Gearbox small sample fault diagnosis method and system

Abstract

The present application relates to the technical field of mechanical fault diagnosis, and particularly relates to a gear box small sample fault diagnosis method and system. A high-precision rigid-flexible coupling dynamic model is constructed to generate a simulation fault signal; scene information in an actual vibration signal of a gear box to be diagnosed is extracted, superimposed on the simulation signal, and combined with a condition generated by a physical information guided conditional generative adversarial network to match and correct the working condition of the simulation data and supplement experimental scene information; a feature extraction network is designed to enhance the impact feature perception ability, an improved Softmax classifier is introduced, and an angle interval regulation mechanism is introduced to improve the inter-class discrimination; an improved joint distribution adaptive strategy is proposed to simultaneously align the edge distribution and class conditional distribution of the simulation domain and the measured domain, and to reduce the cross-domain difference; and finally, a virtual-real sample training diagnosis model is fused to significantly improve the gear box multi-fault classification precision under small sample conditions.

Description

Technical Field

[0001] This invention relates to the field of mechanical fault diagnosis technology, and in particular to a method and system for diagnosing small-sample faults in gearboxes. Background Technology

[0002] In modern industrial systems, gearboxes, as critical transmission devices, are widely used in energy, power, manufacturing, and transportation sectors. Their operational status directly affects the stability and reliability of the entire mechanical equipment. A gearbox malfunction can lead to equipment downtime, production interruptions, severe economic losses, and even safety accidents, threatening personnel lives.

[0003] In actual operation, due to safety and continuous production requirements, most gearbox equipment maintains a healthy operating condition for extended periods. This operational characteristic makes it difficult to collect typical fault conditions on-site, resulting in a severe scarcity of real fault samples. Furthermore, due to differences in working conditions, fault types, and data collection methods, on-site data often exhibits a severely uneven distribution, posing a challenge to data-driven intelligent diagnostic methods.

[0004] Traditional gearbox fault diagnosis methods mostly rely on a large number of labeled samples for feature extraction and model training. However, they struggle to achieve effective diagnosis under conditions of small sample sizes and imbalance. To address the problem of insufficient samples, existing technologies attempt to generate simulation data using digital modeling. This involves establishing a gearbox dynamic model and introducing different types of gear faults, such as broken teeth, missing teeth, pitting, and cracks. Multiple typical speed and load combinations are then set to simulate the impact of these faults on the vibration response of the gear transmission system, obtaining simulated vibration samples under different fault conditions to supplement the fault sample source.

[0005] However, since the simulated vibration samples are based on idealized modeling assumptions and do not fully consider real physical factors such as environmental noise, installation boundaries, operating condition fluctuations and scene interference in actual working conditions, they are not compatible with actual application scenarios. The generated data has certain differences from the actual measured signals in terms of time and frequency characteristics, which affects its applicability in diagnostic models. As a result, the fault diagnosis accuracy of gearbox fault diagnosis using simulated vibration samples as training samples is poor. Summary of the Invention

[0006] Therefore, the technical problem to be solved by the present invention is to overcome the defect that the fault diagnosis accuracy of gearbox fault diagnosis using simulated vibration samples as training samples is poor due to the distribution difference between the idealized modeling data and the measured signal.

[0007] To address the aforementioned technical problems, this invention provides a method for diagnosing small-sample faults in gearboxes, comprising:

[0008] Obtain the actual vibration signal set of the gearbox to be diagnosed. The actual vibration signal set includes multiple fault vibration signals and non-fault vibration signals.

[0009] A weighted normalized spectrum model is constructed using a bias term and a weight vector, where each element in the weight vector corresponds to a frequency point in the actual vibration signal.

[0010] Based on the normalized Fourier amplitude spectrum of each actual vibration signal, the optimal solution of the weighted normalized spectrum and the bias term and weight vector in the model is obtained.

[0011] Using the percentile of the amplitude of each element in the optimal solution of the weight vector, the segmentation threshold for distinguishing the components of interest, the reference components, and the scene information is determined. Each element in the weight vector is then categorized, and only the element values ​​belonging to the scene information are retained, while the values ​​of the remaining elements are set to 0, thus obtaining the separated frequency domain scene information.

[0012] The separated frequency domain scene information is converted from the frequency domain to the time domain to obtain the time domain scene information signal;

[0013] By fusing time-domain scene information signals with simulated fault vibration signals, an enhanced simulated fault signal is obtained;

[0014] The gearbox fault diagnosis model is trained using enhanced simulated fault signals as training samples; the trained gearbox fault diagnosis model is then used to diagnose the faults in the gearbox to be diagnosed.

[0015] Preferably, the method for solving the weighted normalized spectrum and the optimal solution of the bias term and weight vector in the model based on the normalized Fourier amplitude spectrum of each actual vibration signal includes:

[0016] Based on the normalized Fourier amplitude spectrum of each actual vibration signal, a maximum likelihood estimation objective function is constructed, and the optimal solution for the bias term and weight vector is obtained by solving the weighted normalized spectrum and the model.

[0017] The objective function for maximum likelihood estimation is:

[0018] ,

[0019] in, To estimate the objective function using maximum likelihood estimation, This represents the total number of non-fault vibration signals. The total number of fault vibration signals, , Indicates transpose. For the weight vector, For bias terms, For indexing actual vibration signals, For the first A sample label of an actual vibration signal, when When the vibration signal is not due to a fault, ,when When it is a fault vibration signal, , The regularization coefficient is . , For the first The normalized spectral vector after the expansion of an actual vibration signal. For the first Normalized Fourier amplitude spectrum of an actual vibration signal.

[0020] Preferably, the method for determining the segmentation threshold for distinguishing between the component of interest, the reference component, and scene information based on the percentile of the magnitude of each element in the optimal solution of the weight vector includes:

[0021] Arrange the magnitudes of each element in the optimal solution of the weight vector in ascending order, calculate the percentile of the magnitude of each element after ascending order, and construct a percentile sequence of magnitudes.

[0022] The amplitude percentile sequence is divided into low amplitude region and high amplitude region;

[0023] For each region, each element within the current region is traversed as a candidate change point. The corresponding sequence of the current region is divided into a subsequence before the candidate change point and a subsequence after the candidate change point. The least squares method is used to fit a linear regression line to the two subsequences respectively. The fitting residuals of each subsequence are calculated and summed to obtain the total fitting error corresponding to the candidate change point. The candidate change point with the smallest total fitting error is selected as the optimal change point of the current region, and its corresponding magnitude is used as the segmentation threshold.

[0024] The segmentation thresholds for low-amplitude and high-amplitude regions are used as the segmentation thresholds to distinguish between the components of interest, the reference components, and the scene information.

[0025] Preferably, the method for classifying the elements in the weight vector includes:

[0026] For each element in the weight vector, if the element value is less than the segmentation threshold of the low amplitude region, then the element belongs to the reference component; if the element value is greater than or equal to the segmentation threshold of the low amplitude region and less than or equal to the segmentation threshold of the high amplitude region, then the element belongs to the scene information; if the element value is greater than the segmentation threshold of the high amplitude region, then the element belongs to the interest component.

[0027] Preferably, after obtaining the enhanced simulation fault signal, the enhanced simulation fault signal is optimized, including:

[0028] Using the operating parameters and prior fault information of the gearbox to be diagnosed, a condition vector is constructed;

[0029] A conditional generative adversarial network is constructed using a condition generator and a condition discriminator.

[0030] The enhanced simulated fault signal and conditional vector are used to obtain the target enhanced simulated fault signal through the conditional generator of the conditional generative adversarial network.

[0031] Preferably, the method for optimizing the gearbox fault diagnosis model after obtaining the trained model includes:

[0032] For each fault category, the kernel density estimation method is used to calculate the class conditional probability of the fault category under the enhanced simulation fault signal set and the fault vibration signal set, respectively.

[0033] The enhanced simulation fault signal set and the actual fault vibration signal set are respectively extracted using a feature extractor to obtain the corresponding feature sets;

[0034] Using correlation alignment and maximum mean difference as metrics, the covariance distribution distance and mean distribution distance between the enhanced simulation fault signal feature set and the actual fault vibration signal feature set are calculated respectively.

[0035] Based on the covariance distribution distance, mean distribution distance, and class conditional probability of the fault category under the enhanced simulation fault signal feature set and the actual fault vibration signal feature set, an improved joint distribution adaptation loss function is constructed. The improved joint distribution adaptation loss function is then used to perform transfer learning on the gearbox fault diagnosis model to obtain the target gearbox fault diagnosis model.

[0036] Preferably, the improved joint distribution adaptive loss function is:

[0037] ,

[0038] in, To improve the joint distribution adaptation loss function, For the maximum mean difference, The distance of the covariance distribution. To enhance the mean distribution distance between the simulated fault signal feature set and the actual fault vibration signal feature set, To enhance the covariance distribution distance between the simulated fault signal feature set and the actual fault vibration signal feature set, To balance the weighting coefficients, The result after feature extraction. For fault category index, Fault Category In the enhanced simulation fault signal set, the total number of samples, Fault Category In the total number of samples in the fault vibration signal set, This represents the total number of fault categories. This is a set of actual fault vibration signal characteristics. To enhance the feature set of simulated fault signals.

[0039] Preferably, the gearbox fault diagnosis model includes: a feature extraction network and a classifier connected in sequence.

[0040] Preferably, the classifier is an improved Softmax classifier, and the loss function of the improved Softmax classifier is constructed based on the features of the training samples and the learnable weight matrix of the fully connected layer;

[0041] The improved loss function for the Softmax classifier is:

[0042] ,

[0043] in, To improve the loss function of the Softmax classifier, The features extracted by the feature extraction network for the nth training sample. , The dimension of the features extracted by the feature extraction network. The total number of training samples, , This represents the total number of fault categories. Let n be the fault category label for the nth training sample. The learnable weight matrix of the fully connected layer. Fault category labels in the learnable weight matrix of the fully connected layer The corresponding column vector, For angle adjustment function, , , m are hyperparameters of the common control decision boundary, For the angle control function parameters, The features extracted by the feature extraction network for the nth training sample and The included angle, Here, n is the index for the fault category, and n is the index for the training samples. Fault category labels in the learnable weight matrix of the fully connected layer For the corresponding column vector, The features extracted by the feature extraction network for the nth training sample and The included angle.

[0044] The present invention also provides a small sample fault diagnosis system for gearboxes, comprising:

[0045] The signal acquisition module is used to acquire the actual vibration signal set of the gearbox to be diagnosed. The actual vibration signal set includes multiple fault vibration signals and non-fault vibration signals.

[0046] The model building module is used to construct a weighted normalized spectrum and model with bias terms and weight vectors, where each element in the weight vector corresponds to a frequency point in the actual vibration signal.

[0047] The solution module is used to solve for the weighted normalized spectrum and the optimal solution of the bias term and weight vector in the model based on the normalized Fourier amplitude spectrum of each actual vibration signal.

[0048] The scene information acquisition module is used to determine the segmentation threshold that distinguishes the components of interest, reference components and scene information by using the percentile of the amplitude of each element in the optimal solution of the weight vector. It classifies each element in the weight vector, retains only the element values ​​belonging to the scene information, and sets the values ​​of the rest to 0, thus obtaining the separated frequency domain scene information.

[0049] The conversion module is used to convert the separated frequency domain scene information from the frequency domain to the time domain to obtain the time domain scene information signal;

[0050] The enhanced simulation module is used to fuse time-domain scene information signals with simulated fault vibration signals to obtain enhanced simulated fault signals.

[0051] The fault diagnosis module is used to train the gearbox fault diagnosis model using enhanced simulated fault signals as training samples; and to perform fault diagnosis on the gearbox to be diagnosed using the trained gearbox fault diagnosis model.

[0052] Compared with the prior art, the above-described technical solution of the present invention has the following advantages:

[0053] The present invention provides a small sample fault diagnosis method and system for gearboxes. In order to make the distribution characteristics of the simulated signal consistent with those of the actual vibration signal, the actual vibration signal is decomposed into three parts: a reference component of the stable background, a fault-induced component of interest, and noise related to the operating conditions. By superimposing the noise related to the operating conditions with the simulated signal, the distribution characteristics of the simulated signal are made consistent with those of the actual vibration signal. However, in actual vibration signals, the three types of components are coupled and superimposed, making it impossible to directly separate pure scene information. Therefore, this invention collects a set of actual vibration signals including both fault and non-fault states, extracts the normalized Fourier amplitude spectrum to eliminate the influence of differences in total signal energy and highlight differences in spectral shape. A weighted normalized spectrum model composed of a weight vector and a bias term is constructed, and the optimal weight vector, i.e., the optimal difference spectrum, is solved, so that the positive and negative spectral lines and zero values ​​correspond to the frequency domain positions of the component of interest, the reference component, and the scene information, respectively. The normalized spectrum value at each frequency point is differentially weighted using the weight vector, quantifying the contribution of each frequency point to the reference component, the component of interest, and the scene information. To achieve automatic and accurate classification of the three types of components, the amplitude values ​​of the optimal weight vector are sorted in ascending order, and an amplitude percentile sequence is constructed to determine the two-class segmentation thresholds. Based on this, each frequency component is classified into the component of interest, the reference component, and the scene information, retaining only the scene information. The frequency domain components corresponding to the information are set to zero, and the remaining components are set to zero to achieve pure separation of scene information in the frequency domain. The frequency domain components of the scene information are reconstructed to obtain a time-domain scene information signal containing only real-world interference and environmental noise. This scene information is then fused with the original simulated fault signal to generate an enhanced simulated fault signal that combines fault physical characteristics with real-world scene distribution characteristics. This fundamentally compensates for the shortcomings of traditional dynamic modeling, such as idealization, lack of real-world noise, boundary conditions, and installation effects, significantly reducing the difference between simulated and measured signals in time-frequency domain characteristics and statistical distribution. Finally, the enhanced simulated fault signal is used as a training sample to construct and train a gearbox fault diagnosis model. This enables the gearbox fault diagnosis model to achieve sufficient and robust fault feature learning even under conditions of small samples and data imbalance, preventing mismatch between simulated vibration samples and actual application scenarios, and improving the fault diagnosis accuracy of the gearbox fault diagnosis model.

[0054] Because there are inherent distribution differences between enhanced simulated fault signals and actual fault vibration signals, directly using the trained model for diagnosis leads to insufficient generalization performance. Therefore, transfer learning is needed to reduce inter-domain differences and improve model adaptability. However, actual vibration signal samples often suffer from scarce labels, and pseudo-labels are often predicted by the model to assist in distribution alignment. However, the estimation process based on pseudo-labels often has large approximation errors and is difficult to effectively cope with complex conditional distribution shifts caused by model simplification and noise interference. Ultimately, this results in the simulation features and measured features of each fault category failing to achieve effective alignment, or even producing significant deviations. To address this, this invention uses kernel density estimation to accurately calculate the class-conditional probabilities of each fault category. This approach provides prior information on categories that better align with the actual data distribution for distribution alignment, avoiding estimation bias caused by pseudo-labels. Simultaneously, it uses correlation alignment and maximum mean difference to measure the distance between covariance and mean distribution, achieving comprehensive matching of first- and second-order statistics. Furthermore, it deeply integrates class-conditional probability with the distance between the two statistical distributions to construct an improved joint distribution adaptation loss function. This allows the model to not only achieve global domain alignment during transfer learning but also perform fine-grained conditional distribution calibration for each fault category, effectively offsetting the effects of model simplification and noise interference. This completely solves the feature alignment failure problem caused by pseudo-label approximation errors, significantly improving the cross-domain adaptability and diagnostic accuracy of the target gearbox fault diagnosis model. Attached Figure Description

[0055] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings, wherein:

[0056] Figure 1 This is a flowchart illustrating a small-sample fault diagnosis method for gearboxes according to the present invention.

[0057] Figure 2 The process of modeling the rigid-flexible coupling dynamics of a gearbox.

[0058] Figure 3 This is a schematic diagram of a gearbox simulation model with multiple fault types.

[0059] Figure 4 For the comparative analysis of simulated and measured vibration spectra, Figure 4 (a) in the figure is the time-domain plot of the acceleration data from the experimental vibration data. Figure 4 (b) in the figure is the time-domain plot of the acceleration of the simulation data. Figure 4 (c) in the figure is the frequency domain plot of the experimental vibration data amplitude. Figure 4 (d) in the figure is the frequency domain plot of the simulation data amplitude.

[0060] Figure 5 This is a diagram of the transfer learning structure.

[0061] Figure 6 This is a structural diagram of a small sample fault diagnosis system for gearboxes according to the present invention. Detailed Implementation

[0062] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0063] Reference Figure 1 As shown, this embodiment provides a small sample fault diagnosis method for gearboxes, including:

[0064] Step S1: Obtain the actual vibration signal set of the gearbox to be diagnosed. The actual vibration signal set includes Q fault vibration signals and P non-fault vibration signals; where Q is the total number of fault vibration signals and P is the total number of non-fault vibration signals.

[0065] This invention assumes complex fault vibration signals It is composed of a linear superposition of a reference component, a component of interest, and scene information noise, and can be represented in the frequency domain as:

[0066] ,

[0067] In the formula, the reference component The stable background vibration in the system refers to the background vibration components that are stable during normal operation of the gearbox system. Specifically, these are inherent vibration signals such as the gear meshing frequency and its harmonics, and the fundamental frequency of shaft rotation under healthy conditions. These components do not disappear with the occurrence of faults or slight fluctuations in operating conditions. They are inherent vibration characteristics of the gearbox transmission system itself and can be accurately obtained by collecting non-fault vibration signals under healthy conditions of the gearbox, providing a stable reference for subsequent component separation.

[0068] Pay attention to ingredients The new vibration component introduced for specific events of the gearbox (mainly various gear faults, such as broken teeth, missing teeth, pitting, cracks, etc.) is the core feature component characterizing the type and degree of gear fault. This component only appears when the fault occurs, and its frequency domain characteristics are directly related to the fault type and fault location. It is also the feature component that needs to be extracted for fault diagnosis in this invention.

[0069] Scene information The missing information between the simulation signal and the measured signal caused by the background noise present during gearbox operation and the idealized modeling in the simulation process (such as ignoring complex factors such as environmental noise, installation gaps, component wear, and load fluctuations in actual working conditions) includes environmental electromagnetic interference, stray vibration caused by equipment installation errors, and random noise caused by poor lubrication. This component interferes with the extraction of fault features and is a key reason for the mismatch between traditional simulation fault signals and measured signals and low diagnostic accuracy. It is also the core content that needs to be separated and supplemented into the simulation signal in the subsequent process of this invention.

[0070] By structurally decomposing complex superimposed fault vibration signals, this method addresses the technical pain points of traditional techniques, such as the inability to accurately separate fault features (components of interest) from interference information (scene information) and the difficulty in compensating for differences between simulated and measured signals. This provides a clear theoretical foundation for subsequent precise separation of the three types of components and extraction of pure scene information through weighted normalized spectrum and model.

[0071] Step S2: Construct the Sum of Weighted Normalized Fourier Spectrum (SWNFS) model using the bias term and weight vector, where each element in the weight vector corresponds to a frequency point in the actual vibration signal;

[0072] The weighted normalized spectrum and model are as follows:

[0073] ,

[0074] in, For weighted normalized spectrum and model, For the weight vector, The term is the bias term, and NFS is the normalized Fourier amplitude spectrum.

[0075] Step S3: Based on the normalized Fourier amplitude spectrum of each actual vibration signal, solve for the optimal solution of the weighted normalized spectrum and the bias term and weight vector in the model;

[0076] In this embodiment, the process of obtaining the normalized Fourier amplitude spectrum of each actual vibration signal includes:

[0077] The Fourier amplitude spectrum is obtained by performing a Fast Fourier Transform (FFT) on each actual vibration signal. The Fourier amplitude spectrum is then normalized using the L1 norm to obtain the Normalized Fourier Spectrum (NFS), which eliminates the influence of differences in total signal energy and highlights differences in spectral shape. The calculation formula is as follows: ,in, is the Fourier amplitude spectrum, and NFS is the normalized Fourier amplitude spectrum.

[0078] In this embodiment, preferably, the method for solving the optimal solution of the weighted normalized spectrum and the bias term and weight vector in the model based on the normalized Fourier amplitude spectrum of each actual vibration signal includes:

[0079] Based on the normalized Fourier amplitude spectrum, weighted normalized spectrum, and model of each actual vibration signal, a maximum likelihood estimation objective function is constructed. The optimal solution for the bias term and weight vector is obtained by solving the weighted normalized spectrum and model.

[0080] The objective function for maximum likelihood estimation is:

[0081] ,

[0082] in, To estimate the objective function using maximum likelihood estimation, This represents the total number of non-fault vibration signals. The total number of fault vibration signals, , Indicates transpose. For the weight vector, For bias terms, For indexing actual vibration signals, For the first A sample label of an actual vibration signal, when When the vibration signal is not due to a fault, ,when When it is a fault vibration signal, , The regularization coefficient is . , For the first The normalized spectral vector after the expansion of an actual vibration signal. For the first Normalized Fourier amplitude spectrum of an actual vibration signal.

[0083] This invention finds the optimal solution for the weight vector, i.e., the optimal difference spectrum, by solving a convex optimization problem, where the frequencies corresponding to the positive, negative, and zero spectral lines respectively indicate the components of interest. Reference ingredients and scene information The frequency position.

[0084] In this embodiment, the maximum likelihood estimation objective function is solved by gradient descent to obtain the optimal difference spectrum, which can clearly indicate the frequency bands where different components are located.

[0085] Step S4: Determine the segmentation threshold for distinguishing between the components of interest, reference components and scene information based on the percentile of the amplitude of each element in the optimal solution of the weight vector. Classify each element in the weight vector, retain only the element values ​​belonging to scene information, and set the values ​​of the remaining elements to 0 to obtain the separated frequency domain scene information.

[0086] In this embodiment, preferably, the method for determining the segmentation threshold for distinguishing between the interest component, the reference component, and the scene information based on the percentile of the magnitude of each element in the optimal solution of the weight vector includes:

[0087] Sort the magnitudes of each element in the optimal solution of the weight vector in ascending order, and calculate the percentile of the magnitude of each element after ascending order. , , After sorting in ascending order, the first The percentile of the element's magnitude This represents the element index of the optimal solution for the weight vector after ascending order. For the length of the weight vector, construct the amplitude percentile point sequence (APPS).

[0088] The amplitude percentile sequence is divided into low amplitude region and high amplitude region;

[0089] For each region, each element within the current region is traversed as a candidate change point. The corresponding sequence of the current region is divided into a subsequence before the candidate change point and a subsequence after the candidate change point. The least squares method is used to fit a linear regression line to the two subsequences respectively. The fitting residuals of each subsequence are calculated and summed to obtain the total fitting error corresponding to the candidate change point. The candidate change point with the smallest total fitting error is selected as the optimal change point of the current region, and its corresponding magnitude is used as the segmentation threshold.

[0090] The segmentation thresholds for low-amplitude and high-amplitude regions are used as the segmentation thresholds to distinguish between the components of interest, the reference components, and the scene information.

[0091] The optimal change points in the low-amplitude and high-amplitude regions are respectively , Then the segmentation thresholds corresponding to the low-amplitude region and the high-amplitude region are respectively: , .

[0092] Let the candidate change points in the current region be The current region's corresponding sequence is divided into subsequences before the candidate change points. and the subsequence after the candidate change point ;in, The subsequence before the candidate change point The percentile of the element's magnitude The subsequence before the candidate change point The value of each element, The subsequence before the candidate change point One element, , This represents the total number of elements in the sequence corresponding to the current region. For the subsequence after the candidate change point The percentile of the element's magnitude For the subsequence after the candidate change point The value of each element, For the subsequence after the candidate change point One element, ;

[0093] The least squares method was used to fit linear regression lines to the two subsequences respectively.

[0094] ,

[0095] in, , The intercept and slope parameters are the corresponding linear regression lines fitted to the subsequences before the candidate change points. , The intercept and slope parameters are the parameters of the linear regression line fitted to the subsequences after the candidate change points.

[0096] The fitting residuals for each subsequence are calculated using the following formula:

[0097] ,

[0098] The total fitting error corresponding to the candidate change point is obtained by summing the results. The candidate change point that minimizes the total fitting error is taken as the optimal change point for the current region. , This is the optimal change point for the current region. The fitting residuals of the subsequences before the candidate change point. The fitting residuals of the subsequences after the candidate change points;

[0099] The optimal change point in the current region Corresponding amplitude Used as the segmentation threshold for the current region.

[0100] In this embodiment, the amplitude percentile sequence is divided into a low amplitude region and a high amplitude region. [0%,X%] is used as the low amplitude region and [(100−X)%,100%] is used as the high amplitude region. X is a set division threshold. In this embodiment, X=16.7.

[0101] This invention applies change point detection in regions with small and large amplitudes respectively to obtain two segmentation thresholds. The attribution of each frequency component is determined based on the segmentation thresholds, thereby accurately distinguishing positive and negative spectral lines from noise spectral lines.

[0102] In this embodiment, the method for classifying the elements in the weight vector specifically includes:

[0103] For each element in the weight vector, if the element value is less than the segmentation threshold of the low amplitude region, then the element belongs to the reference component; if the element value is greater than or equal to the segmentation threshold of the low amplitude region and less than or equal to the segmentation threshold of the high amplitude region, then the element belongs to the scene information; if the element value is greater than the segmentation threshold of the high amplitude region, then the element belongs to the interest component.

[0104] like Then determine its frequency. This is a component of concern. ,like Then determine its frequency. Reference component ,like Then determine its frequency. Belongs to scene information ,in, , These are the segmentation thresholds corresponding to the low-amplitude and high-amplitude regions, respectively. Represents the first weight in the weight vector. The element value of each element. The first in the weight vector Each element corresponds to a frequency. This is the index of an element in the weight vector.

[0105] Step S5: Convert the separated frequency domain scene information from the frequency domain to the time domain to obtain the time domain scene information signal;

[0106] In this embodiment, the method for converting the separated frequency domain scene information from the frequency domain to the time domain includes:

[0107] The separated frequency domain scene information is subjected to inverse fast Fourier transform to obtain the time domain scene information signal.

[0108] Step S6: Fuse the time-domain scene information signal with the simulated fault vibration signal to obtain the enhanced simulated fault signal;

[0109] The obtained scene information spectral components Perform Inverse Fast Fourier Transform (IFFT): Transmit time-domain scene information signals Superimposed on simulated fault vibration signal Above, generate enhanced simulation fault signals. , This is the fusion coefficient, used to adjust the fusion strength of scene information.

[0110] In this embodiment, specifically, the time-domain scene information signal is superimposed onto the simulated fault signal according to a set fusion coefficient to generate an enhanced simulated fault signal.

[0111] This invention, based on optimal difference spectrum analysis, extracts systematic scene information of the actual environment from real vibration signals. Through optimized modeling and change point detection of the normalized Fourier spectrum, it achieves precise separation and localization of reference components, components of interest, and scene noise. The extracted scene information is linearly fused with the simulation signal to generate a fully informative enhanced simulation signal. A conditional generative adversarial network (GAN) is constructed, introducing fused average rotational speed and key physical parameters of load as conditional vectors to guide the generator to focus on physical characteristics during simulation data correction. Through this two-stage collaborative mechanism, the differences between simulation and experimental data in statistical distribution and dynamic response are effectively reduced, ultimately generating high-fidelity enhanced simulation data.

[0112] like Figure 2 As shown, Figure 2 Modeling process for rigid-flexible coupling dynamics of gearbox;

[0113] In this embodiment, specifically, the process of acquiring the simulated fault vibration signal includes:

[0114] Based on the actual physical characteristics of the gearbox, and taking into account key influencing factors such as the periodic variation of meshing stiffness, tooth surface contact impact, and flexible linkage of components, a gearbox dynamic model (rigid-flexible coupled multibody dynamics simulation framework) is constructed. Typical working conditions and operating parameters are set to generate vibration signals of the gearbox under normal operating conditions that match the actual working conditions, providing a foundation for subsequent fault modeling. The gearbox dynamic model is used to accurately reproduce the vibration response characteristics of the gearbox under different working conditions and different fault states, providing core support for subsequent fault simulation and vibration sample generation.

[0115] Based on the gearbox dynamics model, various typical gear faults such as broken teeth, missing teeth, pitting, and cracks were set up. At the same time, multiple typical speed and load combinations were configured to simulate the impact of different fault types and different operating conditions on the vibration response of the gear transmission system. Finally, simulated vibration samples covering multiple fault types and multiple operating conditions were obtained.

[0116] The process of constructing the gearbox dynamics model includes:

[0117] Considering the periodic variation of gear meshing stiffness, tooth surface contact impact effect, and shaft system flexible deformation effect, a gearbox dynamic model consistent with actual working conditions is established.

[0118] For a gear meshing pair, its time-varying meshing stiffness function is defined as:

[0119] ,

[0120] in, Indicates average meshing stiffness. Indicates the magnitude of stiffness variation. Indicates the meshing frequency. Indicates the initial phase angle. Indicates time, The function representing the time-varying meshing stiffness of the gear pair characterizes the periodic fluctuations in stiffness caused by alternating single and double tooth meshing.

[0121] Based on the time-varying meshing stiffness function of the gear meshing pair, the excitation force vector generated by the time-varying meshing stiffness is obtained;

[0122] Based on the excitation force vector generated by time-varying meshing stiffness, the Newton-Euler equations, and Hertzian contact theory, the dynamic control equations of the gear transmission system are constructed as follows:

[0123] ,

[0124] In the formula, , , These are the system mass matrix, damping matrix, and stiffness matrix, respectively. It is a generalized displacement vector. The excitation force vector generated by the time-varying meshing stiffness. This represents the impact force vector at the tooth surface contact point. Indicates to Differentiate, Indicates to Find the derivative.

[0125] To further improve the simulation accuracy of the model and compensate for the deficiency of the basic rigid dynamic simulation model in failing to accurately reflect the flexible deformation of key components, and to achieve high-precision simulation of vibration data, a systematic rigid-flexible coupling modeling method is adopted to optimize the basic dynamic model. The core logic of this method is to accurately reproduce the structural dynamic characteristics of key components such as gears and shafts by introducing flexible bodies. The specific operation process is as follows: First, the gear shaft connection interface is defined as a rigid connection area and a remote point is set. The modal superposition method is used to solve the problem and generate an accurate gear flexible body model. Then, the motion constraints and contact definitions of the original rigid gear parts are removed, and the rigid parts are replaced with the generated flexible body model. Finally, a constraint system integrating the revolute joint and the high-fidelity rigid-flexible coupling contact relationship is re-established, completing the initial construction of the gearbox rigid-flexible coupling dynamic simulation model. This process is always based on the basic dynamic control equations established above, ensuring that the rigid-flexible coupling optimization does not deviate from the core dynamic laws.

[0126] To clarify the dynamic behavior of the flexible body, accurately describe its motion state during simulation, and further improve the dynamic characteristics of the rigid-flexible coupling model, the position vector of any node P on the flexible body in the global coordinate system is determined. The mathematical definition is as follows:

[0127] ,

[0128] In the formula, Let be the rotation transformation matrix from the local coordinate system to the inertial coordinate system. The vector representing the undeformed position of the node. Here is the node translation mode matrix. This is the modal coordinate vector.

[0129] Simultaneously, based on the Lagrange equation, the differential equation of motion for the flexible body is derived, clarifying the dynamic response law of the flexible body. This equation, together with the fundamental dynamic control equation of the gear transmission system constructed earlier, works synergistically to improve the dynamic modeling of the entire rigid-flexible coupling system, ensuring the accuracy and rationality of the model. Its expression is:

[0130] ,

[0131] In the formula, , , These are the modal mass matrix, damping matrix, and stiffness matrix, respectively. This is a nonlinear term in rigid-flexible coupling. It is a generalized force vector. For modal coordinate vectors, Indicates to Differentiate, Indicates to Find the derivative.

[0132] The rigid-flexible coupling dynamic simulation model is subjected to precise load and constraint application. The rigid-flexible coupling dynamic simulation model is used as the gearbox dynamic model to complete the final construction and calibration of the model, ensuring that the model can accurately simulate the actual operating state of the gearbox.

[0133] By applying input rotational speed and external load, a rigid-flexible coupling dynamic simulation model considering flexible response, meshing contact, and structural coupling characteristics is established. Tangential friction force is calculated using Coulomb's law, where the tangential contact force is proportional to the normal force. Tooth surface contact force is calculated using the impulse function method based on Hertz contact theory, balancing computational efficiency and accuracy by equating variable curvature contact to constant curvature contact at the meshing point.

[0134] Among them, normal contact force Solve using the penalty function method:

[0135] ,

[0136] In the formula, For normal contact force, Here is the Hertz contact stiffness coefficient. The normal penetration depth, Indicates to Differentiation, i.e., normal penetration rate, , For the maximum permissible penetration depth, for Corresponding damping value.

[0137] Gear tangential friction The expression is:

[0138] ,

[0139] in, The relative slip velocity of the gears. The coefficient of kinetic friction is . The static friction coefficient is The relative sliding velocity due to kinetic friction. The maximum static friction relative slip velocity, For smooth step functions, It represents the absolute value.

[0140] Through the above complete process, from considering core factors and defining key parameters (time-varying meshing stiffness), to integrating these parameters to construct basic dynamic control equations, and then to rigid-flexible coupling optimization, load constraint application, and contact parameter calibration, a high-precision gearbox dynamic simulation model considering flexible response, meshing contact, and structural coupling characteristics is finally constructed, providing reliable model support for the generation of subsequent simulated fault vibration signals.

[0141] Based on the gearbox dynamics model, typical gear faults such as broken teeth, missing teeth, cracks, wear, and pitting are set up, and multiple typical speed and load combinations are configured. The process of generating simulated vibration samples includes:

[0142] Five types of gear defect models were constructed based on actual fault conditions and incorporated into the established gearbox dynamics model.

[0143] like Figure 3 As shown, Figure 3 This is a schematic diagram of a gearbox simulation model with multiple fault types.

[0144] Tooth breakage faults simulate the failure state of partial tooth loss by generating a fracture surface perpendicular to the tooth width direction at the tooth root.

[0145] Missing tooth faults are caused by directly removing the geometry of a single complete tooth, resulting in an empty tooth groove structure with abrupt pitch changes.

[0146] Crack failure is addressed by setting through-type linear cracks in the stress concentration area at the tooth root, with the crack direction tangent to the tooth root arc.

[0147] Wear failure is simulated by correcting the involute equation in the working area (meshing segment) of the tooth surface and setting the wear compensation amount to simulate the progressive material loss of the tooth surface.

[0148] Pitting defects simulate surface fatigue spalling by generating hemispherical pit clusters at the pitch line of the tooth surface.

[0149] The operating condition settings cover a combination of two variables: speed and load. In this way, a total of multiple typical operating condition combinations are formed, which fully represent the spectrum of actual operating conditions.

[0150] In this embodiment, specifically, tooth breakage is simulated by generating a fracture surface perpendicular to the tooth width direction at the tooth root, with a fracture depth of 50% of the tooth height, to simulate the failure state of partial tooth loss; missing tooth is simulated by directly removing the geometry of a single complete tooth to form an empty tooth groove structure with abrupt tooth pitch; crack is simulated by setting 0.1mm wide through-type linear cracks in the stress concentration area at the tooth root, with the crack direction tangent to the tooth root arc; wear is simulated by correcting the involute equation in the working area (meshing segment) of the tooth surface and setting a wear compensation amount of 0.2mm to simulate progressive material loss on the tooth surface; pitting is simulated by generating a group of three hemispherical pits with a diameter of 1.0mm and a depth of 0.3mm at the pitch line of the tooth surface, with a pit spacing of 4mm, to simulate surface fatigue spalling.

[0151] The operating condition settings cover combinations of both speed and load. Specifically, the speed setting involves setting the input shaft to three speeds: 900 rpm, 1200 rpm, and 1500 rpm (corresponding to meshing frequencies of 300 Hz, 400 Hz, and 500 Hz, respectively). The load setting involves applying five torque levels to the output: 0 N•m, 20 N•m, 40 N•m, 60 N•m, 80 N•m, and 100 N•m (covering 20–100% of the rated load). This results in a total of 3 (speed) × 5 (load) = 15 typical operating condition combinations, comprehensively representing the spectrum of actual operating conditions.

[0152] Measurement points were set in the horizontal and vertical directions of the output shaft bearing housing, and vibration acceleration signals were acquired at a sampling frequency of 10240 Hz. For each fault type, 500 sets of samples were generated for each working condition (window of 2048 points, step size of 512 points). The experimental and simulated waveforms showed consistent periodicity of fault impact (such as impact interval and amplitude attenuation) within the same time window, and highly matched in characteristic spectrum and its sideband distribution, confirming that it can reproduce the time-frequency characteristics of fault impact with high fidelity. Finally, a high-fidelity simulation vibration sample library of five types of faults under fifteen working conditions was constructed.

[0153] Measurement points were set up in the horizontal and vertical directions of the gearbox. A large number of samples were generated for each fault type under each working condition. The experimental and simulated waveforms showed consistent periodicity of fault impact (such as impact interval and amplitude attenuation) within the same time window, and were highly consistent in the characteristic spectrum and its sideband distribution, which proved that it can reproduce the time-frequency characteristics of fault impact with high fidelity. Finally, a high-fidelity simulation vibration sample library under various working conditions for five types of faults was constructed.

[0154] In this embodiment, preferably, after obtaining the enhanced simulation fault signal, the enhanced simulation fault signal is optimized, including:

[0155] Using the operating parameters and prior fault information of the gearbox to be diagnosed, a condition vector is constructed;

[0156] A Conditional Generative Adversarial Network (cGAN) is constructed using a condition generator G and a condition discriminator D.

[0157] Enhance simulated fault signals Conditional vector The condition generator of the conditional generative adversarial network outputs a target-enhanced simulation fault signal through deterministic mapping. The formula is: .

[0158] In this embodiment, optionally, the operating parameter of the gearbox to be diagnosed is the average speed. Load information Fault prior information This includes fault characteristics such as defect frequency and corresponding amplitude, and constructing a condition vector. This conditional vector will serve as additional input to the conditional generative adversarial network to guide the generation and discrimination process.

[0159] The discriminator simultaneously receives data (actual vibration signal) Or target-enhanced simulation fault signal ) and its corresponding condition vector Determine whether the data conforms to the true distribution and is consistent with the conditions.

[0160] The discriminator's training objective is based on Wasserstein distance and includes a gradient penalty term to achieve stable training. Its loss function is:

[0161] ,

[0162] in, Let the loss function of the discriminator be , For expectation operator, Here is the gradient penalty function. These are random interpolation points between real and generated data. This indicates that the gradient is calculated with respect to the interpolation point. This represents the condition vector.

[0163] The generator's adversarial loss function is:

[0164] ,

[0165] in, Let be the loss function of the discriminator.

[0166] By alternately optimizing the discriminator and generator, this invention can output corrected simulation data that conforms to specific operating conditions and fault conditions, effectively reducing the difference between simulation data and experimental data.

[0167] To improve the usability and effectiveness of simulation data in real-world fault diagnosis tasks, this invention introduces conditional generative adversarial networks (GANs) to integrate domain knowledge, building upon traditional GANs. This conditional information, derived from operating parameters and fault attributes in the actual system, effectively constrains the generation process, ensuring that the generated signals not only closely approximate real data distributions but also maintain physical plausibility.

[0168] This invention extracts systematic scene information from actual vibration signals and integrates it into simulation signals, solving the problem of missing components in the simulation signals. The integrated enhanced signal, along with corresponding physical conditions (such as rotational speed), is input into a conditional generative adversarial network. The operating parameters and fault attributes of the actual system effectively constrain the generation process, further reducing the differences between the two in statistical characteristics and dynamic response. Through the collaborative work of these two stages, high-fidelity enhanced simulation data is finally generated that not only contains information about the actual environmental scene but also statistically closely approximates the real experimental signals.

[0169] like Figure 4 As shown, Figure 4 For the comparative analysis of simulated and measured vibration spectra, Figure 4 (a) in the figure is the time-domain plot of the acceleration data from the experimental vibration data. Figure 4(b) in the figure is the time-domain plot of the acceleration of the simulation data. Figure 4 (c) in the figure is the frequency domain plot of the experimental vibration data amplitude. Figure 4 (d) in the figure is the frequency domain plot of the simulation data amplitude.

[0170] Step S7: Use the enhanced simulation fault signal as training sample to train the gearbox fault diagnosis model; use the trained gearbox fault diagnosis model to perform fault diagnosis on the gearbox to be diagnosed.

[0171] In this embodiment, specifically, the gearbox fault diagnosis model is any one of the deep learning models composed of a convolutional neural network model, a residual neural network model, a Transformer coding network model, or a combination thereof.

[0172] In this embodiment, the gearbox fault diagnosis model specifically includes a feature extraction network and a classifier connected in sequence.

[0173] In this embodiment, preferably, the feature extraction network includes an input layer, a first depthwise separable convolutional block, a second depthwise separable convolutional block, a one-dimensional adaptive average pooling layer, a linear layer, a Permute function, a Transformer encoder, and a fully connected layer connected in sequence.

[0174] In this embodiment, a feature extraction network based on depthwise separable convolution and multi-head self-attention mechanism is constructed. The depthwise separable convolution layer is used to extract local features at multiple scales from the input vibration signal to efficiently capture transient impact components in the signal. The local feature sequence is then processed through the multi-head self-attention mechanism to model the long-range global dependencies and temporal correlations in the signal, thereby enhancing the representation of key fault features in complex vibration signals.

[0175] As shown in Table 1, Table 1 contains the network structure parameters of the feature extraction network.

[0176] Table 1

[0177]

[0178] Depthwise separable convolution consists of two steps: depthwise convolution and pointwise convolution. The depthwise convolutional layer performs convolution operations independently on each channel of the input vibration signal, extracts local temporal features within each channel, fuses multi-channel features, and adjusts the channel dimensions to achieve cross-channel information interaction.

[0179] Let the input signal of the depthwise separable convolution be... ( For timing length, (Number of channels) The input signal is passed through a depthwise convolution with depthwise separable convolution to output the first feature map. The first feature map is processed by point convolution with depthwise separable convolution, and the second feature map is output. The formula is: , The point convolution weight matrix is... This is a bias term.

[0180] Depthwise separable convolution reduces the number of parameters to that of traditional convolution. , The time-domain window size is set to reduce computational load while preserving feature extraction capabilities, making it suitable for fine-grained analysis of vibration signals.

[0181] This invention obtains the target second feature map by pooling and projecting the second feature map output from the second depthwise separable convolutional block. A multi-head self-attention mechanism is introduced to model global dependencies, enhancing sensitivity to fault impact features. Linear mapping to query matrix ( ), key matrix ( ) and value matrix ( ):

[0182] ,

[0183] in, For query matrix The linear mapping matrix, Key matrix The linear mapping matrix, Value matrix The linear mapping matrix.

[0184] We compute h attention heads in parallel (experimental optimization value h=4), and each head independently learns subspace features:

[0185] ,

[0186] in, For the output of the r-th attention head, Let r be the query matrix of the attention head. Let r be the key matrix of the attention head. Let h be the value matrix of the r-th attention head, where r is the index of the attention head and h is the total number of attention heads. Let be the dimension of the key matrix. This is a scaling factor used to prevent the softmax gradient from vanishing due to an excessively large dot product.

[0187] The outputs of h attention heads are concatenated and projected to obtain the output of the multi-head attention mechanism. The formula is: , For the projection matrix, As a multi-head attention mechanism, This indicates a splicing operation.

[0188] When components are in normal condition, the transmission process is usually smooth, and there are no obvious impact features in the vibration signal. At this time, most samples contribute relatively evenly to the model output. However, when a component malfunctions, obvious impact features appear in the vibration signal. In this case, the multi-head self-attention mechanism will focus more attention on these impact segments, thereby increasing the weight of impact features in the output result and improving the accuracy of fault detection.

[0189] In this embodiment, preferably, the classifier is an improved Softmax classifier. The loss function of the improved Softmax classifier is constructed based on the features extracted by the feature extraction network of the training samples and the learnable weight matrix of the fully connected layer, so as to enhance the model's ability to distinguish gearbox fault categories.

[0190] Traditional Softmax classifiers suffer from inherent drawbacks when handling mixed datasets, including excessive intra-class dispersion and insufficient inter-class separability. To fundamentally address this bottleneck, a decision boundary reconstruction strategy with dual hyperparameter constraints is introduced. This strategy explicitly compresses the feature distribution density of similar samples while expanding the feature margin distance of dissimilar samples. The core loss function of this classifier is defined as a high-order nonlinear expression:

[0191] The improved loss function for the Softmax classifier is:

[0192] ,

[0193] in, To improve the loss function of the Softmax classifier, The features extracted by the feature extraction network for the nth training sample. , The dimension of the features extracted by the feature extraction network. The total number of training samples, , This represents the total number of fault categories. Let n be the fault category label for the nth training sample. The learnable weight matrix of the fully connected layer. Fault category labels in the learnable weight matrix of the fully connected layer The corresponding column vector, For angle adjustment function, The features extracted by the feature extraction network for the nth training sample and The angle between the two points, and the inner product operation of the two points satisfy the following conditions. Differential geometric relations, Fault category labels in the learnable weight matrix of the fully connected layer For the corresponding column vector, The features extracted by the feature extraction network for the nth training sample and The included angle, is the fault category index, and n is the training sample index.

[0194] The angle adjustment function is expressed as:

[0195] ,

[0196] In the formula, , m are hyperparameters of the common control decision boundary. These are the parameters for the angle control function.

[0197] To accurately optimize the dual hyperparameters This invention integrates the tree-structured Parzen estimator (TPE) with an adaptive early stopping mechanism to form a Bayesian optimization framework, the specific process of which is as follows:

[0198] Define two hyperparameters (m, The search space is defined, and a historical observation set is constructed at each iteration. ,in, For the first The historical observation set of the next iteration For the first The parameter combination for the next iteration For the first The corresponding loss value for each iteration. This is the index for the number of iterations of the hyperparameter. For the first The hyperparameter m of the next iteration. For the first Hyperparameters of the next iteration .

[0199] Divide the historical observation set into optimal subsets With the worst subset Then, kernel density estimation models were established for the two subsets respectively:

[0200] ,

[0201] ,

[0202] in, For the kernel density estimation of the worst subset, For the kernel density estimation of the optimal subset, , These are the Gaussian kernel and the Epanechnikov kernel function, respectively. , This is the bandwidth parameter of the kernel function. These are the two hyperparameters to be evaluated.

[0203] The expected improvement criterion driving parameter is selected as follows: The median pruning algorithm is used to monitor the loss convergence in real time. If the following conditions are met... The current experiment is then terminated, as the hyperparameters have converged to their optimal values; among them, For the front The median benchmark of the loss in the next iteration, where `median` is the median benchmark and `IQR` is the discreteness metric. The interquartile range coefficient, in this embodiment, This optimization process achieves an order-of-magnitude improvement in search efficiency by executing multiple sets of experiments in parallel using an asynchronous distributed architecture. The final optimal dual hyperparameters are then substituted into the angle control function.

[0204] This invention introduces an improved Softmax classifier (T-Softmax) based on angular interval control into the classifier. By reconstructing the decision boundary in the angular space, it explicitly increases the feature interval between different fault categories, while compressing the feature distribution within the same fault category, effectively improving the model's class discrimination ability and generalization performance under complex feature distributions.

[0205] like Figure 5 As shown, Figure 5 This is a diagram of the transfer learning structure.

[0206] In this embodiment, preferably, the method for optimizing the gearbox fault diagnosis model after obtaining the trained gearbox fault diagnosis model includes:

[0207] For each fault category, the kernel density estimation method is used to calculate the class conditional probability of the fault category under the enhanced simulation fault signal set and the fault vibration signal set, respectively.

[0208] The enhanced simulation fault signal set and the actual fault vibration signal set are respectively extracted using a feature extractor to obtain the corresponding feature sets;

[0209] Using correlation alignment and maximum mean difference as metrics, the covariance distribution distance and mean distribution distance between the enhanced simulation fault signal feature set and the actual fault vibration signal feature set are calculated respectively.

[0210] Based on the covariance distribution distance, mean distribution distance, and class conditional probability of the fault category under the enhanced simulation fault signal feature set and the actual fault vibration signal feature set, an improved joint distribution adaptation loss function is constructed. The improved joint distribution adaptation loss function is then used to perform transfer learning on the gearbox fault diagnosis model to obtain the target gearbox fault diagnosis model.

[0211] To address the issue of distribution discrepancies between simulation and experimental data, the model synchronously aligns edge distributions and class conditional distributions, resolving the differences in domain distributions between simulation and experimental data, particularly the offset of conditional distributions under the same fault category. This significantly improves the model's adaptability in cross-domain diagnostic scenarios.

[0212] When adapting to conditional distributions (CDA), the joint distribution adaptation method often suffers from large approximation errors in its pseudo-label-based estimation process, making it difficult to effectively address complex conditional distribution shifts caused by model simplification and noise interference.

[0213] Using Bayes' theorem, the conditional probability distribution is transformed into a quasi-conditional probability distribution:

[0214] ,

[0215] in, By calculating kernel density, feature space clustering is optimized using source domain label information and target domain pseudo-labels. Adopting a domain-adaptive weighting strategy:

[0216] ,

[0217] In the formula, , These represent the fault categories. In enhancing the simulation of fault signal set (source domain), the total number of samples and fault categories are... The total number of samples in the set of fault vibration signals (target domain), , These represent the total number of samples in the enhanced simulation fault signal set and the fault vibration signal set, respectively.

[0218] Improved joint distribution adaptation Since the acquired gearbox vibration signal approximately follows a Gaussian distribution, the distribution difference is evaluated using Correlation Alignment (CORAL) and Maximum Mean Discrepancy (MMD).

[0219] RJDA combines Maximum Mean Difference (MMD) and Correlation Alignment (CORAL) to measure distribution distance. MMD aligns the first-order statistic (mean) in the Reproducing Kernel Hilbert Space (RKHS), and is defined as follows:

[0220] ,

[0221] In the formula, For the maximum mean difference, , These represent the total number of samples in the enhanced simulation fault signal set and the fault vibration signal set, respectively. For the source domain The feature vector of each sample Target domain The feature vector of each sample For mapping functions, Let be the norm in the RKHS space.

[0222] CORAL achieves distribution alignment by matching second-order covariance statistics, which are defined as follows:

[0223] ,

[0224] Wherein, the covariance matrix The standard calculation form is:

[0225] ,

[0226] The loss function expression for RJDA is:

[0227] ,

[0228] in, To improve the joint distribution adaptation loss function, For the maximum mean difference, The distance of the covariance distribution. To enhance the mean distribution distance between the simulated fault signal feature set and the actual fault vibration signal feature set, To enhance the covariance distribution distance between the simulated fault signal feature set and the actual fault vibration signal feature set, To balance the weighting coefficients, The result after feature extraction. For fault category index, Fault Category In the enhanced simulation fault signal set, the total number of samples, Fault Category In the total number of samples in the fault vibration signal set, This represents the total number of fault categories. For feature extractors, This is a set of actual fault vibration signal characteristics. To enhance the feature set of simulated fault signals.

[0229] An improved Refined Joint Distribution Adaptation (RJDA) mechanism is adopted to simultaneously align the marginal distribution and class-conditional distribution of the source domain composed of simulation data and the target domain composed of measured data. By introducing class-conditional distribution estimation based on Bayesian inference and an adaptive weighting strategy, more refined cross-domain distribution alignment is achieved, significantly reducing the distribution differences between domains and improving the adaptability and robustness of the diagnostic model in cross-domain scenarios.

[0230] This invention fuses enhanced simulated fault signals (finite element simulation samples) processed by transfer alignment with actual vibration signals (experimental measured samples) to construct a training dataset. This dataset is then input into a converged fault diagnosis network. A feature extractor, composed of depthwise separable convolutions and multi-head self-attention mechanisms, extracts features, and an improved classifier outputs the final gearbox fault category. By introducing an improved joint distribution adaptation mechanism to align the feature distributions of the source and target domains, inter-domain differences are reduced, thereby achieving high-precision classification and stable identification of various gearbox fault states.

[0231] To address the low accuracy of diagnosing actual measurement data using generated data, a series of gearbox fault diagnosis methods based on transfer learning have emerged in recent years. These methods attempt to achieve cross-domain knowledge transfer by aligning features between the source and target domains. However, most existing transfer strategies only align marginal or global features, neglecting conditional distribution differences and category discrimination information. This leads to unstable transfer effects and decreased diagnostic accuracy in practical applications, making it difficult to fully utilize the supplementary role of simulation data. Existing transfer learning methods fail to adequately address the issue of distribution differences between virtual and real data, affecting the accuracy and reliability of fault diagnosis. Therefore, it is urgent to construct a high-fidelity modeling mechanism with controllable structural complexity and design transfer strategies with fine-grained feature alignment capabilities to improve the fault diagnosis performance of gearboxes under small-sample imbalanced conditions.

[0232] refer to Figure 6 This second embodiment provides a small sample fault diagnosis system for gearboxes, including:

[0233] Signal acquisition module 10 is used to acquire the actual vibration signal set of the gearbox to be diagnosed. The actual vibration signal set includes multiple fault vibration signals and non-fault vibration signals.

[0234] Model building module 20 is used to construct a weighted normalized spectrum and model with bias terms and weight vectors, wherein each element in the weight vector corresponds to a frequency point in the actual vibration signal.

[0235] The solver module 30 is used to solve the weighted normalized spectrum and the optimal solution of the bias term and weight vector in the model based on the normalized Fourier amplitude spectrum of each actual vibration signal.

[0236] The scene information acquisition module 40 is used to determine the segmentation threshold that distinguishes the components of interest, reference components and scene information by using the percentile of the amplitude of each element in the optimal solution of the weight vector. It classifies each element in the weight vector, retains only the element values ​​belonging to the scene information, and sets the values ​​of the remaining elements to 0, so as to obtain the separated frequency domain scene information.

[0237] The conversion module 50 is used to convert the separated frequency domain scene information from the frequency domain to the time domain to obtain the time domain scene information signal;

[0238] The enhanced simulation module 60 is used to fuse the time-domain scene information signal with the simulated fault vibration signal to obtain the enhanced simulated fault signal.

[0239] The fault diagnosis module 70 is used to train the gearbox fault diagnosis model using enhanced simulation fault signals as training samples; and to perform fault diagnosis on the gearbox to be diagnosed using the trained gearbox fault diagnosis model.

[0240] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0241] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0242] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0243] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0244] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A method for diagnosing small-sample faults in gearboxes, characterized in that, include: Obtain the actual vibration signal set of the gearbox to be diagnosed. The actual vibration signal set includes multiple fault vibration signals and non-fault vibration signals. A weighted normalized spectrum model is constructed using a bias term and a weight vector, where each element in the weight vector corresponds to a frequency point in the actual vibration signal. Based on the normalized Fourier amplitude spectrum of each actual vibration signal, the optimal solution of the weighted normalized spectrum and the bias term and weight vector in the model is obtained. Using the percentile of the amplitude of each element in the optimal solution of the weight vector, the segmentation threshold for distinguishing the components of interest, the reference components, and the scene information is determined. Each element in the weight vector is then categorized, and only the element values ​​belonging to the scene information are retained, while the values ​​of the remaining elements are set to 0, thus obtaining the separated frequency domain scene information. The method for determining the segmentation threshold that distinguishes between the interest component, the reference component, and the scene information based on the percentile of the magnitude of each element in the optimal solution of the weight vector includes: Arrange the magnitudes of each element in the optimal solution of the weight vector in ascending order, calculate the percentile of the magnitude of each element after ascending order, and construct a percentile sequence of magnitudes. The amplitude percentile sequence is divided into low amplitude region and high amplitude region; For each region, each element within the current region is traversed as a candidate change point. The corresponding sequence of the current region is divided into a subsequence before the candidate change point and a subsequence after the candidate change point. The least squares method is used to fit a linear regression line to the two subsequences respectively. The fitting residuals of each subsequence are calculated and summed to obtain the total fitting error corresponding to the candidate change point. The candidate change point with the smallest total fitting error is selected as the optimal change point of the current region, and its corresponding magnitude is used as the segmentation threshold. The segmentation thresholds for low-amplitude and high-amplitude regions are used as the segmentation thresholds to distinguish between the components of interest, the reference components, and the scene information. Methods for classifying the elements in the weight vector include: For each element in the weight vector, if the element value is less than the segmentation threshold of the low amplitude region, then the element belongs to the reference component; if the element value is greater than or equal to the segmentation threshold of the low amplitude region and less than or equal to the segmentation threshold of the high amplitude region, then the element belongs to the scene information; if the element value is greater than the segmentation threshold of the high amplitude region, then the element belongs to the interest component. The separated frequency domain scene information is converted from the frequency domain to the time domain to obtain the time domain scene information signal; By fusing time-domain scene information signals with simulated fault vibration signals, an enhanced simulated fault signal is obtained; The gearbox fault diagnosis model is trained using enhanced simulated fault signals as training samples; the trained gearbox fault diagnosis model is then used to diagnose the faults in the gearbox to be diagnosed.

2. The method for diagnosing small-sample faults in a gearbox according to claim 1, characterized in that, The method for solving the weighted normalized spectrum and the optimal solution of the bias term and weight vector in the model based on the normalized Fourier amplitude spectrum of each actual vibration signal includes: Based on the normalized Fourier amplitude spectrum of each actual vibration signal, a maximum likelihood estimation objective function is constructed, and the optimal solution for the bias term and weight vector is obtained by solving the weighted normalized spectrum and the model. The objective function for maximum likelihood estimation is: ， in, To estimate the objective function using maximum likelihood estimation, This represents the total number of non-fault vibration signals. The total number of fault vibration signals, , Indicates transpose. For the weight vector, For bias terms, For indexing actual vibration signals, For the first A sample label of an actual vibration signal, when When the vibration signal is not due to a fault, ,when When it is a fault vibration signal, , The regularization coefficient is . , For the first The normalized spectral vector after the expansion of an actual vibration signal. For the first Normalized Fourier amplitude spectrum of an actual vibration signal.

3. The method for diagnosing small-sample faults in a gearbox according to claim 1, characterized in that, After obtaining the enhanced simulation fault signal, the enhanced simulation fault signal is optimized, including: Using the operating parameters and prior fault information of the gearbox to be diagnosed, a condition vector is constructed; A conditional generative adversarial network is constructed using a condition generator and a condition discriminator. The enhanced simulated fault signal and conditional vector are used to obtain the target enhanced simulated fault signal through the conditional generator of the conditional generative adversarial network.

4. The method for diagnosing small-sample faults in a gearbox according to claim 1, characterized in that, After obtaining the trained gearbox fault diagnosis model, methods for optimizing the gearbox fault diagnosis model include: For each fault category, the kernel density estimation method is used to calculate the class conditional probability of the fault category under the enhanced simulation fault signal set and the fault vibration signal set, respectively. The enhanced simulation fault signal set and the actual fault vibration signal set are respectively extracted using a feature extractor to obtain the corresponding feature sets; Using correlation alignment and maximum mean difference as metrics, the covariance distribution distance and mean distribution distance between the enhanced simulation fault signal feature set and the actual fault vibration signal feature set are calculated respectively. Based on the covariance distribution distance, mean distribution distance, and class conditional probability of the fault category under the enhanced simulation fault signal feature set and the actual fault vibration signal feature set, an improved joint distribution adaptation loss function is constructed. The improved joint distribution adaptation loss function is then used to perform transfer learning on the gearbox fault diagnosis model to obtain the target gearbox fault diagnosis model.

5. The method for diagnosing small-sample faults in a gearbox according to claim 4, characterized in that, The improved joint distribution adaptive loss function is: ， in, To improve the joint distribution adaptation loss function, For the maximum mean difference, The distance of the covariance distribution. To enhance the mean distribution distance between the simulated fault signal feature set and the actual fault vibration signal feature set, To enhance the covariance distribution distance between the simulated fault signal feature set and the actual fault vibration signal feature set, To balance the weighting coefficients, The result after feature extraction. For fault category index, Fault Category In the enhanced simulation fault signal set, the total number of samples, Fault Category In the total number of samples in the fault vibration signal set, This represents the total number of fault categories. This is a set of actual fault vibration signal characteristics. To enhance the feature set of simulated fault signals.

6. The method for diagnosing small-sample faults in a gearbox according to claim 1, characterized in that, The gearbox fault diagnosis model includes: a feature extraction network and a classifier connected in sequence.

7. A method for diagnosing small-sample faults in a gearbox according to claim 6, characterized in that, The classifier is an improved Softmax classifier, whose loss function is constructed based on the features of the training samples and the learnable weight matrix of the fully connected layers. The improved loss function for the Softmax classifier is: ， in, To improve the loss function of the Softmax classifier, The features extracted by the feature extraction network for the nth training sample. , The dimension of the features extracted by the feature extraction network. The total number of training samples, , This represents the total number of fault categories. Let n be the fault category label for the nth training sample. The learnable weight matrix of the fully connected layer. Fault category labels in the learnable weight matrix of the fully connected layer The corresponding column vector, For angle adjustment function, , , m are hyperparameters of the common control decision boundary. For the angle control function parameters, The features extracted by the feature extraction network for the nth training sample and The included angle, Here, n is the index for the fault category, and n is the index for the training samples. Fault category labels in the learnable weight matrix of the fully connected layer For the corresponding column vector, The features extracted by the feature extraction network for the nth training sample and The included angle.

8. A small-sample fault diagnosis system for gearboxes, characterized in that, include: The signal acquisition module is used to acquire the actual vibration signal set of the gearbox to be diagnosed. The actual vibration signal set includes multiple fault vibration signals and non-fault vibration signals. The model building module is used to construct a weighted normalized spectrum and model with bias terms and weight vectors, where each element in the weight vector corresponds to a frequency point in the actual vibration signal. The solution module is used to solve for the weighted normalized spectrum and the optimal solution of the bias term and weight vector in the model based on the normalized Fourier amplitude spectrum of each actual vibration signal. The scene information acquisition module is used to determine the segmentation threshold that distinguishes the components of interest, reference components and scene information by using the percentile of the amplitude of each element in the optimal solution of the weight vector. It classifies each element in the weight vector, retains only the element values ​​belonging to the scene information, and sets the values ​​of the rest to 0, thus obtaining the separated frequency domain scene information. The method for determining the segmentation threshold to distinguish between the interest component, the reference component, and the scene information based on the percentile of the magnitude of each element in the optimal solution of the weight vector includes: Arrange the magnitudes of each element in the optimal solution of the weight vector in ascending order, calculate the percentile of the magnitude of each element after ascending order, and construct a percentile sequence of magnitudes. The amplitude percentile sequence is divided into low amplitude region and high amplitude region; For each region, each element within the current region is traversed as a candidate change point. The corresponding sequence of the current region is divided into a subsequence before the candidate change point and a subsequence after the candidate change point. The least squares method is used to fit a linear regression line to the two subsequences respectively. The fitting residuals of each subsequence are calculated and summed to obtain the total fitting error corresponding to the candidate change point. The candidate change point with the smallest total fitting error is selected as the optimal change point of the current region, and its corresponding magnitude is used as the segmentation threshold. The segmentation thresholds for low-amplitude and high-amplitude regions are used as the segmentation thresholds to distinguish between the components of interest, the reference components, and the scene information. Methods for classifying the elements in the weight vector include: For each element in the weight vector, if the element value is less than the segmentation threshold of the low amplitude region, then the element belongs to the reference component; if the element value is greater than or equal to the segmentation threshold of the low amplitude region and less than or equal to the segmentation threshold of the high amplitude region, then the element belongs to the scene information; if the element value is greater than the segmentation threshold of the high amplitude region, then the element belongs to the interest component. The conversion module is used to convert the separated frequency domain scene information from the frequency domain to the time domain to obtain the time domain scene information signal; The enhanced simulation module is used to fuse time-domain scene information signals with simulated fault vibration signals to obtain enhanced simulated fault signals. The fault diagnosis module is used to train the gearbox fault diagnosis model using enhanced simulated fault signals as training samples; and to perform fault diagnosis on the gearbox to be diagnosed using the trained gearbox fault diagnosis model.

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