A rolling bearing fault diagnosis method based on envelope spectrum knowledge distillation

Abstract

The application claims a rolling bearing fault diagnosis method based on envelope spectrum knowledge distillation, which comprises the following steps: obtaining rolling bearing vibration signals and performing sample division and normalization processing; calculating the spectral kurtosis of source working condition samples, and determining the center frequency and bandwidth of envelope demodulation based on the spectral kurtosis, thereby performing envelope demodulation, and sending the demodulated samples to a teacher network Φ for pre-training; inputting original vibration samples and envelope spectrum samples under the source working condition into a student network Ψ and the pre-trained teacher network Φ respectively, extracting bearing health state representations learned by the two networks, establishing envelope spectrum knowledge distillation loss, and calculating the prediction loss of the student network, the cross-working condition sample probability distribution alignment loss and the diversity loss of the health state representation; performing multi-loss back propagation, and adopting an Adam optimizer to optimize the weights and biases of the fault diagnosis network; finally, inputting target working condition samples into the trained fault diagnosis model for performance testing.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of rolling bearing fault diagnosis and classification under variable working conditions, and designs a domain-invariant representation learning model based on envelope spectrum knowledge distillation, which is suitable for rolling bearing fault diagnosis under variable working conditions. BACKGROUND

[0002] Rolling bearing fault diagnosis has made great progress with the help of deep learning technology, improving the accuracy and reliability of diagnosis. These technologies usually assume that training and testing samples are independent and identically distributed. However, this condition is usually difficult to meet in practical applications, especially when different rotating speeds and loads are involved in rolling bearing health state monitoring. The change of such working conditions poses unique requirements for rolling bearing fault pattern diagnosis.

[0003] After searching, the closest prior art is patent publication CN110160791B, a bearing fault diagnosis system and method for induction motor based on wavelet-spectral kurtosis, which includes a wavelet-spectral kurtosis analysis module, a time domain parameter statistical analysis module, an FFT analysis module, a Hilbert envelope demodulation analysis module, a spectral kurtosis analysis module, etc. The wavelet-spectral kurtosis analysis module includes two data preprocessing methods, wavelet and wavelet packet, which can realize the identification and feature extraction of multiple faults in the vibration signal of motor bearing coupling faults. The time domain parameter statistical analysis module monitors whether the motor bearing is abnormal by calculating the kurtosis value of the time domain sensitive parameter. The frequency spectrum analysis module and the Hilbert envelope demodulation analysis module mainly determine the feature extraction of single bearing fault of the motor. From the perspective of solving the problem, patent CN110160791B does not consider the challenges brought by the change of bearing operating conditions to the diagnosis method, while the present application mainly solves the problems of internal covariance drift of bearing vibration signals under cross-working conditions, etc., and has stronger universality. From the perspective of implementation technology path, patent CN110160791B uses traditional signal analysis and processing methods, which have strong dependence on artificial experience. The present application uses an end-to-end deep learning model, which is more convenient to deploy and use. SUMMARY

[0004] The present application aims to solve the problems of the above prior art. A rolling bearing fault diagnosis method based on envelope spectrum knowledge distillation is proposed. The technical solution of the present application is as follows:

[0005] A rolling bearing fault diagnosis method based on envelope spectrum knowledge distillation, characterized by the following steps:

[0006] S1: Obtain the rolling bearing vibration signal, divide the vibration signal into samples, and perform normalization processing;

[0007] S2: calculate the spectral kurtosis of the source working condition sample, determine the center frequency and bandwidth of envelope demodulation according to the spectral kurtosis, perform envelope demodulation on the source working condition sample according to the demodulation parameters, and send the demodulated sample to the teacher network Φ for pre-training;

[0008] S3: extract envelope spectrum knowledge representation from the source working condition sample by using the pre-trained teacher network;

[0009] S4: input the original signal under the source working condition into the student network Ψ, and use the student network to learn the health state knowledge representation of the source working condition signal;

[0010] S5: calculate the spectrum knowledge distillation loss based on the envelope spectrum knowledge representation and the original signal knowledge representation, calculate the alignment loss of the health state representation between the multi-source domain samples, determine the representation diversity loss by using the L2 norm, and obtain the prediction loss according to the cross-entropy of the predicted health state and the actual rolling bearing health state;

[0011] S6: perform loss back propagation, and use the Adam optimizer to optimize the weights and biases of the fault diagnosis network;

[0012] S7: input the target working condition sample into the trained fault diagnosis model for performance test.

[0013] Further, the step S2 calculates the spectral kurtosis of the source working condition sample, determines the center frequency and bandwidth of envelope demodulation according to the spectral kurtosis, performs envelope demodulation on the source working condition sample according to the demodulation parameters, and sends the demodulated sample to the teacher network Φ for pre-training, and specifically includes:

[0014] S21: perform short-time Fourier transform STFT on the signal x to obtain its time-frequency representation, and STFT divides the signal into multiple overlapping small segments, and performs Fourier transform on each segment;

[0015] S22: square each time window of the STFT result to obtain the power spectral density, and calculate the average value and standard deviation of the power spectral density;

[0016] S23: calculate the spectral kurtosis SK(f) of each signal segment according to the following formula, and determine the center frequency f s and the bandwidth parameter b n of the corresponding signal segment based on the maximum spectral kurtosis;

[0017]

[0018] wherein X(f,t) is the STFT result of the signal at frequency f and time t, and E[] represents the expected value.

[0019] the center frequency f sis the position where the spectral kurtosis value reaches the maximum, that is: f s = argmin f SK(f)。Bandwidth b n reflects the frequency spectrum extension range of the rolling bearing vibration signal, which is calculated as follows: first, a threshold value SK threshold = η × SK(f s ) is set, usually η is 0.5, that is, 50% kurtosis peak; find the left and right boundary frequency points of the spectral kurtosis equal to the threshold value, that is, SK(f low ) = SK(f high ) = SK threshold , then the bandwidth is calculated as: b n = f high -f low .

[0020] Further, the step S3 performs envelope demodulation on the source working condition sample based on the center frequency f s and the bandwidth parameter b n , and sends the demodulated sample to the teacher network Φ for pre-training, specifically including:

[0021] S31: design a band-pass filter with a center frequency f s and a bandwidth parameter b n , to filter out other frequency components in the signal and retain components within the target frequency range;

[0022] S32: perform Hilbert transform on the filtered signal x bp (t), that is, perform Hilbert transform on the band-pass filtered signal to obtain the analytic signal of the signal. The Hilbert transform converts the signal from the real number domain to the complex number domain, so that the real part of the signal is the original signal and the imaginary part is the Hilbert transform of the original signal, which is represented as follows:

[0023] x a (t) = x bp (t) + j*H{x bp (t)} (2)

[0024] S33: calculate the signal envelope and obtain the corresponding phase spectrum, the envelope and phase spectrum calculation is shown in formulas (3) and (4);

[0025]

[0026] Phase(E(f)) = arg{FFT[e(t)]} (4)

[0027] Where e(t) represents the modulus value of the Hilbert analytic signal, Phase(E(f)) represents the envelope demodulation phase spectrum, and FFT represents the fast Fourier transform;

[0028] S34: feeding the envelope demodulation phase spectrum into the teacher model Φ for training.

[0029] Further, the step S4: using the pre-trained teacher network Φ to extract the envelope spectrum knowledge representation rep Φ from each source working condition sample phase(E(f)) Φ is calculated as shown in equation (5);

[0030] rep Φ = Featurizer Φ {Phase(E(f))} (5)

[0031] Featurizer is the health state representation extraction module of the network, and Φ represents the teacher network; Featurizer Φ represents the bearing health state representation extraction module of the teacher network; the following Featurizer Ψ represents the health state representation extraction module of the student network.

[0032] Further, the step S5 inputs the original signal under the source working condition into the student network Ψ, and uses the student network to learn the health state knowledge representation rep Ψ , whose calculation formula is as follows:

[0033] rep Ψ = Featurizer Ψ {x} (6)

[0034] Further, the step S6 respectively calculates the spectrum knowledge distillation loss, the alignment loss, the diversity loss and the prediction loss in the health state prediction model training process, specifically including:

[0035] S61: calculating the spectrum knowledge distillation loss based on the envelope spectrum knowledge representation and the original signal knowledge representation, and the distillation loss L spe is calculated as follows:

[0036]

[0037] Wherein, n represents the dimension of the health state deep representation obtained by the fault diagnosis model; respectively correspond to the rolling bearing health state representation learned by the teacher network and the student network;

[0038] S62: calculating the alignment loss of the high-order statistics between the health state representations of the multi-source domain samples to obtain the cross-condition representation, and the alignment loss L ali is calculated as follows:

[0039]

[0040] where F denotes the Frobenius norm, respectively denote the health state representation learned under the i-th and j-th source working condition, and C is a covariance matrix.

[0041] S63: Determine the representation of diversity loss L using L2 norm div , whose calculation formula is as follows:

[0042]

[0043] S64: Obtain the prediction loss L from the cross-entropy of the predicted health state and the actual rolling bearing health state cla ,

[0044]

[0045] where N is the number of health state categories, y i is the distribution of the true health state label, where the position corresponding to the health state is 1, and the others are 0, is the probability distribution predicted by the diagnosis model.

[0046] Further, the teacher network and the student network both use the same network architecture parameters, and each network includes a feature extraction module Featurizer, a bottleneck module Bottleneck, and a classification module Classification. The feature extraction module Featurizer is a front-end module designed for deep network, which is used to convert the original input data (including original vibration signals or envelope demodulation spectrum) into health state representation in the feature space. The bottleneck module Bottleneck is an intermediate layer between Featurizer and Classification in the deep network, mainly used for dimension reduction and fusion of rolling bearing health state representation, and filters out redundant or unimportant feature representation. The classification module Classification is the terminal part of the deep learning network, which is used for the final classification of the feature representation compressed by Bottleneck.

[0047] An electronic device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor implements the envelope spectrum knowledge distillation-based rolling bearing fault diagnosis method according to any one of the preceding embodiments when executing the program.

[0048] A non-transitory computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the envelope spectrum knowledge distillation-based rolling bearing fault diagnosis method according to any one of the preceding embodiments.

[0049] The advantages and beneficial effects of the present application are as follows:

[0050] The present application is directed to the fact that the traditional fault diagnosis model relies on the stability of the device signal generation mechanism, and in the process of rolling bearing fault recognition, it is difficult to meet the above conditions due to the change of rotating speed and load. Therefore, the present application proposes a domain-invariant representation learning strategy based on envelope spectrum knowledge distillation for diagnosing rolling bearing faults under different working conditions. The purpose is to effectively distinguish the rolling bearing fault state and adapt to the change of working condition, thereby promoting the migration and application of labeled fault knowledge under different working conditions.

[0051] The present application utilizes envelope spectrum knowledge distillation to capture Fourier features as domain-invariant features, and ensures robust health state representation by aligning the high-order statistics of samples under different working conditions. In addition, an innovative loss function is designed to enrich the representation diversity. Unlike traditional models that require training and testing samples to follow independent and identical distribution conditions, the present application provides a more flexible method. The average AUC on the Paderborn rolling bearing dataset is improved from 0.68 to 0.99, and the rolling bearing fault diagnosis accuracy under variable working conditions is 98.5%, which is 3.4 percentage points higher than the traditional machine learning model decision tree.

[0052] The bearing diagnosis model proposed by the present application is innovative in that the loss function contained therein is composed of four parts. The first part is the classification loss function, which is responsible for the preliminary identification of the health state of the rolling bearing; the second part is the envelope spectrum knowledge distillation loss, which enables the trained diagnosis network to still learn the fault characteristics in the signal when the input is the original vibration signal; the third part is the diversity loss of health state representation, which reduces the redundant information between health state representations and enhances the diversity of the representation; and the fourth part is the sample probability distribution adaptation loss, which adapts the probability distribution state of the cross-condition samples. Based on the classification loss, envelope spectrum knowledge, representation diversity measurement, and probability distribution adaptation are introduced to improve the generalization performance of the diagnosis model. BRIEF DESCRIPTION OF DRAWINGS

[0053] Figure 1 is the domain-invariant representation learning framework based on envelope spectrum knowledge distillation provided by the present application;

[0054] Figure 2 is the envelope spectrum knowledge distillation schematic diagram;

[0055] Figure 3 is the source working condition sample spectral kurtosis diagram;

[0056] Figure 4 is the model parameter grid optimization three-dimensional diagram;

[0057] Figure 5 is the loss change and verification accuracy curve during the model training process;

[0058] Figure 6 ROC curve of the fault diagnosis model (a) model proposed in the application (b) model without spectrum knowledge distillation;

[0059] Figure 7 Confusion matrix of the fault diagnosis model on the working condition generalization task (a) decision tree model (b) one-dimensional convolution model based on MMD (c) Fourier spectrum knowledge distillation model (d) model proposed in the application;

[0060] Figure 8 The flowchart of the rolling bearing fault diagnosis method based on envelope spectrum knowledge distillation of the application is shown. DETAILED DESCRIPTION

[0061] The technical solutions in the embodiments of the application will be described in detail below with reference to the drawings in the embodiments of the application. The described embodiments are only some of the embodiments of the application.

[0062] The technical solution of the application to solve the above technical problems is:

[0063] Figure 1 The model framework of the fault diagnosis network is given. From the perspective of model running, the framework is mainly divided into model training and model testing. From the structure, the framework is composed of a teacher network and a student network. The teacher network and the student network use the same network architecture parameters. Each network includes a feature extraction module Featurizer, a bottleneck module Bottleneck and a classification module Classification.

[0064] The deep learning model constructed by the feature extraction module, the bottleneck module and the classification module is used as the basis of the application. First, the knowledge distillation is used to extract the robust representation of the rolling bearing health state reflecting the frequency domain features; then, the high-order statistics of the rolling bearing samples under cross-working conditions are calculated to improve the consistency of the sample probability distribution under different working conditions, so as to promote the learning of the universal representation of the rolling bearing health state; finally, an additional loss function is designed to enhance the diversity of the learned rolling bearing health state representation, further improving the generalization ability of the rolling bearing fault diagnosis model. Specifically, the following steps are included:

[0065] S1: Obtain the rolling bearing vibration sample and normalize it.

[0066] S2: Calculate the spectral kurtosis of the source working condition sample, and determine the center frequency and bandwidth of the envelope demodulation according to the spectral kurtosis. Demodulate the source working condition sample according to the demodulation parameters, and send the demodulated sample to the teacher network Φ for pre-training.

[0067] S21: Short-time Fourier transform (STFT) is performed on the signal x to obtain its time-frequency representation. The STFT divides the signal into multiple overlapping small segments, and performs Fourier transform on each segment.

[0068] S22: Square each time window of the STFT result to obtain the power spectral density, and calculate the mean and standard deviation of the power spectral density.

[0069] S23: Calculate the spectral kurtosis of each segment of the signal according to the following formula, and determine the center frequency f s and bandwidth parameter b n of the corresponding signal segment based on the maximum spectral kurtosis.

[0070]

[0071] where X(f, t) is the STFT result of the signal at frequency f and time t, denotes the expected value.

[0072] S3: Envelope demodulation is performed on the source working condition samples based on the center frequency f s and bandwidth parameter b n , and the demodulated samples are fed into the teacher network Φ for pre-training.

[0073] S31: A band-pass filter with center frequency f s and bandwidth parameter b n is designed to filter out other frequency components in the signal and retain components within the target frequency range.

[0074] S32: Hilbert transform is performed on the filtered signal x bp (t) to obtain the analytic signal of the signal. Hilbert transform converts the signal from real number domain to complex number domain, so that the real part of the signal is the original signal and the imaginary part is its Hilbert transform. It is represented as follows:

[0075] x a (t)=x bp (t)+j*H{x bp (t)} (12)

[0076] S33: The signal envelope is obtained, and the corresponding phase spectrum is obtained. The envelope and phase spectrum calculation is shown in formulas (3) and (4).

[0077]

[0078] Phase(E(f))=arg{FFT[e(t)]} (14)

[0079] S34: The envelope demodulation phase spectrum is fed into the teacher model Φ for training.

[0080] S4: Extract the envelope spectrum knowledge representation rep from each source condition sample Phase(E(f)) using the pre-trained teacher network Φ Φ The structure parameters of the teacher network are shown in the following table. rep Φ is calculated as shown in equation (5).

[0081] rep Φ = Featureizer Φ {Phase(E(f))} (15)

[0082] Table 1 Structure parameters of the teacher network

[0083]

[0084]

[0085] S5: Input the original signal under the source condition into the student network Ψ, and use the student network to learn the health state knowledge representation rep of the source condition signal Ψ , whose calculation formula is as follows:

[0086] rep Ψ = Featureizer Ψ {x} (16)

[0087] S6: Calculate the spectrum knowledge distillation loss, alignment loss, diversity loss, and prediction loss of the health state prediction model training process, respectively.

[0088] S61: Calculate the spectrum knowledge distillation loss based on the envelope spectrum knowledge representation and the original signal knowledge representation, and the basic principle of spectrum knowledge distillation is shown in Figure 2 The calculation formula of the distillation loss L spe is as follows:

[0089]

[0090] Where n represents the dimension of the health state deep representation obtained by the fault diagnosis model. respectively correspond to the health state representations learned by the teacher network and the student network.

[0091] S62: Calculate the alignment loss of the cross-condition representation between the high-order statistics of the health state representations of the multi-source domain samples, and the calculation formula of the alignment loss L ali is as follows:

[0092]

[0093] Where F represents the Frobenius norm. respectively represent the health state representation learned under the i-th and j-th source working condition, and C(·) represents the covariance matrix.

[0094] S63: Determine the diversity loss L using the L2 norm div , whose calculation formula is as follows:

[0095]

[0096] S64: Obtain the prediction loss L from the cross-entropy between the predicted health state and the actual rolling bearing health state cla .

[0097]

[0098] where N is the number of health state categories, y i is the distribution of the true health state label (usually a one-hot encoding vector, where the position corresponding to the health state is 1, and the others are 0), is the probability distribution predicted by the diagnosis model.

[0099] S7: Perform loss backpropagation and use the Adam optimizer to optimize the weights and biases of the fault diagnosis network.

[0100] S8: Input the target working condition sample into the trained fault diagnosis model for performance testing.

[0101] Example One

[0102] This embodiment provides a fault diagnosis case based on the Paderborn rolling bearing dataset, which adopts 6 health states in the dataset, and the fault positions are inner ring, outer ring, and mixed fault of inner and outer rings. The fault types include pitting, deformation, etc. The data details are shown in the following table.

[0103] Table 2 Details of Paderborn rolling bearing dataset

[0104]

[0105] S1: Dataset division: select 4-second long vibration signals for model building, use source working condition samples as model training samples, and use target working condition samples as model testing samples.

[0106] S2: Determine the demodulation parameters: analyze the source working condition samples using the spectral kurtosis method, as shown in Figure 3 , determine the new order center frequency rich in fault information as 4.8 kHz and the bandwidth as 1.0667 kHz based on the extreme value in the spectral kurtosis diagram

[0107] S3: Pre-training of teacher model: train the teacher model using the resonance demodulation phase spectrum.

[0108] S4: Model training parameter optimization: The learning rate and batch size of the rolling bearing fault diagnosis model are optimized using the grid search method, as shown in FIG. 3. It is worth noting that different combinations of learning rate and batch size will result in different accuracy levels. The x-axis parameter (learning rate) is between 0.001 and 0.01, while the y-axis parameter (batch size) is between 32 and 1024. Analysis shows that a learning rate of 0.001 and a batch size of 256 can achieve higher diagnostic accuracy. On the contrary, a larger learning rate will result in a decrease in accuracy due to its amplification effect on the parameter update step, potentially reducing the parameter search space of the fault diagnosis model and causing the search parameters of the diagnostic model to swing on both sides of the optimal value, making it difficult to achieve the best results. Figure 4

[0109] S5: The source working condition is fed into the student network, and the spectral knowledge distillation loss, alignment loss, diversity loss, and prediction loss of the health state prediction model training process are calculated respectively. The diagnostic network model is built based on Python 3.9, the core framework includes PyTorch 1.9.1, and the integrated development environment used is PyCharm 2021. The model runs on hardware with an i9 processor and an RTX 4060 GPU. Figure 5 The overall loss value of the training process and the change of the verification accuracy are given. Obviously, with more iterative training, the loss value steadily decreases and eventually stabilizes. This means that the deep diagnostic model gradually converges to a balance point, indicating that it has high convergence efficiency. In addition, the verification accuracy gradually improves, indicating that the predicted health state is gradually approaching its actual health state.

[0110] S6: Analysis of the role of envelope spectrum knowledge distillation in domain-invariant representation learning, Figure 6 The ROC curve of the method of the present application and the envelope spectrum knowledge distillation model without envelope spectrum knowledge distillation is compared. The true positive rate TPR and the false positive rate FPR are calculated as follows:

[0111]

[0112] In the formula, TP is the number of positive examples correctly predicted as positive; FN represents the number of positive examples incorrectly predicted as negative; FP represents the number of negative examples incorrectly predicted as positive; and TN is the number of negative examples correctly predicted as negative.

[0113] For the multi-class rolling bearing fault diagnosis task, the average area under the ROC curve of A1 is 0.68. In contrast, the method of the present application achieves an average area under the ROC curve of 0.99, showing nearly perfect accuracy on the Paderborn dataset. This means that there is a suitable threshold that can make this model achieve good fault diagnosis results.

[0114] ​S7: The confusion matrix analysis model is used to analyze the identification ability of the rolling bearing health state, as shown in Figure 7 This embodiment carefully selects three methods, namely the decision tree Figure 7 a) one-dimensional convolution model based on MMD Figure 7 (b) and Fourier spectrum knowledge distillation model Figure 7 (c), to illustrate the advantages of the method. The comparison method represents the benchmark model in the fields of deep learning and transfer learning. The confusion matrix shows that the Fourier spectrum knowledge distillation model has the worst fault diagnosis performance. The collected rolling bearing vibration signals usually exhibit signal modulation, in which the rolling bearing fault feature frequency is modulated by the natural characteristic frequency of the system. Simply applying the fast Fourier transform to the rolling bearing vibration signal cannot effectively highlight the rolling bearing fault features. Therefore, the spectrum knowledge distillation will impair the performance of the fault diagnosis model. Compared with the Fourier spectrum knowledge distillation model, the fault diagnosis performance of the decision tree is improved by 3.5%. However, traditional machine learning methods mainly rely on handcrafted features, and rules need to be defined to filter these features to achieve competitive performance. The one-dimensional convolution model based on MMD enhances the cross-condition generalization ability of the model by combining MMD in the deep learning architecture. MMD aligns the probability distribution of samples under different conditions, so that the diagnostic accuracy of the one-dimensional convolution model based on MMD reaches 97.9%; and the present application aligns the high-order statistics of samples under different conditions, so that the diagnostic accuracy of the model reaches the highest.

[0115] The above-mentioned system, device, module or unit illustrated in the embodiment can be specifically implemented by a computer chip or entity, or by a product with certain functions.

[0116] The computer readable medium includes permanent and non-permanent, removable and non-removable media, which can be implemented by any method or technology to store information. The information can be computer readable instructions, data structures, program modules 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, compact disc read-only memory (CD-ROM), digital versatile disc (DVD) or other optical storage, magnetic cassette, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other non-transmission medium that can be used to store information accessible to a computing device. According to the definition in this paper, computer readable medium does not include transitory computer readable medium, such as modulated data signals and carriers.

[0117] It is also to be noted that the terms "comprising", "including", or any other variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but can also include other elements not expressly listed or inherent to such process, method, article, or apparatus. An element proceeded by "comprises a..." does not, without further restriction, exclude the existence of additional elements of a like kind in the process, method, article, or apparatus that comprises the element.

[0118] The above examples are to be understood only as illustrative of the application and not a restriction on the scope of protection of the application. After reading the specification, the skilled person can make various changes or modifications to the application, and these equivalent changes and modifications also fall within the scope defined by the claims of the application.

Claims

1. A method for diagnosing rolling bearing faults based on envelope spectrum knowledge distillation, characterized in that, Includes the following steps: S1: Acquire the vibration signal of the rolling bearing, divide the vibration signal into samples, and perform normalization processing; S2: Calculate the spectral kurtosis of the source operating condition sample, determine the center frequency and bandwidth of the envelope demodulation based on the spectral kurtosis, perform envelope demodulation on the source operating condition sample according to the demodulation parameters, and send the demodulated sample into the teacher network Φ for pre-training. S3: Utilize a pre-trained teacher network to extract a rolling bearing health status representation based on envelope spectrum knowledge from source operating condition samples; S4: Input the original signal under the source condition into the student network Ψ, and use the student network to learn the health status representation of the source condition signal. S5: Calculate the spectral knowledge distillation loss based on the envelope spectrum knowledge representation and the original signal knowledge representation, calculate the higher-order statistics between the health status representation covariance matrices of multi-source domain samples to obtain the probability distribution alignment loss of cross-operating condition representation, use the L2 norm to determine the representation diversity loss, and obtain the prediction loss based on the cross-entropy between the predicted health status and the actual rolling bearing health status. S6: Perform backpropagation of the loss and use the Adam optimizer to optimize the weights and biases of the rolling bearing fault diagnosis network; S7: Input the target working condition sample into the trained fault diagnosis model for performance testing; The spectral knowledge distillation loss, probability distribution alignment loss, diversity loss, and prediction loss are calculated separately during the training process of the health status prediction model, including: S61: Calculate the spectral knowledge distillation loss based on envelope spectrum knowledge representation and original signal knowledge representation, where the distillation loss L is... spe The calculation formula is as follows: Where n represents the dimension of the health status representation obtained by the fault diagnosis model; These correspond to the health status representations learned from the teacher network and the student network, respectively. S62: Calculate the higher-order statistics between the covariance matrices of the health status representations of multi-source domain samples to obtain the alignment loss across operating conditions, where the alignment loss L is... ali The calculation formula is as follows: Where F represents the Frobenius norm, Let represent the rolling bearing health status representations learned under the i-th and j-th source conditions, respectively, and C be the covariance matrix; S63: Determine the L2 norm to represent the diversity loss L div The calculation formula is as follows: S64: The predicted loss L is obtained based on the cross-entropy between the predicted health state and the actual rolling bearing health state. cla as follows: Where N is the number of rolling bearing health status categories, y i This represents the distribution of actual health status labels, where the position corresponding to a health status is 1, and the others are 0. It is the probability distribution predicted by the diagnostic model.

2. The rolling bearing fault diagnosis method based on envelope spectrum knowledge distillation according to claim 1, characterized in that, Step S2 calculates the spectral kurtosis of the source operating condition sample, determines the center frequency and bandwidth of the envelope demodulation based on the spectral kurtosis, performs envelope demodulation on the source operating condition sample according to the demodulation parameters, and sends the demodulated sample to the teacher network Φ for pre-training, specifically including: S21: Perform a short-time Fourier transform (STFT) on the signal x to obtain its time-frequency representation. The STFT divides the signal into multiple overlapping segments, and performs a Fourier transform on each segment. S22: Squaring the STFT results for each time window yields the power spectral density, and calculating the mean and standard deviation of the power spectral density; S23: Calculate the spectral kurtosis SK(f) of each signal segment according to the following formula, and determine the center frequency f of the corresponding signal segment based on the maximum spectral kurtosis value. s and bandwidth parameter b n ; Where X(f,t) is the STFT result of the signal at frequency f and time t. Indicates the expected value; Center frequency f s The position where the spectral kurtosis value reaches its maximum value, i.e.: f s =argmin f SK(f); bandwidth b n This reflects the spectral range of the rolling bearing vibration signal, and its calculation is as follows: First, a threshold SK is set. threshold =η×SK(f s Typically, η is taken as 0.5, which is the 50% kurtosis peak; find the left and right boundary frequency points in the spectral kurtosis that are equal to this threshold, i.e., SK(f low ) = SK(f high ) = SK threshold The bandwidth is then calculated as: b n =f high -f low .

3. The rolling bearing fault diagnosis method based on envelope spectrum knowledge distillation according to claim 2, characterized in that, Based on the center frequency f s and bandwidth parameter b n The source operating condition samples are envelope demodulated, and the demodulated samples are fed into the teacher network Φ for pre-training, specifically including: S31: Design a center frequency of f s And the bandwidth parameter is b n A bandpass filter is used to filter out other frequency components in a signal and retain the components within the target frequency range. S32: For the filtered signal x bp (t) Perform a Hilbert transform on the bandpass filtered signal to obtain the analytic signal. The Hilbert transform converts the signal from the real domain to the complex domain, so that the real part of the signal is the original signal and the imaginary part is its Hilbert transform, which is expressed as follows: x a (t)=x bp (t)+j*H{x bp (t)} (6) S33: Calculate the signal envelope and obtain the corresponding phase spectrum. The calculation of the envelope and phase spectrum is shown in formulas (7) and (8). Phase(E(f))=arg{FFT[e(t)]} (8) Where e(t) represents the magnitude of the Hilbert analytic signal, Phase(E(f)) represents the envelope demodulated phase spectrum, and FFT is the Fast Fourier Transform; S34: Feed the envelope demodulated phase spectrum into the teacher model Φ for training.

4. The rolling bearing fault diagnosis method based on envelope spectrum knowledge distillation according to claim 3, characterized in that, The envelope spectrum knowledge representation rep is extracted from Phase(E(f)) of each source operating condition sample using a pre-trained teacher network Φ. Φ ,rep Φ The calculation is shown in equation (9); rep Φ =Featurizer Φ {Phase(E(f))} (9) Featurizer is the module for extracting the health status representation of the network; Φ represents the teacher network. Φ The bearing health status representation extraction module of the teacher network; the Featurer below Ψ This indicates the health status extraction module of the student network.

5. The rolling bearing fault diagnosis method based on envelope spectrum knowledge distillation according to claim 4, characterized in that, The original vibration signal under the source operating condition is input into the student network Ψ, and the student network is used to learn the health status representation rep of the source operating condition signal. Ψ The calculation formula is as follows: rep Ψ =Featurizer Ψ {x} (10)。 6. A method for diagnosing rolling bearing faults based on envelope spectrum knowledge distillation according to any one of claims 1-5, characterized in that, Both the teacher and student networks use the same network architecture parameters. Each network includes a Feature Extraction module (Featurizer), a Bottleneck module (Bottleneck), and a Classification module (Classification). The Feature Extraction module (Featurizer) is the front-end module of the deep network, used to transform the raw input data into a health state representation in the feature space. The Bottleneck module is an intermediate layer in the deep network between the Feature Extraction module and the Classification module. It is mainly used for dimensionality reduction and fusion of the rolling bearing health state representation, and to filter out redundant or unimportant feature representations. The Classification module is the end part of the deep learning network, used to perform the final classification on the feature representation compressed by the Bottleneck module.

7. An electronic device, characterized in that, The method includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, implements the rolling bearing fault diagnosis method based on envelope spectrum knowledge distillation as described in any one of claims 1 to 6.

8. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the rolling bearing fault diagnosis method based on envelope spectrum knowledge distillation as described in any one of claims 1 to 6.

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