Bearing fault diagnosis method based on dynamical model under small sample condition

Abstract

The invention discloses a dynamical model-based bearing fault diagnosis method under a small sample condition, and relates to the technical field of fault diagnosis, and the method constructs a plurality of multi-degree-of-freedom dynamical models to generate simulation data covering an inner ring, an outer ring, a rolling body and a fault-free state, remarkably reduces the dependence on real fault data, and improves the fault diagnosis efficiency. The problem of data scarcity caused by difficult sensor installation and long-term fault-free operation of equipment is solved; then feature enhancement processing is conducted on the simulation data based on the fault data enhancement model, synthetic data consistent with the simulation data in feature are generated, the synthetic data and the simulation data are integrated to form a virtual data set, the data diversity is effectively improved, and dependence on real data is greatly reduced; and finally, pre-training a transfer learning model by using the virtual data set, and adapting small sample experiment data through a dynamic parameter adjustment strategy to complete bearing fault classification. And based on the classification result, determining the fault state of the bearing, and realizing the diagnosis of the bearing fault.

Description

Technical Field

[0001] This application generally relates to the technical field of fault diagnosis, and particularly relates to a bearing fault diagnosis method based on a dynamic model under small sample conditions. Background Art

[0002] As a core component of rotating mechanical equipment, bearings play a crucial role in the operation of mechanical equipment, mainly responsible for supporting and transmitting the rotational motion of mechanical components; however, the working environment where bearings are located is extremely complex, and they often face harsh conditions such as variable speed and load, high temperature and humidity, and fatigue damage. These factors make bearings extremely prone to failure, seriously affecting the safe and stable operation of equipment; therefore, monitoring the health status of bearings, timely judging potential faults and conducting fault diagnosis have important research value.

[0003] In recent years, with the rapid development of intelligent algorithms, bearing fault diagnosis algorithms have gradually become more intelligent; due to their strong feature extraction ability, deep learning methods have been widely used in bearing fault diagnosis; however, fault diagnosis models based on deep learning require a large amount of real fault data for training; in practical applications, obtaining bearing data faces two major challenges: firstly, the harsh operating environment of bearings makes it difficult to install sensors, and it is difficult to obtain fault data of bearings under real working conditions; secondly, most of the equipment is in a fault-free state during operation, resulting in a small sample size of fault data, which is difficult to meet the requirements of model training. Summary of the Invention

[0004] In view of the above-mentioned defects or deficiencies in the prior art, it is desirable to provide a bearing fault diagnosis method based on a dynamic model under small sample conditions.

[0005] This application provides a bearing fault diagnosis method based on a dynamic model under small sample conditions, including the following steps: S100: Construct multiple multi-degree-of-freedom dynamic models, and respectively generate simulation data containing corresponding fault features based on each of the multi-degree-of-freedom dynamic models; wherein, each dynamic model corresponds to a preset fault state of the bearing, and each preset fault state has corresponding fault features, and the preset fault states include: inner ring fault, outer ring fault, rolling element fault, and no fault; S200: Perform feature enhancement processing on the simulation data based on the CCWGAN-GP fault data enhancement model, generate synthetic data with the same features as the simulation data, and integrate the synthetic data with the simulation data to form a virtual data set; S300: Use the virtual data set to pre-train a transfer learning model, and adapt to small sample experimental data through a dynamic parameter adjustment strategy to complete bearing fault classification; S400: Based on the bearing fault classification result, determine the fault state the bearing is in, and realize the diagnosis of bearing faults.

[0006] According to the technical solution provided by this application, the multiple multi-degree-of-freedom dynamics models are four, namely the inner race fault dynamics model, the outer race fault dynamics model, the rolling element fault dynamics model, and the fault-free dynamics model.

[0007] According to the technical solution provided by this application, each preset fault state has a corresponding fault location. The steps of generating simulation data containing corresponding fault characteristics based on each of the multi-degree-of-freedom dynamics models include: S110: For different preset fault states, judge whether to trigger the corresponding fault switch according to the corresponding fault location; S120: When the fault switch is triggered, calculate the local fault radial deformation; S130: According to the local fault radial deformation, calculate the rolling element deformation using Formula 1; Formula 1; Where, is the displacement of the outer race in the horizontal direction, is the displacement of the outer race in the vertical direction, is the displacement of the inner race in the horizontal direction, is the displacement of the inner race in the vertical direction, is the bearing clearance, is the i angular position of the th rolling element; is the fault switch function, is the local fault radial deformation; S140: Judge whether the rolling element deformation is greater than 0; S150: When the rolling element deformation is greater than 0, the switch function of the rolling element is 1 at this time; otherwise, the switch function of the rolling element is 0; Formula 2; Formula 3; Where, is the non-linear contact force of the bearing in the horizontal direction, is the non-linear contact force of the bearing in the vertical direction, is the equivalent contact stiffness between the rolling element and the inner and outer raceways, is the rolling element deformation, is the angular position of the i th rolling element, is the switching function of the rolling element; S170: Substitute the non - linear contact force of the bearing in the horizontal direction and the non - linear contact force of the bearing in the vertical direction into Equation Four to obtain the simulation data of the corresponding fault characteristics; Equation Four; where, is the mass of the outer ring, is the mass of the rolling element, is the mass of the inner ring, is the comprehensive damping coefficient of the outer ring, is the damping coefficient of the rolling element in the horizontal direction, is the damping coefficient of the rolling element in the vertical direction, is the damping coefficient of the inner ring in the horizontal direction, is the damping coefficient of the inner ring in the vertical direction, is the stiffness coefficient of the outer ring in the horizontal direction, is the stiffness coefficient of the outer ring in the vertical direction, is the stiffness coefficient of the rolling element in the horizontal direction, is the stiffness coefficient of the rolling element in the vertical direction, is the stiffness coefficient of the inner ring in the horizontal direction, is the stiffness coefficient of the inner ring in the vertical direction, is the displacement of the outer ring in the horizontal direction, is the displacement of the outer ring in the vertical direction, is the velocity of the outer ring in the horizontal direction, is the velocity of the outer ring in the vertical direction, is the acceleration of the outer ring in the horizontal direction, is the acceleration of the outer ring in the vertical direction, is the displacement of the rolling element in the horizontal direction, is the displacement of the rolling element in the vertical direction, is the velocity of the rolling element in the horizontal direction, is the velocity of the rolling element in the vertical direction, is the acceleration of the rolling element in the horizontal direction, is the acceleration of the rolling element in the vertical direction, is the displacement of the inner ring in the horizontal direction, is the displacement of the inner ring in the vertical direction, is the velocity of the inner ring in the horizontal direction, is the velocity of the inner ring in the vertical direction, is the acceleration of the inner ring in the horizontal direction, is the acceleration of the inner ring in the vertical direction, W is the gravity borne by the bearing.

[0008] According to the technical solution provided by the present application, the fault switch function includes: an inner ring fault switch function , an outer ring fault switch function , a fault switch function for the contact between the rolling element and the outer ring , a fault switch function for the contact between the rolling element and the inner ring , and a no-fault switch function ; Step S110 includes the following steps: S111: Based on the inner ring fault dynamics model, when the value of the inner ring fault position satisfies Formula Five, trigger the inner ring fault switch. At this time, the value of the inner ring fault switch function is 1; otherwise, the value of the inner ring fault switch function is 0; Formula Five; S112: Based on the outer ring fault dynamics model, when the value of the outer ring fault position satisfies Formula Six, trigger the outer ring fault switch. At this time, the value of the outer ring fault switch function is 1; otherwise, the value of the outer ring fault switch function is 0; Formula Six; S113: Based on the rolling element fault dynamics model, when the value of the rolling element fault position simultaneously satisfies Formula Seven and Formula Eight, trigger the rolling element fault switch. At this time, the values of the fault switch function for the contact between the rolling element and the outer ring and the fault switch function for the contact between the rolling element and the inner ring are both 1; otherwise, the values of the fault switch function for the contact between the rolling element and the outer ring and the fault switch function for the contact between the rolling element and the inner ring are both 0; Formula Seven; Formula Eight; wherein, is the inner ring radius, is the outer ring radius, L is the fault width, is the i th angular position of the rolling element; S114: Trigger the fault-free switch based on the fault-free dynamics model, and the value of the fault-free switch function is 0.

[0009] According to the technical solution provided by the present application, the step S120 includes the following steps: S121: If the inner-race fault switch is triggered, when , calculate the local fault radial deformation using Equation Nine; otherwise, the value of the local fault radial deformation is h ; Equation Nine; S122: If the outer-race fault switch is triggered, when , calculate the local fault radial deformation using Equation Ten; otherwise, the value of the local fault radial deformation is h ; Equation Ten; S123: If the rolling element fault switch is triggered, when , calculate the local fault radial deformation using Equation Eleven; otherwise, the value of the local fault radial deformation is h ; Equation Eleven; where is the rolling element radius, L is the fault width, is the inner-race radius, is the outer-race radius, h is the fault height; S124: If the fault-free switch is triggered, the value of the local fault radial deformation is 0.

[0010] According to the technical solution provided by the present application, calculate the angular position of the i th rolling element using Equation Twelve; Equation Twelve; where Z is the total number of rolling elements, i is the rolling element number, is the rolling element diameter, is the bearing pitch diameter, is the inner-race rotational speed, is the initial angular position of the cage.

[0011] According to the technical solution provided by the present application, the outer-race fault position is a fixed value. Calculate the inner-race fault position using Equation Thirteen and calculate the rolling element fault position using Equation Fourteen; Equation Thirteen; Formula XIV; wherein, is the bearing rotation speed, is the rolling element diameter, is the bearing pitch diameter, t is time, d is the bearing inner diameter.

[0012] According to the technical solution provided by the present application, the CCWGAN-GP fault data enhancement model is provided with a channel attention mechanism to enhance the key features of the simulation data. The feature enhancement process of the simulation data based on the CCWGAN-GP fault data enhancement model includes the following steps: Perform average pooling operation and max pooling operation on the simulation data to generate average pooling features and max pooling features; Input the average pooling features and max pooling features into a shared multi-layer perceptron respectively to generate corresponding average pooling attention weights and max pooling attention weights; Normalize the average pooling attention weights and max pooling attention weights through the Sigmoid function and fuse them into the final weights, and multiply them with the simulation data by channel weighting to enhance the key features of the simulation data.

[0013] According to the technical solution provided by the present application, the adaptation of small-sample experimental data through the dynamic parameter adjustment strategy to complete bearing fault classification includes the following steps: S31: Freeze the feature extraction layer of the transfer learning model and adjust the parameters of the fully connected layer based on the small-sample experimental data; S32: Monitor the loss value of the validation set in real time. If the loss of the validation set does not decrease within the preset number of iterations, dynamically unfreeze some parameters of the feature extraction layer; S33: Repeat step S32 until the classification performance of the model reaches the preset optimal threshold to complete bearing fault classification.

[0014] According to the technical solution provided by the present application, after step S100 and before step S200, the following steps are further included: S11: Based on the bearing fault theoretical model, calculate the outer ring theoretical fault frequency using Formula XV , calculate the inner ring theoretical fault frequency using Formula XVI , and calculate the rolling element theoretical fault frequency using Formula XVII ; Formula XV; Formula XVI; Formula XVII; wherein, is the bearing rotation frequency, Z is the total number of rolling elements, is the rolling element diameter, is the bearing pitch diameter, d is the bearing inner diameter, is the contact angle; S12: Obtain the outer ring theoretical fault period , the inner ring theoretical fault period and the rolling element theoretical fault period respectively according to the outer ring theoretical fault frequency, the inner ring theoretical fault frequency and the rolling element theoretical fault frequency; S13: Compare and analyze the fault periods of the simulation data and the small sample experimental data with the outer ring theoretical fault period, the inner ring theoretical fault period and the rolling element theoretical fault period respectively. If the fault period error between the simulation data and the small sample experimental data is less than the preset threshold, it is determined that the simulation data is valid.

[0015] Compared with the prior art, the beneficial effects of the present application are: The present application provides a bearing fault diagnosis method based on a dynamic model under small sample conditions. By constructing multiple multi-degree-of-freedom dynamic models to generate simulation data covering the inner ring, outer ring, rolling elements and fault-free states respectively, the dependence on real fault data is significantly reduced, and the problem of data scarcity caused by difficult sensor installation and long-term fault-free operation of equipment in practical applications is solved; at the same time, the present application generates synthetic data highly consistent with the characteristics of the simulation data based on the CCWGAN-GP fault data enhancement model, and combines the simulation data and the synthetic data into a virtual data set, effectively improving data diversity and greatly reducing the dependence on real data.

[0016] It should be understood that the description of technical features, technical solutions, beneficial effects or similar languages in the present application does not imply that all features and advantages can be achieved in any single embodiment. On the contrary, it can be understood that the description of features or beneficial effects means that at least one embodiment includes specific technical features, technical solutions or beneficial effects. Therefore, the description of technical features, technical solutions or beneficial effects in this specification does not necessarily refer to the same embodiment. Furthermore, the technical features, technical solutions and beneficial effects described in this embodiment can be combined in any appropriate manner. Those skilled in the art will understand that an embodiment can be implemented without one or more specific technical features, technical solutions or beneficial effects of a specific embodiment. In other embodiments, additional technical features and beneficial effects can also be identified in specific embodiments that do not embody all embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Other features, objects, and advantages of the present application will become more apparent from the following detailed description of non-limiting embodiments read in conjunction with the accompanying drawings: Figure 1 Flowchart of a bearing fault diagnosis method based on a kinetic model under small sample conditions provided for this embodiment; Figure 2 Schematic structural framework diagram of the CCWGAN-GP fault data enhancement model provided for this embodiment; Figure 3 Schematic structural framework diagram of the transfer learning model provided for this embodiment; Figure 4 Experimental data graph under the outer race fault state provided for this embodiment; Figure 5 Simulation data graph under the outer race fault state provided for this embodiment; Figure 6 Experimental data graph under the inner race fault state provided for this embodiment; Figure 7 Simulation data graph under the inner race fault state provided for this embodiment; Figure 8 Experimental data graph under the rolling element fault state provided for this embodiment; Figure 9 Simulation data graph under the rolling element fault state provided for this embodiment; Figure 10 Comparison graph of experimental data and simulation data under the fault-free state provided for this embodiment; Figure 11 Comparison graph of time-domain characteristics of synthetic data and simulation data under the fault-free state provided for this embodiment; Figure 12 Comparison graph of time-domain characteristics of synthetic data and simulation data under the outer race fault state provided for this embodiment; Figure 13 Comparison graph of time-domain characteristics of synthetic data and simulation data under the inner race fault state provided for this embodiment; Figure 14 Comparison graph of time-domain characteristics of synthetic data and simulation data under the rolling element fault state provided for this embodiment; Figure 15 Schematic diagram of the confusion matrix result of the virtual dataset provided for this embodiment; Figure 16 Comparison graph of the diagnostic results before and after fine-tuning provided for this embodiment. Detailed implementation manners

[0018] To enable those skilled in the art to better understand the technical solution of the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the accompanying drawings. The description in this part is only exemplary and explanatory, and should not have any restrictive effect on the protection scope of the present application. Specifically, the described embodiments are only some of the embodiments of the present application, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present application without creative efforts shall fall within the protection scope of the present application.

[0019] It should be noted that similar reference numerals and letters denote similar items in the following drawings. Therefore, once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings. In addition, the terms "comprising" and "having" and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device that comprises a series of steps or units does not necessarily have to be limited to those steps or units clearly listed, but may include other steps or units not clearly listed or inherent to these processes, methods, products or devices.

[0020] Embodiment 1 Please refer to Figure 1 , the flowchart of a bearing fault diagnosis method based on a kinetic model under small sample conditions provided in this embodiment includes the following steps: S100: Construct a plurality of multi-degree-of-freedom kinetic models, and respectively generate simulation data containing corresponding fault characteristics based on each of the multi-degree-of-freedom kinetic models; wherein, each kinetic model corresponds to a preset fault state of the bearing, and each preset fault state has corresponding fault characteristics. The preset fault states include: inner ring fault, outer ring fault, rolling element fault, and no fault. Specifically, a bearing is a mechanical component used to support a rotating shaft, reduce friction, and ensure smooth rotation of mechanical components. A typical rolling bearing mainly consists of an inner ring (rotating in cooperation with the shaft), an outer ring (fixed or supported), rolling elements (such as balls, rollers, etc., located between the inner and outer rings), and a cage (separating and guiding the rolling elements); therefore, in the present application, four preset fault states are provided, namely: inner ring fault state, outer ring fault state, rolling element fault state, and no fault state. Specifically, the multi-degree-of-freedom kinetic model in the present application is a six-degree-of-freedom kinetic model. The six-degree-of-freedom kinetic model is a mathematical model used to describe the motion state of an object in three-dimensional space. The "six degrees of freedom" specifically refers to the translational degrees of freedom along the three rectangular coordinate axes of x, y, and z, as well as the rotational degrees of freedom about these three coordinate axes.

[0021] In this embodiment, optionally, the multiple multi-degree-of-freedom dynamic models are four, namely an inner race fault dynamic model, an outer race fault dynamic model, a rolling element fault dynamic model, and a fault-free dynamic model; the inner race fault dynamic model is used to generate a simulation signal containing inner race fault characteristics, the outer race fault dynamic model is used to generate a simulation signal containing outer race fault characteristics, the rolling element fault dynamic model is used to generate a simulation signal containing rolling element fault characteristics, and the fault-free dynamic model is used to generate a simulation signal containing fault-free characteristics.

[0022] Specifically, in view of the common characteristics of the four multi-degree-of-freedom dynamic models in the process of generating simulation signals; Therefore, in this embodiment, optionally, each preset fault state has a corresponding fault position, and the step of generating simulation data containing corresponding fault characteristics based on each of the multi-degree-of-freedom dynamic models includes: S110: For different preset fault states, determine whether to trigger the corresponding fault switch according to the corresponding fault position; In this embodiment, optionally, for the four preset fault states, the fault switch function includes: an inner race fault switch function , an outer race fault switch function , a fault switch function for the contact between the rolling element and the outer race , a fault switch function for the contact between the rolling element and the inner race , and a fault-free switch function ; Step S110 includes the following steps: S111: Based on the inner race fault dynamic model, when the value of the inner race fault position satisfies Formula Five, it indicates that the inner race fault position falls into the preset trigger area, and the inner race fault switch is triggered. At this time, the value of the inner race fault switch function is 1, and the operation of the inner race fault dynamic model in the inner race fault state is activated; otherwise, the value of the inner race fault switch function is 0; Formula Five; S112: Based on the outer race fault dynamic model, when the value of the outer race fault position satisfies Formula Six, it indicates that the outer race fault position falls into the preset trigger area, and the outer race fault switch is triggered. At this time, the value of the outer race fault switch function is 1, and the operation of the outer race fault dynamic model in the outer race fault state is activated; otherwise, the value of the outer race fault switch function is 0; Formula Six; S113: Based on the rolling element fault dynamics model, when the values of the rolling element fault positions simultaneously satisfy Formula Seven and Formula Eight, the surface rolling element fault positions simultaneously satisfy the fault triggering conditions of contact with the inner and outer rings, triggering the rolling element fault switch. The fault switch function for the contact between the rolling element and the outer ring and the fault switch function for the contact between the rolling element and the inner ring both have a value of 1, activating the rolling element fault dynamics model in the rolling element fault state; otherwise, the fault switch function for the contact between the rolling element and the outer ring and the fault switch function for the contact between the rolling element and the inner ring both have a value of 0; is the inner ring radius, L is the outer ring radius, is the fault width, i is the angular position of the S114: Based on the fault-free dynamics model, trigger the fault-free switch. The fault-free switch function has a value of 0, indicating that the current state is fault-free. The fault-free dynamics model runs to generate fault-free simulation data as a reference benchmark for the normal operation of the bearing.

[0023] In this embodiment, optionally, the angular position of the i rolling element is calculated using Formula Twelve; Formula Twelve; where Z is the total number of rolling elements, i is the rolling element number, is the rolling element diameter, is the bearing pitch diameter, is the inner ring rotational speed, is the initial angular position of the cage.

[0024] In this embodiment, optionally, the outer ring fault position is a fixed value. The inner ring fault position is calculated using Formula Thirteen, and the rolling element fault position is calculated using Formula Fourteen; Formula Thirteen; Formula Fourteen; where is the bearing rotational speed, is the rolling element diameter, is the bearing pitch diameter, and t is the time. d is the bearing inner diameter.

[0025] S120: When the fault switch is triggered, calculate the local fault radial deformation. Specifically, considering that the fault location is different, the value of the local fault radial deformation is also different. Therefore, in this embodiment, optionally, the step S120 includes the following steps: S121: If the inner ring fault switch is triggered, when , calculate the local fault radial deformation using Equation Nine; otherwise, the value of the local fault radial deformation is h ; Equation Nine; S122: If the outer ring fault switch is triggered, when , calculate the local fault radial deformation using Equation Ten; otherwise, the value of the local fault radial deformation is h ; Equation Ten; S123: If the rolling element fault switch is triggered, when , calculate the local fault radial deformation using Equation Eleven; otherwise, the value of the local fault radial deformation is h ; Equation Eleven; Among them, is the rolling element radius, L is the fault width, is the inner ring radius, is the outer ring radius, h is the fault height; S124: If the no-fault switch is triggered, the value of the local fault radial deformation is 0.

[0026] S130: According to the local fault radial deformation, calculate the rolling element deformation using Equation One; Equation One; Among them, is the displacement of the outer ring in the horizontal direction, is the displacement of the outer ring in the vertical direction, is the displacement of the inner ring in the horizontal direction, is the displacement of the inner ring in the vertical direction, is the bearing clearance, is the i angular position of the th rolling element; is the radial deformation amount of the local fault; Specifically, during the operation of the bearing, based on the magnitude and distribution characteristics of the radial load it bears, the raceway can be divided into a load-bearing area and a non-load-bearing area; within the load-bearing area, the rolling elements generate contact due to the load, which is the core area where deformation occurs; when calculating the deformation amount of the rolling elements using Formula 1, it is precisely based on the force-deformation mechanism of the rolling elements in the load-bearing area; by integrating parameters such as the displacement of the inner and outer rings, the bearing clearance, the fault switch function, and the radial deformation amount of the local fault, the actual deformation of the rolling elements in the load-bearing area is accurately quantified; this calculation result is not only a direct reflection of the force state of the rolling elements, but also provides a key input for subsequent contact force calculation based on Hertz contact theory and the solution of the dynamic differential equation, ultimately effectively mapping the dynamic characteristics of the bearing under normal operation or fault conditions.

[0027] Specifically, only when the deformation amount caused by the load borne by the rolling element is greater than 0 will a contact force be generated; Therefore, in this embodiment, S140: Determine whether the deformation amount of the rolling element is greater than 0; S150: When the deformation amount of the rolling element is greater than 0, the switch function of the rolling element at this time is 1; otherwise, the switch function of the rolling element is 0; S160: Based on Hertz contact theory, use Formula 2 to calculate the nonlinear contact force of the bearing in the horizontal direction, and use Formula 3 to calculate the nonlinear contact force of the bearing in the vertical direction; Formula 2; Formula 3; Among them, is the nonlinear contact force of the bearing in the horizontal direction, is the nonlinear contact force of the bearing in the vertical direction, is the equivalent contact stiffness between the rolling element and the inner and outer raceways, is the deformation amount of the rolling element, is the i angular position of the th rolling element, is the switch function of the rolling element; Formula 4; Among them, is the mass of the outer ring, is the mass of the rolling element, is the mass of the inner ring, is the comprehensive damping coefficient of the outer ring, is the damping coefficient of the rolling element in the horizontal direction, is the damping coefficient of the rolling element in the vertical direction, is the damping coefficient of the inner ring in the horizontal direction, is the damping coefficient of the inner ring in the vertical direction, is the stiffness coefficient of the outer ring in the horizontal direction, is the stiffness coefficient of the outer ring in the vertical direction, is the stiffness coefficient of the rolling element in the horizontal direction, is the stiffness coefficient of the rolling element in the vertical direction, is the stiffness coefficient of the inner ring in the horizontal direction, is the stiffness coefficient of the inner ring in the vertical direction, is the displacement of the outer ring in the horizontal direction, is the displacement of the outer ring in the vertical direction, is the velocity of the outer ring in the horizontal direction, is the velocity of the outer ring in the vertical direction, is the acceleration of the outer ring in the horizontal direction, is the acceleration of the outer ring in the vertical direction, is the displacement of the rolling element in the horizontal direction, is the displacement of the rolling element in the vertical direction, is the velocity of the rolling element in the horizontal direction, is the velocity of the rolling element in the vertical direction, is the acceleration of the rolling element in the horizontal direction, is the acceleration of the rolling element in the vertical direction, is the displacement of the inner ring in the horizontal direction, is the displacement of the inner ring in the vertical direction, is the velocity of the inner ring in the horizontal direction, is the velocity of the inner ring in the vertical direction, is the acceleration of the inner ring in the horizontal direction, is the acceleration of the inner ring in the vertical direction, W is the gravity borne by the bearing; Specifically, in this embodiment, the simulation data is an acceleration signal.

[0028] After step S100 and before step S200, the following steps are further included: S11: Based on the bearing fault theoretical model, calculate the outer ring theoretical fault frequency using formula fifteen , calculate the inner ring theoretical fault frequency using formula sixteen , and calculate the rolling element theoretical fault frequency using formula seventeen ; Formula fifteen; Formula XVI; Formula XVII; wherein, is the bearing rotation frequency, Z is the total number of rolling elements, is the rolling element diameter, is the bearing pitch diameter, d is the bearing inner diameter, is the contact angle; S12: Obtain the outer ring theoretical fault period , inner ring theoretical fault period and rolling element theoretical fault period respectively according to the outer ring theoretical fault frequency, inner ring theoretical fault frequency and rolling element theoretical fault frequency; S13: Compare and analyze the fault periods of the simulation data and the small sample experimental data with the outer ring theoretical fault period, inner ring theoretical fault period and rolling element theoretical fault period respectively. If the fault period error between the simulation data and the small sample experimental data is less than the preset threshold, it is determined that the simulation data is valid.

[0029] Specifically, this verification mechanism ensures the reliability of the simulation data through the analysis of the period matching degree between the theory and the actual data, provides a high-quality data basis for the data enhancement of the subsequent CCWGAN-GP fault data model and the training of the transfer learning model, and guarantees the accuracy and stability of the bearing fault diagnosis method.

[0030] S200: Perform feature enhancement processing on the simulation data based on the CCWGAN-GP fault data enhancement model, generate synthetic data with the same features as the simulation data, and integrate the synthetic data and the simulation data to form a virtual data set; In this embodiment, preferably, the CCWGAN-GP fault data enhancement model is provided with a channel attention mechanism to enhance the key features of the simulation data. The feature enhancement processing of the simulation data based on the CCWGAN-GP fault data enhancement model includes the following steps: Perform average pooling operation and max pooling operation on the simulation data to generate average pooling features and max pooling features; Input the average pooling features and max pooling features into a shared multi-layer perceptron respectively to generate corresponding average pooling attention weights and max pooling attention weights; Normalize the average pooling attention weights and max pooling attention weights through the Sigmoid function and fuse them into the final weight, and multiply them by the simulation data channel by channel to enhance the key features of the simulation data.

[0031] Specifically, as Figure 2 shown in the structural framework diagram of the CCWGAN-GP fault data augmentation model, the CCWGAN-GP (Conditional Channel Wasserstein Generative Adversarial Networks with Gradient Penalty) fault data augmentation model includes a discriminator D and a generator G. The discriminator D and the generator G are alternately optimized through a game relationship to achieve the goal that while the generator G generates high-quality samples, the discriminator D accurately judges true and false. The objective function is shown in Equation XVIII; Equation XVIII; Among them, a represents the input data, o represents the class label, u represents the random noise, represents the gradient penalty coefficient, represents the generated data distribution, represents the real data distribution, represents the uniform sampling points on the line connecting the two, represents the calculation result of the discriminator for the simulation data under the given conditions, indicating the expectation of calculating the discriminator for all data sampled from the real data distribution a (under the given conditions o ), and the meanings of other functions are deduced by analogy; represents the gradient operator; represents the gradient operator; represents the 2-norm; Specifically, based on the CCWGAN-GP fault data augmentation model, this application introduces a channel attention mechanism. By assigning attention weights to each channel, the model improves the focus on important channels, while suppressing the interference of secondary channels, increasing the attention of the model to the key features of one-dimensional vibration signals (simulation data), thereby improving the overall performance of the model; In the channel attention mechanism, the input feature X (simulation data) performs average pooling operation and max pooling operation respectively in each channel to generate the corresponding average pooling attention weight and max pooling attention weight ; Subsequently, they are sent to the shared multi-layer perceptron MLP to generate the corresponding average pooling attention weight and max pooling attention weight , and its formula is: ; Among them, s represents the number of channels, JDenotes the sample length, and respectively denote the feature dimensionality reduction and feature recovery weight matrices, is the Sigmoid function; The average pooling attention weight and the max pooling attention weight are fused into the final weight after being normalized by the Sigmoid function , and are multiplied by the simulation data channel-wise and weighted to output enhanced features , so as to enhance the key features of the simulation data; the specific formula is as follows: ; Specifically, the simulation data obtained in this application is input into the CCWGAN-GP fault data enhancement model for data augmentation to obtain augmented synthetic data. Using the cosine similarity as the evaluation index, a qualitative and quantitative comparative analysis of the consistency between the synthetic data and the simulation data is carried out to verify the feasibility of the generated synthetic data; subsequently, the synthetic data and the simulation data are combined into a virtual data set, which are jointly used as the input data for subsequent diagnosis.

[0032] S300: Use the virtual data set to pre-train a transfer learning model, and adapt to the small-sample experimental data through a dynamic parameter adjustment strategy to complete bearing fault classification; In this embodiment, preferably, the step of adapting to the small-sample experimental data through a dynamic parameter adjustment strategy to complete bearing fault classification includes the following steps: S31: Freeze the feature extraction layer of the transfer learning model, and adjust the parameters of the fully connected layer based on the small-sample experimental data; S32: Monitor the validation set loss value in real time. If the validation set loss does not decrease within the preset number of iterations, then dynamically unfreeze some of the parameters of the feature extraction layer; S33: Repeat step S32 until the model classification performance reaches the preset optimal threshold to complete bearing fault classification.

[0033] Specifically, after obtaining a virtual data set that is highly similar to the small-sample experimental data, a transfer learning method is used to perform cross-domain diagnosis on the experimental data based on the virtual data set; the transfer learning framework is as Figure 3 shown. Transfer learning is a technology that obtains relevant knowledge from the source domain and source task to improve the prediction ability of the target task in the target domain; in this step, the source domain is the virtual data set, and the target domain is the small-sample experimental data collected; Using a parameter-based transfer learning method and introducing a fine-tuning strategy based on the validation set loss can significantly improve the diagnostic effect. The specific diagnostic steps are as follows: First, use CNN as the basic model and pre-train it with a virtual dataset to save the model parameters and obtain a transfer learning model; then, freeze the feature extraction layer of the transfer learning model and adjust the parameters of the fully connected layer based on the small sample experimental data to enable the model to better adapt to the data characteristics of the target task; monitor the validation set loss value in real time. If the validation set loss does not decrease within the preset number of iterations, dynamically unfreeze some of the parameters of the feature extraction layer; repeat step S32 until the classification performance of the model reaches the preset optimal threshold to complete the bearing fault classification; Specifically, use the test set to calculate metrics such as diagnostic accuracy, precision, recall, and F1 value to evaluate the diagnostic effect of the transfer learning model. The evaluation results will verify whether the model can effectively distinguish different categories of samples, and then determine its actual application effect in the target task.

[0034] S400: Based on the bearing fault classification result, determine the fault state of the bearing to achieve the diagnosis of the bearing fault.

[0035] For the convenience of those skilled in the art to understand, select the drive-end SKF6205 bearing as the research object. The bearing states include four types: inner ring fault state, outer ring fault state, rolling element fault state, and no-fault state. Taking the acceleration signals collected at a sampling frequency of 12 kHz under four preset fault states as simulation data as an example, the present invention will be further described in detail: S100: Construct multiple multi-degree-of-freedom dynamic models, and respectively generate simulation data containing corresponding fault characteristics based on each of the multi-degree-of-freedom dynamic models; among them, each dynamic model corresponds to a preset fault state of the bearing, and each preset fault state has corresponding fault characteristics. The preset fault states include: inner ring fault, outer ring fault, rolling element fault, and no-fault; The units and values of the basic physical parameters of the multiple constructed multi-degree-of-freedom dynamic models are shown in Table 1; Table 1 Basic physical parameters of the multi-degree-of-freedom dynamic model

[0036] Substitute the basic physical parameters in Table 1 into the four multi-degree-of-freedom dynamic models respectively to obtain simulation data containing corresponding fault characteristics, as Figure 4 - Figure 5 shown in the comparison between the simulation data and the experimental data under the outer ring fault state, Figure 6 - Figure 7 is the comparison between the simulation data and the experimental data under the inner ring fault state, Figure 8 - Figure 9 is the comparison between the simulation data and the experimental data under the rolling element fault state, Figure 10It is a comparison between simulation data and experimental data under the fault-free state.

[0037] According to Figure 4 - Figure 10 Evaluate the similarity between the simulation data and experimental data obtained from the multi-degree-of-freedom dynamics model. Select the experimental data and simulation data from 0.1 s to 0.15 s under different preset fault states of the bearing. The experimental data and simulation data under the outer ring fault state are as Figure 4 and Figure 5 shown. Their impact amplitudes are relatively uniform, reflecting the continuous influence of this type of fault. The average fault periods of the two are 9.23 ms and 9.38 ms respectively, and the relative deviation is 1%. The experimental data and simulation data under the inner ring fault state are as Figure 6 and Figure 7 shown. Their impact response processes are relatively short, reflecting the immediate influence of local defects on the vibration signal. The average fault periods of the two are 5.97 ms and 6.17 ms respectively, and the relative deviation is 3%. The experimental data and simulation data under the rolling element fault state are as Figure 8 and Figure 9 shown. Their impact amplitudes have significant fluctuations, indicating the complexity and instability of the fault state. The average fault periods of the two are 7.22 ms and 6.96 ms respectively, and the relative deviation is 3%. The above analysis shows that the fault periods of the simulation data are relatively consistent with those of the actual data under the inner ring, outer ring, and rolling element fault states. The overall shape and change trend of the simulation data are relatively consistent with those of the experimental data under the fault-free state. According to the formula Calculate the fault frequency under the outer ring fault state to be 104.56 Hz, then the calculated result of the theoretical fault period of the outer ring is 9.56 ms. According to the formula Calculate the fault frequency under the inner ring fault state to be 157.94 Hz, and its theoretical fault period of the inner ring is 6.33 ms. According to the formula Calculate the fault frequency of the rolling element to be 137.48 Hz, then the theoretical fault period of the rolling element is 7.27 ms. Through calculation, it can be seen that under the inner ring, outer ring, and rolling element fault states, the fault periods of the simulation data, the fault periods of the experimental data, and the theoretical fault periods are all consistent, further indicating that the simulation results accurately reflect the dynamic characteristics of the bearing under different fault states, and there is a high degree of consistency between the simulation data and the experimental data, which can realize the replacement of the experimental data.

[0038] S200: Perform feature enhancement processing on the simulation data based on the CCWGAN-GP fault data enhancement model, generate synthetic data with the same characteristics as the simulation data, and integrate the synthetic data and the simulation data to form a virtual data set.

[0039] The CCWGAN-GP model uses the Pytorch framework, with the Adam optimizer, a learning rate set to 0.001, a maximum number of iterations of 200, and a batch size of 32. In this model, the structural parameters of the generator G and the discriminator D are shown in Tables 2 and 3; Table 2 Structural Parameters of Generator G

[0040] Table 3 Structural Parameters of Discriminator D

[0041] The comparison results of the time-domain characteristics between the synthetic data and the input simulation data are as Figure 11 - Figure 14 shown. It can be seen from the figure that under the conditions of no fault, outer race fault, and inner race fault, the synthetic data and the simulation data show relatively consistent periodicity and fluctuation amplitude; under the condition of rolling element fault, although the overall periodicity of the two signals is weak and the signal characteristics are complex, the synthetic data and the simulation data are highly similar in the overall trend and can capture the complex changes of the characteristics. Zooming in on the Figure 13 、 Figure 14 blue elliptical area in shows that there are slight differences in the peak size and change trend between the synthetic data and the simulation data, indicating that the synthetic data does not completely replicate the simulation data, thus avoiding the overfitting problem caused by the completely consistent data in the fault diagnosis model; Through the above qualitative analysis, it can be seen that under different bearing conditions, the data generated by the CCWGAN-GP fault data enhancement model is highly consistent with the change trend of the simulation data, proving that the model can perform data enhancement on the basis of retaining the key features of the simulation data; the generated data neither completely replicates the waveform features of the input data nor degrades its original features, verifying the feasibility of the CCWGAN-GP fault data enhancement model in this paper; In addition, to further quantitatively evaluate the consistency between synthetic data and simulation data in the feature space, this paper uses cosine similarity as an index to measure data consistency, intuitively reflecting the learning ability of the CCWGAN-GP fault data augmentation model for input data. The value of cosine similarity ranges from -1 to 1. When it is close to 1, it indicates that the two sets of data are highly consistent in the feature space. When it is close to 0, it means there is a lack of correlation between them. If it is negative, it implies an inverse relationship between the two sets of data. In practical applications, when the cosine similarity is greater than 0.6, it can be determined that there is a significant consistency between the two sets of data. The cosine similarity calculation results of the two types of data are shown in Table 4. As can be seen from the table, the cosine similarities between the synthetic data and the simulation data under the four bearing states are 0.93, 0.98, 0.90, and 0.94 respectively, all significantly higher than 0.6, indicating that the synthetic data and the simulation data have extremely high consistency, verifying that the CCWGAN-GP fault data augmentation model can effectively learn the signal features of different input data. Table 4 Cosine Similarity between Synthetic Data and Simulation Data

[0042] From the results of qualitative and quantitative analyses, the CCWGAN-GP fault data augmentation model can not only accurately learn the key features of simulation data, generate synthetic data highly similar to the simulation data in the feature space, but also ensure that there are subtle differences between the synthetic data and the simulation data, effectively enhancing the diversity of the generated data. The similar and diverse synthetic data significantly increases the data volume, providing sufficient sample support for subsequent fault diagnosis.

[0043] S300: Pre-train a transfer learning model using the virtual dataset and adapt it to the small-sample experimental data through a dynamic parameter adjustment strategy to complete bearing fault classification.

[0044] The structural parameters of the transfer learning model are shown in Table 5; Table 5 Structural Parameters of the Transfer Learning Model

[0045] Use the virtual dataset composed of simulation data and synthetic data of four preset fault states as the source domain data, and the small-sample experimental data as the target domain data. Apply transfer learning to the diagnostic scenario of the experimental data, transfer the fault feature parameters learned from the virtual dataset to the experimental data, and realize the fault diagnosis of the small-sample actual data. The specific steps are as follows: First, pre-train the virtual dataset according to the transfer learning model shown in Table 5. The accuracy obtained from the pre-training is 98.75%, the precision is 98.81%, the recall rate is 98.75%, and the F1 value is 98.74%. The confusion matrix results are as Figure 15As shown, labels 0, 1, and 2 represent no fault, outer race fault, and inner race fault respectively. The diagnostic accuracy rates for these three types of faults can all reach 100%; label 3 represents rolling element fault, and its diagnostic accuracy rate is 94.74%, which also has a relatively high diagnostic accuracy rate. This indicates that the transfer learning model can effectively classify the virtual dataset; save the feature parameters learned from the virtual dataset for subsequent cross-domain fault diagnosis of the target domain; The experimental data includes two working conditions. The sample size for each working condition is 50, and the sample length is 1024. Among them, the rotational speed of working condition 1 is 1797 rpm, which is the same as the simulation working condition, and the rotational speed of working condition 2 is 1772 rpm; use the transfer learning model fine-tuned based on the validation set loss to diagnose working conditions 1 and 2 respectively, and compare with the diagnosis when only the last classification layer is unfrozen (i.e., before fine-tuning). The diagnostic results before and after fine-tuning are shown in Table 6, and the visual evaluation results are as Figure 16 shown; Since the rotational speed, geometric dimensions, etc. of working condition 1 are the same as those of the virtual data training set, high diagnostic accuracy can be achieved both before and after fine-tuning in working condition 1, indicating that the virtual data training set and the experimental data have reached diagnostic conditions with high similarity; in working condition 1, the diagnostic accuracy rate reaches 100% both before and after fine-tuning, and the other three evaluation indicators can also reach 100% after fine-tuning, showing a significant improvement compared to the performance before fine-tuning; in working condition 2, the classification accuracy rate can reach 81.82% before fine-tuning, indicating that this transfer learning model can already effectively classify bearings in different states. The accuracy rate after fine-tuning can reach 93.18%, and the other evaluation indicators also reach more than 90%, showing a significant improvement compared to before fine-tuning. The above analysis verifies that fine-tuning based on the validation set loss is beneficial to improving the diagnostic accuracy and has a certain generalization ability.

[0046] Table 6 Results of evaluation indicators before and after fine-tuning

[0047] S400: Based on the bearing fault classification result, determine the fault state of the bearing to achieve the diagnosis of bearing faults.

[0048] To verify the classification effect of the method in this paper under the condition of small samples, bearing data with 30, 40, and 50 fault samples were selected respectively, and diagnostic research was carried out under the above two working conditions. The diagnostic results are shown in Table 7. The results show that the diagnostic accuracy rate under different sample sizes in Working Condition 1 can reach 100%, indicating that the features of the target domain (experimental data) can be highly matched with the features of the source domain (virtual data set); the diagnostic accuracy rate under different sample sizes in Working Condition 2 is above 90%, and the precision, recall rate, and F1 value parameter indicators are also above 90%, indicating that the method can effectively identify the fault categories under different working conditions under the condition of small samples and maintain a high classification performance, with a certain generalization ability; as the sample size decreases, the diagnostic accuracy rate of Working Condition 2 decreases, which also proves that the small sample problem will indeed affect the diagnostic results; in summary, the migration diagnosis method based on simulation data shows good diagnostic ability and generalization ability under the condition of small samples and can adapt to the fault classification tasks under different working conditions.

[0049] Table 7 Classification accuracy of different working conditions under different samples

[0050] In this paper, specific examples are used to elaborate on the principle and implementation manner of this application. The description of the above embodiments is only used to help understand the method and its core idea of this application. The above is only the preferred implementation manner of this application. It should be noted that due to the limited nature of written expression and objectively infinite specific structures, for those of ordinary skill in the art in this technical field, without departing from the principle of this application, several improvements, retouches, or changes can be made, or the above technical features can be combined in an appropriate manner; these improvements, retouches, changes, or combinations, or directly applying the inventive concept and technical solution to other occasions without improvement, should all be regarded as the protection scope of this application.

Claims

1. A bearing fault diagnosis method based on a dynamic model under small sample conditions, characterized in that: The steps include: S100: constructing a plurality of multi-degree-of-freedom dynamic models, and generating simulation data containing corresponding fault characteristics based on each of the multi-degree-of-freedom dynamic models; wherein each dynamic model corresponds to a preset fault state of the bearing, each preset fault state has a corresponding fault characteristic, and the preset fault states include: inner ring fault, outer ring fault, rolling element fault and no fault; S200: performing feature enhancement processing on the simulation data based on the CCWGAN-GP fault data enhancement model to generate synthetic data consistent with the features of the simulation data, and integrating the synthetic data with the simulation data to form a virtual data set; S300: pre-training a transfer learning model using the virtual data set, and adapting a small sample experimental data through a dynamic parameter adjustment strategy to complete bearing fault classification; S400: Based on the bearing fault classification result, determine the fault state of the bearing to diagnose the bearing fault.

2. The bearing fault diagnosis method based on a dynamic model under small sample conditions according to claim 1 is characterized in that: There are four multiple multi-degree-of-freedom dynamic models, namely, an inner ring fault dynamic model, an outer ring fault dynamic model, a rolling element fault dynamic model and a no-fault dynamic model.

3. The bearing fault diagnosis method based on dynamic model under small sample conditions according to claim 2 is characterized in that: Each preset fault state has a corresponding fault location, and the steps of respectively generating simulation data containing corresponding fault characteristics based on each of the multi-degree-of-freedom dynamic models include: S110: for different preset fault states, judging whether to trigger a corresponding fault switch according to the corresponding fault position; S120: When the fault switch is triggered, the radial deformation of the local fault is calculated; S130: Calculate the rolling element deformation using formula 1 according to the radial deformation of the local fault; Formula 1; in, is the horizontal displacement of the outer ring, is the vertical displacement of the outer ring, is the horizontal displacement of the inner ring, is the vertical displacement of the inner ring, is the bearing clearance, For the i Angular position of the rolling elements; is the fault switching function, is the radial deformation of the local fault; S140: Determine whether the deformation of the rolling element is greater than 0; S150: When the rolling body deformation is greater than 0, the rolling body switch function is 1; otherwise, the rolling element switching function is 0; S160: Based on Hertz contact theory, Formula 2 is used to calculate the nonlinear contact force of the bearing in the horizontal direction, and Formula 3 is used to calculate the nonlinear contact force of the bearing in the vertical direction; Formula 2: Formula 3; in, is the nonlinear contact force of the bearing in the horizontal direction, is the nonlinear contact force of the bearing in the vertical direction, is the equivalent contact stiffness between the rolling element and the inner and outer raceways, is the rolling element deformation, For the i The angular position of the rolling element, is the switching function of the rolling element; S170: Substituting the nonlinear contact force of the bearing in the horizontal direction and the nonlinear contact force of the bearing in the vertical direction into Formula 4 to obtain simulation data corresponding to the fault characteristics; Formula 4; in, is the mass of the outer ring, is the mass of the rolling element, is the mass of the inner ring, is the comprehensive damping coefficient of the outer ring, is the damping coefficient of the rolling element in the horizontal direction, is the damping coefficient of the rolling element in the vertical direction, is the damping coefficient of the inner ring in the horizontal direction, is the damping coefficient of the inner ring in the vertical direction, is the stiffness coefficient of the outer ring in the horizontal direction, is the stiffness coefficient of the outer ring in the vertical direction, is the stiffness coefficient of the rolling element in the horizontal direction, is the stiffness coefficient of the rolling element in the vertical direction, is the stiffness coefficient of the inner ring in the horizontal direction, is the stiffness coefficient of the inner ring in the vertical direction, is the horizontal displacement of the outer ring, is the vertical displacement of the outer ring, is the speed of the outer ring in the horizontal direction, is the speed of the outer ring in the vertical direction, is the horizontal acceleration of the outer ring, is the acceleration of the outer ring in the vertical direction, is the horizontal displacement of the rolling element, is the vertical displacement of the rolling element, is the speed of the rolling element in the horizontal direction, is the speed of the rolling element in the vertical direction, is the horizontal acceleration of the rolling element, is the acceleration of the rolling element in the vertical direction, is the horizontal displacement of the inner ring, is the vertical displacement of the inner ring, is the speed of the inner ring in the horizontal direction, is the speed of the inner ring in the vertical direction, is the horizontal acceleration of the inner ring, is the vertical acceleration of the inner ring, W The gravity borne by the bearing.

4. The bearing fault diagnosis method based on dynamic model under small sample conditions according to claim 3 is characterized in that: The fault switch function Includes: Inner ring fault switch function , outer ring fault switching function , the fault switching function of the rolling element and the outer ring contact , the fault switching function of the rolling element and the inner ring contact , and the trouble-free switching function ; Step S110 includes the following steps: S111: Based on the inner ring fault dynamics model, when the inner ring fault position When the value of satisfies Formula 5, the inner ring fault switch is triggered. At this time, the inner ring fault switch function The value is 1; otherwise, the inner ring fault switch function The value is 0; Formula 5; S112: Based on the outer ring fault dynamics model, when the outer ring fault position When the value of satisfies formula 6, the outer ring fault switch is triggered. At this time, the outer ring fault switch function The value is 1; otherwise, the outer ring fault switch function The value is 0; Formula 6; S113: Based on the rolling element failure dynamics model, when the rolling element failure position When the value of satisfies both Formula 7 and Formula 8, the rolling element fault switch is triggered. At this time, the fault switch function of the rolling element in contact with the outer ring And the fault switching function of the rolling element and the inner ring contact The value of is 1; otherwise, the fault switch function of the rolling element in contact with the outer ring And the fault switching function of the rolling element and the inner ring contact The value of is 0; Formula 7; Formula 8; in, is the inner circle radius, is the outer radius, L is the fault width, For the i Angular position of each rolling element; S114: Based on the fault-free dynamics model, trigger the fault-free switch, the fault-free switch function The value is 0.

5. The bearing fault diagnosis method based on dynamic model under small sample conditions according to claim 4 is characterized in that: The step S120 includes the following steps: S121: If the inner ring fault switch is triggered, When , the local fault radial deformation is calculated using Formula 9; otherwise, the local fault radial deformation is taken as h ; Formula 9; S122: If the outer ring fault switch is triggered, When , the local fault radial deformation is calculated using Formula 10; otherwise, the local fault radial deformation is taken as h ; Formula 10; S123: If the rolling element fault switch is triggered, When , the local fault radial deformation is calculated using Formula 11; otherwise, the local fault radial deformation is taken as h ; Formula XI; in, is the rolling element radius, L is the fault width, is the inner circle radius, is the outer radius, h is the fault height; S124: If the fault-free switch is triggered, the local fault radial deformation value is 0.

6. The bearing fault diagnosis method based on dynamic model under small sample conditions according to claim 3 is characterized in that: Formula 12 is used to calculate the i Angular position of each rolling element; Formula twelve; in, Z is the total number of rolling elements, i is the rolling element number, is the rolling element diameter, is the bearing pitch diameter, is the inner ring speed, is the initial angular position of the cage.

7. The bearing fault diagnosis method based on dynamic model under small sample conditions according to claim 4 is characterized in that: The outer ring fault position is a fixed value, the inner ring fault position is calculated using Formula 13, and the rolling element fault position is calculated using Formula 14; Formula XIII; Formula 14; in, is the bearing speed, is the rolling element diameter, is the bearing pitch diameter, t is the time, d is the bearing inner diameter.

8. The bearing fault diagnosis method based on dynamic model under small sample conditions according to claim 1 is characterized in that: The CCWGAN-GP fault data enhancement model is provided with a channel attention mechanism to enhance key features of the simulation data. The feature enhancement processing of the simulation data based on the CCWGAN-GP fault data enhancement model comprises the following steps: Performing an average pooling operation and a maximum pooling operation on the simulation data to generate an average pooling feature and a maximum pooling feature; The average pooling features and the maximum pooling features are respectively input into a shared multi-layer perceptron to generate corresponding average pooling attention weights and maximum pooling attention weights; The average pooling attention weight and the maximum pooling attention weight are normalized by the Sigmoid function and fused into the final weight, and multiplied with the simulation data by channel weight to enhance the key features of the simulation data.

9. The bearing fault diagnosis method based on dynamic model under small sample conditions according to claim 1 is characterized in that: The method of adapting the small sample experimental data through the dynamic parameter adjustment strategy to complete the bearing fault classification includes the following steps: S31: Freeze the feature extraction layer of the transfer learning model and adjust the parameters of the fully connected layer based on the small sample experimental data; S32: monitoring the validation set loss value in real time, and if the validation set loss does not decrease within a preset number of iterations, dynamically unfreezing some parameters of the feature extraction layer; S33: Repeat step S32 until the model classification performance reaches a preset optimal threshold, and the bearing fault classification is completed.

10. The bearing fault diagnosis method based on dynamic model under small sample conditions according to claim 1 is characterized in that: After step S100 and before step S200, the following steps are also included: S11: Based on the bearing failure theory model, the outer ring theoretical failure frequency is calculated using formula 15 , use formula 16 to calculate the theoretical fault frequency of the inner ring , and use formula 17 to calculate the theoretical failure frequency of the rolling element ; Formula 15; Formula 16; Formula XVII; in, is the bearing rotation frequency, Z is the total number of rolling elements, is the rolling element diameter, is the bearing pitch diameter, d is the bearing inner diameter, is the contact angle; S12: Obtain the outer ring theoretical failure period according to the outer ring theoretical failure frequency, the inner ring theoretical failure frequency and the rolling element theoretical failure frequency respectively. , Inner ring theoretical failure cycle and rolling element theoretical failure cycle ; S13: Compare and analyze the failure cycles of the simulation data and the small sample experimental data with the outer ring theoretical failure cycle, the inner ring theoretical failure cycle and the rolling element theoretical failure cycle respectively. If the failure cycle error between the simulation data and the small sample experimental data is less than a preset threshold, the simulation data is determined to be valid.

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