A Method for Multi-Source Heterogeneous Analysis and Fault Diagnosis of Bearings Based on Convolutional Depth Expansion and Gated Attention Fusion

Abstract

This invention discloses a method for multi-source heterogeneous analysis and fault diagnosis of bearings based on convolutional depth extension and gated attention fusion, belonging to the field of bearing equipment fault diagnosis technology. The method includes the following steps: S1, data acquisition and sample construction, standardizing and augmenting vibration and current signals; S2, branch feature extraction, mining multi-level deep features of each sensor data; S3, multi-source feature fusion, fusing the deep features extracted from branches level by level through multi-layer gated attention fusion; S4, model prediction and training; S5, importing sensor data from new operating conditions or new bearings, and outputting the fault diagnosis result for that bearing. This invention uses the residual-enhanced Inception module to improve the stability and efficiency of multi-scale feature extraction, and combines it with gated attention fusion to achieve comprehensive representation capabilities of multi-source heterogeneous data, thereby significantly enhancing the robustness and generalization ability of the model under complex operating conditions, and further improving the accuracy and stability of bearing fault diagnosis.

Description

Technical Field

[0001] This invention belongs to the field of bearing equipment fault diagnosis technology, and specifically relates to a bearing multi-source heterogeneous analysis and fault diagnosis method based on convolution depth expansion and gated attention fusion. Background Technology

[0002] Bearings are among the most common basic components in major equipment such as rotating machinery and manufacturing equipment, and are widely used in fields such as power, transportation, aerospace, and nuclear industry. Their operating condition directly affects the performance and safety of the entire machine. Once a bearing fails, it will not only reduce production efficiency, but may also lead to equipment downtime or even serious accidents, causing huge economic losses. Therefore, accurate condition identification and fault diagnosis of bearings are of great significance.

[0003] In recent years, bearing fault diagnosis methods have been mainly divided into three categories: fault mechanism-based methods, knowledge-based methods, and data-driven methods. Among them, data-driven intelligent diagnosis methods have received widespread attention and have already seen numerous technologies and applications. These methods utilize only a large amount of monitoring data, employing machine learning or deep learning to construct fault diagnosis models. Through deep feature extraction and state recognition, they achieve automatic mapping between monitoring sensor data and fault states, helping to improve the intelligence level of equipment condition monitoring and fault diagnosis.

[0004] The development of deep learning technology has provided efficient analytical tools for bearing fault diagnosis. Models such as Convolutional Neural Networks (CNNs), Residual Neural Networks (ResNets), and Temporal Convolutional Networks can automatically extract deep features, improving the performance and efficiency of fault diagnosis models. However, existing deep learning-based methods still have some problems, including: First, most methods use only single sensor signals for feature extraction, making it difficult to comprehensively represent multimodal information under complex working conditions; second, feature fusion methods for multi-source sensor data often employ concatenation or weighting methods, and the heterogeneity of sensors can easily lead to feature redundancy, conflicts, and loss; third, deep networks may still experience gradient vanishing or model instability during training, limiting their practical application in industrial scenarios.

[0005] To address the aforementioned issues, scholars have recently proposed methods combining multi-sensor fusion with attention mechanisms to expand the representational capabilities and diagnostic performance of multi-source data. However, existing multimodal feature fusion methods fail to distinguish the importance of different modalities, resulting in a lack of dynamic variation in weight settings. Furthermore, the efficiency and stability of multi-scale feature extraction need improvement. Therefore, there is an urgent need to research efficient fusion methods for multi-source heterogeneous sensor data, aiming to achieve multi-scale feature extraction and adaptive cross-modal feature fusion. Moreover, for the practical needs of bearing fault diagnosis, intelligent models should be able to balance low noise sensitivity and good generalization ability, providing practical technology for intelligent monitoring and fault diagnosis of the entire system. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of existing bearing fault diagnosis methods, addressing issues such as insufficient information from single sensor data, poor fusion of multi-source heterogeneous data, instability in deep network training, and insufficient noise resistance. This invention provides a bearing multi-source heterogeneous data analysis and fault diagnosis method based on convolutional depth expansion and gated attention fusion. This method achieves efficient extraction and stability enhancement of multi-scale features, and dynamically fuses multi-source heterogeneous data features through a gated attention mechanism, thereby significantly improving the accuracy and robustness of bearing fault diagnosis.

[0007] The objective of this invention is achieved through the following technical solution: a method for multi-source heterogeneous analysis and fault diagnosis of bearings based on convolutional depth expansion and gated attention fusion, comprising the following steps:

[0008] S1. Data Acquisition and Sample Construction: Collect multi-source heterogeneous sensor data from the monitored bearing, including but not limited to vibration sensors and current sensors, perform z-score normalization and data augmentation on the collected data, and construct a training sample set.

[0009] S2. Branch Feature Extraction: Deep feature extraction is performed on data from multiple heterogeneous sensors. Each branch primarily consists of a three-layer Inception-ResNet feature extraction module, providing primary, intermediate, and deep features for feature fusion. Each module includes two Inception-ResNet layers and one Global Average Pooling (GAP) layer. The Inception-ResNet layers employ a parallel multi-scale convolutional branch structure to enhance deep feature extraction capabilities. After concatenating the output features of each branch along the channel dimension, the network outputs multi-level features extracted from each sensor data through a residual structure and a ReLU activation function, enhancing network stability.

[0010] In step S2, branch feature extraction involves performing deep feature extraction on each heterogeneous sensor data. Each branch primarily comprises a three-layer Inception-ResNet feature extraction module. Each module contains two Inception-ResNet layers and one global mean pooling layer. The Inception-ResNet layers employ a parallel multi-scale convolutional branch structure, where the features from the previous layer are input into multiple convolutions, including 1×1, 1×3, and 1×5 convolutions, leveraging different receptive fields to enhance feature mining capabilities. Each Inception-ResNet layer includes four branches: the first directly transmits the output data from the previous layer to the stitching module; the second, after passing through the first 1×1 convolution, inputs into the third 1×1 convolution; the third, sequentially passes through the second 1×1, 1×3, and third 1×1 convolutions; and the fourth, sequentially passes through the fourth 1×1 and 1×5 convolutions before inputting into the third 1×1 convolution. The output of the third 1×1 convolution is transmitted to the stitching module. After the output features of each branch are stitched together along the channel dimension, they are added to the input features through residual connections, as shown below:

[0011] ;

[0012] Where x is the concatenated feature, y is the output feature, and F(x,{w i}) is the convolution extraction function, {w i} represents the set of convolution weights; the output y is processed by the ReLU activation function to extract features, thereby achieving multi-scale feature extraction and stable gradient propagation.

[0013] S3. Multi-source feature fusion: The multimodal deep features obtained in step S2 are input into the multi-layer gated attention fusion (GAF) module and the dimensionality transformation (DT) module. This fully utilizes the features extracted from different depths by the multi-source sensors through branch extraction. Through a gating mechanism and a multi-layer fusion structure, deep fusion features F of the multi-source heterogeneous data are obtained. g ;

[0014] In step S2, the outputs of the first global mean pooling layer in each deep feature extraction branch are concatenated and input into the first multi-layer gated attention fusion GAF module, and then passed through the first dimension transformation DT module. The output of the first dimension transformation DT module is concatenated with the output of the second global mean pooling layer in each deep feature extraction branch and input into the second multi-layer gated attention fusion GAF module, and then passed through the second dimension transformation DT module. The output of the second dimension transformation DT module is concatenated with the output of the third global mean pooling layer in each deep feature extraction branch and input into the third multi-layer gated attention fusion GAF module, and then passed through the third dimension transformation DT module and the fifth global mean pooling layer in sequence. The output of the fifth global mean pooling layer is concatenated with the output of the fourth global mean pooling layer in each deep feature extraction branch and input into the fourth multi-layer gated attention fusion GAF module to obtain the fused feature F. g ;

[0015] S4. Model Prediction and Training: Input the fused features into the fully connected layer and the Softmax classifier, and output the category label of the analyzed bearing to represent its operating status (health or fault type); calculate the loss function value based on cross-entropy, and use cosine annealing learning rate to update the network parameters; when the stopping condition is met, that is, when the number of training times reaches the preset maximum number of training times or the loss function value is less than the preset value, the network stops training and the trained model is obtained.

[0016] S5. Bearing Fault Diagnosis: Collect sensor data of bearings or new bearings under different operating conditions, import them into the trained model, and output the fault diagnosis results of the bearing.

[0017] Compared with existing technologies, the advantages of this invention are as follows: Addressing the issues of poor fusion performance of multi-source heterogeneous data and inadequate bearing fault diagnosis performance, this invention designs a bearing multi-source heterogeneous data analysis and fault diagnosis method based on convolutional depth expansion and gated attention fusion. Utilizing the characteristics of multi-scale convolution and residual networks, an Inception-ResNet module is designed. Convolutional depth expansion balances network depth, feature representation capability, and optimization difficulty, enabling the extraction of features at different depths from single sensor data. This not only improves the diversity and stability of deep feature extraction but also effectively avoids the gradient vanishing problem. Simultaneously, the backbone network employs a multi-level gated attention fusion (GAF) module to achieve adaptive weighted fusion of multimodal features, effectively suppressing feature redundancy and noise interference, and enhancing the deep fusion performance of multi-source heterogeneous sensors. The model exhibits good robustness and generalization ability under complex working conditions and strong noise. In summary, this method not only improves the accuracy and stability of bearing fault diagnosis but can also be extended to intelligent monitoring and fault diagnosis of other rotating machinery, providing reliable technical support for the safe operation of industrial equipment.

[0018] The method proposed in this invention can also be used for health monitoring and degradation assessment of other mechanical equipment or equipment with similar mechanisms, providing an effective technology for fault diagnosis and health management of key equipment, and ensuring the safe operation of the entire equipment. Attached Figure Description

[0019] Figure 1 This is a flowchart of a bearing multi-source heterogeneous analysis and fault diagnosis method based on convolutional depth expansion and gated attention fusion according to the present invention. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] As attached Figure 1 As shown, the present invention provides a method for multi-source heterogeneous analysis and fault diagnosis of bearings based on convolutional depth expansion and gated attention fusion, comprising the following steps:

[0022] S1. Data Acquisition and Sample Construction: Data from multiple heterogeneous sensors, including but not limited to vibration sensors and current sensors, is collected from the monitored bearing. The collected dataset X = {x...} j} j = 1, …, N1 The i-th sensor data x j After z-score normalization, it is represented as:

[0023]

[0024] Where μ is the population mean, σ is the population standard deviation, and N1 is the sample size.

[0025] In this embodiment, each collected sensor data point contains 10240 data points; the length of each sample is set to 1024 data points, and the overlap rate between adjacent samples is 50%; the fault label n corresponding to each sample is determined. (n = 1,…, C), where C is the number of categories; a total of N samples are obtained to form the sample set required for model training.

[0026] 2. Branch Feature Extraction: Deep feature extraction is performed on data from multiple heterogeneous sensors. Each branch mainly consists of a three-layer Inception-ResNet feature extraction module, with each module containing two Inception-ResNet layers and one Global Average Pooling (GAP) layer. The Inception-ResNet layers employ a parallel multi-scale convolutional branch structure. Features from the previous layer are input into multiple convolutions, including 1×1, 1×3, and 1×5 convolutions, leveraging different receptive fields to enhance feature mining capabilities. The output features of each branch are concatenated along the channel dimension and then added to the input features via residual connections, as shown below:

[0027]

[0028] Where x is the input feature, y is the output feature, and F(x, {w}) i}) is the convolution extraction function, {w i} represents the set of convolutional weights. The output y is processed by the ReLU activation function to extract features, thereby achieving multi-scale feature extraction and stable gradient propagation.

[0029] S3. Multi-source feature fusion: A backbone network is set up to gradually fuse features at different scales extracted from multiple source sensors. The backbone network consists of three sets of gated attention fusion (GAF) modules connected in series with dimension transformation (DT). Each gated attention fusion (GAF) module fuses features at different depths from multi-source heterogeneous sensor data.

[0030] The Gated Attention Fusion (GAF) module includes a global average pooling layer, a fully connected layer, and a gating mechanism. First, feature F is obtained from the s-th sensor signal through a 1D convolution. s ∈ R B×L×M Where s = 1, 2; B represents the batch size (the number of samples used in each training iteration), L represents the spatial dimension of the feature, and M represents the number of channels of the feature. It is simplified to feature F through global mean pooling. s1 , F s2 ∈ R B×M The two are spliced ​​together to form the initial fusion feature F c = [F s1 , F s2 Then, it is input into the fully connected layer to calculate the weight coefficients for each mode.

[0031]

[0032] Where W and b are the weight and bias, respectively.

[0033] Furthermore, a gating mechanism is used to adaptively adjust the weight values ​​of each modality, that is, the Sigmoid function is used to quantize them in the range of [0,1] to characterize the difference in attention to each modality, expressed as:

[0034]

[0035] According to splicing characteristics F c The dimensions corresponding to the weights of different sensor channels can be represented as S = [s1, s2]. Therefore, the output of the fusion module is a weighted sum of the features from multiple sensors, expressed as:

[0036]

[0037] The Dimension Transformation (DT) module fuses the features of the current layer with the fusion features of the lower layer. The DT module contains one convolutional layer and one pooling layer. When the feature dimensions of the two fusion points are the same, the output of the DT module is a combination of the current layer features and the fusion of the lower layer features, represented as:

[0038]

[0039] Among them, f (i+1) F(i+1) is the fused output of the (i+1)th layer, z is the fused GAF ​​output feature of the (i+1)th layer, and a is obtained by convolution and pooling of the output of the lower layer fusion points.

[0040] Repeat the above fusion process. After obtaining the third-layer fusion output, the backbone fusion feature is processed by global mean pooling and then fused with the features extracted from the two branches. The output of the fourth GAF module is then obtained as the final fusion feature F. g .

[0041] S4. Model Prediction and Training: Fusing features F g The input is a fully connected layer and a softmax function; the model output is the predicted value o for sample k. n The confidence level (predicted probability) of {n = 1, …, C} is expressed as:

[0042]

[0043] Its range is [0, 1], and it satisfies the condition that the sum of the predicted probabilities for all categories is 1. The category n corresponding to the highest confidence level in the vector is the label (operating status) of the analyzed bearing.

[0044] The model is trained using an end-to-end joint optimization approach, and the loss function of the model is defined using cross-entropy, expressed as:

[0045]

[0046] in, For the nth class true label of sample k, Let be the predicted value for the nth class of sample k. The training process employs a cosine annealing learning rate adjustment strategy to improve the model's convergence speed and generalization ability.

[0047] When the stopping condition is met, that is, when the number of training iterations reaches the preset maximum number of training iterations or the loss function value is less than the preset value, the network stops training and obtains the trained model.

[0048] S5. Bearing Fault Diagnosis: Collect sensor data of bearings or new bearings under different operating conditions, import them into the trained model, and output the fault diagnosis results of the bearing.

[0049] Example:

[0050] In this embodiment, a bearing dataset collected by Lessmeier et al. from the University of Paderborn, Germany, was selected to verify the effectiveness and superiority of the method described in this invention. The healthy bearing dataset (K002, K003, K004, K005, K006), the outer ring fault set (KA04, KA15, KA16, KA22, KA30), and the inner ring fault set (Kl04, Kl16, Kl17, Kl18, Kl21) were selected from this dataset. These bearing faults were generated through accelerated life testing, and the degree of fault varies within the fault sets, making these data closer to actual bearing fault data. The bearing data acquisition conditions for Task 1 were a motor speed of 1500 rpm, a load torque of 0.7 Nm, and a radial load of 1000 N; the bearing data acquisition conditions for Task 2 were a motor speed of 1500 rpm, a load torque of 0.1 Nm, and a radial load of 1000 N. During the experiment, vibration signals were collected by an accelerometer mounted on the bearing housing, and current signals were collected from the motor power supply terminal. The vibration signal sampling frequency is 64 kHz, and the current signal sampling frequency is 10 kHz.

[0051] To verify the generalization performance of the model, different working conditions were used for the training and test sets. The training set used the Task 1 dataset, and the test set used the Task 2 dataset, denoted as Task 1→2; if Task 2 was used for the training set, the test set used the Task 2 dataset, denoted as Task 2→1. Using the method described in this invention, the fault diagnosis accuracy for Task 1→2 was 98.3%, and the fault diagnosis accuracy for Task 2→1 was 98.0%. In contrast, using the Attention Mechanism and Multilayer Fusion Network (AMMFN), the fault diagnosis accuracy for Task 1→2 was 96.1%, and the fault diagnosis accuracy for Task 2→1 was 94.0%.

[0052] To verify the robustness of the model, strong Gaussian white noise was added to the original signal in this embodiment, with a signal-to-noise ratio of -3dB. Using the method described in this invention, the fault diagnosis accuracy for Task 1→2 was 95.0%, and for Task 2→1 it was 87.9%. In contrast, using AMMFN, the fault diagnosis accuracy for Task 1→2 was 83.9%, and for Task 2→1 it was 80.7%.

[0053] The above experimental and comparative results show that, under different operating conditions and strong noise, the method of the present invention can significantly improve the accuracy of bearing fault diagnosis and exhibit enhanced robustness and generalization ability, while demonstrating the feasibility of applying the method of the present invention to actual bearing fault diagnosis.

[0054] In summary, this embodiment verifies the feature depth fusion and bearing fault diagnosis performance of the present invention under multi-source heterogeneous data conditions, indicating that the method has high robustness and accuracy in complex working conditions and high noise environments, providing an effective technology for the intelligent upgrading of health monitoring and fault diagnosis of industrial equipment.

Claims

1. A method for multi-source heterogeneous analysis and fault diagnosis of bearings based on convolutional depth expansion and gated attention fusion, characterized in that, Includes the following steps: S1. Data Acquisition and Sample Construction; Data from multiple heterogeneous sensors, including vibration sensors and current sensors, were collected from the monitored bearing. The collected data were then subjected to z-score normalization and data augmentation to construct a training sample set. S2, Branch Feature Extraction; Deep feature extraction is performed on each heterogeneous sensor data. The deep feature extraction branch first passes through a first convolutional layer and a first global average pooling layer, and then sequentially through three Inception-ResNet feature extraction modules to provide primary, intermediate, and deep features for feature fusion. Each Inception-ResNet feature extraction module contains two Inception-ResNet layers and one global average pooling layer (GAP). The global average pooling layers in the three Inception-ResNet feature extraction modules are defined as the second, third, and fourth global average pooling layers, respectively. The designed Inception-ResNet layers adopt a parallel multi-scale convolutional branch structure, which enhances feature extraction capability by expanding the convolutional depth, balancing network depth, feature representation capability, and optimization difficulty. After the output features of each branch are concatenated along the channel dimension, the multi-level features extracted from each sensor data are output through a residual structure and the ReLU activation function, enhancing the stability of the network. S3, Multi-source feature fusion; In step S2, the outputs of the first global mean pooling layer in each deep feature extraction branch are concatenated and input into the first multi-layer gated attention fusion GAF module, and then passed through the first dimension transformation DT module. The output of the first dimension transformation DT module is concatenated with the output of the second global mean pooling layer in each deep feature extraction branch and input into the second multi-layer gated attention fusion GAF module, and then passed through the second dimension transformation DT module. The output of the second dimension transformation DT module is concatenated with the output of the third global mean pooling layer in each deep feature extraction branch and input into the third multi-layer gated attention fusion GAF module, and then passed through the third dimension transformation DT module and the fifth global mean pooling layer in sequence. The output of the fifth global mean pooling layer is concatenated with the output of the fourth global mean pooling layer in each deep feature extraction branch and input into the fourth multi-layer gated attention fusion GAF module to obtain the fused feature F. g ; S4. Model prediction and training; The fused features are input into the fully connected layer and the Softmax classifier, and the output is the category label of the analyzed bearing, which represents its operating status: healthy or faulty. The loss function value based on cross-entropy is calculated, and the network parameters are updated using the cosine annealing learning rate. When the stopping condition is met, that is, when the number of training times reaches the preset maximum number of training times or the loss function value is less than the preset value, the network stops training and the trained model is obtained. S5. Bearing Fault Diagnosis: Collect sensor data of bearings or new bearings under different operating conditions, import them into the trained model, and output the fault diagnosis results of the bearing.

2. The bearing multi-source heterogeneous analysis and fault diagnosis method based on convolutional depth expansion and gated attention fusion according to claim 1, characterized in that, In step 1, multi-source heterogeneous sensor data is collected from the monitoring bearing, and the collected dataset X={x j } j =1,…,N1 The j-th sensor data x j After z-score normalization, it is represented as: Where μ is the population mean, σ is the population standard deviation, and N1 is the number of samples; more samples are constructed through data augmentation, and the longer data collected each time is evenly divided into n1 shorter samples, and the fault label n corresponding to each sample is determined, n=1,…,C, where C is the number of categories; a total of N samples are obtained to form the sample set required for model training.

3. The bearing multi-source heterogeneous analysis and fault diagnosis method based on convolutional depth expansion and gated attention fusion as described in claim 1, characterized in that, In step S2, branch feature extraction involves performing deep feature extraction on each heterogeneous sensor data. Each branch primarily comprises a three-layer Inception-ResNet feature extraction module. Each module contains two Inception-ResNet layers and one global mean pooling layer. The Inception-ResNet layers employ a parallel multi-scale convolutional branch structure, where the features from the previous layer are input into multiple convolutions, including 1×1, 1×3, and 1×5 convolutions, leveraging different receptive fields to enhance feature mining capabilities. Each Inception-ResNet layer includes four branches: the first directly transmits the output data from the previous layer to the stitching module; the second, after passing through the first 1×1 convolution, inputs into the third 1×1 convolution; the third, sequentially passes through the second 1×1, 1×3, and third 1×1 convolutions; and the fourth, sequentially passes through the fourth 1×1 and 1×5 convolutions before inputting into the third 1×1 convolution. The output of the third 1×1 convolution is transmitted to the stitching module. After the output features of each branch are stitched together along the channel dimension, they are added to the input features through residual connections, as shown below: ； Where x is the concatenated feature, y is the output feature, and F(x,{w i }) is the convolution extraction function, {w i } represents the set of convolution weights; the output y is processed by the ReLU activation function to extract features, thereby achieving multi-scale feature extraction and stable gradient propagation.

4. The bearing multi-source heterogeneous analysis and fault diagnosis method based on convolutional depth expansion and gated attention fusion according to claim 1, characterized in that: In step S3, a backbone network is set up to gradually fuse features of different scales extracted by multi-source sensors. The Gated Attention Fusion (GAF) module includes a global average pooling layer, a fully connected layer, and a gating mechanism. First, the feature F is obtained from the s-th sensor signal through a 1D convolution. s ∈R B×L×M s=1, 2, B represents the batch size, L represents the spatial dimension of the feature, and M represents the number of channels of the feature; The feature set is simplified to features F1, F2 ∈ R by global mean pooling. B×M The two are spliced ​​together to form the initial fusion feature F c =[F1,F2]; then, input it into the fully connected layer to calculate the weight coefficients of each mode; ； Where W and b are the weights and biases, This indicates a fully connected network. A gating mechanism is used to adaptively adjust the weight values ​​of each modality, that is, the Sigmoid function is used to quantize them in the range of [0,1] to characterize the difference in attention to each modality, expressed as: ； According to splicing characteristics F c The dimensions are defined, and the weights for different sensor channels are S=[s1,s2]; the output of the fusion module is obtained. The weighted sum of features from multiple sensors is expressed as: ； The Dimension Transformation (DT) module fuses the features of the current layer with the fusion features of the lower layer. The DT module contains one convolutional layer and one pooling layer. When the feature dimensions of the two fusion points are the same, the output of the DT module is a combination of the current layer features and the fusion features of the lower layer, represented as: ； Among them, f (i+1) This is the fused output of the (i+1)th layer. The output feature of the gated attention fusion GAF module at layer i+1 is 'a', which is obtained by convolution and pooling of the output of the lower layer fusion points. Repeat the above fusion process. After obtaining the third-layer fusion output, the backbone fusion feature is processed by global mean pooling and then fused with the features extracted from the two branches to obtain the final fusion feature F. g .

5. The bearing multi-source heterogeneous analysis and fault diagnosis method based on convolutional depth expansion and gated attention fusion according to claim 1, characterized in that: In step S4, the fusion feature F g The input consists of a fully connected layer and a softmax function; the model output is the predicted value for sample k. confidence level The predicted probability is expressed as: ； Its range is [0,1], and the sum of the predicted probabilities for all categories is 1. ; n=1,…,C, the category n corresponding to the highest confidence level in the vector is the label of the bearing being analyzed; The model is trained using an end-to-end joint optimization approach, and the loss function of the model is defined using cross-entropy. , is represented as: ； in, For the nth class true label of sample k, Let be the predicted value of the nth class for sample k; the training process uses a cosine annealing learning rate adjustment strategy to improve the model's convergence speed and generalization ability.

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