Bearing fault diagnosis method based on dynamic activation mechanism under sample scarcity condition

Abstract

The application relates to a bearing fault diagnosis method based on a dynamic activation mechanism under a sample scarcity condition, which comprises the following steps: S1, vibration signal acquisition and pretreatment, to obtain original fault samples x 0; S2, original fault samples are optimized by using forward diffusion and reverse denoising, to obtain generated samples close to real fault data; S3, a deep residual network PRNet fault diagnosis model with multiple activation mechanisms is constructed, original fault samples x 0 and generated samples close to real fault data are mixed to form a fault sample set x i , a fault diagnosis model is input, and a cross-entropy loss function L CE is used for network training, and finally, bearing fault categories are output. The bearing fault diagnosis method based on the dynamic activation mechanism under the sample scarcity condition effectively solves the problem of sample scarcity in the bearing fault diagnosis process, and significantly improves the accuracy and stability of bearing fault diagnosis.

Description

Technical Field

[0001] This invention relates to the field of bearing fault diagnosis technology, and in particular to a bearing fault diagnosis method based on a dynamic activation mechanism under conditions of scarce samples. Background Technology

[0002] Bearings are indispensable transmission components in large mechanical equipment, their main function being to support and position the rotating shafts of the machinery. According to relevant data, bearing failures account for nearly one-third of all mechanical failures. Bearing fault diagnosis technology can significantly improve bearing reliability and service life, prevent mechanical accidents caused by bearing problems, and increase production efficiency. Therefore, quickly and effectively identifying bearing failure types and promptly performing equipment maintenance and component replacement are of paramount importance for ensuring continuous equipment operation, reducing the probability of failure, minimizing economic losses, and protecting personnel safety.

[0003] In practical industrial applications, bearings operate in a normal state most of the time, with few failures. This results in a scarcity of fault samples; the vast majority of collected data consists of normal samples, while faulty samples constitute only a small proportion. However, deep learning-based fault diagnosis models require a large amount of data for feature extraction to achieve accurate diagnostic results. Data scarcity significantly reduces the performance of fault diagnosis models, especially for fault categories with small sample sizes, leading to a high false diagnosis rate. Therefore, researching bearing fault diagnosis under conditions of data scarcity is beneficial for promoting the development of intelligent fault diagnosis technology and is an important guarantee for further improving the level of mechanical equipment fault diagnosis.

[0004] In recent years, many scholars have proposed various feasible solutions to improve fault diagnosis performance in situations where data samples are scarce. These methods can be mainly divided into two categories: model-based strategies and data-based strategies.

[0005] (1) Model-based strategies can improve the model's ability to learn features from minority class samples more effectively by designing new loss functions or optimizing the model architecture. For example, the BPSO-Adaboost-KNN ensemble algorithm proposed by Guo et al. combines feature selection with reinforcement learning, thereby improving the classification performance of imbalanced datasets; Khan et al. proposed a cost-sensitive deep neural network that can automatically learn robust feature representations of the majority and minority classes; Zhao et al. proposed a method based on deep Laplacian mapping (DLapAE), which improves the model's ability to learn the original data manifold structure by introducing a Laplacian regularization term into the objective function of the autoencoder. This improvement enables the model to learn features and classify more effectively when data samples are scarce, thereby improving its performance in such problems. Although the above methods improve the fault diagnosis effect when data samples are scarce, most of them only focus on the impact on model learning, while ignoring the problem that the model's ability to capture the true feature distribution of data is insufficient when data distribution differences and scarcity coexist. Therefore, these methods are difficult to extend to cross-domain fault diagnosis tasks when data is scarce.

[0006] (2) Data-based strategies are mainly divided into two categories: random sampling and data generation. Among them, random sampling strategies mainly include undersampling and oversampling methods. These methods achieve the balance of the number of categories in the dataset by randomly removing, copying samples, or adjusting the sampling frequency. Among them, Wu et al. proposed an effective imbalanced data learning scheme called Easy-SMT. This method increases the number of samples of a minority of fault categories of wind turbines by using SMOTE (Synthetic Minority Over-sampling Technique), and at the same time combines the Easy-Ensemble algorithm to transform the originally imbalanced fault classification problem into a relatively balanced problem. Douzas et al. proposed an oversampling method that combines k-means clustering and SMOTE, which effectively alleviates the imbalance between and within categories. Fan et al. used principal component analysis (PCA) and SMOTE to oversample the minority fault sample set (accounting for only 5%), which significantly improved the balance of the samples. However, although these sampling techniques have mitigated the negative impact of the scarcity of faulty samples to some extent, when the data scarcity ratio increases further, the samples generated by oversampling techniques tend to be too similar to the original data, which often leads to overfitting problems.

[0007] Data generation primarily relies on generative models such as Variational Autoencoders (VAEs) and Generative Adversarial Networks (GANs). For example, Islam et al. used VAEs to generate a large number of collision samples from limited training data, significantly expanding the data scale. Zhou et al. designed a novel generator to generate fault features rather than fault data, improving classification accuracy through alternating optimization of the generator, discriminator, and deep neural network (DNN) fault diagnosis model. Guo et al. proposed a multi-generator GAN based on local weight sharing, achieving efficient generation of multi-class fault data. Liu et al. used Frequency Slice Wavelet Transform (FSWT) to extract two-dimensional time-frequency features from the original vibration signal and used these features as input to the GAN network to generate high-quality new time-frequency features. Experimental results show that this method can achieve higher stability and diagnostic accuracy in fault diagnosis problems with scarce fault samples. Although GAN-based methods have shown potential in the field of fault diagnosis, their application is still immature. Mode collapse or gradient vanishing phenomena often occur during training, making it difficult for the model to converge stably and affecting the quality of generated data. Furthermore, the performance of GANs often depends on the number of samples and the operating conditions, thus limiting their practical applications.

[0008] In summary, existing model-based and data-based solutions have mitigated the impact of scarce fault samples on fault diagnosis performance to some extent. However, the applicability and generalization ability of these methods in real-world industrial scenarios remain limited. Traditional geometric transformation methods only apply shallow perturbations to the signal morphology, failing to effectively embed the physical propagation mechanism of bearing faults and thus unable to address the problem of fault diagnosis under conditions of scarce fault samples. Summary of the Invention

[0009] To address the aforementioned problems, the purpose of this invention is to provide a bearing fault diagnosis method based on a dynamic activation mechanism under conditions of sample scarcity.

[0010] To achieve the above objectives, the present invention adopts the following technical solution: a bearing fault diagnosis method based on a dynamic activation mechanism under conditions of scarce samples, comprising the following steps:

[0011] S1. Vibration signal acquisition and preprocessing to obtain original fault samples. x 0, specifically including the following steps:

[0012] S101. Vibration signal acquisition: Acquire bearing vibration signal samples for different fault categories under varying speed conditions. x ( z );

[0013] S102. Data Preprocessing: After data acquisition, a sliding window data segmentation method is used to preprocess the data. x (z Processing is performed; then continuous wavelet transform is used to... x ( z The original fault samples are decomposed into time-frequency characteristics of different frequency bands. x 0;

[0014] S2. Optimize the original fault samples using forward diffusion and reverse denoising. x 0, to obtain generated samples that closely resemble real fault data. Specifically, it includes the following steps:

[0015] S201, Forward Diffusion: Add Gaussian noise to the original fault sample x In 0, the time-domain sample after adding Gaussian noise is obtained. x T ;

[0016] S202, Reverse Denoising: Construct a U-Net noise prediction network and apply Gaussian noise to the time-domain samples. x T Process and output predicted noise;

[0017] S203, Using the loss function L By constraining the U-Net noise prediction network, generated samples that closely resemble real fault data are obtained. ;

[0018] S3. Construct a deep residual network PRNet fault diagnosis model with multiple activation mechanisms, and process the original fault samples. x 0 and generated samples that closely resemble real fault data Mix to form a fault sample set x i Input the fault diagnosis model and use the cross-entropy loss function L CE The network is trained to ultimately output the bearing fault category. .

[0019] Furthermore, in step S102, the formula for continuous wavelet transform is as follows:

[0020] ;

[0021] In equation (1), x 0 represents the original fault sample. s Here, represents the translation parameter, indicating the translation of the wavelet along the time axis; x ( z ) represents the input vibration signal sample; τ is the translation factor, used to control the width of the wavelet; z is the number of sampling points; These are wavelet basis functions. ,in, It's a scaling parameter. Describes the wavelet mother function. Where π is the value of a circle's circumference, which is 3.141592654. e It is a natural constant, approximately equal to 2.71828, and is the base of the natural logarithm; j Indicates different scales. j ∈Z, where Z represents an integer; f c σ is the center frequency of the wavelet, and σ is the time spread parameter.

[0022] Furthermore, the forward diffusion in step S201 is represented by a Markov chain as follows:

[0023] ;

[0024] Where t represents the diffusion step number, t ∈{0, T}, T Indicates the total step size; q ( x t | x t-1 ) indicates the forward diffusion process from t- 1 to t Step data distribution; , representing a normal distribution, where I It is the identity matrix; x t This represents the output characteristic at step t of the forward diffusion process; β t It is a noise hyperparameter; β t ∈[0,1]; β t I It is the covariance matrix;

[0025] In equation (2), the noise hyperparameter β t Using spectral regularization design, its equations satisfy:

[0026] ;

[0027] In equation (3), γ For frequency domain attenuation factor; where, in the initial stage when t < T / 3, ensure β t <0.1, to preserve fault-sensitive characteristics; when t>2T / 3, increase... β t ≈ 0.5, to achieve feature regularization;

[0028] By deriving the global analytical solution of the characteristic perturbation, the asymptotic mapping closed-form solution is obtained:

[0029] ;

[0030] In equation (4), q ( x t | x 0) indicates the data distribution of the forward diffusion process; This indicates the proportion of samples retained, which varies with the number of diffusion steps. t Decrease; , is the cumulative value of the sample retention ratio, representing the degree to which the original data information is retained; β s This represents the noise increment, which determines the amount of noise increase at each step; It is the cumulative noise intensity;

[0031] When the diffusion steps t Reach the preset total step size T At that time, the time-domain sample with Gaussian noise added was obtained. x T This completes the forward diffusion process.

[0032] Furthermore, the specific process of reverse denoising in step S202 is as follows:

[0033] S2021. Constructing the U-Net noise prediction network: The U-Net noise prediction network includes an encoder and a decoder. The encoder is used for downsampling to extract high-level features, and the decoder is used for upsampling to restore resolution and perform pixel-level prediction.

[0034] S2022, Time-domain samples with added Gaussian noise x T The input is fed into the U-Net noise prediction network. x T ∈ R Tin ×Fin×Cin ;

[0035] in, T in Indicates the size of the input time dimension; F in Indicates the size of the input frequency dimension; C in Indicates the number of input channels; R Represents the set of real numbers;

[0036] S2023, via encoder x T The encoding and encoder calculation formulas are as follows:

[0037] ;

[0038] In equation (5), Indicates encoder output characteristics; Encoder Indicates encoding; This represents the output feature at step t-1 of the reverse denoising process; θ Indicates model parameters;

[0039] S2024, Output features from encoder The input is fed into the decoder, and the decoder calculates it using the following formula:

[0040] ;

[0041] in, This indicates the decoder output prediction noise; Decoder Indicates decoding; Indicates encoder output characteristics; θ Indicates model parameters;

[0042] S2025. Obtain the output predicted noise characteristics of the reverse denoising process. The formula is as follows:

[0043] ;

[0044] In equation (7), This represents the output predicted noise feature at step t of the reverse denoising process; This represents the output predicted noise characteristics at step t-1 of the reverse denoising process; This indicates the decoder output prediction noise; t Indicates the number of diffusion steps. t ∈{0, T};

[0045] Inverse denoising process network Conditional distributions can be represented by Markov chains as follows:

[0046] ;

[0047] in, This represents the conditional distribution of the reverse denoising process from step T to step 0; Indicates the inverse denoising process. t The conditional distribution of the steps; θ Indicates model parameters; This represents the conditional distribution of the reverse denoising process from step t to step t-1.

[0048] Furthermore, step S203 specifically includes the following steps:

[0049] S2031. Constructing the variational lower bound loss function L vlb The calculation formula is:

[0050] ;

[0051] In equation (10), θ Indicates model parameters; This represents the conditional distribution of the reverse denoising process from step 1 to step 0; q ( x T () represents the data distribution at step T of the forward diffusion process; q ( x t | x 0) represents the data distribution from step 0 to step t in the forward diffusion process; KL This represents the Kullback-Leibler divergence between two probability distributions; x t This indicates the first step of the forward diffusion process. t The output features of the step, t ∈{0, T}; Indicates the inverse denoising process. t The output features of the step, t ∈{0, T}; q ( x t-1 | x t , x 0) indicates that in the known x Under condition 0, the forward diffusion process from step t-1 to... t Step data distribution;

[0052] S2032, due to KL ( q ( x T | x 0)|| q ( x T It does not depend on model parameters. θ ,therefore KL ( q ( x T | x 0)|| q ( x T ))≈0; thus further simplifying L vlbThe simplified variational lower bound loss function is obtained. L simple The formula is:

[0053] ;

[0054] In equation (11), E t Indicates the number of diffusion steps t Expectations t ∈{0, T}; E x0～p(x0) This represents the expected value of the initial weights; x 0~ p ( x 0) indicates the original fault sample. x 0 Obedience p ( x 0) distribution, p ( x 0) is x The distribution of 0; Indicates the desired level of noise;

[0055] S2033. To constrain the physical characteristics of the vibration signal, a physical loss function is introduced. L physics The calculation formula is:

[0056] ;

[0057] In equation (12), M , Q , Y , F For constants, where M Represents the mass matrix, Q Represents the damping matrix. Y Represents the stiffness matrix. F Indicates the load received;

[0058] S2034, Combining the simplified variational lower bound loss function L simple and physical loss function L physics The loss function is obtained. L The formula is shown below:

[0059] ;

[0060] S2035, through the loss function L Constraints are applied to generate sample data that closely approximates real fault data. As shown in the following formula:

[0061] ;

[0062] In equation (14), This represents a generated sample that closely approximates real fault data.

[0063] Furthermore, the PRNet fault diagnosis model of the deep residual network with multi-activation mechanism collaboration in step S3 specifically includes an initial convolutional layer, a first KAN residual block, a second KAN residual block, a third KAN residual block, a fourth KAN residual block, an FC fully connected layer, and a Softmax layer; the first KAN residual block includes two KAN network unsampling residual blocks of the same size, and the second, third, and fourth KAN residual blocks each include one KAN network downsampled residual block and one KAN network unsampling residual block;

[0064] The fault sample set x i The input is processed using the PRNet fault diagnosis model, and the cross-entropy loss function is applied. L CE The fault diagnosis model is trained into a network, and the bearing fault category is finally output. Specifically, it includes the following steps:

[0065] S301, Fault Sample Set x i Input the initial convolutional layer, the initial convolutional layer to x i The initial convolutional layer output features are obtained by sequentially processing the Conv3×3 convolutional kernel, batch normalization and ReLU activation function, and max pooling layer. As shown in the following formula:

[0066] ;

[0067] in, MaxPool Indicates the max pooling layer; ReLu It is an activation function; BN Indicates batch normalization; Conv Indicates a convolutional layer;

[0068] S302, will The input is fed into the first KAN residual block for basic feature extraction, resulting in the output features of the first KAN residual block. The formula is: ;

[0069] S303, will The input is fed into the second KAN residual block for intermediate semantic feature extraction, resulting in the output features of the second KAN residual block. The formula is: ;

[0070] S304, will The input is fed into the third KAN residual block for high-level abstraction feature extraction, resulting in the output features of the third KAN residual block. The formula is: ;

[0071] S305, will The input is fed into the fourth KAN residual block for global upper and lower information integration to obtain the output features of the fourth KAN residual block. The formula is: ;

[0072] In equations (16), (17), (18), and (19), KAN1 is the first KAN residual block; KAN2 is the second KAN residual block; KAN3 is the third KAN residual block; and KAN4 is the fourth KAN residual block.

[0073] S306, will The input is processed by the FC fully connected layer to obtain the fault category logic value. G The expression is as follows:

[0074] ;

[0075] in, G This represents the raw output of the fully connected layer, i.e., the fault category logic value; W represents the weight. b i Indicates bias;

[0076] S307. Output the fault category logic value from the FC fully connected layer. G Input to the Softmax layer, where the Softmax function converts the vector... Convert to probability distribution P Each probability component p i The calculation is as follows:

[0077] ;

[0078] in, It is a vector that contains the logical value for each fault category in the classification task. G ; It is a vector The Middle i Each fault category logical value; N It is the total number of samples; yes The index;

[0079] Take probability components p iThe fault category corresponding to the maximum value is used as the prediction label. ;

[0080] S308, Using the cross-entropy loss function L CE As the optimization objective, the fault diagnosis model is trained to output the bearing fault category. ;

[0081] The cross-entropy loss function L CE The mathematical expression is:

[0082] ;

[0083] Where N is the total number of samples; y i The one-hot encoding representing the actual label; This indicates the predicted label.

[0084] Furthermore, the operation process of the KAN network without downsampling residual blocks specifically includes:

[0085] Features of the input , l For each element in the range {1,2,3,4}, both main branch and shortcut branch operations are performed. The features obtained from both operations are summed element-wise, and then the final output is obtained by applying the ReLU activation function. Specifically, the main branch operation includes Conv1×1 compression and dynamically activated convolutional units. KANConv Conv1×1 expansion and BN batch normalization; direct output of quick branch operations. The overall expression for calculating the KAN network's unsampled residual blocks is:

[0086] ;

[0087] in, This indicates that the KAN network is computed without downsampling residual blocks; BN ( ) represents batching into a unified operation; Indicates input features, l ∈{1,2,3,4}; KANConv ( ) indicates that the convolutional unit is dynamically activated for computation; Conv ( ) indicates Conv1×1 compression calculation; RELU ( ) serves as a fixed nonlinear activation function; ⊕ indicates element-wise addition;

[0088] The operation process of downsampling residual blocks in the KAN network specifically includes:

[0089] Features of the input , lThe features obtained from the main branch and shortcut branch operations are summed element-wise for ∈{2,3,4}, and then the final output is obtained by applying the ReLU activation function. The main branch operation is the same as the main branch operation in the KAN network's unsampled residual block. The shortcut branch operation specifically includes Conv1×1 convolution and BN batch normalization. The overall expression for calculating the KAN network's downsampled residual block is:

[0090] ;

[0091] in, This indicates the calculation of the downsampled residual block in the KAN network.

[0092] Furthermore, the KAN network without downsampling residual blocks and the dynamically activated convolutional units in the KAN network downsampling residual blocks. KANConv It consists of a convolutional neural network (CNN) and dynamically activated convolutional layers (KAN); and in the dynamically activated convolutional layers... KANConv Introducing B-spline basis functions B k ( u As a dynamic nonlinear mapping, its standard form is as follows:

[0093] ;

[0094] in, B k ( u ) is the k-th order spline basis function; u Indicates the node interval; t k For nodes;

[0095] For input features Each input feature Corresponding to a set of B-spline basis functions , Indicates the first i one sample k Step B spline k Indicates the order, k The value of must satisfy 2≤ k ≤N+1, where N is the total number of samples;

[0096] In formulas (22) and (23) ,but:

[0097] ;

[0098] in, f i ( x Conv) represents the location-dependent dynamic B-spline basis function; ω i,k Indicates weight, b i This indicates the bias, where N is the total number of samples;

[0099] exist f i ( x Conv Based on this, we obtain dynamically activated convolutional units. KANConv By introducing dynamic nonlinear mapping into convolution operations, adaptive activation of bearing vibration signal features is achieved. The calculation process is as follows:

[0100] ;

[0101] in, KANConv ( x Conv () indicates that the convolutional unit is dynamically activated for computation. m Indicates the node location; Ω represents the local receptive field; f i ( x Conv ) represents the location-dependent dynamic B-spline basis function; v im Indicates spatial attention weights; x Conv express .

[0102] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0103] (1) In the bearing vibration signal acquisition and preprocessing stage, the present invention uses a sliding window data segmentation method to process the vibration signal collected by the sensor and accurately extract the fault impact cycle. Subsequently, continuous wavelet transform is used to decompose the vibration signal into a series of time-frequency features of different frequency bands, effectively capturing the non-stationary characteristics of the signal, thereby extracting high-quality fault features and balancing the number of fault samples.

[0104] (2) This invention optimizes the original fault samples through forward diffusion and reverse denoising processes. x 0, and construct a loss function L, which adopts the variational lower bound loss function. And introduce a physical information loss function. This constrains the U-Net noise prediction network in the inverse denoising process, generating samples that closely approximate real fault data. This ensures that the data generation model can generate minority class samples. Balance the dataset to compensate for the problem of scarce samples.

[0105] (3) In the fault diagnosis stage, this invention constructs a deep residual network PRNet fault diagnosis model with multiple activation mechanisms. This model adopts a dual-branch hierarchical feature fusion architecture and uses dynamic activation convolutional units in the first to fourth KAN residual blocks. KANConv Through KANConv Introducing B-spline basis functions B k ( u This approach integrates dynamic nonlinear mapping into convolution operations to achieve dynamic modulation of feature representation and adaptive activation of bearing vibration signal features. This significantly enhances the nonlinear feature extraction capability and the efficiency of deep information transfer, improving the accuracy and stability of fault diagnosis. This design allows the model to maintain high accuracy even with insufficient samples. Finally, a cross-entropy function is constructed... L CE Enhance the model's ability to distinguish between different types of faults and optimize hyperparameter configuration to improve training stability and generalization ability.

[0106] Through the combined effect of the above design, the bearing fault diagnosis method based on dynamic activation mechanism under the condition of sample scarcity in this invention effectively solves the problem of sample scarcity in bearing fault diagnosis and significantly improves the accuracy and stability of bearing fault diagnosis. Attached Figure Description

[0107] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this application, illustrate the invention and are used to explain it, but do not constitute an undue limitation of the invention.

[0108] Figure 1 This is a flowchart of the bearing fault diagnosis method based on dynamic activation mechanism under the condition of scarce samples according to the present invention;

[0109] Figure 2 This is a schematic diagram of the bearing vibration signal data collected and the obtained time-frequency characteristics in step S1 of the bearing fault diagnosis method based on dynamic activation mechanism under the condition of scarce samples of the present invention.

[0110] Figure 3 This diagram illustrates the window partitioning process for data preprocessing and the time-frequency features formed after continuous wavelet transform in step S1 of the bearing fault diagnosis method based on dynamic activation mechanism under the condition of scarce samples in this invention.

[0111] Figure 4 In step S2 of the bearing fault diagnosis method based on dynamic activation mechanism under the condition of scarce samples in this invention, forward diffusion and reverse denoising are used to optimize the original fault samples to obtain generated samples that are close to the real fault data. A flowchart;

[0112] Figure 5This is a schematic diagram of the deep residual network PRNet fault diagnosis model of the component in step S3 of the bearing fault diagnosis method based on dynamic activation mechanism under the condition of scarce sample in the present invention.

[0113] Figure 6 The flowcharts show the operation of the KAN network with and without downsampling residual blocks; among which... Figure 6 (a) is a flowchart of the operation of the KAN network without downsampling residual blocks. Figure 6 (b) Operation flowchart of the KAN network downsampling residual block;

[0114] Figure 7 This is a schematic diagram of the bearing test bench in an embodiment of the present invention;

[0115] Figure 8 This is a schematic diagram showing the installation position of the acceleration sensor on the bearing test bench in an embodiment of the present invention;

[0116] Figure 9 This is a diagram showing the confusion matrix results of the PRNet deep residual network fault diagnosis model of the present invention on the test set under different proportions of generated data; wherein, Figure 9 (a) is a diagram showing the confusion matrix of the test set with a data ratio of 0.8; Figure 9 (b) is a diagram showing the confusion matrix of the test set with a data ratio of 0.9; Figure 9 (c) is a diagram showing the confusion matrix of the test set with a data ratio of 0.96; Figure 9 (d) is a diagram showing the confusion matrix of the test set with a generated data ratio of 0.98;

[0117] Figure 10 The graph shows the test results of precision, recall, and F1 score for different fault diagnosis models when the data ratio is 0.8.

[0118] In the diagram: 1. Bearing, 2. Drive motor, 3. Motor controller, 4. Accelerometer, 5. Dynamic torque sensor, 6. Magnetic powder brake, 7. Signal acquisition device, 8. PC. Detailed Implementation

[0119] The technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments.

[0120] Reference Figure 1 A bearing fault diagnosis method based on dynamic activation mechanism under conditions of scarce samples includes the following steps:

[0121] Reference Figures 2-3S1. Vibration signal acquisition and preprocessing to obtain the original fault sample. x 0, specifically including the following steps:

[0122] S101. Vibration Signal Acquisition: Fault diagnosis experiments were conducted using a bearing test bench, and bearing vibration signal samples of different fault types were acquired under varying speed conditions. x ( z );

[0123] S102. Data Preprocessing: After data acquisition, a sliding window data segmentation method is used to preprocess the data. x ( z The process involves: first, selecting a window, which slides from the signal start point to the signal end point with a fixed step size, generating a sample each time it slides, until the right boundary of the window is less than one step away from the signal end point;

[0124] Then, through continuous wavelet transform, x ( z Convolve the result with a wavelet basis function to obtain the original value. x ( z The original fault samples are decomposed into time-frequency characteristics of different frequency bands. x 0; Wavelet transform can simultaneously provide information about a signal in both the time and frequency domains, thus better capturing the non-stationary characteristics of the signal; the formula for continuous wavelet transform is as follows:

[0125] ;

[0126] In equation (1), x 0 represents the original fault sample. s Here, represents the translation parameter, indicating the translation of the wavelet along the time axis; x ( z ) represents the input vibration signal sample; τ is the translation factor, used to control the width of the wavelet; z is the number of sampling points; These are wavelet basis functions. ,in, It's a scaling parameter. Describes the wavelet mother function. Where π is the value of a circle's circumference, which is 3.141592654. e It is a natural constant, approximately equal to 2.71828, and is the base of the natural logarithm; j Indicates different scales. j ∈Z, where Z represents an integer; f c σ is the center frequency of the wavelet, and σ is the time spread parameter.

[0127] In step S2 of this invention, a forward diffusion chain is constructed through forward diffusion to achieve an asymptotic mapping of the original data distribution to the Gaussian noise space, and the data manifold structure is reconstructed through a learnable reverse denoising process.

[0128] Reference Figure 4 S2. Optimize the original fault samples using forward diffusion and reverse denoising. x 0, to obtain generated samples that closely resemble real fault data. Specifically, it includes the following steps:

[0129] S201, Forward Diffusion: Gaussian noise is iteratively added to the original fault samples. x In 0, the time-domain sample after adding Gaussian noise is obtained. x T Forward diffusion can be represented by a Markov chain as follows:

[0130] ;

[0131] Where t represents the diffusion step number, t ∈{0, T}, T Indicates the total step size; q ( x t | x t-1 ) indicates the forward diffusion process from t- 1 to t Step data distribution; , representing a normal distribution, where I It is the identity matrix; x t This represents the output characteristic at step t of the forward diffusion process; β t It is a noise hyperparameter; β t ∈[0,1]; β t I It is the covariance matrix;

[0132] In equation (2), the noise hyperparameter β t Using spectral regularization design, its equations satisfy:

[0133] ;

[0134] In equation (3), γ For frequency domain attenuation factor; where, in the initial stage when t < T / 3, ensure β t<0.1, to preserve fault-sensitive characteristics; when t>2T / 3, increase... β t ≈ 0.5, to achieve feature regularization;

[0135] By deriving the global analytical solution of the characteristic perturbation, the asymptotic mapping closed-form solution is obtained:

[0136] ;

[0137] In equation (4), q ( x t | x 0) indicates the data distribution of the forward diffusion process; This indicates the proportion of samples retained, which varies with the number of diffusion steps. t Decrease; , is the cumulative value of the sample retention ratio, representing the degree to which the original data information is retained; β s This represents the noise increment, which determines the amount of noise increase at each step; It is the cumulative noise intensity;

[0138] When the diffusion steps t Reach the preset total step size T At that time, the time-domain sample with Gaussian noise added was obtained. x T The forward diffusion process is completed;

[0139] S202, Reverse Denoising: Construct a U-Net noise prediction network and apply Gaussian noise to the time-domain samples. x T Process and output predicted noise features The specific process is as follows:

[0140] S2021. Constructing the U-Net noise prediction network: The U-Net noise prediction network includes an encoder and a decoder. The encoder is used for downsampling to extract high-level features, and the decoder is used for upsampling to restore resolution and perform pixel-level prediction.

[0141] S2022, Time-domain samples with added Gaussian noise x T The input is fed into the U-Net noise prediction network. x T ∈ R Tin ×Fin×Cin ;

[0142] in, T in Indicates the size of the input time dimension; Fin Indicates the size of the input frequency dimension; C in Indicates the number of input channels; R Represents the set of real numbers;

[0143] S2023, via encoder x T Encoding: The encoder consists of four stacked encoding modules. Each module contains two consecutive convolutional layers (3×3 convolutional kernels) and one pooling layer. By stacking convolutional and pooling layers, the temporal and frequency dimensions of the feature map are gradually reduced, while the number of channels is increased to capture more abstract features. The encoder calculation formula is as follows:

[0144] ;

[0145] In equation (5), Indicates encoder output characteristics; Encoder Indicates encoding; This represents the output feature at step t-1 of the reverse denoising process; θ Indicates model parameters;

[0146] S2024, Output features from encoder Input to the decoder: The decoder consists of upsampling layers, skip connections, and convolutional layers. By stacking upsampling and convolution, the time and frequency dimensions are gradually restored, and skip connections are used to preserve detailed information.

[0147] The decoder calculation formula is as follows:

[0148] ;

[0149] in, This indicates the decoder output prediction noise; Decoder Indicates decoding; Indicates encoder output characteristics; θ Indicates model parameters;

[0150] S2025. Obtain the output predicted noise characteristics of the reverse denoising process. The formula is as follows:

[0151] ;

[0152] In equation (7), This represents the output predicted noise feature at step t of the reverse denoising process; This represents the output predicted noise characteristics at step t-1 of the reverse denoising process; This indicates the decoder output prediction noise; t Indicates the number of diffusion steps. t ∈{0,T};

[0153] Inverse denoising process network Conditional distributions can be represented by Markov chains as follows:

[0154] ;

[0155] in, This represents the conditional distribution of the reverse denoising process from step T to step 0; Indicates the inverse denoising process. t The conditional distribution of the steps; θ Indicates model parameters; This represents the conditional distribution of the reverse denoising process from step t to step t-1.

[0156] S203, Using the loss function L By constraining the U-Net noise prediction network, generated samples that closely resemble real fault data are obtained. Specifically, it includes the following steps:

[0157] S2031. In order to optimize the network parameters for the reverse denoising process... Conditional distribution and forward diffusion process q ( x t | x 0) Consistent data distribution is used to approximate the true conditional distribution, and a variational lower bound loss function is constructed. L vlb :

[0158] A variational lower bound loss function is constructed by minimizing the negative log-likelihood of the model and the KL divergence of the data distribution during the forward diffusion process and the reverse denoising process. L vlb The calculation formula is:

[0159] ;

[0160] In equation (10), θ Indicates model parameters; This represents the conditional distribution of the reverse denoising process from step 1 to step 0; q ( x T () represents the data distribution at step T of the forward diffusion process; q ( x t | x 0) represents the data distribution from step 0 to step t in the forward diffusion process; KL This represents the Kullback-Leibler divergence between two probability distributions; x tThis indicates the first step of the forward diffusion process. t The output features of the step, t ∈{0, T}; Indicates the inverse denoising process. t The output features of the step, t ∈{0, T}; q ( x t-1 | x t , x 0) indicates that in the known x Under condition 0, the forward diffusion process from step t-1 to... t Step data distribution;

[0161] S2032, due to KL ( q ( x T | x 0)|| q ( x T It does not depend on model parameters. θ ,therefore KL ( q ( x T | x 0)|| q ( x T ))≈0; thus further simplifying L vlb The simplified variational lower bound loss function is obtained. L simple The formula is:

[0162] ;

[0163] In equation (11), E t Indicates the number of diffusion steps t Expectations t ∈{0, T}; E x0～p(x0) This represents the expected value of the initial weights; x 0~ p ( x 0) indicates the original fault sample. x 0 Obedience p ( x 0) distribution, p ( x 0) is x The distribution of 0; Indicates the desired level of noise;

[0164] S2033. To constrain the physical characteristics of the vibration signal, a physical loss function is introduced into the network module built during the reverse denoising process. L physics The physical loss function for this part is calculated by substituting the physical quantities predicted by the network into the corresponding physical laws and obtaining the residuals. The calculation formula is as follows:

[0165] ;

[0166] In equation (12), M , Q , Y , F For constants, where M Represents the mass matrix, Q Represents the damping matrix. Y Represents the stiffness matrix. F Indicates the load received;

[0167] S2034, Combining the simplified variational lower bound loss function L simple and physical loss function L physics The loss function is obtained. L The formula is shown below:

[0168] ;

[0169] S2035, through the loss function L Constraints are applied to generate sample data that closely approximates real fault data. As shown in the following formula:

[0170] ;

[0171] In equation (14), This represents a generated sample that closely approximates real fault data.

[0172] Reference Figure 5 S3. Construct a deep residual network PRNet fault diagnosis model with multiple activation mechanisms, and process the original fault samples. x 0 and generated samples that closely resemble real fault data Mix to form a fault sample set x i , set of fault samples x i The input is processed using the PRNet fault diagnosis model, and the cross-entropy loss function is applied. L CEThe fault diagnosis model is trained into a network, and the bearing fault category is finally output. The PRNet fault diagnosis model with multi-activation mechanism collaboration specifically includes an initial convolutional layer, a first KAN residual block, a second KAN residual block, a third KAN residual block, a fourth KAN residual block, an FC fully connected layer, and a Softmax layer. The first KAN residual block includes two KAN network unsampled residual blocks of the same size. The second, third, and fourth KAN residual blocks each include one KAN network downsampled residual block and one KAN network unsampled residual block.

[0173] The fault sample set x i The input is processed using the PRNet fault diagnosis model, and the cross-entropy loss function is applied. L CE The fault diagnosis model is trained into a network, and the bearing fault category is finally output. Specifically, it includes the following steps:

[0174] S301, Fault Sample Set x i The initial convolutional layer is input to extract basic texture and edge features. Simultaneously, pooling operations are used to reduce the feature map size and computational cost, laying the foundation for subsequent deep feature learning. The initial convolutional layer... x i The initial convolutional layer output features are obtained by sequentially processing the Conv3×3 convolutional kernel, batch normalization and ReLU activation function, and max pooling layer. As shown in the following formula:

[0175] ;

[0176] in, MaxPool Indicates the max pooling layer; ReLu It is an activation function; BN Indicates batch normalization; Conv Indicates a convolutional layer;

[0177] S302, will The input is fed into the first KAN residual block for basic feature extraction, mainly learning low-level local features. The output features of the first KAN residual block are obtained by processing the residual blocks of two KAN networks without downsampling. The formula is: ;

[0178] S303, will The input is fed into the second KAN residual block for intermediate semantic feature extraction, further extracting intermediate semantic information to enhance the discriminative power of the features. The output features of the second KAN residual block are obtained by processing the residuals through one downsampled KAN network and one undownsampled KAN network. The formula is: ;

[0179] S304, will The input is fed into the third KAN residual block for high-level abstraction feature extraction. The focus is on learning these high-level abstract features, enabling the network to distinguish key patterns for different fault types. The output features of the third KAN residual block are obtained by processing the residuals through one downsampled KAN network and one undownsampled KAN network. The formula is: ;

[0180] S305, will The information is input into the fourth KAN residual block for global integration of upper and lower information, making the classification more stable and robust. The output features of the fourth KAN residual block are obtained by processing the residuals through one downsampled KAN network and one undownsampled KAN network. The formula is: ;

[0181] In equations (16), (17), (18), and (19), KAN1 is the first KAN residual block; KAN2 is the second KAN residual block; KAN3 is the third KAN residual block; and KAN4 is the fourth KAN residual block.

[0182] Reference Figure 6 The operation process of the KAN network without downsampling residual blocks specifically includes: processing the input features... , l For each element in the range {1,2,3,4}, both main branch and shortcut branch operations are performed. The features obtained from both operations are summed element-wise, and then the final output is obtained by applying the ReLU activation function. Specifically, the main branch operation includes Conv1×1 compression and dynamically activated convolutional units. KANConv Conv1×1 expansion and BN batch normalization; direct output of quick branch operations. The overall expression for calculating the KAN network's unsampled residual blocks is:

[0183] ;

[0184] in, This indicates that the KAN network is computed without downsampling residual blocks; BN ( ) represents batching into a unified operation; Indicates input features, l ∈{1,2,3,4}; KANConv ( ) indicates that the convolutional unit is dynamically activated for computation; Conv ( ) indicates Conv1×1 compression calculation; RELU ( ) serves as a fixed nonlinear activation function; ⊕ indicates element-wise addition;

[0185] Reference Figure 6 The operation process of the KAN network downsampling residual block specifically includes: processing the input features... , l The features obtained from the main branch and shortcut branch operations are summed element-wise for ∈{2,3,4}, and then the final output is obtained by applying the ReLU activation function. The main branch operation is the same as the main branch operation in the KAN network's unsampled residual block. The shortcut branch operation specifically includes Conv1×1 convolution and BN batch normalization. The overall expression for calculating the KAN network's downsampled residual block is:

[0186] ;

[0187] in, This indicates the calculation of the downsampled residual block in the KAN network.

[0188] In S302-S305, the KAN network without downsampled residual blocks and the dynamically activated convolutional units in the KAN network downsampled residual blocks are described. KANConv It consists of a convolutional neural network (CNN) and dynamically activated convolutional layers (KAN); and in the dynamically activated convolutional layers... KANConv Introducing B-spline basis functions B k ( u As a dynamic nonlinear mapping that takes into account the data characteristics of different modes, its standard form is as follows:

[0189] ;

[0190] in, B k ( u ) is the k-th order spline basis function; u Indicates the node interval; t k For nodes;

[0191] For input features Each input feature Corresponding to a set of B-spline basis functions , Indicates the first i one sample k Step B spline k Indicates the order, kThe value of must satisfy 2≤ k ≤N+1, where N is the total number of samples; if k =1, the B-spline basis functions will degenerate into piecewise functions, therefore k At least 2;

[0192] In formulas (22) and (23) ,but:

[0193] ;

[0194] in, f i ( x Conv ) represents the location-dependent dynamic B-spline basis function; ω i,k Indicates weight, b i This indicates the bias, where N is the total number of samples;

[0195] exist f i ( x Conv Based on this, we obtain dynamically activated convolutional units. KANConv By introducing dynamic nonlinear mapping into convolution operations, adaptive activation of bearing vibration signal features is achieved. The calculation process is as follows:

[0196] ;

[0197] in, KANConv ( x Conv () indicates that the convolutional unit is dynamically activated for computation. m Indicates the node location; Ω represents the local receptive field; f i ( x Conv ) represents the location-dependent dynamic B-spline basis function; v im Indicates spatial attention weights; x Conv express .

[0198] The PRNet model of this invention employs dynamically activated convolutional units. KANConv By introducing dynamic nonlinear mapping into convolution operations, the nonlinear feature extraction capability and depth information transmission efficiency are enhanced, achieving adaptive activation of bearing vibration signal features, thereby improving the accuracy and stability of fault diagnosis. This invention combines a KAN network downsampled residual block with a KAN network without downsampled residual block, incorporating a fixed activation mechanism (…). RELUActivation functions and dynamic activation mechanisms (dynamically activated convolutional units) KANConv The computational approach achieves a balance between flexibility and stability in feature extraction. The fixed activation mechanism provides stable feature mapping, ensuring the effectiveness of gradient propagation and improving network convergence; the dynamic activation mechanism, through learnable nonlinear transformations, enables the model to adaptively adjust the feature space to adapt to complex time-frequency feature variations. This residual module combines the deep feature learning capabilities of the residual structure, effectively mitigating the gradient vanishing problem and enhancing the ability to identify complex fault modes.

[0199] S306, will The input is processed by the FC fully connected layer to obtain the fault category logic value. G The expression is as follows:

[0200] ;

[0201] in, G This represents the raw output of the fully connected layer, i.e., the fault category logic value; W represents the weight. b i Indicates bias.

[0202] S307. Output the fault category logic value from the FC fully connected layer. G The input to the Softmax layer compresses these original predicted values ​​into a true probability distribution. Within the Softmax layer, the Softmax function transforms the vector... Convert to probability distribution P Each probability component p i The calculation is as follows:

[0203] ;

[0204] in, It is a vector that contains the logical value for each fault category in the classification task. G ; It is a vector The Middle i Each fault category logical value; N It is the total number of samples; yes The exponent; the denominator It is the sum of the logical value exponents of all fault categories, ensuring all probability components. p i The sum of is 1, therefore P This constitutes an effective probability distribution;

[0205] Take probability components p iThe fault category corresponding to the maximum value is used as the prediction label. ;

[0206] S308, Using the cross-entropy loss function L CE As an optimization objective, to enable it to effectively measure the information entropy difference between the category probability distribution output by the fault diagnosis model and the true label, the fault diagnosis model is trained as a network, ultimately outputting the bearing fault category. The cross-entropy loss function L CE The mathematical expression is:

[0207] ;

[0208] Where N is the total number of samples; y i The one-hot encoding representing the actual label; This indicates the predicted label.

[0209] To evaluate the performance of this invention in bearing fault diagnosis, the following experiments were conducted:

[0210] 1. Design of the bearing test bench: To construct an experimental dataset for bearing fault diagnosis research, this invention conducts fault diagnosis experiments based on a bearing test bench, such as... Figure 7 As shown, the bearing test bench includes a bearing 1, a drive motor 2, a motor controller 3, an acceleration sensor 4, a dynamic torque sensor 5, a magnetic powder brake 6, a signal acquisition instrument 7, and a PC 8. Bearing 1 is a NU206EM type bearing, and its specific parameters are shown in Table 1. The drive motor 2 drives the shaft to rotate the bearing 1. The motor controller 3 controls the drive motor 2. The magnetic powder brake 6 is installed at the end of the shaft to provide torque. A dynamic torque sensor 5 is installed on the shaft to measure torque data. Due to the high-frequency transient characteristics of bearing failure impact vibration, the acceleration sensor 4 is directly coupled to the top of the NU206EM type bearing housing (e.g., ...) via a magnetic base. Figure 8 As shown in the figure, after finite element simulation optimization, the accelerometer 4 is installed at the top position where the axial-radial composite vibration is most significant, ensuring sufficient excitation and capture of fault characteristics and minimizing energy attenuation in the signal transmission path. The accelerometer 4 is model 1A313E, with a frequency response range of 0.5-8kHz. The sampling parameters of the signal acquisition instrument 7 are configured based on the Nyquist sampling theorem (Shannon sampling theorem), combined with the theoretically calculated value of the bearing fault characteristic frequency (the highest fault frequency is 2.3kHz), reserving more than twice the bandwidth margin to ensure signal fidelity in time-frequency domain analysis. The data acquired by the signal acquisition instrument 7 is sent to the PC 8.

[0211] .

[0212] Single-point damage faults, including inner ring faults and roller faults, were pre-fabricated on the NU206EM bearing using electrical discharge machining (EDM). During the experiment, the ambient temperature (25±2℃) and radial load (1.5kN) were kept constant, and the consistency of the load conditions was ensured by online monitoring using a dynamic torque sensor.

[0213] Vibration signal acquisition: In order to fully cover the operating conditions of the equipment, the vibration signal data of bearing faults of different fault categories were collected by changing the speed of drive motor 2 under differentiated speed conditions (speed set to 50Rpm, 100Rpm and 150Rpm), 5kHz sampling frequency and 0hp motor load.

[0214] Dataset Establishment: The collected bearing fault vibration signal samples were labeled with fault tags according to different fault categories. The fault tags were named using the format "position_speed", with speed expressed in revolutions per minute (Rpm). For example, "IR100" indicates an inner race fault at an operating speed of 100 RPM. The fault categories are N050, N100, N150, IR050, IR100, IR150, B050, B100, and B150. Among them, N050, N100, and N150 represent normal bearings without faults, whose vibration signals, temperature, noise, and other parameters are all within the normal range allowed by design.

[0215] In this invention, the number of samples collected for each fault category is equal. 1000 samples are extracted from each fault category for classification experiments, and the data are divided into training, validation, and test sets in a 10:1:1 ratio to ensure the balance of samples across different fault categories. Both the training and validation sets include the original fault samples. x 0 (raw data) and generated samples that closely resemble real fault data The test set contains a mixed sample of generated data, but does not include generated samples that closely resemble real fault data. This ensures the authenticity and impartiality of the assessment and accurately measures the model's diagnostic results and generalization ability on real data. The faulty bearing dataset of this invention is set up as shown in Table 2: .

[0216] 2. Accuracy Assessment

[0217] The accuracy of this invention and several other fault diagnosis models was evaluated under different generated data ratios. The generated data ratio is the ratio of generated data to the sum of original data and generated data. The generated data ratios were the same in the training and validation sets. During testing, a mixed training and validation set was used to train and fine-tune each model. The performance of different fault diagnosis models was then evaluated using a test set to obtain the test accuracy. The test results are shown in Table 3.

[0218] Precision measures a model's ability to accurately predict positive class samples. It is achieved by preparing multiple training and testing sets using cross-validation on a pre-defined dataset. Predictions are then performed on the test set, and this training and evaluation process is repeated until the model achieves the expected performance. The formula for precision is as follows:

[0219] ;

[0220] Where TP represents the correctly predicted samples; AP represents the total number of samples.

[0221] .

[0222] Explanation of Fault Diagnosis Models: CNN (Convolutional Neural Network), GoogleNet (also known as Inception-v1), is a deep convolutional neural network proposed by Google researchers in 2014. KAN (Kolmogorov–Arnold Networks), VggNet (Visual Geometry Group Network), AlexNet (Alex Krizhevsky), Residual Neural Network, PRNet (Residual Neural Network), and PRNet fault diagnosis model based on a multi-activation mechanism deep residual network.

[0223] As shown in Table 3, under the conditions of generated data proportions of 0.8, 0.9, 0.96, and 0.98, the accuracy of the PRNet model of this invention is higher than that of other models such as CNN. Therefore, it can be seen that the PRNet model of this invention shows a significant improvement in the accuracy of bearing fault diagnosis. When fault data is severely lacking, i.e., the proportion of generated data reaches 0.98%, the accuracy of the PRNet model of this invention still reaches 95.80%, indicating that the PRNet model of this invention still has good diagnostic accuracy when fault data samples are severely lacking. The PRNet model of this invention has good fault diagnosis effectiveness and robustness.

[0224] In addition, from Figure 9 As shown in the diagram of the confusion matrix results of the PRNet model of the present invention with different proportions of generated data on the test set, it can be observed that... Figure 9 (a) and Figure 9 In (b), when the proportion of generated data is 0.8 and 0.9, the PRNet model of this invention achieves relatively ideal classification results for each fault category, maintaining high recognition accuracy for almost all categories, with only a few fault categories showing minor misclassification. When the proportion of generated data increases to... Figure 9 (c) 0.96 and Figure 9 Even when the threshold of (d) reaches 0.98 (i.e., the degree of missing original fault data increases continuously), the PRNet model of this invention can still accurately identify most fault categories, with an accuracy still above 95%. These results demonstrate that the classification performance of the PRNet model of this invention is relatively stable. Even when original fault data is extremely scarce, it can still maintain a high recognition rate for most fault categories, further verifying the effectiveness of the PRNet model in improving the identifiability of small sample categories in imbalanced fault data scenarios and mitigating the impact of scarce fault samples.

[0225] 3. Performance evaluation of precision, recall, and F1 score:

[0226] To comprehensively evaluate the performance of each fault diagnosis model, the precision, recall, and F1 score of each model were further tested when the proportion of generated data was 0.8. Since the scarcity of fault samples when the proportion of generated data is 0.8 is closer to the severe but not extreme data loss problem that may be encountered in industrial practice, its analysis results are more universal and have more reference value. Among them, the formula for calculating precision is Equation (28); Recall is an important indicator for evaluating the performance of fault diagnosis models. It measures the model's ability to identify positive samples, that is, whether the model can effectively detect all potential fault samples. The fault diagnosis model is trained on the divided training set and predicted on the test set. Then, the recall is calculated on the test set. The formula for calculating the recall is as follows: ;

[0227] The F1 score is the harmonic mean of precision and recall, and the specific formula is as follows:

[0228] ;

[0229] The F1 value ranges from 0 to 1. The closer the value is to 1, the better the model performs in both aspects.

[0230] Test Results: When the generated data ratio is 0.8, the test results of the evaluation performance indicators of different models are shown in Table 4 and... Figure 10 As shown:

[0231] .

[0232] From Table 4 and Figure 10 From the test results, we can draw the following conclusions:

[0233] In terms of accuracy, the PRNet model of this invention achieves an accuracy of 98.30%, significantly outperforming ResNet (97.80%) and CNN (92.50%). In comparison, ResNet improves accuracy by 5.3% compared to CNN, while the PRNet model of this invention further improves accuracy by 0.5% on top of ResNet, indicating its stronger feature extraction capability. Compared to ResNet and CNN, PRNet maintains higher accuracy, helping to reduce false positive rates and improve the reliability of fault diagnosis.

[0234] In terms of recall, the PRNet model of this invention achieves a recall of 98.60%, which is superior to other models. Furthermore, the PRNet model of this invention exhibits a higher recall than precision on the bearing fault dataset, indicating that the PRNet model can not only maintain a high fault detection rate in complex data environments but also effectively reduce the false detection rate. This characteristic is of great significance for early fault warning in practical applications, as early faults often manifest as weak signals, requiring the model to possess high sensitivity and robustness for accurate identification.

[0235] In terms of F1 score, the PRNet model of this invention still has the highest F1 score of 0.9845 compared to other models, indicating that the classification performance of the model of this invention is still the best.

[0236] The experimental results above show that, compared with traditional deep learning models such as CNN, GoogleNet, and KAN, the PRNet model of this invention can exhibit stronger stability and generalization ability in complex fault pattern recognition tasks where fault samples are scarce. Its application value in the field of bearing fault diagnosis provides important theoretical support and practical reference for the development of subsequent bearing fault diagnosis technology.

[0237] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the invention by those skilled in the art. Any modifications, equivalent substitutions, or improvements made to the present invention should be included within the scope of protection of the present invention.

Claims

1. A bearing fault diagnosis method based on dynamic activation mechanism under conditions of scarce samples, characterized in that, Includes the following steps: S1. Vibration signal acquisition and preprocessing to obtain original fault samples. x 0, specifically including the following steps: S101. Vibration signal acquisition: Acquire bearing vibration signal samples for different fault categories under varying speed conditions. x ( z ); S102. Data Preprocessing: After data acquisition, a sliding window data segmentation method is used to preprocess the data. x ( z Processing is performed; then continuous wavelet transform is used to... x ( z The original fault samples are decomposed into time-frequency characteristics of different frequency bands. x 0; S2. Optimize the original fault samples using forward diffusion and reverse denoising. x 0, to obtain generated samples that closely resemble real fault data. Specifically, it includes the following steps: S201, Forward Diffusion: Add Gaussian noise to the original fault sample x In 0, the time-domain sample after adding Gaussian noise is obtained. x T ; S202, Reverse Denoising: Construct a U-Net noise prediction network and apply Gaussian noise to the time-domain samples. x T Process and output predicted noise; S203, Using the loss function L By constraining the U-Net noise prediction network, generated samples that closely resemble real fault data are obtained. ; S3. Construct a deep residual network PRNet fault diagnosis model with multiple activation mechanisms, and process the original fault samples. x 0 and generated samples that closely resemble real fault data Mix to form a fault sample set x i Input the fault diagnosis model and use the cross-entropy loss function L CE The network is trained to ultimately output the bearing fault category. ; The PRNet fault diagnosis model of the deep residual network with multi-activation mechanism collaboration specifically includes an initial convolutional layer, a first KAN residual block, a second KAN residual block, a third KAN residual block, a fourth KAN residual block, an FC fully connected layer, and a Softmax layer; the first KAN residual block includes two KAN network unsampled residual blocks of the same size, and the second, third, and fourth KAN residual blocks each include one KAN network downsampled residual block and one KAN network unsampled residual block; The fault sample set x i The input is processed using the PRNet fault diagnosis model, and the cross-entropy loss function is applied. L CE The fault diagnosis model is trained into a network, and the bearing fault category is finally output. Specifically, it includes the following steps: S301, Fault Sample Set x i Input the initial convolutional layer, the initial convolutional layer to x i The initial convolutional layer output features are obtained by sequentially processing the Conv3×3 convolutional kernel, batch normalization and ReLU activation function, and max pooling layer. As shown in the following formula: ； in, MaxPool Indicates the max pooling layer; ReLu It is an activation function; BN Indicates batch normalization; Conv Indicates a convolutional layer; S302, will The input is fed into the first KAN residual block for basic feature extraction, resulting in the output features of the first KAN residual block. The formula is: ; S303, will The input is fed into the second KAN residual block for intermediate semantic feature extraction, resulting in the output features of the second KAN residual block. The formula is: ; S304, will The input is fed into the third KAN residual block for high-level abstraction feature extraction, resulting in the output features of the third KAN residual block. The formula is: ; S305, will The input is fed into the fourth KAN residual block for global upper and lower information integration to obtain the output features of the fourth KAN residual block. The formula is: ; In equations (16), (17), (18), and (19), KAN1 is the first KAN residual block; KAN2 is the second KAN residual block; KAN3 is the third KAN residual block; and KAN4 is the fourth KAN residual block. S306, will The input is processed by the FC fully connected layer to obtain the fault category logic value. G The expression is as follows: ； in, G This represents the raw output of the fully connected layer, i.e., the fault category logic value; W represents the weight. b i Indicates bias; S307. Output the fault category logic value from the FC fully connected layer. G Input to the Softmax layer, where the Softmax function converts the vector... Convert to probability distribution P Each probability component p i The calculation is as follows: ； in, It is a vector that contains the logical value for each fault category in the classification task. G ; It is a vector The Middle i Each fault category logical value; N It is the total number of samples; yes The index; Take probability components p i The fault category corresponding to the maximum value is used as the prediction label. ; S308, Using the cross-entropy loss function L CE As the optimization objective, the fault diagnosis model is trained to output the bearing fault category. ; The cross-entropy loss function L CE The mathematical expression is: ； Where N is the total number of samples; y i The one-hot encoding representing the actual label; This indicates the predicted label.

2. The bearing fault diagnosis method based on dynamic activation mechanism under sample scarcity conditions as described in claim 1, characterized in that, In step S102, the formula for continuous wavelet transform is as follows: ； In equation (1), x 0 represents the original fault sample. s Here, represents the translation parameter, indicating the translation of the wavelet along the time axis; x ( z ) represents the input vibration signal sample; τ is the translation factor, used to control the width of the wavelet; z is the number of sampling points; These are wavelet basis functions. ,in, It's a scaling parameter. Describes the wavelet mother function. Where π is the value of a circle's circumference, which is 3.141592654. e It is a natural constant, approximately equal to 2.71828, and is the base of the natural logarithm; j Indicates different scales. j ∈Z, where Z represents an integer; f c σ is the center frequency of the wavelet, and σ is the time spread parameter.

3. The bearing fault diagnosis method based on dynamic activation mechanism under sample scarcity conditions as described in claim 1, characterized in that, The forward diffusion in step S201 is represented by a Markov chain as follows: ； Where t represents the diffusion step number, t ∈{0, T }, T Indicates the total step size; q ( x t | x t-1 ) indicates the forward diffusion process from t- 1 to t Step data distribution; , representing a normal distribution, where I It is the identity matrix; x t This represents the output characteristic at step t of the forward diffusion process; β t It is a noise hyperparameter; β t ∈[0,1]; β t I It is the covariance matrix; In equation (2), the noise hyperparameter β t Using spectral regularization design, its equations satisfy: ； In equation (3), γ For frequency domain attenuation factor; where, in the initial stage when t < T / 3, ensure β t <0.1, to preserve fault-sensitive characteristics; when t>2T / 3, increase... β t ≈ 0.5, to achieve feature regularization; By deriving the global analytical solution of the characteristic perturbation, the asymptotically mapped closed-form solution is obtained: ； In equation (4), q ( x t | x 0) indicates the data distribution of the forward diffusion process; This indicates the proportion of samples retained, which varies with the number of diffusion steps. t Decrease; , is the cumulative value of the sample retention ratio, representing the degree to which the original data information is retained; β s This represents the noise increment, which determines the amount of noise increase at each step; It is the cumulative noise intensity; When the diffusion steps t Reach the preset total step size T At that time, the time-domain sample with Gaussian noise added was obtained. x T This completes the forward diffusion process.

4. The bearing fault diagnosis method based on dynamic activation mechanism under sample scarcity conditions as described in claim 1, characterized in that, The specific process of reverse denoising in step S202 is as follows: S2021. Constructing the U-Net noise prediction network: The U-Net noise prediction network includes an encoder and a decoder. The encoder is used for downsampling to extract high-level features, and the decoder is used for upsampling to restore resolution and perform pixel-level prediction. S2022, Time-domain samples with added Gaussian noise x T The input is fed into the U-Net noise prediction network. x T ∈ R Tin×Fin×Cin ; in, T in Indicates the size of the input time dimension; F in Indicates the size of the input frequency dimension; C in Indicates the number of input channels; R Represents the set of real numbers; S2023, via encoder x T The encoding and encoder calculation formulas are as follows: ； In equation (5), Indicates encoder output characteristics; Encoder Indicates encoding; This represents the output feature at step t-1 of the reverse denoising process; θ Indicates model parameters; S2024, Output features from encoder The input is fed into the decoder, and the decoder calculates it using the following formula: ； in, This indicates the decoder output prediction noise; Decoder Indicates decoding; Indicates encoder output characteristics; θ Indicates model parameters; S2025. Obtain the output predicted noise characteristics of the reverse denoising process. The formula is as follows: ； In equation (7), This represents the output predicted noise feature at step t of the reverse denoising process; This represents the output predicted noise characteristics at step t-1 of the reverse denoising process; This indicates the decoder output prediction noise; t Indicates the number of diffusion steps. t ∈{0, T }; Inverse denoising process network Conditional distributions can be represented by Markov chains as follows: ； in, This represents the conditional distribution of the reverse denoising process from step T to step 0; Indicates the inverse denoising process. t The conditional distribution of the steps; θ Indicates model parameters; This represents the conditional distribution of the reverse denoising process from step t to step t-1.

5. The bearing fault diagnosis method based on dynamic activation mechanism under sample scarcity conditions as described in claim 1, characterized in that, Step S203 specifically includes the following steps: S2031. Constructing the variational lower bound loss function L vlb The calculation formula is: ; In equation (10), θ Indicates model parameters; This represents the conditional distribution of the reverse denoising process from step 1 to step 0; q ( x T () represents the data distribution at step T of the forward diffusion process; q ( x t | x 0) represents the data distribution from step 0 to step t in the forward diffusion process; KL This represents the Kullback-Leibler divergence between two probability distributions; x t This indicates the first step of the forward diffusion process. t The output features of the step, t ∈{0, T }; Indicates the inverse denoising process. t The output features of the step, t ∈{0, T }; q ( x t-1 | x t , x 0) indicates that in the known x Under condition 0, the forward diffusion process from step t-1 to... t Step data distribution; S2032, due to KL ( q ( x T | x 0)|| q ( x T It does not depend on model parameters. θ ,therefore KL ( q ( x T | x 0)|| q ( x T ))≈0; thus further simplifying L vlb The simplified variational lower bound loss function is obtained. L simple The formula is: ； In equation (11), E t Indicates the number of diffusion steps t Expectations t ∈{0, T }; E x0～p(x0) This represents the expected value of the initial weights; x 0~ p ( x 0) indicates the original fault sample. x 0 Obedience p ( x 0) distribution, p ( x 0) is x The distribution of 0; Indicates the desired level of noise; S2033. To constrain the physical characteristics of the vibration signal, a physical loss function is introduced. L physics The calculation formula is: ； In equation (12), M , Q , Y , F For constants, where M Represents the mass matrix, Q Represents the damping matrix. Y Represents the stiffness matrix. F Indicates the load received; S2034, Combining the simplified variational lower bound loss function L simple and physical loss function L physics The loss function is obtained. L The formula is shown below: ； S2035, through the loss function L Constraints are applied to generate sample data that closely approximates real fault data. As shown in the following formula: ； In equation (14), This represents a generated sample that closely approximates real fault data.

6. The bearing fault diagnosis method based on dynamic activation mechanism under sample scarcity conditions as described in claim 1, characterized in that, The operation process of the KAN network without downsampling residual blocks specifically includes: Features of the input , l For each element in the range {1,2,3,4}, both main branch and shortcut branch operations are performed. The features obtained from both operations are summed element-wise, and then the final output is obtained by applying the ReLU activation function. Specifically, the main branch operation includes Conv1×1 compression and dynamically activated convolutional units. KANConv Conv1×1 expansion and BN batch normalization; direct output of quick branch operations. The overall expression for calculating the KAN network's unsampled residual blocks is: ； in, This indicates that the KAN network is computed without downsampling residual blocks; BN ( ) represents batching into a unified operation; Indicates input features, l ∈{1,2,3,4}; KANConv ( ) indicates that the convolutional unit is dynamically activated for computation; Conv ( ) indicates Conv1×1 compression calculation; RELU ( ) serves as a fixed nonlinear activation function; ⊕ indicates element-wise addition; The operation process of downsampling residual blocks in the KAN network specifically includes: Features of the input , l The features obtained from the main branch and shortcut branch operations are summed element-wise for ∈{2,3,4}, and then the final output is obtained by applying the ReLU activation function. The main branch operation is the same as the main branch operation in the KAN network's unsampled residual block. The shortcut branch operation specifically includes Conv1×1 convolution and BN batch normalization. The overall expression for calculating the KAN network's downsampled residual block is: ； in, This indicates the calculation of the downsampled residual block in the KAN network.

7. The bearing fault diagnosis method based on dynamic activation mechanism under sample scarcity conditions as described in claim 6, characterized in that, The KAN network without downsampling residual blocks and the dynamically activated convolutional units in the KAN network downsampling residual blocks. KANConv It consists of a convolutional neural network (CNN) and dynamically activated convolutional layers (KAN); and in the dynamically activated convolutional layers... KANConv Introducing B-spline basis functions B k ( u As a dynamic nonlinear mapping, its standard form is as follows: ； in, B k ( u ) is the k-th order spline basis function; u Indicates the interval of nodes; t k For nodes; For input features Each input feature Corresponding to a set of B-spline basis functions , Indicates the first i one sample k Step B spline k Indicates the order, k The value of must satisfy 2≤ k ≤N+1, where N is the total number of samples; In formulas (22) and (23) ,but: ； in, f i ( x Conv ) represents the location-dependent dynamic B-spline basis function; ω i,k Indicates weight, b i This indicates the bias, where N is the total number of samples; exist f i ( x Conv Based on this, we obtain dynamically activated convolutional units. KANConv By introducing dynamic nonlinear mapping into convolution operations, adaptive activation of bearing vibration signal features is achieved. The calculation process is as follows: ； in, KANConv ( x Conv () indicates that the convolutional unit is dynamically activated for computation. m Indicates the node location; Ω represents the local receptive field; f i ( x Conv ) represents the location-dependent dynamic B-spline basis function; v im Indicates spatial attention weights; x Conv express .

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