Rolling bearing fault diagnosis method based on working condition and simulation-real migration learning

Abstract

The application claims a rolling bearing fault diagnosis method based on working condition and simulation-real migration learning, belonging to the technical field of mechanical equipment state monitoring and intelligent fault diagnosis. Firstly, a mapping relationship between real simulation working conditions is established; then a six-degree-of-freedom dynamic model with the inner ring, outer ring and rolling body two-dimensional translation as the degree of freedom is constructed, and combined with the Hertz contact theory, local defect displacement excitation function, time-varying contact stiffness and bearing area function, the fault vibration response under different working conditions is solved; finally, the simulation samples and real samples are preprocessed, the physical prior features and deep features are further extracted and fused for classification, and the rolling bearing fault category and confidence are output. The application can improve the fault diagnosis accuracy, robustness and explainability of the rolling bearing under complex working conditions, and is suitable for industrial rotating machinery state monitoring and predictive maintenance scenes.

Description

Technical Field

[0001] This invention belongs to the field of rotating machinery fault diagnosis, condition monitoring and intelligent operation and maintenance technology, and specifically relates to a fault diagnosis method based on rolling bearing physical modeling, simulation fault data generation, simulation-measurement cross-domain feature fusion and intelligent classification and recognition. Background Technology

[0002] Rolling bearings are critical support components in motors, gearboxes, pumps, fans, compressors, and other rotating machinery. Their operating condition directly affects the overall system's performance, reliability, and service life. During long-term service, rolling bearings are susceptible to cyclic loads, lubrication degradation, material fatigue, manufacturing errors, installation deviations, and external impacts, leading to typical failure modes such as outer ring failure, inner ring failure, rolling element failure, and cage failure. When a rolling bearing experiences localized damage, periodic contact impacts occur between the faulty area and the rolling elements. These impacts, transmitted through the structure, excite system resonance, resulting in a vibration response with significant modulation characteristics. Traditional fault diagnosis methods typically rely on time-domain statistical features, frequency-domain features, and envelope spectrum features for fault identification. However, under varying operating conditions, high noise levels, and cross-equipment conditions, relying solely on empirical features or black-box classification models suffers from insufficient generalization.

[0003] While existing simulation-assisted diagnostic methods can alleviate the problem of insufficient real fault samples, they often describe local defect excitation only with simplified impact functions or single displacement functions. They fail to simultaneously characterize the coupling mechanism of time-varying displacement excitation and time-varying contact stiffness excitation, and also fail to clearly define the motion and force relationships of the inner ring, outer ring, and rolling elements under multi-degree-of-freedom conditions. This results in significant discrepancies between simulated and real responses. Especially when dealing with the correspondence between public datasets and actual equipment operating conditions, if a one-to-one mapping between discrete operating condition labels and rotational speed and radial load is not established, the operating conditions, local contact states, and fault characteristic frequencies of the simulated samples may differ from those of the real samples, thus affecting subsequent transfer learning and classification diagnostic results. Furthermore, existing solutions often directly enter the transfer learning or classification stage after generating simulation data, lacking prior quality verification of the inter-class separability and intra-class compactness of the simulation samples. This easily leads to a situation where, although the number of simulation samples is sufficient, there is severe class aliasing, which in turn affects the effectiveness of subsequent cross-domain alignment and classification diagnostics.

[0004] Therefore, there is an urgent need to provide a rolling bearing fault diagnosis scheme that can simultaneously take into account working condition consistency, six-degree-of-freedom dynamic modeling, local defect displacement excitation, contact stiffness solution, numerical integral simulation, cross-domain distribution alignment, and feature fusion classification.

[0005] A search revealed application CN110220709B, which discloses a method for diagnosing rolling bearing faults based on a CNN model and transfer learning. The method includes the following steps: First, using computer simulation, simulation data of different categories of rolling bearing faults are constructed to train and test the CNN model. Then, a new training set is constructed using the first target domain data and the simulation dataset, transferring most of the CNN model's parameters to the target domain data to obtain a new CNN model. Next, the dataset from the second target domain is added to the original training set to reconstruct the training set, and transfer learning and model parameters are performed sequentially. Using this method, the CNN model converges more easily, reducing the training cost and the requirement for a large amount of sample data in the target domain. The resulting new CNN model exhibits stronger robustness and applicability.

[0006] The CN110220709B patent primarily addresses the problem of "how to train a CNN and perform transfer learning using simulated data when there are insufficient samples in the target domain." Its core lies in the generation of the simulated time-domain graph, CNN training, and successive parameter transfer on the target domain data. While this approach reduces the dependence on the number of labeled samples in the target domain, it still suffers from several issues, including simplified representation of the simulation mechanism, lack of mapping constraints between real and simulated conditions, lack of separability verification of simulated sample quality, lack of explicit distribution alignment in transfer learning, and insufficient utilization of physical prior features.

[0007] To address the aforementioned shortcomings, this invention proposes a complete technical route: "Operating Condition Mapping Optimization—Six-DOF Dynamic Simulation—Separability Verification—Simulation-Real Distribution Alignment—Fuse Classification of Physical Prior Features and Data-Driven Features." This route first ensures consistency between the simulation input and the actual acquired operating conditions through operating condition mapping optimization; then, it enhances the physical realism of the simulation samples through a six-DOF dynamic model; subsequently, it improves the usability and cross-domain adaptability of the simulation samples through separability verification and distribution alignment; finally, it completes fault identification through multi-scale deep features, physical prior features, and a Kolmogorov-Arnold Network classification model. Therefore, this invention can simultaneously solve the problems of operating condition mismatch, insufficient simulation realism, domain shift, and insufficient classification robustness, exhibiting stronger engineering applicability, interpretability, and cross-operating condition diagnostic capabilities compared to existing patents. Summary of the Invention

[0008] This invention aims to address the problems of operating condition mismatch, insufficient expression of dynamic mechanisms, insufficient real fault samples, and insufficient cross-domain generalization ability in existing technologies. It proposes a rolling bearing fault diagnosis method based on operating condition and simulation-real-world transfer learning. The technical solution of this invention is as follows:

[0009] A method for diagnosing rolling bearing faults based on operating conditions and simulation-real-world transfer learning includes the following steps:

[0010] S1. Based on the working condition labels of real rolling bearing data, establish an initial mapping relationship between the working condition labels and the rotational speed and radial load. With the consistency between the simulation sample and the real sample in the time domain, frequency domain, envelope spectrum and class separability as the optimization objective, correct the working condition parameters to obtain the optimized working condition mapping relationship.

[0011] S2. Based on the optimized working condition mapping relationship, a six-degree-of-freedom rolling bearing dynamic model is constructed with the translational motion of the inner ring, outer ring and rolling element in the two-dimensional direction as the degree of freedom. Combined with the local defect displacement excitation function, time-varying contact stiffness, load-bearing zone function and nonlinear contact force calculation, a simulation fault sample corresponding to the real working condition is generated.

[0012] S3. Perform unified preprocessing and separability verification on the simulated fault samples and real samples, and perform cross-domain transformation on the simulated fault samples through a distribution alignment model to obtain simulated corrected samples.

[0013] S4. Extract physical prior features and data-driven features from the real samples and the simulation correction samples. The data-driven features are obtained through a multi-scale feature extraction network. After fusing the physical prior features and data-driven features, input them into the Kolmogorov-Arnold Network classification model. Process the fused features through a one-dimensional nonlinear mapping function expanded by the basis function to obtain the rolling bearing fault category and the corresponding confidence level.

[0014] Furthermore, the working condition mapping is a one-to-one correspondence between discrete working condition labels and rotational speed and radial load;

[0015] Multiple discrete operating condition labels are mapped to their corresponding rotational speed parameters and radial load parameters, and an operating condition vector is constructed.

[0016]

[0017] in, Indicates operating condition label, For the first The speed corresponding to each operating condition label For the first The radial load corresponding to each working condition label is used to ensure that the generation process of the simulated fault sample is consistent with the acquisition conditions of the real sample.

[0018] Furthermore, the dynamic equation for local defects in a six-degree-of-freedom rolling bearing is as follows:

[0019] --25

[0020] in, For the quality matrix, Here is the damping matrix. Here is the support stiffness matrix; This is the Hertz contact force vector; This is the external radial load vector; This is the additional excitation vector caused by speed fluctuations, centrifugal effects, unbalanced excitation, or noise disturbances; This is a generalized coordinate vector for a six-degree-of-freedom rolling bearing system, used to describe the inner ring, outer ring, and rolling elements in motion. , Displacement state in two directions.

[0021]

[0022] in, Indicates the inner circle is , Displacement in the direction; , Indicates the outer ring is , Displacement in the direction; , Indicates that the rolling element is in , Equivalent displacement in the direction.

[0023] The external load vector is represented as:

[0024]

[0025] in, This indicates the radial load acting on the bearing system.

[0026] Furthermore, step three involves performing unified preprocessing on both the simulated rolling bearing signal and the actual acquired signal, specifically including:

[0027] (1) Signal segmentation and transient removal

[0028] For the original vibration signal or discrete signal Processing:

[0029] After removing the initial transient segment, the sample set is obtained by sliding segmentation of fixed length:

[0030] ;

[0031] in, Indicates the first Segmented samples, This indicates the sequence number of the discrete sampling point within the sample segment. This represents the total number of samples obtained after segmentation.

[0032] (2) Mean removal processing;

[0033] Remove DC components, eliminate bias, and improve spectral stability:

[0034]

[0035] in, Represents the original discrete vibration signal. This represents the signal after removing the mean. This indicates the total number of sampling points in the current sample segment. This represents the index of the sampling point during the summation process.

[0036] (3) Amplitude normalization and standardization:

[0037]

[0038] in, The mean, Standard deviation;

[0039] (4) Hilbert transform and envelope extraction

[0040] In envelope extraction, it is preferable to first perform bandpass filtering to extract the signal within the structural resonance frequency band, and then use Hilbert transform to construct the analytical signal:

[0041]

[0042] in, This represents a discrete vibration signal after being demeaned, normalized, or standardized. Represents the Hilbert transform operator; Represents the imaginary unit; Indicates the signal with the real part The analytic signal is formed by the result of the Hilbert transform and the Hilbert transform.

[0043] The envelope signal is:

[0044]

[0045] in, Indicates analytic signal The amplitude, i.e. the envelope of the vibration signal.

[0046] (5) Envelope spectrum calculation

[0047] For envelope signal Perform a Fourier transform to obtain the envelope spectrum:

[0048]

[0049] in, Used to characterize the energy distribution of the envelope signal at different frequencies, in order to extract bearing fault characteristic frequencies such as BPFO, BPFI, BSF, and FTF.

[0050] (6) Construct separability evaluation index;

[0051] The Fisher discriminant metric used to assess the separability of two classes of samples is:

[0052]

[0053] in, and Let represent the means of the features of the two classes of samples, respectively. and Let represent the variances of the features of the two classes of samples, respectively. This represents the Fisher separability evaluation index. The larger the value, the greater the difference in mean between the two classes of samples and the smaller the intra-class fluctuation, indicating better class separability.

[0054] The Pearson correlation coefficient between two signals or feature vectors is:

[0055]

[0056] in, and These represent the two signals or two eigenvectors at the th... The value at each position and These represent the means of two signals or feature vectors, respectively. Indicates the length of the signal or eigenvector. This represents the Pearson correlation coefficient between the two.

[0057] In the analysis of the separability of rolling element failures, the sideband energy ratio can be expressed as:

[0058]

[0059] in, Indicates the characteristic frequency of rolling element failure. This indicates the cage failure characteristic frequency or cage rotation frequency. This represents the energy near the characteristic frequency of rolling element failure in the envelope spectrum. and These represent the energy at the sidebands on either side of the characteristic frequency of the rolling element failure.

[0060] This index is used to characterize the cage modulation features in rolling element fault signals. When When the value is larger, it indicates that the rolling element fault-related sideband is more pronounced.

[0061] The inter-class or intra-class separability index can be expressed as:

[0062]

[0063] in, Indicates the first Class of samples and the first The average inter-class distance between samples of different classes. Indicates the first Average intra-class distance within a class sample Indicates the first The average intra-class distance within a class of samples. Indicates the first Class and the Indicators of separability between classes. The larger the value, the greater the inter-class distance compared to the intra-class distance, and the easier it is to distinguish between the two classes of samples.

[0064] Furthermore, a local defect displacement excitation function is introduced during the simulation sample generation process to describe the contact and separation process between the rolling element and the defect area.

[0065] Furthermore, step S3 also includes performing separability verification on the simulation samples to evaluate the distinguishability between samples of different categories; the distribution alignment model is used to reduce the distribution difference between the simulation samples and the real samples, so that the transformed simulation samples approximate the distribution of the real samples while maintaining the fault category information.

[0066] Furthermore, the physical prior features include at least one of time-domain features, frequency-domain features, or envelope features;

[0067] The data-driven features are extracted by a deep learning model;

[0068] The physical prior features and data-driven features are fused and input into the classification model to output the state category of the rolling bearing and its corresponding confidence level.

[0069] Furthermore, step four involves fusing the physical prior features and data-driven features and inputting the fused features into the Kolmogorov-Arnold Network classification model. The fused features are then processed using a one-dimensional nonlinear mapping function expanded from the basis functions to obtain the rolling bearing fault category and its corresponding confidence level. Specifically, this includes:

[0070] Further, in step four, the physical prior features and data-driven features are fused and then input into the Kolmogorov-Arnold Network classification model. The Kolmogorov-Arnold Network classification model includes several one-dimensional nonlinear mapping functions, which are used to perform nonlinear transformations on the feature components of each dimension in the fused features.

[0071] Let the fusion feature be:

[0072]

[0073] Then the Kolmogorov-Arnold Network Each output node can be represented as:

[0074]

[0075] in, The first in the fusion feature Each feature component Indicates the connection of the first The input feature and the first A one-dimensional nonlinear mapping function with output nodes.

[0076] In a preferred embodiment, the one-dimensional nonlinear mapping function is expressed as follows through basis function expansion:

[0077]

[0078] in, Indicates the first basis functions This represents the corresponding learnable coefficient. This indicates the number of basis functions.

[0079] After processing by the above one-dimensional nonlinear mapping function, the classification output vector is obtained:

[0080]

[0081] The final fault category is:

[0082]

[0083] The corresponding confidence level is:

[0084]

[0085] in, The category of rolling bearing failure is indicated, which includes at least one of normal condition, outer ring failure, inner ring failure, and rolling element failure. This represents the confidence level of the classification model in the current fault category.

[0086] The advantages and beneficial effects of this invention are as follows:

[0087] Compared with existing technologies, the technical effect of this invention does not stem from a single working condition mapping, a single dynamic simulation, a single transfer learning model, or a single deep classification model. Instead, it arises from the synergistic effect between "working condition mapping optimization—six-degree-of-freedom physical modeling—simulation sample separability verification—simulation-real distribution alignment—fusion classification of physical prior features and data-driven features." These steps are interconnected and mutually constraining, collectively solving the problems of insufficient real fault samples, inconsistencies between simulation and real data working conditions, aliasing of simulation sample categories, and insufficient cross-domain generalization ability in rolling bearing fault diagnosis.

[0088] 1) Reducing discrepancies in operating conditions through condition mapping optimization. This invention first establishes a one-to-one correspondence between operating condition labels and rotational speed and radial load based on the operating condition labels of real rolling bearing data, and uses this mapping relationship to constrain the subsequent simulation sample generation process. This step corresponds to step S1 in claim 1 and the content described in claims 2 and 8. Unlike the prior art where simulation rotational speed and load parameters are directly and randomly set, this invention constrains the simulation samples to real operating conditions from the source of generation, thereby reducing fault characteristic frequency shifts and diagnostic errors caused by speed and load mismatches.

[0089] 2) Improving the physical realism and interpretability of simulation samples through six-degree-of-freedom dynamic modeling. Based on the optimized working condition mapping relationship, this invention further constructs a six-degree-of-freedom rolling bearing dynamic model with the translational motion of the inner ring, outer ring, and rolling elements in two dimensions as degrees of freedom. This model is then combined with the local defect displacement excitation function, time-varying contact stiffness, load-bearing zone function, and nonlinear contact force to calculate and generate simulated fault samples. This part corresponds to step S2 in claim 1 and the content described in claims 3, 4, and 5. Through this model, the simulation samples not only contain rotational speed and load information consistent with real working conditions, but also characterize the contact disengagement, re-contact, impact response, and modulation characteristics generated when the rolling elements pass through the defect area, thereby enhancing the simulation data's ability to retain the real fault mechanism.

[0090] 3) Improve cross-domain generalization ability through separability verification and simulation-real distribution alignment. Before the simulated samples enter the classification model, this invention performs unified preprocessing on both simulated and real samples, and performs separability verification on the simulated samples to evaluate the discriminative power between samples of different fault categories. Subsequently, a distribution alignment model is used to perform cross-domain transformation on the simulated samples, so that the transformed simulated corrected samples approximate the distribution of real samples while maintaining fault category information. This part corresponds to step S3 in claim 1 and the content described in claim 6. Unlike the prior art that directly mixes simulated and real samples for training, this invention constrains the simulation data at two levels: "sample quality" and "inter-domain distribution," which avoids low-quality simulated samples interfering with the classification model and reduces the distribution offset between the simulation domain and the real domain.

[0091] 4) Improving classification robustness through the fusion of physical prior features and data-driven features. This invention further extracts at least one of time-domain features, frequency-domain features, or envelope spectrum features as physical prior features, while simultaneously utilizing a multi-scale feature extraction network to obtain data-driven features. The two are then fused and input into the Kolmogorov-Arnold Network classification model. This part corresponds to step S4 in claim 1 and the content described in claim 7. Physical prior features can reflect the characteristic frequency, impact energy, and modulation law of rolling bearing faults, while data-driven features can automatically learn complex nonlinear fault modes. The fusion of the two can improve the model's fault identification capability under noisy backgrounds, load fluctuations, and sample imbalance conditions.

[0092] 5) Enhancing the nonlinear expressive power of fused features through the Kolmogorov-Arnold Network classification model. This invention inputs the fused physical prior features and data-driven features into the Kolmogorov-Arnold Network classification model, and processes the fused features using a one-dimensional nonlinear mapping function expanded from the basis functions to obtain the rolling bearing fault categories and their corresponding confidence scores. Compared with ordinary fully connected classifiers, this classification method can more finely express the nonlinear relationships of different dimensions in the fused features, and is particularly suitable for handling classification scenarios where the boundaries between inner race faults, outer race faults, and rolling element faults are close and the features are mutually coupled.

[0093] 6) Forming a non-obvious synergistic technical route through continuous constraints between steps. This invention does not simply juxtapose existing physical simulation, transfer learning, and deep classification methods, but rather forms a closed-loop technology with sequential dependencies: operational condition mapping optimization provides realistic operational condition constraints for six-DOF dynamic simulation; the six-DOF dynamic model provides physically meaningful source domain samples for distribution alignment; separability verification is used to screen and constrain the quality of simulation samples; the distribution alignment model further reduces the domain difference between simulation samples and real samples; and the fusion classification of physical prior features and data-driven features utilizes the aforementioned high-quality samples to complete fault identification. There is a clear synergistic relationship between the above steps, which can simultaneously improve problems such as operational condition mismatch, insufficient simulation realism, sample class aliasing, domain shift, and insufficient classification generalization. Therefore, it is not a simple combination of conventional techniques in this field.

[0094] 7) Suitable for engineering deployment. The method of this invention can be used for offline model training as well as deployed in online condition monitoring systems. After acquiring new rolling bearing vibration signals, the fault category and confidence level can be obtained by following a unified preprocessing, feature extraction, feature fusion, and classification output process. Therefore, this invention is applicable to condition monitoring, fault early warning, and predictive maintenance scenarios for industrial motors, gearboxes, pumps, fans, compressors, and other rotating machinery.

[0095] In summary, this invention ensures consistency between simulation and real-world operating conditions through operational condition mapping optimization, guarantees the physical realism of simulation samples through six-degree-of-freedom dynamic modeling, ensures the usability and cross-domain adaptability of simulation samples through separability verification and simulation-real distribution alignment, and improves the final classification performance through the fusion of physical prior features and data-driven features, as well as the Kolmogorov-Arnold Network classification model. These technical features work together to form a complete closed-loop technical solution for rolling bearing fault diagnosis, effectively improving the accuracy, robustness, and interpretability of fault diagnosis under complex operating conditions. Attached Figure Description

[0096] Figure 1 This is a flowchart of the overall method of the preferred embodiment of the present invention;

[0097] Figure 2 This is a diagram illustrating the overall architecture of the method of the present invention;

[0098] Figure 3 This is a schematic diagram of the network structure for aligning the simulation domain to the real domain.

[0099] Figure 4 This is a schematic diagram of a multi-branch feature extraction and classification network structure;

[0100] Figure 5 This is a schematic diagram of the feature extraction network structure. Detailed Implementation

[0101] The technical solutions of the embodiments of the present invention will be clearly and thoroughly described below with reference to the accompanying drawings. The described embodiments are merely some embodiments of the present invention.

[0102] The technical solution of the present invention to solve the above-mentioned technical problems is:

[0103] The technical solution of this invention to solve the above-mentioned technical problems is: a rolling bearing fault diagnosis method based on working condition mapping optimization and simulation-real transfer learning, which includes the following steps:

[0104] S1. Construct a one-to-one mapping relationship between real and simulated operating conditions: Based on the speed and load information corresponding to each load number in the real bearing data, establish an operating condition mapping table, map the load labels to the corresponding speed and radial load parameters respectively, and use this mapping relationship as a unified operating condition constraint for subsequent simulation sample generation to align with the real samples.

[0105] S2. Establish a rolling bearing failure mechanism model and generate simulation signals: Based on the rolling bearing geometric parameters, Hertzian contact theory, the impact mechanism of local pitting / stripping due to failure, and the speed-load coupling relationship, construct a dynamic model that includes normal operation, outer ring failure, inner ring failure, and rolling element failure, and output the corresponding vibration response signals.

[0106] S3. Perform unified preprocessing on simulated and real samples: including removing transient segments, resampling, normalization, segmentation, filtering, envelope demodulation, and feature band enhancement, to ensure that the input data format and statistical scale are consistent.

[0107] S4. Alignment of Simulation Domain and Real Domain Distribution: An adversarial transfer learning network is used to perform domain transformation on the simulation signal, so that the transformed simulation signal approximates the real signal distribution in terms of time domain statistical characteristics, frequency domain distribution and envelope characteristics, while keeping the fault category information unchanged.

[0108] S5. Fault Feature Extraction, Fusion and Classification: Extract time-domain features, frequency-domain features, envelope spectrum features and deep network automatically learned features, and fuse the physical mechanism prior features with the deep features before inputting them into the classifier to output the diagnostic results of normal, outer ring fault, inner ring fault and rolling element fault.

[0109] The following is in conjunction with the appendix Figure 1-5 The specific steps of S1-S5 are described in detail in the example implementation process of the present invention.

[0110] Step 1: Establish operating condition mapping

[0111] Establish a working condition mapping based on the load number and corresponding speed and load from the real dataset. Establish the mapping function:

[0112]

[0113] in, Indicates operating condition label, Indicates rotational speed. This represents the radial load. This mapping function is used to constrain the load input during the simulation data generation process, ensuring that the operating state of the simulation signal matches the load conditions of the real data.

[0114] First, the four load conditions in the real CWRU dataset are mapped to four unified load condition labels: load0, load1, load2, and load3. The subsequent training, validation, and testing of the model are carried out according to the fixed load conditions: the training set is load0 and load1, the validation set is load2, and the test set is load3.

[0115] Step 2: Establish a six-degree-of-freedom dynamic model and generate simulation signals

[0116] (1) Define the system's degrees of freedom

[0117] Establish a six-degree-of-freedom dynamic model of the rolling bearing and define the generalized coordinates of the system:

[0118]

[0119] in, , They represent the inner circle in , Displacement components in the direction; , They represent the outer ring in , Displacement components in the direction, , These respectively represent the rolling elements in , Equivalent displacement in the direction.

[0120] (2) Calculate the position of the roll angle

[0121] No. The revolution angle of each rolling element is:

[0122]

[0123] in, To maintain the frame angular velocity, The number of rolling elements. This is the initial phase.

[0124] (3) Establish a local contact deformation model

[0125]

[0126]

[0127] in, It is a relative displacement function. and These are the defect excitation functions for the inner and outer rings, respectively. For the carrying area function, It is a positive value operator.

[0128] (4) Construct the defect displacement excitation function

[0129] For different fault types, construct defect displacement excitation functions:

[0130]

[0131]

[0132]

[0133] in, , , These are the defect displacement excitation functions for the outer ring, inner ring, and rolling element, respectively.

[0134] (5) Calculate Hertz contact force

[0135] After determining the local contact deformation, the contact force amplitude can be obtained according to Hertz contact theory:

[0136]

[0137]

[0138] Furthermore, the first The contact force components of the rolling elements in the x and y directions are as follows:

[0139]

[0140]

[0141] in, and They represent the first The x- and y-direction contact force components of each rolling element acting on the inner ring side; and They represent the first The x- and y-direction contact force components of each rolling element acting on the outer ring side; For the first The revolution angle position of each rolling element.

[0142] For all Summing the contact force components of each rolling element yields the total Hertz contact force acting on the inner ring, outer ring, and rolling element system. The resultant Hertz contact force on the inner ring can be expressed as:

[0143]

[0144]

[0145] The resultant Hertz contact force on the outer ring can be expressed as:

[0146]

[0147]

[0148] The resultant contact force on the rolling element can be expressed according to the interaction relationship between the contact forces on the inner and outer ring sides as follows:

[0149]

[0150]

[0151] in, , This represents the resultant component of the Hertz contact force acting on the inner ring. , This represents the resultant component of the Hertz contact force acting on the outer ring; , This represents the resultant contact force component acting on the rolling element system.

[0152] (6) Establish the six-degree-of-freedom dynamic equations

[0153] The dynamic equations for local defects in a six-degree-of-freedom rolling bearing can be written in matrix form:

[0154] --25

[0155] in, For the quality matrix, Here is the damping matrix. Here is the support stiffness matrix; This is the Hertz contact force vector; This is the external radial load vector; This is the additional excitation vector caused by speed fluctuations, centrifugal effects, unbalanced excitation, or noise disturbances.

[0156] Setting external loads and excitations

[0157] The external load vector can be represented as:

[0158] ---27

[0159] in, This represents the radial load acting on the bearing system. The direction of load application in the external load vector can be adjusted according to the actual installation orientation.

[0160] (7) Numerically solve the dynamic equations and output simulation signals.

[0161] The displacement is obtained by solving the ODE using the numerical integration method. ,speed acceleration .

[0162]

[0163] Based on different defect locations, four types of simulation data samples are generated: normal, outer ring fault, inner ring fault, and ball fault. The model calculates the characteristic frequencies of outer ring BPFO, inner ring BPFI, and rolling element BPFB faults based on bearing geometric parameters, rotational speed, and load, and determines the main fault modulation components in the subsequent time domain, frequency domain, and envelope spectrum.

[0164] The six-degree-of-freedom dynamic model constructed by the present invention through the above steps can generate rolling bearing vibration signals with real physical characteristics under the conditions of considering nonlinear contact, local defect excitation and multibody coupling effect, thereby providing high-quality simulation data for subsequent cross-domain transfer learning and fault diagnosis.

[0165] Step 3: Perform unified preprocessing on the simulated and actual acquired signals of the rolling bearing.

[0166] (1) Signal segmentation and transient removal

[0167] For the original vibration signal or discrete signal Processing:

[0168] After removing the initial transient segment (first 10%–20%), the sample set is obtained by sliding segmentation of fixed length:

[0169]

[0170] (2) Mean removal processing

[0171] Remove DC components, eliminate bias, and improve spectral stability:

[0172]

[0173] (3) Amplitude normalization and standardization:

[0174]

[0175] in, The mean, The standard deviation is denoted as .

[0176] (4) Hilbert transform and envelope extraction

[0177] In envelope extraction, it is preferable to first perform bandpass filtering to extract the signal within the structural resonance frequency band, and then use Hilbert transform to construct the analytical signal:

[0178]

[0179] The envelope signal is:

[0180]

[0181] (5) Envelope spectrum calculation

[0182] Spectral analysis is performed on the envelope signal to extract BPFO, BPFI, BSF, and FTF.

[0183]

[0184] (6) Constructing separability evaluation index

[0185] The Fisher discriminant metric used to assess the separability of two classes of samples is:

[0186]

[0187] The Pearson correlation coefficient between two signals or feature vectors is:

[0188]

[0189] In the analysis of the separability of rolling element failures, the sideband energy ratio can be expressed as:

[0190]

[0191] The inter-class or intra-class separability index can be expressed as:

[0192]

[0193] When the similarity matrix has a low off-diagonal value and a separability index When the value exceeds a preset threshold, the generated simulation samples can be determined to have good inter-class separability. Based on the separability index, overlapping samples between classes are removed, and high-discrimination data are retained.

[0194] (7) Construct real samples in the target domain and standardize the input format.

[0195] ① Real sample segmentation

[0196] The original CWRU data was divided into sample segments of fixed length 2048 and organized uniformly.

[0197] ② Standardized input

[0198] The network model uniformly reads the output of the aligned correction module and the true CWRU segmented output, with a fixed input length of 2048. During evaluation, the number of segments pruned per file is 2, ensuring that the data of the input feature extraction and classification network model architecture is a 1D vibration segment processed with a uniform length.

[0199] Step 4: Simulation Correction Signal Generation

[0200] (1) Input simulation signal With real signals

[0201] (2) Constructing a distribution alignment model

[0202] By learning mapping functions:

[0203]

[0204] Make

[0205]

[0206] (3) Adversarial distribution alignment

[0207]

[0208] Adding constraints ensures consistency between category and spectrum:

[0209] Category retention:

[0210]

[0211] Spectral consistency:

[0212]

[0213] (4) Generate simulation signals and construct training datasets

[0214]

[0215] Through the above-mentioned preprocessing and simulation correction process, this invention achieves the unification of the statistical distribution and spectral structure of the simulated signal and the real signal, thereby significantly improving the generalization ability and recognition accuracy of the subsequent fault diagnosis model under actual working conditions.

[0216] Step 5: Fault Feature Extraction and Classification

[0217] (1) The input tensor is in the form of:

[0218]

[0219] in The batch size is 1, which represents a single-channel vibration signal, and 2048 represents a uniform time length.

[0220] (2) Multi-scale feature extraction

[0221] Multi-scale fault modes are automatically extracted from the original vibration segments by using different convolutional kernel lengths. The original main model first uses three parallel convolutional branches to extract local features under different receptive fields:

[0222] Branch 1: Convolution kernel 9

[0223] Branch 2: Convolution kernel 15

[0224] Branch 3: Convolution kernel 30

[0225] The three outputs are then concatenated along the channel dimension and fused using a 1×1 convolution. The purpose of this is to simultaneously preserve short-term local impulse features, mesoscale modulation structures, and periodic patterns within a longer time window.

[0226] (3) Deep convolutional feature encoding

[0227] High-level fault representations are extracted by compressing the temporal dimension layer by layer; residual connections alleviate the training difficulties of deep networks; and Dropout improves generalization ability. The fused features are sequentially passed through three convolutional residual blocks:

[0228] Layer 1 convolution kernel: 7

[0229] Second layer convolution kernel: 5

[0230] 3rd layer convolution kernel: 5

[0231] Each convolutional block consists of: Conv1d, BatchNorm1d, SiLU activation, Dropout, BatchNorm1d, SiLU, and Shortcut residual connections.

[0232] (4) Global pooling yields a global fault representation.

[0233] The convolutionally encoded features are then subjected to global average pooling using AdaptiveAvgPool1d, outputting a fixed-length global fault vector, feat. This global vector serves as a low-dimensional representation of the current sample in the fault feature space, the input source for subsequent t-SNE visualization, and the input feature for the KAN classification head.

[0234] (5) The KAN classification head completes the category determination.

[0235] The KAN-style basis function expansion enhances the nonlinear expressive power, making it more effective in distinguishing fault categories with similar boundaries, especially the fine-grained differences between the inner and outer circles. Pooled features are input into two layers of KANLinear, and the final output is the classification result. The core of KANLinear consists of a regular linear branch (base) and a nonlinear branch (spline) based on RBF basis function expansion; the sum of these two branches is the output.

[0236] (6) Model output and evaluation

[0237] The model ultimately outputs four labels: normal, outer circle, inner circle, and rolling body. After training and evaluation, the output includes: accuracy, macro-F1, precision / recall / F1 for each category, confusion matrix, and t-SNE feature distribution map.

[0238] (6) Model training settings

[0239]

[0240] To verify the effectiveness of the proposed rolling bearing fault diagnosis method based on condition mapping optimization and simulation-real transfer learning, it will be compared with other existing methods on the Case Western Reserve University bearing dataset. Partial data from the selected CWRU bearing dataset is shown in the table, including bearing fault data of four different sizes, loads, and types.

[0241] Taking the CWRU dataset as an example, the operating condition labels, speed information, and load information corresponding to the real rolling bearing samples are obtained, and a one-to-one mapping relationship between real and simulated operating conditions is established, as shown in the table. The real data is first organized into four load conditions and mapped to four operating condition labels: load0 to load3. Then, the original vibration signal is segmented into sample segments of uniform length and unified with the simulated signal to the same input format. In the current implementation, the network model configuration adopts the adapted_plus_real training mode, with training conditions load0 and load1, validation condition load2, and test condition load3. The uniform input length is 2048, and two segments are extracted from each test file for evaluation.

[0242] The role of the simulation correction module is not to replace the real data alone, but to bring the distribution of the simulation samples closer to that of the real samples, thereby outputting the "aligned simulation samples". At this stage, time-domain waveforms, amplitude spectra, envelope spectra, similarity matrices and sideband energy analysis are usually combined to check whether the simulation samples are more consistent with CWRU at key frequencies such as BPFO, BPFI, BSF / FTF.

[0243] Based on the aforementioned working condition mapping relationship, a rolling bearing fault mechanism model is constructed. The model, grounded in Hertzian contact theory, defines the system state as a 12-dimensional vector, describing the displacement and velocity of the three mass blocks in the x and y directions. The model input includes variables such as mass, damping, stiffness, bearing geometric parameters, radial clearance, elastic modulus, Poisson's ratio, rotational speed, load, and fault type. Parameters such as defect width, defect phase, defect edge slope, and waviness error are introduced for outer ring, inner ring, and rolling element faults, respectively. Subsequently, the rotational frequency, cage frequency, and fault characteristic frequencies such as BPFO, BPFI, and BPFB are calculated based on the rotational speed and geometric relationship, thereby generating fault impact, modulation, and load-bearing area gating effects in the time-domain response. Furthermore, diverse strategies such as parameter dispersion, working condition fluctuations, manufacturing errors, background noise, external excitation, sensor variations, and structural resonance filtering are superimposed to generate four types of simulation samples: normal, outer ring, inner ring, and rolling element, forming the source domain dataset.

[0244] In the network model construction phase, the input signal is first represented as a one-dimensional tensor [B, 1, 2048] and fed into the multi-scale feature extraction module. The original main model consists of three parallel convolutional branches forming MultiScaleStem, with convolutional kernels of 9, 15, and 31, used to extract short-term impacts, mesoscale modulation, and long-term periodic patterns. After the three feature branches are concatenated in the channel dimension, they are fused through 1×1 convolutions and then sequentially fed into three ConvBlock residual blocks with convolutional kernels of 7, 5, and 5, respectively. Deep feature encoding is completed through BatchNorm, SiLU, and shortcut connections. Then, adaptive average pooling is used to obtain the global feature vector, which is fed into a classification head composed of two KANLinear layers to complete four-class classification. The KANLinear is not a simple linear layer, but a combination of "basic linear mapping + RBF basis function expansion branch" to enhance nonlinear expressive power, so that categories with closer boundaries, such as inner / outer ring and rolling body / inner ring, can be better distinguished.

[0245] In terms of experimental setup, the current basic training parameters are: total training rounds 120, warmup rounds 10, initial learning rate 3e-4, minimum learning rate ratio 0.05, weight decay 1e-4, training batch size 64, validation / test batch size 128, and AdamW and cosine annealing strategies are adopted. In the comparative experiments, in addition to the complete model, SimpleCNN1D, ResNet1D, and MultiScaleCNN1D (without KAN) models were also set up to verify the necessity of multi-scale extraction, KAN classification head, and simulation-real joint training. The accuracy results are shown in the table.

[0246] Existing results show that the complete model can achieve a test accuracy of approximately 98.70% and a Macro-F1 score of 98.59% under CWRU conditions, which is significantly higher than the 48.85% achieved using only the original simulation, the 55.6% achieved using only aligned data, and the 89.85% achieved using only real data. It also outperforms the Simple_CNN baseline of 74.6% and the Multi-Scale_CNN baseline without KAN of 91.88%, indicating that the entire process of "six-degree-of-freedom physical modeling + simulation - real distribution alignment + multi-scale / KAN fault classification" is effective and necessary.

[0247] To demonstrate the effectiveness of the proposed matrix module and task calibration loss, ablation experiments were conducted. The same operating conditions data as in Table 3 were selected. The models used for comparison included those with the KAN splitter removed, Real_data_only, and Sim_data_only. The ablation experiment accuracy comparison results are shown in the table.

[0248] The systems, devices, modules, or units described in the above embodiments can be implemented by computer chips or entities, or by products with certain functions.

[0249] The systems, devices, modules, or units described in the above embodiments can be implemented by computer chips or entities, or by products with certain functions.

[0250] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0251] The above embodiments should be understood as illustrative only and not as limiting the scope of protection of the present invention. After reading the description of the present invention, those skilled in the art can make various alterations or modifications to the present invention, and these equivalent changes and modifications also fall within the scope defined by the claims of the present invention.

Claims

1. A method for diagnosing rolling bearing faults based on operating conditions and simulation-real-world transfer learning, characterized in that, Includes the following steps: S1. Based on the working condition labels of real rolling bearing data, establish an initial mapping relationship between the working condition labels and the rotational speed and radial load. With the consistency between the simulation sample and the real sample in the time domain, frequency domain, envelope spectrum and class separability as the optimization objective, correct the working condition parameters to obtain the optimized working condition mapping relationship. S2. Based on the optimized working condition mapping relationship, a six-degree-of-freedom rolling bearing dynamic model is constructed with the translational motion of the inner ring, outer ring and rolling element in the two-dimensional direction as the degree of freedom. Combined with the local defect displacement excitation function, time-varying contact stiffness, load-bearing zone function and nonlinear contact force calculation, a simulation fault sample corresponding to the real working condition is generated. S3. Perform unified preprocessing and separability verification on the simulated fault samples and real samples, and perform cross-domain transformation on the simulated fault samples through a distribution alignment model to obtain simulated corrected samples. S4. Extract physical prior features and data-driven features from the real samples and the simulation correction samples. The data-driven features are obtained through a multi-scale feature extraction network. After fusing the physical prior features and data-driven features, input them into the Kolmogorov-Arnold Network classification model. Process the fused features through a one-dimensional nonlinear mapping function expanded by the basis function to obtain the rolling bearing fault category and the corresponding confidence level.

2. The rolling bearing fault diagnosis method based on working condition and simulation-real transfer learning according to claim 1, characterized in that, The working condition mapping is a one-to-one correspondence between discrete working condition labels and rotational speed and radial load; Multiple discrete operating condition labels are mapped to their corresponding rotational speed parameters and radial load parameters, and an operating condition vector is constructed. in, Indicates operating condition label, For the first The speed corresponding to each operating condition label For the first The radial load corresponding to each working condition label is used to ensure that the generation process of the simulated fault sample is consistent with the acquisition conditions of the real sample.

3. The rolling bearing fault diagnosis method based on operating conditions and simulation-real transfer learning according to claim 1, characterized in that, The dynamic equation for local defects in a six-degree-of-freedom rolling bearing is: --25 in, For the quality matrix, Here is the damping matrix. Here is the support stiffness matrix; This is the Hertz contact force vector; This is the external radial load vector; This is the additional excitation vector caused by speed fluctuations, centrifugal effects, unbalanced excitation, or noise disturbances; This is a generalized coordinate vector for a six-degree-of-freedom rolling bearing system, used to describe the inner ring, outer ring, and rolling elements in motion. , Displacement states in two directions; in, Indicates the inner circle is , Displacement in the direction; , Indicates the outer ring is , Displacement in the direction; , Indicates that the rolling element is in , Equivalent displacement in the direction; The external load vector is represented as: ---27 in, This indicates the radial load acting on the bearing system.

4. The rolling bearing fault diagnosis method based on operating conditions and simulation-real transfer learning according to claim 3, characterized in that: Step three: Perform unified preprocessing on the simulated rolling bearing signal and the actual acquired signal, specifically including: (1) Signal segmentation and transient removal For the original vibration signal or discrete signal Processing: After removing the initial transient segment, the sample set is obtained by sliding segmentation of fixed length: ； in, Indicates the first Segmented samples, This indicates the sequence number of the discrete sampling point within the sample segment. This represents the total number of samples obtained after segmentation. (2) Mean removal processing; Remove DC components, eliminate bias, and improve spectral stability: in, Represents the original discrete vibration signal. This represents the signal after removing the mean. This indicates the total number of sampling points in the current sample segment. Indicates the index of the sampling point during the summation process; (3) Amplitude normalization and standardization: in, The mean, Standard deviation; (4) Hilbert transform and envelope extraction In envelope extraction, it is preferable to first perform bandpass filtering to extract the signal within the structural resonance frequency band, and then use Hilbert transform to construct the analytical signal: in, This represents a discrete vibration signal after being demeaned, normalized, or standardized. Represents the Hilbert transform operator; Represents the imaginary unit; Indicates the signal with the real part The analytic signal formed by the result of the Hilbert transform; The envelope signal is: in, Indicates analytic signal The amplitude, i.e., the envelope of the vibration signal; (5) Envelope spectrum calculation For envelope signal Perform a Fourier transform to obtain the envelope spectrum: in, Used to characterize the energy distribution of the envelope signal at different frequencies, in order to extract bearing fault characteristic frequencies such as BPFO, BPFI, BSF and FTF; (6) Construct separability evaluation index; The Fisher discriminant metric used to assess the separability of two classes of samples is: in, and Let represent the means of the features of the two classes of samples, respectively. and Let represent the variances of the features of the two classes of samples, respectively. This represents the Fisher separability evaluation index; The larger the value, the greater the difference in mean between the two classes of samples and the smaller the intra-class fluctuation, indicating better class separability. The Pearson correlation coefficient between two signals or feature vectors is: in, and These represent the two signals or two eigenvectors at the th... The value at each position and These represent the means of two signals or feature vectors, respectively. Indicates the length of the signal or eigenvector. This represents the Pearson correlation coefficient between the two. In the analysis of the separability of rolling element failures, the sideband energy ratio can be expressed as: in, Indicates the characteristic frequency of rolling element failure. This indicates the cage failure characteristic frequency or cage rotation frequency. This represents the energy near the characteristic frequency of rolling element failure in the envelope spectrum. and These represent the energy at the sidebands on either side of the characteristic frequency of rolling element failure; This index is used to characterize the cage modulation features in rolling element fault signals; when When the value is larger, it indicates that the sideband related to the rolling element failure is more pronounced; The inter-class or intra-class separability index can be expressed as: in, Indicates the first Class of samples and the first The average inter-class distance between samples of different classes. Indicates the first Average intra-class distance within a class sample Indicates the first The average intra-class distance within a class of samples. Indicates the first Class and the Indicators of separability between classes; The larger the value, the greater the inter-class distance is relative to the intra-class distance, and the easier it is to distinguish between the two classes of samples. When the similarity matrix has a low off-diagonal value and a separability index When the value exceeds the preset threshold, the generated simulation samples can be determined to have good inter-class separability; based on the separability index, mixed inter-class samples are removed, and high-discrimination data is retained.

5. The rolling bearing fault diagnosis method based on operating conditions and simulation-real transfer learning according to claim 1, characterized in that: The simulation sample generation process introduces a local defect displacement excitation function to describe the contact and separation process between the rolling element and the defect area.

6. The rolling bearing fault diagnosis method based on working condition and simulation-real transfer learning according to claim 1, characterized in that: Step S3 further includes performing separability verification on the simulation samples to evaluate the distinguishability between samples of different categories; the distribution alignment model is used to reduce the distribution difference between the simulation samples and the real samples, so that the transformed simulation samples approximate the distribution of the real samples while maintaining the fault category information.

7. The rolling bearing fault diagnosis method based on working condition and simulation-real transfer learning according to claim 1, characterized in that: The physical prior features include at least one of time-domain features, frequency-domain features, or envelope features; The data-driven features are extracted by a deep learning model; The physical prior features and data-driven features are fused and input into the classification model to output the state category of the rolling bearing and its corresponding confidence level.

8. The rolling bearing fault diagnosis method based on operating conditions and simulation-real transfer learning according to claim 1, characterized in that, Step four involves fusing the physical prior features and data-driven features and inputting the fused features into the Kolmogorov-Arnold Network classification model. The fused features are then processed using a one-dimensional nonlinear mapping function expanded from the basis functions to obtain the rolling bearing fault category and its corresponding confidence level. Specifically, this includes: Step four involves fusing the physical prior features and data-driven features and then inputting them into the Kolmogorov-Arnold Network classification model. The Kolmogorov-Arnold Network classification model includes several one-dimensional nonlinear mapping functions, which are used to perform nonlinear transformations on the feature components of each dimension in the fused features. Let the fusion feature be: Then the Kolmogorov-Arnold Network Each output node can be represented as: in, The first feature in the fusion is represented by the second feature. Each feature component Indicates the connection of the first The input feature and the first A one-dimensional nonlinear mapping function with output nodes; In a preferred embodiment, the one-dimensional nonlinear mapping function is expressed as follows through basis function expansion: in, Indicates the first basis functions This represents the corresponding learnable coefficient. Indicates the number of basis functions; After processing by the above one-dimensional nonlinear mapping function, the classification output vector is obtained: The final fault category is: The corresponding confidence level is: in, The category of rolling bearing failure is indicated, which includes at least one of normal condition, outer ring failure, inner ring failure, and rolling element failure. This represents the confidence level of the classification model in the current fault category.

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