Incremental sparse network vibration signal denoising method based on differential attention

Abstract

The invention discloses an incremental sparse network vibration signal denoising method based on differential attention, and belongs to a vibration signal denoising technology. The method comprises the following steps: collecting an original bearing vibration signal, and adding composite noise into the preprocessed signal; combining a sparse connection neural network and a differential attention mechanism to construct a target denoising network; constructing a multi-target loss function, and performing end-to-end training on the target denoising network; inputting a vibration signal to be denoised into the trained denoising network to obtain a high-fidelity denoised signal; and when a new noise type or working condition occurs, incremental updating is performed on the denoising network based on a new sample, network parameters are adjusted through elastic weight consolidation and a knowledge distillation technology, and adaptive optimization and performance improvement of the model are realized. According to the method, denoising parameters do not need to be independently adjusted for different signals, vibration signal denoising in a multi-task scene can be effectively completed, and accurate implementation of subsequent spectrum analysis and intelligent fault diagnosis is facilitated.

Description

Technical Field

[0001] This invention relates to vibration signal denoising technology, and particularly to an incremental sparse network-based vibration signal denoising method based on differential attention. Background Technology

[0002] Accurate fault diagnosis in rotating machinery is crucial for ensuring operational safety and preventing costly downtime in modern industrial systems. However, extracting reliable fault characteristics from bearing vibration signals remains a significant challenge. These signals, generated under complex operating conditions, are highly susceptible to noise contamination. This inherent noise severely masks critical fault characteristics, hindering accurate diagnosis and prediction.

[0003] To address this challenge, effective signal denoising techniques are an essential preprocessing step. While various denoising methods exist, many struggle to adequately preserve the subtle, transient temporal characteristics indicating early faults while effectively suppressing complex noise patterns in real-world scenarios.

[0004] In the field of vibration signal processing, common denoising methods mainly include filtering techniques, wavelet transform, and time-frequency analysis. The core of filtering methods lies in eliminating interference components within a specific frequency range of the signal. Wavelet transform is particularly suitable for processing non-stationary vibration signals, effectively separating useful information from noise. Time-frequency analysis methods, such as Empirical Mode Decomposition (EMD), Variational Mode Decomposition (VMD), and their improved algorithms, are more suitable for signals with strong nonlinearity and non-stationarity, providing more detailed feature representations. For different equipment vibration characteristics, noise types, and signal-to-noise ratio levels, the most suitable denoising strategy should be selected, a process that usually requires expert knowledge. To further improve the adaptive performance of denoising methods, researchers often introduce evaluation criteria such as kurtosis and combine them with parameter optimization algorithms such as genetic algorithms to achieve better noise suppression effects.

[0005] While signal processing-based denoising techniques can effectively suppress noise, they still rely heavily on expert experience when dealing with complex noise scenarios, and their adaptability to diverse noise in varying environments remains limited. In contrast, deep learning methods, in an end-to-end manner, can directly extract features from the original signal and output denoising results. Furthermore, by fusing information such as the characteristics and morphology of noise, they can effectively model uncertainties in the environment, thereby enhancing the robustness and reliability of the denoising system. Therefore, embedding traditional denoising strategies into deep learning models, integrating the advantages of both, can play a significant role in improving denoising accuracy and adaptability. For example, some studies have adopted CNN-based denoising models, extracting features from the signal by constructing multiple convolutional layers and reconstructing the denoised signal using deconvolutional or upsampling layers. In addition, some studies have applied RNNs or Long Short-Term Memory (LSTM) networks to vibration signal denoising. These network structures can capture temporal information in the signal and have good performance in processing continuous vibration signals.

[0006] Existing vibration signal denoising methods still have significant limitations when dealing with non-stationary, strong noise interference, and variable operating conditions, especially in terms of the discriminative ability of signal feature extraction, model generalization, and computational efficiency. Traditional deep learning denoising models often rely on fixed structures, making it difficult to adaptively focus on the differences between key components and noise, and they usually have a large computational burden, limiting their widespread application in real-time monitoring systems. Summary of the Invention

[0007] Purpose of the invention: To address the above problems, the purpose of this invention is to provide an incremental sparse network-based vibration signal denoising method based on differential attention. By introducing a sparse network structure, the method effectively separates signals from noise. At the same time, the differential attention mechanism is introduced to enhance the ability to distinguish useful components from noise in vibration signals. Furthermore, by combining an incremental learning mechanism with a sparse network structure, the method significantly reduces computational resource consumption while improving denoising accuracy, thereby enhancing the adaptability and practicality of the model under different noise environments.

[0008] Technical solution: The present invention provides a method for denoising vibration signals using incremental sparse networks based on differential attention, comprising:

[0009] Raw bearing vibration signals are collected, standardized, and segmented preprocessed. By adding composite noise to the preprocessed signals, complex noise environments in real-world working conditions are simulated, generating noise-clean paired samples for building a signal sample set for model training and validation.

[0010] A target denoising network is constructed by combining sparse connection neural networks and differential attention mechanisms;

[0011] A multi-objective loss function is constructed by combining difference loss, sparse constraint loss and topology regularization loss. The target denoising network is trained end-to-end to simultaneously optimize the denoising effect and model efficiency, resulting in a well-trained denoising network. The input term of the target denoising network is the noisy signal, and the output term is the denoised signal.

[0012] The vibration signal to be denoised is input into the trained denoising network to obtain a high-fidelity denoised signal;

[0013] When new noise types or operating conditions emerge, the denoising network is incrementally updated based on the new samples. The network parameters are adjusted through elastic weight consolidation and knowledge distillation techniques to achieve adaptive optimization and performance improvement of the model.

[0014] Furthermore, the steps for end-to-end training of the target denoising network include:

[0015] Let the noisy signal be ,in For batch size, The signal length is the noisy signal converted from the preprocessed clean signal. By linear superposition of composite noise The noisy signal is then input into a sparsely connected neural network to obtain a denoised signal. , is represented as:

[0016] ,

[0017] in, It is a sparse dictionary designed to capture typical waveforms in bearing vibration signals; sparsity coefficient, The non-zero elements in the signal correspond to the presence of significant fault components.

[0018] Furthermore, by updating the sparse dictionary separately and sparsity coefficient The method for solving its value includes:

[0019] First, fix the sparse dictionary and use the differential attention mechanism to solve for the sparse coefficients;

[0020] Then, with the sparsity coefficients fixed, the sparse dictionary is updated using gradient descent. The updated sparse dictionary is represented as follows:

[0021] ,

[0022] In the formula, The learning rate is used to control the update step size. Represents the gradient operator. This represents the input noisy signal.

[0023] Furthermore, the steps for solving for sparse coefficients using the differential attention mechanism include:

[0024] For the The sparsity coefficient of the wheel and fixed sparse dictionary Calculate the gradient descent step to obtain intermediate feature variables, as shown in the formula:

[0025] ,

[0026] Project intermediate feature variables into a query ,key Sum , respectively represented as:

[0027] ,

[0028] ,

[0029] ,

[0030] In the formula, , , These are the adaptive parameters of the differential attention model.

[0031] The differential attention operator is calculated using the following formula:

[0032] ,

[0033] In the formula, Represents the soft threshold function. The coefficients used to adjust the stepwise characteristics of attention weights are expressed as:

[0034] ,

[0035] In the formula, , , , For learnable vectors, For initialization The constant is controlled between 0 and 1;

[0036] The sparsity coefficients for the current round are calculated using the differential attention operator, and the expression is as follows:

[0037]

[0038] In the formula, This represents the Hadamard product. This represents the regularization parameter.

[0039] Furthermore, composite noise Gaussian noise including pink noise characteristics Power frequency interference noise Baseline drift noise and impulse noise ;

[0040] Composite noise is represented as:

[0041] ,

[0042] In the formula, Represents the original signal. These are the weighting coefficients corresponding to the noise.

[0043] Furthermore, after incrementally updating the denoising network, the final multi-objective loss function of the denoising network is expressed as:

[0044] ,

[0045] In the formula, For the difference loss function, To constrain the loss function, For topological regularization loss, To consolidate losses with elastic weights, This is due to distillation losses; , , These represent the weights of the corresponding loss functions.

[0046] Beneficial effects: Compared with the prior art, the significant advantages of this invention are:

[0047] 1. This invention relies on sparse network design to capture the inherent sparsity characteristics of bearing vibration signals in the transform domain, suppress non-sparse components and retain key features; it introduces a differential attention mechanism to effectively distinguish noise components and useful information in vibration signals; and it combines an incremental learning strategy to gradually optimize the network structure to enhance its adaptability to different noise conditions.

[0048] 2. This invention constructs an end-to-end vibration signal processing framework, which can achieve high-fidelity denoising under low signal-to-noise ratio conditions, improve vibration signal quality, and provide a reliable data foundation for subsequent fault diagnosis and condition monitoring; it can achieve high-quality signal recovery under various noise backgrounds, significantly improving the accuracy and reliability of subsequent fault diagnosis and condition monitoring.

[0049] 3. This invention enhances the ability to distinguish between noise and effective components through differential attention mechanism, utilizes incremental learning strategy to achieve online adaptation to new noise patterns and network structure optimization, and significantly reduces the consumption of computing and storage resources by means of sparse network design. Attached Figure Description

[0050] Figure 1 This is a flowchart of the incremental sparse network vibration signal denoising method based on differential attention according to the present invention.

[0051] Figure 2 This is a visualization of the result of denoising sample 1 using the present invention;

[0052] Figure 3 A visualization of the result after denoising sample 1 using the Unet denoising network;

[0053] Figure 4 This is a visualization of the result of denoising sample 2 using the present invention;

[0054] Figure 5 This is a visualization of the result after denoising sample 2 using the Unet denoising network. Detailed Implementation

[0055] The embodiments of the present invention will be further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely illustrative of the present invention and not intended to limit the scope of the invention. Furthermore, it should be noted that, for ease of description, the accompanying drawings show only the parts relevant to the embodiments of the present invention, and not all structures.

[0056] In the following description, specific details such as target system architecture and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods are omitted so as not to obscure the description of this application with unnecessary detail.

[0057] It should be understood that, when used in this application specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or a collection thereof.

[0058] It should also be understood that the term “and / or” as used in this application specification and the appended claims means any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0059] Furthermore, in the description of this application and the appended claims, the terms "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0060] References to "one embodiment" or "some embodiments" in this specification mean that one or more embodiments of this application include the target features, structures, or characteristics described in connection with that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of this specification do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized.

[0061] The flowchart of the incremental sparse network vibration signal denoising method based on differential attention described in this embodiment is as follows: Figure 1 As shown, the method includes the following steps:

[0062] Step 1: Collect the original bearing vibration signal, standardize and segment it for preprocessing, add composite noise to the preprocessed signal to simulate the complex noise environment in real working conditions, and generate noise-clean paired samples for building the signal sample set for model training and validation.

[0063] The standardization process uses normalization to scale the data to a uniform size for easier subsequent learning. The segmentation process cuts continuous long sequences of signals into fixed-length segments, transforming them into a sample set suitable for network input. To simulate complex noise conditions in real-world operating environments, this example adds composite noise during the noise addition process. To simulate the actual composition of mechanical vibration signals and noise in real-world operating environments, Gaussian noise with pink noise characteristics, power frequency interference noise, baseline drift noise, and impulse noise are added.

[0064] Furthermore, composite noise Gaussian noise including pink noise characteristics Power frequency interference noise Baseline drift noise and impulse noise ;

[0065] Composite noise is represented as:

[0066] ,

[0067] In the formula, Represents the original signal. These are the weighting coefficients corresponding to the noise.

[0068] To generate background noise with spectral characteristics that better match those of the real physical world, Gaussian noise with pink noise characteristics is added to the composite noise, as shown in the following formula:

[0069] ,

[0070] In the formula, This indicates taking the real part of a complex number, because the result after the inverse Fourier transform may be a complex number, but the physical signal is a real signal, so the real part is taken. and These represent the Fourier transform and the inverse Fourier transform, respectively. This represents a Gaussian white noise sequence, where each sampling point independently follows a normal distribution with a mean of 0 and a standard deviation of 1. This represents the actual frequency corresponding to each frequency point after the Fourier transform; As a minimal constant, it prevents the denominator from being zero and ensures the stability of numerical calculations.

[0071] Power frequency interference noise The formula used to simulate the periodic interference introduced by alternating current and its harmonics is as follows:

[0072] ,

[0073] In the formula, It is a preset amplitude coefficient that will be used in subsequent weighting and overall scaling; For interference frequency, It is the sampling point index. Sampling frequency, For phase.

[0074] Baseline drift noise The formula for extremely low-frequency interference caused by sensor temperature drift or slow system variations is as follows:

[0075] ,

[0076] In the formula, It is the amplitude. For the drift frequency, The sampling frequency.

[0077] Pulse noise The formula for simulating instantaneous, high-energy impact events (such as collisions or electric sparks) is as follows:

[0078] ,

[0079] In the formula, Indicates the number of pulses. It is the first The amplitude of each pulse, This is the unit impulse function, used to represent the specific position of the pulse on the time axis; It is the first The location where each pulse occurs This represents the polarity of the pulse.

[0080] Therefore, the formula for calculating the generation of composite noise is as follows:

[0081] ,

[0082] This formula linearly mixes four noise sources with different characteristics in a preset ratio to generate a more realistic and complex composite noise, allowing the denoising model to learn to cope with various interferences. Represents the final synthesized composite noise. Represents the original signal. This represents the weighting ratio of Gaussian noise in the composite noise. This represents the weighting ratio of power frequency interference in the composite noise. This represents the weighting ratio of baseline drift in the composite noise. This represents the weighting ratio of impulse noise in the composite noise.

[0083] Original clean signal In linear superposition of composite noise Noisy signal was then obtained. The formula is as follows:

[0084] .

[0085] Step 2: Construct a target denoising network by combining sparse connection neural networks and differential attention mechanisms.

[0086] Step 3: Construct a multi-objective loss function by combining difference loss, sparse constraint loss, topology regularization loss, and domain-specific loss, and perform end-to-end training on the target denoising network to simultaneously optimize denoising effect and model efficiency, thereby obtaining a trained denoising network; where the input term of the target denoising network is the noisy signal, and the output term is the denoised signal.

[0087] Furthermore, the multi-objective loss function includes difference loss, sparse constraint loss, and topological regularization loss.

[0088] A composite loss function combining difference loss, sparse constraint loss, and topology regularization loss is constructed to train the network end-to-end, thereby simultaneously optimizing denoising performance and model efficiency.

[0089] The expression for the multi-objective loss function is:

[0090] ,

[0091] In the formula, This represents the total loss function of the sparse model. For the difference loss function, Represents sparse constraint loss; Represents the topological regularization loss. and These represent the sparse constraint loss weight and the topological regularization loss weight, respectively.

[0092] The difference loss uses a smoothed L1 loss function because its growth rate decreases from quadratic to linear when the error is large. This makes it less sensitive to impulse noise or outliers in the training data, resulting in a more stable training process that is less prone to large fluctuations due to individual outliers. The formula is:

[0093] ,

[0094] In the formula, It is the sample length. It is the first A clean, original signal. It is the first A denoised signal It is a threshold parameter.

[0095] The sparse constraint loss originates from the mathematical model of compressed sensing, which forces each intermediate representation in the network to be sparsity-constrained. The energy should be minimized so that the model obtains the sparsest solution while satisfying the observation constraints. The expression is:

[0096] ,

[0097] In the formula, Represents the number of network layers. Represents the expectation operator.

[0098] To make the output changes of adjacent network layers smooth and gradual, a topology regularization loss is added to the loss function, expressed as:

[0099] .

[0100] Furthermore, the steps for end-to-end training of the target denoising network include:

[0101] Let the noisy signal be ,in For batch size, The signal length is the noisy signal converted from the preprocessed clean signal. By linear superposition of composite noise The noisy signal is then input into a sparsely connected neural network to obtain a denoised signal. , is represented as:

[0102] ,

[0103] in, It is a sparse dictionary designed to capture typical waveforms in bearing vibration signals; sparsity coefficient, The non-zero elements in the signal correspond to the presence of significant fault components.

[0104] Furthermore, by updating the sparse dictionary separately and sparsity coefficient The method for solving its value includes:

[0105] First, fix the sparse dictionary and use the differential attention mechanism to solve for the sparse coefficients;

[0106] Then, with the sparsity coefficients fixed, the sparse dictionary is updated using gradient descent. The updated sparse dictionary is represented as follows:

[0107] ,

[0108] In the formula, The learning rate is used to control the update step size. Represents the gradient operator. This represents the input noisy signal.

[0109] Furthermore, the steps for solving for sparse coefficients using the differential attention mechanism include:

[0110] For the The sparsity coefficient of the wheel and fixed sparse dictionary Calculate the gradient descent step to obtain intermediate feature variables, as shown in the formula:

[0111] ,

[0112] Project intermediate feature variables into a query ,key Sum , respectively represented as:

[0113] ,

[0114] ,

[0115] ,

[0116] In the formula, , , These are the adaptive parameters of the differential attention model.

[0117] The differential attention operator is calculated using the following formula:

[0118] ,

[0119] In the formula, Represents the soft threshold function. The coefficients used to adjust the stepwise characteristics of attention weights are expressed as:

[0120] ,

[0121] In the formula, , , , For learnable vectors, For initialization The constant is controlled between 0 and 1;

[0122] The sparsity coefficients for the current round are calculated using the differential attention operator, and the expression is as follows:

[0123]

[0124] In the formula, This represents the Hadamard product. This represents the regularization parameter.

[0125] Step 4: Input the vibration signal to be denoised into the trained denoising network to obtain a high-fidelity denoised signal.

[0126] Step 5: When a new type of noise or operating condition appears, the denoising network is incrementally updated based on the new samples. The network parameters are adjusted through elastic weight consolidation and knowledge distillation techniques to achieve adaptive optimization and performance improvement of the model.

[0127] Furthermore, after incrementally updating the denoising network, the final multi-objective loss function of the denoising network is expressed as:

[0128] ,

[0129] In the formula, For the difference loss function, To constrain the loss function, For topological regularization loss, To consolidate losses with elastic weights, This is due to distillation losses; , , These represent the weights of the corresponding loss functions.

[0130] When encountering new noise types or operating conditions, the network is incrementally updated based on new samples without complete retraining. Only some parameters are fine-tuned or a small number of network nodes are expanded to achieve adaptive optimization and performance improvement of the model.

[0131] After the incremental update, an elastic weighted consolidation loss was added to the original total loss function. and distillation loss Among them, the elastic weighted consolidation loss can autonomously adjust the update rate of important parameters by calculating their importance, and its expression is:

[0132] ,

[0133] In the formula, Used to control the strength of elastic weight consolidation regularization. Representing the A Fisher information matrix with parameters is used to calculate the expected value of the gradient bifurcation on old task data. This is the current parameter value. These are the optimal parameter values ​​for the old task.

[0134] Knowledge distillation, widely used in incremental learning, is also incorporated. It allows the model to mimic the behavior and output of older models while learning new tasks, resulting in a new model that performs well on both tasks. A feature-matching-based distillation loss is used to accurately reconstruct individual samples, expressed as:

[0135] ,

[0136] In the formula, Represents batch size. Represents the characteristic length. The student model is in the first The sample at the th Output in each dimension The representative teacher model in the The sample at the th Output in each dimension This is a temperature parameter used to control the output difference of knowledge distillation. The student model refers to the denoising network learning a new task; it needs to learn the signal characteristics of new noise types or operating conditions without forgetting existing knowledge. The teacher model refers to the pre-trained denoising network, which has already mastered the knowledge of previous tasks.

[0137] Simultaneously, the relative relationships between samples are learned using a relation-preserving distillation loss.

[0138] ,

[0139] In the formula, Represents a similarity measurement function. The complete output represents the student model. This represents the complete output of the teacher model.

[0140] The final result is the total distillation loss, using and The weights for accurately reconstructing individual samples and the weights for the structural relationships between samples are respectively controlled as follows:

[0141] .

[0142] To fully verify the superiority of the denoising method described in this invention, it is compared with the existing Unet denoising network. Figures 2 to 5 The diagram shows a comparison of the spectra of two different samples after denoising under -5dB noise using an existing denoising method (Unet denoising network) and the denoising method of this invention. The blue, green, and red waveforms in the time-domain waveforms on the left side of each sub-plot represent the noisy, clean, and denoised vibration signals, respectively. Figure 2 and Figure 4 The images shown are visualizations of the denoising results for Sample 1 and Sample 2 using the method described in this invention. Figure 3 and Figure 5 The denoising results for samples 1 and 2 are visualized using the U-Net network. As can be seen from the figures, for the same noisy signal, the denoising method described in this invention outperforms U-Net, and the waveform of the noisy signal is essentially restored to the clarity and accuracy of the original signal. The right side of each sub-figure shows the wavelet scale diagram of the vibration signal. A comparison demonstrates that the method described in this invention retains the time-frequency characteristics of the original signal after denoising, showing superior fidelity compared to the contrasting methods.

[0143] The method described in this invention was applied to noisy vibration signals and compared with the existing Unet denoising network. Tables 1 and 2 show the denoising effects of the two methods on dynamic vibration signal noise datasets with different signal-to-noise ratio ranges.

[0144] Table 1. Denoising evaluation indicators of the denoising method of the present invention under different signal-to-noise ratio ranges.

[0145]

[0146] Table 2. Denoising evaluation metrics of Unet network under different signal-to-noise ratio ranges

[0147]

[0148] As shown in Tables 1 and 2, both models strictly adhere to the fundamental principle that "noise intensity is negatively correlated with performance." Under the extreme noise condition of (20,5), all error indicators (sum of squared errors SSD / maximum absolute errors MAD / percentage root mean square errors PRD) reach their peaks, while the quality indicators (cosine similarity COS_SIM / peak signal-to-noise ratio PSNR) are at their lowest points. As the signal-to-noise ratio range increases to (0,5), U-Net's PRD decreases from 107.34% to 61.31%, and DMDA decreases from 88.94% to 54.54%, representing reductions of 46.03% and 36.41%, respectively. This demonstrates that noise intensity is the primary factor affecting denoising performance. Overall, this invention outperforms U-Net across all five signal-to-noise ratio ranges, particularly in the -10dB to 0dB noise band.

Claims

1. A method for denoising vibration signals using incremental sparse networks based on differential attention, characterized in that, include: Raw bearing vibration signals are collected, standardized, and segmented preprocessed. By adding composite noise to the preprocessed signals, complex noise environments in real-world working conditions are simulated, generating noise-clean paired samples for building a signal sample set for model training and validation. A target denoising network is constructed by combining sparse connection neural networks and differential attention mechanisms; A multi-objective loss function is constructed by combining difference loss, sparse constraint loss and topology regularization loss. The target denoising network is trained end-to-end to simultaneously optimize the denoising effect and model efficiency, resulting in a well-trained denoising network. The input term of the target denoising network is the noisy signal, and the output term is the denoised signal; The vibration signal to be denoised is input into the trained denoising network to obtain a high-fidelity denoised signal; When new noise types or operating conditions emerge, the denoising network is incrementally updated based on the new samples. The network parameters are adjusted through elastic weight consolidation and knowledge distillation techniques to achieve adaptive optimization and performance improvement of the model.

2. The incremental sparse network vibration signal denoising method based on differential attention according to claim 1, characterized in that, The steps for end-to-end training of the target denoising network include: Let the noisy signal be ,in For batch size, The signal length is the noisy signal converted from the preprocessed clean signal. By linear superposition of composite noise The noisy signal is then input into a sparsely connected neural network to obtain a denoised signal. , is represented as: ， in, It is a sparse dictionary designed to capture typical waveforms in bearing vibration signals; sparsity coefficient, The non-zero elements in the signal correspond to the presence of significant fault components.

3. The incremental sparse network vibration signal denoising method based on differential attention according to claim 2, characterized in that, By updating the sparse dictionary separately and sparsity coefficient The method for solving its value includes: First, fix the sparse dictionary and use the differential attention mechanism to solve for the sparse coefficients; Then, with the sparsity coefficients fixed, the sparse dictionary is updated using gradient descent. The updated sparse dictionary is represented as follows: ， In the formula, The learning rate is used to control the update step size. Represents the gradient operator, This represents the input noisy signal.

4. The incremental sparse network vibration signal denoising method based on differential attention according to claim 3, characterized in that, The steps for solving sparse coefficients using the differential attention mechanism include: For the The sparsity coefficient of the wheel and fixed sparse dictionary Calculate the gradient descent step to obtain intermediate feature variables, as shown in the formula: ， Project intermediate feature variables into a query ,key Sum , respectively represented as: ， ， ， In the formula, , , These are the adaptive parameters of the differential attention model. The differential attention operator is calculated using the following formula: ， In the formula, Represents the soft threshold function. The coefficients used to adjust the stepwise characteristics of attention weights are expressed as: ， In the formula, , , , For learnable vectors, For initialization The constant is controlled between 0 and 1; The sparsity coefficients for the current round are calculated using the differential attention operator, and the expression is as follows: In the formula, This represents the Hadamard product. This represents the regularization parameter.

5. The incremental sparse network vibration signal denoising method based on differential attention according to claim 1, characterized in that, Composite noise Gaussian noise including pink noise characteristics Power frequency interference noise Baseline drift noise and impulse noise ; Composite noise is represented as: ， In the formula, Represents the original signal. These are the weighting coefficients corresponding to the noise.

6. The incremental sparse network vibration signal denoising method based on differential attention according to claim 1, characterized in that, After incremental updates to the denoising network, the final multi-objective loss function of the denoising network is expressed as: ， In the formula, For the difference loss function, To constrain the loss function, For topological regularization loss, To consolidate losses with elastic weights, This is due to distillation losses; , , These represent the weights of the corresponding loss functions.

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