A Cross-Condition Fault Diagnosis Method Based on a Stable Causal Graph Convolutional Domain Generalization Network

Abstract

This invention relates to the field of fault diagnosis technology, specifically disclosing a cross-operating-condition fault diagnosis method based on a stable causal graph convolutional domain generalization network. This method acquires multi-channel observation data of equipment under different operating conditions and explicitly introduces operating condition variables to label the corresponding operating conditions. Based on the multi-channel observation data and operating condition variables, a cross-operating-condition stable causal graph is constructed. The causal strength between adjacent observation variables in the cross-operating-condition stable causal graph is quantified to generate a causal strength matrix. Using the causal strength matrix as graph topological weights, the multi-channel observation data is input as node features into a graph convolutional network for feature extraction to obtain graph-level embedding vectors. A diagnostic model including a classification branch and a domain generalization branch is constructed and trained. The trained diagnostic model is used to diagnose faults in equipment data under target operating conditions. This invention improves the generalization performance and fault diagnosis accuracy of the diagnostic model when facing unknown operating conditions.

Description

Technical Field

[0001] This invention relates to the field of fault diagnosis technology, specifically to a cross-condition fault diagnosis method based on a stable causal graph convolutional domain generalization network, as well as a computer terminal and a computer-readable storage medium for applying this method. Background Technology

[0002] With breakthroughs in artificial intelligence technology and the accumulation of massive amounts of monitoring data, deep learning has been widely applied in the field of intelligent bearing fault diagnosis. However, these methods typically rely heavily on the assumption of independent and identically distributed source and target domains. This limits the generalization ability of the learned fault features under out-of-distribution scenarios such as changing operating conditions. Introducing causal theory provides an effective way to solve this problem, shifting the research focus from the statistical correlation at the data surface to the underlying stable causal mechanism, thereby significantly improving the generalization performance and diagnostic reliability of the diagnostic model under unknown operating conditions.

[0003] Currently, methods for integrating causal theory into fault diagnosis mainly fall into two categories. The first category relies on manually pre-defined causal network structures to extract cross-domain stable causal invariant features, and improves generalization performance by enhancing the representational power of these features and suppressing non-causal interference. However, this type of method heavily depends on pre-defined causal prior knowledge, while the operating mechanisms and causal relationships of equipment in real-world industrial scenarios are often extremely complex. Manually pre-defined structures struggle to accurately reflect real physical laws, thus limiting the final performance of the diagnostic model. The second category attempts to discover causality directly based on observational data, capturing invariant causal mechanisms and root cause associations through a data-driven approach. However, traditional causal discovery algorithms are mostly based on the assumption of independent and identically distributed causal relationships within a single environment. When applied to scenarios with data distribution shifts, such as cross-condition diagnosis, they are prone to misjudging common-cause interference caused by changes in operating conditions as causal relationships between variables, introducing spurious correlations. This results in a large number of false edges in the generated causal graph, failing to provide accurate topological guidance for downstream diagnostic models.

[0004] Meanwhile, in existing domain-generalized bearing fault diagnosis frameworks, the extraction of domain-invariant features is a core module for achieving high-precision diagnosis across operating conditions. Existing domain generalization methods typically focus on obtaining cross-domain invariant features through data augmentation, distribution difference alignment, or multi-scale feature extraction. However, traditional domain generalization diagnostic frameworks generally lack guidance from real physical causal structures during the feature extraction stage. Since the initial features extracted from each source domain are often deeply coupled to specific operating condition distributions and are not stable representations themselves, directly forcing alignment of these biased features results in so-called "domain-invariant features" that fail to reflect the true fault mechanism, causing the model to still fail to achieve effective generalization when faced with entirely new operating conditions. Summary of the Invention

[0005] To address the technical problems in existing technologies, this invention provides a cross-condition fault diagnosis method based on a stable causal graph convolutional domain generalization network. The method aims to suppress spurious correlations introduced by distribution offsets, obtain more accurate causal graphs, and combine causal strength and domain generalization training strategies to construct a more accurate fault diagnosis framework with stronger cross-condition generalization capabilities.

[0006] To achieve the above objectives, the present invention provides the following technical solution: This invention discloses a cross-condition fault diagnosis method based on a stable causal graph convolution domain generalization network, including steps S1 to S6.

[0007] S1. Acquire multi-channel observation data of the equipment under different operating conditions, and explicitly introduce operating condition variables to label the corresponding operating conditions.

[0008] S2. Based on the multi-channel observation data and the operating condition variables, construct a cross-operating condition stable causal graph to suppress operating condition distribution offset interference; the directed edges between the observation variable nodes in the cross-operating condition stable causal graph are used to characterize the real physical causal relationship between the observation variables after removing operating condition interference.

[0009] S3. Quantify the causal strength between adjacent observed variables in the cross-condition stable causal graph and generate a causal strength matrix.

[0010] S4. Using the causal strength matrix as the graph topology weights, the multi-channel observation data is used as the initial features of the graph nodes and input into the graph convolutional network for feature extraction to obtain the graph-level embedding vector.

[0011] S5. Construct a diagnostic model that includes a classification branch and a domain generalization branch. Input the graph-level embedding vector into the classification branch and the domain generalization branch respectively to obtain the fault category prediction probability and domain generalization feature respectively. Calculate the total loss consisting of the classification loss and the domain generalization loss, and use the total loss to perform multi-source domain joint training on the diagnostic model.

[0012] S6. Use the trained diagnostic model to diagnose faults in equipment data under target operating conditions.

[0013] As a further improvement to the above scheme, step S2 specifically includes steps S21 to S25.

[0014] S21. Construct a complete undirected graph containing all observed variables and operating condition variables.

[0015] S22. Use a kernel-based conditional independence test method to examine the conditional independence relationship between each observed variable and the operating condition variable, identify the module-variable variables whose causal mechanism changes with the operating condition, and the module-stable variables whose causal mechanism does not change with the operating condition, and determine the causal direction from the operating condition variable to the module-variable variable.

[0016] S23. Remove edges in a completely undirected graph that do not have a direct causal relationship and restore the causal skeleton.

[0017] S24. Combining the unmasked triplet formed by the module change variables, module stability variables, and operating condition variables, the results of the conditional independence test are used to orient some undirected edges in the causal skeleton, and orienting rules are introduced to determine the direction of the remaining available undirected edges, thus obtaining a complete partially directed acyclic graph.

[0018] S25. Establish a continuous optimization objective function with the complete partially directed acyclic graph as a constraint, and determine the direction of the remaining undirected edges through continuous optimization to obtain a stable causal graph across operating conditions.

[0019] As a further improvement to the above scheme, in step S25, the expression formula for the continuous optimization objective function is as follows: ; In the formula, The objective function is continuously optimized; The number of nodes for the observed variables; This refers to the total number of samples used in the continuous optimization phase. For the first In the nth sample, the nth Observed values ​​of one variable; For the first In the sample, except for the first one The set of observations for all variables other than the one variable; Let be the adjacency matrix of the cause-effect graph. Softplus guarantees that the edge weights are non-negative. For Hadamard product, For learnable parameter matrix, An n×n 0 / 1 mask matrix created from the complete partially directed acyclic graph; In the current graph structure Given the remaining observed variables At that time, the target observed variable The conditional probability density; , To balance hyperparameters, Adjacency matrix From the node Pointing to node The weight of the directed edge. Adjacency matrix From the node Pointing to node The weight of the directed edge; The spectral radius is not constrained by acyclic constraints.

[0020] As a further improvement to the above scheme, step S3 specifically includes steps S31 to S34.

[0021] S31. For each directed edge in the cross-condition stable causal graph, extract the target node and its corresponding set of parent nodes.

[0022] S32. While keeping the other parent nodes of the target node unchanged, construct the conditional probability distribution of the target node before and after cutting the directed edge.

[0023] S33. The difference in the conditional probability distribution is measured using relative entropy as the original causal strength of the directed edge.

[0024] S34. Perform global normalization on the original causal intensity to obtain the dimensionless causal intensity, and assign the connection weight of each directed edge in the adjacency matrix corresponding to the cross-condition stable causal graph to the corresponding dimensionless causal intensity to generate the causal intensity matrix.

[0025] As a further improvement to the above scheme, step S4 specifically includes steps S41 to S43.

[0026] S41. Add self-loops to the causal intensity matrix and calculate its corresponding degree matrix to generate a normalized adjacency matrix.

[0027] S42. The multi-channel observation data is used as the initial features of the graph nodes and input into a multi-layer graph convolutional network. Under the action of the nonlinear activation function, the network performs convolutional forward propagation along the causal topology represented by the normalized adjacency matrix, and aggregates to obtain multi-channel causal relationship features.

[0028] S43. Perform graph pooling on the multi-channel causal relationship features to obtain graph-level embedding vectors.

[0029] As a further improvement to the above scheme, in step S5, the formula for expressing the total loss is: ; In the formula, The classification loss is described using classification cross-entropy loss, which is employed to optimize the diagnostic model's prediction accuracy for fault labels. This is a cross-domain correlation alignment loss used to calculate the difference between the feature covariance matrices of different source domains in order to align the feature distributions of different source domains. The triplet loss is used to make samples of the same class close to each other and samples of different classes have a distance greater than a preset interval coefficient in the feature space. and This constitutes the domain generalization loss; and These are the weighting coefficients.

[0030] As a further improvement to the above scheme, the formula for calculating the classification loss is as follows: ; In the formula, The number of source domains; For the first The number of samples in each source domain; This represents the total number of fault categories, including normal states. For the first In the source domain, the first The training sample corresponds to the first... The actual label indication value for each fault category; For the first In the source domain, the first The training sample corresponds to the first... The predicted probability value for each fault category.

[0031] The formula for calculating the cross-domain correlation alignment loss is as follows: ; In the formula, The dimension of the domain generalization feature; For the first The characteristic covariance matrix of each source domain; For the first The characteristic covariance matrix of each source domain; It is the Frobenius norm.

[0032] The formula for calculating the triplet loss is as follows: ; In the formula, For a set of triples, where the anchor sample Compared with positive samples Negative samples belong to the same fault category but different operating conditions. They belong to different fault categories; To select the maximum value; This is the interval coefficient.

[0033] As a further improvement to the above solution, the device is a bearing, and the fault diagnosis includes the identification of the bearing's normal condition, inner ring fault, outer ring fault, and ball fault.

[0034] The present invention also discloses a computer terminal, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps of the cross-condition fault diagnosis method based on a stable causal graph convolutional domain generalization network as described above.

[0035] The present invention also discloses a computer-readable storage medium having a computer program stored thereon, wherein when the program is executed by a processor, it implements the steps of the cross-condition fault diagnosis method based on a stable causal graph convolutional domain generalization network as described above.

[0036] Compared with the prior art, the beneficial effects of the present invention are: 1. The present invention discloses a cross-condition fault diagnosis method based on a stable causal graph convolutional domain generalization network. By explicitly incorporating condition variables into causal modeling to construct a cross-condition stable causal graph, feature extraction is performed by combining a causal strength matrix and a graph convolutional network. Furthermore, a dual-branch structure of classification and domain generalization is introduced into the constructed diagnostic model to carry out a multi-source domain joint training mechanism. This effectively eliminates false correlations introduced by the distribution shift of cross-condition data and extracts graph-level embedding vectors that have both discriminative and generalizable properties. As a result, the generalization performance and fault diagnosis accuracy of the diagnostic model when facing unknown conditions are improved.

[0037] 2. This fault diagnosis method uses the conditional independence test to examine the independence relationship between each observed variable and the operating condition variable to distinguish between module-changing variables and module-stable variables. It also combines unmasked triples and continuous optimization objective functions to apply an edge-oriented strategy to the causal skeleton. This achieves accurate restoration of the real physical causal mechanism between variables while weakening the specific distribution assumptions made on the causal function model, providing a reliable topological prior structure for downstream graph convolutional network feature extraction.

[0038] 3. This fault diagnosis method calculates the difference in conditional probability distribution of target nodes before and after cutting off directed edges, and uses relative entropy (Kullback–Leibler divergence, KL divergence) to measure the original causal strength and generate a normalized causal strength matrix. This enables a quantitative assessment of the relative strength of causal effects between observed variables, allowing graph convolutional networks to perform graph feature aggregation along real and high-weighted causal edges, effectively suppressing the interference of redundant connections and operating condition-related noise features.

[0039] 4. This fault diagnosis method achieves the goal of aligning the distribution of features from different source domains and extracting domain-invariant features by jointly calculating the cross-domain correlation alignment loss and triplet loss in the domain generalization branch. At the same time, it promotes the similar samples to be close to each other in the feature space and keeps the distance between different samples above the preset interval. This solves the problem of category boundary ambiguity that is easily caused by global distribution alignment and ensures the category judgment of diagnostic features under new working conditions.

[0040] 5. The computer terminal and computer-readable storage medium disclosed in this invention can achieve the same beneficial effects by applying the above-described fault diagnosis method, and will not be elaborated further here. Attached Figure Description

[0041] Figure 1 This is a flowchart of the cross-condition fault diagnosis method based on a stable causal graph convolutional domain generalization network in Embodiment 1 of the present invention.

[0042] Figure 2 This is an example of the cross-condition stability causality discovery process in Embodiment 1 of the present invention; Figure 2 In the diagram, (a) is a completely undirected graph; (b) is a change causal module detection; (c) is causal skeleton recovery; (d) is causal orientation between observed variables; (e) is a completely partially directed acyclic graph based on Meek orientation; (f) is the adjacency matrix corresponding to the completely partially directed acyclic graph (e); (g) is the continuous optimization of the constraints of the completely partially directed acyclic graph; and (h) is the directed acyclic graph corresponding to the adjacency matrix (g).

[0043] Figure 3 This is a schematic diagram of the causal strength of the relative entropy measurement in Embodiment 1 of the present invention.

[0044] Figure 4 This is a schematic diagram of graph convolution feature modeling and generalization training with fused causal strength in Embodiment 1 of the present invention.

[0045] Figure 5 This is a schematic diagram of the overall framework for cross-condition fault diagnosis based on a stable causal graph convolutional domain generalization network in Embodiment 1 of the present invention.

[0046] Figure 6 This is a comparison of the causal skeleton recovery performance of different methods on synthetic data in Embodiment 1 of the present invention; Figure 6 In the above, (a) corresponds to 6 nodes and 600 samples; (b) corresponds to 8 nodes and 600 samples; (c) corresponds to 8 nodes and 900 samples; and (d) corresponds to 10 nodes and 1200 samples.

[0047] Figure 7 This is a comparison of the performance of different methods in the directed causal graph recovery of synthetic data in Embodiment 1 of the present invention; Figure 7In the above, (a) corresponds to 6 nodes and 600 samples; (b) corresponds to 8 nodes and 600 samples; (c) corresponds to 8 nodes and 900 samples; and (d) corresponds to 10 nodes and 1200 samples.

[0048] Figure 8 The structural configuration and sensor distribution of the bearing fault test bench used for data acquisition in Embodiment 1 of the present invention are shown.

[0049] Figure 9 This refers to the causal graph and matrix obtained from multi-channel experimental data in Task 1 of Embodiment 1 of the present invention. Figure 9 In the diagram, (a) is the stable causal graph across operating conditions; (b) is the corresponding normalized relative entropy causal intensity matrix.

[0050] Figure 10 This is a comparison of the accuracy of the six methods in Embodiment 1 of the present invention on five cross-domain fault diagnosis tasks.

[0051] Figure 11 This is the confusion matrix of different methods on the laboratory dataset set in Task 1 during the 10th run of Embodiment 1 of the present invention; Figure 11 In the diagram, (a) represents the CCDG method; (b) represents the DGNIS method; (c) represents the Whitening-Net method; (d) represents the CCN method; (e) represents the CDDG method; and (f) represents the method of this invention.

[0052] Figure 12 This is a schematic diagram of the structure of the computer terminal in Embodiment 2 of the present invention. Detailed Implementation

[0053] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0054] Example 1 This embodiment provides a cross-condition fault diagnosis method based on a stable causal graph convolutional domain generalization network, applicable to bearings. Fault diagnosis includes the identification of normal bearing condition, inner race fault, outer race fault, and ball bearing fault. In some embodiments, it can also be applied to other types of mechanical equipment. This invention first starts with multi-source bearing data under various operating conditions, explicitly incorporating operating condition variables into causal modeling. A stable cross-condition causal structure is determined through conditional independence testing and continuous optimization methods. Second, the causal strength between observed variables is measured using KL divergence. The causal strength matrix and node observation data are jointly embedded into a graph convolutional network (GCN) to extract more discriminative and generalizable features. Finally, the model is trained for domain generalization using classification cross-entropy loss, cross-domain correlation alignment loss, and triplet loss, resulting in a complete domain generalization diagnostic framework based on causal discovery.

[0055] Please see Figure 1 The fault diagnosis method of the present invention includes steps S1 to S6.

[0056] S1. Acquire multi-channel observation data of the equipment under different operating conditions, and explicitly introduce operating condition variables to label the corresponding operating conditions.

[0057] S2. Based on the multi-channel observation data and the operating condition variables, construct a cross-operating condition stable causal graph to suppress operating condition distribution offset interference; the edges between the observation variable nodes in the cross-operating condition stable causal graph represent the real physical causal relationship between the observation variables after removing operating condition interference.

[0058] In real-world scenarios, the influence pattern of the operating condition variables and their corresponding domain indices on the observed variables is unknown and nonlinear. Therefore, this embodiment employs a nonparametric kernel-based conditional independence test (KCI-test) to capture this nonlinear dependency and the conditional independence relationship between the observed variables, thereby determining the complete causal framework of the explicitly modeled operating condition variables. Step S2 specifically includes steps S21 to S25.

[0059] S21. Construct a complete undirected graph containing all observed and condition variables. A directed acyclic graph is defined as... The initial node set of the graph is defined as follows: (All observed variables + operating condition variables); Connect any two nodes in the node set to form a completely undirected graph. .

[0060] S22. Use a kernel-based conditional independence test method to examine the conditional independence relationship between each observed variable and the operating condition variable, identify the module-variable variables whose causal mechanism changes with the operating condition, and the module-stable variables whose causal mechanism does not change with the operating condition, and determine the causal direction from the operating condition variable to the module-variable variable.

[0061] Specifically, the observed variables are tested through conditional independence tests. Conditional independence relationship with operating condition variable C. For each observed variable... traversal Other observed variable subsets ,test Whether it holds true: If a certain set of variables exists For the test to be valid, it means The causal module does not change with the operating condition variable C, and the completely undirected graph is removed. middle Let the edge with the operating condition variable C be denoted as For module-stable variables; conversely, if they do not exist, it means... The causal module changes with the operating condition variable C, preserving a completely undirected graph. middle Let the edge with the operating condition variable C be denoted as For module change variables.

[0062] For module change variables Its core characteristic is that its local causal mechanism changes with the operating condition variable C, a feature that directly reflects the changes in module variables. The mechanism change is driven by the operating condition variable C, rather than This has a reverse effect on the operating condition variable C. Therefore, the operating condition variable C is compared with the module change variable. The causal direction is clearly set as .

[0063] S23. Remove edges in a completely undirected graph that do not have a direct causal relationship and restore the causal skeleton.

[0064] After eliminating spurious correlations introduced by operating conditions, the structure between observed variables is further determined. For any pair of variables... Iterate through all possible sets of conditions. ,test Whether it holds true: If there exists a set of variables S such that the test holds true, it means that the observed variables... and There is no direct causal relationship; remove the completely undirected graph. middle and Edges; conversely, preserve the completely undirected graph. middle and The edge.

[0065] S24. Combining the unmasked triplet formed by the module change variables, module stability variables, and operating condition variables, the results of the conditional independence test are used to orient some undirected edges in the causal skeleton, and orienting rules are introduced to determine the direction of the remaining available undirected edges, thus obtaining a complete partially directed acyclic graph.

[0066] If the edge to be oriented In, there is a variable It belongs to the module change variable and is adjacent to the operating condition variable C. It is a module-stable variable and is not adjacent to the operating condition variable C. , , form Unmasked triples (where the middle variable is directly connected to both end variables, but there are no directly adjacent edges between the two end variables). For unmasked triples... The results of the conditional independence test from the previously mentioned causal detection module can be used for testing. Whether it is true: If the test finds ( Not included ) is established, indicating The distribution is essentially independent of the operating conditions and is directional. If the test finds but This indicates that C is correct. The influence is entirely through Transmission, Direction .

[0067] Similarly, for unmasked triples that do not contain the operating condition variable C... Similarly, the results of the conditional independence test for restoring the causal framework mentioned above can be used to verify this. Is it valid? If the test finds... ( Not included Then the unshielded triple will be oriented as Conversely, because no operating condition variables in the unmasked triplet provide additional information for orientation, orientation is temporarily impossible.

[0068] By employing the above steps of causal module detection, causal skeleton, and direction recognition, a complete partially directed acyclic graph (CPDAG) that is stable across operating conditions can be obtained, such as... Figure 2 As shown in (a)–(e) of the diagram. However, the orientation of some edges in the causal skeleton remains uncertain, and further orientation will be achieved through continuous optimization.

[0069] S25. Establish a continuous optimization objective function with the complete partially directed acyclic graph as a constraint, and determine the direction of the remaining undirected edges through continuous optimization to obtain a stable causal graph across operating conditions.

[0070] The CPDAG graph has parts of its skeleton missing orientation and undirected edges. Unable to distinguish or This leads to ambiguity in the causal mechanism and makes it impossible to quantify causal effects. Traditional methods for determining causal direction using causal asymmetry, such as LiNGAM / ANM / PNL, require specific assumptions about the causal function model and require the data to follow independent and identically distributed (ICD) patterns. However, complex bearing fault data in reality rarely meets these specific assumptions, leading to misjudgments of causal direction. Therefore, choosing a causal discovery method based on CPDAG with continuous optimization not only reduces the need for these assumptions but also decreases the search space for continuous optimization, resulting in more stable and faster optimization.

[0071] Since the causal relationship between the operating condition variables and the observed variables has been determined previously, we will now only consider the set of observed variables in the CPDAG. An n×n 0 / 1 mask matrix is ​​created using CPDAG. : ; The edges outside the CPDAG skeleton are set , oriented edge settings Undirected edges are temporarily set to The direction is determined through subsequent optimization. The actual adjacency matrix. From learnable parameters generate: ; In this context, softplus ensures that the edge weights are non-negative. This is a Hadamard product, ensuring that the weights between skeletonless variables are always 0, without updating the gradient and weights. Used to prevent self-looping.

[0072] The formula for the continuous optimization objective function is as follows: ; In the formula, The objective function is continuously optimized; The number of nodes for the observed variables; This refers to the total number of samples used in the continuous optimization phase. For the first In the nth sample, the nth Observed values ​​of one variable; For the first In the sample, except for the first one The set of observations for all variables other than the one variable; Let be the adjacency matrix of the cause-effect graph. Softplus guarantees that the edge weights are non-negative. For Hadamard product, For learnable parameter matrix, An n×n 0 / 1 mask matrix created from the complete partially directed acyclic graph; In the current graph structure Given the remaining observed variables At that time, the target observed variable The conditional probability density; , To balance hyperparameters, Adjacency matrix From the node Pointing to node The weight of the directed edge. Adjacency matrix From the node Pointing to node The weight of the directed edge; The spectral radius is not constrained by acyclic constraints.

[0073] S3. Quantify the causal correlation strength between adjacent observed variables in the cross-condition stable causal graph and generate a causal strength matrix.

[0074] After obtaining the cross-condition stable directed acyclic graph (DAG), quantitative strengths are assigned to the causal edges between observed variables, and a weighted causal graph input graph convolutional neural network is constructed. The cross-condition stable DAG learned from multi-source domain data can provide a more stable and reliable structural prior under unseen conditions, making the features extracted by the GCN less sensitive to changes in operating conditions and maintaining consistent characterization of potential failure mechanisms. Step S3 specifically includes steps S31 to S34.

[0075] S31. For each directed edge in the cross-condition stable causal graph, extract the target node and its corresponding set of parent nodes.

[0076] S32. While keeping the other parent nodes of the target node unchanged, construct the conditional probability distribution of the target node before and after cutting the directed edge.

[0077] S33. The difference in the conditional probability distribution is measured using relative entropy as the original causal strength of the directed edge.

[0078] S34. Perform global normalization on the original causal intensity to obtain the dimensionless causal intensity, and assign the connection weight of each directed edge in the adjacency matrix corresponding to the cross-condition stable causal graph to the corresponding dimensionless causal intensity to generate the causal intensity matrix.

[0079] In this embodiment, given a stable DAG structure, its corresponding causal decomposition can be represented as the following joint distribution: ; in For nodes The set of parent nodes. Let's denote the set of edges cut in the DAG. back, The set of remaining parent nodes is: .

[0080] Considering the impact of cutting the edge while keeping other parent nodes unchanged, a causal strength definition based on KL divergence is adopted, such as... Figure 3 As shown. Values ​​are taken for each given parent node. The original conditions are distributed as follows If Replace with Independent random variables Based on this, the conditional distribution after edge breakage is constructed. Then the causal strength of that edge is defined as: ; Intuitively, if cut right If the distribution has a relatively small impact, then the causal strength between the two is relatively small. Lower; if cut off back The conditional distribution changes significantly, indicating the strength of the causal relationship between the two. Relatively high.

[0081] The causal strength based on KL divergence can be used to obtain the set of observed variables. Weighted directed graph The edge set is Weight matrix The element is defined as: ; in To The dimensionless intensity after global maximum normalization, where To prevent extremely small constants with a denominator of 0, the adjacency matrix A of the DAG mentioned earlier is therefore... Replace with causal strength The causal strength matrix is ​​obtained. , It encodes both edge-based and edgeless causal topological structures and reflects the relative strength of the causal effect of each edge.

[0082] S4. Input the causal intensity matrix and the multi-channel observation data into a graph convolutional network for feature extraction to obtain a graph-level embedding vector. Step S4 specifically includes steps S41 to S43.

[0083] S41. Add self-loops to the causal intensity matrix and calculate its corresponding degree matrix to generate a normalized adjacency matrix.

[0084] S42. The multi-channel observation data is used as the initial features of the graph nodes and input into a multi-layer graph convolutional network. Under the action of the nonlinear activation function, the network performs convolutional forward propagation along the causal topology represented by the normalized adjacency matrix, and aggregates to obtain multi-channel causal relationship features.

[0085] S43. Perform graph pooling on the multi-channel causal relationship features to obtain graph-level embedding vectors.

[0086] The weighted causal graph is input into the GCN along with the multi-channel observation data, such as... Figure 4 As shown. For each sample, denote the observed variables in that sample. The original or preprocessed features are: The i-th row is a variable The feature vector within this time window, where d is the feature dimension. To preserve node information during graph convolution, the weight matrix... Adding a self-loop to the top yields: ; remember for The degree matrix, i.e.: ; The normalized adjacency matrix used in graph convolution is defined as: ; Based on this, the forward propagation of the L-layer GCN is as follows: ; in For the first Layer learnable weights It is a non-linear activation function. This refers to the number of layers in the GCN. Node representation is achieved through multi-layer graph convolution. It incorporates both the single-channel features of the nodes themselves and the multi-channel causal relationship features obtained by aggregating along the causal topology. Subsequently, graph pooling is used to obtain sample-level embedding vectors. ; This serves as the input for subsequent fault diagnosis, classification, and generalization learning.

[0087] S5. Construct a diagnostic model that includes a classification branch and a domain generalization branch. Input the graph-level embedding vector into the classification branch and the domain generalization branch respectively to obtain the fault category prediction probability and domain generalization feature respectively. Calculate the total loss consisting of the classification loss and the domain generalization loss, and use the total loss to perform multi-source domain joint training on the diagnostic model.

[0088] Through causality matrix By leveraging the weighting effect, GCN's graph convolutions only aggregate neighborhood information along truly existing and high-strength causal edges, highlighting physically meaningful and statistically stable channel coupling patterns, thus forming more discriminative and generalizable fault feature representations. Building upon this, a multi-source domain joint training strategy is employed, utilizing source domain data containing K different operating conditions. The model is trained end-to-end.

[0089] For those from the Source domain arbitrary input samples The graph-level embedding vector is extracted by the GCN module. Based on this graph-level embedding, a two-branch structure is constructed: a classification branch and a domain generalization branch, as follows: Figure 4 As shown.

[0090] (1) Classification branches The classification head uses a fully connected layer plus a softmax function to determine the fault category. ; in , For classification layer parameters, This represents the predicted category probability distribution.

[0091] Classification cross-entropy loss: Classification cross-entropy loss provides the model with basic fault identification capabilities and optimizes the prediction accuracy of fault labels. ; In the formula, The number of source domains; For the first The number of samples in each source domain; This represents the total number of fault categories, including normal states. For the first In the source domain, the first The training sample corresponds to the first... The actual label indication value for each fault category; For the first In the source domain, the first The training sample corresponds to the first... The predicted probability value for each fault category.

[0092] (2) Domain generalization branch Introducing a lightweight projection embed vector Mapping to domain generalization features : ; in This is the nonlinear activation function in the projection head. , These are the parameters for the projection layer. The subsequent classification loss and domain generalization loss are constructed using the bi-headed output of the graph-level embedding vectors.

[0093] Cross-domain correlation alignment loss: Due to the offset in the distribution of data from different source domains, even under the constraint of a cross-condition stable causal graph, the feature distributions extracted from different domains still differ. Therefore, a correlation alignment loss based on covariance is introduced to learn domain-invariant features. For each source domain k, its corresponding feature covariance matrix is ​​approximately: ; in Let be the characteristic matrix of the k-th field. The vector is composed entirely of 1s. The correlation alignment loss is defined as the sum of the Frobenius norms of the covariance differences across all domains: ; In the formula, The dimension of the domain generalization feature; For the first The characteristic covariance matrix of each source domain; For the first The characteristic covariance matrix of each source domain; It is the Frobenius norm.

[0094] Triple Loss: Aligning feature distributions from different source domains at the global level can lead to blurred class boundaries. To ensure that the aligned features still have good class discriminative power, a metric-based triple loss is introduced. Constructing a set of triples... Anchor point samples Compared with positive samples Negative samples belong to the same fault category but different operating conditions. These belong to different fault categories. The triplet loss is defined as: ; In the formula, For a set of triples, where the anchor sample Compared with positive samples Negative samples belong to the same fault category but different operating conditions. They belong to different fault categories; To select the maximum value; The interval coefficient is used. The triplet loss-driven model satisfies the following in the feature space: samples of the same class (even those from different operating conditions) are close to each other, and samples of different classes are at least [distance missing]. This enhances the clustering of features of similar fault samples and improves the separability between features of different fault categories.

[0095] In summary, the total loss function is: ; In the formula, The classification loss is described using classification cross-entropy loss, which is employed to optimize the diagnostic model's prediction accuracy for fault labels. and This constitutes the domain generalization loss; and To balance the hyperparameters that affect different losses, .

[0096] S6. Use the trained diagnostic model to diagnose faults in equipment data under target operating conditions.

[0097] Minimize on multi-condition source domain data The parameters of GCN and the classification head are optimized synchronously to ensure high-precision classification while achieving good generalization performance for unknown working conditions. The complete execution flow of the proposed framework is as follows: Figure 5 As shown.

[0098] To verify the effectiveness of the proposed method, this embodiment also provides two core experiments: The first experiment compares various causal discovery methods on a synthetic dataset to verify the advantages of the proposed cross-condition stable causal discovery algorithm in dealing with distribution shifts; the second experiment uses a multi-channel laboratory bearing dataset to compare with the latest mainstream generalized diagnostic benchmarks and conduct ablation experiments to verify the generalization performance of the diagnostic framework embedded with cross-condition causal strength relationships constructed in this paper and the effectiveness of each module.

[0099] Experiment 1: Verification of Stable Causal Discovery Across Operating Conditions (1) Synthetic Dataset and Evaluation Metrics: To verify the causal discovery performance of the method of this invention in cross-condition scenarios, three domains were set up in the experiment to simulate fault diagnosis scenarios across conditions. Each domain shares the same causal topology, but some causal mechanisms are allowed to change with the domain. The distribution shift of changing causal mechanisms in different domains is simulated by adjusting the causal strength and noise variance in the functional causal model. For variables with fixed causal mechanisms, the data generation function remains unchanged in each domain. As shown in Table 1, four scenarios with different numbers of nodes and sample sizes (N) were designed in the experiment.

[0100] Table 1: Synthetic dataset configuration schemes for evaluating causal discovery methods

[0101] For evaluation metrics, the experiment used precision, recall, F1 score, and accuracy to comprehensively assess the consistency between the reconstructed causal graph and the true causal topology. Precision measures the proportion of true causal relationships predicted by the algorithm; recall represents the proportion of true causal relationships correctly identified by the algorithm; the F1 score is the harmonic mean of precision and recall, used to balance bias; and accuracy represents the proportion of all possible node pairs correctly identified by the algorithm. The specific calculation formulas for each metric are as follows: ; ; ; ; in, , , and These represent True Positive, False Positive, True Negative, and False Negative, respectively.

[0102] (2) Experimental results analysis: The method of the present invention is compared with three mainstream causal discovery algorithms, PC-stable, CPC and SDCD, on a synthetic dataset.

[0103] Figure 6This paper showcases the performance of various methods on the undirected causal skeleton recovery task. Under different data complexity settings, the proposed method demonstrates significant advantages over other methods in various metrics. Specifically, the precision of the proposed method remains above 80.00% across four different sample complexity scenarios, reaching a maximum of 87.50% in the 8-node, 900-sample scenario. In contrast, the baseline method, SDCD, achieved the highest precision across all sample complexity scenarios at only 81.82%. Furthermore, the F1 score of the proposed method consistently remains above 66.67%, significantly outperforming the comparative algorithms. This strongly demonstrates that the proposed method, through explicit modeling of working condition variables, effectively eliminates false edges caused by distribution shifts, obtaining a purer causal skeleton. Traditional causal discovery methods, when facing cross-domain scenarios, are prone to misjudging spurious correlations introduced by data distribution shifts as genuine causal relationships, leading to increased false positive rates and decreased precision.

[0104] Figure 7 The performance of various methods in directed causal graph reconstruction is further demonstrated. In directed graph reconstruction involving direction inference, the algorithm of this invention maintains its leading position across all metrics. In the most complex scenario with 10 nodes and 1200 samples, the method of this invention achieves an accuracy of 83.33% and a precision of 88.89%. In contrast, other methods achieve an average accuracy of only 50.26% and an average precision of 85.56% in this complex scenario. These results demonstrate that the method of this invention achieves excellent overall performance in cross-condition scenarios through explicit modeling of condition variables and continuous optimization of the orientation strategy. It can accurately reconstruct the true physical causal mechanism between variables, thus providing solid and reliable topological prior support for subsequent graph convolution feature extraction and diagnostic decisions.

[0105] Experiment 2: Validation of a domain generalization diagnostic framework incorporating causal strength (1) Laboratory Dataset and Experimental Setup: The structural configuration and sensor distribution of the laboratory bearing test bench are as follows: Figure 8 As shown in Table 2, the experiment used four 6205 deep groove ball bearings to simulate four health states: normal (N), inner ring fault (I), outer ring fault (O), and ball fault (B). Data acquisition was performed using a multi-channel sensor as shown in Table 2. The sampling frequency was set to 51.2 kHz, each sample had a length of 2048 points, and 500 samples were collected for each fault state. The relevant data structure is shown in Table 3.

[0106] Table 2: Variables in the laboratory dataset used for causal discovery and fault diagnosis

[0107] Table 3: Laboratory dataset configuration for evaluating cross-condition fault diagnosis methods

[0108] (2) Generalization Performance Analysis: To verify the superiority of the proposed generalization diagnostic framework embedding stable causal relationships across operating conditions, experiments were conducted to comprehensively compare it with five state-of-the-art mainstream domain generalization methods, including: CCDG, DGNIS, Whitening-Net, CCN, and CDDG. Before comparing the final generalization diagnostic accuracy, Figure 9 This paper first demonstrates the cross-condition stable causal graph and corresponding normalized KL causal strength matrix obtained by the model of this invention in Task 1 using multi-channel experimental data. This causal topology and strength prior provides a foundation for subsequent fault diagnosis. Furthermore, to reduce the impact of random errors, each method was independently tested 10 times in each generalized diagnostic task. The diagnostic accuracy comparison of each method in the five cross-domain tasks is shown in Table 4. Figure 10 As shown.

[0109] Table 4: Performance comparison of the baseline model and ablation variants on tasks 1-5 (Results from 10 runs: mean ± standard deviation, %)

[0110] The experimental results show that the method of the present invention (Ours) achieved the best diagnostic accuracy in all generalization tasks, with an average accuracy of 89.60%, which is 4.65 percentage points higher than the second best CDDG method (84.95%), and significantly outperforms CCDG (80.12%) and DGNIS (82.79%).

[0111] Figure 11 The confusion matrix in the figure shows the specific classification results of the six methods in Task 1 (10th experimental run). The results show that all six methods have a lot of misclassifications of inner ring fault samples. In particular, CCDG and DGNIS correctly identified no more than 40 inner ring fault samples, indicating very poor classification performance. The other baseline methods also did not correctly identify more than 60 samples. In contrast, the method of this invention correctly identified 81 inner ring fault samples, achieving good results. The above results show that the diagnostic framework proposed in this invention, which integrates cross-condition stable causality strength and generalization loss function, has better generalization performance.

[0112] (3) Ablation Experiment Analysis: In order to further evaluate the contribution of each core module in the framework of this paper, four ablation variants were designed and tested under the same cross-domain task. Among them, M1 refers to the model with the causal strength module removed, M2 represents the model with the causal module removed and the traditional graph construction method used, M3 is the model with the correlation alignment loss removed, and M4 is the model with the triple loss removed.

[0113] The lower half of Table 4 lists the performance of the ablation models. When the causal module or correlation alignment loss was removed, the diagnostic accuracy of the models significantly decreased. Specifically, the average accuracy of M2 dropped to 83.84%, and the average accuracy of M3 dropped to 75.98%, demonstrating that a stable causal prior structure across operating conditions plays a crucial role in guiding the model to effectively extract fault features. This also indicates that the correlation alignment loss, as a distribution alignment tool, is particularly important for generalization. Meanwhile, the performance of M1 (85.80%) and M4 (86.04%) also decreased to varying degrees, further demonstrating that introducing causal strength based on causal topological relationships can provide effective weighted gains for feature learning by quantifying the strength of the causal mechanism. The triplet loss significantly enhances class judgment, and both contribute significantly to improving the overall generalization accuracy of the models.

[0114] In summary, this invention proposes a novel stable causal graph convolutional domain generalization framework. This method explicitly models operating condition variables by combining kernel-based conditional independence testing with continuous optimization, thereby suppressing spurious correlations caused by distribution shifts and reconstructing a domain-invariant physical causal topology. Furthermore, it embeds causal strength based on KL divergence into the graph convolutional network and employs a multi-domain joint training strategy combining correlation alignment loss and triplet loss to effectively correct diagnostic biases caused by changes in operating conditions. Experimental results on a multi-channel bearing dataset demonstrate that the proposed framework exhibits superior generalization performance compared to existing state-of-the-art baseline methods, providing a reliable solution for condition monitoring in unknown environments.

[0115] Example 2 This embodiment provides a computer terminal, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the cross-condition fault diagnosis method based on a stable causal graph convolutional domain generalization network as described in Embodiment 1.

[0116] like Figure 12 As shown, the computer terminal provided in this embodiment includes: at least one processor 101, and a memory 102 connected to at least one processor 101. This embodiment does not limit the specific connection medium between the processor 101 and the memory 102. Figure 12 The example shown is the connection between processor 101 and memory 102 via bus 100. Bus 100 is... Figure 12 The connections between other components are shown in bold lines and are for illustrative purposes only, not as limiting information. Bus 100 can be divided into address bus, data bus, control bus, etc., for ease of representation. Figure 12The bus is represented by a single thick line, but this does not indicate that there is only one bus or one type of bus. Alternatively, the processor 101 may also be called a controller; there is no restriction on the name.

[0117] In this embodiment, the memory 102 stores instructions that can be executed by at least one processor 101. The at least one processor 101 can execute the aforementioned method by executing the instructions stored in the memory 102.

[0118] The processor 101 is the control center of the device. It can connect to various parts of the control device through various interfaces and lines. By running or executing instructions stored in memory 102 and calling data stored in memory 102, the processor can perform various functions and process data, thereby monitoring the device as a whole.

[0119] In one possible design, processor 101 may include one or more processing units. Processor 101 may integrate an application processor and a modem processor, wherein the application processor mainly handles the operating system, user interface, and applications, and the modem processor mainly handles wireless communication. It is understood that the modem processor may also not be integrated into processor 101. In some embodiments, processor 101 and memory 102 may be implemented on the same chip; in some embodiments, they may also be implemented on separate chips.

[0120] Processor 101 can be a general-purpose processor, such as a central processing unit (CPU), digital signal processor, application-specific integrated circuit, field-programmable gate array or other programmable logic device, discrete gate or transistor logic device, or discrete hardware component, capable of implementing or executing the methods, steps, and logic block diagrams disclosed in the embodiments. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the cross-condition fault diagnosis method based on a stable causal graph convolutional domain generalization network disclosed in Embodiment 1 can be directly implemented by a hardware processor, or implemented by a combination of hardware and software modules in processor 101.

[0121] Memory 102, as a non-volatile computer-readable storage medium, can be used to store non-volatile software programs, non-volatile computer-executable programs, and modules. Memory 102 may include at least one type of storage medium, such as flash memory, hard disk, multimedia card, card-type memory, random access memory (RAM), static random access memory (SRAM), programmable read-only memory (PROM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), magnetic storage, magnetic disk, optical disk, etc. Memory 102 can be any other medium capable of carrying or storing desired program code in the form of instructions or data structures that can be accessed by a computer, but is not limited thereto. In this embodiment, memory 102 can also be a circuit or any other device capable of implementing storage functions for storing program instructions and / or data.

[0122] By designing and programming the processor 101, the code corresponding to the cross-condition fault diagnosis method based on a stable causal graph convolutional domain generalization network described in the foregoing embodiments can be embedded into the chip, thereby enabling the chip to execute the code during runtime. Figure 1 The steps of the cross-condition fault diagnosis method based on a stable causal graph convolutional domain generalization network are shown. How to design and program the processor 101 is a technique well-known to those skilled in the art and will not be described further here.

[0123] Example 3 The present invention also discloses a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the cross-condition fault diagnosis method based on a stable causal graph convolutional domain generalization network in Embodiment 1.

[0124] The computer-readable storage medium may include flash memory, hard disk, multimedia card, card-type memory (e.g., SD or DX memory), random access memory (RAM), static random access memory (SRAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), programmable read-only memory (PROM), magnetic memory, magnetic disk, optical disk, etc. In some embodiments, the storage medium may be an internal storage unit of a computer device, such as the hard disk or memory of the computer device. In other embodiments, the storage medium may also be an external storage device of the computer device, such as a plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, etc., provided on the computer device. Of course, the storage medium may include both internal storage units and external storage devices of the computer device. In this embodiment, the memory is typically used to store the operating system and various application software installed on the computer device. In addition, the memory can also be used to temporarily store various types of data that have been output or will be output.

[0125] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A cross-condition fault diagnosis method based on a stable causal graph convolutional domain generalization network, characterized in that, Including the following steps: S1. Acquire multi-channel observation data of the equipment under different operating conditions, and explicitly introduce operating condition variables to label the corresponding operating conditions; S2. Based on the multi-channel observation data and the operating condition variables, a cross-operating condition stable causal graph that suppresses operating condition distribution offset interference is constructed; the directed edges between the observation variable nodes in the cross-operating condition stable causal graph are used to characterize the real physical causal relationship between the observation variables after removing operating condition interference. S3. Quantify the causal strength between adjacent observed variables in the cross-condition stable causal graph, and generate a causal strength matrix; step S3 specifically includes: S31. For each directed edge in the cross-condition stable causal graph, extract the target node and its corresponding set of parent nodes; S32. While keeping the other parent nodes of the target node unchanged, construct the conditional probability distribution of the target node before and after cutting the directed edge; S33. The difference in the conditional probability distribution is measured using relative entropy as the original causal strength of the directed edge; S34. Perform global normalization on the original causal intensity to obtain the dimensionless causal intensity, and assign the connection weight of each directed edge in the adjacency matrix corresponding to the cross-condition stable causal graph to the corresponding dimensionless causal intensity to generate the causal intensity matrix. S4. Using the causal strength matrix as the graph topology weight, the multi-channel observation data is input as the initial features of the graph nodes into the graph convolutional network for feature extraction to obtain the graph-level embedding vector; S5. Construct a diagnostic model that includes a classification branch and a domain generalization branch. Input the graph-level embedding vector into the classification branch and the domain generalization branch respectively to obtain the fault category prediction probability and domain generalization feature respectively. Calculate the total loss consisting of the classification loss and the domain generalization loss. Use the total loss to perform multi-source domain joint training on the diagnostic model. S6. Use the trained diagnostic model to diagnose faults in equipment data under target operating conditions.

2. The cross-condition fault diagnosis method based on a stable causal graph convolutional domain generalization network according to claim 1, characterized in that, Step S2 specifically includes: S21. Construct a complete undirected graph containing all observed variables and operating condition variables; S22. Use a kernel-based conditional independence test method to examine the conditional independence relationship between each observed variable and the operating condition variable, identify the module-varying variables whose causal mechanism changes with the operating condition, and the module-stable variables whose causal mechanism does not change with the operating condition, and determine the causal direction from the operating condition variable to the module-varying variable. S23. Remove edges in a completely undirected graph that do not have a direct causal relationship and restore the causal skeleton; S24. Combining the unmasked triplet formed by the module change variables, module stability variables, and operating condition variables, the results of the conditional independence test are used to orient some undirected edges in the causal skeleton, and orienting rules are introduced to determine the direction of the remaining available undirected edges, thus obtaining a complete partially directed acyclic graph. S25. Establish a continuous optimization objective function with the complete partially directed acyclic graph as a constraint, and determine the direction of the remaining undirected edges through continuous optimization to obtain a stable causal graph across operating conditions.

3. The cross-condition fault diagnosis method based on a stable causal graph convolutional domain generalization network according to claim 2, characterized in that, In step S25, the formula for the continuously optimized objective function is: In the formula, The objective function is continuously optimized; The number of nodes for the observed variables; This refers to the total number of samples used in the continuous optimization phase. For the first In the nth sample, the nth Observed values ​​of one variable; For the first In the sample, except for the first one The set of observations for all variables other than the one variable; Let be the adjacency matrix of the cause-effect graph. Softplus guarantees that the edge weights are non-negative. For Hadamard product, For learnable parameter matrix, An n×n 0 / 1 mask matrix created from the complete partially directed acyclic graph; In the current graph structure Given the remaining observed variables At that time, the target observed variable The conditional probability density; , To balance hyperparameters, Adjacency matrix From the node Pointing to node The weight of the directed edge. Adjacency matrix From the node Pointing to node The weight of the directed edge; The spectral radius is not constrained by acyclic constraints.

4. The cross-condition fault diagnosis method based on a stable causal graph convolutional domain generalization network according to claim 1, characterized in that, Step S4 specifically includes: S41. Add self-loops to the causal intensity matrix and calculate its corresponding degree matrix to generate a normalized adjacency matrix; S42. The multi-channel observation data is used as the initial features of the graph nodes and input into a multi-layer graph convolutional network. Under the action of the nonlinear activation function, the network performs convolutional forward propagation along the causal topology represented by the normalized adjacency matrix and aggregates to obtain multi-channel causal relationship features. S43. Perform graph pooling on the multi-channel causal relationship features to obtain graph-level embedding vectors.

5. The cross-condition fault diagnosis method based on a stable causal graph convolutional domain generalization network according to claim 1, characterized in that, In step S5, the formula for expressing the total loss is: In the formula, The classification loss is described using classification cross-entropy loss, which is employed to optimize the diagnostic model's prediction accuracy for fault labels. This is a cross-domain correlation alignment loss used to calculate the difference between the feature covariance matrices of different source domains in order to align the feature distributions of different source domains. The triplet loss is used to make samples of the same class close to each other and samples of different classes have a distance greater than a preset interval coefficient in the feature space. and This constitutes the domain generalization loss; and These are the weighting coefficients.

6. The cross-condition fault diagnosis method based on a stable causal graph convolutional domain generalization network according to claim 5, characterized in that, The formula for calculating the classification loss is: In the formula, The number of source domains; For the first The number of samples in each source domain; This represents the total number of fault categories, including normal states. For the first In the source domain, the first The training sample corresponds to the first... The actual label indication value for each fault category; For the first In the source domain, the first The training sample corresponds to the first... Predicted probability values ​​for each fault category; The formula for calculating the cross-domain correlation alignment loss is as follows: In the formula, The dimension of the domain generalization feature; For the first The characteristic covariance matrix of each source domain; For the first The characteristic covariance matrix of each source domain; It is the Frobenius norm; The formula for calculating the triplet loss is as follows: In the formula, For a set of triples, where the anchor sample Compared with positive samples Negative samples belong to the same fault category but different operating conditions. They belong to different fault categories; To select the maximum value; This is the interval coefficient.

7. The cross-condition fault diagnosis method based on a stable causal graph convolutional domain generalization network according to claim 1, characterized in that, The device is a bearing, and the fault diagnosis includes the identification of the bearing's normal condition, inner ring fault, outer ring fault, and ball fault.

8. A computer terminal comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the cross-condition fault diagnosis method based on a stable causal graph convolutional domain generalization network as described in any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps of the cross-condition fault diagnosis method based on a stable causal graph convolutional domain generalization network as described in any one of claims 1 to 7.

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