Fault diagnosis model construction method based on distributed causal discovery and federated learning

Abstract

The invention relates to the technical field of fault diagnosis, in particular to a fault diagnosis model construction method based on distributed causal discovery and federated learning. According to the method, a covariance tensor containing statistical association information of an observation variable and an agent variable is obtained, a global causal graph is obtained by combining a federal causal discovery method introducing the agent variable, then a converted causal intensity matrix is embedded into a graph convolutional neural network, and finally a personalized and global diagnosis model is trained by using a FedAvg framework fused with a Dito algorithm. According to the method, distributed heterogeneous data can be effectively processed while data privacy is protected, model interpretability is improved by mining a causal relationship between variables, global generalization and client personality requirements are considered, the accuracy and generalization ability of fault diagnosis are remarkably improved, and the fault diagnosis efficiency is improved. The method is especially suitable for fault diagnosis of industrial bearings and other scenes needing dispersed sensitive data processing.

Description

Technical Field

[0001] The present invention relates to the field of fault diagnosis technology, and in particular to a method for constructing a fault diagnosis model based on distributed causal discovery and federated learning. Background Art

[0002] Bearings are core components of industrial equipment, and their health status is directly related to equipment safety and production efficiency. Therefore, fault diagnosis is of great significance. However, industrial bearing data is often distributed across different equipment and factories and contains sensitive information, making it difficult to directly share centrally. Federated learning, as a distributed machine learning framework, can process this dispersed and private data to diagnose bearing fault categories. However, it is inherently unable to explore the causal relationships within the data, lacks interpretability, and is prone to falling into correlation traps. To this end, the emergence of federated causal discovery technology provides a key supplement. It can process distributed bearing fault data across equipment and factories, effectively identify causal relationships between variables, analyze the internal mechanisms of faults, and thus guide the federated learning framework to more accurately identify fault categories. Existing federated learning bearing fault diagnosis methods are mostly data-driven and do not involve causal embedding. Such traditional models are often regarded as "black boxes" and their decision-making processes are difficult to explain. Patent application CN117591999A discloses a federated graph isomorphic network wind turbine bearing fault diagnosis method based on causal discovery. This method can improve the accuracy and interpretability of the wind turbine bearing fault diagnosis model while ensuring the data privacy of wind turbine participants. The above-mentioned existing technology constructs a participant causal model through the FedDAG algorithm, obtains a global causal graph, and converts the global causal graph into an adjacency matrix input graph isomorphic network. However, it should be noted that the federated causal discovery algorithm and federated learning algorithm it adopts essentially rely on the FedDAG algorithm, focus on global shared model training, and form a unified model by aggregating client parameters.

[0003] In real-world scenarios, data from multiple devices and factories is often heterogeneous, making it difficult for a unified model to accommodate the personalized needs of different clients, which can easily lead to poor model performance for some clients. Furthermore, the aforementioned method does not involve causal strength calculations. The input adjacency matrix can only characterize the existence and direction of causality between variables, but ignores differences in the strength of causal relationships. This prevents the model from understanding the importance and influence of different causal relationships, and the understanding and utilization of causal relationships between fault features is insufficient, which in turn affects the accuracy and efficiency of diagnosis. In summary, the aforementioned method still has obvious limitations in terms of adaptability to heterogeneous data and the depth of causal relationship utilization, and therefore needs to be addressed urgently. Summary of the Invention

[0004] To avoid and overcome the technical problems of existing technologies, this paper provides a method for constructing a fault diagnosis model based on distributed causal discovery and federated learning. This method effectively processes distributed heterogeneous data while protecting data privacy. By mining causal relationships, it improves model interpretability, balances global commonality with client specificity, and enhances fault diagnosis accuracy and generalization capabilities.

[0005] To achieve the above object, the present invention provides the following technical solutions: A method for constructing a fault diagnosis model based on distributed causal discovery and federated learning includes the following construction steps: S1. Obtain local bearing fault data of each client, and construct a covariance tensor of each client based on the local bearing fault data. The covariance tensor contains statistical correlation information of observed variables and proxy variables. S2. Use the federated causal discovery method that introduces proxy variables to process the sample size and covariance tensor to obtain a global causal graph; S3. Calculate the average causal effect between variables in the global causal graph, convert the global causal graph into a causal strength matrix, and embed the causal strength matrix into the graph convolutional neural network of each client; S4. Based on the graph convolutional neural network embedded with the causal strength matrix, the FedAvg federated learning framework integrated with the Ditto algorithm is used for model training to obtain the personalized diagnosis model of each client and the global diagnosis model of the server.

[0006] As a further solution of the present invention: the process of obtaining the covariance tensor is as follows: S11. The nonlinear relationship between the observed variables and the proxy variables is converted into a linear feature space through random Fourier eigenmapping to obtain the random Fourier eigenvector of each variable. The formula used in the eigenmapping is as follows: ; In the formula, x represents the input variable, which is an observed variable or a proxy variable; Table x’s feature map; h represents the hidden feature dimension; are the 1st to hth random weights that obey the standard Gaussian distribution N(0,1); represents the 1st to hth random biases uniformly distributed in [0,2π]. T is the matrix transpose.

[0007] S12. Calculate the covariance matrix of a variable pair consisting of any two variables in the local bearing fault data of each client based on the obtained random Fourier eigenvector; ; Where, represents the covariance matrix; is the sample size of client k; and are the values ​​of variables X and Y in the i-th sample of client k, respectively; and They are and feature map; and are the means of the random Fourier eigenvectors of variables X and Y, respectively.

[0008] S13. Integrate the covariance matrices of all variable pairs and use each covariance matrix as an element to construct a local covariance tensor containing the observed variables and the proxy variables.

[0009] As a further solution of the present invention: the proxy variable is a virtual variable representing the client or domain index, which is used to explicitly model the data heterogeneity between different clients, including at least one difference in bearing model, load, and speed.

[0010] As a further solution of the present invention: the steps for obtaining the global causal graph are as follows: S21. Construct summary statistics, which include the total sample size of all clients and the global covariance tensor. The global covariance tensor is obtained by weighting the local covariance tensor of each client by the sample size. S22, test the conditional independence between variables based on the federated conditional independence test and determine the causal skeleton; S23. Based on the principle of federated independent change, the causal direction in the causal skeleton is determined to obtain a global causal graph.

[0011] As a further solution of the present invention: the federal conditional independence test converts the operator operation in infinite dimensional space into finite dimensional matrix operation through random feature approximation kernel function, and uses the F-norm square of the empirical partial covariance matrix as the test statistic.

[0012] As a further solution of the present invention: the federated independent variation principle is based on the normalized Hilbert-Schmidt independence criterion to determine the causal direction. If the normalized Hilbert-Schmidt independence criterion value satisfies When , the causal direction is X→Y, otherwise it is Y→X, where represents the normalized correlation between variable X and variable Y when controlling variable Z. It represents the normalized correlation between variable Y and variable X while controlling for variable Z.

[0013] As a further solution of the present invention, the process of embedding the causal strength matrix into the graph convolutional neural network is as follows: S31. Convert the global causal graph into a causal adjacency matrix, where the corresponding position of the variable pair with a causal relationship is 1, otherwise it is 0; S32. Calculate the average causal effect ACE between each variable pair, and replace the 1 in the corresponding position in the causal adjacency matrix with the ACE value to obtain the causal intensity matrix; S33. Embed the causal strength matrix into the graph convolutional neural network and participate in model training as the adjacency matrix of the graph convolutional neural network.

[0014] As a further solution of the present invention: the calculation formula of the average causal effect ACE is: ; Where, represents the average causal effect of variable X on variable Y; Indicates intervention in the value of variable X, setting it to 1; It represents the average value of variable Y when the value of variable X is set to 1; Indicates intervention in the value of variable X, setting it to 0; Indicates the average value of variable Y when the value of variable X is set to 0.

[0015] As a further solution of the present invention, the process of constructing the personalized diagnosis model and the global diagnosis model is as follows: S41. The server generates a graph convolutional neural network based on causal strength matrix embedding as a global graph convolutional neural network and sets its model parameters Distributed to each client, the client personalizes the initial parameters of the graph convolutional neural network Synchronize to , k is the client number; S42. Local update of global graph convolutional neural network: Based on the local bearing fault data, the client performs multiple gradient descents on the global graph convolutional neural network embedded with the causal strength matrix to obtain a temporary updated model, and calculates and sends the updated difference to the server; Personalized graph convolutional neural network training: The personalized graph convolutional neural network is updated based on local bearing fault data. Regularization terms are introduced to constrain the difference between it and the temporary update model, while maintaining the network structure embedded in the causal strength matrix unchanged. S43, server aggregation: aggregate all updated differences according to the sample size weight of each client, update the global graph convolutional neural network parameters and distribute them to each client; S43, iteration termination: repeat steps S42 and S43 to the preset rounds to obtain the final client personalized graph convolutional neural network and server global graph convolutional neural network, that is, the client personalized diagnosis model and the server global diagnosis model.

[0016] As a further solution of the present invention: the object of the fault diagnosis is an industrial bearing, and the observed variables include at least one of temperature, vibration frequency, and noise.

[0017] Compared with the prior art, the present invention has the following beneficial effects: By collecting heterogeneous data from multiple clients, identifying observations and proxy variables, and combining random Fourier feature mapping with covariance calculation, this approach effectively linearizes nonlinear relationships and explores intervariate correlations. Proxy variables also adapt to data heterogeneity, laying the foundation for subsequent causal analysis and accurately capturing data correlations across scenarios and characteristics. Leveraging federated conditional independence testing and the principle of independent variation, while ensuring data privacy, this approach utilizes reproducing kernel Hilbert space operations and random feature approximation to accurately test variable conditional independence and determine causal direction. The resulting global causal graph clearly visualizes the inherent causal relationships in the data, providing an interpretable framework for fault diagnosis and distinguishing true causal relationships from spurious ones. The causal graph is converted into a causal strength matrix, quantifying causal relationships using average causal effects, and then embedded in a graph convolutional neural network. This approach preserves the quantitative information of causal relationships while leveraging GCN to prioritize paths with high causal strength, improving the interpretability of fault diagnosis, ensuring that model decisions are more aligned with the inherent logic of the data, and enhancing the credibility of diagnostic results. Using a federated learning framework, this approach prioritizes local updates followed by aggregation, balancing global commonality with client-specificity through gradient descent and regularization. Personalized training adapts to local data differences, and global aggregation absorbs multi-client experience. The model obtained after iterative optimization can not only accurately diagnose the unique faults of each client, but also grasp the global common fault modes, taking into account efficiency and accuracy, and also ensuring data privacy and security. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 Construct a flow chart for the model of the present invention. DETAILED DESCRIPTION

[0019] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0020] See also Figure 1 In one embodiment of the present invention, a method for constructing a fault diagnosis model based on distributed causal discovery and federated learning is implemented. This method builds a fault diagnosis model through four core steps: obtaining a covariance tensor, acquiring a global causal graph, constructing and embedding a causal strength matrix, and training personalized and global diagnostic models. This process ensures data privacy while exploring causal relationships in data, balancing global commonality with client individuality.

[0021] 1. Obtain the covariance tensor of each client 1. Collect data Local bearing failure data was collected from each client (different factories, Factory A and Factory B), and observed and proxy variables were identified. Observed variables included temperature T, vibration frequency F, and noise N. The proxy variable Ω was a dummy variable used to characterize client data heterogeneity, such as differences in bearing model, speed, and load. For example, if Factory A's bearing model was W and its speed was 1000 rpm, while Factory B's bearing model was V and its speed was 1500 rpm, the proxy variable Ω would capture these differences.

[0022] The sample size of each client is counted. Factory A has 500 data items and Factory B has 600 data items.

[0023] 2. Random Fourier feature map A random Fourier feature approximation kernel function (such as a Gaussian kernel) is used to transform the nonlinear relationship of variables into a linear feature space. For variable X, the random feature mapping formula is: ; In the formula, x represents the input variable, which is an observed variable or a proxy variable; represents the feature map of x; h represents the hidden feature dimension, and the value of h in this embodiment is 100; are the 1st to hth random weights that obey the standard Gaussian distribution N(0,1); represents the 1st to hth random biases uniformly distributed in [0,2π]. T is the matrix transpose.

[0024] 3. Calculate the covariance matrix Based on the obtained random Fourier eigenvector, the covariance matrix of the variable pair consisting of any two variables in the local bearing fault data of each client is calculated; ; Where, represents the covariance matrix; is the sample size of client k; and are the values ​​of variables X and Y in the i-th sample of client k, respectively; and They are and feature map; and are the means of the random Fourier eigenvectors of variables X and Y, respectively. For example, the covariance matrix of the vibration frequency F and temperature T of the bearings in factory A is calculated to reflect the correlation between the two in the factory data.

[0025] 4. Constructing the covariance tensor Integrate the covariance matrix of all variable pairs (including observed variables and proxy variables Ω) of client k to form a local covariance tensor , whose dimensions are , where d is the number of observed variables + 1 proxy variable Ω. For example, for a client containing temperature T, vibration frequency F, noise N, and proxy variable Ω, the covariance matrices for all pairs of variables, such as Ω and F, Ω and T, and F and T, must be calculated and integrated into a covariance tensor.

[0026] 2. Obtaining a Global Causal Graph 1. Construct summary statistics Total sample size: , K is the total number of clients; for example, the total sample size of Factory A and Factory B is n=500+600=1100.

[0027] Global covariance tensor: , directly summing the local covariance tensors of each client or weighting them by sample size, such as .

[0028] 2. Federal Conditional Independence Test (FCIT) Core principle: Based on the partial cross-covariance operator of the reproducing kernel Hilbert space (RKHS), the infinite-dimensional operation is converted into a finite-dimensional matrix operation through random feature approximation to test the conditional independence between variables.

[0029] Null hypothesis H0: X⊥Y|Z, which means that variables X and Y are independent when controlling for variable Z, which is equivalent to the Hilbert-Schmidt norm of the partial cross-covariance operator being 0; Alternative hypothesis H1: Variables X and Y are not independent when controlling for variable Z.

[0030] Empirical partial cross-covariance matrix calculation: ; Where, It represents the partial mutual covariance matrix of variables X and Y after controlling for variable Z. If the norm of this matrix is ​​close to 0, it means that variables X and Y are independent under the condition of variable Z; otherwise, there is a correlation. Represents the mutual covariance matrix of variables X and Y in the feature space. Based on the random Fourier eigenmap (which converts nonlinear relationships into linear features), the covariance of the eigenvectors is calculated to reflect the overall association between the two (including the interference of variable Z). Represents the mutual covariance matrix of variables X and Z in the feature space, reflecting the association between variables X and Z and used to remove the influence of variable Z on variable X. Represents the autocovariance matrix (square matrix) of variable Z in the feature space, where the diagonal is the variance of each feature of variable Z and the off-diagonal is the covariance between features. is the regularization coefficient, used to avoid Singularity,improves the numerical stability of matrix inversion. is the identity matrix, whose dimensions are The diagonal is 1 and the rest are 0. The inverse matrix of the autocovariance matrix of variable Z after regularization is used to calculate the "regression effect of variable Z on variables X and Y" and remove the interference of variable Z.

[0031] Represents the mutual covariance matrix of variables Y and Z in the feature space, reflects the association between variables Y and Z, and is used to remove the influence of variable Z on variable Y.

[0032] Test statistic: , express The F-norm squared. If If the value is significantly greater than the critical value, then H0 is rejected, and it is determined that there is an association between the variables. For example, after controlling for the proxy variable Ω, the independence of F and T is tested. If H0 is rejected, it is believed that there is a causal relationship between the two.

[0033] 3. Federal Independent Change Principle (FICP) The causal direction is determined based on the normalized Hilbert-Schmidt independence criterion (HSIC). Calculation: ; ; ; ; Where, A statistic indicating that variable X is the cause and variable Y is the effect. A statistic indicating that variable Y is the cause and variable X is the effect. represents the residual of variable Y, represents the residual of variable X. Represents variables X and The regularized cross-covariance matrix in the high-dimensional feature space, Represents the variables Y and Regularized cross-covariance matrix in high-dimensional feature space. express The square of the F-norm, express The squared F-norm of . represents the regularized autocovariance matrix of variable X in the high-dimensional feature space, Representing variables The regularized autocovariance matrix in the high-dimensional feature space, represents the regularized autocovariance matrix of variable Y in the high-dimensional feature space, Representing variables The regularized autocovariance matrix in the high-dimensional feature space, Representation matrix traces, Representation matrix traces, Representation matrix traces, Representation matrix traces.

[0034] Direction judgment: If , then the causal direction is X→Y. For example, we can calculate , so the causal direction between vibration frequency and temperature is determined to be: F→T.

[0035] Thus, a global causal graph is finally formed, such as Ω→F, indicating that the proxy variable affects the vibration frequency; F→T, indicating that the vibration frequency affects the temperature; F→N, indicating that the vibration frequency affects the noise.

[0036] 3. Constructing and Embedding the Causal Intensity Matrix 1. Generate causal adjacency matrix Convert the global causal graph into an M×M dimensional causal adjacency matrix , where M is the total number of variables. If there is , then the element at the corresponding position The value is 1, otherwise it is 0. For example, based on the above global causal graph, The corresponding positions of Ω to F, F to T, and F to N in All are 1, and the rest are 0.

[0037] 2. Calculate the average causal effect ACE ACE calculation formula: , represents the average change in variable Y after intervening with variable X. For example, if F increases by 1 unit, T increases by 2 units on average, then For the global causal graph The edge is replaced by the ACE value The 1 in the corresponding position in the causal strength matrix is ​​obtained , and the rest of the places without causal relationship are still 0.

[0038] 3. Embedded Graph Convolutional Neural Network GCN Causal Intensity Matrix As the adjacency matrix of the GCN, the model prioritizes paths with high causal strength during feature extraction. For example, if the weight of F→T is 2, the model will focus on learning this association, improving interpretability and diagnostic accuracy.

[0039] 4. Training Personalized Diagnostic Models and Global Diagnostic Models 1. Initialization The server initializes the global GCN model parameters , distributed to each client, the initial parameters of the client personalized GCN model Synchronize to , k is the client number.

[0040] 2. Local updates and personalized training Local update of the global model: Client k performs r gradient descents on the global model based on local bearing data, calculates the updated difference and sends it to the server.

[0041] ; Where, It represents the set of model parameters after an iterative update of client k, indicating the updated state. Represents the set of initial model parameters of client k before the start of this iteration, which serves as the starting point for the update. Represents the global learning rate, usually set to 0.01; For client k based on the initial parameters , the loss function calculated on its local data gradient.

[0042] Personalized model training: Client k performs p gradient descents on the personalized model, introducing regularization terms to constrain the difference from the global model.

[0043] ; Where, It represents the parameter set of the personalized model after the client k is updated, and represents the updated model status. It represents the initial parameter set of the personalized model of client k before the start of this update, which is the starting state of the update operation. Indicates the personalized learning rate, and the commonly used value is 0.005. It represents the initial parameter set of the global model at the corresponding stage, and is used to associate constraints with the client's personalized parameters, reflecting the connection between "personalization" and "global commonality". Represents the regularization coefficient, and a common value is 0.1, which ensures that the personalized model is both adapted to local data and associated with the global model. Indicates that client k is based on the initial parameters of its own personalized model , the loss function calculated on the local bearing data The gradient reflects the direction and magnitude of model parameter optimization driven by local bearing data.

[0044] 3. Server aggregation The server aggregates and updates the difference by sample size weight: ; ; Where, Indicates the new global model parameter set obtained after the server-side global model is aggregated and updated, representing the updated global model state. Represents the initial parameter set of the server-side global model before this aggregation update, which is the basic state of the aggregation operation. The weight coefficient of client k is usually related to the sample size and importance of the client data. It is used to weight the update contribution of each client, so that clients with more samples and more importance have a greater influence in the global aggregation. Represents the parameter update difference of client k relative to the initial global model parameters after local training.

[0045] Update the global model and distribute it to each client.

[0046] 4. Iteration termination Repeat the local update and aggregation steps to the preset rounds, and finally obtain the personalized diagnosis model of each client and the global diagnosis model of the server.

[0047] This implementation method handles data heterogeneity by introducing proxy variables, uses the FedCDH method to mine global causal relationships and quantify causal strength, and combines the Ditto-FedAvg algorithm to achieve collaborative optimization of personalized and global models, ultimately achieving high-precision and explainable diagnosis of industrial bearing faults while protecting data privacy.

[0048] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with the technical field, within the technical scope disclosed by the present invention, who makes equivalent replacements or changes based on the technical solution and inventive concept of the present invention, should be covered by the scope of protection of the present invention.

Claims

1. A method for constructing a fault diagnosis model based on distributed causal discovery and federated learning, characterized in that: The following build steps are included: S1. Obtain local bearing fault data of each client, and construct a covariance tensor of each client based on the local bearing fault data. The covariance tensor contains statistical correlation information of observed variables and proxy variables. S2. Use the federated causal discovery method that introduces proxy variables to process the sample size and covariance tensor to obtain a global causal graph; S3. Calculate the average causal effect between variables in the global causal graph, convert the global causal graph into a causal strength matrix, and embed the causal strength matrix into the graph convolutional neural network of each client; S4. Based on the graph convolutional neural network embedded with the causal strength matrix, the FedAvg federated learning framework integrated with the Ditto algorithm is used for model training to obtain the personalized diagnosis model of each client and the global diagnosis model of the server.

2. A method for constructing a fault diagnosis model based on distributed causal discovery and federated learning according to claim 1, characterized in that: The process of obtaining the covariance tensor is as follows: S11, converting the nonlinear relationship between the observed variables and the proxy variables into a linear feature space through random Fourier eigenmapping to obtain the random Fourier eigenvector of each variable; S12. Calculate the covariance matrix of a variable pair consisting of any two variables in the local bearing fault data of each client based on the obtained random Fourier eigenvector; S13. Integrate the covariance matrices of all variable pairs and use each covariance matrix as an element to construct a local covariance tensor containing the observed variables and the proxy variables.

3. A method for constructing a fault diagnosis model based on distributed causal discovery and federated learning according to claim 2, characterized in that: The proxy variable is a dummy variable representing the client or domain index, which is used to explicitly model the data heterogeneity between different clients, including at least one difference in bearing model, load, and speed.

4. A method for constructing a fault diagnosis model based on distributed causal discovery and federated learning according to any one of claims 1 to 3, characterized in that: The steps to obtain the global causal graph are as follows: S21. Construct summary statistics, which include the total sample size of all clients and the global covariance tensor. The global covariance tensor is obtained by weighting the local covariance tensor of each client by the sample size. S22, test the conditional independence between variables based on the federated conditional independence test and determine the causal skeleton; S23. Based on the principle of federated independent change, the causal direction in the causal skeleton is determined to obtain a global causal graph.

5. A method for constructing a fault diagnosis model based on distributed causal discovery and federated learning according to claim 4, characterized in that: The federated conditional independence test converts the operator operation in infinite-dimensional space into finite-dimensional matrix operation through random feature approximation kernel function, and uses the F-norm square of the empirical partial covariance matrix as the test statistic.

6. A method for constructing a fault diagnosis model based on distributed causal discovery and federated learning according to claim 5, characterized in that: The federated independent change principle is based on the normalized Hilbert-Schmidt independence criterion to determine the causal direction. If the normalized Hilbert-Schmidt independence criterion satisfies the value of When , the causal direction is X→Y, otherwise it is Y→X, where It represents the normalized correlation between variable X and variable Y when controlling variable Z; It represents the normalized correlation between variable Y and variable X while controlling for variable Z.

7. A method for constructing a fault diagnosis model based on distributed causal discovery and federated learning according to claim 6, characterized in that: The process of embedding the causal strength matrix into the graph convolutional neural network is as follows: S31. Convert the global causal graph into a causal adjacency matrix, where the corresponding position of the variable pair with a causal relationship is 1, otherwise it is 0; S32. Calculate the average causal effect ACE between each variable pair, and replace the 1 in the corresponding position in the causal adjacency matrix with the ACE value to obtain the causal intensity matrix; S33. Embed the causal strength matrix into the graph convolutional neural network and participate in model training as the adjacency matrix of the graph convolutional neural network.

8. A method for constructing a fault diagnosis model based on distributed causal discovery and federated learning according to claim 7, characterized in that: The calculation formula of average causal effect ACE is: ； Where, represents the average causal effect of variable X on variable Y; Indicates intervention in the value of variable X, setting it to 1; It represents the average value of variable Y when the value of variable X is set to 1; Indicates intervention in the value of variable X, setting it to 0; Indicates the average value of variable Y when the value of variable X is set to 0.

9. A method for constructing a fault diagnosis model based on distributed causal discovery and federated learning according to claim 8, characterized in that: The construction process of personalized diagnosis model and global diagnosis model is as follows: S41. The server generates a graph convolutional neural network based on causal strength matrix embedding as a global graph convolutional neural network and sets its model parameters Distributed to each client, the client personalizes the initial parameters of the graph convolutional neural network Synchronize to , k is the client number; S42. Local update of global graph convolutional neural network: Based on the local bearing fault data, the client performs multiple gradient descents on the global graph convolutional neural network embedded with the causal strength matrix to obtain a temporary updated model, and calculates and sends the updated difference to the server; Personalized graph convolutional neural network training: The personalized graph convolutional neural network is updated based on local bearing fault data. Regularization terms are introduced to constrain the difference between it and the temporary update model, while maintaining the network structure embedded in the causal strength matrix unchanged. S43, server aggregation: aggregate all updated differences according to the sample size weight of each client, update the global graph convolutional neural network parameters and distribute them to each client; S43, iteration termination: repeat steps S42 and S43 to the preset rounds to obtain the final client personalized graph convolutional neural network and server global graph convolutional neural network, that is, the client personalized diagnosis model and the server global diagnosis model.

10. A method for constructing a fault diagnosis model based on distributed causal discovery and federated learning according to claim 9, characterized in that: The object of the fault diagnosis is an industrial bearing, and the observed variables include at least one of temperature, vibration frequency, and noise.

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