Variable working condition bearing fault diagnosis method based on domain adversarial hybrid graph convolutional network

Abstract

The invention belongs to the technical field of equipment fault diagnosis, and discloses a variable working condition bearing fault diagnosis method based on a domain adversarial hybrid graph convolutional network. According to the specific technical scheme, the method comprises the specific steps that firstly, a convolutional neural network is used for conducting feature extraction on input data, obtained features serve as nodes, secondly, an adjacent matrix is obtained through a graph generation layer, an association graph is constructed according to the input matrix, and thirdly, the association graph is obtained. Inputting the constructed graph into a multi-receptive-field mixed graph convolutional network to extract structural information, capturing local structural information and global structural information of the graph from the perspective of the graph convolutional network and graph sampling and aggregation by using the multi-receptive-field mixed graph convolutional network, and finally, extracting the structural information of the graph from the perspective of the multi-receptive-field mixed graph convolutional network. And fault classification is carried out on the obtained features through a transfer learning method, so that the fault diagnosis capability of the model on a target domain is improved, and the expression capability, the generalization performance and the robustness of the model are remarkably improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of equipment fault diagnosis, and specifically relates to a variable operating condition bearing fault diagnosis method based on a domain adversarial hybrid graph convolutional network. Background Art

[0002] With the vigorous development of equipment manufacturing industry, rotating machinery has been widely used in all walks of life. As an important part of rotating machinery, rolling bearings work in harsh environments for a long time, so their health has a great impact on the safe use of machinery. Because the working environment of bearings is mostly under high temperature and high pressure, the environment is harsh, which makes it easy to have various faults. When the bearing fails, the machine must be stopped, and expensive maintenance costs will be incurred. In serious cases, there will be casualties. In order to avoid irreparable losses caused by rotating machinery failures, it is necessary to diagnose the bearing faults.

[0003] In recent years, the rapid development of artificial intelligence technology has promoted the transformation of research methods in the field of fault diagnosis from traditional machine learning to deep learning (DL). This method has attracted the attention of most scholars because of its ability to extract features and train models from input to output. The DL-based method constructs a neural network model for fault diagnosis. It can automatically extract data features and perform well when processing complex data. Therefore, in the field of fault diagnosis, the DL method is very helpful in improving the diagnosis effect. Typical methods include convolutional neural networks (CNN), residual neural networks, recurrent neural networks, autoencoders, and graph convolutional neural networks (GCNN). Although CNN appeared earlier, many scholars are still committed to its optimization and improvement, and have successfully applied it to the field of fault diagnosis, achieving remarkable results.

[0004] Although the use of DL methods has significantly improved the diagnostic performance, these methods still have some defects that cannot be ignored. First, most DL-based methods are carried out under the condition that the distribution of samples is the same during training and testing, but the actual situation is that the operating conditions of the machine will change due to factors such as mechanical fault conditions and external interference. This may lead to inconsistent probability distributions between training samples and test samples, making the above assumptions difficult to hold. Secondly, DL models need to be trained with large-scale data. However, the actual situation is that there are very few labeled sample data in large-scale data, and due to various factors, it is almost impossible to label all data. The lack of a large amount of labeled data will make these methods very ineffective, affecting their use in fault diagnosis in related industries.

[0005] Gopalan et al. solved the defects of DL by using unsupervised domain adaptation (UDA). This method can divide the dataset into two parts, one with labels as the source domain and one without labels as the target domain. Then, by narrowing the distribution difference between the two domains, the model can perform classification without data labels.

[0006] In recent years, it has become increasingly common to solve the problem of insufficient sample data in fault diagnosis through the UDA method. At present, some UDA methods only model class labels and domain labels, but ignore the important information of data structure. Modeling the structural information in the data can effectively reduce the data distribution difference and make the source domain samples perform better when diagnosing the target domain samples. Therefore, it is very beneficial to model the data structure information in the UDA method. In order to model the structural information of the data more effectively, the structural information of the data is modeled by introducing graph convolutional networks (GCNs). Through the graph convolution operation, the node features of the central node are aggregated along the neighboring nodes connected to it to form new node features, so that the hidden representation and label of the central node can be obtained, and the newly formed node features have rich data structure information.

[0007] However, the traditional GCN has two limitations. First, the size of the receptive field is fixed, and the aggregated neighbor node information is also unchanged, so the extracted information will be incomplete; second, the edge values ​​of each node used in the graph convolution operation are the same, which means that they are equally important to the neighbor nodes. However, in reality, the importance of these nodes cannot be the same. Therefore, Li et al. improved the graph convolution network. By parallelizing multiple graph convolution networks with different receptive fields, it can flexibly process and integrate neighborhood information from different ranges, thus overcoming the limitations of GCN in processing large-scale graph data. In addition, MRF-GCN will weight each node according to its importance to its neighbor nodes when composing the graph, so that the network can more accurately capture the complex relationship between nodes, thereby improving the accuracy and effectiveness of information transmission.

[0008] Li et al. proposed a method combining MRF-GCN with domain adversarial graph convolutional network (DAGCN), which not only models class labels and domain labels, but also considers data structure information. For the modeling of data structure information, the association graph is first constructed using the graph generation layer, and then the MRF-GCN model is used for modeling. DAGCN achieves high-accuracy cross-domain fault diagnosis by minimizing the differences in three types of information between different domains. Kavianpour et al. proposed an ARMA graph convolution method, which is combined with an adversarial adaptive method to significantly improve the performance of bearing fault diagnosis. This method models data structure information through ARMA graph convolution and uses an adversarial adaptive method to reduce the differences in structural distribution between domains.

[0009] At the same time, MK-LMMD is used to reduce the distribution differences of subdomains of the same category, so that the model can maintain high diagnostic performance even under the conditions of lack of data and changes in working conditions. Li et al. proposed a method that can effectively improve the efficiency of data structure information extraction. This method first uses ResNet-18 to extract information, and then integrates three graph convolution layers (MRF-Conv, LE-Conv and GAT-Conv) to effectively mine data structure information, thereby improving feature extraction and classification capabilities. Then, the data structure differences are aligned through the correlation alignment (CORAL) indicator. Experiments have verified that this method significantly enhances the classification and feature extraction capabilities and effectively improves the diagnostic performance.

[0010] The above research work has made outstanding contributions to cross-domain unsupervised domain adaptation, but there are still some problems: MRF-GCN can only extract a single type of graph structure information and it is difficult to capture local and global graph structure information at the same time. This limitation will lead to insufficient information expression ability of convolutional output features, thereby limiting its application in complex graph structures.

[0011] MMD can only evaluate the marginal distribution differences of the data structure and ignores the conditional distribution differences. In addition, MMD only considers first-order statistics, which will result in the inability to fully align the feature structures of the source domain and the target domain during transfer learning. Summary of the invention

[0012] In order to solve the technical problems existing in the prior art, the present invention provides a variable operating condition bearing fault diagnosis method based on domain adversarial hybrid graph convolutional network to solve the problems existing in MRF-GCN and MMD and improve the classification ability under variable operating conditions.

[0013] To achieve the above-mentioned purpose, the technical solution adopted by the present invention is: a variable operating condition bearing fault diagnosis method based on domain adversarial hybrid graph convolutional network. The network structure of DAHGCN (domain adversarial hybrid graph convolutional network) is divided into four components: similar steps to the DAGCN network. First, CNN (convolutional neural network) is used to extract features of the input data, and the obtained features are used as nodes. Secondly, GGL (graph generation layer) is used to obtain the adjacency matrix, and the association graph is constructed according to the input matrix. Thirdly, the constructed graph is input into MRF-HGCN (multi-receptive field hybrid graph convolution) to extract structural information. Finally, the obtained features are used for fault classification through transfer learning method.

[0014] The specific process of the method proposed by the present invention is as follows:

[0015] First, a four-layer CNN is used to extract features from the input data, and the node feature X is obtained as:

[0016] X = CNN(X input ) (1)

[0017] X input is the input matrix;

[0018] By using GGL to obtain the adjacency matrix A of the graph, the association graph is constructed based on X and A. The calculation process of the adjacency matrix A is shown in formula (2):

[0019]

[0020] Among them, MLP is a multi-layer perceptron, normlize means normalization, Top-k means finding the top k largest elements from a set of data, and GGL stands for graph generation layer.

[0021] The multi-receptive field graph convolutional network (MRF-GCN) can extract features from multiple receptive fields and fuse these features to enhance feature representation. In the experiment, it was found that the diagnostic effect was best when the number of receptive field layers was 3 and the receptive field sizes were 1, 2, and 3 respectively; MRF-GCN is a graph convolution layer operation with three receptive fields in parallel. The node feature matrix of MRF-GCN is defined as follows:

[0022]

[0023] Among them, θ k ′ represents the weight parameter, K represents the receptive field size, and W is θ k ′ in matrix form, represents the rescaled Laplacian matrix, T k represents the k-order Chebyshev polynomial, and H1 represents the feature obtained by concatenating the features of the three layers of graph convolutional layers:

[0024] Graph Sampling and Aggregation (Graph-SAGE) belongs to inductive learning and is one of the representative algorithms in graph neural networks. Graph-SAGE follows the main idea of ​​graph neural networks. Graph-SAGE learns a mapping that generates an embedded representation for each node, and trains a feature vector containing neighbor information by aggregating the feature information of neighbor nodes. First, any number of neighbor nodes are randomly selected from the target node, and then the target node and its neighbor node information are aggregated to obtain a new embedded representation of the target node. The new embedded representation contains the feature information of the target node and its neighboring nodes.

[0025] Use Graph-SAGE to fully utilize neighborhood features to identify outliers and define them through aggregation k Aggregate neighbor node information to the target node, The aggregation functions are shown in formulas (4) and (5):

[0026]

[0027]

[0028] In the formula, is the embedding representation of node v at layer k, is the embedding representation of node v at the k-1 layer, u represents the neighbor node of v, represents the set of neighbor nodes of node v, W k is the weight parameter of the kth layer, σ is the activation function, AGGREGATE k represents the selected aggregation function, and CONCAT represents the concatenation of features. Formulas (4) and (5) show that: first, the k-1 layer embedding representation of node v’s neighbor nodes is used to generate the k-th layer aggregate representation of its neighbor nodes. Then and the k-1th layer representation of node v After concatenation, a nonlinear transformation is performed to generate the k-th layer embedding representation of node v.

[0029] In the graph, the neighbor nodes of the nodes are unordered, and the constructed aggregation function is symmetrical and has high expressive power. The symmetric performance of the aggregation function ensures that the neural network model can be trained and applied to node neighbor node feature sets in any order;

[0030] Graph-SAGE has three aggregation functions:

[0031] Mean aggregation: By calculating the mean of each dimension of the central node and the neighboring nodes, or averaging each dimension of the neighboring nodes and then concatenating them with the features of the central node, the specific formula is as follows:

[0032]

[0033] Among them, mean indicates the use of the mean aggregation function.

[0034] LSTM aggregation: Since LSTM is sensitive to the input order of the sequence, it does not have permutation invariance. Therefore, it is necessary to first randomize the order of neighbor nodes and then use the embedded representation of the neighbor sequence as the input of LSTM to adapt LSTM to operate on unordered sets.

[0035] Pooling aggregation: Pooling aggregation is both symmetric and trainable. It first performs a nonlinear transformation on the embedding vectors of the target node's neighbor nodes, then performs a pooling operation (maximum pooling or mean pooling), and then concatenates the result with the representation vector of the target node. Finally, it performs another nonlinear transformation to obtain the k-th layer representation vector of the target node.

[0036]

[0037] Among them, max is the maximum pooling operation.

[0038] The MRF-HGCN proposed in the present invention effectively captures the multi-level structural information of nodes by using Graph-SAGE and GCN with different receptive fields (K=2 and K=3) in parallel. These two convolution methods have their own characteristics and extract information from the graph from different angles. Specifically, Graph-SAGE is good at capturing local features of the graph, while GCN with multiple receptive fields can better extract global features of the graph. In addition, due to the use of the Graph-SAGE method, the model shows strong generalization ability and adaptability when processing different types of graph data, especially when processing large-scale sparse graphs, it can more effectively aggregate information of distant nodes. Through this multi-perspective, multi-level feature extraction method, the model can more comprehensively understand the relationship between nodes, thereby improving the efficiency and quality of feature extraction. In the present invention, the aggregation function uses mean aggregation, so the node feature matrix of MRF-HGCN is defined as follows:

[0039]

[0040] The objective function to be optimized consists of three parts: feature extractor (F), domain discriminator (D) and label classifier (C). In order to extract migration features and construct class labels, domain labels, and data structure information, the overall objective function includes classification loss, domain alignment loss, and structural difference alignment loss:

[0041] 1. Sample classification loss: This part of the loss is the loss generated when the unlabeled samples in the source domain are classified after training with the labeled samples in the source domain. In order to accurately identify the fault type in the source domain, this part of the loss should be as small as possible. The cross entropy loss is used as the measurement standard. The specific formula is shown in (9):

[0042]

[0043] Among them, I is the prediction result of the label classifier, L C (·) represents the classification loss, represents the predicted label of the source domain, Υ s represents the true label of the source domain, E(·) represents the expectation, represents the i-th sample in the source domain, Represents the true label corresponding to the i-th sample in the source domain.

[0044] 2. Domain alignment loss: In order to capture domain invariant features, this part of the loss is needed to evaluate whether the domain discriminator can distinguish whether the data is from the source domain or the target domain. The binary cross entropy loss is used as the measurement standard for this part of the loss. The specific formula is shown in (10):

[0045]

[0046] Among them, L DA (·) denotes the domain alignment loss, represents the characteristics of the jth sample in the target domain, represents the characteristics of the i-th sample in the source domain, represents the predicted label of the source domain, Represents the predicted label of the target domain. The value of D is used to determine which domain the sample data comes from. The source domain is 1 and the target domain is 0.

[0047] 3. Structural alignment loss: When aligning the feature structures of the source domain and the target domain, the loss function of embedding joint maximum mean difference (JMMD) and correlation alignment (CORAL) is used as the structural difference alignment loss, which realizes the simultaneous alignment of marginal distribution and conditional distribution in an unsupervised case.

[0048] The JMMD calculation formula is as follows:

[0049]

[0050] Among them, P s represents the joint distribution of the source domain, Q t represents the joint distribution of the target domain, is a centerless cross-variance operator, It means that the calculation process is carried out in the reproducing kernel Hilbert space.

[0051] The calculation formula of CORAL is as follows:

[0052]

[0053] Among them, C s represents the covariance matrix of the source domain, C t represents the covariance matrix of the target domain, ||·|| F represents the Frobenius norm, X s Represents the data matrix form of the source domain, X t Represents the data matrix form of the target domain, n s Represents the number of source domain samples, n t represents the number of samples in the target domain, d represents the dimension of the feature vector, and 1 represents a full 1 vector.

[0054] The present invention uses JMMD and CORAL as structural alignment loss. JMMD can measure the marginal distribution and conditional distribution of data structure at the same time, while CORAL can align the second-order statistical characteristics of data structure. The weight distribution can simultaneously utilize different statistical characteristics of data to provide the model with more comprehensive domain adaptation capabilities. Therefore, the structural alignment loss L SA The calculation formula is as follows:

[0055] L SA =αL JMMD +(1-α)L CORAL (14)

[0056] Among them, α is the weight coefficient.

[0057] In summary, combined with the three different loss functions defined, the overall objective function L Total for:

[0058] L Total =L C +γL DA +κL SA (15)

[0059] Among them, γ and κ are weight coefficients.

[0060] Model parameter update: The parameters that need to be updated are in equation (15), where θ F is the parameter of the feature extractor, θC is the parameter of the classifier, θ D are the parameters of the domain discriminator. During the model training process, the three parameters are expressed by formulas (16), (17), and (18):

[0061]

[0062] It means that the partial derivative of the function needs to be calculated, and η represents the learning rate set when updating the parameters.

[0063] The process of DAHCGN parameter update is shown in formula (19):

[0064]

[0065] By minimizing L in formula (15) Total And optimize the parameters of DAHGCN to reduce the distribution difference between the source domain and the target domain, so that the classifier trained with sample data from the source domain can achieve the same classification accuracy as the source domain when classifying target domain data with the same distribution.

[0066] Compared with the prior art, the present invention has the following beneficial effects:

[0067] 1. The present invention proposes a multi-receptive field hybrid graph convolutional network, which extracts the local and global structural information of the graph more comprehensively through the GCN and Graph-SAGE methods. Graph-SAGE is an inductive learning method that can realize feature self-learning on new nodes by learning the feature aggregation function of neighbor nodes, thereby significantly improving the expressiveness, generalization performance and robustness of the model.

[0068] 2. The present invention jointly uses the joint maximum mean difference and correlation alignment as the structural alignment loss. JMMD can simultaneously measure the marginal distribution difference and the conditional distribution difference, while CORAL can align the second-order statistical characteristics of the data. By jointly using these two loss functions, the different statistical characteristics of the data can be fully utilized, thereby providing the model with more comprehensive domain adaptation capabilities.

[0069] 3. This paper constructs a graph transfer learning framework based on MRF-HGCN. The framework first uses CNN to extract spatial features, then uses MRF-HGCN to extract structural features, and finally reduces the distribution difference between the source domain and the target domain by minimizing the sum of three losses. This framework can achieve high-accuracy bearing variable operating condition fault diagnosis. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 Schematic diagram of DAHGCN network framework.

[0071] Figure 2 This is a schematic diagram of the structure of the graph generation layer GGL.

[0072] Figure 3 Schematic diagram of the structure of the double-layer MRF-GCN.

[0073] Figure 4 Schematic diagram of the sampling and aggregation process of Graph-SAGE.

[0074] Figure 5 Schematic diagram of the structure of the double-layer MRF-HGCN.

[0075] Figure 6 Schematic diagram of the diagnostic process of DAHGCN.

[0076] Figure 7 This is a schematic diagram of the structure of the CWRU gearbox test bench.

[0077] Figure 8 Migrate Task A for the CWRU dataset 01 Accuracy and loss curves.

[0078] Fig. 9 Migrate Task A for the CWRU fault dataset 01 The confusion matrix of .

[0079] Fig.10 The histogram of experimental results for the CWRU dataset.

[0080] Fig.11 This is a site photo of the JNU bearing failure operation test bench.

[0081] Fig.12 Figure 2 shows three different fault states of JNU bearings.

[0082] Fig.13 Migrate Task B for the JNU dataset 01 Accuracy and loss curves.

[0083] Fig.14 Migrate Task B for the JNU Fault Dataset 01 The confusion matrix of .

[0084] Fig.15 This is the experimental result of the JNU dataset migration task.

[0085] Fig.16 Visualization of the migration task 0→1 for the CWRU dataset.

[0086] Fig.17 Visualization of the 0→1 migration task for the noisy CWRU dataset.

[0087] Fig.18 Visualization of the migration task 0→1 for the JNU dataset. DETAILED DESCRIPTION

[0088] In order to make the technical problems, technical solutions and beneficial effects to be solved by the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0089] A variable-condition bearing fault diagnosis method based on domain adversarial hybrid graph convolutional network, the framework diagram of DAHGCN (domain adversarial hybrid graph convolutional network) is shown in Figure 1 As shown in the figure, the network is divided into four components, which are similar to the steps of DAGCN (Domain Adversarial Graph Convolutional Network). First, the CNN network (Convolutional Neural Network) is used to extract features of the input data, and the obtained features are used as nodes. Secondly, the GGL (Graph Generation Layer) is used to construct the association graph. Thirdly, the constructed graph is input into MRF-HGCN (Multi-Receptive Field Hybrid Graph Convolutional Network) to extract structural information. Finally, the obtained features are used for fault classification through transfer learning. The specific process of the proposed method is as follows:

[0090] First, a four-layer CNN is used to extract features from the input data, and the node feature X is obtained as:

[0091] X = CNN(X input ) (1)

[0092] X input is the input matrix;

[0093] Then, by using GGL, we can get the adjacency matrix A of the graph, and then we can build the association graph based on X and A. The process is as follows: Figure 2 As shown, the calculation process of the adjacency matrix A is shown in formula (2):

[0094]

[0095] Among them, MLP is a multi-layer perceptron, normlize means normalization, Top-k means finding the top k largest elements from a set of data, and GGL stands for graph generation layer.

[0096] The multi-receptive field graph convolutional network (MRF-GCN) extracts features from multiple receptive fields and fuses these features to enhance feature representation. In the experiment, it was found that the diagnostic effect was best when the number of receptive field layers was 3 and the receptive field sizes were 1, 2, and 3 respectively. Figure 3 As shown in the figure, MRF-GCN is a graph convolution layer operation with three receptive fields in parallel, and its node feature matrix is ​​defined as follows:

[0097]

[0098] Among them, θ k ′ represents the weight parameter, K represents the receptive field size, and W is θ k ′ in matrix form, represents the rescaled Laplacian matrix, T k represents the k-th order Chebyshev polynomial, and H1 represents the feature obtained by concatenating the features of the three graph convolutional layers.

[0099] Graph Sampling and Aggregation (Graph-SAGE) belongs to inductive learning and is one of the representative algorithms in graph neural networks. Graph-SAGE follows the main idea of ​​graph neural networks. Graph-SAGE does not try to learn the embedded representation of all nodes on a graph, but learns a mapping that generates an embedded representation for each node. The feature vector containing the neighbor information is trained by aggregating the feature information of neighbor nodes. The sampling and aggregation process of the two-layer Graph-SAGE is as follows: Figure 4 As shown, firstly, any number of neighbor nodes are randomly selected from the target node, and then the target node and its neighbor node information are aggregated to obtain a new embedding representation of the target node. The new embedding representation contains the feature information of the target node and its neighboring nodes.

[0100] Graph-SAGE can fully utilize neighborhood features to identify outliers and define them through aggregation. k Aggregate neighbor node information to the target node, The aggregation functions are shown in formulas (4) and (5):

[0101]

[0102] In the formula, is the embedding representation of node v at layer k, is the embedding representation of node v at the k-1 layer, u represents the neighbor node of v, represents the set of neighbor nodes of node v, W k is the weight parameter of the kth layer, σ is the activation function, AGGREGATE k represents the selected aggregation function, and CONCAT represents the concatenation of features. Formulas (4) and (5) explain: First, the k-1 layer embedding representation of the neighboring nodes of node v is used to generate the k-th layer aggregation representation of its neighboring nodes. Then and the k-1th layer representation of node v After concatenation, a nonlinear transformation is performed to generate the k-th layer embedding representation of node v.

[0103] The neighbor nodes of the nodes in the graph are unordered, and the constructed aggregation function is symmetric (that is, the output of the function remains unchanged for various permutations of its input) and has high expressive power. The symmetry of the aggregation function ensures that the neural network model can be trained and applied to node neighbor node feature sets in any order;

[0104] Graph-SAGE has three aggregation functions:

[0105] Mean aggregation: By calculating the mean of each dimension of the central node and the neighboring nodes, or averaging each dimension of the neighboring nodes and then concatenating them with the features of the central node, the formula is as follows:

[0106]

[0107] Among them, mean indicates the use of the mean aggregation function.

[0108] LSTM aggregation: Since LSTM is sensitive to the input order of the sequence (asymmetric), it does not have permutation invariance. Therefore, it is necessary to first randomize the order of neighbor nodes, and then use the embedded representation of the neighbor sequence as the input of LSTM, so that LSTM can adapt to operating on unordered sets;

[0109] Pooling aggregation: Pooling aggregation is both symmetric and trainable. It first performs a nonlinear transformation on the embedding vectors of the target node's neighbor nodes, then performs a pooling operation (maximum pooling or mean pooling), and then concatenates the result with the representation vector of the target node. Finally, it performs another nonlinear transformation to obtain the k-th layer representation vector of the target node.

[0110]

[0111] Among them, max is the maximum pooling operation.

[0112] The MRF-HGCN proposed in the present invention effectively captures the multi-level structural information of nodes by using Graph-SAGE and GCN with different receptive fields (K=2 and K=3) in parallel. These two convolution methods have their own characteristics and extract information from the graph from different angles. Specifically, Graph-SAGE is good at capturing local features of the graph, while GCN with multiple receptive fields can better extract global features of the graph. In addition, due to the use of the Graph-SAGE method, the model demonstrates strong generalization and adaptability when processing different types of graph data, especially when processing large-scale sparse graphs, it can more effectively aggregate information from distant nodes. Through this multi-perspective, multi-level feature extraction method, the model can more comprehensively understand the relationship between nodes, thereby improving the efficiency and quality of feature extraction. In the present invention, the aggregation function uses mean aggregation, so, if Figure 5 The structure of MRF-HGCN is shown, and its node feature matrix is ​​defined as follows:

[0113]

[0114] The objective function to be optimized consists of three parts: feature extractor (F), domain discriminator (D) and label classifier (C). In order to extract migration features and construct class labels, domain labels, and data structure information, the overall objective function includes classification loss, domain alignment loss, and structural alignment loss:

[0115] 1. Sample classification loss: This part of the loss is the loss generated when the unlabeled samples in the source domain are classified for fault classification after training with the labeled samples in the source domain. In order to accurately identify the fault type in the source domain, this part of the loss should be as small as possible. The cross entropy loss is used as the measurement standard. The formula is shown in (9):

[0116]

[0117] Among them, I is the prediction result of the label classifier, L C (·) represents the classification loss, represents the predicted label of the source domain, Υ s represents the true label of the source domain, E(·) represents the expectation, represents the i-th sample in the source domain, Represents the true label corresponding to the i-th sample in the source domain.

[0118] 2. Domain alignment loss: In order to capture domain invariant features, this part of the loss is needed to evaluate whether the domain discriminator can distinguish whether the data is from the source domain or the target domain. The binary cross entropy loss is used as the measure of this part of the loss. The formula is shown in (10):

[0119]

[0120] Among them, L DA (·) denotes the domain alignment loss, represents the characteristics of the jth sample in the target domain, represents the characteristics of the i-th sample in the source domain, represents the predicted label of the source domain, Represents the predicted label of the target domain. The value of D is used to determine which domain the sample data comes from. The source domain is 1 and the target domain is 0.

[0121] 3. Structural alignment loss: When aligning the feature structures of the source domain and the target domain, the loss function of embedding joint maximum mean difference (JMMD) and correlation alignment (CORAL) is used as the structural alignment loss, which achieves the simultaneous alignment of marginal distribution and conditional distribution in an unsupervised case.

[0122] The JMMD calculation formula is as follows:

[0123]

[0124] Among them, P s represents the joint distribution of the source domain, Q t represents the joint distribution of the target domain, is a centerless cross-variance operator, It means that the calculation process is carried out in the reproducing kernel Hilbert space.

[0125] The calculation formula of CORAL is as follows:

[0126]

[0127] Among them, C s represents the covariance matrix of the source domain, C t represents the covariance matrix of the target domain, ||·|| F represents the Frobenius norm, X s Represents the data matrix form of the source domain, X t Represents the data matrix form of the target domain, n s Represents the number of source domain samples, n t represents the number of samples in the target domain, d represents the dimension of the feature vector, and 1 represents a full 1 vector.

[0128] The present invention uses JMMD and CORAL as structural alignment loss. JMMD can measure the marginal distribution and conditional distribution of data structure at the same time, while CORAL can align the second-order statistical characteristics of data structure. The weight distribution can simultaneously utilize different statistical characteristics of data to provide the model with more comprehensive domain adaptation capabilities. Therefore, the structural alignment loss L SA The calculation formula is as follows:

[0129] L SA =αL JMMD +(1-α)L CORAL (14)

[0130] Among them, α is the weight coefficient.

[0131] In summary, combined with the three different loss functions defined above, the overall objective function L Total for:

[0132] L Total =L C +γL DA +κL SA (15)

[0133] Among them, γ and κ are weight coefficients.

[0134] The parameters that need to be updated are in equation (15), where θ F ,θ C and θ D are the parameters of the feature extractor, classifier and domain discriminator. During the model training process, the three parameters are expressed by formulas (16), (17) and (18):

[0135]

[0136] It means that the partial derivative of the function needs to be calculated, and η represents the learning rate set when updating the parameters.

[0137] The process of DAHCGN parameter update is shown in formula (19):

[0138]

[0139] By minimizing L in formula (15) Total And optimize the parameters of DAHGCN to reduce the distribution difference between the source domain and the target domain, so that the classifier trained with sample data from the source domain can achieve the same classification accuracy as the source domain when classifying target domain data with the same distribution. Therefore, the detailed flowchart of using the proposed DAHGCN to achieve diagnosis is as follows: Figure 6 shown.

[0140] Experimental studies are conducted on the Case Western Reserve University (CWRU) fault dataset and the Jiangnan University (JNU) fault dataset, and the effectiveness and accuracy of the proposed method in UDA variable operating condition fault diagnosis are verified by comparing with other models.

[0141] In the CWRU data experiment, the gearbox test bench consists of a drive motor, bearings, gearbox and load. Figure 7 As shown, this experimental simulation selected 9 types of rolling bearing fault categories, including slight failure of rolling element, slight failure of outer ring, slight failure of inner ring, moderate failure of rolling element, moderate failure of outer ring, moderate failure of inner ring, severe failure of rolling element, severe failure of outer ring, severe failure of inner ring, and finally the normal state, a total of 10 categories. The experiment collected vibration signals through the acceleration vibration sensor installed on the gearbox. The sampling frequency of the sensor was 10240HZ. Four different rotation speeds of 1730rpm, 1772rpm, 1797rpm and 1750rpm were simulated, and they were regarded as four working conditions, using 0, 1, 2 and 3 to represent these four different working conditions. Therefore, the experiment conducted 12 cross-domain transfer learning tasks, using A ab To represent the variable working condition migration task a→b, it means that the model is trained with the data of working condition a and tested with the data of working condition b.

[0142] In this experiment, the input data is standardized by the standard deviation normalization method, and then the original signal is divided into sub-samples with a length of 1024 and no intersection between each sample. There are 1760 samples in the CWRU data set, which are divided into 8:2 ratios, 80% of which are training sets and 20% of which are test sets. Therefore, for each working condition, there are 1408 samples in the training set and 352 samples in the test set.

[0143] In order to highlight the superiority of the proposed model DAHGCN, comparative experiments were conducted. The comparative methods are: JAN, CORAL, Graph-SAGE, and DAGCN. The above aspects all use a four-layer CNN network for feature extraction. However, Graph-SAGE first uses a four-layer CNN network and then passes through two layers of Graph-SAGE, while DAGCN first passes through a four-layer CNN and then uses a two-layer MRF-GCN network for feature extraction. In the model proposed by the present invention, a four-layer CNN is first used to extract data features and then an MRF-HGCN network is used to extract structural features, so that the model can capture graph structure information and node feature information more comprehensively from different angles.

[0144] In model training, the number of training iterations is set to 300, and in the first 50 iterations, the target domain samples are not used, and only the source domain samples are used for pre-training. The initial learning rate is set to 0.001, and the learning rate decay is calculated at iterations 150 and 250*0.1. The two weight parameters γ and κ are calculated by [1-exp(-τe) / (1+exp-τe)], where e=1 when transfer learning is performed, otherwise τ=10 and e=0.

[0145] The following is an experiment of the migration task 0→1 where random Gaussian noise with a standard deviation of 2 is added to the sample data of the training set and the test set. By plotting the relationship between the accuracy and loss of DAHGCN and its corresponding confusion matrix, the state of the model testing process can be better observed, such as Figure 8 and Fig. 9 As shown:

[0146] The evaluation index of the CWRU experiment is the accuracy of fault diagnosis. The experimental results are listed in Table 1. The accuracy here is obtained by calculating the average of the last 20 iterations out of 300 iterations. The corresponding histogram is shown in Fig.10 shown.

[0147] Table 1 Comparative experiment of CWRU gearbox dataset

[0148]

[0149] The comparative experimental results show that in the 12 working condition migration fault diagnosis tasks of the CWRU bearing dataset, the model DAGCN performs better than other methods, with an average accuracy of 0.92% higher than JAN, 0.01% higher than CORAL, and 0.05% higher than Graph-SAGE. In addition, the diagnostic accuracy of the model DAHGCN surpasses DAGCN in each working condition, and the average accuracy is improved by 1.50%. These results show that DAHGCN can still maintain a high level of diagnostic accuracy in a noisy environment and show good robustness.

[0150] Jiangnan University Bearing Dataset: In this experiment, Fig.11 As shown, the JNU bearing dataset is used to experiment with the performance and applicability of the DAHGCN model.

[0151] The bearing data set of Jiangnan University (JNU) is collected by using an acceleration vibration sensor to obtain the vibration signal of the experimental bearing. The sampling duration is 20s and the sampling frequency is set to 50kHz. Fig.12 The figure shows three different failure modes of JNU rolling bearings, namely inner ring failure, outer ring failure, rolling element failure, and a total of four categories including normal state. And the data of each failure mode has three different speeds, and the data is regarded as three operating conditions, recorded as 0, 1 and 2. When performing fault diagnosis, the bearing data in the JNU data set are normalized by standard deviation. Each sample contains 1024 data points, and there is no intersection between sample sets. In the JNU data set, the total number of samples is 2930, which is divided into 8:2 ratios, 80% of which are training sets and 20% of which are test sets. Therefore, for each operating condition, the training set has 2344 samples and the test set has 586 samples.

[0152] In the JNU bearing fault diagnosis experiment, by setting up 6 cross-domain migration fault diagnosis tasks, the diagnostic accuracy of DAHGCN in variable working condition cross-domain fault diagnosis was obtained, and its superiority was highlighted by comparing with other methods. ab Represents the migration task a→b.

[0153] In this experiment, the model performance in the bearing classification task will be evaluated, where classification accuracy is the main evaluation indicator. Specifically, the present invention uses the average of the classification accuracy of the last 20 iterations out of 300 iterations as the final result. In addition, the experiment also includes the accuracy and loss relationship diagram of the DAHGCN model (see Fig.13 ) and the corresponding confusion matrix (see Fig.14 ). The comparison results of the classification accuracy of various network models in this experiment are shown in Table 2, and the histogram of the classification accuracy is shown in Fig.15 As shown, through these charts and data, the present invention can intuitively compare the classification performance of different models.

[0154] Table 2 Comparative experiment of JNU fault dataset

[0155]

[0156] Through comparative experiments, it can be seen that the diagnostic accuracy of DAGCN in each migration task is better than that of JAN, CORAL and Graph-SAGE. Specifically, the average accuracy of DAGCN is 6.67% higher than that of JAN, 5.77% higher than that of CORAL, and 4.71% higher than that of Graph-SAGE. However, the diagnostic accuracy of DAHGCN proposed in this invention surpasses DAGCN in each migration task, and the average accuracy is also 0.31% higher than that of DAGCN. It reaches 99.04%.

[0157] By combining the experimental results of the CWRU dataset and the JNU dataset, it can be seen that the average diagnostic accuracy of DAHGCN is relatively high in each migration task of the two datasets, indicating that this method performs better than DAGCN and has higher robustness and adaptability.

[0158] In order to evaluate the feature extraction ability of DAHGCN, we use the migration task 0→1. Fig.16 , Fig.17 , Fig.18 It is a complement to the T-SNE visualization of DAHGCN on the noise-free CWRU dataset, the noisy CWRU dataset, and the JNU dataset.

[0159] from Fig.16 and Fig.17As can be seen from the figure, the features of the two different domains in the CWRU dataset can be well divided into 10 parts; Fig.18 It can be seen that in the JNU dataset, the features of the two different domains can also be well divided into four parts, and each part has no overlap and is independent. At the same time, the feature alignment effect of the same fault category in the source domain and the target domain is also good, which verifies that the DAHGCN proposed in this invention is also relatively good in feature clustering and extraction.

[0160] In order to distinguish the impact of various parts of DAHGCN on the model function, an ablation experiment was conducted, and two different methods were further derived from DAHGCN: Method 1 (the structural alignment loss uses the joint alignment method of JMMD and CORAL, and the others remain unchanged); Method 2 (using the MRF-HGCN network and the structural alignment loss uses MMD). The dataset uses the JNU dataset, and the ablation experiment results are shown in Table 3.

[0161] Table 3 Ablation test results on JNU gearbox dataset

[0162]

[0163] According to the results of the ablation experiment, the diagnostic classification accuracy of DAHGCN in each migration task is improved to varying degrees compared with the two methods, and the average accuracy is 0.22% and 0.63% higher, respectively. This fully demonstrates that the MRF-HGCN data structure feature extraction and the structural features based on the joint alignment of JMMD and CORAL can improve the cross-domain fault diagnosis ability of the model to a certain extent.

[0164] In order to solve the problem that the multi-receptive field graph convolutional network can only extract a single type of graph structure information, it is difficult to capture both local and global graph structure information at the same time, resulting in insufficient information representation capability of the convolution output features, thus limiting the application of the model in complex graph structures, the present invention proposes the following method:

[0165] (1) MRFHGCN: This network combines the advantages of two graph convolution methods, Graph-SAGE and GCN. It not only uses the propagation mechanism of GCN to deeply mine the local structural information of the graph, but also captures the global structural features through the inductive learning strategy of Graph-SAGE. This fusion method enhances the model's ability to understand graph data by learning the feature aggregation function of neighbor nodes, enabling it to self-learn features for unseen nodes, significantly improving the model's expressiveness, generalization performance, and robustness.

[0166] (2) Improve the structural feature alignment ability of transfer learning: Because the maximum mean difference (MMD) can only measure the marginal distribution difference of the data structure and adjust the first-order statistics, this paper uses JMMD to capture the conditional distribution difference of the data structure, and uses CORAL to align the covariance matrix to adjust the second-order statistics. In the process of transfer learning, this method can fully align the feature structure between the two domains and improve the model domain adaptation ability.

[0167] Through two sets of cross-domain fault diagnosis experiments, it can be seen that the method proposed in this paper performs well in cross-domain fault diagnosis of rolling bearings. Even in a noisy environment, the model still has good performance and robustness. In addition, the generalization ability of the DAHGCN method is verified by ablation experiments, which further proves the effectiveness and applicability of DAHGCN in fault classification under multiple working conditions.

[0168] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims

1. A variable-condition bearing fault diagnosis method based on domain adversarial hybrid graph convolutional network, characterized in that: The specific steps are as follows: Step 1: Use convolutional neural network to extract features from input data and use the obtained features as nodes; Step 2: Use the graph generation layer to obtain the adjacency matrix and construct the association graph based on the input matrix; Step 3: Input the constructed graph into the multi-receptive field mixed graph convolution to extract the structural information; Step 4: Use the obtained features to classify faults through transfer learning method.

2. According to claim 1, the variable operating condition bearing fault diagnosis method based on domain adversarial hybrid graph convolutional network is characterized in that: In step 1, a four-layer CNN is used to extract features from the input data, and the node feature X obtained is: X=CNN(X input ) (1) X input is the input matrix.

3. The variable operating condition bearing fault diagnosis method based on domain adversarial hybrid graph convolutional network according to claim 2 is characterized in that: In step 2, the adjacency matrix A of the graph is obtained by using GGL, and the association graph is constructed based on X and A. The calculation process of the adjacency matrix A is shown in formula (2): Among them, MLP is a multi-layer perceptron, normlize means normalization, Top-k means finding the top k largest elements from a set of data, and GGL stands for graph generation layer.

4. The variable operating condition bearing fault diagnosis method based on domain adversarial hybrid graph convolutional network according to claim 3 is characterized in that: In step 3, MRF-GCN performs graph convolution operations on three receptive fields in parallel. The node feature matrix of MRF-GCN is defined as follows: Among them, θ k ′ is the weight parameter, K is the receptive field size, and W is θ k ′ in matrix form, represents the rescaled Laplacian matrix, T k represents the k-order Chebyshev polynomial, and H1 represents the feature obtained by concatenating the features of the three layers of graph convolutional layers: The feature vector containing the neighbor information is trained by aggregating the feature information of the neighbor nodes. Any number of neighbor nodes are randomly selected from the target node, and the information of the target node and its neighbor nodes is aggregated to obtain a new embedding representation of the target node. The new embedding representation contains the feature information of the target node and its neighboring nodes. Use Graph-SAGE to identify outliers using neighborhood features and define them through aggregation k Aggregate neighbor node information to the target node. The aggregation function is shown in formulas (4) and (5): In the formula, is the embedding representation of node v at layer k, is the embedding representation of node v at the k-1 layer, u represents the neighbor node of v, represents the set of neighbor nodes of node v, W k is the weight parameter of the kth layer, σ is the activation function, AGGREGATE k Indicates the selected aggregation function, CONCAT means concatenating the features; Use the k-1 layer embedding representation of node v’s neighbor nodes to generate the k-th layer aggregate representation of its neighbor nodes Will and the k-1th layer representation of node v Concatenate and generate the k-th layer embedding representation of node v through a nonlinear transformation; Mean aggregation is achieved by calculating the mean of each dimension of the central node and neighboring nodes, and then concatenating them with the features of the central node. The specific formula is as follows: Among them, mean means using the mean aggregation function; After using mean aggregation, the node feature matrix of MRF-HGCN is defined as follows:

5. The variable operating condition bearing fault diagnosis method based on domain adversarial hybrid graph convolutional network according to claim 4 is characterized in that: In step 4, the objective function consists of three parts: feature extractor (F), domain discriminator (D) and label classifier (C). In order to extract migration features and construct class labels, domain labels and data structure information, the overall objective function includes classification loss, domain alignment loss and structural alignment loss. The cross entropy loss is used as the measure of sample classification loss. The specific formula of sample classification loss is shown in (8): Among them, I is the prediction result of the label classifier, L C (·) represents the classification loss, represents the predicted label of the source domain, Υ s represents the true label of the source domain, E(·) represents the expectation, represents the i-th sample in the source domain, Represents the true label corresponding to the i-th sample in the source domain; The binary cross entropy loss is used as the measure of domain alignment loss. The specific formula is shown in (9): Among them, L DA (·) denotes the domain alignment loss, represents the characteristics of the jth sample in the target domain, represents the characteristics of the i-th sample in the source domain, represents the predicted label of the source domain, Represents the predicted label of the target domain. The value of D is used to determine which domain the sample data comes from. The source domain is 1 and the target domain is 0. When aligning the feature structures of the source domain and the target domain, the loss function of embedding joint maximum mean difference and correlation alignment is used as the structural alignment loss to achieve simultaneous alignment of marginal distribution and conditional distribution in an unsupervised case. The JMMD calculation formula is as follows: Among them, P s represents the joint distribution of the source domain, Q t represents the joint distribution of the target domain, is a centerless cross-variance operator, It means that the computation process is carried out in the reproducing kernel Hilbert space; The calculation formula of CORAL is as follows: Among them, C s represents the covariance matrix of the source domain, C t represents the covariance matrix of the target domain, ||·|| F represents the Frobenius norm, X s Represents the data matrix form of the source domain, X t Represents the data matrix form of the target domain, n s Represents the number of source domain samples, n t represents the number of samples in the target domain, d represents the dimension of the feature vector, and 1 represents a vector of all 1s; Structural alignment loss L SA The calculation formula is as follows: L SA =αL JMMD +(1-α)L CORAL (13) Among them, α is the weight coefficient; The overall objective function L Total for: L Total =L C +γL DA +κL SA (14) Among them, γ and κ are weight coefficients; θ F is the parameter of the feature extractor, θ C is the parameter of the classifier, θ D are the parameters of the domain discriminator. During the model training process, the three parameters are expressed by formulas (15), (16), and (17): Indicates that the partial derivative of the function is to be calculated, and η represents the learning rate set when updating the parameters; The process of DAHCGN parameter update is shown in formula (18): By minimizing L in formula (14) Total And optimize the parameters of DAHGCN to reduce the distribution difference between the source domain and the target domain, and use the proposed DAHGCN to achieve diagnosis.

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