Rolling bearing multi-working-condition data expansion method based on digital twinning

Abstract

The invention provides a rolling bearing multi-working-condition data expansion method based on digital twinning, and the method comprises the steps: collecting original vibration signals of a rolling bearing under various working conditions through a physical experiment table system, and recognizing an equivalent boundary condition; solving the six-degree-of-freedom coupling dynamic model to obtain an acceleration vibration signal for fault diagnosis; performing model fault verification on the six-degree-of-freedom coupling dynamic model through the five evaluation dimensions to obtain a high-fidelity model; based on the high-fidelity model, utilizing an AGA algorithm and a KAN network to construct a nonlinear mapping relation between a working condition and an optimal physical parameter vector, outputting an accurate model parameter suitable for a new working condition, and obtaining an adaptive digital twinborn model; and automatically generating a hybrid enhanced data set by utilizing a batch processing interface of the constructed virtual interaction platform. According to the method, data generation and expansion of the rolling bearing under multiple working conditions can be realized, and rich and controllable data support is provided for fault diagnosis, health monitoring and model training.

Description

Technical Field

[0001] This invention relates to the field of digital twin technology, and in particular to a method for expanding multi-condition data of rolling bearings based on digital twins. Background Technology

[0002] Rolling bearings are critical fundamental components in modern machinery, their performance directly affecting the long-term stable and safe operation of the entire unit, and also reflecting the technological and equipment level of the manufacturing industry to a certain extent. As industrial systems continue to develop towards larger scale, higher speed, and greater automation, bearings are often subjected to combined stresses under high loads, high speeds, strong coupling, and complex environments. Once a failure occurs, it can lead to equipment downtime and increased maintenance costs, or even trigger cascading failures and serious safety accidents. Surveys indicate that rolling bearings account for approximately 30% of failures in machinery using them, making them one of the components with the highest failure rate in mechanical equipment. Once a failure occurs, it not only affects the stable operation of the entire machine, but in severe cases can cause huge economic losses, even catastrophic casualties, resulting in adverse social impacts. Therefore, condition monitoring and fault diagnosis of rolling bearings have always been a key focus in engineering and academia. In recent years, end-to-end data-driven methods based on deep learning have demonstrated good fault identification capabilities in controlled experimental environments. However, the usability and transferability of these methods in real-world industrial scenarios still face significant limitations, mainly in the following two aspects: 1. Sensor deployment in industrial settings is limited by space, environment, and cost. Acquired signals are susceptible to noise interference and suffer from inconsistent sampling frequencies and significant differences in data distribution across equipment and operating conditions. Fault events are inherently low-probability phenomena, resulting in scarce real-world fault samples, poor label integrity, and signals often exhibiting weak responses, strong noise, and partial missing data. This leads most supervised learning models to overfit to "ideal data" during training, and in practical applications, domain shifts and inter-class distribution changes occur, significantly reducing the model's generalization ability across equipment and operating conditions, as well as its sensitivity to early fault warnings.

[0003] 2. To alleviate sample scarcity, commonly used data augmentation and generation methods mostly rely on extrapolation from empirical distributions, which easily leads to spurious samples with unidirectional patterns, blurred inter-class boundaries, and non-physical consistency. Such generated samples typically lack clear physical parameters and calibration criteria, making it difficult to meet the interpretability and verifiability requirements of practical engineering. Even with the introduction of simulation models, problems such as model idealization, uncertain boundary conditions, and uncalibrated parameters often result in significant discrepancies between simulation and reality, reducing the credibility and practical value of virtual samples.

[0004] To address the above issues, relying solely on data-driven methods is insufficient to cope with the complexity of real-world scenarios and the challenges of data scarcity. The core problems of low-quality and scarce real samples and low credibility of virtual samples still exist in industrial settings. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies, the purpose of this invention is to provide a method for expanding rolling bearing data under multiple operating conditions based on digital twins. This method can generate and expand rolling bearing data under multiple operating conditions, providing rich and controllable data support for fault diagnosis, health monitoring, and model training.

[0006] To achieve the above objectives, the present invention provides the following solution: a method for expanding multi-condition data of rolling bearings based on digital twins, comprising: The original vibration signals of rolling bearings under various working conditions were collected using a physical experimental platform system, and the equivalent boundary conditions were identified. Based on the original vibration data and the equivalent boundary conditions, a six-degree-of-freedom coupled dynamic model is constructed, and then the six-degree-of-freedom coupled dynamic model is solved to obtain the acceleration vibration signal used for fault diagnosis. Based on the acceleration vibration signal, the six-degree-of-freedom coupled dynamic model is verified for model failure through five evaluation dimensions to obtain a high-fidelity model. Based on the high-fidelity model, the AGA algorithm is used to optimize and calibrate the key position parameters to obtain the optimal physical parameter vector. Then, the KAN network is used to construct a nonlinear mapping relationship between the working condition and the optimal physical parameter vector, and output accurate model parameters suitable for the new working condition to obtain an adaptive digital twin model. Based on the adaptive digital twin model, a virtual interaction platform is constructed, and then the batch processing interface of the virtual interaction platform is used to automatically generate a hybrid enhanced dataset including normal operating conditions, extreme operating conditions, and compound fault conditions.

[0007] Optionally, the original vibration signals of the rolling bearing under various operating conditions can be acquired using a physical experimental platform system, and equivalent boundary conditions can be identified, including: The data acquisition specifications are obtained by listing the coverage conditions of the physical experimental platform in an Excel spreadsheet; the coverage conditions include rotational speed, load, and fault type. Based on the physical experimental platform and in accordance with the data acquisition specifications, accelerometers are used at key points of the bearing housing to collect health and fault data and record the original vibration signals. The support stiffness, damping, coupling alignment status, sensor bandwidth and noise level of the rolling bearing are identified to obtain identification data. The identification data is then converted into corresponding equivalent mass, equivalent stiffness and damping parameters to obtain equivalent boundary conditions.

[0008] Optionally, based on the original vibration data and the equivalent boundary conditions, a six-degree-of-freedom coupled dynamic model is constructed, and then the six-degree-of-freedom coupled dynamic model is solved to obtain the acceleration vibration signal used for fault diagnosis, including: Based on the original vibration data and the equivalent boundary conditions, and according to the vibration in both horizontal and vertical directions, a dynamic model of the bearing and rotor, including three subsystems—inner ring, outer ring, and bearing housing—is constructed using the lumped parameter method, thus obtaining the dynamic model framework. Based on the aforementioned dynamic model framework, Hertzian contact theory is introduced to calculate the nonlinear contact stiffness between the rolling element and the raceway, and the modulation effect of different fault types on the vibration signal is simulated to construct a time-varying displacement excitation model including an outer ring fault model, an inner ring fault model, and a rolling element fault model, thereby obtaining an enhanced dynamic model including nonlinear contact stiffness and fault-addition displacement function. Based on the enhanced dynamic model, a six-degree-of-freedom coupled dynamic model is constructed, including the inner ring and rotor sub-equations, the outer ring equations, and the bearing seat sub-equations, according to the inertial force, nonlinear contact force, oil film damping force, gravity, and external load of each component of the rolling bearing. Based on the six-degree-of-freedom coupled dynamic model, the nonlinear contact stiffness and the fault-addition displacement function are solved using the fourth-order Runge-Kutta numerical integration method. The time step is set, and the displacement response of the inner ring, outer ring and bearing housing is iteratively calculated. Then, the displacement response is processed by second-order difference to obtain the acceleration vibration signal used for fault diagnosis.

[0009] Optionally, the calculation expressions for the inner ring and rotor sub-equations are as follows: ; The expression for calculating the outer circle equation is: ; The equation for the bearing housing is calculated as follows: ; in, This refers to the equivalent mass of the inner ring and the rotor. The physical mass of the bearing outer ring; The equivalent mass of the bearing housing; Unbalanced mass; It is the eccentricity; For unbalanced mass moment; This is the equivalent damping coefficient of the inner ring or rotor system; This is the damping coefficient between the outer ring and the bearing housing; This is the contact stiffness coefficient between the outer ring and the bearing housing; This is the bearing housing's support damping coefficient relative to the ground; This is the bearing housing's support stiffness coefficient relative to the ground; For inner circle displacement; This represents the displacement of the outer ring; This represents the displacement of the bearing housing; Vibration velocity; It is the vibration acceleration; For the first Nonlinear Hertzian contact force of each rolling element; For the first Oil film damping force at each rolling element; External radial load; For rotor weight; The weight of the outer ring and the weight of the bearing housing; This represents the amplitude of the centrifugal force. The number of rolling elements; For the first The angular position of each rolling element; ω is the rotational angular velocity of the axis; The time variable in the simulation; This is the acceleration due to gravity.

[0010] Optionally, based on the acceleration vibration signal, the six-degree-of-freedom coupled dynamic model is subjected to model fault verification through five evaluation dimensions to obtain a high-fidelity model, including: Based on the acceleration vibration signal, a parameterized fault module is configured in the six-degree-of-freedom coupled dynamic model. The parameterized fault module is used to adjust the defect size and defect location to simulate different types of local faults and generate corresponding fault simulation vibration data. Based on five evaluation dimensions—frequency location, test band structure, energy distribution, time-domain statistics, and residual energy—the simulated vibration data of the fault is compared with the physical experimental vibration data under the corresponding working conditions to obtain the fidelity index evaluation results. The six-degree-of-freedom coupled dynamic model is then verified based on the fidelity index evaluation results to obtain a high-fidelity model.

[0011] Optionally, based on the high-fidelity model, the AGA algorithm is used to optimize and calibrate the key position parameters to obtain the optimal physical parameter vector. Then, a KAN network is used to construct a nonlinear mapping relationship between the working condition and the optimal physical parameter vector, outputting accurate model parameters suitable for the new working condition, thus obtaining an adaptive digital twin model, including: The key unknown parameters to be calibrated in the high-fidelity model are obtained, and an adaptive genetic algorithm is used to optimize among the key unknown parameters to obtain the calibration problem; the key unknown parameters include equivalent contact stiffness, oil film damping coefficient and nonlinear clearance. The problem to be calibrated is defined as a multi-objective optimization problem. Based on the multi-objective optimization problem, a weighted Euclidean distance between the physical experimental data and the simulation data in terms of time-domain statistical indicators and frequency-domain features is set to obtain the objective function. The time-domain statistical indicators include the root mean square value and kurtosis, and the frequency-domain features include the fault characteristic frequency amplitude and the envelope spectrum energy distribution. Based on the objective function, the AGA algorithm is used to iterate the multi-objective optimization problem in multiple rounds to obtain the optimal physical parameter vector that minimizes the residual between the simulated signal and the real signal under typical experimental conditions. Then, the optimal physical parameter vector and the corresponding operating condition vector are integrated into an operating condition and parameter training dataset. The operating condition vector includes rotational speed, load, fault location, and fault degree. Using the aforementioned working conditions and parameter training dataset, a KAN network model is designed and trained. The new working condition vector is then input into the KAN network model to perform adaptive parameter prediction across the entire working condition domain. This yields accurate model parameters suitable for the new working conditions, thus completing the construction of the adaptive digital twin model.

[0012] Optionally, based on the adaptive digital twin model, a virtual interaction platform is constructed, and then the batch processing interface of the virtual interaction platform is used to automatically generate a hybrid augmented dataset including normal operating conditions, extreme operating conditions, and compound fault conditions, including: Based on the aforementioned adaptive digital twin model, a virtual interactive platform is obtained by using a B / S architecture for front-end and back-end separation development. The front-end is used for the visual interaction of working condition configuration, and the back-end is used to encapsulate the six-degree-of-freedom coupled dynamics model solver and KAN network model based on the Python Web framework. The virtual interactive platform is used to sequentially perform user parameter input and front-end transmission, back-end parameter mapping and physical alignment, dynamic equation solving and signal generation, and data feedback and front-end visualization operations to complete the simulation experience of digital twin. Using the batch processing interface of the virtual interactive platform, network search or Monte Carlo sampling is performed within a preset working condition space to automatically generate a simulation dataset covering all working conditions. The simulation dataset is then fused with real data collected from physical experiments to obtain a hybrid enhanced dataset including normal working conditions, extreme working conditions, and compound fault working conditions.

[0013] This invention discloses the following technical effects by providing a method for expanding multi-condition data of rolling bearings based on digital twins: 1. By using digital twin technology, we can efficiently expand the multi-condition data of rolling bearings, reduce the reliance on physical experiments, and save costs and time.

[0014] 2. By combining physical calibration and automatic mapping, the fidelity of simulation data is ensured, avoiding data deviations caused by parameter inaccuracies in traditional simulations.

[0015] 3. The generated data covers both health and fault status, supports the enhancement of imbalanced datasets, and improves the adaptability of intelligent diagnostic models in real-world scenarios.

[0016] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a schematic diagram of the method flow provided in an embodiment of the present invention; Figure 2 A schematic diagram of a six-degree-of-freedom bearing model provided in an embodiment of the present invention; Figure 3 This is a schematic diagram of the outer ring and inner ring defects of a rolling bearing provided in an embodiment of the present invention; Figure 4 A flowchart of physical calibration and KAN parameter adaptive mapping based on AGA provided for embodiments of the present invention; Figure 5 This is a diagram of the KAN network structure provided in an embodiment of the present invention; Figure 6 This is a diagram of the MLP network structure provided in an embodiment of the present invention; Figure 7 This is a diagram illustrating the digital twin data augmentation architecture provided in an embodiment of the present invention. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0021] like Figure 1As shown, this invention provides a method for augmenting multi-condition data of rolling bearings based on digital twins, including: Step 1: Collect raw vibration signals of the rolling bearing under various operating conditions using a physical experimental platform system, and identify equivalent boundary conditions. Step 1 includes: 1.1 The coverage range of the physical experimental platform is listed in an Excel spreadsheet to obtain the data acquisition specifications. The coverage range includes rotational speed (low, medium, high), load (no load, light load, heavy load), and fault type (health status, inner race fault, outer race fault, rolling element fault, etc.). The sample size, sampling duration, and sampling rate for each type of condition must be clearly defined to ensure the standardization and repeatability of data generation. Priority is given to covering extreme points (such as rotational speed boundaries), common operating points, and mechanistic transition regions to enhance the model's adaptability in complex scenarios.

[0022] 1.2 Based on the physical experimental platform, and in accordance with the data acquisition specifications, accelerometers are used at key points of the bearing housing to collect health and fault data and record the original vibration signals.

[0023] 1.3 Identify the support stiffness, damping, coupling alignment status, sensor bandwidth and noise level of the rolling bearing to obtain identification data, and convert the identification into corresponding equivalent mass, equivalent stiffness and damping parameters to obtain equivalent boundary conditions.

[0024] Under representative operating conditions, accelerometers were installed at key points on the bearing housing to collect health and fault data of the rolling bearing in both horizontal and vertical directions, recording the raw vibration signals. Simultaneously, equivalent boundary conditions were identified using an experimental platform, including support stiffness, damping, coupling alignment, sensor bandwidth, and noise level. These parameters were integrated into the model as equivalent mass, stiffness, and damping, reducing the complexity of device-level modeling and ensuring consistency between the virtual model and the physical entity in the operating environment.

[0025] Step 2: Based on the original vibration data and the equivalent boundary conditions, construct a six-degree-of-freedom coupled dynamic model, and then solve the six-degree-of-freedom coupled dynamic model to obtain the acceleration vibration signal used for fault diagnosis. Step 2 includes: 2.1 Based on the original vibration data and the equivalent boundary conditions, and according to the vibration in both horizontal and vertical directions, a dynamic model of the bearing and rotor, including three subsystems—inner ring, outer ring, and bearing housing—is constructed using the lumped parameter method, thus obtaining the dynamic model framework.

[0026] Specifically: Based on the lumped parameter method, a bearing-rotor dynamics model is constructed, comprising three subsystems: the inner ring, the outer ring, and the bearing housing. The model considers vibrations in both the horizontal (x) and vertical (y) directions, forming a six-degree-of-freedom (6-DOF) system. (See...) Figure 2 Based on Hertzian contact theory, nonlinear contact stiffness, oil film damping, and geometric displacement excitation caused by various local faults are introduced. To establish a six-degree-of-freedom bearing dynamics model, the following assumptions are made: (1) The outer ring is fixed to the bearing housing, and the inner ring rotates synchronously with the shaft; (2) Ignore the mass of the rolling elements and their gyroscopic torque, and assume that the rolling elements are uniformly distributed along the raceway under the action of the cage; (3) The contact between the rolling element and the raceway conforms to the nonlinear Hertzian contact theory, and the contact force is generated only when the element is under pressure. (4) Consider the sliding and oil film damping effects between the rolling elements and the raceway.

[0027] The specific dynamic equations are as follows: Assume the bearing includes There are rolling elements, with a pitch circle diameter of [missing information]. .exist At that moment, the angular position of each rolling element Defined as: (1); In the formula, To maintain the orbital angular velocity of the frame, The initial phase angle. The cage angular velocity and the shaft rotation angular velocity. The relationship is: (2); in: : Number of rolling elements, the total number of balls or rollers inside the bearing. This parameter determines the degree of discretization of the model and the number of terms in the summation calculation.

[0028] The bearing pitch circle diameter, the circumference diameter of the circle containing the center of the rolling element, is a key geometric dimension for calculating the cage speed and characteristic frequency.

[0029] Simulation time: A continuous time variable in the dynamic simulation process, measured in seconds (s).

[0030] : No. The angular position of each rolling element Time of the first The angular position of each rolling element relative to the horizontal axis. This angle increases linearly as the cage rotates.

[0031] : Cage revolution angular velocity, the average angular velocity of the rolling element assembly rotating about the bearing center.

[0032] Initial phase angle, The initial angular position of the first rolling element at any given moment is used to define the initial state.

[0033] : Rotational angular velocity of the shaft / inner ring, the rotational speed of the drive shaft and inner ring, in rad / s.

[0034] Rolling element diameter: The diameter of the ball or roller. The ratio of this parameter to the pitch circle diameter directly affects the characteristic frequency and contact stiffness.

[0035] Contact angle: The angle between the normal to the contact point between the rolling element and the raceway and the radial plane. For deep groove ball bearings, it is usually assumed that under radial load... .

[0036] 2.2 Based on the aforementioned dynamic model framework, Hertzian contact theory is introduced to calculate the nonlinear contact stiffness between the rolling element and the raceway, and the modulation effect of different fault types on the vibration signal is simulated to construct a time-varying displacement excitation model including an outer ring fault model, an inner ring fault model, and a rolling element fault model, thereby obtaining an enhanced dynamic model including nonlinear contact stiffness and fault-addition displacement function.

[0037] Specifically: 1) Calculation of Hertzian contact force and nonlinear stiffness: Total contact deformation between the rolling element and the inner and outer raceways It is determined by the relative displacement of each component and the initial radial clearance. The inner ring displacement is defined as... The outer ring displacement is Then the first The radial deformation at each rolling element is: (3); In the formula This represents the initial radial clearance of the bearing; The time-varying additional displacement function is caused by local faults (stripping, pitting).

[0038] Based on Hertzian contact theory, the first Nonlinear elastic restoring force generated by each rolling element The calculation is as follows: (4); In the formula, This is the equivalent contact stiffness coefficient between the ball and the raceway; For ball bearings, the contact deformation index is taken as... For roller bearings Introducing the Heaviside step function. To describe the switching of contact states, the above equation can be rewritten as: (5); in: : No. The total contact deformation of each rolling element, and the geometric overlap between the raceway and the rolling element in the radial direction. Positive values ​​indicate deformation under pressure, while negative values ​​indicate the presence of clearance.

[0039] Inner ring displacement: the vibrational displacement of the geometric center of the inner ring relative to the equilibrium position.

[0040] : Outer ring displacement, the vibrational displacement of the geometric center of the outer ring relative to the equilibrium position.

[0041] Radial clearance is the total geometric clearance between the inner and outer raceways and the rolling elements when the bearing is unloaded. This parameter contributes to the dead-zone nonlinearity of the system.

[0042] Total fault additional displacement function, which is the sum of geometric dimensional changes caused by various local faults. This value is non-zero when the rolling element passes through the fault zone.

[0043] Elastic contact force, based on Hertzian theory, is determined by the amount of contact deformation. The resulting restorative force.

[0044] Hertzian contact stiffness coefficient is a constant that depends on material properties (elastic modulus, Poisson's ratio) and contact geometry (radius of curvature).

[0045] The contact deformation index is an index describing the degree of nonlinearity. For ball bearings (point contact), it is taken as... Roller bearings (line contact) .

[0046] The Heaviside step function is a switching function used to determine the contact state. When the deformation... The function value is 1 when the function is active (it generates force), and 0 otherwise (it disengages from contact).

[0047] 2) Time-varying displacement excitation model for multiple types of faults: To simulate the modulation effect of different fault types on vibration signals, a unified fault time-varying displacement model is established.

[0048] 2.1) Outer Race Fault Model Assume the outer ring has a width of Maximum depth is Localized spalling, with the fault center located at a fixed angle. Place. When the first Additional displacement generated when a rolling element sweeps across the fault area for: (6); In the formula The central angle of the semicircle corresponding to the fault width.

[0049] in: Fault width: The arc length of the fault spalling area along the circumference of the raceway.

[0050] Maximum fault depth: The deepest dimension of the fault pit, usually equal to the maximum magnitude of the additional displacement.

[0051] : The center angle position of the outer ring fault, the fixed angular position of the outer ring fault point in the stator coordinate system.

[0052] Fault half-width angle, fault width Half of the corresponding central angle, i.e. It defines the length of the "time window" for the rolling element to fall into the fault pit.

[0053] Additional displacement caused by outer ring fault, the first The amount of geometric displacement change that occurs when a rolling element passes through the fault area of ​​the outer ring.

[0054] 2.2) Inner Race Fault Model The inner ring fault rotates synchronously with the shaft, its angular position It is a time-varying function: At this point, additional displacement for: (7); in: The instantaneous angular position of the inner ring fault is a function of time, as the inner ring rotates with the shaft.

[0055] : Initial phase of inner ring fault The initial angle of the inner circle fault point relative to the rotating coordinate system at any given time.

[0056] Additional displacement caused by inner ring fault, number The amount of displacement change that occurs when a rolling element passes through the fault area of ​​the rotating inner ring.

[0057] 2.3) Rolling Element Fault Model Rolling element failures are the most complex, involving the coupling of rotation and revolution. Let the angular velocity of the rolling element's rotation be... , No. The defect phase on each rolling element is Since the defect alternately impacts the inner and outer rings, its additional displacement function is described by a two-pulse sequence: (8); In the formula: : The angular velocity of a rolling element's rotation, the speed at which a rolling element rotates around its own central axis.

[0058] : Rolling element defect phase, the phase angle of the defect point on the rolling element surface as it rotates.

[0059] : Depth of rolling element defects, the maximum depth of spalling on the surface of the rolling element.

[0060] : Contact switch function, describing the pulse function of the contact state between the rolling element defect and the inner and outer raceways. Because the rolling element rotates, the defect will alternately impact the inner and outer raceways.

[0061] Kronecker notation, the mathematical selection operator. If we assume the first... If one of the rolling elements fails, then when The value is 1 if the fault occurs, and 0 otherwise. This ensures that the fault stimulus is applied only to the specific faulty rolling element.

[0062] 2.3 Based on the enhanced dynamic model, a six-degree-of-freedom coupled dynamic model is constructed according to the inertial forces, nonlinear contact forces, oil film damping forces, gravity, and external loads of each component of the rolling bearing; including the inner ring and rotor sub-equations, the outer ring equations, and the bearing housing equations; wherein: The equations for the inner ring and rotor sub-ring are as follows: The inner ring bears the radial load of the bearing. Unbalanced magnetic pull or centrifugal force of the rotor And the reaction force of the rolling elements; the calculation expression is: (9); in, This refers to the equivalent mass of the inner ring and the rotor. For the first Oil film damping force at each rolling element For unbalanced mass moment; The outer ring equation: The outer ring acts as an intermediate floating body, connecting the inner rolling elements and the outer bearing housing; the calculation expression is: (10); in, This refers to the fit stiffness between the outer ring and the bearing housing. Structural damping between the outer ring and the bearing housing; The bearing housing equation is as follows: The bearing housing is installed on the foundation and is mainly affected by the force transmitted by the outer ring and the reaction force of the foundation support; the calculation expression is: (11); In the above equations: The equivalent mass of the inner ring and the rotor; The physical mass of the bearing outer ring. In the model, the outer ring is considered as an intermediate floating body, connecting the inner rolling elements and the outer bearing housing; The equivalent mass of the bearing housing. It is the equivalent mass of the stationary component that fixes or supports the outer ring of the bearing. Unbalanced mass. A tiny mass that causes eccentric vibration in the rotor, usually originating from manufacturing errors or material inhomogeneity; Eccentricity. Unbalanced mass. The distance to the axis of rotation; Unbalanced mass moment. and The product of and is a key physical quantity for measuring the degree of rotor imbalance and directly determines the magnitude of centrifugal force.

[0063] Damping and stiffness parameters: : Equivalent damping coefficient of the inner ring / rotor system. Characterizes the structural or air damping experienced by the rotor system during motion, used to dissipate vibration energy; : Damping coefficient between the outer ring and the bearing housing. Since there is a clearance or contact surface between the outer ring and the bearing housing bore, this parameter characterizes the friction or structural damping generated during their relative motion. : Contact stiffness coefficient between the outer ring and the bearing housing. It characterizes the elastic resistance of the mating surfaces between the outer ring and the bearing housing. If the fit is tight, this stiffness is high; if there is looseness, the stiffness will change non-linearly. The bearing housing's damping coefficient relative to the ground. The damping characteristics of the bearing housing's mounting foundation (such as a base or frame). : The bearing housing's support stiffness coefficient to the ground. The elastic characteristics of the bearing housing mounting foundation reflect the hardness or softness of the ground or frame.

[0064] Displacement and motion state parameters: Displacement of the inner ring (rotor). The instantaneous displacement of the geometric center of the inner ring relative to the absolute coordinate origin in the horizontal (x) and vertical (y) directions; Displacement of the outer ring. The instantaneous displacement of the geometric center of the outer ring in the horizontal and vertical directions; Displacement of the bearing housing. The vibrational displacement of the bearing housing in the horizontal and vertical directions; Velocity. The first derivative of the displacement with respect to time represents the vibration velocity; Acceleration. The second derivative of the displacement with respect to time represents the vibration acceleration (i.e., the inertial force term).

[0065] Force and load parameters: : No. The nonlinear Hertzian contact force of the rolling element. When the... When a rolling element is compressed, the elastic restoring force generated by the contact between the ball and the inner and outer raceways is the main source of the system's nonlinearity. : No. The oil film damping force at each rolling element. The viscous resistance generated by the lubricating oil film during the rolling element compression process; External radial load. A constant or time-varying external force applied to the shaft (such as belt tension, gear meshing force, etc.). Rotor gravity. The weight of the rotor system itself, which typically acts in the negative y-direction ( ); : Outer ring gravity and bearing housing gravity; Centrifugal force amplitude. The magnitude of the rotational centrifugal force caused by the unbalanced mass, whose direction changes periodically with the rotation of the shaft.

[0066] Geometric and temporal parameters: : Number of rolling elements. The total number of balls or rollers in the bearing determines the sign of the summation. The upper limit; : No. The angular position of the rolling element. A rolling element in The angle of the moment relative to the x-axis. It determines the projected components of the contact force in the x and y directions (via...). and ); The angular velocity of the shaft. The rotor's rotational speed (radians / second) determines the fault impact frequency and the unbalanced excitation frequency; Time. The time variable in the simulation; : Gravitational acceleration. A constant, usually taken as... .

[0067] 2.4 such as Figure 3 As shown, based on the six-degree-of-freedom coupled dynamic model, the nonlinear contact stiffness and the fault-addition displacement function are solved using the fourth-order Runge-Kutta numerical integration method, with a set time step. Iterative calculation of the displacement response of the inner ring, outer ring, and bearing housing. Then, the displacement response is subjected to second-order difference processing to obtain the acceleration vibration signal used for fault diagnosis. .

[0068] Step 3: Based on the acceleration vibration signal, perform model fault verification on the six-degree-of-freedom coupled dynamic model through five evaluation dimensions to obtain a high-fidelity model. Step 3 includes: 3.1 Based on the acceleration vibration signal, a parameterized fault module is configured in the six-degree-of-freedom coupled dynamic model. The parameterized fault module is used to adjust the defect size and defect location to simulate different types of local faults and generate corresponding fault simulation vibration data.

[0069] 3.2 Based on five evaluation dimensions—frequency location, test strip structure, energy distribution, time-domain statistics, and residual energy—the simulated vibration data of the fault is compared with the physical experimental vibration data under the corresponding working conditions to obtain the fidelity index evaluation results. The six-degree-of-freedom coupled dynamic model is then verified based on the fidelity index evaluation results to obtain a high-fidelity model.

[0070] Frequency position: Peak alignment of BPFI / BPFO / BSF / FTF; Side band structure: The side bands of the envelope spectrum are symmetrical and their intensity ratios are close; Energy distribution: The energy curves of the target frequency bands are similar; Time-domain statistics: Kurtosis / kurtosis / impact are similar; Residual energy: The difference between measured and simulated energy should be as small as possible within the "allowable frequency band".

[0071] This verification process ensures that the simulation data is consistent with the physical data in terms of core fault identification, providing a reliable foundation for subsequent data expansion.

[0072] Step 4: Based on the high-fidelity model, the AGA algorithm is used to optimize and calibrate the key position parameters to obtain the optimal physical parameter vector. Then, a KAN network is used to construct a nonlinear mapping relationship between the working condition and the optimal physical parameter vector, outputting accurate model parameters suitable for the new working condition, thus obtaining an adaptive digital twin model. Step 4 includes: 4.1 Obtain the key unknown parameters to be calibrated in the high-fidelity model, and use an adaptive genetic algorithm to find the optimization among the key unknown parameters to obtain the calibration problem; the key unknown parameters include equivalent contact stiffness, oil film damping coefficient and nonlinear clearance.

[0073] 4.2 The problem to be calibrated is defined as a multi-objective optimization problem, and based on the multi-objective optimization problem, a weighted Euclidean distance between the physical experimental data and the simulation data in terms of time-domain statistical indicators and frequency-domain features is set to obtain the objective function; wherein, the time-domain statistical indicators include the root mean square value and kurtosis, and the frequency-domain features include the fault characteristic frequency amplitude and the envelope spectrum energy distribution.

[0074] 4.3 Based on the objective function, the AGA algorithm is used to perform multiple iterations on the multi-objective optimization problem to obtain the optimal physical parameter vector with the minimum residual between the simulated signal and the real signal under typical experimental conditions. Then, the optimal physical parameter vector and the corresponding operating condition vector are integrated into an operating condition and parameter training dataset. The operating condition vector includes rotational speed, load, fault location, and fault degree.

[0075] 4.4 Using the aforementioned working conditions and parameter training dataset, design and train a KAN network model. Input the new working condition vector into the KAN network model to perform adaptive parameter prediction across the entire working condition domain, obtain accurate model parameters suitable for the new working conditions, and complete the construction of the adaptive digital twin model.

[0076] Specifically, such as Figure 4 As shown: To ensure that the established digital twin model accurately reflects the dynamic response of rolling bearings in real physical environments, this step constructs a two-layer correction system comprising "physical parameter calibration" and "operating condition-parameter adaptive mapping," such as... Figure 4 As shown, the system first uses an intelligent optimization algorithm to invert the optimal physical parameters at discrete experimental operating points. Then, it introduces KAN networks (Kolmogorov-Arnold Networks) based on the Kolmogorov-Arnold representation theorem to construct a high-precision nonlinear mapping relationship from operating conditions to model parameters, thereby achieving high-fidelity model across the entire operating condition domain.

[0077] During the physical parameter calibration phase, an Adaptive Genetic Algorithm (AGA) was used to calibrate key unknown parameters in the six-degree-of-freedom dynamic model, including the equivalent contact stiffness of each component. Oil film damping coefficient and nonlinear gap Optimization is performed. The calibration problem is defined as a multi-objective optimization problem, with the objective function... The weighted Euclidean distance between physical experimental data and simulation data is defined as the time-domain statistical index (root mean square value, kurtosis) and frequency-domain characteristics (fault characteristic frequency amplitude, envelope spectrum energy distribution).

[0078] The AGA algorithm searches for the global optimum in the parameter space by simulating the biological evolution process. The specific process is as follows: First, the parameters to be identified are determined based on the physical properties of the experimental platform. The upper and lower limits of the values ​​are determined, and the population is randomly initialized within these limits. Next, the parameters of each group of individuals are substituted into the dynamic equations for numerical solution to calculate their fitness values. During the evolutionary process, an adaptive crossover probability is introduced. and mutation probability The operator is dynamically adjusted based on the fitness dispersion of the population. When individual fitness tends to be consistent, the mutation rate is increased to escape local minima; when fitness is dispersed, the mutation rate is decreased to accelerate convergence. Through multiple iterations, the optimal physical parameter vector that minimizes the residual between the simulated and real signals under typical experimental conditions is finally obtained. .

[0079] In the automatic parameter mapping stage, in order to generalize the calibration results of discrete operating points to the continuous operating state domain, this invention uses KAN (Kolmogorov-Arnold Networks) to construct a multidimensional state input and model physical parameters. The nonlinear regression model between them, with input layer vectors Expand to These represent rotational speed, load, fault location (inner ring / outer ring / rolling element), and fault severity (defect size), respectively. This design considers the nonlinear coupling effects of different fault types and severity on the system's structural stiffness and damping characteristics. Unlike traditional multilayer perceptrons (MLPs) that use fixed activation functions at nodes and linear weights at edges (…), this design… Figure 4 The KAN network is entirely based on the Kolmogorov-Arnold Representation Theorem, which states that any multivariate continuous function... All of them can be represented as a superposition of a finite number of continuous univariate functions. Their mathematical expressions are: (12); in: This represents the operating condition vector input to the network. Specifically, in the text... .

[0080] : The number of input variables. Values ​​will be taken from the text. (Corresponding to the above 4 operating conditions).

[0081] Input vector The first in Each component.

[0082] The target physical parameters predicted by the network. In the text, this specifically refers to unknown parameters in the dynamic model, such as "equivalent contact stiffness", "oil film damping coefficient" or "nonlinear clearance".

[0083] The index of the outer summation represents the node of the hidden layer in the KAN network. According to the Kolmogorov-Arnold representation theorem, for 3D input, only Any continuous multivariate function can be accurately represented by the superposition of univariate function terms. Range: From arrive .

[0084] : Outer function, the post-processing nonlinear function of the network, maps the internal summation result to the output.

[0085] The inner unary function is a learnable unary nonlinear activation function. It does not use a fixed weight matrix, but rather applies weights to each input component. Perform independent nonlinear transformations.

[0086] like Figure 5, Figure 6 As shown, The input vector is (in this scheme, it is rotational speed, load, fault location, and fault severity). For the input dimension, and All are learnable univariate nonlinear functions. In the KAN network architecture, each connection edge is parameterized as a learnable B-spline function, i.e., the activation function on the edge. Represented as a linear combination of basis functions: (13); in: : Corresponding to formula 12 That is, the activation function that connects the input and the hidden layer.

[0087] (B-spline basis functions): A set of predefined, fixed-shape basis functions, usually bell curves, which are used to fit nonlinear curves of arbitrary shapes through linear combination.

[0088] Trainable coefficients / weights are those obtained by adjusting... Size, change basis function The range, thereby adjusting The shape is designed to fit physical laws.

[0089] In practice, an input layer is constructed as follows: The output layer is The KAN network. The "operating condition-optimal parameters" obtained during the physical parameter calibration phase are used to... As a training dataset, the spline coefficients in the network are trained by minimizing the mean square error (MSE) between the predicted and calibrated parameters. Because the KAN network has good mathematical interpretability and far surpasses the accuracy of MLPs in fitting such low-dimensional physical functions, it can accurately capture the complex nonlinear laws governing the changes in system physical parameters with rotational speed, load, and fault evolution. After training, for any given new operating condition... (Including combinations of rotational speeds or fault levels that have not been tested), the KAN network can directly output the corresponding accurate model parameters: (14); in: The predicted model parameters output as accurate physical parameters applicable to the new working conditions. Specifically, this refers to the corrected stiffness. Damping or gap Physical quantities can be directly substituted into the dynamic equations.

[0090] The trained KAN model is a nonlinear mapping function that has been trained using AGA-optimized data.

[0091] : New operating condition vector, user-defined operating conditions that have not appeared in the experiment.

[0092] No time-consuming physical calibration is required. This ensures that the digital twin model is accurate not only in a healthy state, but also maintains extremely high physical consistency during the occurrence and evolution of failures, laying a solid foundation for generating extended data that conforms to real failure mechanisms.

[0093] Step 5: Based on the adaptive digital twin model, construct a virtual interaction platform, and then use the batch processing interface of the virtual interaction platform to automatically generate a hybrid augmented dataset including normal operating conditions, extreme operating conditions, and compound fault conditions. For example... Figure 7 As shown, this step involves adjusting operating parameters (such as rotational speed, load, fault type, and fault severity) to generate simulated acceleration signals, envelope spectra, and other data from the model. These data are then fused with the physical data to form a rich dataset. Step 5 includes: 5.1 Based on the aforementioned adaptive digital twin model, a virtual interactive platform is obtained by using a B / S architecture for front-end and back-end separation development. The front-end is used for visual interaction of working condition configuration, and the back-end is used to encapsulate the six-degree-of-freedom coupled dynamics model solver and KAN network model based on a Python Web framework. Specifically: The platform adopts a front-end and back-end separation development model. The front-end is built on the Three.js engine based on the WebGL technology standard, loading a lightweight 3D model of the rolling bearing in the browser and providing an immersive visual interactive interface. The interface integrates a working condition configuration module, allowing users to configure the rotational speed (…). ), load ( ), Fault location ( (inner / outer rings, rolling elements) and degree of failure ( The four-dimensional parameter vectors (crack width / depth) are adjusted in real time. The backend is built on a Python web framework to provide scientific computing services, which internally encapsulate the six-degree-of-freedom dynamic equation solver (ODE Solver) established in step one and the KAN parameter mapping network trained in step two.

[0094] 5.2 Using the virtual interactive platform, user parameters are input and transmitted to the front end, back end parameters are mapped and physically aligned, dynamic equations are solved and signals are generated, and data is transmitted back and visualized to the front end, thus completing the simulation experience of the digital twin.

[0095] The specific parameter-driven dynamic simulation evolution process is as follows: (1) Parameter input and mapping: Users adjust operating parameters on the front-end interface, such as increasing the speed from 1800rpm to 2400rpm, or setting a 0.5mm crack on the inner / outer ring. The front-end transmits the state vector via WebSocket. The request is sent to the backend. Upon receiving the request, the backend first invokes the pre-trained KAN network to infer the optimal physical model parameters corresponding to the current operating condition in real time. This enables automatic alignment of physical boundary conditions.

[0096] (2) Dynamic solution: The backend uses the Runge-Kutta algorithm (ode45) to numerically integrate the dynamic differential equation after updating the parameters, and generates a time-domain sequence of bearing housing vibration acceleration containing nonlinear characteristics.

[0097] (3) Data feedback and visualization: The original signal generated by the simulation and the envelope spectrum data after FFT transformation are fed back to the front end. The front end uses Chart.js or D3.js to perform real-time waveform rendering and synchronously drives the three-dimensional model to display the corresponding operating status, realizing the digital twin simulation experience.

[0098] 5.3 Using the batch processing interface of the virtual interactive platform, network search or Monte Carlo sampling is performed within the preset working condition space to automatically generate a simulation dataset covering all working conditions. The simulation dataset is then fused with real data collected from physical experiments to obtain a hybrid enhanced dataset including normal working conditions, extreme working conditions, and compound fault working conditions.

[0099] Specifically, utilizing the batch processing interface of the virtual interactive platform, an automated data augmentation strategy is executed: within a defined operating space, grid search or Monte Carlo sampling is performed to systematically generate simulation data covering the entire speed range, the entire load spectrum, and different fault evolution stages. The generated simulation signals, after statistical calibration with physical experimental data, are fused according to the principle of "simulation data as the primary source and experimental data as a supplement." This ultimately constructs a hybrid augmented dataset with accurate labels and complete operating conditions. This dataset not only includes samples of conventional operating conditions but also focuses on supplementing extreme operating conditions and composite fault samples that are difficult to obtain through physical experiments. It effectively solves the problems of scarce fault samples and class imbalance in industrial big data scenarios, providing a high-quality data foundation for the subsequent training of intelligent diagnostic models.

[0100] Therefore, this invention provides a method for expanding rolling bearing data under multiple operating conditions based on digital twins, which enables the generation and expansion of rolling bearing data under multiple operating conditions, providing rich and controllable data support for fault diagnosis, health monitoring and model training.

[0101] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0102] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for expanding multi-condition data of rolling bearings based on digital twins, characterized in that, include: The original vibration signals of rolling bearings under various working conditions were collected using a physical experimental platform system, and the equivalent boundary conditions were identified. Based on the original vibration data and the equivalent boundary conditions, a six-degree-of-freedom coupled dynamic model is constructed, and then the six-degree-of-freedom coupled dynamic model is solved to obtain the acceleration vibration signal used for fault diagnosis. Based on the acceleration vibration signal, the six-degree-of-freedom coupled dynamic model is verified for model failure through five evaluation dimensions to obtain a high-fidelity model. Based on the high-fidelity model, the AGA algorithm is used to optimize and calibrate the key position parameters to obtain the optimal physical parameter vector. Then, the KAN network is used to construct a nonlinear mapping relationship between the working condition and the optimal physical parameter vector, and output accurate model parameters suitable for the new working condition to obtain an adaptive digital twin model. Based on the adaptive digital twin model, a virtual interaction platform is constructed, and then the batch processing interface of the virtual interaction platform is used to automatically generate a hybrid enhanced dataset including normal operating conditions, extreme operating conditions, and compound fault conditions.

2. The method for expanding multi-condition data of rolling bearings based on digital twins according to claim 1, characterized in that, The raw vibration signals of rolling bearings under various operating conditions were collected using a physical experimental platform system, and equivalent boundary conditions were identified, including: The data acquisition specifications are obtained by listing the coverage conditions of the physical experimental platform in an Excel spreadsheet; the coverage conditions include rotational speed, load, and fault type. Based on the physical experimental platform and in accordance with the data acquisition specifications, accelerometers are used at key points of the bearing housing to collect health and fault data and record the original vibration signals. The support stiffness, damping, coupling alignment status, sensor bandwidth and noise level of the rolling bearing are identified to obtain identification data. The identification data is then converted into corresponding equivalent mass, equivalent stiffness and damping parameters to obtain equivalent boundary conditions.

3. The method for expanding multi-condition data of rolling bearings based on digital twins according to claim 2, characterized in that, Based on the original vibration data and the equivalent boundary conditions, a six-degree-of-freedom coupled dynamic model is constructed, and then the six-degree-of-freedom coupled dynamic model is solved to obtain the acceleration vibration signal used for fault diagnosis, including: Based on the original vibration data and the equivalent boundary conditions, and according to the vibration in both horizontal and vertical directions, a dynamic model of the bearing and rotor, including three subsystems—inner ring, outer ring, and bearing housing—is constructed using the lumped parameter method, thus obtaining the dynamic model framework. Based on the aforementioned dynamic model framework, Hertzian contact theory is introduced to calculate the nonlinear contact stiffness between the rolling element and the raceway, and the modulation effect of different fault types on the vibration signal is simulated to construct a time-varying displacement excitation model including an outer ring fault model, an inner ring fault model, and a rolling element fault model, thereby obtaining an enhanced dynamic model including nonlinear contact stiffness and fault-addition displacement function. Based on the enhanced dynamic model, a six-degree-of-freedom coupled dynamic model is constructed, including the inner ring and rotor sub-equations, the outer ring equations, and the bearing seat sub-equations, according to the inertial force, nonlinear contact force, oil film damping force, gravity, and external load of each component of the rolling bearing. Based on the six-degree-of-freedom coupled dynamic model, the nonlinear contact stiffness and the fault-addition displacement function are solved using the fourth-order Runge-Kutta numerical integration method. The time step is set, and the displacement response of the inner ring, outer ring and bearing housing is iteratively calculated. Then, the displacement response is processed by second-order difference to obtain the acceleration vibration signal used for fault diagnosis.

4. The method for expanding multi-condition data of rolling bearings based on digital twins according to claim 3, characterized in that: The calculation expressions for the inner ring and rotor sub-equations are as follows: ； The expression for calculating the outer circle equation is: ； The equation for the bearing housing is calculated as follows: ； in, This refers to the equivalent mass of the inner ring and the rotor. The physical mass of the bearing outer ring; The equivalent mass of the bearing housing; Unbalanced mass; It is the eccentricity; For unbalanced mass moment; This is the equivalent damping coefficient of the inner ring or rotor system; This is the damping coefficient between the outer ring and the bearing housing; This is the contact stiffness coefficient between the outer ring and the bearing housing; This is the bearing housing's support damping coefficient relative to the ground; This is the bearing housing's support stiffness coefficient relative to the ground; For inner circle displacement; This represents the displacement of the outer ring; This represents the displacement of the bearing housing; Vibration velocity; It is the vibration acceleration; For the first Nonlinear Hertzian contact force of each rolling element; For the first Oil film damping force at each rolling element; External radial load; For rotor weight; The weight of the outer ring and the weight of the bearing housing; This represents the amplitude of the centrifugal force. The number of rolling elements; For the first The angular position of each rolling element; ω is the rotational angular velocity of the axis; The time variable in the simulation; This is the acceleration due to gravity.

5. The method for expanding multi-condition data of rolling bearings based on digital twins according to claim 4, characterized in that, Based on the acceleration vibration signal, the six-degree-of-freedom coupled dynamic model is validated for model failure through five evaluation dimensions to obtain a high-fidelity model, including: Based on the acceleration vibration signal, a parameterized fault module is configured in the six-degree-of-freedom coupled dynamic model. The parameterized fault module is used to adjust the defect size and defect location to simulate different types of local faults and generate corresponding fault simulation vibration data. Based on five evaluation dimensions—frequency location, test band structure, energy distribution, time-domain statistics, and residual energy—the simulated vibration data of the fault is compared with the physical experimental vibration data under the corresponding working conditions to obtain the fidelity index evaluation results. The six-degree-of-freedom coupled dynamic model is then verified based on the fidelity index evaluation results to obtain a high-fidelity model.

6. The method for expanding multi-condition data of rolling bearings based on digital twins according to claim 5, characterized in that, Based on the high-fidelity model, the AGA algorithm is used to optimize and calibrate key position parameters to obtain the optimal physical parameter vector. Then, a KAN network is used to construct a nonlinear mapping relationship between the working condition and the optimal physical parameter vector, outputting accurate model parameters suitable for the new working condition, thus obtaining an adaptive digital twin model, including: The key unknown parameters to be calibrated in the high-fidelity model are obtained, and an adaptive genetic algorithm is used to optimize among the key unknown parameters to obtain the calibration problem; the key unknown parameters include equivalent contact stiffness, oil film damping coefficient and nonlinear clearance. The problem to be calibrated is defined as a multi-objective optimization problem. Based on the multi-objective optimization problem, a weighted Euclidean distance between the physical experimental data and the simulation data in terms of time-domain statistical indicators and frequency-domain features is set to obtain the objective function. The time-domain statistical indicators include the root mean square value and kurtosis, and the frequency-domain features include the fault characteristic frequency amplitude and the envelope spectrum energy distribution. Based on the objective function, the AGA algorithm is used to iterate the multi-objective optimization problem in multiple rounds to obtain the optimal physical parameter vector that minimizes the residual between the simulated signal and the real signal under typical experimental conditions. Then, the optimal physical parameter vector and the corresponding operating condition vector are integrated into an operating condition and parameter training dataset. The operating condition vector includes rotational speed, load, fault location, and fault degree. Using the aforementioned working conditions and parameter training dataset, a KAN network model is designed and trained. The new working condition vector is then input into the KAN network model to perform adaptive parameter prediction across the entire working condition domain. This yields accurate model parameters suitable for the new working conditions, thus completing the construction of the adaptive digital twin model.

7. The method for expanding multi-condition data of rolling bearings based on digital twins according to claim 6, characterized in that, Based on the aforementioned adaptive digital twin model, a virtual interaction platform is constructed. Then, utilizing the batch processing interface of the virtual interaction platform, a hybrid augmented dataset is automatically generated, including normal operating conditions, extreme operating conditions, and composite fault conditions. Based on the aforementioned adaptive digital twin model, a virtual interactive platform is obtained by using a B / S architecture for front-end and back-end separation development. The front-end is used for the visual interaction of working condition configuration, and the back-end is used to encapsulate the six-degree-of-freedom coupled dynamics model solver and KAN network model based on the Python Web framework. The virtual interactive platform is used to sequentially perform user parameter input and front-end transmission, back-end parameter mapping and physical alignment, dynamic equation solving and signal generation, and data feedback and front-end visualization operations to complete the simulation experience of digital twin. Using the batch processing interface of the virtual interactive platform, network search or Monte Carlo sampling is performed within a preset working condition space to automatically generate a simulation dataset covering all working conditions. The simulation dataset is then fused with real data collected from physical experiments to obtain a hybrid enhanced dataset including normal working conditions, extreme working conditions, and compound fault working conditions.

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