Bearing fault diagnosis method based on physically-driven cross-domain digital twinning framework

Abstract

The invention discloses a bearing fault diagnosis method based on a physically-driven cross-domain digital twinning framework, and the method comprises the steps: obtaining the actual data of a target scene, and generating virtual data through a manifestation model; respectively extracting respective feature correlation graphs of the actual data and the virtual data, and respectively generating a corresponding actual feature transition graph and a corresponding virtual feature transition graph based on the respective feature correlation graphs; respectively generating an actual data feature map and a virtual data feature map by aligning feature distribution of two domains of the actual feature transition map and the virtual feature transition map; performing fault classification on the actual data feature map and the virtual data feature map to obtain a fault classification result; the fault classification result comprises a fault type and a fault severity degree. According to the method, comprehensive capture and accurate classification of fault features in a target scene are realized, the accuracy and reliability of fault classification are improved, deep fusion and optimization of multi-scale features are realized, and a firmer technical support is provided for fault detection and diagnosis.

Description

Technical Field

[0001] The present invention belongs to the technical field of industrial equipment condition monitoring and fault diagnosis, and particularly relates to a bearing fault diagnosis method based on a physics-driven cross-domain digital twin framework. Background Art

[0002] Rolling bearings are important components widely used in rotating machinery, and their working conditions directly affect the overall performance and safety of the equipment. However, during the long-term operation of bearings, they are easily affected by factors such as load fluctuations, speed changes, and environmental noise, resulting in failures. Traditional fault diagnosis methods usually rely on manual feature extraction, statistical analysis, or models based on steady-state signals. These methods have poor adaptability under non-stationary working conditions and are difficult to accurately detect and classify fault types.

[0003] In recent years, data-driven deep learning methods have made significant progress in the field of bearing fault diagnosis. However, these methods highly rely on a large amount of labeled data, and fault data in industrial fields are often difficult to obtain. In addition, due to changes in data distribution, models trained in laboratory environments are difficult to directly migrate to actual working conditions, resulting in insufficient generalization ability of the models. Therefore, there is an urgent need for a bearing fault diagnosis method that can combine physical modeling and data-driven methods and can effectively adapt to non-stationary working conditions. Summary of the Invention

[0004] To solve the deficiencies of the prior art and achieve the purpose of bearing health monitoring and anomaly detection under non-stationary working conditions, the present invention adopts the following technical solutions:

[0005] A bearing fault diagnosis method based on a physics-driven cross-domain digital twin framework includes the following steps:

[0006] Step 101: Obtain the actual data of the target scenario and generate virtual data through a phenomenological model;

[0007] Use vibration sensors to collect the characteristic information of multiple working condition data at different positions in the target scenario respectively, so as to obtain the one-dimensional vibration waveforms corresponding to each working condition data as the actual data, generate high-quality simulated signals, cover a virtual data set of various fault types and non-stationary working conditions, create virtual data for training, and simulate the bearing behavior under different speed changes;

[0008] Step 102: Extract the respective feature correlation diagrams of the actual data and the virtual data, and generate corresponding actual feature transition diagrams and virtual feature transition diagrams based on the respective feature correlation diagrams;

[0009] Perform short-time Fourier transform on virtual data and actual data, and transform the vibration signal in the time domain into a vibration domain signal in the angular domain; calculate the instantaneous autocorrelation function after angular alignment, and use double Fourier transform to obtain the order-frequency cyclic spectrum correlation feature correlation diagram. The generated actual feature correlation diagram and virtual feature correlation diagram show the distribution of fault features at different frequencies and modulation frequencies, which helps to extract and retain the physical features related to bearing faults, thereby improving the accuracy and reliability of fault diagnosis;

[0010] Step 103: Generate an actual data feature map and a virtual data feature map respectively by aligning the feature distributions in the two domains of the actual feature transition map and the virtual feature transition map;

[0011] Input the actual feature transition map and the virtual feature transition map into the domain adaptation module, and generate an actual data feature map and a virtual data feature map respectively by aligning the feature distributions in their respective domains; the domain adaptation module includes a global domain discriminator and a local domain discriminator, and adjusts according to the observed differences in the global and local distributions to achieve an optimal balance between aligning the marginal and conditional distributions;

[0012] Step 104: Classify the faults of the actual data feature map and the virtual data feature map to obtain a fault classification result, where the fault classification result includes the fault type and an index for measuring the severity of the fault.

[0013] Further, in the step 101, the process of generating virtual data of bearing faults includes the following steps:

[0014] Step 201: Define a fault model and parameters, and generate a speed curve;

[0015] Determine the type of bearing fault to be simulated (such as inner race fault, outer race fault, rolling element fault, etc.), set the physical parameters of the bearing, including the number of rolling elements, the diameter of the rolling elements, the pitch diameter, the contact angle, etc., and define the speed change curve of the bearing according to the actual working conditions or experimental requirements, including the acceleration, constant speed, and deceleration stages;

[0016] Step 202: Calculate the fault characteristic frequency and generate an impact signal;

[0017] Calculate the fault characteristic frequency according to the physical parameters and fault type of the bearing, such as the inner race fault frequency, the outer race fault frequency, and the rolling element fault frequency; generate a signal simulating the fault impact according to the fault characteristic frequency and the speed change;

[0018] Step 203: Simulate random sliding and generate a vibration response;

[0019] To simulate the random sliding and time fluctuations in the actual bearing operation, randomness is introduced into the impact signal. For example, the random fluctuations at the impact moment are simulated through a normal distribution, and the impact signal is input into a simplified single-degree-of-freedom system model to simulate the vibration response of the structure;

[0020] Step 204: Add noise to generate virtual data;

[0021] To make the simulated signal closer to the actually measured signal, a certain level of noise needs to be added; the power of the noise can be controlled by the signal-to-noise ratio; all the generated signals (including the vibration response and the noise) are synthesized to obtain the final simulated signal.

[0022] Further, in the said step 203, the vibration response generation formula is as follows:

[0023]

[0024] where, t represents the moment, x(t) represents the vibration signal at the time t, h(t) represents the response to a single impact, T represents the impact interval, τ i represents the time deviation of the i-th impact, h(t - iT - τ i ) represents the impulse response function at the time t - iT - τ i , q(T) represents the periodic modulation signal, q(iT) represents the modulation signal in the i-th period, and n(t) represents the noise.

[0025] Further, in the said step 102, the vibration signal in the time domain is transformed into a vibration domain signal in the angular domain, and the formula is as follows:

[0026] x o (θ) = x(t(θ))

[0027] where, θ represents the rotation angle, x o (θ) represents the vibration signal in the angular domain, t(θ) is a function that converts the rotation angle θ into time t, and x(t(θ)) represents the vibration signal at the time point t(θ) corresponding to the specific angle θ.

[0028] Further, in the said step 102, the autocorrelation function formula is as follows:

[0029]

[0030] where, α represents the cyclic frequency, f represents the conventional frequency, τ represents the time delay, S x (α, f) represents the cyclic spectral correlation function, which describes the cyclic stationarity of the signal, represents the normalization factor, which is used to normalize the energy of the signal to the window width W, E[·] represents the expectation, F θ→α，τ→fIndicates performing a double Fourier transform, where θ is transformed to the cyclic frequency α and τ is transformed to the conventional frequency f. is x o (θ - τ) complex conjugate, representing the complex conjugate of the signal at the angle θ - τ.

[0031] Furthermore, in step 103, by constructing the losses of the global domain discriminator, the local domain discriminator, and the weight parameters, the total loss function of adaptive domain adaptation is obtained, and the calculation formula is as follows:

[0032]

[0033] Where, represents the total loss function of adaptive domain adaptation, represents the loss of the global domain discriminator, represents the loss of the local domain discriminator.

[0034] Furthermore, the global domain discriminator is used for adversarial training. By learning to distinguish whether the input feature transition map comes from the actual feature transition map or the virtual feature transition map, the global distribution difference between the actual data and the virtual data is minimized;

[0035] Where, the loss function learned by the global domain discriminator is as follows:

[0036]

[0037] Where, represents the loss of the global domain discriminator, N s and N t respectively represent the sample numbers of the virtual data and the actual data, x i represents the input sample, d i is the domain label, indicating whether the sample comes from the virtual data or the actual data, G f represents the global domain discriminator, represents the feature representation of the i-th sample, α represents the cyclic frequency, f represents the conventional frequency, represents given the feature the probability that the global domain discriminator predicts whether the sample comes from the virtual data or the real data.

[0038] Furthermore, the local domain discriminator is used to achieve the conditional distribution alignment of each fault category. The local domain discriminator works independently for each fault category. By learning to distinguish whether the features of a specific category come from the virtual data or the actual data, the feature distributions of the virtual data and the actual data at each category level are made consistent;

[0039] Where, the loss function learned by the local domain discriminator is as follows:

[0040]

[0041] Among them, represents the loss of the local domain discriminator, N s and N t respectively represent the number of samples of virtual data and actual data, x i represents the input sample, d i represents the domain label, d i，c represents the probability that the sample x i belongs to the category c, G f，c represents the local domain discriminator, α represents the cycle frequency, f represents the regular frequency, represents the feature representation of the i-th virtual data sample, represents the feature representation of the i-th actual data sample, and respectively represent the predicted probabilities that the model assigns the virtual data and the actual data sample i to the category c.

[0042] Furthermore, according to the observed differences between the global and local distributions for adjustment, to achieve the optimal balance between marginal and conditional distribution alignment, the formula for the constructed weight parameter is as follows:

[0043]

[0044] Among them, ω represents the adaptive weight, and respectively represent the data sets of virtual data and actual data, and respectively represent the data subsets of the c-th category in virtual data and actual data, C is the total number of categories, represents the loss of the global domain discriminator, measuring the global distribution difference between virtual data and actual data ; represents the loss of the local domain discriminator, measuring the distribution difference between virtual data and actual data under the specific category c.

[0045] Furthermore, in step 104, the virtual feature map and the actual feature map are input into the adaptive domain adaptation network framework to obtain a fault classification; the execution process of the adaptive domain adaptation network is as follows:

[0046] First, features are extracted from the virtual data and the actual data to generate corresponding virtual feature maps and actual feature maps. The feature maps are then fed into a shared feature extractor to extract key features that can represent the characteristics of the data. Next, the key features are input into a classifier for fault classification. During this process, two losses are calculated: the classification loss used to evaluate the performance of the classifier in the classification task, and the domain adaptation loss used to reduce the distribution difference between the virtual data and the actual data. The two losses are integrated through a comprehensive loss function where λ is a weight parameter used to balance the influence of the classification loss and the domain adaptation loss.

[0047] The advantages and beneficial effects of the present invention are as follows:

[0048] The present invention performs a series of refined processing steps on the actual data of the target scenario and the virtual data generated through the phenomenological model respectively to achieve in-depth mining and fusion of data features. Specifically, the feature correlation maps of the actual data and the virtual data are extracted respectively. Based on these feature correlation maps, in-depth feature extraction is carried out to obtain the actual feature transition map and the virtual feature transition map respectively. By aligning the actual feature transition map and the virtual feature transition map, the feature distributions of the two domains are made consistent and coordinated, and the actual data feature map and the virtual data feature map are generated respectively. Fault classification processing is performed on the actual data feature map and the virtual data feature map to obtain the fault classification result. The fault classification result not only includes the fault type but also covers the indicators for measuring the severity of the fault. Through the above steps, it is possible to comprehensively capture and accurately classify the fault features in the target scenario. At the same time, with the supplement and enhancement of the virtual data to the actual data, the accuracy and reliability of fault classification are further improved. Through the extraction of feature correlation maps, the generation of feature transition maps, and the alignment of feature distributions, the in-depth fusion and optimization of multi-scale features are realized, providing a more solid technical support for fault detection and diagnosis. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 is the overall flowchart of the method in the embodiment of the present invention.

[0050] Figure 2 is the process diagram of generating virtual data for bearing faults in the embodiment of the present invention.

[0051] Figure 3 is the data processing flowchart in the embodiment of the present invention.

[0052] Figure 4 is the in-depth feature extraction flowchart in the embodiment of the present invention.

[0053] Figure 5It is a diagram of the adaptive domain adaptation module in an embodiment of the present invention.

[0054] Figure 6 It is a diagram of the adaptive domain adaptation network framework in an embodiment of the present invention. Detailed implementation manners

[0055] The following will explain in detail the specific implementation manners of the present invention with reference to the accompanying drawings. It should be understood that the specific implementation manners described herein are only for explaining and interpreting the present invention, and are not used to limit the present invention.

[0056] Bearing fault detection plays a crucial role in industrial applications, aiming to ensure the reliability and safety of mechanical systems. As a key rotating component in mechanical equipment, the health status of bearings directly affects the operating efficiency and lifespan of the entire system. Therefore, timely and accurately detecting bearing faults and performing maintenance is the key to avoiding unexpected shutdowns and significant losses.

[0057] Traditional bearing fault detection methods mainly rely on technologies such as vibration analysis, sound detection, and temperature monitoring. These methods can identify abnormal states of bearings to a certain extent, but have disadvantages such as poor adaptability to non-stationary working conditions and insufficient interpretability. In response to these challenges, this study proposes a physics-driven cross-domain digital twin framework to improve the accuracy and interpretability of bearing fault diagnosis under non-stationary conditions.

[0058] As Figure 1 shown, a bearing fault diagnosis method based on a physics-driven cross-domain digital twin framework includes the following steps:

[0059] Step 101: Obtain the actual data of the target scenario and generate virtual data through a phenomenological model.

[0060] For different target scenarios, vibration sensors are used to collect the characteristic information of multiple working condition data at different positions in the target scenario respectively, so as to obtain the one-dimensional vibration waveforms corresponding to each working condition data as the actual data. The position and number of sensors are not limited in this specification.

[0061] In one embodiment, as Figure 2 shown, the process of generating bearing fault virtual data includes the following steps:

[0062] Step 201: Define the fault model and parameters and generate a speed curve.

[0063] First, determine the type of bearing fault to be simulated (such as inner race fault, outer race fault, rolling element fault, etc.), and set the physical parameters of the bearing, including the number of rolling elements, the diameter of the rolling elements, the pitch diameter, the contact angle, etc. According to the actual working conditions or experimental requirements, define the rotational speed change curve of the bearing, including the acceleration, constant speed, and deceleration stages.

[0064] Step 202: Calculate the fault characteristic frequencies and generate impact signals.

[0065] According to the physical parameters and fault type of the bearing, calculate the fault characteristic frequencies, such as the inner race fault frequency, the outer race fault frequency, and the rolling element fault frequency. Generate signals simulating the fault impacts based on the fault characteristic frequencies and the rotational speed changes.

[0066] Step 203: Simulate random slip and generate vibration responses.

[0067] To simulate the random slip and time fluctuations in the actual operation of the bearing, introduce randomness into the impact signals, such as simulating the random fluctuations at the impact moments through a normal distribution. Input the impact signals into a simplified single-degree-of-freedom system model to simulate the vibration responses of the structure. The vibration response generation formula is as follows:

[0068]

[0069] where t represents the time, x(t) represents the vibration signal at time t, h(t) represents the response to a single impact, T is the impact interval, τ i represents the time deviation of the i-th impact, and h(t - iT - τ i ) represents the impulse response function at time t - iT - τ i , q(T) is the periodic modulation signal, q(iT) represents the modulation signal at the i-th period, and n(t) represents the noise.

[0070] Step 204: Add noise to generate virtual data.

[0071] To make the simulated signals closer to the actually measured signals, a certain level of noise needs to be added. The power of the noise can be controlled by the signal-to-noise ratio. Synthesize all the generated signals (including the vibration responses and the noise) to obtain the final simulated signals.

[0072] Through these steps and methods, high-quality simulated signals can be generated, covering virtual data sets of various fault types and non-stationary working conditions, creating virtual data for training, and simulating the bearing behavior under different speed changes.

[0073] Step 102: Extract the respective feature correlation diagrams of the actual data and the virtual data, and respectively generate the corresponding actual feature transition diagrams and virtual feature transition diagrams based on their respective feature correlation diagrams.

[0074] In one embodiment, as Figure 3 shown, the data processing flow includes the following steps:

[0075] Perform short-time Fourier transform on the virtual data and the actual data, and convert the vibration signal in the time domain into a vibration domain signal in the angular domain. The formula is as follows:

[0076] x o (θ) = x(t(θ))

[0077] where θ represents the rotation angle, x o (θ) represents the vibration signal in the angular domain, t(θ) is a function that converts the rotation angle θ into time t, and x(t(θ)) represents the vibration signal at the time point t(θ) corresponding to the specific angle θ;

[0078] Calculate the instantaneous autocorrelation function after angle alignment, and obtain the order-frequency cyclic spectrum correlation characteristic correlation diagram by using double Fourier transform. The formula is as follows:

[0079]

[0080] where α is the cyclic frequency, f is the conventional frequency, θ is the angle transformation, τ is the time delay, S x (α, f) represents the cyclic spectrum correlation function, which describes the cyclic stationarity of the signal, is the normalization factor, which is used to normalize the energy of the signal to the window width W, E[·] represents the expectation, and F θ→α，τ→f represents performing double Fourier transform, θ is transformed into the cyclic frequency α, τ is transformed into the conventional frequency f, and x o (θ) is the vibration signal in the angular domain, is the complex conjugate of x o (θ - τ), which represents the complex conjugate of the signal at the angle θ - τ.

[0081] Through the above embodiments, an actual characteristic correlation diagram and a virtual characteristic correlation diagram can be generated. These diagrams show the distribution of fault characteristics at different frequencies and modulation frequencies, which helps to extract and retain the physical characteristics related to bearing faults, thereby improving the accuracy and reliability of fault diagnosis.

[0082] In one embodiment, as Figure 4 shown, by performing deeper feature extraction on the actual characteristic correlation diagram and the virtual characteristic correlation diagram, using the powerful representation ability of the optimal ResNet50 deep learning model and combining the unique mechanism of the gradient reversal layer, the comprehensive capture and accurate classification of fault characteristics in the target scenario are realized.

[0083] Through the above embodiments, an actual feature transition map and a virtual feature transition map are generated. These transition maps not only retain the rich information of the original data, but also further enhance the feature expression ability through the optimization process of the deep learning model.

[0084] Step 103, by aligning the feature distributions of the two domains of the actual feature transition map and the virtual feature transition map, an actual data feature map and a virtual data feature map are respectively generated.

[0085] In one embodiment, the actual feature transition map and the virtual feature transition map are input into a domain adaptation module, and an actual data feature map and a virtual data feature map are respectively generated by aligning the feature distributions of their respective domains; wherein, the domain adaptation module includes a global domain discriminator and a local domain discriminator, and is adjusted according to the observed differences in the global and local distributions to achieve an optimal balance between marginal and conditional distribution alignment.

[0086] As Figure 5 shown, in the adaptive domain adaptation module, the global domain discriminator is used for adversarial training, and by learning to distinguish whether the input feature transition map comes from the actual feature transition map or the virtual feature transition map, the global distribution difference between the actual data and the virtual data is minimized;

[0087] Among them, the loss function learned by the global domain discriminator is as follows:

[0088]

[0089] Among them, is the loss of the global domain discriminator, N s and N t are the sample numbers of the virtual data and the actual data respectively, x i is the input sample, d i represents the domain label, d i =1 indicates that the sample comes from the virtual data, d i =0 indicates that the sample comes from the actual data, G f is the global domain discriminator, is the feature representation of the i-th sample, α is the cycle frequency, f is the conventional frequency, is the probability that the global domain discriminator predicts whether the sample comes from the virtual data or the real data given the feature

[0090] In the figure, the local domain discriminator is used to achieve the conditional distribution alignment of each fault category. The local domain discriminator works independently for each fault category, and by learning to distinguish whether the features of a specific category come from the virtual data or the actual data, it ensures that the feature distributions of the virtual data and the actual data are consistent at each category level;

[0091] ​Among them, the loss function learned by the local domain discriminator is as follows:

[0092]

[0093] Among them, represents the loss of the local domain discriminator, N s and N t are the sample numbers of virtual data and actual data respectively, x i is the input sample, d i is the domain label, d i,c represents the probability that the sample x i belongs to the category c, G f，c is the local domain discriminator, α is the cycle frequency, f is the regular frequency, is the feature representation of the i-th virtual data sample, is the feature representation of the i-th actual data sample, and represent the predicted probabilities that the model assigns to the virtual data and the actual data sample i belonging to the category c respectively.

[0094] It is adjusted according to the observed differences between the global and local distributions to achieve the optimal balance between marginal and conditional distribution alignment. The formula is as follows:

[0095]

[0096] Among them, ω is the adaptive weight, and represent the data sets of virtual data and actual data respectively, and represent the data subsets of the c-th category in virtual data and actual data respectively. C is the total number of categories, is the loss of the global domain discriminator, measuring the global distribution difference between virtual data and actual data ; opt is the loss of the local domain discriminator, measuring the distribution difference between virtual data and actual data under a specific category c. opt

[0097] The adaptive domain loss in the figure The calculation formula is as follows:

[0098]

[0099] Among them, is the total loss function of adaptive domain adaptation, ω is a weight parameter, is the loss of the global domain discriminator, is the loss of the local domain discriminator.

[0100] Step 104, perform fault classification on the actual data feature map and the virtual data feature map to obtain a fault classification result; the fault classification result includes a fault type and an index for measuring the severity of the fault.

[0101] In one embodiment, as Figure 6 shown, input the virtual feature map and the actual feature map into an adaptive domain adaptation network framework to obtain fault classification. The working process of the adaptive domain adaptation network framework is as follows:

[0102] First, extract features from the virtual data and the actual data to generate corresponding virtual feature maps and actual feature maps. These features are then fed into a shared feature extractor to extract key features that can represent the characteristics of the data. Next, these features are input into a classifier for fault classification. During this process, two losses are calculated: the classification loss used to evaluate the performance of the classifier in the classification task, and the domain adaptation loss optimally used to reduce the distribution difference between the virtual data and the actual data. These two losses are integrated through a comprehensive loss function where λ is a weight parameter used to balance the influence of the classification loss and the domain adaptation loss.

[0103] Through the above embodiments, the fault classification results are successfully obtained. These results not only cover specific types but also include key indicators for evaluating the severity of faults, providing profound insights into the mechanical health status, so that corresponding maintenance measures can be taken.

[0104] The above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. Bearing fault diagnosis method based on physically driven cross-domain digital twin framework, characterized by The steps include: Step 101: Acquire actual data of a target scene and generate virtual data through a phenomenological model; Using a vibration sensor to collect characteristic information of a plurality of working condition data at different positions in the target scene, so as to obtain vibration waveforms corresponding to each working condition data as actual data; Step 102: extracting the feature correlation graphs of the actual data and the virtual data respectively, and generating corresponding actual feature transition graphs and virtual feature transition graphs respectively based on the respective feature correlation graphs; Perform short-time Fourier transform on virtual data and actual data, and transform the vibration signal in the time domain into the vibration signal in the angle domain; calculate the instantaneous autocorrelation function after angle alignment, and use double Fourier transform to obtain the characteristic correlation diagram of order-frequency cyclic spectrum correlation; Step 103, generating an actual data feature map and a virtual data feature map respectively by aligning feature distributions of two domains of the actual feature transition map and the virtual feature transition map; Inputting the actual feature transition map and the virtual feature transition map into a domain adaptation module, generating the actual data feature map and the virtual data feature map respectively by aligning the feature distributions of their respective domains; the domain adaptation module includes a global domain discriminator and a local domain discriminator, which are adjusted according to the observed differences between global and local distributions to achieve an optimal balance between marginal and conditional distribution alignment; Step 104: perform fault classification on the actual data characteristic graph and the virtual data characteristic graph to obtain a fault classification result.

2. The bearing fault diagnosis method based on the physically driven cross-domain digital twin framework according to claim 1 is characterized in that: In step 101, the process of generating virtual data of bearing fault includes the following steps: Step 201, define fault model and parameters, and generate speed curve; Determine the type of bearing fault that needs to be simulated, set the physical parameters of the bearing, and define the speed change curve of the bearing according to the actual working conditions; Step 202, calculating the fault characteristic frequency and generating an impact signal; According to the physical parameters and fault type of the bearing, the fault characteristic frequency is calculated, and according to the fault characteristic frequency and speed change, a signal simulating the fault impact is generated; Step 203, simulating random sliding to generate vibration response; Introduce randomness into the impact signal, input the impact signal into the single-degree-of-freedom system model, and simulate the vibration response of the structure; Step 204: Add noise to generate virtual data.

3. The bearing fault diagnosis method based on the physically driven cross-domain digital twin framework according to claim 2 is characterized in that: In step 203, the vibration response generation formula is as follows: Where t represents the time, x(t) represents the vibration signal at time t, h(t) represents the response of a single shock, T represents the shock interval, τ i represents the time deviation of the ith impact, h(t-iT-τ i ) represents the time t-iT-τ i The impulse response function of , q(T) represents the periodic modulation signal, q(iT) represents the modulation signal in the i-th period, and n(t) represents the noise.

4. The bearing fault diagnosis method based on the physically driven cross-domain digital twin framework according to claim 1 is characterized in that: In step 102, the vibration signal in the time domain is converted into a vibration signal in the angle domain, and the formula is as follows: x o (θ)=x(t(θ)) Among them, θ represents the rotation angle, x o (θ) represents the vibration signal in the angle domain, t(θ) is the function that converts the rotation angle θ into time t, and x(t(θ)) represents the vibration signal at the time point t(θ) corresponding to a specific angle θ.

5. The bearing fault diagnosis method based on the physically driven cross-domain digital twin framework according to claim 4 is characterized in that: In step 102, the autocorrelation function formula is as follows: Where α is the cycle frequency, f is the regular frequency, τ is the time delay, S x (α, f) represents the cyclic spectral correlation function, which describes the cyclostationarity of the signal. represents the normalization factor, which is used to normalize the signal energy to the window width W, E[·] represents the expectation, and F θ→α，τ→f Indicates double Fourier transform, θ is transformed to cyclic frequency α, τ is transformed to regular frequency f, is x o The complex conjugate of (θ-τ) represents the complex conjugate of the signal at the angle θ-τ.

6. The bearing fault diagnosis method based on the physically driven cross-domain digital twin framework according to claim 1 is characterized in that: In step 103, by constructing the loss of the global domain discriminator, the loss of the local domain discriminator and the weight parameter, the total loss function of the adaptive domain adaptation is obtained, and the calculation formula is as follows: in, represents the total loss function of adaptive domain adaptation, represents the loss of the global domain discriminator, represents the loss of the local domain discriminator.

7. The bearing fault diagnosis method based on the physically driven cross-domain digital twin framework according to claim 6 is characterized in that: The global domain discriminator is used for adversarial training, and minimizes the global distribution difference between the actual data and the virtual data by learning to distinguish whether the input feature transition map is from the actual feature transition map or the virtual feature transition map; Among them, the loss function of the global domain discriminator learning is as follows: in, represents the loss of the global domain discriminator, N s and N t Represents the sample size of virtual data and actual data, x i represents the input sample, d i is the domain label, indicating whether the sample comes from virtual data or real data, G f represents the global domain discriminator, represents the characteristic representation of the i-th sample, α represents the cyclic frequency, f represents the regular frequency, Indicates that given a feature In the case of , the global domain discriminator predicts the probability that the sample comes from virtual data or real data.

8. The bearing fault diagnosis method based on the physically driven cross-domain digital twin framework according to claim 6 is characterized in that: The local domain discriminator is used to achieve conditional distribution alignment of each fault category. The local domain discriminator works independently for each fault category and distinguishes whether the features of a specific category come from virtual data or actual data through learning, so that the feature distribution of virtual data and actual data at each category level is consistent; Among them, the loss function of the local area discriminator learning is as follows: in, represents the loss of the local domain discriminator, N s and N t Represents the sample size of virtual data and actual data, x i represents the input sample, d i Indicates the domain label, d i，c Represents sample x i The probability of belonging to category c, G f，c represents the local domain discriminator, α represents the cycle frequency, f represents the regular frequency, represents the feature representation of the i-th virtual data sample, represents the feature representation of the i-th actual data sample, and They represent the model's predicted probability that the virtual data and actual data sample i belong to category c, respectively.

9. The bearing fault diagnosis method based on the physically driven cross-domain digital twin framework according to claim 6 is characterized in that: Adjustments are made based on the observed differences between global and local distributions to achieve the optimal balance between marginal and conditional distribution alignment. The formula for the weight parameter is constructed as follows: Among them, ω represents the adaptive weight, and represent datasets of virtual data and real data respectively, and denote the data subset of category c in virtual data and actual data respectively, C is the total number of categories, represents the loss of the global domain discriminator, measuring the virtual data and actual data The global distribution difference between represents the loss of the local domain discriminator, which measures the distribution difference between virtual data and real data under a specific category c.

10. The bearing fault diagnosis method based on the physically driven cross-domain digital twin framework according to claim 1 is characterized in that: In the step 104, the virtual feature map and the actual feature map are input into the self-adaptive domain adaptation network framework to obtain the fault classification; The execution process of the adaptive domain adaptation network is as follows: First, features are extracted from virtual data and actual data to generate corresponding virtual feature maps and actual feature maps. The feature maps are then fed into a shared feature extractor to extract key features that can represent the characteristics of the data. Next, the key features are fed into a classifier for fault classification. In this process, two types of losses are calculated: classification loss Used to evaluate the performance of classifiers on classification tasks, domain adaptation loss Used to reduce the distribution difference between virtual data and actual data; the two losses are combined through the loss function is integrated, where λ is a weight parameter used to balance the impact of classification loss and domain adaptation loss.

Images