Bearing imbalance sample fault diagnosis method based on dynamic modeling and causal interpretable GAN

Abstract

The invention relates to a bearing unbalanced sample fault diagnosis method based on dynamic modeling and a causal interpretable GAN, and belongs to the technical field of mechanical intelligent detection. Aiming at the problems of low model diagnosis precision caused by data imbalance in the prior art and deficient physical significance and poor interpretability of existing GAN network generation samples, the invention provides a technical scheme of fusing dynamic modeling and an interpretable generative adversarial network. The method comprises the following steps: generating a fault response signal with physical significance through a two-degree-of-freedom dynamic model; constructing a GabcauACGAN network, combining a causal loss function to restrain the relevance between the generated features and fault tags, and extracting time-frequency features by adopting a learnable Gabor filtering layer. The method has the technical effects that the time-frequency similarity SSIM of a generated fault sample and a real signal reaches 99%, and the diagnosis accuracy is improved to 98% or above.

Description

Technical Field

[0001] The present invention belongs to the technical field of mechanical intelligent detection, and relates to a bearing imbalance sample fault diagnosis method based on dynamic modeling and causally interpretable GAN. Background Art

[0002] Bearings are key components of industrial equipment, and their performance directly affects the operating efficiency and reliability of machinery. With the continuous improvement of the complexity of production systems and the diversity of equipment operating environments, the importance of intelligent diagnosis technology in bearing fault diagnosis has increased significantly. By integrating big data analysis and deep learning, intelligent diagnosis can continuously monitor the health status of bearings and automatically analyze potential fault patterns. Therefore, bearing intelligent diagnosis can not only improve the reliability and safety of equipment, but also play an important role in improving productivity and optimizing maintenance strategies, and is an important part of modern intelligent manufacturing and Industry 4.0.

[0003] In practical applications, mechanical equipment usually operates in a safe and stable state, so there are few fault samples. In addition, in some environments, collecting fault data may be challenging, resulting in a generally imbalanced fault dataset. This data imbalance causes the model to tend to learn the characteristics of normal samples during training, thus ignoring the characteristics of fault samples. Therefore, the sensitivity and diagnostic accuracy of fault detection will be greatly reduced. Therefore, solving the data imbalance problem is crucial for improving the reliability and accuracy of intelligent diagnosis systems.

[0004] Dynamic models and data-driven generative models are two effective methods for solving data imbalance. Dynamic modeling provides a physics-based method for generating fault data, ensuring that the generated data is consistent with physical properties. However, obtaining dynamic responses is time-consuming and requires a large amount of computing resources. In addition, due to physical parameter errors and model simplification, this method often leads to a significant gap between dynamic responses and measured signals. Data-driven generative models can generate high-quality samples through end-to-end learning of a large amount of labeled data. Common generative models include adversarial autoencoders (AAEs), diffusion models, and generative adversarial networks (GANs). GANs can learn more subtle features through the adversarial training process, thus generating more intuitive and realistic samples.

[0005] GAN has many variants, and the most common ones include Deep Convolutional GAN (DCGAN), Cycle-Consistent GAN (CycleGAN), Wasserstein GAN with Gradient Penalty (WGAN-GP), and Auxiliary Classifier GAN (ACGAN), etc. ACGAN generates samples with specific categories by combining an auxiliary classifier and conditional information, so it is particularly suitable for tasks that require explicit classification of the generated samples. Common bearing fault types include inner race faults, outer race faults, and rolling element faults, and each type has different characteristics and performances. In the generation of bearing fault samples, ACGAN can generate corresponding fault samples by inputting different fault type labels. However, as the number of categories increases and the complexity of label injection improves, the ACGAN generator needs to learn more complex mapping relationships to generate distinguishable cross-category samples. In other words, the relationship between the sample content and the category label may become unclear, thus reducing the usability and accuracy of the generated samples.

[0006] The causal mechanism refers to effectively decoupling the different parts in the system through causal relationship analysis to ensure that each variable is only affected by specific causal factors. Inspired by this, a causal mechanism is introduced into the ACGAN network. By designing the objective function, it helps the generator more clearly distinguish the input category label and the generated sample features, thus avoiding the model from generating confounding and hard-to-understand samples.

[0007] In addition, all of the above data-driven generative models rely on the statistical properties of the input data for generation, unlike dynamic models based on physical laws or dynamic equations, and the generated samples lack a physical basis. Moreover, the generative model usually consists of a series of convolutional layers. Due to the black-box nature of the convolutional network, the generated samples often lack interpretability. ACGAN also has these problems. In recent years, many experts and scholars have conducted a large number of studies to improve the interpretability of convolutional networks. For example, Li et al. incorporated wavelet transform theory into the Convolutional Neural Network (CNN), designed a wavelet convolutional layer as the first layer of the network to improve the interpretability of the network. Liu et al. designed a wavelet filter layer to extract features with unique physical meanings. Li et al. proposed an interpretable wavelet packet kernel-constrained convolutional network, which combines the feature extraction ability of wavelet bases and the learning ability of convolutional kernels for fault diagnosis.

[0008] To generate high-quality samples with clear physical meaning and interpretability, it is proposed to first use a dynamic model to generate dynamic responses with actual physical meaning, and then design an interpretable mapping generation network GabcauACGAN to bridge the gap between the dynamic response and the actual measured signal. Specifically, a Gabor filter layer that can capture multi-scale and multi-directional features is designed to enhance the interpretability of the mapping network. In addition, a subjective function based on causal mechanism is designed to effectively strengthen the relationship between causal features and class labels, thereby further improving the quality of the generated samples. At the same time, the integration of the causal mechanism also enhances the interpretability of the ACGAN network. This method not only improves the quality of the generated samples, but also provides deeper physical and interpretable insights, meeting the requirements of high-quality analog signal generation. The main innovations and contributions of the present invention are as follows:

[0009] (1) A novel data generation method is proposed for bearing fault diagnosis under data imbalance. High-quality sample generation is achieved through dynamic modeling and the interpretable mapping network GabcauACGAN.

[0010] (2) A causal mechanism is introduced into the mapping network to construct a causal decoupling objective function to more accurately generate signals related to specific fault types.

[0011] (3) A Gabor filter layer is designed to capture multi-scale and multi-directional features, enhance the interpretability of the ACGAN network, and thus generate credible samples. Summary of the Invention

[0012] In view of this, the purpose of the present invention is to provide a bearing imbalance sample fault diagnosis based on dynamic modeling and causally interpretable GAN.

[0013] To achieve the above object, the present invention provides the following technical solutions:

[0014] A bearing imbalance sample fault diagnosis method based on dynamic modeling and causally interpretable GAN, comprising the following steps:

[0015] S1: Analyze the physical structure parameters of the target bearing, establish a two-degree-of-freedom dynamic model of the rolling bearing, and solve the model by the Runge-Kutta method to obtain the dynamic simulation signal of the bearing fault;

[0016] S2: Respectively transform the dynamic simulation signal and the actual measured signal into time-frequency spectrograms through continuous wavelet transform and process them into grayscale images;

[0017] S3: Construct a GabcauACGAN mapping network, including:

[0018] The generator network, whose first layer is a learnable multi-scale Gabor filter layer, two convolutional layers, and two upsampling convolutional layers, is used to capture time-frequency features;

[0019] The discriminator network, which includes three convolutional layers and an auxiliary classifier to predict the sample class;

[0020] The objective function integrates a causal mechanism to constrain the causal feature similarity between the generated samples and the real samples through a correlation matrix;

[0021] S4: Input the grayscale images of the dynamic simulation signals and the measured signal grayscale images into GabcauACGAN for training to generate enhanced data corresponding to the fault type labels;

[0022] S5: Evaluate the quality of the generated samples through MMD and SSIM, and add the enhanced data to the imbalanced dataset for training the fault diagnosis model.

[0023] Furthermore, the dynamic modeling specifically includes:

[0024] Based on a two-degree-of-freedom dynamic model, the dynamic response is solved by the fourth-order Runge-Kutta algorithm, where:

[0025] The maximum displacement excitation ΔH caused by a local fault is calculated by the following formula:

[0026]

[0027] ΔH′ = 0.5D - ((0.5D) 2 - (0.5min(L, B)) 2 ) 0.5

[0028] where L, B, and H respectively represent the length, width, and height of the fault size; D is the diameter of the rolling element;

[0029] The contact deformation δ j is calculated by the following formula:

[0030] δ j = δ x cosθ j + δ y sinθ j - ε - h j

[0031] where δ x and δ y respectively represent the vibration displacements of the rolling bearing in the X and Y directions, and ε is the tolerance of the bearing;

[0032] The two-degree-of-freedom dynamic equation is expressed by the following formula:

[0033]

[0034] where m represents the bearing mass; K represents the equivalent stiffness of the bearing; c represents the equivalent damping coefficient of the bearing; μ j is the judgment coefficient of the j-th rolling element in the contact area.

[0035] Furthermore, the parameters of the Gabor filter layer are set as follows:

[0036]

[0037] where λ represents the wavelength, controlling the spatial period of the filter; θ determines the direction of the filter; σ is the standard deviation, controlling the spatial width of the Gabor filter; ψ controls the waveform of the filter; λ is the aspect ratio; a and b are the coordinates in the two-dimensional space where the Gabor filter is located; the wavelength λ and the standard deviation σ are learnable parameters; the direction θ is fixed at 90° to match the time-frequency characteristic distribution of bearing faults.

[0038] Furthermore, the objective function of the causal mechanism includes the following steps:

[0039] Construct a correlation matrix CM of the features of the generated samples and the real samples, defined as follows:

[0040]

[0041] In the formula: <·> represents the inner product operation; N represents the number of sample features; and respectively represent the feature matrices M extracted from the generated samples and the measured samples o and M a The Z-score normalization value of the i-th column;

[0042] Calculate the causal loss term through the following formula, constraining CM to approach the identity matrix:

[0043]

[0044] where I is the identity matrix.

[0045] Furthermore, the loss function of the generator is:

[0046]

[0047] where, is the true / false loss, is the classification loss, and λ is the weight coefficient.

[0048] Furthermore, the loss function of the discriminator is:

[0049]

[0050] Among them, is the true - false loss, is the classification loss.

[0051] Furthermore, the sample quality assessment includes:

[0052] Using the Maximum Mean Discrepancy (MMD) to measure the distribution difference between the generated data and the real data;

[0053] Using the Structural Similarity Index (SSIM) to evaluate the consistency of the time - frequency features between the generated image and the real image.

[0054] Furthermore, the specific content of S5 is as follows: adding the enhanced data to the imbalanced dataset according to a preset ratio, inputting it into the ResNet - 18 network for fault diagnosis, and verifying the enhancement effect through the diagnostic accuracy rate.

[0055] The beneficial effects of the present invention are as follows:

[0056] (1) Dynamically model to generate fault response signals with clear physical meanings, providing a physical basis for data enhancement;

[0057] GabcauACGAN maps the dynamic response to a high - fidelity measurement signal through adversarial training. The generated samples are highly consistent with the real signals in time - frequency features (SSIM reaches 99%), effectively making up for the scarcity of fault samples, alleviating the model bias problem caused by data imbalance, and the fault diagnosis accuracy rate is improved to more than 98% under the 1:1 imbalance ratio.

[0058] (2) The dynamic model simulates the fault mechanism based on the two - degree - of - freedom dynamics equation, and the generated signals contain the physical characteristics of real bearing faults; the Gabor filtering layer captures multi - scale and multi - direction time - frequency features. The generated samples not only conform to physical laws (such as the matching of envelope spectrum characteristic frequencies), but also have the statistical characteristics of actual measurement signals, avoiding the physical distortion problem caused by pure data - driven in traditional generation models.

[0059] (3) Construct a causal loss function through the correlation matrix to constrain the alignment of causal features between the generated samples and the real samples. The correlation between the fault - related features (such as the impact components of inner - ring / outer - ring faults) in the generated samples and the labels is significantly enhanced, avoiding the feature mixing problem of ACGAN in multi - class scenarios and improving the credibility of fault classification.

[0060] (4) The first layer of the generator uses a Gabor filter with learnable parameters, and the direction is fixed at 90° to match the time - frequency energy distribution of bearing faults. The feature map output by the Gabor layer directly reflects the time - frequency position of fault impacts, has a clear physical meaning compared with the traditional convolutional layer, improves the interpretability of the model decision - making process, and meets the credibility requirements of industrial diagnosis scenarios.

[0061] (5) The kinetic model generates multi - condition simulation signals by adjusting physical parameters (rotation speed, load); GabcauACGAN maps the dynamic response to different measurement conditions through mapping learning. In the CWRU and RTS bearing datasets, the generated samples maintain high fidelity at various rotation speeds (1750 - 3000 RPM) and loads (0 - 2 HP), supporting fault diagnosis tasks under unbalanced samples.

[0062] (6) Kinetic modeling only requires a small number of physical parameters to generate initial signals, avoiding the high computational cost of traditional dynamic methods; GabcauACGAN reduces the dependence on large - scale labeled data through end - to - end mapping. On the premise of ensuring the generation quality, the training time is reduced by more than 50% compared with pure dynamic modeling, which is suitable for industrial real - time diagnosis scenarios.

[0063] Other advantages, objectives, and features of the present invention will, to some extent, be described in the subsequent specification, and to some extent, will be obvious to those skilled in the art based on the study of the following text, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be achieved and obtained through the following specification. Brief Description of the Drawings

[0064] In order to make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be described in detail preferably with reference to the accompanying drawings, where:

[0065] Figure 1 is the overall framework diagram of the present invention;

[0066] Figure 2 are samples of three fault types under condition 1 generated by different generation models; Figure 2 (a) is the measured sample; Figure 2 (b) is the dynamic response; Figure 2 (c) is the AAE; Figure 2 (d) is the WGAN - GP; Figure 2 (e) is the DCGAN; Figure 2 (f) is the CauACGAN; Figure 2 (g) is the CabACGAN; Figure 2 (h) is Ours;

[0067] Figure 3 is the unbalanced fault diagnosis result in Case 1;

[0068] Figure 4 is the JDIRTS test bench;

[0069] Figure 5 are samples of three fault types under condition 1 generated by different generation models; Figure 5(a) is the measurement sample; Figure 5 (b) is the dynamic response; Figure 5 (c) is the AAE; Figure 5 (d) is the WGAN-GP; Figure 5 (e) is the DCGAN; Figure 5 (f) is the CauACGAN; Figure 5 (g) is the CabACGAN; Figure 5 (h) is Ours.

[0070] Figure 6 It is the unbalanced fault diagnosis result in Case 2;

[0071] Figure 7 It is the feature output of the interpretable filter layer and the convolutional layer for the outer raceway fault; Figure 7 (a) is the original signal; Figure 7 (b) is the output of the Gabor filter layer; Figure 7 (c) is the sample generated by the proposed method; Figure 7 (d) is the output of the convolutional layer; Figure 7 (e) is the sample generated by the DCGAN.

[0072] Figure 8 It is the feature output of the interpretable filter layer and the convolutional layer for the inner raceway fault; Figure 8 (a) is the original signal; Figure 8 (b) is the output of the Gabor filter layer; Figure 8 (c) is the sample generated by the proposed method; Figure 8 (d) is the output of the convolutional layer; Figure 8 (e) is the sample generated by the DCGAN. Specific implementation manner

[0073] The following illustrates the implementation manners of the present invention through specific specific examples. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific implementation manners. Various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the diagrams provided in the following embodiments only illustrate the basic concept of the present invention schematically. Without conflict, the following embodiments and the features in the embodiments can be combined with each other.

[0074] Among them, the attached drawings are only for illustrative purposes, showing only schematic diagrams rather than physical diagrams, and should not be construed as a limitation to the present invention; to better illustrate the embodiments of the present invention, some components in the attached drawings will be omitted, enlarged or reduced, which do not represent the dimensions of the actual product; for those skilled in the art, it is understandable that some well-known structures and their descriptions in the attached drawings may be omitted.

[0075] In the attached drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components; in the description of the present invention, it should be understood that if there are terms such as "upper", "lower", "left", "right", "front", "rear", etc. indicating the orientation or positional relationship, they are based on the orientation or positional relationship shown in the attached drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, the terms describing the positional relationship in the attached drawings are only for illustrative purposes and should not be construed as a limitation to the present invention. For those of ordinary skill in the art, the specific meanings of the above terms can be understood according to specific circumstances.

[0076] I. Theoretical basis

[0077] (1) ACGAN

[0078] Auxiliary Classifier Generative Adversarial Network (ACGAN) is an enhanced model based on GAN, aiming to improve the generation of traditional GAN. Different from traditional GAN, ACGAN enables the generator to control the category of samples during the generation process by introducing category labels. At the same time, it also adds an auxiliary classifier, which is not only used to identify the authenticity of images but also to predict the category of images. In this way, ACGAN can generate multiple types of data simultaneously, making ACGAN more efficient and flexible in multi-category data generation tasks.

[0079] (2) Causal mechanism

[0080] Causal mechanism, causal factors, and non-causal factors are three closely related concepts, which together form the basis of system behavior. The causal mechanism essentially describes the process by which causal factors affect the system result through a certain path. Causal factors determine the core behavior and change law of the system and are the "core" driving force for promoting system behavior change. Non-causal factors refer to factors that are related to system changes but do not directly cause system changes. In complex systems, the observed signals are usually the result of the superposition and co-action of causal factors (such as fault characteristics, the actual working state of the system, etc.) and non-causal factors (such as noise, working conditions, environmental changes, etc.). In fault diagnosis, extracting causal features can more accurately identify and locate the root cause of system faults, thereby improving the accuracy of fault diagnosis.

[0081] (3) Proposed method

[0082] A novel data augmentation method is introduced. In addition, the integration strategy of the mapping network and the Gabor layer and the causal embedding mechanism are also introduced. At the same time, the method for evaluating the quality of the generated samples is also described. The overall framework of the proposed method is as shown in Figure 1 Figure

[0083] 1) Analyze the structural parameters of the physical model, establish the dynamic model, and generate dynamic simulation signals with physical significance. Since the time-frequency spectrogram contains rich time-domain and frequency-domain features of the vibration signal, the continuous wavelet transform (CWT) is used to convert the time-domain signal into a time-frequency spectrogram. Finally, the color time-frequency spectrogram is converted into a grayscale image for mapping.

[0084] 2) Process the unbalanced measurement signal into a grayscale image in the same way. Then, the measurement signal and the analog signal to be mapped are input into the constructed GabcauACGAN for training. The fault type label of the data that needs to be augmented is input into the trained Caucabor-ACGAN for data augmentation.

[0085] 3) Evaluate the quality of the augmented data to ensure its reliability.

[0086] 4) Gradually integrate the augmented data into the unbalanced samples, and data with different augmentation ratios are fed into ResNet-18 for fault diagnosis.

[0087] (4) Dynamic modeling and dynamic response acquisition

[0088] Based on the two-degree-of-freedom dynamic model, the dynamic simulation signal in the present invention is obtained by solving with the fourth-order Runge-Kutta algorithm. The maximum displacement excitation ΔH caused by local faults during the modeling process has the following expression:

[0089]

[0090] ΔH′ = 0.5D - ((0.5D) 2 - (0.5min(L, B)) 2 ) 0.5

[0091] where L, B, and H respectively represent the length, width, and height of the fault size; D is the diameter of the rolling element.

[0092] To represent the influence of local faults on the bearing vibration response, a half-sine displacement excitation function is adopted, and its expression is as follows:

[0093]

[0094] where represents the angle between the rolling element and the X-axis when it enters the fault area, Denotes the angle between the rolling element and the X-axis when leaving the fault area, θ j Denotes the angular position of the j-th rolling element.

[0095] Among them, the expression of contact deformation is:

[0096] δ j =δ x cosθ j +δ y sinθ j -ε - h j (3)

[0097] Among them, δ x and δ y respectively represent the vibration displacements of the rolling bearing in the X and Y directions, and ε is the tolerance of the bearing.

[0098] Finally, the two-degree-of-freedom dynamic equation of the rolling bearing is:

[0099]

[0100] Among them, m represents the bearing mass; K represents the equivalent stiffness of the bearing; c represents the equivalent damping coefficient of the bearing; μ j is the judgment coefficient of the j-th rolling element in the contact area.

[0101] (5) Gabcauor ACGAN with Gabor filter layer

[0102] Designed an interpretable GabcauACGAN for mapping dynamic responses to measurement signals. First, a multi-scale, multi-directional Gabor layer was constructed as the first layer of the CauGabor-ACGAN network generator. The Gabor filter is expressed as:

[0103]

[0104] Among them, λ represents the wavelength, controlling the spatial period of the filter; θ determines the direction of the filter; σ is the standard deviation, controlling the spatial width of the Gabor filter; ψ controls the waveform of the filter; λ is the aspect ratio. a and b are the coordinates in the two-dimensional space where the Gabor filter is located. a' and b' are described as follows:

[0105]

[0106] Since the parameters λ and σ determine the shape of the Gabor filter, these two parameters are set as learnable parameters to adaptively capture features of different frequencies. It can be seen from the time-frequency diagram that the bearing fault features mainly appear at 90°. Therefore, θ is set to 90°; on this basis, the design of the Gabor filter layer is as follows:

[0107] O = G(λ, σ) * x (7)

[0108] where x is the input sample. During the BP process, the Gabor filter layer only needs to update the parameters λ and σ, and during the BP process, the Gabor filter layer only needs to update the parameters λ and σ.

[0109] The backpropagation process can be defined as

[0110]

[0111] Then, the parameters λ and σ can be obtained as follows:

[0112]

[0113] Therefore, the Gabor filter layer can capture multi-scale and multi-directional features, making the generated samples more detailed and realistic. In the early stage of network training, the Gabor filter layer can effectively capture the time-frequency features of the input analog signal. During the continuous adversarial learning process of the generator and discriminator, the Gabor filter layer can also effectively capture the features of the real measurement signal, thereby improving the effectiveness of the mapping network

[0114] (6) Design of the objective function based on causality

[0115] The function of the target ACGAN network is crucial for its performance. It prompts the generator to generate high-quality samples while ensuring that these samples have the correct class labels. For the discriminator, the objective function can not only enable the discriminator to determine the authenticity of the samples but also predict the class labels of the images. In terms of sample expansion for fault diagnosis, the generated samples preferably contain the basic causal features for determining the fault type. Because fault diagnosis based on deep learning is basically achieved according to fault features. To make the generated samples have basic causal features and at the same time alleviate the problem of unclear relationship between samples and labels that may exist when the ACGAN generator generates multiple fault types, a causal loss function term L is constructed cm .

[0116] The basic idea of the causal mechanism is to decouple or distinguish features by maximizing the correlation between features in the same dimension while minimizing the correlation between features in different dimensions. To achieve the above goal, first, a correlation matrix CM needs to be constructed i,j as follows:

[0117]

[0118] In the formula: <·> represents the inner product operation; N represents the number of sample features; and respectively represent the feature matrices M extracted from the generated samples and the measured samples o and M a The Z-score normalization value of the i-th column. When the generated samples and the measured samples belong to the same type of fault, CM i,j should be as large as possible. Therefore, can be described as:

[0119]

[0120] where I is the identity matrix. To enable the generator to have the ability to correctly classify and generate real images, true-false loss and classification loss are introduced in the generator and are described as follows:

[0121]

[0122] Finally, the loss function of the generator is described as:

[0123]

[0124] where λ takes 0.4; this method of constructing the generator loss function can effectively reduce the ACGAN feature overlap, help the generator generate high-quality samples with causal features and perform correct classification.

[0125] The discriminator 's loss function also includes true-false and classification loss

[0126]

[0127] Finally, 's loss function is described as:

[0128]

[0129] (7) Quality criteria for sample generation

[0130] To measure the quality of the generated samples and the characteristics of the proposed A model, the maximum mean discrepancy (MMD), the structural similarity index (SSIM), and the diagnostic accuracy when the generated signal is used as a fault sample are adopted.

[0131] MMD is a powerful indicator for evaluating the similarity of the distributions of two sets of data. By calculating the mean difference in the feature space, the distribution difference between the generated data and the real data can be effectively evaluated. The smaller the MMD, the higher the quality of the generated samples. The mathematical expression is as follows

[0132]

[0133] Among them, n and m are the numbers of the two data sets X and Y respectively; x i and x j are samples in the two data sets X and Y respectively; k() represents the kernel function, which is used to calculate the similarity between two samples, and the Gaussian kernel function is adopted.

[0134] In addition, SSIM is used to evaluate the quality of the generated images. It is a metric that aims to measure the similarity between images by simultaneously considering changes in luminance, contrast, and structure. SSIM is widely used to evaluate image generation tasks. Its mathematical expression is as follows

[0135]

[0136] where μ x and μ y are the average luminances of the pictures x and y respectively; and are the luminance variances of x and y, and σ x,y is their covariance; C1 and C2 are constants used to prevent division by zero in the denominator. It should be noted that the SSIM value ranges from -1 to 1, and the closer the value is to 1, the higher the similarity between the two images.

[0137] Finally, the generated samples are added to a series of data imbalance scenarios to verify the impact of data augmentation on the accuracy of fault diagnosis, and also indirectly illustrate the quality of the generated samples. It should be noted that the test samples do not participate in the model training.

[0138] (8) Experiments and result analysis

[0139] To verify the effectiveness and superiority of the proposed method, sufficient comparative and ablation experiments were carried out. The experiments used a group of CWRU data sets and a group of self-made rolling bearing data sets.

[0140] Case 1: CWRU data set

[0141] 1) Data set description: The CWRU data set is a standard data set widely used for rolling bearing fault diagnosis. The test bench consists of a two-phase motor, a torsional sensor / encoder, a power meter, and a control electronic unit. In this example, the data with a fault size of 7 mils at the drive end was used, and the signal sampling frequency was 12 kHz. The detailed data description is shown in Table 1.

[0142] Table 1 Detailed data

[0143] Motor load (horsepower) Speed ​​(rpm) Fault type condition 2 1750 Sphere, inner ring, outer ring Condition 1 0 1797 Sphere, inner ring, outer ring Condition 2

[0144] 2) Dynamic simulation signal acquisition and data preprocessing: First, a dynamic model is established based on the physical structure parameters of the target bearing. By comparing the fault characteristic frequencies in the simulated signal envelope spectrum with those of the measured signal, the correctness of the model is verified. After the model verification is completed, various loads and rotational speeds are applied to the corrected model to generate the simulated signals listed in Table 1.

[0145] Then, 100 samples are extracted from each fault type of the simulated signal and the measured signal, and the length of each sample is 1024. The time-domain signal is converted into a time-frequency spectrogram using CWT. Then these spectrograms are processed into grayscale images with a resolution of 128×128 pixels for further analysis and model training. Taking the signal with a motor speed of 1750 RPM in Table 1 as an example, Figure 2 are samples of three fault types under working condition 1 generated by different generative models; Figure 2 (a) is the measured sample; Figure 2 (b) is the dynamic response; Figure 2 (c) is the AAE; Figure 2 (d) is the WGAN-GP; Figure 2 (e) is the DCGAN; Figure 2 (f) is the CauACGAN; Figure 2 (g) is the CabACGAN; (h) is ours;

[0146] Figure 2 (a) and (b) respectively show the time-frequency spectrograms of the dynamic response and the measured signal of different fault types. From Figure 2 (a) and Figure 2 (b), it can be seen that there is an obvious gap between the dynamic signal and the measured signal. Next, the dynamic signal is input into the trained mapping network CauGabor-ACGAN for transformation.

[0147] 3) Experimental implementation and result comparison: During the training process of the mapping model CauGabor-ACGAN, the learning rates of the generator and discriminator are set to 0.0001 and 0.00001 respectively. The model is trained for 3000 batches with a batch size of 16. To verify the superiority of the proposed method, it is compared with the classical Deep Convolutional Generative Adversarial Network (DCGAN), Wasserstein GAN with Gradient Penalty (WGAN-GP), and adversarial autoencoder (AAE) methods. In addition, to evaluate the effectiveness of the Gabor filtering layer and the embedded causal mechanism, CauACGAN (without the Gabor filtering layer) and GabACGAN (without the causal mechanism) are used for ablation experiments. Tables 2 and 3 list the MMD scores and SSIM scores between the generated samples and the real samples of different models under two working conditions respectively. Taking Condition 1 as an example, Figure 2 shows the samples generated by different generative models. As shown in Tables 2 and 3, the proposed method has significant advantages. In addition, Figure 2 this view is also confirmed because the samples generated by the proposed method are highly consistent with the actual measured signals, while the samples generated by other models are disturbed to varying degrees.

[0148] Table 2 MMD scores between the measured samples and the generated samples in Case 1

[0149]

[0150]

[0151] Table 3 SSIM scores between the measured samples and the generated samples in Case 1

[0152]

[0153] 4) Diagnostic accuracy after data augmentation: To verify the effectiveness of the generated samples for fault diagnosis under unbalanced conditions, the samples generated according to Condition 2 are added to the unbalanced dataset at different ratios. In the unbalanced fault diagnosis scenario, 200 rolling element fault measurement samples and 10 inner and outer ring fault measurement samples are used. Then different numbers of generated samples are added to this unbalanced dataset to create datasets with different degrees of imbalance. The detailed composition of these datasets is shown in Table 4. The experimental diagnostic results are as Figure 3As shown. It should be noted that the test set did not participate in the model training. As can be seen from the figure, the samples generated by the proposed method effectively alleviated the impact of sample imbalance on the accuracy of fault diagnosis. At the same time, the proposed generation method embeds a causal mechanism, making the samples generated by the ACGAN network essentially contain causal features corresponding to different fault types. Therefore, the samples generated by the proposed model have strong discriminative ability and can achieve high classification accuracy under the same imbalance ratio.

[0154] Table 4 Composition imbalance of the dataset in Condition 1

[0155] Ball Games internal external generate Proportion 200 10 10 0 20:1 200 10 10 20 10:1 200 10 10 60 5:1 200 10 10 180 2:1 200 10 10 380 1:1

[0156] Case 2: RTS bearing dataset

[0157] 1) Dataset description: This dataset comes from a proprietary bearing fault test bench in the laboratory. As Figure 4 shown, the test bench mainly consists of a motor, a tachometer display screen, a control box, and other important components. In Case 2, six types of data were collected, including inner race faults, outer race faults, and compound faults at rotational speeds of 2000 RPM and 3000 RPM. The sampling frequency for this set of experiments was set to 8000 Hz.

[0158] 2) Experiment implementation and result comparison: The dynamic signals, data preprocessing, and model training processes were similar to those of the CWRU dataset. The difference in this set of experiments was that the sample length was set to 512. Tables 5 and 6 list the MMD and SSIM metrics respectively, which were used to evaluate the quality of the time-frequency spectrograms generated by the proposed method and the comparison methods. Taking Consition1 in Case 2 as an example, Figure 5 shows the samples generated by different generation models, verifying the effectiveness and superiority of the proposed generation model.

[0159] Table 5 MMD scores between measured samples and generated samples in Case 2

[0160]

[0161] Table 6 SSIM scores between measured samples and generated samples in Case 2

[0162]

[0163] Figure 5 are the samples of three fault types under working condition 1 generated by different generation models; Figure 5 (a) is the measured sample; Figure 5 (b) is the dynamic response; Figure 5 (c) is the AAE; Figure 5 (d) is the WGAN-GP; Figure 5(e) is DCGAN; Figure 5 (f) is CauACGAN; Figure 5 (g) is CabACGAN; Figure 5 (h) is Ours.

[0164] 3) Diagnostic accuracy after data augmentation: In this set of experiments, unbalanced fault diagnosis was also carried out, and Table 4 lists the unbalance ratios in Case 1. The corresponding fault diagnosis results are as Figure 6 shown. At a ratio of 1:1, the diagnostic accuracy of the samples generated by the proposed model reached 98%, effectively alleviating the negative impact of sample imbalance on fault diagnosis.

[0165] 1) Interpretability analysis: To evaluate whether the proposed Gabor filter layer can effectively capture physical features and enhance the interpretability of the model, the outer-race fault samples and inner-race fault samples in the CWRU dataset under Condition 2 were input into the trained model to view the features captured by the Gabor filter kernel. Here, heatmaps were used as visualization tools for the target layer. At the same time, the first convolutional layer in the DCGAN model was also used for visualization. Figure 7 (a) shows the original input samples, Figure 7 (b) shows the feature maps output by the Gabor filter layer of the proposed method, Figure 7 (c) shows the samples generated by the proposed method. Figure 7 (d) and Figure 7 (e) show the feature maps output by the first convolutional layer of DCGAN and the finally generated samples, respectively.

[0166] The Gabor filter layer effectively captured the physical features of the samples, and it was found that the fault components in the samples from the energy concentration of the feature maps. In contrast, although the finally generated samples showed a similar feature distribution to the input samples, the feature maps of the standard convolutional layer did not show the energy concentration corresponding to the fault features. This indicates that the Gabor filter layer can effectively capture features with clear physical meanings, thereby improving the interpretability of the mapping model.

[0167] Figure 8 For the feature outputs of the interpretable filter layer and the convolutional layer for inner-race faults. Figure 8 (a) is the original signal. Figure 8 (b) is the output of the Gabor filter layer. Figure 8 (c) is the sample generated by the proposed method. Figure 8 (d) is the output of the convolutional layer. Figure 8 (e) is the sample generated by DCGAN.

[0168] 2) Causal analysis: To evaluate the richness of causal features in the samples generated by the proposed method, use Figure 1The trained feature extractor extracts features from simulated samples and measured samples as shown.

[0169] Taking the samples of Condition 1 in Case 1 as an example, the quantitative results between the extracted features are calculated according to formula (12). The corresponding quantitative results of different models are shown in Table 7. Compared with other models, the proposed method has a higher value under the evaluation method. This improvement is attributed to the integration of the composite loss function based on the causal mechanism, which enhances the similarity between the features of simulated samples and measured samples. Therefore, the generated samples can more effectively incorporate the causal features crucial for accurate fault diagnosis.

[0170] Table 7 Corresponding quantitative results of different models

[0171] AAE WGAN-GP DCGAN Gabu Agen The present invention Ball Games 0.58 0.68 0.64 0.80 0.99 internal 0.57 0.61 0.66 0.41 0.99 external 0.69 0.67 0.62 0.82 0.99

[0172] The present invention proposes a novel sample generation method based on a kinetic model and an ACGAN model for rolling bearing fault diagnosis under the condition of sample imbalance. To ensure highly reliable sample generation, a kinetic model is first used to generate dynamic responses with clear physical meanings. To narrow the gap between these responses and the measured signals, a mapping network named GabcauACGAN is constructed. A Gabor interpretable filter layer and objective function based on the causal mechanism are designed and integrated into the mapping model to improve the interpretability and quality of the generated samples. The effectiveness of the proposed method is verified using two datasets under four different operating conditions. The evaluation metrics include MMD, SSIM, and fault diagnosis accuracy. The experimental results show that MMD is increased by more than 10%, SSIM reaches 99% on average, and the fault diagnosis accuracy under unbalanced conditions exceeds 98%.

[0173] In future work, the goal is to generate samples of unknown operating conditions based on the existing conditional samples. In addition, it is also planned to design a more efficient and interpretable model architecture by integrating lightweight interpretation modules or embedding prior knowledge. These improvements are expected to increase the credibility and persuasiveness of model interpretability, thus promoting more reliable and transparent fault diagnosis.

[0174] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the spirit and scope of the present technical solution, and they should all be covered within the scope of the claims of the present invention.

Claims

1. A bearing unbalance sample fault diagnosis method based on kinetic modeling and causally interpretable GAN, characterized in that: It includes the following steps: S1: Analyze the physical structure parameters of the target bearing, establish a two-degree-of-freedom dynamic model of the rolling bearing, and solve the model through the Runge-Kutta method to obtain the dynamic simulation signal of the bearing fault; S2: Respectively transform the dynamic simulation signal and the actual measurement signal into time-frequency spectrograms through continuous wavelet transform and process them into grayscale images; S3: Construct a GabcauACGAN mapping network, including: A generator network, the first layer of which is a learnable multi-scale Gabor filter layer, two convolutional layers, and two upsampling convolutional layers for capturing time-frequency features; A discriminator network, including three convolutional layers and an auxiliary classifier for predicting the sample category; The objective function integrates a causal mechanism to constrain the causal feature similarity between the generated samples and the real samples through the correlation matrix; S4: Input the grayscale images of the dynamic simulation signal and the measurement signal into GabcauACGAN for training to generate enhanced data corresponding to the fault type label; S5: Evaluate the quality of the generated samples through MMD and SSIM, and add the enhanced data to the imbalanced dataset for training the fault diagnosis model.

2. The bearing imbalance sample fault diagnosis method based on kinetic modeling and causally interpretable GAN according to claim 1, characterized in that: The specific dynamic modeling includes: Based on the two-degree-of-freedom dynamic model, solve the dynamic response through the fourth-order Runge-Kutta algorithm, where: The maximum displacement excitation ΔH caused by the local fault is calculated by the following formula: ΔH′ = 0.5D - ((0.5D) 2 - (0.5min(L, B)) 2 ) 0.5 where L, B, and H respectively represent the length, width, and height of the fault size; D is the diameter of the rolling element; Contact deformation δ j Calculated by the following formula: δ j = δ x cosθ j + δ y sinθ j - ε - h j where δ x and δ y represent the vibration displacements of the rolling bearing in the X and Y directions respectively, and ε is the tolerance of the bearing; The two-degree-of-freedom dynamic equation is expressed by the following formula: where m represents the bearing mass; K represents the equivalent stiffness of the bearing; c represents the equivalent damping coefficient of the bearing; μ j is the judgment coefficient of the j-th rolling element in the contact area.

3. The bearing imbalance sample fault diagnosis method based on dynamic modeling and causally interpretable GAN according to claim 1, wherein: The parameters of the Gabor filter layer are set as: where λ represents the wavelength, controlling the spatial period of the filter; θ determines the direction of the filter; σ is the standard deviation, controlling the spatial width of the Gabor filter; ψ controls the waveform of the filter; λ is the aspect ratio; a and b are the coordinates in the two-dimensional space where the Gabor filter is located; the wavelength λ and the standard deviation σ are learnable parameters; the direction θ is fixed at 90° to match the time-frequency feature distribution of the bearing fault.

4. The bearing unbalance sample fault diagnosis method based on kinetic modeling and causally interpretable GAN according to claim 1, characterized in that: The objective function of the causal mechanism includes the following steps: Construct a correlation matrix CM of the features of the generated samples and the real samples, defined as follows: Where: <·> represents the inner product operation; N represents the number of sample features; and respectively represent the feature matrices M o and M a The Z-score normalization value of the i-th column; Calculate the causal loss term through the following formula to constrain CM to approach the identity matrix: where I is the identity matrix.

5. The bearing imbalance sample fault diagnosis method based on dynamic modeling and causally interpretable GAN according to claim 1, wherein: The loss function of the generator is: Among them, L tg is the true / false loss, is the classification loss, and λ is the weight coefficient.

6. The bearing unbalance sample fault diagnosis method based on dynamic modeling and causally interpretable GAN according to claim 1, wherein: The loss function of the discriminator is: Among them, is the true / false loss, is the classification loss.

7. The bearing imbalance sample fault diagnosis method based on dynamic modeling and causally interpretable GAN according to claim 1, characterized in that: The sample quality evaluation includes: Use the maximum mean discrepancy MMD to measure the distribution difference between the generated data and the real data; Use the structural similarity index SSIM to evaluate the time-frequency feature consistency between the generated image and the real image.

8. The bearing unbalance sample fault diagnosis method based on kinetic modeling and causally interpretable GAN according to claim 1, characterized in that: The specific S5 includes: adding the enhanced data to the imbalanced dataset according to a preset ratio, inputting it into the ResNet-18 network for fault diagnosis, and verifying the enhancement effect through the diagnostic accuracy.

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