A cross-working-condition fault diagnosis method for axle box bearing based on random walk graph kernel

Abstract

A kind of cross-condition axle box bearing fault diagnosis method based on random walk graph kernel, comprising: constructing graph node feature matrix, and then obtaining source domain node feature matrix and target domain node feature matrix;Source domain graph adjacency matrix and target domain graph adjacency matrix are constructed;Graph convolution source domain node feature matrix and graph convolution target domain node feature matrix are obtained by feature extraction;Initial kernel similarity matrix between source domain node and target domain node is calculated using radial basis kernel function with adaptive bandwidth;Initial kernel similarity matrix is iteratively propagated by synchronous random walk mechanism, and geometric random walk kernel matrix is constructed using finite-order cumulant expansion method;Random walk kernel alignment loss is calculated;Joint optimization objective function is constructed, and the model after training is used to predict the fault class of target domain data.The present application can improve the cross-condition stability of graph topology, and solve the problem that fault class is easily confused during migration.

Description

Technical Field

[0001] This invention relates to the field of axle box bearing fault diagnosis technology, and specifically to a cross-condition axle box bearing fault diagnosis method based on random walk graph kernel. Background Technology

[0002] Axle box bearings are critical power components in rail transit train bogies, power equipment transmission systems, and industrial manufacturing equipment. Their operating status directly affects the overall safety and system reliability. In actual operation, operating parameters such as speed and load exhibit significant time-varying characteristics, and vibration signals collected under different operating conditions differ in statistical characteristics and spectral distribution. When operating conditions change, deep learning-based fault diagnosis models often experience a decline in diagnostic performance due to the distribution shift between training and test data. Therefore, how to achieve cross-condition fault knowledge transfer under unlabeled target operating conditions is a significant technical challenge currently facing the field of industrial intelligent diagnostics.

[0003] Currently, cross-condition fault diagnosis mainly relies on transfer learning and unsupervised domain adaptation methods. These methods transfer models trained in the source domain to the target domain by reducing the difference in feature distribution between the source and target domains. However, most existing methods treat vibration signals collected by multiple sensors as independent samples and use statistical distance based on Euclidean space for inter-domain alignment. This approach does not consider the coupling dependency between multiple sensors on the same mechanical equipment due to rigid connections and vibration transmission, which easily leads to the loss of structural correlation information between sensors under cross-condition conditions, affecting the consistent expression of fault features across different conditions.

[0004] In recent years, graph neural networks (GNNs) have been introduced into the field of axle box bearing fault diagnosis due to their ability to describe the connections between sensor nodes. GNN-based methods map sensors to graph nodes and represent the information interaction paths between sensors through edge connections. However, existing methods generally rely on data-driven strategies such as Euclidean distance, cosine similarity, or K-nearest neighbors for graph topology construction, lacking physical constraints on the mechanical transmission path and vibration coupling mechanism. Under varying operating conditions, the amplitude and frequency components of vibration signals shift, and graph structures built solely based on statistical similarity are prone to introducing connections unrelated to the actual mechanical force transmission path, affecting the cross-condition stability of the graph structure representation.

[0005] Furthermore, existing cross-domain graph alignment methods typically aggregate node features into a single graph-level vector before using statistical distance for distribution alignment when measuring the graph structure differences between the source and target domains. This process is prone to losing the connectivity between nodes, affecting the preservation of structure between cross-domain graphs, and consequently leading to confusion of fault categories during migration. Summary of the Invention

[0006] In view of this, the present invention provides a cross-condition bearing fault diagnosis method based on random walk graph kernel, so as to improve the cross-condition stability of graph topology and solve the problem that fault categories are easily confused during the migration process.

[0007] A method for fault diagnosis of axle box bearings across operating conditions based on random walk graph kernels includes: Step S1: Obtain vibration signals collected by multiple sensors on the axle box bearing, perform sliding window segmentation on the vibration signals, extract frequency domain features to construct a graph node feature matrix, and then obtain the source domain and target domain node feature matrices. Step S2: Based on the node feature matrices of the source domain and the target domain, the coupling strength between the sensor channels in the source domain and the target domain is calculated using the full-band energy weighted coherence function, and a physically constrained graph adjacency matrix of the source domain and the target domain is constructed. Step S3: Using the adjacency matrix as a topological constraint, use a graph convolutional network to extract features from the source and target domain graphs to obtain the graph convolutional source domain node feature matrix and the graph convolutional target domain node feature matrix. Step S4: Based on the feature matrix of the source domain nodes and the feature matrix of the target domain nodes in the graph convolution, calculate the initial kernel similarity matrix between the source domain nodes and the target domain nodes using the radial basis kernel function with adaptive bandwidth. Step S5: Construct random walk transition probability matrices for the source and target domain graphs based on the adjacency matrix. In the product graph space, use the random walk transition probability matrix and iteratively propagate the initial kernel similarity matrix through a synchronous random walk mechanism to construct a geometric random walk kernel matrix. Step S6: Construct an empirical topological kernel matrix based on the geometric random walk kernel matrix, and then construct an ideal semantic kernel matrix. Calculate the normalized cosine distance between the empirical topological kernel matrix and the ideal semantic kernel matrix as the random walk kernel alignment loss, and derive the gradient of the random walk kernel alignment loss with respect to node features, so that the gradient propagates backward along the physically coupled topological path. Step S7: Construct a joint optimization objective function based on random walk kernel alignment loss and source domain supervised classification loss to train the cross-operating condition fault diagnosis model, and use the trained diagnosis model to predict the fault category of the target domain data.

[0008] The cross-condition bearing fault diagnosis method based on random walk graph kernel provided by the present invention has the following advantages: 1. This invention constructs a graph topology using a full-band energy-weighted coherence function, embedding vibration energy transfer relationships and phase coordination relationships into the adjacency matrix of the graph structure. Under varying operating conditions, this physical constraint helps reduce non-real connections introduced by statistical similarity fluctuations, improving the cross-condition stability of the graph topology.

[0009] 2. This invention establishes an initial similarity matrix for cross-domain nodes using a radial basis function with adaptive bandwidth, enabling the bandwidth parameter to adaptively adjust during network training and dynamically match the distribution characteristics of the current feature space. Furthermore, this invention models the topological relationship between the source and target domain graphs by performing synchronous random walks in the product graph space, directly measuring the structural similarity between cross-domain graphs at the topological level while preserving the connectivity between nodes.

[0010] 3. This invention constructs consistency constraints between empirical topological kernels and ideal semantic kernels directly using node-level features in the kernel space, thereby preserving the connection relationships between nodes and avoiding the loss of topological structure caused by graph-level aggregation. At the same time, this consistency constraint ensures that feature alignment takes into account both structural similarity and category discriminability between cross-domain graphs, and the use of soft labels to construct semantic kernels can reduce the impact of uncertainty in target domain prediction, thus effectively reducing the risk of confusion of fault categories during the migration process.

[0011] 4. In the backpropagation process, this invention uses gradient propagation of the alignment loss through the transition probability matrix determined by the physical coupling relationship, enabling sensor node pairs with higher coupling strength to obtain higher contribution weights in parameter updates. Furthermore, this invention integrates physical graph construction, graph convolution feature extraction, and orthographic graph spatial kernel alignment into an end-to-end training framework, avoiding error accumulation in multi-stage training. Attached Figure Description

[0012] Figure 1 This is a flowchart illustrating the cross-condition bearing fault diagnosis method based on random walk graph kernel provided in an embodiment of the present invention. Figure 2 For task T 20 The diagnostic accuracy response surface plot below; Figure 3 For task T 02 The diagnostic accuracy response surface plot below. Detailed Implementation

[0013] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain embodiments of the present invention, and should not be construed as limiting the present invention.

[0014] This invention provides a cross-condition bearing fault diagnosis method based on a random walk graph kernel. First, a physically constrained graph topology is constructed using a full-band energy-weighted coherence function. The vibration energy transfer relationship and phase coordination relationship between multiple sensors are embedded in the adjacency matrix of the graph structure. The physical prior graph topology characterizes the transient coupling strength between sensor channels on a sample-by-sample basis, avoiding the spurious connectivity problem introduced by traditional data-driven graph construction methods based on Euclidean distance or correlation coefficients under varying operating conditions, thus providing a stable topological foundation for cross-domain feature propagation.

[0015] Then, the source and target domain graphs are mapped to a unified direct product graph space, and the higher-order topological diffusion behavior is modeled through a synchronous random walk process. This process constructs a joint diffusion kernel in the direct product graph space from the random walk transition probability matrices of the source and target domain graphs in the form of a Kronecker product, and constructs a geometric random walk kernel matrix in the form of a finite-order cumulative expansion, thereby realizing a quantitative measure of the higher-order structural similarity between cross-domain graphs.

[0016] Building upon this foundation, an empirical topological kernel matrix is ​​constructed using a geometric random walk kernel matrix, employing spatial constraint masking and average pooling. An ideal semantic kernel matrix is ​​then constructed using the source domain's true label and the target domain's predicted probability. The normalized cosine distance between these two matrices is calculated as the random walk kernel alignment loss. This loss model unifies topological constraints and category semantic constraints in the kernel space, thereby achieving adaptive alignment of category semantic boundaries while maintaining topological consistency.

[0017] Finally, the random walk kernel alignment loss and the source domain classification loss are weighted and summed to construct a joint optimization objective function, which is then used to update the model's network parameters through backpropagation. During backpropagation, the alignment loss is propagated through the gradient of the transition probability matrix determined by the physical coupling relationship, allowing sensor node pairs with higher coupling strength to receive higher contribution weights in parameter updates. Ultimately, the trained model is used to predict the fault category of the target domain data.

[0018] Please see Figure 1 The method specifically includes steps S1 to S7: Step S1: Obtain vibration signals collected by multiple sensors on the axle box bearing, perform sliding window segmentation on the vibration signals, extract frequency domain features to construct a graph node feature matrix, and then obtain the source domain and target domain node feature matrices.

[0019] In this embodiment, vibration signals synchronously collected by multiple sensors arranged on the axle box bearing are acquired. The vibration signals are divided into sliding windows with a fixed length time window, and frequency domain features are extracted to construct a graph node feature matrix. The node features are then standardized to obtain the source domain node feature matrix and the target domain node feature matrix.

[0020] Specifically, the number of channels is constructed at the key components of the axle box bearing. A multi-sensor vibration acquisition system is used to acquire synchronous vibration response signals at different measurement points.

[0021] Preferably, at the sampling frequency Vibration signals are acquired using a length of... A non-overlapping sliding window is used to equidistantly truncate the time-domain signals of each channel, generating... There are 10 short-term observation samples, each sample having a dimension of 1. ,in The total number of sensor channels; the source domain samples and target domain samples come from different operating conditions; the source domain samples contain known fault category labels, while the target domain samples do not contain manually labeled information. The overall task belongs to the unsupervised domain adaptive fault diagnosis task.

[0022] For each sample, the first Perform a Fast Fourier Transform on the time-domain signals of each channel to extract the single-sided amplitude spectrum. Frequency domain feature dimension ;right The frequency domain signals of each sensor channel are normalized to zero mean and unit variance to eliminate scale shifts caused by differences in sensor installation location and sensitivity magnitude, thus obtaining the source domain node feature matrix. With the target domain node feature matrix , Let be the set of real numbers, where each row of the matrix corresponds to the frequency domain feature vector of a sensor node.

[0023] Step S2: Based on the node feature matrices of the source domain and the target domain, the coupling strength between the sensor channels in the source domain and the target domain is calculated using the full-band energy weighted coherence function, and a physically constrained graph adjacency matrix of the source domain and the target domain is constructed.

[0024] This step is used to construct a graph topology with mechanical and physical constraints. Frequency domain coherence analysis combined with energy weighting is employed to ensure that the constructed graph topology accurately reflects the actual vibration transmission paths between sensors.

[0025] Step S2 specifically includes: Step S21: Calculate the channel using the Welch method. With channel Cross-power spectral density and passage Self-power spectral density and channels Self-power spectral density In this embodiment, the parameters of the Welch method are configured as follows: the window function is the Hanning window, the segmented window length is set to 2048 sampling points, and the overlap length between adjacent segments is set to 1024 sampling points, i.e., the overlap rate is 50%. Under the above parameter configuration, the amplitude squared coherence function is calculated using the following formula. for:

[0026] in, The value range is [0,1], and it is used to measure the channel. With channel The signal at frequency The closer the phase consistency value is to 1, the higher the linear coupling between the two channels at that frequency.

[0027] Step S22, based on channel Self-power spectral density Calculate frequency domain energy weights and will Normalized to the [0,1] interval, the full-band coherence function is weighted and integrated using frequency domain energy weights to obtain the channel. With channel Coupling strength between :

[0028] This weighting method reduces the contribution of the coherence value in the low-energy frequency band to the final coupling strength, while enhancing the coherence relationship in the high-energy frequency band.

[0029] Step S23: Arrange the coupling strengths between all channels calculated in step S22 according to their subscripts, and construct the source domain weight matrix for the source domain samples. Construct a target domain weight matrix for the target domain samples. Set up the channel self-coupling strength , respectively and Symmetry processing is performed, and the element-wise maximum value of each matrix and its transpose is taken. The above graph construction process is consistent in both the source and target domains, and is calculated independently on a per-sample basis, thus obtaining the adjacency matrix of the source domain graph. Adjacency matrix of the target domain graph .

[0030] Step S3: Using the adjacency matrix as a topological constraint, use a graph convolutional network to extract features from the source and target domain graphs, and obtain the graph convolutional source domain node feature matrix and the graph convolutional target domain node feature matrix.

[0031] In this process, a graph convolutional network is constructed as a feature extractor. This network uses the physical adjacency matrix generated in step S2 as a topological constraint, and the adjacency matrix does not participate in gradient updates.

[0032] Specifically, step S3 includes: Step S31: Map each sensor channel to a graph node, defining the number of graph nodes as equal to the total number of sensor channels. The source domain node feature matrix With the target domain node feature matrix Initial node embeddings are obtained by mapping to a low-dimensional latent space through fully connected layers. Specifically, it is divided into the embedding of the initial node of the source domain. Embedded with the initial node of the target domain Hidden layer dimensions Set to 256; Step S32, for the adjacency matrix Add the identity matrix Obtain the extended adjacency matrix containing self-loops. Adjacency matrix Divided into source domain graph adjacency matrix Adjacency matrix of target domain graph ,in, The purpose is to assign a connection to itself to each sensor node, so that the graph convolution operation can retain the frequency domain characteristics of the node itself while aggregating information from neighboring nodes, and then calculate the extended adjacency matrix. degree matrix Specifically, it is divided into the degree matrix corresponding to the source domain. The degree matrix corresponding to the target domain , The main diagonal element in , Represents the extended adjacency matrix The Middle Line number The elements of the column, subsequently, are embedded with the initial node output from step S31. For input, perform normalized graph convolution according to the following formula:

[0033] in, This is the node feature matrix output by the convolutional layer of the first image. Here, ReLU is the first-layer learnable weight matrix, and ReLU is the non-linear activation function. It should be noted that information propagation between nodes is constrained by adjacency weights, and only when the adjacency matrix... The Middle Line number Column elements At that time, node Respond and aggregate from nodes The characteristics of this feature are positively correlated with the coupling weight.

[0034] Step S33, with Execute a second graph convolutional layer for the input:

[0035] in, This is the node feature matrix output by the convolutional layer in the second graph. This is the second-layer learnable weight matrix; Step S34, will and Element-by-element addition is performed to obtain the residual fusion result. The residual fusion result of the source domain is used as the feature matrix of the source domain nodes in the graph convolution. The residual fusion result of the target domain is used as the feature matrix of the target domain nodes in the graph convolution. ; Step S35, for Global average pooling is performed along the node dimension to obtain a graph-level vector representation, specifically divided into source domain graph-level vectors and target domain graph-level vectors. These are input into a fully connected classifier, which outputs the predicted probability of the fault category. Specifically, the source domain graph-level vector is input into the fully connected classifier, which outputs the predicted probability of the source domain fault category. Input the target domain graph-level vector into the same fully connected classifier, and output the predicted probability of the target domain fault category. The predicted probability of the fault category is used in the subsequent step S6 to construct the ideal semantic kernel matrix. and used in step S7 to calculate the source domain supervised classification loss. .

[0036] It should be noted that the random walk kernel alignment operation in subsequent steps S4 to S6 is performed before the global average pooling.

[0037] Step S4: Based on the feature matrix of the source domain nodes and the feature matrix of the target domain nodes in the graph convolution, calculate the initial kernel similarity matrix between the source domain nodes and the target domain nodes using a radial basis kernel function with adaptive bandwidth.

[0038] This step is used to establish the initial feature correspondence between source domain graph nodes and target domain graph nodes, providing an initial metric for subsequent random walk topological diffusion in the product graph space.

[0039] Specifically, step S4 includes: Based on the feature matrix of source domain nodes in graph convolution Convolution with the target domain node feature matrix The local feature similarity between cross-domain node pairs is calculated using a radial basis kernel function with an adaptive bandwidth parameter, expressed as follows:

[0040] in, For the source domain The node and the target domain Local feature similarity between nodes Indicates the first Each graph convolution source domain node feature vector Indicates the first Each graph convolution of the target domain node feature vector For learnable kernel function bandwidth parameters, Represents the Euclidean norm; For all cross-domain node pairs, the calculated local feature similarity is as follows: , Arrange the kernel similarity matrix to obtain the initial kernel similarity matrix. Initial kernel similarity matrix It is used to describe the local feature correspondence between the source domain graph and the target domain graph, and to provide initial structural constraints for subsequent higher-order topology diffusion.

[0041] Step S5: Construct random walk transition probability matrices for the source and target domain graphs based on the adjacency matrix. In the product graph space, use the random walk transition probability matrices and iteratively propagate the initial kernel similarity matrix through a synchronous random walk mechanism to construct a geometric random walk kernel matrix.

[0042] This step is used to model the high-order topological diffusion behavior between the source and target domain graphs based on the initial kernel similarity through a synchronous random walk mechanism in the product graph space. A geometric random walk kernel matrix that characterizes cross-domain structural similarity is constructed using a finite-order cumulative expansion method.

[0043] Specifically, step S5 includes: Step S51, based on the source domain graph adjacency matrix Adjacency matrix of the target domain graph Construct the corresponding source domain degree matrix respectively. With the target domain degree matrix Perform row-wise normalization on the adjacency matrix to obtain the random walk transition probability matrix of the source domain graph. With the target domain graph random walk transition probability matrix The expression is:

[0044]

[0045] The random walk transition probability matrix is ​​used to constrain the direction and intensity of information propagation between nodes during the random walk, thereby maintaining the dynamic coupling relationship in the original mechanical topology.

[0046] Step S52, in the product graph space, The initial kernel state matrix of the random walk diffusion process Then, the source domain graph random walk transition probability matrix is ​​used. With the target domain graph random walk transition probability matrix Furthermore, a higher-order topological diffusion is performed on the cross-domain graph structure through a synchronous random walk mechanism to characterize the higher-order topological similarity between the source and target domain graphs. The update process of the kernel matrix for a random walk is defined as follows:

[0047] in, Indicates the first The kernel matrix after one random walk. Indicates the first The kernel matrix after one random walk. Indicates transpose; To synthesize topological diffusion information under different orders of random walks, the data from 0 to... The geometric random walk kernel matrix is ​​obtained by performing a finite-order cumulative expansion on the random walk kernel matrix. :

[0048] in, This represents the maximum number of random walk steps (preferably 6). This represents the higher-order attenuation factor (preferably 0.01). express factorial.

[0049] By using a finite-order expansion method, the oversmoothing phenomenon caused by infinite-step random walks can be avoided, while reducing the computational complexity caused by matrix inversion operations.

[0050] Step S6: Construct an empirical topological kernel matrix based on the geometric random walk kernel matrix, and then construct an ideal semantic kernel matrix. Calculate the normalized cosine distance between the empirical topological kernel matrix and the ideal semantic kernel matrix as the random walk kernel alignment loss, and derive the gradient of the random walk kernel alignment loss with respect to node features, so that the gradient propagates backward along the physically coupled topological path.

[0051] This step is used to construct a kernel target alignment loss function based on the geometric random walk kernel matrix, to achieve consistency constraints between cross-domain graph topology and category semantics, and to derive the gradient propagation path of this loss with respect to node features.

[0052] Specifically, step S6 includes: Step S61: Under the batch training mechanism, a spatial constraint mask matrix is ​​introduced. This matrix is ​​a hard-coded matrix with fixed values: diagonal elements are set to 2.0, and off-diagonal elements are set to 0.1. These values ​​are used to explicitly distinguish between nodes from the same source channel and nodes from different sources: diagonal positions correspond to nodes from the same sensor in both the source and target domains, and are given higher weights to enhance their similarity contribution, ensuring that kernel alignment prioritizes maintaining the structural consistency of the same source channel; off-diagonal positions correspond to nodes from different sensors, and are given lower weights to retain weak constraints and avoid the loss of cross-channel structural information caused by setting them to zero.

[0053] For the first in the source domain batch The first image sample and the first in the target domain batch Given a graph sample, obtain the geometric random walk kernel matrix of that sample in the product graph space. After performing spatial constraint filtering using Hadamard product, the individual scalar similarity is obtained through average pooling. :

[0054] in, This indicates the average pooling operation. Represents the Hadamard product; Repeat the above calculation for all source-target domain sample pairs in the current batch to obtain A graph-level empirical topological similarity scalar Indicates batch size, and is ordered by sample index. Arranged to form an empirical topological kernel matrix :

[0055] Therefore, the empirical topological kernel matrix can be obtained. The general expression is: .

[0056] Using the source domain real label matrix With the target domain prediction probability matrix Constructing an ideal semantic kernel matrix , Total number of fault categories:

[0057] Constructing a semantic kernel using probabilistic soft labels can alleviate the noise accumulation problem caused by the uncertainty of target domain prediction.

[0058] Step S62: Define the random walk kernel alignment loss using the normalized cosine distance in Frobenius space. :

[0059] in, Represents the Frobenius inner product. Denotes the Frobenius norm; By minimizing the random walk kernel alignment loss, the empirical topological kernel matrix gradually approximates the ideal semantic kernel matrix, thereby achieving joint alignment between cross-domain graph structure and category semantics.

[0060] Step S63, define normalized cosine similarity. for:

[0061] The gradient of the random walk kernel alignment loss with respect to the empirical topological kernel matrix is ​​then... for:

[0062] in, Indicates partial derivative; The gradients mentioned above are used to drive the empirical topology to gradually approach the ideal semantic structure.

[0063] Furthermore, the geometric random walk kernel matrix with respect to the initial kernel state matrix... The gradient propagation process is as follows:

[0064] As shown in the above formula, the loss error will propagate backward along the random walk path in the topology of the source and target domain graphs. Since the random walk transition probability is determined by the mechanical coupling topology, nodes with higher coupling strength have a greater propagation weight during gradient propagation, thus enabling the parameter update process to maintain the consistency of the original dynamic structure.

[0065] Subsequently, the gradient is further propagated back to the node feature space, representing the gradient of the graph convolution source domain node features. for:

[0066] in, In the initial kernel state matrix, the source domain is represented by the first... The node and the target domain The local feature similarity values ​​between nodes; The gradient of the node features in the target domain of the graph convolution is : .

[0067] As can be seen from the above formula, the gradient directions of the node features in the source domain and the target domain are opposite, which makes nodes of the same category across domains move closer to each other in the feature space, while nodes of different categories move further apart.

[0068] Step S7: Construct a joint optimization objective function based on random walk kernel alignment loss and source domain supervised classification loss to train the cross-operating condition fault diagnosis model, and use the trained diagnosis model to predict the fault category of the target domain data.

[0069] To address the problem of cross-condition fault diagnosis under unlabeled target domain conditions, this invention employs a joint optimization strategy of supervised classification loss and random walk kernel alignment loss to collaboratively train the graph feature extractor, classifier, and kernel function parameters of the cross-condition fault diagnosis model.

[0070] Specifically, step S7 includes: Random walk kernel alignment loss Source domain supervised classification loss Weighted summation to construct the joint optimization objective function The expression is:

[0071] in, This is the loss trade-off coefficient (preferably 0.1). Source domain supervised classification loss Defined as:

[0072] in, Represents the source domain sample set, For source domain samples In fault category The real label (unique hot encoding) on ​​it. Predict the probability of the class output by the classifier. Index for fault categories.

[0073] Specifically, in the joint optimization process, cross-entropy loss is used to enhance the ability to distinguish source domain fault categories, and random walk kernel alignment loss is used to constrain the consistency of cross-domain graph topology. Model training uses the Adam optimizer for parameter updates, with the initial learning rate preferably set to 0.001, the batch size preferably set to 64, and the maximum number of training epochs preferably set to 200 epochs.

[0074] definition Indicates the parameters of the graph feature extractor. Indicates classifier parameters, The parameter update process for the cross-condition fault diagnosis model, representing the learning rate, is as follows:

[0075]

[0076]

[0077] in, Indicates source domain supervised classification loss gradient, Indicates the random walk kernel alignment loss pair gradient, Indicates source domain supervised classification loss gradient, Indicates the random walk kernel alignment loss pair The gradient.

[0078] As shown in the first formula of the parameter update process, the graph feature extractor simultaneously receives composite gradient signals from the classification loss and alignment loss. The classification loss enhances fault detection capabilities, while the alignment loss promotes cross-domain topological consistency. The second formula shows that the classifier is updated solely by the source domain classification loss to avoid interference from target domain pseudo-label errors on the classification decision boundary. The third formula reveals that the kernel bandwidth parameter is adaptively adjusted through the alignment loss to match the receptive field of the radial basis function kernel with the current feature space distribution.

[0079] Through the aforementioned joint optimization and gradient backpropagation process, the model can maintain its ability to distinguish fault categories while achieving consistent migration of cross-domain graph topology, thereby improving cross-domain fault diagnosis performance and model generalization ability under complex operating conditions.

[0080] To verify the effectiveness of the proposed method, this embodiment selects the Xi'an Jiaotong University gearbox dataset (XJTU dataset) and the high-speed rail traction motor bearing dataset (HRTM dataset) for experimental verification. Both datasets have a sampling length of 4096. The XJTU dataset includes three operating conditions: 15 Hz, 20 Hz, and 0-20-0 Hz, denoted as Condition 0, Condition 1, and Condition 2, respectively. The HRTM dataset includes three constant speed operating conditions: 16.67 Hz, 25 Hz, and 33.33 Hz, denoted as Condition 0, Condition 1, and Condition 2, respectively. The cross-condition migration diagnostic task is uniformly denoted as T. ij Where i represents the source domain condition index and j represents the target domain condition index. For example, task T 01 This indicates that the source domain samples come from operating condition 0, the target domain samples come from operating condition 1, and task T. 20This indicates that the source domain samples come from condition 2 and the target domain samples come from condition 0. In the comparative experiment, the average accuracy and standard deviation of the test results of the last 20 rounds of model training were used as the performance evaluation index. The diagnostic performance of the method of this invention was compared with that of four domain adaptation methods: Multi-Kernel Maximum Mean Discrepancy (MK-MMD), Correlation Alignment (CORAL), Joint Adaptation Network (JAN), and Local Maximum Mean Discrepancy (LMMD).

[0081] Table 1 presents the diagnostic results of the proposed method and its comparative methods on six cross-condition migration tasks in the XJTU dataset. As shown in Table 1, the proposed method achieves higher diagnostic accuracy in most migration tasks, with an average accuracy of 90.22% across the six tasks, significantly outperforming the MK-MMD, CORAL, JAN, and LMMD methods, which have average accuracies of 86.00%, 85.91%, 85.38%, and 86.26%, respectively. These results indicate that under variable speed gearbox conditions, the random walk graph kernel constructed in this invention can more effectively characterize the higher-order topological relationships between the source and target domains, thereby improving the alignment effect of cross-condition fault features and enhancing the model's adaptability to complex operating conditions. Table 2 presents the diagnostic results of the proposed method and its comparative methods on six cross-condition migration tasks in the HRTM dataset. As shown in Table 2, the method of this invention also exhibits excellent transfer diagnostic performance on this dataset, with an average accuracy of 97.53% across six tasks, higher than the average level of the comparative methods. Specifically, the average accuracy of the MK-MMD, CORAL, JAN, and LMMD methods ranges from 95.03% to 97.36%. These results demonstrate that, under the multi-speed operating conditions corresponding to the high-speed rail traction motor bearing data, the method of this invention can more stably extract fault representations with domain invariance. Furthermore, through random walk propagation and kernel alignment mechanisms in the direct product graph space, it effectively maintains the consistency of the cross-domain graph structure, thereby achieving higher diagnostic accuracy.

[0082] Table 1 Comparison of XJTU dataset results

[0083] Table 2 Comparison of HRTM dataset results

[0084] The experimental results in Tables 1 and 2 show that the method of this invention outperforms the traditional distributed alignment method in both types of rotating machinery cross-condition fault diagnosis tasks. This indicates that the proposed random walk graph kernel alignment mechanism can effectively measure the topological similarity between the source and target domains, enhance the structural migration capability and fault identification accuracy under cross-condition conditions, and has good method effectiveness and engineering applicability.

[0085] Furthermore, to determine the maximum number of random walk steps in the kernel alignment of the random walk graph... With higher order decay factor To determine the optimal configuration, this embodiment conducted parameter sensitivity analysis on a cross-condition task using the HRTM dataset. The experimental results are as follows: Figure 2 and Figure 3 As shown. Figure 2 For task T 20 Diagnostic accuracy response surface plot under (source domain condition 2 to target domain condition 0) Figure 3 For task T 02 The diagnostic accuracy response surface plot under (source domain condition 2 to target domain condition 0) represents the maximum number of random walk steps in a specific cross-condition diagnostic task. and higher order decay factor Sensitivity analysis of parameters affecting the diagnostic accuracy of the model.

[0086] Among them, the maximum number of random walk steps The value range is set to [1, 2, 4, 6, 12, 30], which is the higher-order attenuation factor. The value range is set to [0.0001, 0.001, 0.01, 0.1, 1]. For example... Figure 2 and Figure 3 As shown, with As the number of cells increases, the diagnostic accuracy shows a trend of first increasing and then decreasing; if... The size is small, random walks are limited to nearest neighbor nodes, and higher-order topological relationships are not fully involved in similarity measurement; if As the diffusion range continued to increase, the excessively long diffusion range did not further improve cross-domain graph structure matching; instead, it led to a decrease in accuracy. Meanwhile, Both excessively small and excessively large values ​​will lead to a decrease in accuracy, indicating that the contribution weight of higher-order walks needs to be controlled within a reasonable range. According to Figure 2 and Figure 3 The joint parameter optimization results, when set It is 6 and When the value is 0.01, the model achieves the highest accuracy under different tasks, realizing the optimal effect of cross-domain graph structure matching.

[0087] Furthermore, regarding the loss tradeoff coefficient in the joint optimization objective function In this embodiment, the preferred choice is... =0.1. This is used to adjust the relative weights of the source domain supervised classification loss and the random walk kernel alignment loss, in order to balance the fault category discrimination ability and the cross-domain topology alignment strength. If If the value is too large, the kernel alignment loss will dominate the parameter update process, easily interfering with the classification boundary and reducing the model's stability in identifying source domain fault categories; if... If the value is too small, the cross-domain topological constraint effect is insufficient, making it difficult to effectively reduce the distribution differences between different working condition diagram structures. Based on the synergistic relationship between the two types of loss terms in joint optimization, the value is chosen... When the value is 0.1, it can maintain the discriminative power of fault categories while giving full play to the cross-domain structure alignment function of the random walk graph kernel, thereby obtaining better cross-condition migration diagnostic performance.

[0088] In summary, the cross-condition bearing fault diagnosis method based on random walk graph kernel according to the above embodiments has the following beneficial effects: 1. This invention constructs a graph topology using a full-band energy-weighted coherence function, embedding vibration energy transfer relationships and phase coordination relationships into the adjacency matrix of the graph structure. Under varying operating conditions, this physical constraint helps reduce non-real connections introduced by statistical similarity fluctuations, improving the cross-condition stability of the graph topology.

[0089] 2. This invention establishes an initial similarity matrix for cross-domain nodes using a radial basis function with adaptive bandwidth, enabling the bandwidth parameter to adaptively adjust during network training and dynamically match the distribution characteristics of the current feature space. Furthermore, this invention models the topological relationship between the source and target domain graphs by performing synchronous random walks in the product graph space, directly measuring the structural similarity between cross-domain graphs at the topological level while preserving the connectivity between nodes.

[0090] 3. This invention constructs consistency constraints between empirical topological kernels and ideal semantic kernels directly using node-level features in the kernel space, thereby preserving the connection relationships between nodes and avoiding the loss of topological structure caused by graph-level aggregation. At the same time, this consistency constraint ensures that feature alignment takes into account both structural similarity and category discriminability between cross-domain graphs, and the use of soft labels to construct semantic kernels can reduce the impact of uncertainty in target domain prediction, thus effectively reducing the risk of confusion of fault categories during the migration process.

[0091] 4. In the backpropagation process, this invention uses gradient propagation of the alignment loss through the transition probability matrix determined by the physical coupling relationship, enabling sensor node pairs with higher coupling strength to obtain higher contribution weights in parameter updates. Furthermore, this invention integrates physical graph construction, graph convolution feature extraction, and orthographic graph spatial kernel alignment into an end-to-end training framework, avoiding error accumulation in multi-stage training.

[0092] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.

Claims

1. A method for fault diagnosis of axle box bearings under multiple operating conditions based on random walk graph kernels, characterized in that, include: Step S1: Obtain vibration signals collected by multiple sensors on the axle box bearing, perform sliding window segmentation on the vibration signals, extract frequency domain features to construct a graph node feature matrix, and then obtain the source domain and target domain node feature matrices. Step S2: Based on the node feature matrices of the source domain and the target domain, the coupling strength between the sensor channels in the source domain and the target domain is calculated using the full-band energy weighted coherence function, and a physically constrained graph adjacency matrix of the source domain and the target domain is constructed. Step S3: Using the adjacency matrix as a topological constraint, use a graph convolutional network to extract features from the source and target domain graphs to obtain the graph convolutional source domain node feature matrix and the graph convolutional target domain node feature matrix. Step S4: Based on the feature matrix of the source domain nodes and the feature matrix of the target domain nodes in the graph convolution, calculate the initial kernel similarity matrix between the source domain nodes and the target domain nodes using the radial basis kernel function with adaptive bandwidth. Step S5: Construct random walk transition probability matrices for the source and target domain graphs based on the adjacency matrix. In the product graph space, use the random walk transition probability matrix and iteratively propagate the initial kernel similarity matrix through a synchronous random walk mechanism to construct a geometric random walk kernel matrix. Step S6: Construct an empirical topological kernel matrix based on the geometric random walk kernel matrix, and then construct an ideal semantic kernel matrix. Calculate the normalized cosine distance between the empirical topological kernel matrix and the ideal semantic kernel matrix as the random walk kernel alignment loss, and derive the gradient of the random walk kernel alignment loss with respect to node features, so that the gradient propagates backward along the physically coupled topological path. Step S7: Construct a joint optimization objective function based on random walk kernel alignment loss and source domain supervised classification loss to train the cross-working condition fault diagnosis model, and use the trained diagnosis model to predict the fault category of the target domain data. Step S2 details include: Step S21: Calculate the channel using the Welch method. With channel Cross-power spectral density and passage Self-power spectral density and channels Self-power spectral density Then, the amplitude squared coherence function is calculated using the following formula. for: Step S22, based on channel Self-power spectral density Calculate frequency domain energy weights and will Normalized to the [0,1] interval, the full-band coherence function is weighted and integrated using frequency domain energy weights to obtain the channel. With channel Coupling strength between : Step S23: Arrange the coupling strengths between all channels calculated in step S22 according to their subscripts, and construct the source domain weight matrix for the source domain samples. , For the set of real numbers, Given the total number of sensor channels, construct a target domain weight matrix for the target domain samples. Set up the channel self-coupling strength , respectively and By performing symmetry transformation and taking the element-wise maximum value of each matrix and its transpose, the adjacency matrix of the source domain graph is obtained. Adjacency matrix of the target domain graph ; Step S6 specifically includes: Step S61, introduce the spatial constraint mask matrix. The Hadamard product pair geometric random walk kernel matrix is ​​used. Perform position filtering and obtain the empirical topology kernel matrix through average pooling, expressed as: in, Represents the empirical topological kernel matrix. Indicates batch size, Represents the Hadamard product. This indicates an average pooling operation; Using the source domain real label matrix With the target domain prediction probability matrix Constructing an ideal semantic kernel matrix , Total number of fault categories: in, Indicates transpose; Step S62: Define the random walk kernel alignment loss using the normalized cosine distance in Frobenius space. : in, Represents the Frobenius inner product. Denotes the Frobenius norm; Step S63, define normalized cosine similarity. for: The gradient of the random walk kernel alignment loss with respect to the empirical topological kernel matrix is ​​then... for: in, Indicates partial derivative; Geometric random walk kernel matrix with respect to initial kernel state matrix The gradient propagation process is as follows: in, This represents the maximum number of random walks. Indicates the higher-order decay factor. Represents the number of random walk steps factorial, Let be the source domain graph random walk transition probability matrix. Let the target domain graph random walk transition probability matrix be denoted as . Gradient of source domain node features in graph convolution for: in, In the initial kernel state matrix, the source domain is represented by the first... The node and the target domain The local feature similarity values ​​between nodes; Indicates the first Each graph convolution source domain node feature vector; Indicates the first Each graph convolution target domain node feature vector; For learnable kernel function bandwidth parameters; The gradient of the node features in the target domain of the graph convolution is : 。 2. The method for fault diagnosis of axle box bearings under different operating conditions based on random walk graph kernels according to claim 1, characterized in that, Step S1 specifically includes: With sampling frequency Vibration signals are acquired using a length of... A non-overlapping sliding window is used to equidistantly truncate the time-domain signals of each channel, generating... There are 10 short-term observation samples, each sample having a dimension of 1. The source domain samples and target domain samples originate from different operating conditions; the source domain samples contain known fault category labels, while the target domain samples do not contain manually labeled information; for each sample, the first... Perform a Fast Fourier Transform on the time-domain signals of each channel to extract the single-sided amplitude spectrum. Frequency domain feature dimension ;right The frequency domain signals of each sensor channel are normalized to zero mean and unit variance to obtain the source domain node feature matrix. With the target domain node feature matrix , where each row of the matrix corresponds to the frequency domain feature vector of a sensor node.

3. The method for fault diagnosis of axle box bearings under different operating conditions based on random walk graph kernels according to claim 2, characterized in that, Step S3 specifically includes: In step S31, each sensor channel is mapped to a graph node, and the number of graph nodes is defined to be equal to the total number of sensor channels , the source domain node feature matrix and the target domain node feature matrix are respectively mapped to a low-dimensional latent space through a fully connected layer to obtain initial node embeddings , the hidden layer dimension is set to 256; Step S32, for the adjacency matrix Add the identity matrix Obtain the extended adjacency matrix containing self-loops. Adjacency matrix Divided into source domain graph adjacency matrix Adjacency matrix of target domain graph Calculate the extended adjacency matrix degree matrix , The main diagonal element in , Represents the extended adjacency matrix The Middle Line 1 The elements of the column, subsequently, are embedded with the initial node output from step S31. For input, perform normalized graph convolution according to the following formula: in, This is the node feature matrix output by the convolutional layer of the first image. Here, ReLU is the first-layer learnable weight matrix, and ReLU is the non-linear activation function. Step S33, with Execute a second graph convolutional layer for the input: in, This is the node feature matrix output by the convolutional layer in the second graph. This is the second-layer learnable weight matrix; Step S34, will and Element-by-element addition is performed to obtain the residual fusion result. The residual fusion result of the source domain is used as the feature matrix of the source domain nodes in the graph convolution. The residual fusion result of the target domain is used as the feature matrix of the target domain nodes in the graph convolution. ; Step S35, for Global average pooling is performed at the node level to obtain a graph-level vector representation, which is then input into a fully connected classifier to output the predicted probability of the fault category.

4. The method for fault diagnosis of axle box bearings under different operating conditions based on random walk graph kernels according to claim 3, characterized in that, Step S4 specifically includes: Based on the feature matrix of source domain nodes in graph convolution Convolution with the target domain node feature matrix The local feature similarity between cross-domain node pairs is calculated using a radial basis kernel function with an adaptive bandwidth parameter, expressed as follows: in, For the source domain The node and the target domain Local feature similarity between nodes Represents the Euclidean norm; For all cross-domain node pairs, the calculated local feature similarity is as follows: , Arrange the kernel similarity matrix to obtain the initial kernel similarity matrix. .

5. The method for fault diagnosis of axle box bearings under different operating conditions based on random walk graph kernels according to claim 4, characterized in that, Step S5 specifically includes: Step S51, based on the source domain graph adjacency matrix Adjacency matrix of the target domain graph Construct the corresponding source domain degree matrix respectively. With the target domain degree matrix Perform row-wise normalization on the adjacency matrix to obtain the random walk transition probability matrix of the source domain graph. With the target domain graph random walk transition probability matrix The expression is: Step S52, in the product graph space, The initial kernel state matrix of the random walk diffusion process Then, the source domain graph random walk transition probability matrix is ​​used. With the target domain graph random walk transition probability matrix And perform higher-order topology diffusion on the cross-domain graph structure through a synchronous random walk mechanism, the first The update process of the kernel matrix for a random walk is defined as follows: in, Indicates the first The kernel matrix after one random walk. Indicates the first The kernel matrix after one random walk; From 0 to The geometric random walk kernel matrix is ​​obtained by performing a finite-order cumulative expansion on the random walk kernel matrix. : 。 6. The method for fault diagnosis of axle box bearings under different operating conditions based on random walk graph kernels according to claim 5, characterized in that, Step S7 specifically includes: Random walk kernel alignment loss Source domain supervised classification loss Weighted summation to construct the joint optimization objective function The expression is: in, For loss trade-off coefficients; Source domain supervised classification loss Defined as: in, Represents the source domain sample set, For source domain samples In fault category The real labels on Predict the probability of the class output by the classifier. Index for fault categories; definition Indicates the parameters of the graph feature extractor. Indicates classifier parameters, The learning rate is represented by the parameter update process of the cross-condition fault diagnosis model as follows: in, Indicates source domain supervised classification loss gradient, Indicates the random walk kernel alignment loss pair gradient, Indicates source domain supervised classification loss gradient, Indicates the random walk kernel alignment loss pair The gradient.

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