Rolling bearing small sample fault diagnosis method based on graph enhancement

Abstract

The invention discloses a graph enhancement-based rolling bearing small sample fault diagnosis method, which comprises the following steps of: firstly, mapping a time-frequency image into a weighted undirected graph capable of accurately describing local texture and global semantic association through a self-adaptive dynamic graph construction strategy by calculating a pixel neighborhood variance and a global expectation thereof and dynamically generating a connection threshold value; the space-frequency dependency relationship between the pixels is explicitly coded; a graph feature enhancement residual block is designed in the diffusion denoising process, and the feature expression of a diffusion model in the denoising process is enhanced by cooperating with the local perception of the convolutional neural network and the global reasoning ability of the graph neural network by using the gating fusion and attention mechanism. And finally, the modules are integrated in the graph enhanced U-shaped network, so that high-quality and high-diversity fault sample generation is realized. Experiments show that the method significantly improves sample diversity and diagnosis accuracy on two bearing data sets, and provides a new approach for intelligent fault diagnosis under small sample conditions.

Description

Technical Field

[0001] This invention relates to the fields of industrial equipment fault diagnosis and artificial intelligence technology, and in particular to a small-sample fault diagnosis method for rolling bearings based on graph-enhanced denoising diffusion probability model (GF-DDPM). Background Technology

[0002] Rolling bearings, as core components of rotating machinery, are widely used in critical fields such as aerospace, transportation, and industrial production. Their operating condition directly determines the overall reliability and service life of the equipment. During long-term service, bearings are susceptible to typical failures such as rolling element wear, inner and outer ring spalling, and cage breakage due to the combined effects of complex operating conditions and non-standard operations. These failures not only cause equipment downtime and reduced production efficiency but may also trigger a chain of safety risks. Therefore, establishing a fault diagnosis mechanism with real-time response capabilities and high identification accuracy is of great significance for ensuring industrial safety, reducing operation and maintenance costs, and improving equipment reliability.

[0003] In recent years, deep learning-based intelligent fault diagnosis technology has made significant progress. However, its large-scale application in industrial settings is encountering a severe bottleneck—the "small sample problem." In real-world scenarios, most equipment operates normally, and specific fault samples, especially those of severe faults, are extremely rare and costly to obtain. This data imbalance and scarcity leads to severe overfitting and a sharp decline in generalization ability in data-driven deep learning models, making it difficult to accurately identify rare fault modes.

[0004] To overcome the small sample size dilemma, data-augmented generative models are considered a promising path. However, existing mainstream technologies each have significant shortcomings. While Generative Adversarial Networks (GANs) can generate seemingly realistic data, their training process is highly unstable due to the game-like nature of the discriminator and generator, often resulting in pattern collapse—that is, the generator "plays the game," producing only a limited number or even a single sample pattern, failing to cover the rich diversity of real faults, thus greatly diminishing the value of the augmented data. On the other hand, the emerging Denoising Diffusion Probability Model (DDPM) shows the potential to surpass GANs in terms of generation quality and stability, but its core denoising network is usually based on Convolutional Neural Networks (CNNs). The inherent local receptive field characteristics of CNNs make it difficult to effectively capture and model the long-range dependencies and global contextual relationships inherent in fault signals (such as vibration waveforms and spectrograms). These complex, non-Euclidean structural features are precisely the key to accurately diagnosing many early or complex faults.

[0005] Therefore, the industry is looking forward to a new solution that can overcome the limitations of existing models under small sample constraints. The core objective of this solution is to generate high-quality, high-fidelity, and physically meaningful fault data. Future breakthroughs are expected to stem from the deep integration of two major technologies: First, the introduction of a generative architecture with global awareness, such as a denoising diffusion model built around the Transformer. Its self-attention mechanism can directly calculate the interrelationships between all elements in a sequence, thereby fundamentally overcoming the locality limitation of CNNs and accurately capturing the global patterns of fault features. Second, embedding physical mechanisms as strong constraints into the data generation process. This means that the generative model not only learns the statistical distribution of the training data but also receives guidance from domain knowledge (such as bearing fault feature frequencies and system dynamic equations) to ensure that the generated samples are not only "formally similar" but also "spiritually similar," conforming to basic physical laws.

[0006] Therefore, the development direction of the next generation of fault diagnosis generation models is shifting from purely data-driven to a new paradigm driven by both "data-driven and knowledge-guided" approaches. By combining physical priors with powerful global generation capabilities represented by Transformer, we can synthesize a sufficiently rich and reliable fault data pool from a very small number of real fault samples. This will fully unleash the enormous potential of intelligent diagnostic models in industrial scenarios, providing a solid guarantee for the safe, stable, and long-term operation of equipment. Summary of the Invention

[0007] This invention addresses the problems of existing generative models' inability to capture global dependencies and traditional graph construction methods' difficulty in adaptively distinguishing fault textures from background noise. It proposes a small-sample fault diagnosis method for rolling bearings based on a graph-enhanced denoising diffusion probability model. By explicitly modeling the spatial and semantic relationships between fault features, high-quality fault data can be generated under small-sample conditions, significantly improving the accuracy and generalization ability of the fault diagnosis model.

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

[0009] A method for small-sample fault diagnosis of rolling bearings using a graph-enhanced denoising diffusion probability model includes the following steps:

[0010] S1. The time-frequency image of bearing failure is mapped into a weighted undirected graph through an adaptive dynamic graph construction strategy. The adaptive dynamic graph construction strategy includes: treating each pixel in the time-frequency image as a graph node, calculating the cosine similarity between node feature vectors as the initial value of the edge weight, and introducing an adaptive threshold mechanism based on local texture statistics to filter the edges, retaining only connections with similarity greater than the adaptive threshold, thereby constructing a weighted undirected graph that explicitly models the local texture changes and global semantic associations between pixels.

[0011] S2. In the reverse denoising process of the diffusion model, graph feature enhancement residual block is used to fuse the local features of the convolutional neural network with the global structural information of the graph neural network.

[0012] S3. Use the constructed graph-enhanced U-shaped network to generate high-quality fault samples to expand the original small sample dataset;

[0013] S4. Combine the generated samples with the original samples to train the fault diagnosis classifier and achieve high-precision fault identification under small sample conditions.

[0014] Furthermore, in step S1, the adaptive thresholding mechanism based on local texture statistics includes:

[0015] Calculate each pixel in the image The local complexity is calculated by examining the variance of pixels within an N×N neighborhood centered on that pixel. get;

[0016] Calculate the expected value of the local complexity of all pixels in the entire image, and combine it with the adjustment coefficient k to obtain the adaptive threshold. The calculation formula is: ;

[0017] Among them, the pixel variance within the neighborhood is used to characterize the degree of texture fluctuation of fault features in the local time-frequency map, and the adaptive threshold is used. Used for dynamically filtering weakly correlated connections caused by background noise.

[0018] Furthermore, the constructed graph structure undergoes feature learning through a graph convolutional network. The graph convolution operation is defined as follows:

[0019]

[0020] in The adjacency matrix for adding self-joins, where D is the corresponding degree matrix. Let H be the trainable weight matrix, and let H and W be the spatial dimensions.

[0021] Further, in step S2, the graph feature enhancement residual block includes:

[0022] Gated fusion mechanism: By using parameterized gating weights, the contribution of local spatial features of CNN and global structural features of GNN is adaptively balanced, and redundant features are dynamically suppressed.

[0023] Attention-driven graph feature aggregation: enhancing key semantic information based on graph attention mechanism;

[0024] Pre-normalized residual connections: After feature fusion, layer normalization and residual connections are used to ensure training stability and alleviate the gradient vanishing problem.

[0025] Furthermore, the characteristic is that the formula for calculating the gate weight g is:

[0026]

[0027] Where σ(·) represents the Sigmoid function, and [·] is the feature concatenation operation. For the gated weight matrix, For bias vectors, For input features at a certain time, These are graph-level semantic features after attention pooling.

[0028] Feature fusion based on gating weights is represented as follows:

[0029]

[0030] Here, ⊙ represents element-wise multiplication, and Broadcast(·) ensures feature dimension matching.

[0031] Furthermore, attention-driven graph feature aggregation introduces a time-step modulation mechanism, represented as:

[0032]

[0033] in and Embedded by time step It is generated through a separate fully connected layer.

[0034] Furthermore, using pre-normalized residual connections, the complete forward propagation process is represented as:

[0035]

[0036] Norm(·) represents the layer normalization operation.

[0037] Furthermore, in step S3, the graph-enhanced U-shaped network integrates graph feature enhancement residual blocks in the encoder-decoder architecture and fuses multi-scale graph features in skip connections to ensure the spatiotemporal consistency of graph features with the generation process.

[0038] Furthermore, in step S4, a multi-dimensional evaluation system is used to quantitatively assess the quality of the generated samples. The multi-dimensional evaluation system includes Frechet Inception distance, structural similarity index, and peak signal-to-noise ratio.

[0039] On the other hand, the present invention also provides a rolling bearing small sample fault diagnosis system, comprising: a processor and a memory, wherein the memory stores a computer program, and the computer program, when executed by the processor, implements the rolling bearing small sample fault diagnosis method based on the graph-enhanced denoising diffusion probability model described above.

[0040] The present invention provides a method for diagnosing small-sample faults in rolling bearings. Compared with the prior art, the advantages of the present invention are as follows:

[0041] 1. More accurate mapping and stronger noise resistance: Unlike existing technologies that rely solely on simple similarity or fixed segmentation for mapping, this invention uses "local texture statistics" as the basis for mapping, which can accurately identify key areas containing fault impact components in the time-frequency graph, thereby preserving effective fault propagation paths and suppressing noise interference in the constructed graph structure.

[0042] 2. High-quality sample generation: By transforming the time-frequency graph into a graph structure, GF-DDPM can simultaneously capture local adjacency relationships and global semantic dependencies. The generated fault samples are significantly better than traditional GAN ​​and original DDPM in terms of visual fidelity (PSNR, SSIM) and feature distribution authenticity (FID).

[0043] 3. Effectively solves the problem of small sample size: This invention can effectively generate a large number of high-quality samples under the extreme condition of only 10-30 training samples per class, providing sufficient and diverse training data for fault diagnosis models.

[0044] 4. Improved diagnostic performance: Validated on two public datasets, CWRU and MFS, the accuracy of the fault diagnosis model after data augmentation using the method of this invention can reach over 98%, which is significantly better than other data augmentation methods. Attached Figure Description

[0045] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0046] Figure 1 The diagram shows the architecture of the graph-enhanced denoising diffusion probability model (GF-DDPM) provided in the embodiments of the present invention.

[0047] Figure 2 The average PSNR index diagram for various fault type samples provided in the embodiments of the present invention.

[0048] Figure 3 This is a schematic diagram of the diffusion process provided in an embodiment of the present invention. Detailed Implementation

[0049] With the deep integration of deep learning technology and industrial intelligence, data-driven fault diagnosis methods have gradually become a research hotspot. Compared to traditional diagnostic strategies that rely on manual feature extraction, deep learning methods possess adaptive representation capabilities for complex data, enabling automation and intelligence in the diagnostic process, and demonstrating significant potential in rotating machinery fault diagnosis. However, intelligent diagnosis faces a key challenge: industrial data generally suffers from class imbalance, with fault samples accounting for a very small percentage of the entire lifecycle of a mechanical system, resulting in a severe shortage of fault data during model training, creating a "small sample dilemma." Existing intelligent diagnostic models suffer from two major bottlenecks: shallow models rely on expert knowledge to construct manually generated features, while deep networks, although capable of automatically extracting features, heavily depend on large-scale labeled data. When fault samples are scarce, models struggle to fully learn fault representations, tending to favor the identification of healthy samples, thus weakening their ability to discriminate fault states. Therefore, how to achieve high-precision intelligent diagnosis with limited samples has become a core issue of significant engineering value and urgent research need.

[0050] Currently, research on small-sample fault classification mainly follows two technical paths: model optimization-based methods and data augmentation-based methods. The former improves the model's generalization ability with limited samples by improving network structure, optimizing feature extraction mechanisms, or introducing transfer learning and meta-learning strategies.

[0051] However, GANs suffer from inherent defects such as training instability and pattern collapse. In contrast, the Denoising Diffusion Probability Model (DDPM) has achieved significant success in multiple generation tasks due to its theoretical completeness and generation quality. Research on fault diagnosis based on diffusion models is still in the exploratory stage: Fan et al. combined multi-depth convolutional transposed attention mechanism (MHTA) to construct a lightweight DDPM; Chen et al. proposed a classifier-free guided diffusion model (CFGDMHD) with mixed loss and diversity loss; studies have been conducted to design and improve DDPM to address the problem of sample scarcity; studies have been conducted to fuse condition guidance information (CGI) and U-Net structure (CGE-UNet) to generate unknown condition signals; and studies have proposed CRR-UNet and IResUnet-DM based on residual connections to alleviate overfitting and training instability.

[0052] Although existing diffusion models can generate high-quality samples, their traditional residual structures rely on CNNs to extract local features, making it difficult to effectively model global semantic relationships in non-Euclidean data structures.

[0053] To this end, this invention proposes a small-sample fault diagnosis method for rolling bearings based on a denoising diffusion probability model using a graph-enhanced residual module. The main contributions include: (1) proposing a DDPM data augmentation method based on graph feature enhancement to generate high-quality fault samples under small-sample conditions; (2) designing an adaptive dynamic graph structure construction strategy to explicitly model the spatial correlation of fault features through pixel-level graphs; (3) establishing a multi-dimensional evaluation system to quantify the quality of generated samples and verifying the diagnostic accuracy of the proposed method on CWRU and MFS datasets.

[0054] To better understand this technical solution, the method of the present invention will be described in detail below with reference to the accompanying drawings.

[0055] This invention provides a method for small-sample fault diagnosis of rolling bearings based on a graph-enhanced residual module-based denoising diffusion probability model (GF-DDPM), aiming to solve the small-sample problem in rolling bearing fault diagnosis. The core of this method lies in the introduction of a structured representation and cross-modal feature fusion mechanism: First, through an adaptive dynamic graph construction strategy, a connection threshold is dynamically generated by calculating the neighborhood variance and global expectation of pixels, mapping the time-frequency image into a weighted undirected graph that accurately characterizes local texture and global semantic relationships, thus explicitly encoding the spatial-frequency dependencies between pixels. Then, a graph feature enhancement residual block (GF-RB) is designed during the diffusion denoising process, utilizing gating fusion and attention mechanisms to coordinate the local perception of convolutional neural networks (CNN) and the global reasoning ability of graph neural networks (GNN) to enhance the feature representation of the diffusion model during denoising. Finally, by integrating the above modules into a graph-enhanced U-Net (U-Net), high-quality and highly diverse fault samples are generated. Experiments show that this method significantly improves sample diversity and diagnostic accuracy on two bearing datasets, providing a new approach for intelligent fault diagnosis under small-sample conditions.

[0056] The graph-enhanced denoising diffusion probability model (GF-DDPM) provided by this invention has the following architecture: Figure 1 As shown, it can generate high-quality, highly diverse fault samples under small sample constraints, effectively overcoming the data scarcity bottleneck in rotating machinery fault diagnosis. The network includes:

[0057] Signal sensing and time-frequency coding. Vibration signals of rolling bearings under different health conditions are collected by sensors and converted into two-dimensional time-frequency images using continuous wavelet transform, providing structured input for subsequent processing.

[0058] Graph structure modeling and relation representation. The core is the introduction of an adaptive dynamic graph structure construction strategy, mapping time-frequency images from a regular pixel grid to an irregular undirected graph. This process explicitly constructs a spatial and frequency-dimensional association model by calculating the semantic similarity between pixels, achieving a unified representation from local adjacency to global dependency.

[0059] Cross-modal feature fusion and sample generation. In the inverse denoising process of the diffusion model, the designed Graph Feature Enhancement Residual Module (GERB) adaptively fuses local details of convolutional features with global topological information of graph features. The Graph Enhancement U-Net (GE-U-Net) integrating this module accurately predicts noise and iteratively generates high-fidelity fault samples through multi-scale feature collaboration. Quantitative evaluation of generated samples. Multiple metrics, including fidelity and diversity, are used to rigorously evaluate the generated samples, ensuring that their visual quality and data distribution can effectively support downstream diagnostic tasks.

[0060] Minimal Sample Diagnostic Model Enhancement. An enhanced training set is constructed by mixing evaluated synthetic samples with the original minimal sample data. A deep classifier is trained on this dataset, significantly improving the model's generalization ability and diagnostic accuracy under limited data conditions by leveraging the rich patterns provided by the synthetic samples.

[0061] This embodiment proposes a denoising diffusion probability model for a graph-enhanced residual module. By introducing an adaptive dynamic graph structure construction strategy, it achieves the transformation from pixel-level time-frequency maps to graph-structured data. This strategy can synergistically fuse local spatial patterns and global semantic context, thereby guiding the model to generate fault samples that are highly compactly distributed in the feature space and have strong inter-class separability.

[0062] Based on the graph-enhanced residual module-based denoising diffusion probability model (GF-DDPM), this invention provides a small-sample fault diagnosis method for rolling bearings, comprising the following steps:

[0063] S1. The time-frequency image of bearing failure is mapped into a weighted undirected graph through an adaptive dynamic graph construction strategy;

[0064] S2. In the reverse denoising process of the diffusion model, graph feature enhancement residual block is used to fuse the local features of the convolutional neural network with the global structural information of the graph neural network.

[0065] S3. Use the constructed graph-enhanced U-shaped network to generate high-quality fault samples to expand the original small sample dataset;

[0066] S4. Combine the generated samples with the original samples to train the fault diagnosis classifier and achieve high-precision fault identification under small sample conditions.

[0067] Specifically, in step S1:

[0068] In rolling bearing fault diagnosis, time-frequency analysis images serve as an important carrier of fault features. The pixels within these images not only exhibit local spatial correlations but also contain complex semantic dependencies reflecting the fault mechanism. While traditional deep learning methods based on convolutional neural networks can effectively extract local features, they have inherent limitations in modeling long-range semantic relationships.

[0069] To address this challenge, this invention designs an adaptive dynamic graph structure construction strategy, which explicitly models the complex correlation of fault features in the spatial and frequency domains by mapping the time-frequency graph to a pixel-level undirected graph, thereby achieving a deep representation of fault modes.

[0070] The adaptive dynamic graph construction strategy includes:

[0071] Each pixel in the time-frequency image is treated as a graph node. The cosine similarity between the feature vectors of the nodes is calculated as the initial value of the edge weight. An adaptive threshold mechanism based on local texture statistics is introduced to filter the edges, retaining only connections with similarity greater than the adaptive threshold. This constructs a weighted undirected graph that explicitly models the local texture changes and global semantic associations between pixels. By mapping the time-frequency image to a pixel-level undirected graph, the complex associations of fault features in the spatial and frequency domains are explicitly modeled, achieving a deep representation of fault modes.

[0072] Specifically, given a time-frequency image of a bearing fault Where H and W are spatial dimensions, and C is the number of channels, we construct a weighted undirected graph. A node set is defined as follows: Each node Corresponding image position The pixels. Node feature vectors are obtained through vectorization operations: This operation converts the features of each pixel across all channels into column vectors, preserving the complete feature information.

[0073] In the edge set construction process, a semantic similarity-based connection strategy is adopted. The semantic association between nodes is quantified using cosine similarity.

[0074]

[0075] in For feature vectors The angle between pixels. This metric effectively captures the semantic correlation between pixels, not just spatial proximity.

[0076] To adapt to the varying complexity of different failure modes, this invention designs an adaptive threshold mechanism based on local texture statistics, including:

[0077] Calculate each pixel in the image The local complexity is calculated by examining the variance of pixels within an N×N neighborhood centered on that pixel. get;

[0078] Calculate the expected value of the local complexity of all pixels in the entire image, and combine it with the adjustment coefficient k to obtain the adaptive threshold. The calculation formula is: ;

[0079] Among them, the pixel variance within the neighborhood is used to characterize the degree of texture fluctuation of fault features in the local time-frequency map, and the adaptive threshold is used. Used for dynamically filtering weakly correlated connections caused by background noise.

[0080] The constructed graph structure is then used for feature learning through a graph convolutional network. The graph convolution operation is defined as follows:

[0081]

[0082] in The adjacency matrix for adding self-joins, where D is the corresponding degree matrix. Let H be the trainable weight matrix, and let H and W be the spatial dimensions.

[0083] by Example of 4×4 neighborhood variance centered on the center, adaptive threshold The calculation formula is:

[0084]

[0085] Where E[·] is the mathematical expectation, used for the local complexity of the global statistical image; Indicates The variance of the 4×4 neighborhood centered at the center is calculated using the following formula:

[0086]

[0087] in The neighborhood mean. Based on the 4-neighborhood traversal strategy, when... At that time, weighted edges are established between nodes, with weights of .

[0088] This method achieves accurate modeling of fault characteristics through dynamic graph structure construction and adaptive threshold mechanism, providing an effective solution for bearing fault diagnosis under small sample conditions.

[0089] In step S2, the graph feature enhancement residual block includes:

[0090] Gated fusion mechanism: By using parameterized gating weights, the contribution of local spatial features of CNN and global structural features of GNN is adaptively balanced, and redundant features are dynamically suppressed.

[0091] Attention-driven graph feature aggregation: enhancing key semantic information based on graph attention mechanism;

[0092] Pre-normalized residual connections: After feature fusion, layer normalization and residual connections are used to ensure training stability and alleviate the gradient vanishing problem.

[0093] Traditional residual structures primarily rely on convolutional neural networks to extract local spatial features, making it difficult to effectively model global semantic relationships in non-Euclidean data structures. To address this, this paper proposes a graph-enhanced residual module. Through a three-stage architecture—gated cross-modal fusion, attention-driven graph feature aggregation, and pre-normalized residual connections—it achieves efficient collaboration between local and global features. The module's gating fusion mechanism adaptively balances the contributions of CNN local features and GNN global features through parameterized gating weights. The formula for calculating the gating weight g is:

[0094]

[0095] Where σ(·) represents the Sigmoid function, and [·] is the feature concatenation operation. For the gated weight matrix, For bias vectors, For input features at a certain time, These are graph-level semantic features after attention pooling.

[0096] Feature fusion based on gating weights is represented as follows:

[0097]

[0098] Here, ⊙ represents element-wise multiplication, and Broadcast(·) ensures feature dimension matching.

[0099] To further enhance temporal adaptability, attention-driven graph feature aggregation introduces a temporal step modulation mechanism, represented as:

[0100]

[0101] in and Embedded by time step It is generated through a separate fully connected layer.

[0102] Using pre-normalized residual connections, the complete forward propagation process can be represented as follows:

[0103]

[0104] Norm(·) represents the layer normalization operation.

[0105] Through this design, the model can dynamically adjust the feature fusion strategy at different diffusion time steps, effectively alleviating the gradient vanishing problem, while ensuring a balanced representation of local details and global semantics, providing a reliable architectural foundation for the generation of high-quality fault samples.

[0106] This document introduces some concepts involved in this embodiment.

[0107] 1. Forward diffusion process.

[0108] The forward diffusion process is a fixed, progressively noisy Markov chain. Its core lies in using a pre-defined noise scheduling scheme to propagate noise from the original data. Gaussian noise is continuously injected into the sample. After a sufficient number of steps T, the effective information of the original data is completely destroyed, ultimately transforming it into a pure noise sample. The sample follows an isotropic standard Gaussian distribution.

[0109] The mathematical essence of this process can be expressed as: at each time step t, the current state... Based solely on its state at the previous moment The decision is made. Its conditional distribution is given by the following formula:

[0110]

[0111] in, It is a predefined noise variance sequence that controls the amount of noise added at each step. This process can analytically derive the relationship between the sample and the original sample at any time t. The relationship allows for efficient direct access from... Sampled This greatly optimizes training efficiency.

[0112] 2. Reverse noise reduction

[0113] The reverse diffusion process aims to diffuse pure noise. The original data was systematically recovered. Essentially, it's the inverse of the forward process. This process is also modeled as a Markov chain, but in the opposite direction to the forward process; the goal of each step is to learn from the current state. Inferring a "cleaner" state from the previous moment .

[0114] According to Bayes' theorem, theoretically from Go back to True posterior distribution While derivative, its computation depends on the entire data distribution, making it difficult to solve directly in practice. Therefore, DDPM employs a parameterized neural network. This approximates the complex posterior distribution. The core task of the network is to predict the posterior distribution given... Given the current time step t, roll back to The required mean and variance.

[0115] A key parameterization technique is that the neural network does not directly predict... Instead, it adds predictions to the forward process. noise components Based on this, the mean value of the denoising process It can be reparameterized as a function of the prediction noise. The function. Ultimately, The sampling update formula is as follows:

[0116]

[0117] in, It is standard Gaussian noise, used to introduce randomness; It is the variance at step t, which is usually set as a hyperparameter; and It is noise scheduling of the forward process. The parameters are derived.

[0118] To train this denoising network, DDPM minimizes the difference between the real noise ε and the network's predicted noise. This is achieved by minimizing the mean squared error between the two data points. This simplified training objective function is mathematically equivalent to minimizing the true data distribution. With model-generated distribution The variational lower bound (VLB) between these values ​​drives the generated samples to approximate the real data infinitely.

[0119] 3. Convolution and Graph Convolution Principles

[0120] In 2D image processing, convolutional neural networks extract features in a regular Euclidean space (e.g., a pixel grid) using learnable convolutional kernels. Their core principle lies in capturing the spatial local features of the data through local connectivity, weight sharing, and downsampling. Specifically, for an input feature map, the convolution operation is implemented by sliding the convolutional kernel across the input data and calculating the dot product of local regions. Its mathematical expression is:

[0121]

[0122] in, Indicates the first Feature map of the layer For convolution kernel weights, For bias terms, This is a non-linear activation function. This operation endows CNNs with powerful local feature extraction capabilities and translation invariance, making them outstanding in tasks such as image recognition. However, traditional convolution operations heavily rely on the regular grid structure of the input data and the assumption of translation invariance, making them difficult to apply directly to graph-structured data in non-Euclidean spaces.

[0123] In contrast, graph convolutional networks extend the convolution operation to graph-structured data. Their core idea is to achieve feature propagation and aggregation through graph adjacency relationships, enabling nodes to integrate feature information from themselves and their neighbors. A typical graph convolution operation can be represented as:

[0124]

[0125] in, This indicates that a self-connected adjacency matrix has been added. Let it be its corresponding degree matrix. This is a trainable weight matrix. This normalization operation helps stabilize the training process. Graph convolution defines the receptive field through the adjacency matrix, which can effectively handle complex relationships and topological structures between nodes, thus overcoming the inherent limitations of traditional CNNs in processing irregular, non-Euclidean data (such as social networks, molecular structures, fault feature association graphs, etc.), and providing a powerful tool for feature learning of complex data structures.

[0126] In step S3, the graph-enhanced U-shaped network integrates graph feature enhancement residual blocks in the encoder-decoder architecture and fuses multi-scale graph features in skip connections to ensure the spatiotemporal consistency of graph features with the generation process.

[0127] In step S4, this invention employs a multi-dimensional evaluation system to quantitatively assess the quality of the generated samples. This system includes Frechet Inception distance, structural similarity index, and peak signal-to-noise ratio. Systematic experiments were conducted on multiple public datasets, including CWRU and MFS. The results show that this method can significantly improve diagnostic accuracy.

[0128] To verify the effectiveness of the model, this embodiment verifies the effectiveness of the proposed method through the fault diagnosis results of two bearing fault diagnosis cases. In this experimental study, we systematically evaluated the performance of the proposed Graph Enhanced Denoising Diffusion Probability Model (GF-DDPM) in rolling bearing fault diagnosis. The experiment was conducted on two public datasets, CWRU and MFS, using continuous wavelet transform to convert the original vibration signal into a time-frequency image as the model input. Through carefully designed experimental settings, we verified the effectiveness of the model under small sample conditions, comprehensively evaluated the quality of the generated samples using three indicators: FID, SSIM, and PSNR, and used t-SNE visualization technology to deeply analyze the feature space distribution characteristics. Experimental results show that GF-DDPM achieved an FID value of 23.23 on the CWRU dataset and an excellent performance of 11.41 on the MFS dataset, significantly outperforming the compared GAN model and the original DDPM. In terms of structural similarity, the SSIM value of the samples generated by GF-DDPM is close to the ideal value of 1, and the PSNR index is improved by 5-15 dB compared to the baseline method, confirming the superior performance of the generated samples in terms of visual fidelity and structural consistency.

[0129] Regarding fault diagnosis accuracy, we designed multiple sets of comparative experiments to verify the data augmentation effect. When using 10 real samples and 120 generated samples per class, the GF-DDPM-assisted 2D-CNN and ResNet models achieved accuracies of 97.86% and 96.57% respectively on the CWRU dataset. Even under extreme conditions using only generated samples, the diagnostic performance remained above 95%. Feature visualization analysis further showed that the feature space augmented by GF-DDPM exhibited clearer class boundaries and higher intra-class aggregation, effectively solving the pattern aliasing problem under small sample conditions. In addition, training process analysis showed that GF-DDPM has a faster convergence speed and better training stability, with the loss curve reaching a stable state within 10 epochs.

[0130] Based on all experimental results, GF-DDPM successfully generated high-quality fault samples by introducing adaptive graph structure construction and feature enhancement mechanisms. This not only significantly improved the diagnostic accuracy under small sample conditions, but also demonstrated good generalization ability and engineering application value, providing an effective solution for intelligent fault diagnosis in the industrial field.

[0131] In addition, the present invention also provides a rolling bearing small sample fault diagnosis system, characterized in that it includes: a processor and a memory, wherein the memory stores a computer program, and the computer program, when executed by the processor, implements the rolling bearing small sample fault diagnosis method based on graph enhancement denoising diffusion probability model as described above.

[0132] If a function is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0133] The above embodiments are merely specific implementations of the present invention, used to illustrate the technical solutions of the present invention, and are not intended to limit it. The scope of protection of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments within the scope of the technology disclosed in the present invention, or make equivalent substitutions for some of the technical features; and these modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for small-sample fault diagnosis of rolling bearings based on a graph-enhanced denoising diffusion probability model, characterized in that, Includes the following steps: S1. The time-frequency image of bearing failure is mapped into a weighted undirected graph through an adaptive dynamic graph construction strategy; The adaptive dynamic graph construction strategy includes: treating each pixel in the time-frequency image as a graph node, calculating the cosine similarity between node feature vectors as the initial value of edge weights, and introducing an adaptive threshold mechanism based on local texture statistics to filter edges, retaining only connections with similarity greater than the adaptive threshold, thereby constructing a weighted undirected graph that explicitly models the local texture changes and global semantic associations between pixels. S2. In the reverse denoising process of the diffusion model, graph feature enhancement residual block is used to fuse the local features of the convolutional neural network with the global structural information of the graph neural network. S3. Use the constructed graph-enhanced U-shaped network to generate high-quality fault samples to expand the original small sample dataset; S4. Combine the generated samples with the original samples to train the fault diagnosis classifier and achieve high-precision fault identification under small sample conditions.

2. The method for small-sample fault diagnosis of rolling bearings based on a graph-enhanced denoising diffusion probability model according to claim 1, characterized in that, In step S1, the adaptive thresholding mechanism based on local texture statistics includes: Calculate each pixel in the image The local complexity is calculated by examining the variance of pixels within an N×N neighborhood centered on that pixel. get; Calculate the expected value of the local complexity of all pixels in the entire image, and combine it with the adjustment coefficient k to obtain the adaptive threshold. The calculation formula is: ; Among them, the pixel variance within the neighborhood is used to characterize the degree of texture fluctuation of fault features in the local time-frequency map, and the adaptive threshold is used. Used for dynamically filtering weakly correlated connections caused by background noise.

3. The method for small-sample fault diagnosis of rolling bearings based on a graph-enhanced denoising diffusion probability model according to claim 1, characterized in that, The constructed graph structure is then used for feature learning through a graph convolutional network. The graph convolution operation is defined as follows: ， in The adjacency matrix for adding self-joins, where D is the corresponding degree matrix. Let H be the trainable weight matrix, and W be the spatial dimensions.

4. The method for small-sample fault diagnosis of rolling bearings based on a graph-enhanced denoising diffusion probability model according to claim 1, characterized in that, In step S2, the graph feature enhancement residual block includes: Gated fusion mechanism: By using parameterized gating weights, the contribution of local spatial features of CNN and global structural features of GNN is adaptively balanced, and redundant features are dynamically suppressed. Attention-driven graph feature aggregation: enhancing key semantic information based on graph attention mechanism; Pre-normalized residual connections: After feature fusion, layer normalization and residual connections are used to ensure training stability and alleviate the gradient vanishing problem.

5. The method for small-sample fault diagnosis of rolling bearings based on a graph-enhanced denoising diffusion probability model according to claim 4, characterized in that, The formula for calculating the gating weight g is: ， Where σ(·) represents the Sigmoid function, and [·] is the feature concatenation operation. For the gated weight matrix, For bias vectors, For input features at a certain time, These are graph-level semantic features after attention pooling; Feature fusion based on gating weights is represented as follows: ， Here, ⊙ represents element-wise multiplication, and Broadcast(·) ensures feature dimension matching.

6. The method for small-sample fault diagnosis of rolling bearings based on a graph-enhanced denoising diffusion probability model according to claim 5, characterized in that, Attention-driven graph feature aggregation, introducing a time-step modulation mechanism, is represented as: ， in and Embedded by time step It is generated through a separate fully connected layer.

7. The method for small-sample fault diagnosis of rolling bearings based on a graph-enhanced denoising diffusion probability model according to claim 6, characterized in that, Using pre-normalized residual connections, the complete forward propagation process can be represented as follows: ， Norm(·) represents the layer normalization operation.

8. The method for small-sample fault diagnosis of rolling bearings based on a graph-enhanced denoising diffusion probability model according to claim 1, characterized in that, In step S3, the graph-enhanced U-shaped network integrates graph feature enhancement residual blocks in the encoder-decoder architecture and fuses multi-scale graph features in skip connections to ensure the spatiotemporal consistency of graph features with the generation process.

9. The method for small-sample fault diagnosis of rolling bearings based on a graph-enhanced denoising diffusion probability model according to claim 1, characterized in that, In step S4, a multi-dimensional evaluation system is used to quantitatively assess the quality of the generated samples. The multi-dimensional evaluation system includes Frechet Inception distance, structural similarity index, and peak signal-to-noise ratio.

10. A rolling bearing small sample fault diagnosis system according to claim 1, characterized in that, include: The processor and memory, wherein the memory stores a computer program that, when executed by the processor, implements the rolling bearing small-sample fault diagnosis method based on a graph-enhanced denoising diffusion probability model as described in any one of claims 1-9.

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