A Zero-Sample Fault Diagnosis Method for Bearings Based on Envelope Order Spectrum Multidimensional Feature Extraction

Abstract

This invention relates to the field of fault diagnosis technology and discloses a zero-sample fault diagnosis method for bearings based on multi-dimensional feature extraction of envelope order spectrum. This method generates simulated fault data through a bearing dynamics model to address the problem of sample scarcity; it combines the simulated data with healthy data to train a multi-scale residual attention network; for the signal to be diagnosed, diagnostic results are obtained through the network model and physical feature threshold rules based on the envelope order spectrum, respectively; finally, the two are weighted and fused to arrive at a conclusion. This invention overcomes the dependence of existing technologies on real fault samples, achieves high-precision diagnosis under zero-sample conditions, and improves the reliability and interpretability of the model through the fusion of physical and data decision layers.

Description

Technical Field

[0001] This invention relates to the field of rolling bearing fault diagnosis technology, and in particular to a zero-sample bearing fault diagnosis method based on envelope order spectrum multidimensional feature extraction. Background Technology

[0002] Rolling bearings are core components of rotating machinery, and their fault diagnosis is crucial for equipment safety. With the development of big data and artificial intelligence technologies, data-driven fault diagnosis methods such as autoencoders, deep belief networks, and convolutional neural networks have become mainstream. These methods extract features from vibration signals and establish a mapping relationship between operating states and fault types to achieve intelligent diagnosis. However, existing technologies face three major challenges in practical applications:

[0003] I. Scarcity of Real Fault Samples for Key Equipment: Due to safety considerations, it is difficult to obtain real fault data for key rotating machinery. This leads to overfitting and a sharp drop in generalization ability in traditional data-driven models due to insufficient training samples. Although data augmentation methods such as adding noise and signal shifting, or generative models such as generative adversarial networks, can be used to expand the samples, the generated features deviate from the real fault features and cannot fully match the actual working conditions.

[0004] 2. Insufficient robustness of models under varying operating conditions: In real industrial scenarios, equipment often faces complex operating conditions such as speed fluctuations, load changes, and multi-source noise interference. Existing methods mostly rely on training data under specific operating conditions. When the operating conditions change, the model's diagnostic accuracy drops significantly. For example, a model trained based on fixed speed data is prone to misjudging fault characteristics due to frequency shifts in speed fluctuation scenarios.

[0005] Third, deep learning models have poor interpretability and lack physical basis for diagnostic results: pure data-driven models are mostly "black box" models, and the diagnostic results lack physical mechanism support, making it difficult to explain the correlation logic between features and fault types. When the diagnostic results are biased, the cause cannot be traced, which limits its application in fields with high reliability requirements such as aerospace. Existing technologies such as generative model data augmentation and order analysis either have deviations between the generated data and the real distribution, or still need to rely on real fault samples, failing to fundamentally solve the problem of high-precision and high-reliability diagnosis under zero-sample conditions.

[0006] Therefore, there is an urgent need for a zero-shot fault diagnosis method that integrates physical mechanisms and deep learning, and possesses both high robustness and interpretability, to meet the needs of practical industrial scenarios. Summary of the Invention

[0007] The purpose of this invention is to overcome the shortcomings of existing technologies and provide a bearing zero-sample fault diagnosis method based on envelope order spectrum multidimensional feature extraction. This method generates data through physical simulation, extracts interpretable physical features based on envelope order spectrum, and integrates deep learning and physical rules for decision-making. It solves the problems of scarce real fault samples, insufficient robustness across operating conditions, and poor interpretability in existing technologies, and achieves high-precision diagnosis without the need for real fault samples of the target equipment.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] This invention provides a bearing zero-sample fault diagnosis method based on envelope order spectrum multidimensional feature extraction, comprising the following steps:

[0010] Simulated fault data is generated based on the bearing dynamics model, and the simulated fault data is the simulated vibration signal simulating the fault state;

[0011] The simulated fault data is combined with the health status vibration signals collected from the target device to construct a training dataset.

[0012] The simulated vibration signal and the healthy state vibration signal are subjected to envelope extraction and angular resampling, converted to the order domain and the order spectrum is calculated; based on the bearing fault characteristic frequency theory, the fault harmonic amplitude in the order spectrum is extracted to form a physical feature vector;

[0013] Construct a multi-scale residual attention convolutional network and train it using the training dataset;

[0014] For the vibration signal to be diagnosed collected from the target device, a first probability distribution is obtained through a trained multi-scale residual attention convolutional network, and a second judgment result is obtained by calculating the physical feature vector extracted from the vibration signal to be diagnosed through threshold logic; the first probability distribution and the second judgment result are fused together to output the final diagnosis result.

[0015] Compared with the prior art, the present invention has at least the following beneficial effects:

[0016] 1. By generating simulated fault data through high-fidelity dynamic models, it completely eliminates the dependence on real fault samples of target equipment and achieves true zero-sample diagnosis; it avoids destructive experiments and expensive data acquisition costs, and is suitable for intelligent operation and maintenance of high-end equipment such as aero engines and wind turbines, reducing costs and improving efficiency.

[0017] 2. Multidimensional features extracted by envelope order spectrum eliminate the influence of rotation speed fluctuations. Multiscale residual attention convolutional network (MR-CNN) enhances noise resistance and feature extraction capabilities. The fusion decision mechanism further improves accuracy. Zero-shot diagnosis achieves high precision and high robustness.

[0018] 3. The diagnostic results are based on a combination of physical characteristics (harmonic energy) and deep learning models, making decisions logically clear, traceable, and highly interpretable, thus meeting the needs of high-reliability fields. Attached Figure Description

[0019] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 This is a flowchart of a bearing zero-sample fault diagnosis method based on envelope order spectrum multidimensional feature extraction, according to an embodiment of the present invention.

[0021] Figure 2 This is a schematic diagram of physical feature vector extraction according to an embodiment of the present invention;

[0022] Figure 3 This is a schematic diagram of MLMod (Multi-Scale Learning Module) according to an embodiment of the present invention;

[0023] Figure 4 This is a schematic diagram of RAMod (residual attention module) according to an embodiment of the present invention;

[0024] Figure 5 This is a confusion matrix combining a fusion strategy in an embodiment of the present invention;

[0025] Figure 6 This is the confusion matrix of the embodiment of the present invention without the fusion strategy;

[0026] Figure 7 This is a diagram showing the correspondence between actual fault modes and diagnostic results when the fusion strategy is not incorporated in this embodiment of the invention.

[0027] Figure 8 This is a diagram showing the correspondence between actual fault modes and diagnostic results when the fusion strategy is combined in an embodiment of the present invention. Detailed Implementation

[0028] The embodiments of this application will now be described in detail with reference to the accompanying drawings.

[0029] The following specific examples illustrate the implementation of this application. Those skilled in the art can easily understand other advantages and effects of this application from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. This application can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this application. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0030] This invention provides a method for zero-sample bearing fault diagnosis based on envelope order spectrum multidimensional feature extraction. For example... Figure 1 As shown, this embodiment uses rolling bearings as the object, and the specific steps are as follows:

[0031] S1. Generating simulation fault data based on bearing dynamics model

[0032] Bearing dynamics models are an effective tool for analyzing the failure mechanism of rotating bearings. They can theoretically simulate the vibration response of faulty bearings in low-speed scenarios, solving the problem of scarce fault samples in real experiments.

[0033] The bearing dynamics model described in this embodiment of the invention adopts a 4-DOF bearing-base dynamics model. Based on the model, simulation fault data is generated, all solutions to the bearing point contact problem are explained, and the Hertz contact stiffness model is derived. The fourth-order Runge-Kutta method is used to perform dimensionless processing on the model variables to generate simulation vibration signals simulating the fault state.

[0034] Specifically, to establish the model and facilitate subsequent analysis and calculation, the following simplified assumptions are made for the bearing: elastohydrodynamic lubrication is not considered; the nonlinearity of the bearing in the model originates from the nonlinear contact force between different components, time-varying stiffness, and the clearance between the rolling elements and the bearing race; the elastic contact between the rolling elements and the inner and outer raceways can be assumed to satisfy Hertz theory; the mass and inertia of the rolling elements and the cage are ignored; there is a constant angular distance between the rolling elements; all translational motions are in the plane (i.e., the xy plane), and all rotations are around the z-axis.

[0035] Based on the above assumptions, the model mainly consists of an inner ring, rolling elements, an outer ring, and a cage. This bearing model captures the motion of the inner and outer rings in the x and y directions, characterizing their displacement in these directions. During the simulation, the stiffness and damping of each component are assumed to be fixed values, and the operating parameters of the simulation model are consistent with those of a real bearing.

[0036] Model parameters are set based on the geometric parameters of the target bearing (such as pitch circle diameter, rolling element diameter, raceway curvature radius, contact angle, etc.) and operating parameters (such as speed, radial clearance, and fault size). By solving a set of nonlinear differential equations based on Hertz contact theory and introducing the deformation release amount characterizing the fault, high-quality vibration response signals under inner ring fault, outer ring fault, and normal conditions are simulated.

[0037] Specifically, the model calculates the rolling element-raceway contact force based on Hertz contact theory, and the contact force... With contact deformation The relationship is

[0038] (1)

[0039] In equation (1), This is the load-deflection coefficient, whose value depends on the geometry of the material and the elastic contact. The load-deflection index, for example, for ball bearings .

[0040] For the A rolling element, for:

[0041] (2)

[0042] In equation (2), and These represent the displacements of the inner and outer rings of the bearing in the x-direction, respectively. and These represent the displacements of the inner and outer rings of the bearing in the y-direction, respectively. This refers to the radial clearance of the bearing. At that moment, the angular position of each rolling element for:

[0043] (3)

[0044] In equation (3), For the number of rolling elements, This is the initial angular position of the first rolling element. To maintain frame speed, for:

[0045] (4)

[0046] In equation (4). The diameter of the rolling element, The bearing pitch circle diameter, Contact angle, This represents the bearing speed.

[0047] Considering only when Compression only occurs when the value is positive; the deformation release amount, which characterizes the fault, is introduced. To modify the amount of contact deformation ,so for:

[0048] (5)

[0049] The contact forces of the main bearing in the x and y directions are summed using equations. (Contact forces) x and y components and It can be represented as:

[0050] (6)

[0051] (7)

[0052] According to Newton's second law, and considering the centrifugal force caused by installation and manufacturing deviations, the four differential equations of motion of the faulty bearing dynamic model in the xy plane related to the inner and outer rings can be expressed as follows:

[0053] (8)

[0054] (9)

[0055] (10)

[0056] (11)

[0057] In equations (8)-(11), It is the acceleration due to gravity. For the mass of the bearing inner ring, This is the damping coefficient of the bearing inner ring. This refers to the stiffness of the bearing's inner ring. For the mass of the bearing outer ring, For the bearing outer ring stiffness, This is the damping coefficient of the bearing outer ring. For the eccentricity, and Let x be the acceleration of the inner and outer rings of the bearing in the x-direction. and Let x represent the velocities of the inner and outer rings of the bearing in the x-direction. and Let be the acceleration of the inner and outer rings of the bearing in the y-direction. and Let be the velocities of the inner and outer rings of the bearing in the y direction. Equations (8)-(11) are solved using the fourth-order Runge-Kutta method to obtain the vibration responses of the rolling elements, inner ring, and outer ring. The dynamic response of the faulty bearing is calculated using the ode45 solver.

[0058] In the above dynamic model, a single-point failure of the bearing race is introduced, simplifying the localized failure into a small rectangular spalling, and reasonably ignoring the complex mechanisms of failure mode differences. Taking the outer ring failure as an example, the detailed geometric relationship of the local fault when the rolling element impacts the rectangular spalling is given.

[0059] When a rolling element enters a spalling zone on the raceway, contact is suddenly lost, and contact is restored when the rolling element leaves the spalling zone. The loss of contact is caused by… The change is caused by the contact deformation of the i-th rolling element when it enters a local fault area of ​​the inner or outer ring. The addition of a positive deformation release amount to the formula will cause this. (Non-fault area) =0), where the positive value of contact under normal conditions becomes zero, causing the contact force to disappear, ultimately leading to the rolling element losing contact with the raceway. Due to raceway failure, a deformation release amount characterizing the failure is introduced. To modify the amount of contact deformation Therefore, the contact deformation of the rolling element after modification for:

[0060] (12)

[0061] In equation (12), For the first The angular position of each rolling element This refers to the radial clearance of the bearing. This represents the amount of deformation released due to localized defects. It is important to note that different types of faults... Different, for example, fault width Less than , Where the rolling element radius is _____._ ... Calculated based on the location of the fault.

[0062] When there is a fault in the outer ring for:

[0063] (13)

[0064] In equation (13), The location angle for the outer ring fault is, for example, this location angle can be set manually; For example, the sensing angle width for outer ring faults. ,in The outer ring radius of the bearing; This is the amount of contact change when the rolling element enters the fault region, which characterizes the change between the original contact position and the new contact position when the rolling element enters the fault region. Let be the angular position of the i-th rolling element.

[0065] Among them, the outer ring fault corresponds to The following can be calculated:

[0066] (14)

[0067] When there is a fault in the inner ring Possible forms:

[0068] (15)

[0069] In equation (15), The location angle of the inner ring fault. This refers to the sensing angle width (i.e., fault angle width) of the inner ring fault. Unlike the outer ring, the fault location of the inner ring rotates with the axis. , , The inner ring radius of the bearing. This represents the fault depth.

[0070] Similar to the outer ring fault situation, the inner ring fault corresponds to... It can be calculated using the following formula:

[0071] (16)

[0072] The bearing dynamics model established using the above method can generate simulated vibration signals. , , and This is to supplement the lack of actual vibration samples, thereby generating simulated vibration signals that simulate fault conditions (inner ring fault, outer ring fault, rolling element fault).

[0073] This step fundamentally solves the "data scarcity" problem by establishing a high-fidelity 4-DOF bearing-base dynamic model to replace the difficult-to-obtain real fault data. The generated simulation data not only has accurate fault labels, but also, because it originates from physical mechanisms, can well preserve the core mode characteristics of real faults such as impact periodicity and harmonics, laying a reliable data foundation for subsequent zero-shot diagnosis and avoiding the feature distortion problems that may be caused by data augmentation or generative models.

[0074] S2. Constructing the training dataset

[0075] The simulated fault data generated in step S1 is combined with the health status vibration signals collected from the target device to form a training dataset.

[0076] Specifically, the large amount of simulated fault data generated in step S1 (e.g., 5000 samples each of the three states of inner race fault, outer race fault, and rolling element fault) is mixed with a segment of healthy vibration data that can be easily measured from the target device (e.g., 100 seconds of data, which is divided into segments to obtain 3514 samples) to form a training set containing 18514 samples. This training set does not contain any real fault samples from the target device, which meets the zero-sample setting.

[0077] In this step, the data construction model of combining simulated fault data with measured health data is key to achieving zero-shot diagnostics. It allows the model to learn the characteristic manifestations of various faults on target devices with only health data, greatly expanding the applicable scenarios of the method.

[0078] S3. Extract physical feature vectors

[0079] Vibration signals are projected onto an invariant feature space using a physics-based algorithm, eliminating the discrepancy between simulated and measured data and providing robust features for subsequent classification. This process, based on the envelope order spectrum, aims to extract essential features of bearing faults, such as the harmonic components of the outer ring spalling frequency (BPFO), inner ring spalling frequency (BPFI), and rolling element spalling frequency (BSF). These frequencies are the fundamental frequencies for bearing fault diagnosis, calculated based on bearing geometry and rotational speed, and used to identify spalling locations. Specifically, the extraction process includes three main steps: envelope signal calculation and order domain transformation, extraction of the fundamental frequency and its harmonic values, and root mean square (RMS) normalization. The extraction process is described in detail below.

[0080] Hilbert transform is performed on the simulated vibration signal generated in step S1 and the healthy state vibration signal collected from the target device in step S2 to extract the envelope signal; the envelope signal is converted to the order domain by angular resampling and the order spectrum is calculated; based on the physical fundamental frequency (BPFO / BPFI / BSF) of the bearing fault, the first N harmonics of various faults are located in the order spectrum and their amplitudes are extracted to form physical feature vectors.

[0081] like Figure 2 The diagram shown illustrates the extraction of physical feature vectors. This step aims to convert the vibration signal into features that are independent of rotational speed and have clear physical meaning.

[0082] Envelope signal calculation and order domain transformation: Specifically, for all the vibration signals mentioned above, i.e. Figure 2 The original vibration signal in s ( tFirst, perform a Hilbert transform to extract its envelope. e ( t The Hilbert transform converts a signal into an analytic signal. (j is the imaginary unit), where The result of the Hilbert transform of s(t) is defined as a convolutional form.

[0083] (17)

[0084] In equation (17), t represents the current time, which is used to determine the time point for performing the Hilbert change; This is the integration variable, used to iterate through all time points from −∞ to +∞.

[0085] Then, the envelope amplitude is calculated:

[0086] (18)

[0087] This step removes the high-frequency carrier and highlights the low-frequency modulation components. To adapt to varying speed conditions, the envelope signal... e ( t The signal is converted to the order domain through angle resampling. Assuming the shaft speed is fr(t), angle resampling synchronizes the sampling points with the shaft rotation period, resulting in the order domain signal e(θ), where θ represents the cumulative rotation angle (in radians). This conversion normalizes the fault frequency to a fixed order (e.g., 1-10 for BPFO). Angle resampling technology is then used to... e ( t The time domain is transformed into the order domain, completely eliminating the influence of speed fluctuations.

[0088] Then, the squared envelope is calculated to enhance the power distribution: Finally, the order power spectral density is calculated to obtain the order spectrum independent of rotational speed. S order ( κ The order-domain envelope spectrum is obtained by performing a Fast Fourier Transform (FFT) on the squared envelope and taking the amplitude. S order ( κ ).

[0089] (19)

[0090] In equation (19), κ represents the order (frequency divided by rotational speed), M represents the signal length, and the subscript indicates taking the single-sided spectrum.

[0091] Fundamental frequency and harmonic value extraction: Bearings exhibit three common faults: outer ring spalling, inner ring spalling, and rolling element spalling. Each spalling fault manifests through fundamental frequency characteristics, which are directly related to the physical phenomena of the rolling element-raceway interaction. Based on the principles of bearing kinematics, the fundamental frequency calculation formula is as follows:

[0092] (20)

[0093] (twenty one)

[0094] (twenty two)

[0095] In equations (20)-(22), n For the number of rolling elements, The shaft speed is d The diameter of the rolling element, D The diameter of the pitch circle, It represents the contact angle.

[0096] Then, using the theoretical values ​​of the physical fundamental frequency model (BPFO, BPFI, BSF) based on bearing faults, the preset Nth harmonic is located in the order spectrum, and the fault harmonic amplitudes at these harmonics are extracted to form a physical feature vector h. For example, the 1st to 10th harmonics (i.e., N=10) are located, and for each harmonic m (m=1…N), within the tolerance range [(1− δ )⋅m⋅ F ,(1+ δ )⋅ m ⋅ F Find the peak value, for example, where δ = 0.02 (considering a 2% slip), where F This corresponds to the fundamental frequency (BPFO, BPFI, or BSF). Finally, a multi-dimensional (30-dimensional) physical feature vector h is output, covering the harmonic energy of the three types of faults;

[0097] (twenty three)

[0098] In equation (23), The m-th harmonic, representing the outer ring peeling frequency (BPFO), has its amplitude in the order spectrum. The amplitude of the m-th harmonic, representing the inner ring peeling frequency (BPFI), in the order spectrum. The value represents the amplitude of the m-th harmonic of the rolling element peeling frequency (BSF) in the order spectrum, where N is the preset harmonic order and m is the harmonic order number, which is an integer from 1 to N.

[0099] Root Mean Square (RMS) Normalization: To eliminate the effect of transfer function decay, the eigenvectors are normalized using the root mean square (RMS). In this embodiment, the normalization formula is as follows (taking 30 dimensions as an example):

[0100]

[0101] This step significantly improves the cross-condition robustness (resistance to speed fluctuations) and interpretability of the features (e.g., outer race faults highlight BPFO harmonic energy, inner race faults highlight BPFI harmonic energy, and rolling element faults exhibit BSF harmonic characteristics). Each feature dimension corresponds to a specific physical event (e.g., the second harmonic energy of an outer race fault), making the subsequent diagnostic decision-making process no longer a "black box" and providing a physical basis for decision fusion.

[0102] S4. Training a multi-scale residual attention convolutional network (MR-CNN)

[0103] This invention introduces a multi-scale residual attention convolutional network (MRA-CNN) as a fault classifier. By fusing multi-scale feature learning with an attention mechanism, it effectively solves the problems of multi-scale distribution of fault features and noise interference in vibration signals. Its core architecture includes a multi-scale learning module (MLMod), a residual attention module (RAMod), and a fault classification layer.

[0104] See Figure 3 , 4 In this step, a dedicated deep learning model was designed to learn the deep features of vibration signals.

[0105] Specifically, such as Figure 3 As shown, the Multi-Scale Learning Module (MLMod) aims to extract multi-scale features from simulated vibration signals and healthy-state vibration signals collected from the target device. MLMod consists of a Basic Kernel (BK) convolutional layer and Res2Net blocks. The parameters of the BK convolutional layer are designed by combining the characteristics of the vibration signal and model efficiency. For example, its core parameters are five 1D convolutional layers with kernels of 32 / 16 / 16 / 8 / 4, and a stride of 2 for each. Let the input vibration signal be... (dimension is) L A real matrix of size × 1 is processed by a BK layer to obtain the basic scale feature map. , where C is the number of channels in the convolutional neural network.

[0106] Res2Net blocks will Divide evenly into S Feature subset Multi-scale features are generated through hierarchical convolution operations:

[0107] (twenty four)

[0108] In equation (24), This is a 1-D convolution operation, and the output is finally obtained through batch normalization (BN) and ReLU activation. .

[0109] like Figure 4 As shown, the residual attention module (RAMod) adaptively weights the feature maps, suppressing noise interference and focusing on the key information most relevant to the fault. RAMod generates an attention mask to weight the multi-scale features of the MLMod output, suppressing noise and enhancing key information. The MLMod output features are... First, channel descriptors are obtained through global average pooling (GAP). and spatial descriptors after convolution (1x1) operation The two matrices are multiplied to generate an attention mask:

[0110] (25)

[0111] In equation (25), σ is the sigmoid activation function. Introducing the Residual Attention Learning (RAL) strategy, after batch normalization and sigmoid processing, the RAMod output is: In the formula, ⊗ represents the element-wise product, and ⊕ represents the element-wise sum. The mask is connected by a shortcut. M It can be directly added to the features to reduce information loss.

[0112] In the fault classification layer, after multiple layers of MLMod and RAMod stacking, the output features are... . It is a real matrix, where R represents the set of real numbers. C F Indicate output features Z F The number of channels, L F Indicate output features Z F The dimensions in the length dimension. Then, they are compressed into feature vectors using GAP. :

[0113] (26)

[0114] In equation (26), v i It is an eigenvector V The i-th element in. v i correspond Z FThe average value of all length position features of the i-th channel is used to summarize the global features of that channel.

[0115] In equation (26), i is the index of the feature channel, and the output feature is... Z F have C F There are several channels (different channels correspond to different fault characteristics), and i is used to traverse these channels. C F One channel (e.g., i = 1, 2, ..., C F ); j is the index of the length dimension, Z F In the "length direction" there is L F Each position (length of the temporal or spatial dimension) is used to traverse this... L F Positions (e.g., j = 1, 2, ..., L F ), It refers to the feature value of the i-th channel at the j-th length position.

[0116] Finally, the probability distribution of fault types is obtained through the SoftMax classification layer:

[0117] (27)

[0118] In equation (27), W and b are parameters of the fully connected layer, k is the total number of fault categories (e.g., a bearing has k categories such as "inner ring fault, outer ring fault, rolling element fault"), and i and j are indices of the fault categories. It is the prediction score for the j-th type of fault. This represents the probability that the model predicts a "type j fault"; during summation, i iterates through all k categories, calculating the normalized probability of the scores for each category. This architecture, through multi-scale feature capture and adaptive attention weighting, maintains high classification accuracy even in noisy environments, and its effectiveness has been validated on relevant bearing fault diagnosis datasets.

[0119] During training, a hybrid loss function fusing cross-entropy and within-class distribution calibration loss was designed to collaboratively address the feature learning problem in single-fault scenarios. The cross-entropy loss function is referenced below:

[0120] (28)

[0121] In equation (28), This represents the probability that the model predicts the i-th sample as belonging to the corresponding category, and O represents the total number of input samples.

[0122] A class-specific distribution calibration loss is proposed, which calculates the distance between each sample feature and the class feature center, and assigns high weights to "outliers", such as early weak faults and fault samples under high noise, to force the model to calibrate the class-specific distribution.

[0123] (29)

[0124] In equation (29), It is the feature vector of sample i; It is the feature center of a single fault category; It is the adaptive weight of sample i (the farther away from the center, the higher the weight). (For adjustment coefficients, controlling the rate of change of weights), where preferred... The specific value of ∈(0,5] needs to be determined by experimental hyperparameter search in combination with the dataset of the specific bearing fault diagnosis task.

[0125] Therefore, the hybrid loss function used to train the network is... L for:

[0126] (30)

[0127] In equation (30), Preferred , ; L wce Cross-entropy loss; L widc Calibrate the loss for the in-class distribution.

[0128] In this step, the design of the MR-CNN structure and its loss function significantly enhances the model's ability to perceive and extract strong noise and multi-scale fault features, thereby improving the model's generalization performance and classification accuracy.

[0129] S5. Fusion diagnosis, output the final diagnostic results.

[0130] For the vibration signal to be diagnosed collected from the target device, the first fault probability distribution is obtained through the MR-CNN trained above. The physical feature vector h is extracted through step S3, and the second fault judgment probability is calculated using a preset threshold logic rule. According to the formula The two are weighted and merged, where, This refers to the probability distribution output by the network, i.e., the first probability distribution. U The probability calculated based on the physical feature threshold logic, i.e., the second fault judgment probability, where α and β are weighting coefficients, is the probability calculated based on the physical feature threshold logic. This represents the final weighted probability distribution. The fault type in the final diagnostic result is determined by... The category corresponding to the highest probability value is determined.

[0131] Specifically, for each input sample, three key physical feature thresholds are extracted in step S3. U 1, U2, U 3) When the preset harmonic order N=10, , , These features reflect the harmonic energy distribution characteristics of different segments of the signal, and after normalization, the physical feature vector is obtained:

[0132]

[0133] Set the fault probability distribution output by MR-CNN as ( :normal, Outer ring malfunction Inner ring malfunction. (Rolling element failure). The decision fusion formula is:

[0134] (31)

[0135] In equation (31), For threshold logical weights, For MR-CNN weights; for example, , .

[0136] The final fault type is determined by the maximum weighted probability, that is, the final diagnosis result is output based on the maximum value of Q.

[0137] (32)

[0138] In equation (32), Represents the output of the MR-CNN network Outer ring malfunction Inner ring malfunction The total failure probability of the rolling element; if the total failure probability output by the MR-CNN network is less than 0.5 or the probability of normal operation... If it is greater than the total probability of failure, then (The classification result) is 0, representing normal; otherwise, according to the decision fusion formula... Select the fault type with the highest probability of failure. , , ).

[0139] In this step, this fusion strategy combines the high precision of deep learning with the high reliability of physical rules. When the model output is uncertain, physical rules can provide strong corroboration or correction (for example, the model may misjudge, but physical features clearly show anomalies in the harmonic energy of a certain type of fault, thus correcting the final result), greatly improving the accuracy and reliability of the diagnostic results.

[0140] To further illustrate the effectiveness of the bearing zero-sample fault diagnosis method based on envelope order spectrum multidimensional feature extraction, this invention uses eight datasets to verify the method. These datasets include a simulation dataset, the Case Western Reserve University (CWRU) dataset, the University of Paderborn (PU) dataset, the PRONOSTIA-FEMTO dataset, the Xi'an Jiaotong University and Changxing Shengyang Technology dataset (XJTU-SY), the Mechanical Failure Prevention Technology (MFPT) dataset, the Natural Bearing Small Block Wind Turbine (NBSWT) dataset, and the Dynamic Model Simulation Dataset (DM). Table 1 summarizes these datasets.

[0141] Table 1 Datasets used in embodiments of the present invention

[0142]

[0143] The training set of this embodiment contains 13,514 samples, consisting of simulated fault data (DS2) generated by the dynamic model, CWRU health data, and DS1 simulation data, excluding any fault samples from the test equipment CWRU; the validation set contains 5,792 samples, integrating five heterogeneous public datasets: MFPT (17), PU (238), XJTU-SY (1,563), PRONOSTIA-FEMTO (43), and NBSWT (50), where the numbers in parentheses represent the number of signals in the dataset, simulating the differences in multi-source operating conditions to optimize the model's generalization ability; the test set contains 221 samples (of which 40 are normal samples, 119 are outer ring faults, 54 are inner ring faults, and 8 are rolling element faults), derived from the health and fault data in the CWRU dataset, whose fault modes (inner ring / outer ring / rolling element peeling) are completely unknown to the test equipment. This division ensures that the model training strictly meets the zero-sample constraint of "no target equipment fault samples required," directly verifying the diagnostic performance of the method for unknown faults of new equipment in real-world scenarios.

[0144] Experimental results as follows Figures 5-8 As shown, experimental results demonstrate that the model combining the fault diagnosis fusion strategy performs exceptionally well in zero-shot fault diagnosis tasks. From the confusion matrix, it can be seen that after adopting the fusion strategy ( Figure 5All 40 normal samples were correctly identified; only 6 out of 119 outer ring fault samples were misclassified; all 54 inner ring fault samples were correctly identified; and there were no misclassifications of the 8 rolling element fault samples. The overall classification accuracy was higher than that of the model that did not use the fusion strategy. Figure 6 ).

[0145] By comparing the correspondence between actual failure modes and diagnostic results ( Figure 7 , Figure 8 This demonstrates that the fusion strategy can, to some extent, solve the problem of misjudging outer ring faults in MR-CNN models. In multiple experiments involving eight heterogeneous datasets, including CWRU, the model maintained stable recognition capabilities for inner ring, outer ring, and rolling element peeling faults that the test equipment had never seen before, and achieved 100% accuracy in recognizing rare faults (such as rolling element faults).

[0146] This result verifies the effectiveness of envelope order spectrum multidimensional feature extraction and multi-scale residual attention network, and proves that threshold logic that integrates physical rules can compensate for the generalization defects of pure data-driven models to a certain extent, providing a reliable solution for bearing fault diagnosis in zero-shot scenarios.

[0147] As described in the above embodiments, the bearing zero-sample fault diagnosis method based on envelope order spectrum multidimensional feature extraction of the present invention overcomes the bottleneck of target equipment fault sample dependence by combining a high-fidelity dynamic model with a small amount of health data for training. Experiments show that in the zero-sample scenario (no target fault samples), the model trained based on simulated fault data and measured health data achieves a diagnostic accuracy of 97.3%±1% for typical faults of the inner ring, outer ring, and rolling elements of rolling bearings, which is more than 29 percentage points higher than the traditional data-driven method (requiring similar fault samples, zero-sample accuracy is 68%). The consistency between simulated data and natural fault data features reaches 92%, the fault impact cycle error is <3%, and the harmonic distribution consistency is >90%, effectively solving the problem of differences between artificially implanted faults and natural fault features. Through the collaborative optimization of order domain transformation and multi-scale residual attention network (MR-CNN), the ability to resist speed fluctuations, noise interference, and load changes is significantly improved. A "physical feature-deep learning" fusion decision-making mechanism is constructed to extract the core characteristic frequencies (BPFO / BPFI / BSF) of the bearing and their first N harmonic amplitude features. Each decision dimension can directly map physical phenomena (e.g., the increase in BPFO harmonic energy corresponds to outer ring peeling). At the same time, by replacing real fault data with simulation data, the costs of data acquisition and equipment operation and maintenance are significantly reduced, avoiding the economic losses of deliberately running equipment to a fault state.

[0148] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, various modifications and variations of the embodiments of the present invention are possible. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A bearing zero-sample fault diagnosis method based on envelope order spectrum multi-dimensional feature extraction, characterized in that, The method comprises the following steps: generating simulation fault data based on a bearing dynamics model, the simulation fault data being a simulation vibration signal simulating a fault state; combining the simulation fault data with a health state vibration signal collected from a target device to construct a training data set; performing envelope extraction and angular resampling on the simulation vibration signal and the health state vibration signal, converting to a order domain and calculating an order spectrum; extracting a fault harmonic amplitude in the order spectrum based on a physical fundamental frequency of a bearing fault to form a physical feature vector; constructing a multi-scale residual attention convolutional network and training the network using the training data set; for a to-be-diagnosed vibration signal collected from a target device, obtaining a first probability distribution through the trained multi-scale residual attention convolutional network, and obtaining a second fault judgment probability through threshold logic calculation based on a physical feature vector extracted from the to-be-diagnosed vibration signal; fusing the first probability distribution and the second fault judgment probability to output a final diagnosis result; The bearing dynamics model is a 4-DOF model for representing the motion of the inner ring and the outer ring of the bearing in the x and y directions; the model calculates the contact force between the rolling elements and the raceway based on the Hertz contact theory, and the contact force is related to the contact deformation as wherein, is the load-deflection coefficient, is the load-deflection index; by introducing a deformation release amount characterizing the fault to modify the contact deformation amount the modified contact deformation amount is wherein, and are the displacements of the inner ring in the x, y directions, and are the displacements of the outer ring in the x, y directions, is the angular position of the ith rolling element, is the radial play of the bearing; The dynamics model is solved to simulate a fault condition corresponding to the simulated fault data by solving a dynamics equation including the modified contact deformation ​ The amount of deformation released According to the fault location calculation: When the outer ring is faulty, When the inner ring is faulty, wherein, is a contact change amount when the rolling element enters the failure region, is a position angle of the outer ring failure, is a position angle of the inner ring failure, is a perceived angle width of the outer ring failure, is a perceived angle width of the inner ring failure, is an angular position of the i-th rolling element.

2. The method of claim 1, wherein, the envelope extraction and angular resampling on the simulation vibration signal and the health state vibration signal, the conversion to the order domain and the calculation of the order spectrum comprise: performing Hilbert transform on the vibration signal to extract an envelope signal thereof; converting the envelope signal to an order domain signal through angular resampling; square enhancing the power distribution of the order domain signal; performing fast Fourier transform on the squared order domain signal and taking the amplitude to obtain the order spectrum.

3. The method according to claim 1 or 2, characterized in that, the physical feature vector h in the extraction of the fault harmonic amplitude in the order spectrum to form the physical feature vector comprises: wherein, an amplitude of the mth harmonic of the outer race spalling frequency (BPFO) in the order spectrum, an amplitude of the mth harmonic of the inner race spalling frequency (BPFI) in the order spectrum, an amplitude of the mth harmonic of the rolling element spalling frequency (BSF) in the order spectrum, N is a preset harmonic number; m is a serial number of the harmonic number, and the value range of m is an integer from 1 to N.

4. The method of claim 3, wherein, For the feature vector Perform root mean square normalization.

5. The method of claim 1, wherein, the multi-scale residual attention convolutional network comprises a multi-scale learning module, a residual attention module and a fault classification layer; the multi-scale learning module extracts multi-scale features of the simulation vibration signal and the health state vibration signal, the residual attention module weights the multi-scale features output by the multi-scale learning module by generating an attention mask, and after multi-layer stacking processing of the multi-scale learning module and the residual attention module, the output features are compressed into a feature vector through global average pooling in the fault classification layer, and finally the fault probability distribution is output through the Softmax classification layer processing.

6. The method of claim 5, wherein, A hybrid loss function is introduced when training the multi-scale residual attention convolutional network, and the hybrid loss function is L : wherein, , L wce is the cross-entropy loss, L widc is the within-class distribution calibration loss.

7. The method of claim 1, wherein, the fusion of the first probability distribution and the second fault judgment probability is performed using a weighted fusion method, and the weighted fusion formula is: wherein is the probability distribution output by the network, i.e. the first probability distribution, is the probability calculated according to the physical feature threshold logic, i.e. the second failure probability, and is a weighting factor, said is the final weighted probability distribution; The The failure type corresponding to the maximum probability value in the middle is output as the final diagnosis result.

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