Bearing fault diagnosis method based on physical driving cross-domain digital twin framework

Abstract

The application discloses a bearing fault diagnosis method based on a physical driving cross-domain digital twin framework, actual data of a target scene is acquired, and virtual data is generated through a phenomenological model; respective feature correlation graphs of the actual data and the virtual data are extracted, and respective actual feature transition graphs and virtual feature transition graphs are generated based on the respective feature correlation graphs; feature distributions of the actual feature transition graph and the virtual feature transition graph are aligned, and actual data feature graphs and virtual data feature graphs are respectively generated; fault classification is performed on the actual data feature graphs and the virtual data feature graphs to obtain fault classification results; the fault classification results include fault types and fault severities. The application realizes comprehensive capture and accurate classification of fault features in the target scene, improves the accuracy and reliability of fault classification, realizes deep fusion and optimization of multi-scale features, and provides more solid technical support for fault detection and diagnosis.

Description

Technical Field

[0001] This invention belongs to the field of industrial equipment condition monitoring and fault diagnosis technology, specifically relating to a bearing fault diagnosis method based on a physical-driven cross-domain digital twin framework. Background Technology

[0002] Rolling bearings are crucial components widely used in rotating machinery, and their operating condition directly affects the overall performance and safety of the equipment. However, bearings are susceptible to factors such as load fluctuations, speed variations, and environmental noise during long-term operation, leading to failures. Traditional fault diagnosis methods typically rely on manual feature extraction, statistical analysis, or models based on steady-state signals. These methods are poorly adapted to non-stationary operating conditions and struggle 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 heavily rely on large amounts of labeled data, while fault data from industrial sites is often difficult to obtain. Furthermore, due to variations in data distribution, models trained in laboratory environments are difficult to directly transfer to real-world operating conditions, resulting in insufficient generalization ability. Therefore, there is an urgent need for a bearing fault diagnosis method that can combine physical modeling with data-driven approaches and effectively adapt to non-stationary operating conditions. Summary of the Invention

[0004] To overcome the shortcomings of existing technologies and achieve the goal of bearing health monitoring and anomaly detection under non-stationary operating conditions, this invention adopts the following technical solution:

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

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

[0007] Vibration sensors are used to collect feature information of multiple working condition data at different locations in the target scenario to obtain one-dimensional vibration waveforms corresponding to each working condition data as actual data. The generated high-quality simulation signals cover virtual datasets of various fault types and non-stationary working conditions, and virtual data for training are created to simulate bearing behavior under different speed changes.

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

[0009] Short-time Fourier transforms are performed on virtual and actual data to transform the vibration signal in the time domain into a vibration signal in the angle domain. The instantaneous autocorrelation function after angle alignment is calculated, and a double Fourier transform is used to obtain the characteristic correlation map of the order-frequency cyclic spectrum correlation. The generated actual and virtual characteristic correlation maps show the distribution of fault features at different frequencies and modulation frequencies, which helps to extract and retain physical features related to bearing faults, thereby improving the accuracy and reliability of fault diagnosis.

[0010] 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 generated respectively;

[0011] The actual feature transition map and the virtual feature transition map are input into the domain adaptation module, and the actual data feature map and the virtual data feature map are generated by aligning the feature distribution 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 the global and local distributions to achieve an optimal balance between the alignment of marginal and conditional distributions.

[0012] Step 104: Perform fault classification on the actual data feature map and the virtual data feature map to obtain fault classification results. The fault classification results include fault types and indicators used to measure the severity of faults.

[0013] Furthermore, in step 101, the bearing fault virtual data generation process includes the following steps:

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

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

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

[0017] Based on the physical parameters and fault type of the bearing, calculate the fault characteristic frequencies, such as the inner ring fault frequency, outer ring fault frequency, and rolling element fault frequency; and generate a signal simulating fault impact based on the fault characteristic frequencies and speed changes.

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

[0019] To simulate the random slippage and time fluctuations in actual bearing operation, randomness is introduced into the impact signal. For example, the random fluctuations at the moment of impact are simulated by using a normal distribution. The impact signal is then 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 analog signal closer to the actual 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 generated signals (including vibration response and noise) are synthesized to obtain the final analog signal.

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

[0023]

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

[0025] Furthermore, in step 102, the vibration signal in the time domain is converted into a vibration signal in the angular domain, as shown in the following formula:

[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 a specific angle θ.

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

[0029]

[0030] Where α represents the cycle frequency, f represents the normal frequency, τ represents the time delay, and S x (α, f) represents the cyclic spectral correlation function, which describes the cyclic stationarity of the signal. E[·] represents the normalization factor used to normalize the energy of the signal to the window width W, and F represents the expectation. θ→α，τ→fThis indicates that a double Fourier transform is performed, with θ transforming to the cyclic frequency α and τ transforming to the normal frequency f. It is x o The complex conjugate of (θ-τ) represents the complex conjugate of the signal at the angle θ-τ.

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

[0032]

[0033] in, This represents the total loss function for adaptive domain adaptation. This represents the loss of the global neighborhood discriminator. This represents the loss of the local neighborhood discriminator.

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

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

[0036]

[0037] in, N represents the loss of the global neighborhood discriminator. s and N t x represents the sample size of the virtual data and the actual data, respectively. i Indicates the input sample, d i For the domain label, G indicates whether the sample comes from virtual data or real data. f This represents a global neighborhood discriminator. Let α represent the feature representation of the i-th sample, α represent the cyclic frequency, and f represent the normal frequency. Indicates that under a given feature In this case, the global domain discriminator predicts the probability that a sample comes from virtual data or real data.

[0038] Furthermore, the local neighborhood discriminator is used to align the conditional distribution of each fault category. The local neighborhood discriminator works independently for each fault category and learns to distinguish whether the features of a specific category come from virtual data or real data, so that the feature distribution of virtual data and real data is consistent at each category level.

[0039] The loss function learned by the local neighborhood discriminator is as follows:

[0040]

[0041] in, N represents the loss of the local neighborhood discriminator. s and N t x represents the sample size of the virtual data and the actual data, respectively. i Indicates the input sample, d i Represents the field label, d i，c Indicates sample x i The probability of belonging to category c, G f，c This represents a local neighborhood discriminator, where α represents the cycling frequency and f represents the normal frequency. This represents the feature representation of the i-th virtual data sample. This represents the feature representation of the i-th actual data sample. and These represent the predicted probabilities of the model for virtual data sample i and real data sample i belonging to category c, respectively.

[0042] Furthermore, adjustments are made based on the observed differences between global and local distributions to achieve an optimal balance between marginal and conditional distribution alignment. The formula for the constructed weight parameters is as follows:

[0043]

[0044] Where ω represents the adaptive weight, and These represent datasets containing virtual data and actual data, respectively. and Let represent the subsets of data in category c from the virtual data and the actual data, respectively, where C is the total number of categories. This represents the loss of the global domain discriminator, measuring the virtual data. and actual data Global distribution differences between them This represents the loss of the local domain discriminator, measuring the distributional difference between virtual and real data under a specific category c.

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

[0046] First, features are extracted from virtual and real data to generate corresponding virtual and real feature maps. These feature maps are then fed into a shared feature extractor to extract key features that represent the data characteristics. Next, these key features are input into a classifier for fault classification. During this process, two losses are calculated: classification loss and classification loss. Domain adaptation loss is used to evaluate the performance of a classifier on classification tasks. This is used to reduce the distributional discrepancy between virtual and real data; the two losses are combined through a loss function. The data is integrated, where λ is a weighting parameter used to balance the effects of classification loss and domain adaptation loss.

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

[0048] This invention performs a series of refined processing steps on both actual data and virtual data generated through a phenomenological model of the target scenario to achieve in-depth mining and fusion of data features. Specifically, feature correlation maps are extracted from both actual and virtual data. Based on these feature correlation maps, deep feature extraction is performed to obtain actual feature transition maps and virtual feature transition maps. By aligning the actual and virtual feature transition maps, the feature distributions of the two domains achieve consistency and coordination, generating actual data feature maps and virtual data feature maps respectively. Fault classification processing is then performed on the actual and virtual data feature maps to obtain fault classification results. These fault classification results not only include fault types but also cover indicators used to measure fault severity. Through these steps, comprehensive capture and accurate classification of fault features in the target scenario can be achieved. Furthermore, the supplementation and enhancement of actual data by virtual data further improves the accuracy and reliability of fault classification. By extracting feature correlation maps, generating feature transition maps, and aligning feature distributions, deep fusion and optimization of multi-scale features are achieved, providing more robust technical support for fault detection and diagnosis. Attached Figure Description

[0049] Figure 1 This is an overall flowchart of the method in the embodiments of the present invention.

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

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

[0052] Figure 4 This is a flowchart of deep feature extraction in an embodiment of the present invention.

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

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

[0055] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are for illustration and explanation only and are not intended 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 critical rotating component in mechanical equipment, the health of bearings directly affects the operating efficiency and lifespan of the entire system. Therefore, timely and accurate detection and maintenance of bearing faults are key to avoiding unexpected downtime and significant losses.

[0057] Traditional bearing fault detection methods mainly rely on vibration analysis, sound detection, and temperature monitoring. While these methods can identify abnormal bearing conditions to some extent, they suffer from poor adaptability to non-stationary operating conditions and insufficient interpretability. To address 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] like Figure 1 As shown, a bearing fault diagnosis method based on a physical-driven cross-domain digital twin framework includes the following steps:

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

[0060] For different target scenarios, vibration sensors are used to collect feature information from multiple operating condition data at different locations within the target scenario, obtaining one-dimensional vibration waveforms corresponding to each operating condition data as actual data. This specification does not limit the location or number of sensors.

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

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

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

[0064] Step 202: Calculate the fault characteristic frequency and generate the impact signal.

[0065] Based on the bearing's physical parameters and fault type, calculate the fault characteristic frequencies, such as the inner ring fault frequency, outer ring fault frequency, and rolling element fault frequency. Then, generate a signal simulating fault impact based on the fault characteristic frequencies and rotational speed variations.

[0066] Step 203: Simulate random sliding to generate vibration response.

[0067] To simulate random slippage and time fluctuations during actual bearing operation, randomness is introduced into the impact signal, such as by using a normal distribution to simulate random fluctuations at the moment of impact. The impact signal is then input into a simplified single-degree-of-freedom system model to simulate the vibration response of the structure. The vibration response generation formula is as follows:

[0068]

[0069] Where t represents time, x(t) represents the vibration signal at time t, h(t) represents the response of a single impact, T is the impact interval, and τ i h(t-iT-τ) represents the time deviation of the i-th impact. i ) represents time t-iT-τ i The impulse response function is given by q(T), where q(iT) is the periodically modulated signal, q(iT) represents the modulated signal in the i-th period, and n(t) represents noise.

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

[0071] To make the analog signal closer to the actual 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 generated signals (including vibration response and noise) are then synthesized to obtain the final analog signal.

[0072] These steps and methods can generate high-quality simulated signals, covering virtual datasets of various fault types and non-stationary operating conditions, creating virtual data for training to simulate bearing behavior under different speed variations.

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

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

[0075] The short-time Fourier transform is performed on both virtual and real data to convert the vibration signal in the time domain into a vibration signal in the angle 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 a specific angle θ;

[0078] The instantaneous autocorrelation function after angle alignment is calculated, and the eigencorrelation map of the order-frequency cyclic spectrum correlation is obtained by using a double Fourier transform. The formula is as follows:

[0079]

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

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

[0082] In one embodiment, such as Figure 4 As shown, by performing deeper feature extraction on the actual feature correlation map and the virtual feature correlation map, and by leveraging the powerful representation capabilities of the optimal ResNet50 deep learning model, combined with the unique mechanism of the gradient inversion layer, we can achieve comprehensive capture and accurate classification of fault features in the target scene.

[0083] Through the above embodiments, actual feature transition maps and virtual feature transition maps were generated. These transition maps not only retain the rich information of the original data, but also further enhance the expressive power of the features through optimization processing by deep learning models.

[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 generated respectively.

[0085] In one embodiment, the actual feature transition map and the virtual feature transition map are input into the domain adaptation module, and the actual data feature map and the virtual data feature map are generated 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 the global and local distributions to achieve an optimal balance between the alignment of marginal and conditional distributions.

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

[0087] The loss function learned by the global domain discriminator is as follows:

[0088]

[0089] in, It is the loss of the global neighborhood discriminator, N s and N t These represent the sample sizes of virtual data and actual data, respectively, x. i For the input sample, d i Represents a domain label, d i =1 indicates that the sample comes from virtual data, d i =0 indicates that the sample comes from actual data, G f It is a global domain discriminator. Here, α is the feature representation of the i-th sample, α is the cyclic frequency, and f is the normal frequency. Given features In this case, the global domain discriminator predicts the probability that a sample comes from virtual data or real data.

[0090] The local neighborhood discriminator in the figure is used to align the conditional distribution of each fault category. The local neighborhood discriminator works independently for each fault category. By learning to distinguish whether the features of a specific category come from virtual data or real data, it ensures that the feature distribution of virtual data and real data is consistent at each category level.

[0091] The loss function learned by the local neighborhood discriminator is as follows:

[0092]

[0093] in, N represents the loss of the local neighborhood discriminator. s and N t These represent the sample sizes of virtual data and actual data, respectively, x. i It is the input sample, d i It's a domain tag, d i,c Indicates sample x i The probability of belonging to category c, G f，c It is a local neighborhood discriminator, where α is the cyclic frequency and f is the normal frequency. It is the feature representation of the i-th virtual data sample. It is the feature representation of the i-th actual data sample. and These represent the predicted probabilities of the model for virtual data sample i and real data sample i belonging to category c, respectively.

[0094] Adjustments are made based on the observed differences between global and local distributions to achieve an optimal balance between marginal and conditional distribution alignment, as shown in the following formula:

[0095]

[0096] Where ω is the adaptive weight. and Data sets representing virtual data and real data, respectively. and Let represent the subsets of data in category c from the virtual data and the actual data, respectively, where C is the total number of categories. It is the loss of the global domain discriminator, used to measure virtual data. and actual data Global distribution differences between them The optimal loss is that of the local neighborhood discriminator, which measures the distributional difference between virtual and real data under a specific category c.

[0097] Adaptive neighborhood loss in the figure The calculation formula is as follows:

[0098]

[0099] in, It is the total loss function for adaptive domain adaptation, where ω is a weight parameter. It is the loss of the global domain discriminator. It is the loss of the local neighborhood discriminator.

[0100] Step 104: Perform fault classification on the actual data feature map and the virtual data feature map to obtain fault classification results; the fault classification results include fault types and indicators used to measure the severity of faults.

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

[0102] First, features are extracted from both virtual and real data to generate corresponding virtual and real feature maps. These features are then fed into a shared feature extractor to extract key features that represent the characteristics of the data. Next, these features are input into a classifier for fault classification. During this process, two types of losses are calculated: classification loss and classification loss. Domain adaptation loss is used to evaluate the performance of a classifier on a classification task. The optimal approach is to reduce the distributional discrepancy between virtual and real data. These two losses are combined using a single loss function. The data is integrated, where λ is a weighting parameter used to balance the effects of classification loss and domain adaptation loss.

[0103] Through the above embodiments, fault classification results were successfully obtained. These results not only cover specific types, but also include key indicators for assessing the severity of faults, providing a deep insight into the health status of the machinery, thereby enabling appropriate maintenance measures to be taken.

[0104] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A bearing fault diagnosis method based on a physically driven cross-domain digital twin framework, characterized by The method comprises the following steps: Step 101, obtaining actual data of a target scene and generating virtual data through a phenomenological model; Step 102, extracting feature correlation graphs of the actual data and the virtual data respectively, and generating actual feature transition graphs and virtual feature transition graphs respectively based on the respective feature correlation graphs; Step 103, generating actual data feature graphs and virtual data feature graphs respectively by aligning the feature distributions of the actual feature transition graphs and the virtual feature transition graphs in two domains; Step 104, classifying faults of the actual data feature graphs and the virtual data feature graphs to obtain fault classification results. In the step 101, the bearing fault virtual data generation process comprises the following steps: Step 201, defining a fault model and parameters to generate a speed curve; Step 202, calculating a fault feature frequency to generate an impact signal; 2. The bearing fault diagnosis method based on the physical drive cross-domain digital twin framework according to claim 1, characterized in that: Step 203, simulating random sliding to generate a vibration response; Step 204, adding noise to generate virtual data. In the step 203, the vibration response generation formula is as follows: In the step 102, the vibration signal in the time domain is converted into the vibration signal in the angle domain, and the formula is as follows: In the step 102, the autocorrelation function formula is as follows: In the 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: The global domain discriminator is used for adversarial training, and by learning to distinguish the feature transition graphs input from the actual feature transition graphs or the virtual feature transition graphs, the global distribution difference between the actual data and the virtual data is minimized; The loss function learned by the global domain discriminator is as follows:

3. The bearing fault diagnosis method based on the physical drive cross-domain digital twin framework according to claim 2, characterized in that: ​ where t represents a time, x(t) represents a vibration signal at the time t, h(t) represents a response of a single impact, T represents an impact interval, τ i represents a time deviation of the i-th impact, h(t-iT-τ i ) represents a pulse response function at the time t-iT-τ i , q(T) represents a periodic modulation signal, q(iT) represents a modulation signal at the i-th period, and n(t) represents a noise.

4. The bearing fault diagnosis method based on the physical drive cross-domain digital twin framework according to claim 1, characterized in that: ​ x o (θ) = x(t(θ)) where θ represents a rotation angle, x o (θ) represents a vibration signal in the angle domain, t(θ) is a function of converting the rotation angle θ to time t, and x(t(θ)) represents a vibration signal at a time point t(θ) corresponding to a specific angle θ.

5. The bearing fault diagnosis method based on the physical drive cross-domain digital twin framework according to claim 4, characterized in that: ​ where a denotes the cyclic frequency, f denotes the regular frequency, τ denotes the time delay, S x (α, f) denotes the cyclic spectral correlation function, describing the cyclostationarity of the signal, denotes a normalization factor, normalizing the energy of the signal to the window width W, E[·] denotes the expectation, F θ→α，τ→f denotes the double Fourier transform, θ transforms to the cyclic frequency a, τ transforms to the regular frequency f, is the complex conjugate of x o (θ - τ), denoting the complex conjugate of the signal at the angle θ - τ.

6. The bearing fault diagnosis method based on the physical drive cross-domain digital twin framework according to claim 1, characterized in that: ​ wherein, represents the total loss function of the adaptation in the adaptive field, 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 physical drive cross-domain digital twin framework according to claim 6, characterized in that: ​ ​ where, represents the loss of the global domain discriminator, N s and N t represent the number of samples of virtual data and real data, respectively, 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 feature representation of the i-th sample, a represents the cycle frequency, and f represents the regular frequency, represents the probability that the global domain discriminator predicts that the sample comes from virtual data or real data given the feature representation.

8. The bearing fault diagnosis method based on the physical drive cross-domain digital twin framework according to claim 6, characterized in that: The local domain discriminator is used to realize the alignment of the conditional distribution of each fault category, the local domain discriminator works independently for each fault category, and the feature distribution of the virtual data and the actual data at each category level is consistent by learning to distinguish whether the features of a specific category come from the virtual data or the actual data; The loss function learned by the local domain discriminator is as follows: where, denotes the loss of the local domain discriminator, N s and N t denote the number of samples of virtual and real data, respectively, x i denotes an input sample, d i denotes a domain label, d i，c denotes a sample x i belongs to class c, G f，c denotes the local domain discriminator, a denotes the cycle frequency, and f denotes the regular frequency, denotes the feature representation of the i-th virtual data sample, denotes the feature representation of the i-th real data sample, and denote the predicted probability of class c for the i-th virtual and real data sample, respectively.

9. The bearing fault diagnosis method based on the physical drive cross-domain digital twin framework according to claim 6, characterized in that: According to the difference between the observed global and local distributions, the optimal balance between the marginal and conditional distribution alignment is realized, and the formula of the weight parameter is as follows: Where ω represents the adaptive weight, and These represent datasets containing virtual data and actual data, respectively. and Let represent the subsets of data in category c from the virtual data and the actual data, respectively, where C is the total number of categories. This represents the loss of the global domain discriminator, measuring the virtual data. and actual data Global distribution differences between them This represents the loss of the local domain discriminator, measuring the distributional difference between virtual and real data under a specific category c.

10. The bearing fault diagnosis method based on the physical drive cross-domain digital twin framework according to claim 1, characterized in that: In the step 104, the virtual feature map and the actual feature map are input into the adaptive domain adaptation network framework to obtain fault classification. The execution process of the adaptive domain adaptation network is as follows: First, features are extracted from both virtual and real data, and corresponding virtual and real feature maps are generated. 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. In this process, two losses are calculated: a classification loss for evaluating the performance of the classifier on the classification task, and a domain adaptation loss for reducing the distribution difference between virtual and real data. The two losses are combined through a comprehensive loss function where λ is a weight parameter for balancing the influence of the classification loss and the domain adaptation loss.

Images