. Dataset A, Dataset B, Dataset C, and Dataset D are the names of the four datasets. There are ten states for each bearing data set, including normal and three fault sizes (0.007, 0.014, and 0.021 inches), that correlate to three fault locations (inner ring, outer ring and rolling body). There are four modes, namely normal condition (NC), inner race fault (IF), ball fault (BF), and outer race fault (OF), for each situation, as depicted in

Table 2. CWRU bearing dataset faults classification.

Fault Size (Inches)	Fault Mode
0	NC
0.007	BF-1	IF-1	OF-1
0.014	BF-2	IF-2	OF-2
0.021	BF-3	IF-3	OF-3

.

We initially trained the MiniImageNet based feature extractor that was utilized in the target dataset, and we divided the training and validation sets into 4:1 categories to test the performance of the proposed method. The driver-end data with a sample frequency of 48 kHz was then chosen from the CWRU database to create the target dataset. To simulate the case of small datasets, three few-shot training settings were used for each dataset, namely 10-way 3-shot, 10-way 5-shot, and 10-way 10-shot, respectively. In each round of the K-way N-shot experimental setup, N samples are taken from 200 test samples for each of the K categories, K × N samples are used as the training set, and K × (200-N) samples are utilized as the test samples. The specific description of the data set is shown in

Table 3. Description of the datasets.

	Dataset Name		Sample Category	Sample Number
Source domain	MinilmageNet	Train	100	100 × 480
		Val	100	100 × 120
Target domain	Dataset A	Train set	10	10 × N (N = 3/5/10)
		Test set	10	10 × (200-N) (N = 3/5/10)
	Dataset B	Train set	10	10 × N (N = 3/5/10)
		Test set	10	10 × (200-N) (N = 3/5/10)
	Dataset C	Train set	10	10 × N (N = 3/5/10)
		Test set	10	10 × (200-N) (N = 3/5/10)
	Dataset D	Train set	10	10 × N (N = 3/5/10)
		Test set	10	10 × (200-N) (N = 3/5/10)

.

Using the MEMTF multiscale morphological method, the original 1D vibration signal is transformed into a 2D image with more feature information. Figure 6 displays the results of the signal conversion to image under normal operating conditions. The resulting image has the dimensions 84 × 84. The results of the conversion under the other 9 state conditions are shown in Figure 7. As can be seen from the converted image results, the images in different fault states look completely dissimilar, providing an intuitive way to classify the method.

4.2.2. Analysis of Results

To compare the diagnosis results of the proposed method with those of VGGNet, Conv5, and ProtoNet, we take the example of 10-way classification from four datasets (Dataset A, Dataset B, Dataset C, Dataset D) generated in CWRU dataset. Figure 8 displays the results based on the CWRU dataset. Our proposed method achieves the best fault diagnostic performance on the CWRU dataset, regardless of the sample size used for training. Among them, when using 10-shot, the accuracy of our proposed algorithm on the four datasets generated by CWRU Dataset A, Dataset B, Dataset C, and Dataset D is 95.22 ± 0.28%, 98.12 ± 0.21%, 96.16 ± 0.23%, and 94.55 ± 0.34%, respectively, with the mean value of the four datasets reaching achieved 96.01%. Its mean results are 13.80% and 8.78% greater than those of VGGNet and Conv5, respectively, and our approach improves by 3.51% compared to the best few-shot learning ProtoNet. By comparing the results for training samples of 3-shot and 5-shot, it is clear that our method performs better than other metods when less training data are used. The fault diagnostic accuracy of the deep learning-based technique is lower than that of the few-shot learning method when compared to the few-shot learning method. This is because the limited amount of data used here could lead to overfitting because traditional deep learning methods need a due amount of training data. Changes in working conditions may also affect the performance of these deep learning systems due to their weak generalization capacity. The experimental results show the adaptability of our proposed cross-domain few-shot learning method.

To illustrate the proposed method classification accuracy and error ratio for the bearings under ten operational scenarios, Figure 9 displays the confusion matrix for the various methods, using an example for each task from the Dataset B dataset for the 10-shot condition. The accuracy rate of each bearing health status is shown in the right column of the confusion matrix, and the recall rate is shown in the bottom row. As illustrated in Figure 9, the proposed method effectively determines the health status of rolling bearings under various operating circumstances. The model performs admirably in each of the ten working conditions. Additionally, it is evident that the NC category has a 100% recognition rate. This indicates that even if the diagnostic errors of the proposed method are primarily caused by incorrect estimation of BF and IF defects, bearing failures can still be identified. In particular, this proposed method ensures that healthy and fault bearings are not misclassified, preventing incorrect information from being delivered in practical applications.

To further evaluate the capability of the contrasting methods, as depicted in Figure 10, we employ t-SNE to display the output of the feature extractor and visualize the extracted features in a 2D plane. It can be seen that the proposed cross-domain few-shot method outperforms VGGNet, Conv5, and ProtoNet in terms of efficiency. The suggested approach enables the embedded features to be as near to independent outside the class and as independent inside each class. The distinguishability of features extracted by the extractor facilitates fault identification by the classifier and aids in the interpretation of classification results to some extent.

Analogously, besides classification performance, the time consumption should also be considered. From

Table 4. Comparison of time consumption of different models.

Model Name	VGGNet	Conv5	ProtoNet-10 Shot	Our Method-10 Shot
Train	400s	80s	12s	15s
Test	6s	2.6s	1s	2s

, we compared the model time consumption for VGGNet, Conv5, ProtoNet-10 shot, and our method-10 shot. Each model was trained under the same configuration. Comparison results showed that Conv5, ProtoNet-10 shot, and our method-10 shot can complete the training quickly due to the small training set and simple model. In contrast, VGGNet takes more time due to the large amount of training operations. Compared with VGGNet, the proposed method greatly reduces the time cost. Of these, ProtoNet has the shortest training time because it is simple and efficient in optimization design and easy to optimize. Due to the attrition design, the proposed method has a slight increase in training time compared to ProtoNet, but it performs better on the dataset compared to the accuracy improvement, and the slight increase in training time is acceptable. Consequently, the proposed method is further demonstrated to be of higher application value.

4.3. Cross-Domain Fault Diagnosis Case 2: Production Line

4.3.1. Test Platform and Data Description

Once the motor in the production line breaks down, the downtime and high maintenance costs will result in a significant loss of revenue for the company. Condition monitoring of the production line bearings was performed to verify the efficacy and engineering suitability of the method proposed in this paper. The measured signal data from the production line of an automotive company are used. Figure 11 depicts the experimental test platform. The four bearing operating states under test are NC, and the fault conditions are BF, IF, and OF.

Throughout the experiments, the acceleration sensor was attached to the motor base. The motor speed was 1480 rpm during the test, and the acceleration sensor model was an IEPE vibration acceleration sensor. The instrument had a sampling rate of 46 kHz. We used the MiniImageNet dataset as the source dataset in the validation collected using the dataset gathered from this platform. For the target dataset, three few-shot training settings, 4-way 3-shot, 4-way 5-shot, and 4-way 10-shot, were employed. The detailed descriptions are displayed in

Table 5. Production line bearing dataset fault classification.

	Dataset Name		Sample Category	Sample Number
Source dataset	MinilmageNet	Train	100	100 × 480
		Val	100	100 × 120
Target dataset	Production data	Train set	4	4 × N (N = 3/5/10)
		Test set	4	4 × (200-N) (N = 3/5/10)

.

The fault data are subjected to multiscale morphological operations using MEMTF multiscale morphological filtering, and the analysis results for each scale are then processed using FFT to produce frequency-scale distribution images, the results of which are depicted in Figure 12 for the transformation under four operating conditions. The converted image results show that there are significant variances in the images of various fault states, which will help to significantly increase the fault classification accuracy.

4.3.2. Analysis of Results

The proposed method is still compared with VGGNet, Conv5, and ProtoNet in order to confirm the testing accuracy of the method, and the results are displayed in Figure 13. It is clear from the data in the figure that our proposed method, regardless of the amount of training samples used, may demonstrate a considerable improvement in fault diagnosis accuracy. Among them, the accuracy rates of VGGNet and Conv5 are 79.64 ± 0.96% and 82.46 ± 0.83%, respectively. Further investigation reveals that the substantial model overfitting issue and the short data sets that are insufficient for training are the primary causes of their subpar classification results, which severely restrict the performance of fault diagnosis. Despite considerable advancements, the fault diagnosis performance of the ProtoNet method is still subpar. The four methods are compared using the 10-shot as an example. Our method improves by 15.52%, 12.70%, and 2.18% compared to VGGNet, Conv5, and ProtoNet 10-shot, respectively. The experimental results demonstrate the high fault diagnosis performance of our proposed cross-domain few-shot learning method.

For each task in the dataset, the confusion matrix of the fault diagnosis results for various method models was examined under 4-way 10-shot conditions, as illustrated in Figure 14, in order to evaluate the performance of the proposed method visually. The predicted and actual health statuses of the test sample are represented by the horizontal and vertical axes, respectively, in the confusion matrix. According to Figure 15, the total average detection accuracy of the experimental data set may reach 95.16 ± 0.20%, and the classification accuracy of the production line bearings under the four working conditions achieves a more desirable result. The two fault kinds of IF and OF, which are often confused, are the principal manifestation of the accuracy difference. The method in this paper has a strong diagnostic performance for the health state of NC, and this shows that the method in this paper has a low risk of false alarms. Overall, the method that is proposed in this paper has a high fault diagnosis accuracy and is adequate to meet the actual requirements of the sector.

The t-SNE algorithm is used to visualize the stream structure of the original samples by projecting each high-dimensional sample onto a data point on a 2D plane. This helps to further evaluate the performance of the proposed method visually. The output similarity vector created by the method presented in this study is applied to the t-SNE algorithm in the analysis, and the final visualization results are displayed in Figure 15. Overall, the proposed method can successfully increase fault identification accuracy. It is clear that data points with similar bearing health statuses are highly grouped together, but data points with various failure categories are well-segregated. As a result, it can be used to classify bearing faults on a production line.

5. Conclusions

This paper offers a unique method of bearing fault diagnosis based on 2D-image- and cross-domain few-shot learning with quick adaptive capabilities, focusing on issues with limited fault data and variable bearing conditions. Firstly, a 2D image conversion method based on the MEMTF multiscale morphological transformation is proposed to address the problem that some commonly used time-frequency analysis methods rely on expert knowledge in converting 1D vibration signals into a 2D image. Secondly, small samples from the target domain are used to fine-tune the extractor trained on the natural image dataset. Additionally, a distance-based classifier was employed to enhance the limited sample capacity for categorization. Finally, the improved cross-domain few-shot learning is used to implement bearing fault diagnosis. To demonstrate the proposed method’s effectiveness and superiority in the presence of few failure data, this paper performs experiments utilizing data from the CWRU and data from the production line, respectively. The findings demonstrate that the proposed method performs better at fault diagnosis than the current methods and is more in line with real-world production applications. In future research, the method should be used in more work, including diagnosing other bearing compound faults, gear faults, etc.