A bearing sound-vibration fusion cross-condition fault diagnosis method based on KA-Transformer

Abstract

This invention discloses a bearing acoustic-vibration fusion cross-condition fault diagnosis method based on KA-Transformer, belonging to the field of rotating machinery fault diagnosis technology. The method first performs frequency domain transformation on the vibration and acoustic signals to obtain spectral features; then, the spectral features are divided into multiple sub-blocks and linearly embedded to construct vibration input sequences and acoustic input sequences; the vibration and acoustic input sequences are input into a weighted rational KA fusion encoder for feature extraction and fusion to obtain a fused fault representation; the fused fault representation is then input into a fault classifier and a domain discriminator, and jointly trained using a gradient inversion mechanism and a conditional distribution alignment strategy based on class prototype constraints to achieve cross-condition bearing fault identification. This invention, by introducing a rational KA fusion encoder, enhances the model's nonlinear representation ability for non-stationary signals, weak fault signals, and cross-condition drift features, thereby improving the accuracy and cross-domain robustness of bearing fault diagnosis under complex operating conditions.

Description

Technical Field

[0001] This invention relates to the field of bearing fault diagnosis technology, and in particular to a bearing acoustic-vibration fusion cross-operating condition fault diagnosis method based on KA-Transformer. Background Technology

[0002] Bearings are critical components in rotating machinery, and their operating condition directly affects the stability and reliability of the equipment. In actual industrial scenarios, bearings typically operate under complex conditions such as speed fluctuations, load variations, and noise interference, making them prone to various failure modes, including inner ring failure, outer ring failure, and rolling element failure. Therefore, conducting bearing fault diagnosis is of great significance.

[0003] Existing fault diagnosis methods primarily analyze vibration signals. While vibration signals can reflect the operating status of equipment, some weak fault features are easily attenuated under complex transmission paths and background noise interference, resulting in insufficient diagnostic information. Acoustic signals are sensitive to some high-frequency abnormal components and can provide supplementary information to vibration signals. Therefore, using vibration and acoustic signals for joint diagnosis is beneficial to improving fault identification capabilities. On the other hand, there are usually significant differences in feature distributions between different operating conditions, making it difficult to directly apply models trained under a single operating condition to other conditions. Most existing deep diagnostic models still use fixed activation functions, making it difficult to adaptively adjust nonlinear mapping relationships according to changes in feature distribution. This can easily affect the fault feature extraction effect and diagnostic robustness when dealing with non-stationary signals and cross-operating condition drift features. Therefore, there is an urgent need to propose a bearing fault diagnosis method that can integrate acoustic and vibration signals, enhance nonlinear characterization capabilities, and improve cross-operating condition diagnostic performance. Summary of the Invention

[0004] To address the technical challenges of insufficient fault feature extraction capabilities for bearings under complex operating conditions and noisy environments, significant differences in feature distribution between different operating conditions, and the difficulty of adaptively representing non-stationary features using fixed activation functions, this invention discloses a bearing acoustic-vibration fusion cross-operating-condition fault diagnosis method based on KA-Transformer.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: a bearing acoustic-vibration fusion cross-operating-condition fault diagnosis method based on KA-Transformer, specifically including the following steps: S1. Acquire vibration and acoustic signals of the bearing under different operating conditions, and use Fast Fourier Transform to perform frequency domain transformation on the vibration and acoustic signals respectively to obtain the corresponding vibration spectrum features and acoustic spectrum features; S2. Divide the vibration spectrum features and acoustic spectrum features obtained in step S1 into multiple sub-blocks, and embed them through linear mapping to construct vibration input sequences and acoustic input sequences; S3. Input the vibration input sequences and acoustic input sequences obtained in step S2 into a weight-shared group rational KA (Kolmogorov-Arnold) fusion encoder for feature extraction to obtain vibration features and acoustic features; S4. Fuse the vibration features and acoustic features obtained in step S3 to obtain a fused fault characterization; S5. Input the fused fault characterization obtained in step S4 into a fault classifier and a domain discriminator, and perform joint training by combining a gradient inversion mechanism and a cross-domain alignment strategy to achieve bearing fault diagnosis under cross-operating-condition conditions.

[0006] Further, the specific process of step S2 is as follows: S21, Divide the vibration spectrum characteristics and acoustic spectrum characteristics into N sub-blocks, each sub-block having a length of P and a spectrum length of L, satisfying: S22. Convert each sub-block into a D-dimensional embedding vector through linear mapping; S23. Concatenate the classification label vector to the front of the embedding sequence and superimpose the positional encoding to obtain the vibration input sequence and the acoustic input sequence; The embedding process is as follows: ; In the formula, This represents the initial input sequence. Indicates vibration mode or acoustic mode. This represents the i-th sub-block. This represents the embedding vector corresponding to the i-th sub-block. and Let these represent the weight matrix and bias vector of the linear mapping, respectively. Represents the classification label vector. This represents the position encoding matrix.

[0007] Further, the specific process of step S3 is as follows: S31, input the vibration input sequence and the acoustic input sequence into several levels of cascaded grouped rational KA attention blocks; S32, in each level of grouped rational KA attention block, establish global correlation between different spectral sub-blocks using a multi-head self-attention mechanism, and then use grouped rational activation sub-layers to perform grouped nonlinear transformation on the features; S33, output the encoded vibration features and acoustic features; in the grouped rational KA fusion encoder, the output process of the encoded block is as follows: ; In the formula, This represents the input sequence of the l-th coded block. This represents the intermediate sequence after passing through the multi-head self-attention sublayer. This represents the output sequence of the l-th coded block. Representation layer normalization, This indicates multi-head self-attention computation. The rational activation operation represents the group; the calculation formula for the multi-head self-attention mechanism is: ; In the formula, , and Let these represent the query matrix, key matrix, and value matrix corresponding to the i-th attention head, respectively. H represents the feature dimension of a single attention head, and H represents the number of attention heads. This indicates the output mapping matrix.

[0008] Further, in step S32, the group rational activation sublayer includes: first, expanding the input features along the channel dimension; then, dividing the expanded feature channels into multiple feature groups; applying a group-shared rational activation function to each feature group; and finally mapping back to the original feature dimension; the expanded feature dimension satisfy: Where R represents the expansion factor and D represents the original feature dimension. This represents the expanded feature dimension; the expanded feature channels are divided according to a preset number of groups, and the group index corresponding to the k-th channel is... for: The shared rational activation function is: In the formula, G represents the number of characteristic groups. This represents a rational activation function. and For learnable polynomial coefficients, and These represent the orders of the numerator and denominator polynomials, respectively.

[0009] Furthermore, in step S4, the fused fault characterization formula is: In the formula, The classification label features representing the output of the vibration branch, The classification label features representing the output of the acoustic branch, This indicates the fusion fault characterization.

[0010] Further, in step S5, the cross-domain alignment strategy is a conditional distribution alignment strategy based on class prototype constraints, specifically including: constructing source domain class prototypes for each fault category based on the labeled samples in the source domain, constructing target domain class prototypes based on the predicted categories of the target domain samples, and reducing the conditional distribution differences between the source and target domains by constraining the distance between source domain class prototypes and target domain class prototypes of the same category; for the c-th type of fault, its source domain class prototype and target domain class prototype are respectively represented as: ; In the formula, This represents the prototype of the source domain class corresponding to the c-th type of fault. This represents the prototype of the target domain class corresponding to the c-th type of fault. and Let represent the fusion failure characterization of the c-th type of source domain and target domain samples, respectively. and These represent the number of samples of the corresponding class in the source and target domains, respectively; the class prototype alignment loss is: .

[0011] Furthermore, in step S5, the weighted sum of fault classification loss, domain adversarial loss, and class prototype alignment loss is used as the total loss function; the formula is: In the formula, Represents the total loss function. Indicates the loss due to fault classification. Indicates domain adversarial loss, Indicates the class prototype alignment loss; , and This represents the weighting coefficient of the corresponding loss term.

[0012] The beneficial effects of this invention are as follows: First, by using joint modeling of vibration and acoustic signals, the complementary information of the two types of signals in fault characterization can be fully utilized, improving the ability to identify weak fault features. Second, by employing a group-rational KA fusion encoder, adaptive nonlinear transformation of features is achieved through group-shared rational activation functions, which enhances the model's ability to characterize non-stationary features and fine-grained fault features. Furthermore, the use of a weight-sharing bi-branch feature extraction structure is beneficial to improving the consistency and stability of the feature extraction process for the two modes. Finally, by combining a gradient reversal mechanism and a cross-domain alignment strategy, this invention can reduce the differences in feature distribution between different working conditions, improving the model's fault diagnosis accuracy and robustness under cross-working conditions. Attached Figure Description

[0013] Figure 1 This is a schematic diagram of the overall framework of the present invention. Detailed Implementation

[0014] 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 a part of the embodiments of the present invention, and not all of them. 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.

[0015] This invention discloses a bearing acoustic-vibration fusion cross-condition fault diagnosis method based on KA-Transformer, such as... Figure 1 As shown, the specific steps include: S1, performing frequency domain transformation on the acquired vibration and acoustic signals to obtain vibration spectrum characteristics and acoustic spectrum characteristics. First, vibration and acoustic signals of the bearing under different health states and operating conditions are acquired. The health states may include normal state, inner ring fault state, outer ring fault state, rolling element fault state, etc.; the operating conditions may include different speeds, different loads, and different noise interference conditions. Since bearing faults often exhibit periodic impact or modulation characteristics with specific frequency distribution patterns, some fault characteristics are not intuitive when directly modeled in the time domain. Therefore, this embodiment preferably converts the time-domain signal to the frequency domain for processing first.

[0016] Specifically, for vibration signals Harmony and acoustic signals Perform Fast Fourier Transform (FFT) on each component to obtain the corresponding frequency domain spectral features, the expression of which is: In the formula, , This represents the input time-domain signal. This represents the corresponding frequency domain spectral characteristics. This represents the Fast Fourier Transform. Through the above processing, the fault-related frequency components in the original time-domain signal can be explicitly presented, thereby improving the sensitivity of subsequent feature extraction processes to fault features, harmonic components, and abnormal frequency components. After processing, vibration spectrum features and acoustic spectrum features are obtained, which serve as inputs to the subsequent embedding module.

[0017] S2. Divide the vibration spectral features and acoustic spectral features into multiple sub-blocks and embed them using linear mapping to generate vibration input sequences and acoustic input sequences. To enable the spectral features to adapt to the sequence input format of the Transformer structure, this implementation further divides the spectral features into multiple sub-blocks and maps each sub-block to a feature space of a unified dimension, constructing an input sequence suitable for subsequent encoding processing.

[0018] Specifically, let the spectrum length be L, the number of sub-blocks after division be N, and the length of each sub-block be P, then the following conditions are met: Based on this, for the spectral features of each modality, they are sequentially divided into N non-overlapping sub-blocks. Then, a linear mapping is used to convert each sub-block into a corresponding embedding vector, calculated as follows: In the formula This represents the i-th sub-block. This represents the corresponding embedding vector. Represents the linear mapping weight matrix. This represents the bias vector. To further preserve the positional information between different sub-blocks, a classification label vector is concatenated to the front of the embedded vector sequence, and a positional encoding is superimposed to construct the initial input sequence, whose expression is: In the formula, Represents the classification label vector. Represents the position encoding matrix, This represents the initial input sequence for the corresponding mode.

[0019] In this step, by embedding sub-blocks, the original spectral features can be transformed into a high-level representation of a unified dimension; by introducing classification label vectors, a global feature aggregation carrier can be provided for subsequent fault identification; and by superimposing positional encoding, the relative positional relationships of each sub-block in the spectrum within the original sequence can be preserved. After processing, vibration input sequences are obtained respectively. Harmony and acoustic input sequence .

[0020] S3. Input the vibration input sequence and the acoustic input sequence into a weighted rational KA fusion encoder for feature extraction to obtain vibration features and acoustic features.

[0021] In this embodiment, a weight-sharing dual-branch structure is used to encode the vibration input sequence and the acoustic input sequence respectively. Weight sharing means that both modes are processed using encoders with the same parameters, which maintains consistency in the feature space mapping process and improves the stability of cross-modal joint modeling. The group rational KA fusion encoder consists of several cascaded group rational KA attention blocks. Each attention block includes a multi-head self-attention sublayer, a layer normalization unit, a residual connection unit, and a group rational activation sublayer. The multi-head self-attention sublayer is mainly used to establish global dependencies between different spectral sub-blocks, while the group rational activation sublayer is mainly used to enhance the adaptive nonlinear transformation capability of the features. Let the input sequence of the l-th layer encoding block be... The intermediate result after passing through the multi-head self-attention sublayer is: Then, after passing through the grouped rational activation sub-layer, the output of the coded block of this layer is obtained: In the formula This represents the intermediate sequence in the l-th layer coded block after multi-head self-attention. This represents the output sequence of the l-th coded block. Representation layer normalization, This indicates multi-head self-attention computation. This indicates that the rational activation operation is applied to the group.

[0022] Specifically, in the design of step S3, the multi-head self-attention mechanism is used to explore the correlation between different spectral sub-blocks, which is particularly suitable for scenarios where there is a coupling relationship between long-distance spectral components in fault signals.

[0023] For example, certain fault characteristics may be present simultaneously near the fundamental frequency and its harmonics; a self-attention mechanism helps enhance the interaction between these relevant information. For the i-th attention head, its output can be expressed as: In the formula, , and Let these represent the query matrix, key matrix, and value matrix corresponding to the i-th attention head, respectively. This represents the feature dimension of a single attention head. The outputs of all attention heads are concatenated, and then the multi-head self-attention result is obtained through output mapping. In the formula, H represents the number of attention heads. This represents the output mapping matrix. Through multi-head parallel modeling, the correlation between spectral features in different subspaces can be learned, thereby improving the global feature extraction capability. Furthermore, to overcome the insufficient nonlinear adaptability of traditional fixed activation functions under complex conditions, this implementation sets up a grouped rational activation sublayer in the attention block. This sublayer does not use the exact same activation method for all channels; instead, it first expands the features by channels, then divides them into groups, and applies a shared rational activation function to different groups. This allows the model to achieve stronger nonlinear adjustment capability while maintaining controllable parameters. Specifically, if the original feature dimension is D and the expansion factor is R, then the expanded feature dimension is: Subsequently, the expanded channels are divided into multiple feature groups. Let G be the number of feature groups, then the group index of the k-th channel is... for: For the t-th label in the input feature across k channels After rational activation, the output is obtained: The rational activation function shared by the group is: In the formula, and For learnable polynomial coefficients, and These represent the orders of the numerator and denominator polynomials, respectively. This step, through "expansion-grouping → rational activation → backprojection," allows different feature groups to exhibit different nonlinear response characteristics, helping to enhance the model's ability to express weak fault components, drift features, and local difference features. After processing each rational KA attention block, the encoded vibration features are obtained respectively. Acoustic characteristics .

[0024] S4. The vibration and acoustic features are fused to obtain a fused fault characterization. Since vibration and acoustic signals are complementary in fault representation, this implementation fuses the high-level features of the two modes after completing the dual-branch encoding, thereby obtaining a more comprehensive fault characterization. Specifically, classification label vectors are extracted from the encoded vibration and acoustic features, denoted as... and The two are then fused to obtain a fused fault characterization, the expression of which is: In the formula, This represents the fused fault characterization. Through the above fusion method, information from vibration modes that is more sensitive to mechanical structural responses can be combined with information from acoustic modes that is more sensitive to high-frequency anomalies, thus forming a more stable and complete fault representation.

[0025] S5. The fused fault representation is input into the fault classifier and domain discriminator, and jointly trained using a gradient reversal mechanism and a cross-domain alignment strategy to achieve bearing fault diagnosis under cross-operating conditions. In this embodiment, the fused fault representation... Simultaneously inputting a fault classifier and a domain discriminator. The fault classifier outputs the fault category result; the domain discriminator distinguishes whether a sample comes from the source domain or the target domain. To achieve cross-condition alignment, a gradient inversion layer is introduced before the domain discriminator, so that the feature extraction process optimizes fault discrimination capability while minimizing the domain offset effect caused by operating condition differences. To further improve the conditional distribution alignment effect, this implementation also adopts a conditional distribution alignment strategy based on class prototype constraints. Specifically, for the c-th type of fault, its source domain class prototype and target domain class prototype are respectively represented as: , In the formula, This represents the prototype of the source domain class corresponding to the c-th type of fault. This represents the prototype of the target domain class corresponding to the c-th type of fault. This represents the fusion failure characterization of the c-th source domain sample. This represents the fusion fault characterization of the c-th class of target domain samples. and Let represent the number of samples of the corresponding class in the source and target domains, respectively. Based on this, the class prototype alignment loss can be defined as: In the formula, C represents the number of fault categories. During model training, the total loss function consists of fault classification loss, domain adversarial loss, and class prototype alignment loss, and its expression is: In the formula, Represents the total loss function. Indicates the loss due to fault classification. Indicates domain adversarial loss, Indicates the class prototype alignment loss; , and This represents the weight coefficient of each loss term. Through the above joint training method, while maintaining the separability of fault categories, the differences in feature distribution between different operating conditions can be reduced, thereby improving the diagnostic accuracy and robustness of the model under the target operating condition.

[0026] Application example: This invention is used to collect acoustic and vibration signals and diagnose faults at different speeds on a specially designed bearing fault test bench.

[0027] Five bearing health states were considered: normal state, inner ring fault state, outer ring fault state, and two rolling element fault states with different damage levels. The sampling frequency was set to 12.8 kHz. Bearing vibration and acoustic signals were collected under five speed conditions (500 rpm, 1000 rpm, 1500 rpm, 1800 rpm, and 2000 rpm) and four load conditions (0 N, 20 N, 40 N, and 60 N) as datasets. Each health state included 500 vibration samples and 500 acoustic samples, with each sample containing 1024 sampling points. 80% of the source domain samples were used as the training set, and the remaining 20% ​​as the validation set; 50% of the target domain samples were used as the adaptation set, and the remaining 50% as the test set.

[0028] To comprehensively evaluate the effectiveness of the method of this invention, two newer methods and a classic cross-domain fault diagnosis method were compared, including the residual attention-guided visual Transformer method RAVIT, the convolutional neural network method ConvNeXt, and the domain adversarial neural network method DANN. The diagnostic accuracy of each method was compared under six transfer tasks: 500 rpm 0 N→1000 rpm 0 N (Task 1), 1000 rpm 0 N→1500 rpm 0 N (Task 2), 2000 rpm 20 N→2000 rpm 40 N (Task 3), 2000 rpm 20 N→2000 rpm 60 N (Task 4), 1500 rpm 20 N→1800 rpm 40 N (Task 5), and 1800 rpm 60 N→1500 rpm 20 N (Task 6). The left-hand side represents the source domain, and the right-hand side represents the target domain. The comparison results of the diagnostic accuracy of each method under different transfer tasks are shown in Table 1 below.

[0029] Table 1. Diagnostic accuracy of each method under different migration tasks.

[0030] As shown in Table 1, among the three comparative methods, DANN's overall diagnostic performance is relatively weak. Its accuracy in multiple transfer tasks is significantly lower than RAVIT and ConvNeXt, indicating that relying solely on domain adversarial methods is still susceptible to feature distribution shifts under complex operating conditions. RAVIT and ConvNeXt show similar overall performance, achieving high diagnostic accuracy in most tasks, demonstrating the advantage of deep feature extraction-based models in cross-condition fault diagnosis. However, both methods exhibit some fluctuations across different tasks, and their diagnostic performance is still affected when operating conditions change further. In contrast, the method of this invention demonstrates superior diagnostic performance in all six transfer tasks, maintaining a high level of accuracy across all tasks. The diagnostic accuracy for Task 1 reaches 100.00%, and the remaining tasks all maintain accuracy above 98%, significantly outperforming the other three comparative methods. This indicates that the proposed method has good adaptability across different transfer tasks, achieving high accuracy not only in easier transfer tasks but also maintaining stable fault identification performance in tasks with more complex operating conditions. Furthermore, in terms of average diagnostic accuracy, RAVIT, ConvNeXt, and DANN have average diagnostic accuracy rates of 97.95%, 98.07%, and 97.44%, respectively, while the method of this invention achieves an average diagnostic accuracy of 99.47%, the highest among the four methods. Compared to RAVIT, the average diagnostic accuracy of the method of this invention is improved by 1.52%; compared to ConvNeXt, it is improved by 1.40%; and compared to DANN, it is improved by 2.03%.

[0031] This demonstrates that the method of the present invention can more effectively improve the fault diagnosis accuracy under cross-operating conditions and has better overall stability. This is because the method of the present invention simultaneously utilizes vibration signals and acoustic signals for joint modeling, which can fully exploit the complementary information of the two types of signals in fault representation; at the same time, it enhances the model's nonlinear representation capability of non-stationary fault features and fine-grained difference features through a rational KA fusion encoder, and reduces the feature distribution differences between different operating conditions by combining a gradient reversal mechanism and a cross-domain alignment strategy. Therefore, the method of the present invention exhibits high diagnostic accuracy and good robustness under various transfer tasks.

[0032] Of course, the above description is not intended to limit the present invention, and the present invention is not limited to the examples given above. Any changes, modifications, additions or substitutions made by those skilled in the art within the scope of the present invention should also fall within the protection scope of the present invention.

Claims

1. A bearing acoustic-vibration fusion cross-condition fault diagnosis method based on KA-Transformer, characterized in that, Specifically, the following steps are included: S1. Collect vibration and acoustic signals of the bearing under different operating conditions, and use fast Fourier transform to perform frequency domain transformation on the vibration and acoustic signals respectively to obtain the corresponding vibration spectrum characteristics and acoustic spectrum characteristics. S2. Divide the vibration spectrum features and acoustic spectrum features obtained in step S1 into multiple sub-blocks, and embed them through linear mapping to construct vibration input sequences and acoustic input sequences; S3. The vibration input sequence and acoustic input sequence obtained in step S2 are fed into a weight-shared group rational KA fusion encoder for feature extraction to obtain vibration features and acoustic features; S4. The vibration and acoustic features obtained in step S3 are fused to obtain a fused fault characterization; S5. Input the fused fault representation obtained in step S4 into the fault classifier and domain discriminator, and perform joint training by combining the gradient reversal mechanism and the cross-domain alignment strategy to achieve bearing fault diagnosis under cross-operating conditions.

2. The bearing acoustic-vibration fusion cross-condition fault diagnosis method based on KA-Transformer according to claim 1, characterized in that, Step S2 detailed process: S21. Divide the vibration spectrum characteristics and acoustic spectrum characteristics into N sub-blocks, each sub-block having a length of P and a spectrum length of L, satisfying the following: ； S22. Convert each sub-block into a D-dimensional embedding vector through a linear mapping; S23. Concatenate the classification marker vector at the front end of the embedded sequence and superimpose the position code to obtain the vibration input sequence and the acoustic input sequence. The embedding process is as follows: ； ； In the formula, This represents the initial input sequence. Indicates vibration mode or acoustic mode. This represents the i-th sub-block. This represents the embedding vector corresponding to the i-th sub-block. and Let these represent the weight matrix and bias vector of the linear mapping, respectively. Represents the classification label vector. This represents the position encoding matrix.

3. The bearing acoustic-vibration fusion cross-condition fault diagnosis method based on KA-Transformer according to claim 1, characterized in that, The specific process of step S3: S31. Input the vibration input sequence and the acoustic input sequence into a group of rational KA attention blocks connected in series at several levels; S32. In each level of grouped rational KA attention block, a multi-head self-attention mechanism is used to establish global correlation between different spectral sub-blocks, and then the grouped rational activation sub-layer is used to perform grouped nonlinear transformation on the features. S33. Output the encoded vibration and acoustic characteristics; In a group rational KA fusion encoder, the output process of the coded block is as follows: ； ； In the formula, This represents the input sequence of the l-th coded block. This represents the intermediate sequence after passing through the multi-head self-attention sublayer. This represents the output sequence of the l-th coded block. Representation layer normalization, This indicates multi-head self-attention computation. This indicates that the rational activation operation is applied to the group. The formula for calculating the multi-head self-attention mechanism is: ； ； In the formula, , and Let these represent the query matrix, key matrix, and value matrix corresponding to the i-th attention head, respectively. H represents the feature dimension of a single attention head, and H represents the number of attention heads. This indicates the output mapping matrix.

4. The bearing acoustic-vibration fusion cross-condition fault diagnosis method based on KA-Transformer according to claim 1, characterized in that, In step S32, the group rational activation sub-layer includes: first, expanding the input features along the channel dimension; then, dividing the expanded feature channels into multiple feature groups; applying a group-shared rational activation function to each feature group; and finally mapping back to the original feature dimension. Expanded feature dimensions satisfy: ； Where R represents the expansion ratio, and D represents the original feature dimension. This represents the expanded feature dimension; The expanded feature channels are divided into a preset number of groups, and the group index corresponding to the k-th channel is... for: ； The shared rational activation function is: ； In the formula, G represents the number of characteristic groups. This represents a rational activation function. and For learnable polynomial coefficients, and These represent the orders of the numerator and denominator polynomials, respectively.

5. The bearing acoustic-vibration fusion cross-condition fault diagnosis method based on KA-Transformer according to claim 1, characterized in that, In step S4, the fusion fault characterization formula is: ； In the formula, The classification label features representing the output of the vibration branch, The classification label features representing the output of the acoustic branch, This indicates the fusion fault characterization.

6. The bearing acoustic-vibration fusion cross-condition fault diagnosis method based on KA-Transformer according to claim 1, characterized in that, In step S5, the cross-domain alignment strategy is a conditional distribution alignment strategy based on class prototype constraints. Specifically, it includes: constructing source domain class prototypes for each fault category based on the labeled samples in the source domain, constructing target domain class prototypes based on the predicted categories of the target domain samples, and reducing the conditional distribution differences between the source domain and the target domain by constraining the distance between the source domain class prototypes and the target domain class prototypes of the same category. For the c-th type of fault, its source domain class prototype and target domain class prototype are represented as follows: ； ； In the formula, This represents the prototype of the source domain class corresponding to the c-th type of fault. This represents the prototype of the target domain class corresponding to the c-th type of fault. and Let represent the fusion failure characterization of the c-th type of source domain and target domain samples, respectively. and These represent the number of samples of the corresponding category in the source and target domains, respectively. The class prototype alignment loss is: 。 7. The bearing acoustic-vibration fusion cross-condition fault diagnosis method based on KA-Transformer according to claim 1, characterized in that, In step S5, the total loss function is a weighted sum of the fault classification loss, domain adversarial loss, and class prototype alignment loss; the formula is: ； In the formula, Represents the total loss function. Indicates the loss due to fault classification. Indicates domain adversarial loss, Indicates the class prototype alignment loss; , and This represents the weighting coefficient of the corresponding loss term.

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