© S. Dou et al., Published by EDP Sciences, 2024

1 Introduction

With the rapid development of modern industry, machinery equipment is more intelligent. It is widely used in the production and processing. Gearbox is the key transmission components of machinery equipment. In practical operation, gearbox faults such as cracks and wear may occur because of long-term work, which could cause the equipment to lose working ability [1]. Timely fault diagnosis is a key to ensure the safe operation of machinery equipment. However, traditional fault diagnosis methods have poor robustness in complex and noisy condition. The methods are limited by prior knowledge and expert experience [2]. Therefore, achieving accurate and fast gearbox fault diagnosis is of great significance.

In recent years, gearbox fault diagnosis methods based on machine learning have become a hot research. Yang et al. proposed a Bayesian network-based model to realize high accuracy fault diagnosis and further proposed cross-validation enhanced digital twin-driven fault diagnosis method for minor faults [3,4]. As one of the fastest developing fields in machine learning, deep learning is widely used in fault diagnosis, which mainly include Autoencoder (AE) [5], Deep Belief Network (DBN) [6], Convolutional Neural Network (CNN) [7], Recurrent Neural Network (RNN) [8], and Long Short-Term Memory (LSTM) [9]. Due to superior classification performance of CNN, it is widely used in gearbox fault diagnosis. Wu et al. constructed a 1D-CNN fault diagnosis model, taking 1D signals as input and achieving intelligent gearbox fault diagnosis [10]. Jiao et al. proposed a deep coupled dense CNN with complementary data, which combined a two-layer information fusion strategy to effectively reduce feature loss and gradient vanishing [11]. Zhang et al. proposed a fault diagnosis method that combined the frequency-domain Markov transformation field (FDMTF) and multi-branch residual convolutional neural network (MBRCNN) to improve gearbox fault recognition accuracy [12].

Although the above methods have achieved good results, there are still some limitations. The fault diagnosis methods based on deep learning often have a large number of parameters and complex network structures, which results in high calculation cost. The application of lightweight network greatly reduces the computational complexity. For example, Zhang et al. designed a lightweight fully connected layer (FC) in multilayer perceptron model for rolling bearing fault diagnosis [13]. Dong et al. presented a fault diagnosis algorithm based on multi-source data and 1D lightweight CNN, which did a better job of balancing the efficiency and robustness [14]. Wang et al. presented a novel multi-branch domain adaptation network (MBDAN). The universal feature extractor with three lightweight branches could capture fault features from different domains, which improved fault diagnosis efficiency [15]. At the same time, the introduction of attention mechanism improves the accuracy of lightweight model. You et al. studied an efficient hybrid neural network with a lightweight attention mechanism for bearing fault diagnosis, which took less running time and achieved excellent diagnosis accuracy [16]. Tong et al. designed a lightweight bearing fault diagnosis network based on the fusion of multi-sensor information and attention mechanism [17]. He et al. proposed a lightweight CNN based on multiscale attentional feature fusion (MA-LCNN), which demonstrated good fault diagnosis performance under noise environments [18].

However, a high-precision CNN requires a large amount of samples as support. In engineering practice, the obtained data is mostly healthy operation data. There is less fault information. If the samples are insufficient, it is easy to lead to poor generalization ability of a model. To solve the above problems, the transfer learning method is introduced in fault diagnosis field. Li proposed an improved adaptive batch normalization (AdaBN) transfer learning bearing fault diagnosis method [19]. Djaballah et al. examined the partial knowledge transfer of bearing fault diagnosis, freezing layers in varying proportions to take advantage of both freezing and fine-tuning strategies [20]. Li et al. proposed a rotating machinery transfer learning fault diagnosis method based on adaptive batch normalization, which aimed to enhance the generalization ability of the model in different working environments [21].

The transfer learning model could solve the problem of lacking numerous labeled samples. However, the faults generated by different components have large data distribution differences. Researchers rarely consider transfer effect under cross-component condition. The recognition accuracy of fault diagnosis models still needs to be improved.

For the above issues, the paper proposes a gearbox fault diagnosis method based on GAF and TLCA-MobileNetV3. The GAF is used to convert 1D gearbox signals into 2D images. The CA is introduced to improve the feature extraction ability of network. The transfer learning is used to achieve fast and accurate fault identification under varying working conditions and cross-component conditions.

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

• The signals are converted into images by GAF and the characterization ability of the signals is enhanced. By further comparing the performance of gramian angular difference field (GADF) and gramian angular summation field (GASF), the maps with better effect are selected as the input of the model.

• A novel model based on MobileNetV3 and attention mechanism is established. The feature maps are encoded by attention mechanism along the horizontal and vertical directions. By considering the relationship between network channel and long-distance position information, the remote dependence is established in space accurately and the performance of network is improved.

• The transfer learning is used to achieve small sample cross-domain fault diagnosis. The lower structures of network are frozen and higher structures of network are fine-tuned using limited samples. Through experimental verification, the model could achieve fast and high-precision fault diagnosis and has strong generalization ability.

The remaining sections are organized as follow. Section 2 introduces the GAF in detail. The introduction of MobileNetV3, CA and transfer learning is illustrated, and TLCA-MobileNetV3 is designed in Section 3. Experimental results are shown in Section 4. Conclusions are presented in Section 5.

2 GAF method

GAF can convert 1D signals into 2D images, which preserves the complete information of time-domain signals and maps the information into images with rich feature [22]. It is suitable for processing non-stationary signals such as gearbox vibration signals.

First, normalize the signal though equation (1) and scale it to the range of [–1, 1].

(1)

Second, the normalized signal is represented in polar coordinates though equation (2). The GAF matrix is obtained based on trigonometric function. is mapped to inverse cosine function, t_i is mapped to radius r_i, and N is the regularization constant coefficient in polar coordinates. Equations (3) and (4) define inner product form with the penalty term to reduce the noise interference.

(2)

(3)

(4)

Finally, scale each element of the matrix to 0∼255 by equation (5). The 2D images can be obtained.

(5)

where I(j,k) represents the pixel value of the point (j,k).int(.)  represents taking an integer, G(j,k) represents the element in the jth row and kth column of GAF matrix. Figure 1 shows the process of converting vibration signals into images through GAF.

Fig. 1 The conversion process of gearbox vibration signal by GAF.

3 Fault diagnosis model based on TLCA-MobileNetV3

3.1 MobileNetV3 network

In recent years, lightweight networks have been widely used in fault diagnosis field due to few parameters and low latency. The Google team has constructed the MobileNet series based on depthwise separable convolution (DSC). MobileNetV3 [23] has been optimized on the basis of MobileNetV2 [24], following DSC and linear bottleneck structure.

Unlike traditional convolution, each channel is only sampled by one convolution kernel when adopting DSC, and then 1*1 convolution is used for operation, which greatly reduces the computational complexity of a network. Assuming the input feature map size is W × H × M, the convolution kernel size is k × k, and the output feature map size is W' × H' × N. The comparison of parameter amount between DSC and traditional convolution is shown in Table 1.

The bottleneck of MobileNetV3 adopts inverted residual structure, as shown in Figure 2. The 1*1 convolution is used to map features to high-dimensional space. Feature extraction is achieved through DSC. Moreover, the weight of each channel is adjusted by SE. The expanded features are compressed into the original dimensions by 1*1 convolution.

Fig. 2 Bottleneck detailed structure.

3.2 CA module

The attention mechanism originates from the human visual attention mechanism, which could highlight beneficial information and reduce noise interference. To improve the recognition accuracy, this paper integrates attention mechanism to enhance the performance of gearbox fault diagnosis model.

CA mechanism [25] is a lightweight channel attention mechanism, which considers the relationship between channels and long-distance position information. It greatly enhances the ability to express features while reducing calculating cost. The detailed structure of CA is shown in Figure 3.

First, average pooling is performed for the feature maps in both width and height directions, which could obtain convolution feature maps of width and height directions, as shown in equations (6) and (7).

(6)

(7)

where, C is the number of channels, H and W are the height and width of feature maps respectively. and represent the set of local features for channel C along with different direction.

Second, concat the feature maps in both directions and use convolution to establish remote dependency, as shown in equation (8).

(8)

Finally, the obtained feature map f is divided into independent feature f^h and f^w in two directions, using 1×1 convolution layer and sigmoid activation function to calculate attention weights g^h and g^w, and obtaining the output of CA through weighted multiplication, as shown in equation (9).

(9)

Therefore, the feature map with powerful representation ability is obtained through CA, enhancing the ability to extract key features from gearbox fault signals.

Fig. 3 CA detailed structure.

3.3 Transfer learning

In transfer learning, the source domain represents the domain with rich knowledge and large numbers of labeled samples, which could be represented as D_s ={ x_s, P(x_s) }. The target domain represents the domain that needs to be assigned knowledge and data labels, which could be represented as D_t ={ x_t, Q(x_t) }. The goal of transfer learning is to utilize knowledge from source domain to improve the performance of target task. The feature distribution of gearbox samples is similar under different working conditions, and it can serve as a powerful set of features to optimize model training. Based on lightweight CNN, this paper adopts a transfer learning strategy to obtain knowledge in source domain, strengthening the ability to process target tasks.

3.4 Establishing TLCA-MobileNetV3 network

This paper introduces CA and transfer learning into MobileNetV3 to construct TLCA-MobileNetV3 network. The detailed parameters of TLCA-MobileNetV3 are shown in Table 2. The feature map is encoded along the horizontal and vertical directions by CA module. By establishing remote dependency in space, the key region in signals is accurately determined to improve network performance. Freeze the lower structure of the network, including the first convolutional layer and the six bottlenecks. Fine-tune the higher structure of the network with the limited samples from different working conditions and components. The fault diagnosis process of TLCA-MobileNetV3 network is shown in Figure 4.

Fig. 4 GAF+TLCA-MobileNetV3 network fault diagnosis process.

4 Experimental analysis and validation

4.1 Experimental data

The gearbox dataset from Southeast University was used to verify the diagnosis capability of TLCA-MobileNetV3 network, which was obtained on the drivetrain dynamic simulator (DDS) [26]. The experiment selected gear and bearing data under 20HZ-0V and 30Hz-2V working conditions. The signals are converted into 224 × 224 RGB images through GAF, as shown in Figure 5 and 6. The source domain data is used for training the model, with a total of 4000 samples. Each fault type is consisted of 800 samples. The dataset is divided into a training set and a validation set in a 4:1 ratio. The target domain data is used to verify the generalization and transfer effects of the proposed model on limited samples. The sample size is 1000. Each fault type is consisted of 200 samples. The samples are divided into a training set and a validation set in a 1:4 ratio. The detailed partitioning is shown in Table 3.

Fig. 5 The GADF images of bearing signals.

Fig. 6 The GADF images of gear signals.

4.2 Experiment and result analysis

The experiments were run on a computer with ubuntu18.04 operating system and RTX 3090 GPU. The proposed network was implemented based on PyTorch framework and Python language. In the experiments, all networks use the Adaptive Moment Estimation (Adam) to update network parameters. The cross entropy function is used to calculate the loss value. BatchSize is set to 32. Dropout is set to 0.2. In terms of learning rate, the initial value is set to 0.001 and a learning rate decay strategy is used. The patience is set to 3, with a decrease of 0.1. The loss of the validation set is used as an indicator. When the loss exceeds three times without any change, a learning rate decay strategy is used to achieve automatic adjustment of learning rate.

4.2.1 Experimental verification of 1D signals and GAF

In this paper, the comprehensive performance of 1D signal, GADF and GASF combined with CA-MobileNetV3 is verified using bearing and gear data under 20 Hz–0 V working conditions. The unprocessed 1D signals and the images generated by GADF and GASF are inputted into CA-MobileNetV3 respectively. To reduce the impact of random initial values, each method is trained 10 times and its average value is taken. The fault diagnosis results are shown in Table 4.

From Table 4, the accuracy of GADF and GASF on both datasets is above 98%. GADF+CA-MobileNetV3 achieves a higher accuracy, reaching 99.63% and 99.25% respectively, with an average iteration time of about 9 s. However, the accuracy of directly inputting 1D signals is about 90%. GAF can reduce the impact of noise and has richer feature information, so it performs better than directly inputting 1D signals. Through comprehensive comparison, with 50 iterations, GADF+CA-MobileNetV3 takes relatively less time and has the higher accuracy. Therefore, the following experiments are based on GADF samples.

To further evaluate the advantages of GADF+CA-MobileNetV3, Figure 7 shows the training and validation accuracy curves of GADF+CA-MobileNetV3 for 50 iterations. After about 10 iterations, the accuracy is above 90%. After approximate 20 iterations, the accuracy gradually stabilizes and converges to 99.63% on bearing dataset. The accuracy converges to 99.25% after approximate 30 iterations on gear dataset.

Fig. 7 Accuracy curves of GADF+CA-MobileNetV3.

4.2.2 Experimental verification of CA module

This research compares the recognition performance of MobileNetV3 network combined with SE, CBMA [27] and CA using bearing and gear data under 20 Hz–0 V working conditions. The addition positions of SE and CBMA are consistent with those of CA. The fault diagnosis results are shown in Table 5.

From Table 5, the performance of CA-MobileNetV3 network is the best, with an accuracy of 99.63% and 99.25% respectively. SE module only focuses on channel information. CBMA module increases the extraction of spatial information, but ignores the relationships between channels and long-distance position information. CA-MobileNetV3 network establishes the remote dependence in space accurately, which could learn richer fault features and improve about 3% based on SE and CBMA module. In terms of training efficiency, the training time of the three models is similar. SE module has two FC and longest fault diagnosis time. The training time of CA-MobileNetV3 is the shortest, with a time of 9.33s and 9.38s respectively. Through comprehensive comparison, with 50 iterations, CA-MobileNetV3 network has the shortest training time and the highest accuracy.

Figure 8 shows the confusion matrix of validation set on bearing samples. SE-MobileNetV3 identifies the faults of Comb and Normal type poorly, and the classification effect of CBMA-MobileNetV3 on Ball and Comb type needs to be improved. Figure 9 shows the confusion matrix of validation set on gear samples. The recognition capacity of SE-MobileNetV3 on Root and Surface type is relatively poor, and CBMA-MobileNetV3 performs poorly on Miss and Root type. In contrast, the proposed method greatly improves the identification accuracy of various types, and only partial misclassification on bearing and gear samples. This once again proves the excellent fault feature learning ability of the proposed network. Figure 10 shows dimension reduction visualization of original signals and FC. Five colors represent the different gear fault types. It can be seen that the data is mixed together before training, and there is a very clear boundary between the five type samples in FC.

Fig. 8 Confusion matrix of bearing samples.

Fig. 9 Confusion matrix of gear samples.

Fig. 10 Dimension reduction results of CA-MobileNetV3 network.

4.2.3 Experimental verification of TLCA-MobileNetV3 network

This paper sets up transfer learning fault diagnosis tasks to verify the performance of the network on untrained limited samples. After the network is trained on the source domain dataset, the lower structures of the network are frozen, the higher structures are fine-tuned with 200 training samples of the target domain. The classification effect is evaluated by 800 validation samples from target domain dataset. The tasks are shown in Table 6. Task A represents transferring bearing fault diagnosis knowledge learned from source domain (20 Hz–0 V) to target domain (30 Hz–2 V).

To verify the effectiveness of TLCA-MobileNetV3, Vgg16 [28], ResNet50 [29], MobileNetV2 [24] and MobileNetV3-L [23] are applied as comparative experiments under same experimental conditions. The accuracy of all networks is shown in Figure 11. TLCA-MobileNetV3 achieves the highest identification accuracy on four tasks. The accuracy is 99.33%, 99.18%, 99.04% and 98.78% on four tasks respectively. The results show the proposed model is effective for diagnosing small samples of varying working condition and cross component. In the comparative network, the accuracy of MobileNetV3-L and MobileNetV2 is worse than TLCA-MobileNetV3 in four tasks, which proves the MobileNetV3 combining CA module can obtain richer signal feature. Vgg16 has bad feature transfer learning ability and the accuracy is lowest. TLCA-MobileNetV3 could achieve cross-domain fault diagnosis and has good generalization ability. It can quickly and effectively extract features under different working conditions and components to realize high-precision fault diagnosis.

For fault diagnosis efficiency, TLCA-MobileNetV3 takes the shortest training time on four tasks from Figure 12. The training time is 7.43 s, 7.62 s, 7.82 s and 7.69 s on four tasks respectively. It can fast extract fault information. In term of model complexity, Params presents the number of parameters of the model. FLOPs presents the number of floating-point operations [30]. The complexity of all network is shown in Table 7. The FLOPs of TLCA-MobileNetV3 is the lowest. The Params of MobileNetV2 and TLCA-MobileNetV3 differ only 0.24 M. Combined with training time of the proposed model, TLCA-MobileNetV3 meets the requirements for model lightweight.

Fig. 11 Accuracy of the different transfer learning models on four tasks.

Fig. 12 Training time of the different transfer learning models on the four tasks.

5 Conclusion

This research proposes a gearbox fault diagnosis method based on GAF and TLCA-MobileNetV3, and realizes the accurate and fast classification of limited samples under varying working conditions and cross-component conditions.

• The 1D signals are converted into GADF and GASF images respectively, and input the 1D signals and images to proposed network. The experimental results show that the accuracy of GADF reaches 99.63% and 99.25% respectively on bearing and gear datasets. GAF has stronger characterization ability than 1D signals.

• CA-MobileNetV3 has been proven to reach 99.63% and 99.25% accuracy, and the training time is 9.33s and 9.38s on bearing and gear dataset. The experimental results show CA module could fast extract the key information in signals to improve the network performance. CA-MobileNetV3 has strong feature extraction ability.

• The transfer learning experiments are carried out and TLCA-MobileNetV3 network is compared with the other transfer learning methods. The identification accuracy is better than other models under varying working conditions and cross component. The training time and computational cost of TLCA-MobileNetV3 show it could meet the requirement for model lightweight. The proposed model is of great significance for solving limited gearbox sample problem in practical engineering.

Acknowledgments

The authors would like to thank the editor and reviewers for the valuable comments and suggestions.

Funding

This work was supported by Beijing Municipal Education Commission & Beijing Natural Science Foundation Co-financing Project (Grant Numbers [KZ202210015019]), the Project of Construction and Support for high-level Innovative Teams of Beijing Municipal Institutions (Grant Numbers [BPHR20220107]).

Conflict of Interest

The authors declare no competing interests.

Data availability

The data may be available from the corresponding author upon request.

Author contribution statement

Study conception and design: S.D., X.C., Y.D.; data collection: S.D., Z.W., Y.L.; analysis and interpretation of results: S.D., X.C., Y.D.; draft manuscript preparation: X.C., S.D. All authors reviewed the results and approved the final version of the manuscript.

References

All Tables

All Figures

	Fig. 1 The conversion process of gearbox vibration signal by GAF.
In the text

	Fig. 2 Bottleneck detailed structure.
In the text

	Fig. 3 CA detailed structure.
In the text

	Fig. 4 GAF+TLCA-MobileNetV3 network fault diagnosis process.
In the text

	Fig. 5 The GADF images of bearing signals.
In the text

	Fig. 6 The GADF images of gear signals.
In the text

	Fig. 7 Accuracy curves of GADF+CA-MobileNetV3.
In the text

	Fig. 8 Confusion matrix of bearing samples.
In the text

	Fig. 9 Confusion matrix of gear samples.
In the text

	Fig. 10 Dimension reduction results of CA-MobileNetV3 network.
In the text

	Fig. 11 Accuracy of the different transfer learning models on four tasks.
In the text

	Fig. 12 Training time of the different transfer learning models on the four tasks.
In the text