A machine learning-based vibration signal denoising reconstruction method, device and medium

By using adaptive time-frequency decomposition and unsupervised generative adversarial networks, the noisy dominant components in the rolling bearing vibration signal are identified and preserved, solving the problem of noise suppression and fault feature preservation in the prior art, and realizing high-quality signal denoising and fault diagnosis under complex working conditions.

CN121542576BActive Publication Date: 2026-04-07WEIFANG FULAIRUI ELECTRONICS TECH CO LTD
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Patent Information

Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2026-01-19
Publication Date
2026-04-07

AI Technical Summary

Technical Problem

Existing technologies struggle to effectively separate non-stationary noise and fault impact components from rolling bearing vibration signals under complex operating conditions, resulting in weak fault characteristics and extremely low signal-to-noise ratios. Existing methods, while suppressing noise, weaken or eliminate weak fault harmonics and envelope characteristics, failing to improve fault diagnosis reliability in the absence of pure labels.

Method used

An adaptive time-frequency decomposition method is used to identify noisy dominant components. An unsupervised generative adversarial network is constructed. By jointly optimizing the adversarial loss and the frequency domain perception loss, the key impact features of rolling bearing faults are preserved. An unsupervised generative adversarial network is constructed and the frequency domain perception loss is introduced. The network is constrained by the pre-trained fault feature extraction method to output a high-quality denoised signal.

Benefits of technology

While effectively suppressing complex noise, it adaptively preserves high-frequency impact and modulation characteristics related to bearing geometry and defect types, significantly improving the reliability of subsequent fault diagnosis. It does not rely on clean labels and is suitable for unsupervised, high-fidelity vibration signal denoising in industrial settings.

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Abstract

This application discloses a vibration signal denoising and reconstruction method, device, and medium based on machine learning, relating to the field of data processing technology. The method includes: firstly, adaptive time-frequency decomposition of the original signal; then, identification of the noisy dominant component based on energy entropy and kurtosis; subsequently, constructing a generative adversarial network (GAN) and performing denoising by jointly optimizing adversarial loss and frequency-domain perceptual loss. The frequency-domain perceptual loss utilizes a convolutional network pre-trained on bearing fault data to extract high-level semantic features, ensuring the preservation of high-frequency impact and modulation features related to bearing structure and defect type; finally, reconstructing the denoised component with the remaining components to output a high-quality signal. This method does not require clean labels, effectively suppressing complex noise while improving the reliability of fault diagnosis.
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Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of data processing, and particularly relates to a vibration signal denoising reconstruction method based on machine learning, a device and a medium. BACKGROUND

[0002] In the condition monitoring of rotating machinery, the health status of rolling bearings as key supporting components directly affects the safety and service life of equipment. Vibration signal analysis is the mainstream means of rolling bearing fault diagnosis, and through the detection of periodic impact characteristics caused by inner ring, outer ring or rolling body defects, early fault warning can be realized. However, under complex working conditions such as high speed, heavy load or poor lubrication, the bearing vibration signal is often severely masked by strong background noise, gear meshing interference and vibration of other components, resulting in weak fault characteristics and extremely low signal-to-noise ratio.

[0003] Existing denoising methods such as wavelet threshold, empirical mode decomposition (EMD) or traditional filters are difficult to effectively separate non-stationary noise and bearing fault impact components, and are prone to cause feature loss or artifact introduction; while the supervised denoising model based on deep learning has superior performance, but it relies on a large number of paired "clean-noisy" bearing vibration signals for training. Since the actual running rolling bearings cannot obtain the corresponding pure signals once a fault occurs, and there are significant domain differences between laboratory simulation signals and field data, the generalization ability of such models is insufficient in real scenarios. More importantly, existing methods generally use global reconstruction loss (such as MSE), which is not optimized for the high-frequency impact characteristics specific to rolling bearing faults, and often smooths the noise while weakening or even eliminating the weak fault harmonics and envelope features.

[0004] Therefore, under the condition of lacking pure labels, how to construct an unsupervised denoising reconstruction method for rolling bearing vibration signals, so that it can effectively suppress complex noise while adaptively preserving high-frequency impact and modulation features related to bearing geometry and defect type, thereby improving the reliability of subsequent fault diagnosis, is a problem to be solved at present. SUMMARY

[0005] The embodiment of the present application provides a vibration signal denoising reconstruction method based on machine learning, a device and a medium, and mainly aims to construct an unsupervised denoising reconstruction method for rolling bearing vibration signals, so that it can effectively suppress complex noise while adaptively preserving high-frequency impact and modulation features related to bearing geometry and defect type, thereby improving the reliability of subsequent fault diagnosis.

[0006] In the first aspect, the embodiment of the present application provides a vibration signal denoising reconstruction method based on machine learning, and the method comprises the following steps:

[0007] perform adaptive time-frequency decomposition on the original vibration signal to obtain a plurality of component signals;

[0008] identify a noisy dominant component from the component signals based on a preset noise sensitivity index;

[0009] construct an unsupervised generative adversarial network and train the generative adversarial network based on the noisy dominant component, wherein in the training process, the generative adversarial network retains key impact features of rolling bearing fault by jointly optimizing an adversarial loss and a frequency domain perception loss;

[0010] de-noise the noisy dominant component based on the trained generative adversarial network to obtain a de-noised component;

[0011] reconstruct the de-noised component and the remaining component signals to output a de-noised rolling bearing vibration signal.

[0012] In an implementation manner of the present application, the adaptive time-frequency decomposition of the original vibration signal to obtain a plurality of component signals comprises:

[0013] calculate the envelope spectrum entropy of the original vibration signal to represent the frequency band complexity;

[0014] construct a fitness function of a particle swarm optimization algorithm based on the envelope spectrum entropy;

[0015] search for an optimal variational mode decomposition parameter combination including decomposition layer number and quadratic penalty factor through the fitness function;

[0016] perform variational mode decomposition on the optimal variational mode parameter combination to generate a plurality of component signals with different center frequencies and bandwidths.

[0017] In an implementation manner of the present application, the identification of a noisy dominant component from the component signals based on a preset noise sensitivity index comprises:

[0018] calculate the energy entropy of each component signal to measure the concentration degree of energy distribution, and calculate the kurtosis of each component signal to evaluate its impact characteristics;

[0019] set a first threshold corresponding to the energy entropy and a second threshold corresponding to the kurtosis, wherein the first threshold is obtained according to historical normal working condition data statistics, and the second threshold is dynamically adjusted according to the upper limit of Gaussian white noise theory;

[0020] select a target component signal with energy entropy higher than the first threshold and kurtosis lower than the second threshold from the component signals, and mark the target component signal as a noisy dominant component.

[0021] In one implementation of this application, the construction of the unsupervised generative adversarial network includes:

[0022] The generator is constructed as a network structure consisting of multiple cascaded one-dimensional residual shrink blocks;

[0023] A channel attention mechanism is integrated into each residual shrinking block to obtain the generative adversarial network, wherein the attention mechanism is used to adaptively weight the importance of different feature channels;

[0024] The discriminator is constructed as a temporal discriminant network containing multiple layers of one-dimensional convolution and nonlinear activation functions, and the generative adversarial network is formed based on the generator and the discriminator;

[0025] Training the generative adversarial network based on the noisy dominant component includes:

[0026] The noisy dominant component is input into the generator, and each residual shrinking block in the generator receives the feature sequence output from the previous stage as input.

[0027] In each residual shrinkage block, a one-dimensional convolution operation is performed on the input feature sequence to extract local temporal features and obtain an intermediate feature map;

[0028] Based on the intermediate feature map, channel attention weights are calculated to generate a soft threshold vector that matches the number of channels;

[0029] The intermediate feature map is shrunk channel by channel using the soft threshold vector to suppress noise-related features;

[0030] The shrunk feature map is added to the input feature sequence to form the corresponding output of the residual shrunk block;

[0031] The feature sequence output by the last residual shrinking block is used as the denoised signal to obtain the denoised component;

[0032] The denoised component and the noisy dominant component are respectively input into the discriminator. By minimizing the adversarial loss of the generator and the discrimination loss of the discriminator, the adversarial training of the generative adversarial network is completed.

[0033] In one implementation of this application, the key impact features of rolling bearing failure are preserved by jointly optimizing adversarial loss and frequency domain sensing loss, including:

[0034] A one-dimensional convolutional neural network is pre-trained on a public dataset of rolling bearings as a bearing fault feature extraction network. The bearing fault feature extraction network contains multiple layers of one-dimensional convolution and max pooling operation layers. The bearing fault feature extraction network is used to extract discriminative fault features of vibration signals in the time domain and frequency domain step by step. The bearing fault feature extraction network is embedded in the loss calculation module of the generative adversarial network. The weight parameters of the bearing fault feature extraction network are in a frozen state.

[0035] The noisy dominant component and the generator output corresponding to the noisy dominant component are respectively input into the bearing fault feature extraction network, and the high-level semantic feature representations of the two are obtained through forward propagation.

[0036] The frequency domain perceptual loss is calculated based on the difference between the high-level semantic feature representations of the two, and the adversarial loss is calculated based on the output of the discriminator.

[0037] By jointly optimizing the adversarial loss and the frequency domain perception loss, key impact features of rolling bearing failures can be preserved.

[0038] In one implementation of this application, calculating the frequency domain sensing loss includes:

[0039] The high-level semantic features are represented as feature maps output by the bearing fault feature extraction network in the deep convolutional layer.

[0040] The frequency domain perceptual loss is obtained by calculating the Euclidean distance between the noisy dominant component and the generator output in the corresponding feature map.

[0041] The frequency domain sensing loss and the adversarial loss are weighted and summed to update the generator parameters based on the calculation results.

[0042] In one implementation of this application, after outputting the denoised rolling bearing vibration signal, the method further includes:

[0043] The denoised rolling bearing vibration signal is input into a pre-trained multi-class fault classification model.

[0044] The fault classification model is constructed based on a deep convolutional or Transformer architecture. The fault classification model is used to distinguish the normal state, inner ring fault, outer ring fault and rolling element fault of the rolling bearing.

[0045] The confidence probability distribution output by the fault classification model is analyzed to obtain the confidence level corresponding to each fault category;

[0046] When the confidence level of any of the aforementioned fault categories exceeds a preset warning threshold, a maintenance warning mechanism is triggered to generate warning information containing the fault type, confidence level, and timestamp.

[0047] The early warning information is uploaded to the equipment health management platform via industrial communication protocols for maintenance personnel to use as a reference for decision-making.

[0048] In one implementation of this application, the acquisition of the raw vibration signal during the operation of the rolling bearing includes:

[0049] The original vibration signal is acquired within a preset acquisition duration based on a preset acquisition frequency;

[0050] The acquired original vibration signal is preprocessed with anti-aliasing filtering and zero-mean normalization to improve the quality of the original vibration signal during subsequent adaptive time-frequency decomposition.

[0051] Secondly, embodiments of this application also provide a vibration signal denoising and reconstruction device based on machine learning. The device includes: at least one processor; and a memory communicatively connected to the at least one processor. The memory stores instructions executable by the at least one processor, which, when executed, enable the at least one processor to: acquire the original vibration signal of a rolling bearing during operation; perform adaptive time-frequency decomposition on the original vibration signal to obtain multiple component signals; identify the noisy dominant component from the component signals based on a preset noise sensitivity index; construct an unsupervised generative adversarial network (GAN), and train the GAN based on the noisy dominant component. During training, the GAN retains key impact features of rolling bearing failures by jointly optimizing adversarial loss and frequency domain perception loss; denoise the noisy dominant component based on the trained GAN to obtain a denoised component; and reconstruct the signal by combining the denoised component with the remaining component signals to output the denoised rolling bearing vibration signal.

[0052] Thirdly, embodiments of this application also provide a non-volatile computer storage medium for vibration signal denoising and reconstruction based on machine learning, storing computer-executable instructions. These instructions are configured to: acquire the original vibration signal of a rolling bearing during operation; perform adaptive time-frequency decomposition on the original vibration signal to obtain multiple component signals; identify the noisy dominant component from the component signals based on a preset noise sensitivity index; construct an unsupervised generative adversarial network (GAN), and train the GAN based on the noisy dominant component. During training, the GAN retains key impact features of rolling bearing failures by jointly optimizing adversarial loss and frequency domain perception loss; denoise the noisy dominant component based on the trained GAN to obtain a denoised component; and reconstruct the signal by combining the denoised component with the remaining component signals to output the denoised rolling bearing vibration signal.

[0053] This application provides a vibration signal denoising and reconstruction method, device, and medium based on machine learning, which has the following beneficial effects: By adaptively decomposing the original vibration signal into time-frequency components, the complex signal is broken down into multiple components with different frequency band characteristics; then, based on noise-sensitive indicators such as energy entropy and kurtosis, the noisy dominant component that concentrates the main noise energy is accurately identified, achieving targeted processing and avoiding accidental damage to potential fault components; on this basis, an unsupervised generative adversarial network is constructed, and a frequency domain-aware loss is introduced. This loss uses a one-dimensional convolutional neural network with pre-trained and frozen weights on the Case Western Reserve University rolling bearing dataset as a fault semantic extractor, forcing the denoising result to be consistent with the noisy input in the high-level feature space, thereby ensuring that high-frequency transient impact and modulation features strongly correlated with bearing geometry (such as inner ring, outer ring, rolling elements) and defect types are adaptively preserved; finally, only the noisy dominant component is denoised, and it is reconstructed with the remaining unprocessed components to output a high-quality denoised signal. This method does not rely on clean labels and effectively suppresses non-stationary and non-Gaussian complex noise while significantly improving the reliability of subsequent fault diagnosis, thus effectively responding to the urgent need in industrial sites for unsupervised, high-fidelity vibration signal denoising technology. Attached Figure Description

[0054] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings:

[0055] Figure 1 A flowchart of a vibration signal denoising and reconstruction method based on machine learning is provided for embodiments of this application;

[0056] Figure 2 This is a schematic diagram of the internal structure of a vibration signal denoising and reconstruction device based on machine learning, provided as an embodiment of this application. Detailed Implementation

[0057] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions of this application will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0058] This application provides a vibration signal denoising and reconstruction method, device, and medium based on machine learning to achieve the following technical effects: constructing an unsupervised denoising and reconstruction method for rolling bearing vibration signals, which can effectively suppress complex noise while adaptively retaining high-frequency impact and modulation features related to bearing geometry and defect types, thereby improving the reliability of subsequent fault diagnosis.

[0059] The technical solutions proposed in the embodiments of this application will be described in detail below with reference to the accompanying drawings.

[0060] Figure 1 This document presents a flowchart of a vibration signal denoising and reconstruction method based on machine learning, as provided in an embodiment of this application. Figure 1 As shown in the figure, the vibration signal denoising and reconstruction method based on machine learning provided in this application embodiment specifically includes the following steps:

[0061] Step 101: Collect the raw vibration signal of the rolling bearing during operation;

[0062] In some embodiments, an accelerometer is installed on the bearing housing housing to continuously acquire the original vibration signal of the rolling bearing under normal or suspected fault conditions at a sampling frequency of not less than 12 kHz, with an acquisition time of not less than 0.5 seconds. After acquisition, the signal is preprocessed with anti-aliasing low-pass filtering and zero-mean normalization to eliminate DC offset and adapt to the input requirements of subsequent algorithms.

[0063] Step 102: Perform adaptive time-frequency decomposition on the original vibration signal to obtain multiple component signals;

[0064] In some embodiments, the envelope spectral entropy of the original vibration signal is calculated to quantify its frequency band complexity; a fitness function for a particle swarm optimization (PSO) algorithm is constructed based on this entropy value; and the optimal combination of variational mode decomposition (VMD) parameters, including the number of decomposition layers, is automatically searched using this fitness function. K and secondary penalty factor α VMD is performed using optimal parameters to decompose the original signal into... KA series of intrinsic mode components with different center frequencies and bandwidths, i.e., multiple component signals.

[0065] Step 103: Identify the noisy dominant component from the component signal based on a preset noise sensitivity index;

[0066] In some embodiments, the energy entropy (reflecting the degree of energy distribution concentration) and kurtosis (reflecting the impact characteristics) of each component signal are calculated separately; a first threshold for energy entropy (statistically derived from historical normal operating data) and a second threshold for kurtosis (dynamically adjusted according to the theoretical upper limit of Gaussian white noise) are set; components with energy entropy higher than the first threshold and kurtosis lower than the second threshold are selected and marked as noisy dominant components.

[0067] Step 104: Construct an unsupervised generative adversarial network and train the generative adversarial network based on the noisy dominant component. During the training process, the generative adversarial network retains the key impact features of rolling bearing failure by jointly optimizing the adversarial loss and the frequency domain perception loss.

[0068] In some embodiments, the generator consists of multiple cascaded one-dimensional residual shrinking blocks, each integrating a channel attention mechanism to generate a soft threshold for feature shrinkage; the discriminator employs a one-dimensional convolutional network structure; during training, only the noisy dominant component is used as input, without the need for clean labels; the loss function consists of a weighted adversarial loss and a frequency-domain perceptual loss, the latter being computed through a fault feature extraction network pre-trained on the Case Western Reserve University bearing dataset with frozen weights, ensuring that the denoising process preserves semantic features related to bearing defects.

[0069] Step 105: Denoise the noisy dominant component based on the trained generative adversarial network to obtain the denoised component;

[0070] In some embodiments, the noisy dominant component to be processed is input into the trained generator; the signal passes through residual shrinking blocks at each level in sequence, and is connected to the residuals by soft threshold shrinking guided by channel attention, and finally outputs the denoised component, i.e. the denoised component, whose dimension is consistent with the input and retains the original impact transient characteristics.

[0071] Step 106: Reconstruct the denoised component and the remaining component signals to output the denoised rolling bearing vibration signal.

[0072] In some embodiments, the denoised component obtained in step 105 is linearly superimposed (i.e., summed and reconstructed) with the remaining component signals that were not identified as noise-dominant in step 102 to restore the complete frequency band information; the output reconstructed signal is the final denoised rolling bearing vibration signal, which can be directly used for subsequent fault diagnosis or condition monitoring.

[0073] This application provides a vibration signal denoising and reconstruction method based on machine learning, which has the following advantages: By performing adaptive time-frequency decomposition on the original vibration signal, the complex signal is decomposed into multiple components with different frequency band characteristics; then, based on noise-sensitive indicators such as energy entropy and kurtosis, the noisy dominant component that concentrates the main noise energy is accurately identified, achieving targeted processing and avoiding accidental damage to potential fault components; on this basis, an unsupervised generative adversarial network is constructed, and a frequency domain-aware loss is introduced. This loss uses a one-dimensional convolutional neural network with pre-trained and frozen weights on the Case Western Reserve University rolling bearing dataset as a fault semantic extractor, forcing the denoising result to be consistent with the noisy input in the high-level feature space, thereby ensuring that high-frequency transient impact and modulation features strongly correlated with bearing geometry (such as inner ring, outer ring, rolling elements) and defect type are adaptively preserved; finally, only the noisy dominant component is denoised, and it is reconstructed with the remaining unprocessed components to output a high-quality denoised signal. This method does not rely on clean labels and effectively suppresses non-stationary and non-Gaussian complex noise while significantly improving the reliability of subsequent fault diagnosis, thus effectively responding to the urgent need in industrial sites for unsupervised, high-fidelity vibration signal denoising technology.

[0074] As a refinement of the above embodiments, when performing the adaptive time-frequency decomposition of the original vibration signal in step 102 to obtain multiple component signals, the following implementation methods can also be adopted, but are not limited to: calculating the envelope spectrum entropy of the original vibration signal to characterize the frequency band complexity; constructing a fitness function for a particle swarm optimization algorithm based on the envelope spectrum entropy; iteratively searching for the optimal variational mode decomposition parameter combination through the fitness function, wherein the variational mode decomposition parameter combination includes the number of decomposition layers and a quadratic penalty factor; performing variational mode decomposition on the optimal variational mode parameter combination to generate multiple component signals with different center frequencies and bandwidths.

[0075] In some embodiments, firstly, the acquired raw vibration signal is processed. x ( t The signal is obtained by performing a Hilbert transform and calculating the envelope signal. Then, a Fourier transform is performed on the envelope signal to obtain the envelope spectrum. Based on the envelope spectrum, the envelope spectrum entropy (ESE) is calculated to quantitatively characterize the complexity of the signal's frequency band energy distribution. A higher entropy value indicates a more dispersed spectrum and more significant noise components. Next, a particle swarm optimization (PSO) is constructed with the goal of minimizing the envelope spectrum entropy: each particle represents a set of VMD parameters (number of decomposition layers). K and secondary penalty factor α The fitness value is the envelope spectral entropy of the reconstructed signal after each modal component obtained from VMD decomposition under the corresponding parameters. The PSO algorithm is used in a pre-defined search space (e.g., ...). Intra-iterative optimization to find the parameter combination that minimizes the fitness function. Finally, this optimal parameter combination is input into the variational mode decomposition (VMD) algorithm to decompose the original vibration signal and output the result. Each of the intrinsic mode components (IMFs) has a compact center frequency and bandwidth, collectively forming a multi-scale time-frequency representation of the original signal. For example, in the signal processing of a bearing with an outer race fault, this method automatically determines... , The fault component containing periodic impacts and the broadband noise-dominant component were successfully separated, laying the foundation for subsequent accurate identification of the noisy dominant component.

[0076] As a refinement of the above embodiments, when performing step 103, which involves identifying the noisy dominant component from the component signals based on a preset noise sensitivity index, the following implementation methods can also be adopted, but are not limited to: calculating the energy entropy of each component signal to measure the concentration of energy distribution, and calculating the kurtosis of each component signal to evaluate its impact characteristics; setting a first threshold corresponding to the energy entropy and a second threshold corresponding to the kurtosis, wherein the first threshold is statistically derived based on historical normal operating data, and the second threshold is dynamically adjusted based on the theoretical upper limit of Gaussian white noise; filtering out target component signals among the component signals whose energy entropy is higher than the first threshold and whose kurtosis is lower than the second threshold, and marking the target component signals as the noisy dominant component.

[0077] For example, the original vibration signal is decomposed into six component signals {IMF1, IMF2, ..., IMF6} through adaptive time-frequency decomposition. For each IMF1, its energy entropy is first calculated: the signal is divided into several time windows, the energy of each window is calculated and normalized, and then substituted into the following Shannon entropy formula:

[0078]

[0079] Wherein, p j Let be the energy percentage of the j-th window; a higher energy entropy indicates a more dispersed energy distribution in the time domain, and is more likely to be broadband noise. Simultaneously, the kurtosis of this component is calculated based on the following formula:

[0080]

[0081] Where K represents the kurtosis value; x represents the amplitude of a single sampling point of the vibration signal; and μ represents the mean of the signal. This represents the mathematical expectation operation.

[0082] Kurtosis reflects the presence of significant transient impacts in a signal. Real bearing faults typically exhibit high kurtosis (>5), while pure noise kurtosis is close to 3 (the theoretical value of a Gaussian distribution). First threshold (e.g., H...)th =2.8) is obtained by analyzing a large number of component signals of similar equipment under historical normal operating conditions; the second threshold (such as K) is obtained by statistical analysis. th =3.5) is dynamically set based on the upper limit of kurtosis of Gaussian white noise at a 95% confidence level (considering sampling length correction). Then, joint discrimination is performed: if a component satisfies energy entropy > 2.8 and kurtosis < 3.5, its main component is determined to be random noise with no significant fault impact. For example, in one experiment, IMF3 had an energy entropy of 3.1 and a kurtosis of 2.9, and was identified as the noisy dominant component; while IMF5 had an energy entropy of 1.9 and a kurtosis of 6.7, and was retained as a potential fault component. Finally, only IMF3 is input into the generative adversarial network for denoising, while the remaining components directly participate in subsequent reconstruction, thus effectively protecting the high-frequency impact characteristics related to bearing defects while suppressing noise.

[0083] As a refinement of the above embodiments, when constructing the unsupervised generative adversarial network in step 104, the following implementation methods can also be adopted, but are not limited to: constructing the generator as a network structure composed of multiple cascaded one-dimensional residual shrinking blocks; integrating a channel attention mechanism in each residual shrinking block to obtain the generative adversarial network, wherein the attention mechanism is used to adaptively weight the importance of different feature channels; constructing a discriminator as a temporal discriminator network containing multiple layers of one-dimensional convolution and nonlinear activation functions, and forming the generative adversarial network based on the generator and the discriminator; the step of training the generative adversarial network based on the noisy dominant component includes: inputting the noisy dominant component into the generator, wherein each residual shrinking block in the generator receives the features output by the previous stage. The sequence is used as input; in each residual shrinking block, a one-dimensional convolution operation is performed on the input feature sequence to extract local temporal features and obtain an intermediate feature map; channel attention weights are calculated based on the intermediate feature map to generate a soft threshold vector matching the number of channels; the intermediate feature map is shrunk channel by channel using the soft threshold vector to suppress noise-related features; the shrunk feature map is added to the input feature sequence to form the corresponding output of the residual shrinking block; the feature sequence output by the last residual shrinking block is used as the denoised signal to obtain the denoised component; the denoised component and the noisy dominant component are respectively input into the discriminator, and the adversarial training of the generative adversarial network is completed by minimizing the adversarial loss of the generator and the discrimination loss of the discriminator.

[0084] In some embodiments, the generator is designed to consist of six cascaded one-dimensional residual shrinking blocks, each receiving the feature sequence output from the previous stage as input. Within each block, local temporal features are first extracted using a one-dimensional convolutional layer (e.g., a kernel size of 9 and 64 channels) to obtain an intermediate feature map. Subsequently, this feature map undergoes global average pooling, and channel attention weights are calculated via two fully connected layers (containing ReLU and Sigmoid activations) to generate a soft thresholding vector matching the number of channels. This vector is then used to perform channel-by-channel soft thresholding shrinking on the intermediate feature map (i.e.,...). ,in F For feature maps, τ The generator uses a soft threshold to adaptively suppress noise-related features. Finally, the shrunk feature map is added to the original input feature sequence to complete residual learning and output the feature representation of the block. The feature sequence output by the last residual shrinking block is the denoised component, which effectively retains the fault impact component in the original noisy dominant component while significantly reducing random noise interference. The training of the generator adversarial network includes: inputting the noisy dominant component into the generator to obtain the denoised component; inputting the denoised component and the noisy dominant component into a discriminator, which is a temporal discriminator network containing multiple layers of one-dimensional convolution and nonlinear activation functions; calculating the adversarial loss based on the output of the discriminator and constructing the joint loss function of the generator by combining a preset frequency domain perception loss (calculated through a frozen bearing fault feature extraction network); minimizing the joint loss function through backpropagation to update the generator parameters and simultaneously update the discriminator parameters to optimize its adversarial discrimination capability, thereby completing the adversarial training of the generator adversarial network.

[0085] In some embodiments, preserving key impact features of rolling bearing failures by jointly optimizing adversarial loss and frequency domain-aware loss includes: pre-training a one-dimensional convolutional neural network as a bearing failure feature extraction network on a publicly available rolling bearing dataset. This bearing failure feature extraction network comprises multiple layers of one-dimensional convolutional and max-pooling operations. The network is used to progressively extract discriminative fault features of vibration signals in the time and frequency domains. The network is embedded in the loss calculation module of the generative adversarial network (GAN), and its weight parameters are frozen. The noisy dominant component and its corresponding generator output are input into the GAN, and their high-level semantic feature representations are obtained through forward propagation. The frequency domain-aware loss is calculated based on the difference between these high-level semantic feature representations, and the adversarial loss is calculated based on the discriminator's output. The key impact features of rolling bearing failures are preserved by jointly optimizing the adversarial loss and the frequency domain-aware loss. The publicly available rolling bearing dataset includes, but is not limited to, the Case Western Reserve University bearing dataset. The aforementioned joint optimization process can be understood in conjunction with the training process of the GAN.

[0086] It is important to understand that the discriminative fault features refer to the inherent patterns of vibration signals captured by the bearing fault feature extraction network, which can effectively distinguish different operating states of rolling bearings (including normal state and typical fault types such as inner ring, outer ring, and rolling elements). This feature extraction network is pre-trained on publicly available rolling bearing datasets (such as the Case Western Reserve University bearing dataset) with fault categories as supervised labels. Its multi-layer one-dimensional convolutional and max-pooling structures learn progressively, automatically focusing on time-frequency characteristics closely related to the physical mechanism of the fault, including but not limited to: the time interval of periodic impact responses (corresponding to fault feature frequencies), energy concentration within the resonant frequency band, modulation sideband structure, and waveform morphology of transient pulses. Because the network optimizes classification accuracy during training, its deep output feature representations naturally possess strong class separability, i.e., high sensitivity and low intra-class variance for different fault types. Introducing such features into the loss calculation of the generative adversarial network aims to constrain the denoising process to retain semantic information crucial for subsequent fault diagnosis, avoiding the loss of key impact components due to excessive smoothing or noise suppression.

[0087] In some embodiments, calculating the frequency domain perceptual loss includes: the high-level semantic features are represented as feature maps output by the bearing fault feature extraction network in deep convolutional layers; calculating the Euclidean distance between the noisy dominant component and the generator output in the corresponding feature maps to obtain the frequency domain perceptual loss; weighting and summing the frequency domain perceptual loss and the adversarial loss based on the joint loss function, and minimizing the calculation result of the joint loss function through backpropagation to update the parameters of the generator.

[0088] It's important to understand that the discriminant loss is the loss function used to train the discriminator. Its goal is to minimize the discriminator's discrimination error between real samples (such as noisy dominant components) and generated samples (such as denoised components). It is usually in the form of binary cross-entropy to enhance the discriminator's ability to distinguish between real and fake signals. The adversarial loss encourages the denoised signal output by the generator to deceive the discriminator as much as possible, thereby improving the temporal authenticity and structural integrity of the signal. The frequency domain perceptual loss, on the other hand, calculates the difference between the noisy signal and the denoised signal in a pre-trained and frozen bearing fault feature extraction network (such as L1 or L2 distance) by inputting them into a high-level feature space. This is used to constrain the generator to retain key fault semantic information and prevent weak impact components from being over-filtered out. The three components work synergistically: the discriminative loss only updates the discriminator, while the adversarial loss and frequency-aware loss are weighted and fused together to guide the generator's parameter updates. The technical means corresponding to the denoising effect without damaging the features are as follows: a frequency-aware loss is constructed by embedding a pre-trained and frozen bearing fault feature extraction network into the loss calculation module of the generative adversarial network; during training, the noisy dominant component and the denoised component output by the generator are respectively input into the feature extraction network to obtain their high-level semantic feature representations; by minimizing the difference between the two in the feature space (such as Euclidean distance), the generator is forced to learn to generate denoising results that are highly consistent with the noisy dominant component at the fault semantic level. Since the feature extraction network is trained under supervision on a labeled rolling bearing fault dataset, its deep features naturally focus on discriminative patterns such as periodic impacts and resonance bands unique to faults such as inner and outer races. Therefore, minimizing this feature difference (such as Euclidean distance) can effectively constrain the denoised signal to retain these key fault features, even if they appear as weak impacts in the time domain and are easily filtered out by traditional denoising methods.

[0089] For example, when jointly optimizing the adversarial loss and the frequency domain sensing loss, a one-dimensional convolutional neural network can be pre-trained on the Case Western Reserve University rolling bearing public dataset (containing vibration signals of different speeds, loads, and inner ring, outer ring, and rolling element fault types) as the bearing fault feature extraction network. This network consists of four layers of one-dimensional convolutions (with kernel sizes of 64, 32, 16, and 8, and channel numbers of 16, 32, 64, and 128 respectively) and alternating max-pooling layers, which can progressively capture discriminative fault features related to time-frequency modulation and periodic impact in the vibration signal. After pre-training, all weight parameters of the network are frozen and embedded into the loss of the generative adversarial network. In the computation module, during training, the noisy dominant component and its corresponding generator output (i.e., the denoised component) are input into the frozen network, and the high-level semantic feature maps of the two at the last convolutional layer are extracted through forward propagation. Subsequently, the Euclidean distance between these two feature maps is used as the frequency domain perceptual loss, and the adversarial loss is calculated based on the discriminator's output results of the noisy dominant component and the denoised component. The frequency domain perceptual loss and the adversarial loss are weighted and summed to form the joint loss function of the generator, and the generator parameters are updated by minimizing the joint loss function through backpropagation, thereby ensuring that the denoising result retains the real critical impact features of the fault while effectively suppressing noise.

[0090] As a refinement of the above embodiments, after outputting the denoised rolling bearing vibration signal, the method can also adopt, but is not limited to, the following implementation methods, for example: inputting the denoised rolling bearing vibration signal into a pre-trained multi-class fault classification model; constructing the fault classification model based on a deep convolution or Transformer architecture, the fault classification model being used to distinguish the normal state, inner ring fault, outer ring fault, and rolling element fault of the rolling bearing; parsing the confidence probability distribution output by the fault classification model to obtain the confidence level corresponding to each fault category; when the confidence level of any fault category exceeds a preset warning threshold, triggering a maintenance warning mechanism to generate warning information containing fault type, confidence level, and timestamp; uploading the warning information to the equipment health management platform via an industrial communication protocol for maintenance personnel to make decisions.

[0091] For example, after the vibration signals of a rolling bearing are denoised, these clean signals are fed into a pre-trained multi-class fault classification model. This model, built on a deep convolutional neural network or Transformer architecture, can effectively identify the normal operating state of the rolling bearing, inner ring faults, outer ring faults, and rolling element faults. The model outputs the probability distribution of each fault category; analyzing this distribution can determine whether early fault modes exist. If the confidence level of any fault type exceeds a preset warning threshold, the system will automatically trigger a maintenance warning mechanism, generating warning information including the fault type (e.g., inner ring fault), the corresponding confidence level (e.g., 85%), and the timestamp of the occurrence. Subsequently, this warning information is uploaded to the equipment health management platform via an industrial communication protocol for further analysis and decision-making by maintenance personnel, thereby enabling timely response and preventative maintenance of potential equipment faults. This not only improves the safety and reliability of equipment operation but also effectively reduces maintenance costs and downtime.

[0092] In some embodiments, when performing step 101 to collect the original vibration signal of the rolling bearing during operation, the following implementation methods may also be adopted, for example: collecting the original vibration signal within a preset collection time based on a preset collection frequency; performing anti-aliasing filtering and zero-mean normalization preprocessing on the collected original vibration signal to improve the quality of the original vibration signal during subsequent adaptive time-frequency decomposition.

[0093] In a specific implementation example, the original vibration signal is acquired by an accelerometer mounted on the bearing housing. The sampling frequency is set to 12.8 kHz, and the acquisition time is 1 second to ensure sufficient coverage of rotation cycles and meet the resolution requirements of fault characteristic frequencies. After acquisition, an anti-aliasing low-pass filter with a cutoff frequency of 6 kHz is first applied to the original signal to eliminate high-frequency interference and prevent spectral aliasing in subsequent digital processing. Subsequently, the filtered signal is subjected to zero-mean normalization, i.e., the mean of the signal is subtracted and divided by its standard deviation, so that the data distribution center is 0 and the variance is 1. This preprocessed signal serves as a high-quality input, effectively improving the stability and component separation accuracy of subsequent adaptive time-frequency decomposition (such as variational mode decomposition), laying the foundation for accurate identification of noisy dominant components.

[0094] Furthermore, in one possible implementation of this application, the generative adversarial network architecture includes a generator, a discriminator, and a bearing fault feature extraction network forming a collaboratively optimized closed-loop structure: the generator is responsible for receiving the noisy dominant component and outputting the denoised vibration signal, and its core function is to learn to recover a clean signal that is real and retains fault semantics from the noise; the discriminator uses the noisy dominant component as the real sample and the generator output as the generated sample, and provides adversarial supervision signals by judging the authenticity of the two, and its function is to drive the generator to improve the temporal authenticity and structural rationality of the output signal; the bearing fault feature extraction network is a one-dimensional convolutional neural network with pre-trained and frozen weights on public bearing datasets such as those from Case Western Reserve University, and does not participate in adversarial games, but is embedded in the loss calculation unit as an external perception module, and its function is to extract the high-level semantic features of the input signal in the deep convolutional layer, and characterize the discriminative patterns such as periodic impacts and resonance frequency bands unique to faults such as the inner circle and outer circle. The interaction process among the three is as follows: In each training iteration, the noisy dominant component and the denoised component output by the generator are respectively fed into the discriminator to calculate the adversarial loss, and simultaneously fed into the frozen fault feature extraction network to calculate the Euclidean distance between the two feature maps as the frequency domain perceptual loss; the generator updates its parameters by jointly minimizing these two losses, pursuing both the naturalness of "deceiving the discriminator" and ensuring the fidelity of "matching the original signal fault semantics", while the discriminator independently minimizes its own discrimination loss to enhance its discrimination ability; thus, the three work together to achieve the dual goals of effectively suppressing noise and accurately preserving the key fault impact features.

[0095] The above are embodiments of the method proposed in this application. Based on the same inventive concept, embodiments of this application also provide a vibration signal denoising and reconstruction device based on machine learning, the structure of which is as follows: Figure 2 As shown.

[0096] Figure 2 This is a schematic diagram of the internal structure of a vibration signal denoising and reconstruction device based on machine learning, provided as an embodiment of this application. Figure 2 As shown, the device includes:

[0097] At least one processor 201;

[0098] And a memory 202 that is communicatively connected to at least one processor;

[0099] The memory 202 stores instructions executable by at least one processor. These instructions are executed by at least one processor 201 to enable the processor 201 to: acquire raw vibration signals during the operation of the rolling bearing; perform adaptive time-frequency decomposition on the raw vibration signals to obtain multiple component signals; identify the noisy dominant component from the component signals based on a preset noise sensitivity index; construct an unsupervised generative adversarial network (GAN) and train the GAN based on the noisy dominant component. During training, the GAN retains key impact features of the rolling bearing failure by jointly optimizing the adversarial loss and frequency domain perception loss; denoise the noisy dominant component based on the trained GAN to obtain a denoised component; and reconstruct the signal by combining the denoised component with the remaining component signals to output the denoised rolling bearing vibration signal.

[0100] This application provides a corresponding embodiment. Figure 1 The non-volatile computer storage medium stores computer-executable instructions, which are configured to: acquire the raw vibration signal of the rolling bearing during operation; perform adaptive time-frequency decomposition on the raw vibration signal to obtain multiple component signals; identify the noisy dominant component from the component signals based on a preset noise sensitivity index; construct an unsupervised generative adversarial network (GAN) and train the GAN based on the noisy dominant component, wherein during the training process, the GAN retains the key impact features of the rolling bearing failure by jointly optimizing the adversarial loss and the frequency domain perception loss; denoise the noisy dominant component based on the trained GAN to obtain a denoised component; reconstruct the signal by combining the denoised component with the remaining component signals, and output the denoised rolling bearing vibration signal.

[0101] The various embodiments in this application are described in a progressive manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the embodiments for IoT devices and media are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0102] The systems, media, and methods provided in this application are one-to-one correspondences. Therefore, the systems and media also have similar beneficial technical effects as their corresponding methods. Since the beneficial technical effects of the methods have been described in detail above, the beneficial technical effects of the systems and media will not be repeated here.

[0103] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0104] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0105] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0106] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0107] In a typical configuration, a computing device includes one or more processors (CPU), input / output interfaces, network interfaces, and memory.

[0108] Memory may include non-persistent storage in computer-readable media, such as random access memory (RAM) and / or non-volatile memory, such as read-only memory (ROM) or flash RAM. Memory is an example of computer-readable media.

[0109] Computer-readable media include both permanent and non-permanent, removable and non-removable media that can store information by any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other non-transferable medium that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transient computer-readable media, such as modulated data signals and carrier waves.

[0110] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0111] The above description is merely an embodiment of this application and is not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.

Claims

1. A vibration signal denoising and reconstruction method based on machine learning, characterized in that, The method includes: Collect raw vibration signals of the rolling bearing during operation; The original vibration signal is subjected to adaptive time-frequency decomposition to obtain multiple component signals; Based on a preset noise sensitivity index, the noisy dominant component is identified from the component signal; An unsupervised generative adversarial network is constructed and trained based on the noisy dominant component. During the training process, the generative adversarial network retains the key impact features of rolling bearing failure by jointly optimizing the adversarial loss and the frequency domain perception loss. The noisy dominant component is denoised based on the trained generative adversarial network to obtain the denoised component. The denoised component is reconstructed with the remaining component signals to output the denoised rolling bearing vibration signal. The step of identifying the noisy dominant component from the component signals based on a preset noise sensitivity index includes: calculating the energy entropy of each component signal to measure the concentration of energy distribution, and calculating the kurtosis of each component signal to evaluate its impact characteristics; setting a first threshold corresponding to the energy entropy and a second threshold corresponding to the kurtosis, wherein the first threshold is statistically derived from historical normal operating data, and the second threshold is dynamically adjusted based on the theoretical upper limit of Gaussian white noise; filtering out target component signals among the component signals whose energy entropy is higher than the first threshold and whose kurtosis is lower than the second threshold, and marking the target component signals as the noisy dominant component; The method for preserving key impact features of rolling bearing failures by jointly optimizing adversarial loss and frequency domain perception loss includes: pre-training a one-dimensional convolutional neural network as a bearing failure feature extraction network on a public rolling bearing dataset. This network contains multiple layers of one-dimensional convolutional and max-pooling operations and is used to progressively extract discriminative fault features of vibration signals in the time and frequency domains. The network is embedded in the loss calculation module of the generative adversarial network (GAN), and its weight parameters are frozen. The noisy dominant component and its corresponding generator output are input into the GAN, and their high-level semantic feature representations are obtained through forward propagation. The frequency domain perception loss is calculated based on the difference between these high-level semantic feature representations, and the adversarial loss is calculated based on the discriminator's output. The key impact features of rolling bearing failures are preserved by jointly optimizing the adversarial loss and the frequency domain perception loss.

2. The vibration signal denoising and reconstruction method based on machine learning according to claim 1, characterized in that, The adaptive time-frequency decomposition of the original vibration signal yields multiple component signals, including: Calculate the envelope spectral entropy of the original vibration signal to characterize the frequency band complexity; The fitness function of the particle swarm optimization algorithm is constructed based on the envelope spectrum entropy. The optimal combination of variational mode decomposition parameters is searched iteratively through the fitness function, and the combination of variational mode decomposition parameters includes the number of decomposition layers and a quadratic penalty factor. Variational mode decomposition is performed on the optimal combination of variational mode parameters to generate multiple component signals with different center frequencies and bandwidths.

3. The vibration signal denoising and reconstruction method based on machine learning according to claim 1, characterized in that, The construction of the unsupervised generative adversarial network includes: The generator is constructed as a network structure consisting of multiple cascaded one-dimensional residual shrink blocks; A channel attention mechanism is integrated into each of the residual shrinking blocks, the attention mechanism being used to adaptively weight the importance of different feature channels; The discriminator is constructed as a temporal discriminant network containing multiple layers of one-dimensional convolution and nonlinear activation functions, and the generative adversarial network is formed based on the generator and the discriminator; Training the generative adversarial network based on the noisy dominant component includes: The noisy dominant component is input into the generator, and each residual shrinking block in the generator receives the feature sequence output from the previous stage as input. In each residual shrinkage block, a one-dimensional convolution operation is performed on the input feature sequence to extract local temporal features and obtain an intermediate feature map; Based on the intermediate feature map, channel attention weights are calculated to generate a soft threshold vector that matches the number of channels; The intermediate feature map is shrunk channel by channel using the soft threshold vector to suppress noise-related features; The shrunk feature map is added to the input feature sequence to form the corresponding output of the residual shrunk block; The feature sequence output by the last residual shrinking block is used as the denoised signal to obtain the denoised component; The denoised component and the noisy dominant component are respectively input into the discriminator. By minimizing the adversarial loss of the generator and the discrimination loss of the discriminator, the adversarial training of the generative adversarial network is completed.

4. The vibration signal denoising and reconstruction method based on machine learning according to claim 1, characterized in that, The calculation of the frequency domain sensing loss includes: The high-level semantic features are represented as feature maps output by the bearing fault feature extraction network in the deep convolutional layer. The frequency domain perceptual loss is obtained by calculating the Euclidean distance between the noisy dominant component and the generator output in the corresponding feature map. The frequency domain sensing loss and the adversarial loss are weighted and summed to update the generator parameters based on the calculation results.

5. The vibration signal denoising and reconstruction method based on machine learning according to claim 1, characterized in that, After outputting the denoised rolling bearing vibration signal, the method further includes: The denoised rolling bearing vibration signal is input into a pre-trained multi-class fault classification model. The fault classification model is constructed based on a deep convolutional or Transformer architecture. The fault classification model is used to distinguish the normal state, inner ring fault, outer ring fault and rolling element fault of the rolling bearing. The confidence probability distribution output by the fault classification model is analyzed to obtain the confidence level corresponding to each fault category; When the confidence level of any of the aforementioned fault categories exceeds a preset warning threshold, a maintenance warning mechanism is triggered to generate warning information containing the fault type, confidence level, and timestamp. The early warning information is uploaded to the equipment health management platform via industrial communication protocols for maintenance personnel to use as a reference for decision-making.

6. The vibration signal denoising and reconstruction method based on machine learning according to claim 5, characterized in that, The acquired raw vibration signals from the rolling bearing during operation include: The original vibration signal is acquired within a preset acquisition duration based on a preset acquisition frequency; The acquired original vibration signal is preprocessed with anti-aliasing filtering and zero-mean normalization to improve the quality of the original vibration signal during subsequent adaptive time-frequency decomposition.

7. A vibration signal denoising and reconstruction device based on machine learning, characterized in that, The device includes: At least one processor; And, a memory communicatively connected to the at least one processor; The memory stores instructions that can be executed by the at least one processor, which are executed by the at least one processor to enable the at least one processor to perform a vibration signal denoising and reconstruction method based on machine learning as described in any one of claims 1-6.

8. A computer storage medium storing computer-executable instructions, characterized in that, When the computer-executable instructions are executed, they implement a vibration signal denoising and reconstruction method based on machine learning as described in any one of claims 1-6.

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