Industrial multi-source data fusion method based on causal inference

Abstract

The invention discloses an industrial multi-source data fusion method based on causal inference in the technical field of computer data processing, and the method is applied to an aero-engine, and comprises the steps: obtaining the original performance data of the aero-engine, carrying out the normalization processing of the original performance data, and obtaining a target variable, the original performance data comprises rotating speed, exhaust temperature, oil pressure, oil temperature and metal abrasive particle component data; constructing a causal inference algorithm to calculate a dynamic threshold value; the causal intensity of each variable pair is calculated from the candidate causal set, variables with the first M ranks of the causal intensity are selected to form an optimization condition set, and a test algorithm is constructed; constructing a symmetric causal intensity matrix; and on the basis of the target variable and the feature matrix, performing quadrature to obtain a new data set after dimension reduction. By constructing the causal inference algorithm, the interpretability and generalization ability of the model can be enhanced, the performance stability is improved, the application range in the industrial field is expanded, and the calculation burden is relieved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of computer data processing, and particularly relates to an industrial multi-source data fusion method based on causal inference. BACKGROUND

[0002] With the improvement of the intelligent level of industrial equipment, in order to ensure the continuous and stable operation of the system, researchers often monitor the equipment state in real time by widely deploying sensors, and construct an intelligent operation and maintenance system based on multi-source monitoring data. However, with the sharp increase of the dimension of monitoring variables, the calculation cost of data processing and modeling increases exponentially, which seriously restricts the real-time analysis and decision-making ability of the system. Therefore, before state modeling, high-dimensional monitoring data must be reduced and purified to extract key features and remove redundant information.

[0003] In the process of processing data, especially the health management of a complex device such as an aero-engine, as the "heart" of the aircraft, the accuracy requirements of abnormal diagnosis and residual life prediction are extremely high. In the monitoring process, multi-source data from different subsystems, heterogeneous and high-dimensional, such as performance parameters (such as rotation speed, exhaust temperature) directly reflecting the working state, high-frequency vibration signals containing mechanical component failure information, and oil system data (such as oil pressure, oil temperature and metal abrasive composition) for diagnosing wear and tear faults will be collected. These parameters interact with each other in the strong coupling physical process inside the engine, making it difficult for traditional fusion methods to distinguish the causal driving relationship between them and the surface statistical correlation, and easily interfered by redundant and misleading information. In order to meet the needs of actual production, it is often necessary to process multi-source data at the same time, and multi-source data fusion refers to integrating data from different data sources, eliminating useless data, and obtaining data more conducive to downstream tasks. For time series output by sensors, multi-source data fusion refers to obtaining a new data set from the original data. After abnormal diagnosis or RUL prediction on the new data set, the model estimation result is closer to the actual state of the equipment.

[0004] Multi-source data fusion technology, by integrating data from different sensors, can effectively compress data size and increase information density, thus providing a better data foundation for subsequent tasks such as anomaly diagnosis and remaining useful life (RUL) prediction. Although traditional correlation-based fusion methods have achieved certain results in some scenarios, they still have significant limitations when processing high-dimensional, highly coupled system data. First, traditional fusion methods have weak interpretability; relying solely on statistical correlation is insufficient to reveal the inherent causal mechanisms between variables, resulting in poor generalization ability of the fusion results across operating conditions or systems. Second, performance stability is insufficient; since correlation is easily affected by noise and confounding factors, the fusion effect decreases significantly when the data distribution changes. On the other hand, traditional methods are difficult to effectively handle the strong multivariate interactions and nonlinear dependencies commonly found in highly coupled complex systems, limiting their practical application in modern industrial equipment monitoring. This not only reduces the accuracy of state estimation and prediction tasks but also increases the computational burden due to the introduction of a large number of invalid features. Summary of the Invention

[0005] The purpose of this invention is to provide an industrial multi-source data fusion method based on causal inference. By mining the essential relationships between monitoring variables, it extracts information that reflects the actual operating status of the system, filters out useless noise, thereby improving the accuracy of equipment anomaly diagnosis and RUL prediction, enhancing the interpretability and generalization ability of the model, improving performance stability, expanding the scope of application in the industrial field, and reducing the computational burden.

[0006] To achieve the above objectives, the present invention provides the following technical solution: A causal inference-based industrial multi-source data fusion method, applied to aero-engines, the method comprising: The raw performance data of the aero-engine is obtained, and the raw performance data is normalized to obtain the target variable. The raw performance data includes data on engine speed, exhaust temperature, oil pressure, oil temperature and metal abrasive composition. Construct a causal inference algorithm to calculate dynamic thresholds; The causal strength of each variable pair is calculated from the candidate causal set, and the variables ranked M by causal strength are selected to form the set of optimization conditions to construct the testing algorithm. Construct a symmetric causal strength matrix; The new dataset after dimensionality reduction is obtained by multiplying the target variable and the feature matrix.

[0007] As a further aspect of the present invention: normalizing the raw performance data, including: Set the time series data expression for the raw performance data as follows: Where X is a time series data set, X NThe original performance data is time-series data, where T is the time length and N is the total number of variables. Using the normalization formula: The time series data were normalized using z-score to obtain time series data with a mean of 0 and a standard deviation of 1, where X i ’ X is the target variable. i μ is a variable. i Let σ be the mean of the variable. i is the standard deviation of the variable.

[0008] As a further aspect of the present invention: a causal inference algorithm is constructed to calculate a dynamic threshold, including: A causal inference algorithm is constructed to calculate the mutual information values ​​between the target variable and all candidate causal variables, and the mutual information matrix is ​​obtained. Candidate causal sets are obtained by retaining variable pairs whose mutual information values ​​are in the top K percentiles, and dynamic thresholds are calculated based on the signal-to-noise ratio characteristics of the data within the sliding window.

[0009] As a further aspect of this invention: a causal inference algorithm is constructed to calculate the mutual information values ​​between the target variable and all candidate causal variables, obtaining a mutual information matrix; variable pairs with mutual information values ​​in the top K percentiles are retained to obtain a candidate causal set; and a dynamic threshold is calculated based on the signal-to-noise ratio characteristics of the data within the sliding window, including: Constructing a causal inference algorithm: The mutual information value is calculated, wherein, It is a joint probability distribution. and It is a marginal distribution. It is a candidate causal variable. , It is the mutual information value; Variable pairs with mutual information values ​​in the top K percentiles are included in the candidate causal set. Eliminate the remaining variable pairs; The normalized data X′ is divided into sliding windows of length W, and the signal-to-noise ratio of the variable is calculated in each window using the signal-to-noise ratio calculation formula.

[0010] As a further aspect of the present invention: the signal-to-noise ratio calculation formula is ,in, It is the signal variance extracted by smoothing filtering. It is the noise variance in the regression residual calculation; Construction formula: Calculate the dynamic threshold, where, and These are the upper and lower bounds of the significance level, respectively. This is the attenuation parameter.

[0011] As a further aspect of the present invention: the causal strength of each variable pair is calculated from the candidate causal set, the variables ranked M by causal strength are selected to form an optimization condition set, and a testing algorithm is constructed, including: The set of optimization conditions is obtained by selecting the M variables with the highest causal strength. The verification algorithm is constructed as follows: , in, .

[0012] As a further aspect of the present invention: constructing a symmetric causal strength matrix, including: Set the causality strength matrix as follows: Principal component analysis was used for data dimensionality reduction. The maximum causal strength is: ,in, Let aij be an element, and if there is no causal relationship, then aij = 0, and S is the strength of the causal relationship; The causal intensity matrix is ​​decomposed into eigenvalues, eigenvalues ​​and corresponding eigenvectors are calculated, the contribution rate of each eigenvalue is obtained, and the eigenvalues ​​are sorted from largest to smallest. The eigenvectors corresponding to the top K eigenvalues ​​with the largest contribution rates are selected to form a dimension reduction matrix. Multiply the original normalized data matrix with the dimension-reduced matrix to reconstruct the data and obtain a new dataset after dimension reduction.

[0013] As a further aspect of the present invention: the eigenvalue decomposition formula is as follows: ,in, For eigenvalues, Let N be the feature vector, and N be the total number of variables.

[0014] As a further aspect of the present invention: the contribution rate of the eigenvalues ​​is The new dataset after dimensionality reduction is X′=XV′, where X′ contains K feature variables.

[0015] As a further aspect of this invention: based on the target variable and the feature matrix, a new dataset after dimensionality reduction and fusion is obtained by multiplying, including: Multiplying the original normalized data X′ by the feature matrix V′ yields a new dataset after dimensionality reduction and fusion: ,in, .

[0016] As a further aspect of the present invention, the new dataset is applied to anomaly diagnosis models and / or remaining life prediction models.

[0017] Compared with the prior art, the beneficial effects of the present invention are: 1. This invention identifies the fundamental causal chain from massive amounts of data, constructs fusion features with clear physical meaning and removes coupling interference, and improves computational efficiency through effective dimensionality reduction. It reconstructs the data fusion framework from the perspective of causal relationships, and achieves more robust and interpretable information extraction by identifying the causal structure between variables, thereby improving the accuracy of anomaly diagnosis and RUL prediction, while reducing computational costs.

[0018] 2. This invention constructs a causal inference algorithm to calculate the mutual information value between the target variable and all candidate causal variables, and retains the variable pairs whose mutual information values ​​are in the top K percentiles to obtain the candidate causal set. This can form a pre-screening mechanism, reduce the number of subsequent conditional independence tests, and significantly reduce computational complexity.

[0019] 3. This invention calculates the mutual information value between the target variable and all candidate causal variables by constructing a causal inference algorithm, which reduces the interference of irrelevant conditional variables, improves the accuracy of causal inference, reduces potential confounding factors, realizes data fusion and dimensionality reduction by constructing a symmetric causal strength matrix, and retains key causal information of equipment abnormality and degradation.

[0020] 4. This invention employs a dynamic significance threshold to enable the algorithm to adapt to the characteristics of signal-to-noise ratio fluctuations in industrial data. In the stage of high data quality, strict standards are used to ensure the reliability of causal relationships, while in the stage of high noise interference, the standards are relaxed to avoid missing key information. This dynamic adjustment mechanism significantly improves the stability and generalization ability of the algorithm in complex industrial environments, overcomes the shortcomings of poor adaptability of fixed thresholds, and effectively reduces the interference of irrelevant variables and potential confounding factors. Attached Figure Description

[0021] Figure 1 (a) is a causal relationship strength matrix diagram of a 5-class dataset constructed by the first J-PCMCI+ algorithm in Embodiment 1 of the present invention. Figure 1 (b) is a causal relationship strength matrix diagram of a 5-class dataset constructed by the second J-PCMCI+ algorithm in Embodiment 1 of the present invention; Figure 2 (a) is the first correlation strength matrix diagram based on a sliding time window in Embodiment 1 of the present invention. Figure 2 (b) is the second correlation strength matrix diagram based on the sliding time window in Embodiment 1 of the present invention; Figure 3 This is a graph showing the relationship between the actual and predicted RUL values ​​of the engine in the N-CMAPSS DS01 subset dataset of Embodiment 1 of the present invention. Figure 4This is a graph showing the relationship between the actual and predicted RUL values ​​of the engine in the N-CMAPSS DS08 subset dataset of Embodiment 1 of the present invention. Figure 5 This is a graph showing the relationship between the actual and predicted RUL values ​​of the CMAPSS engine in Embodiment 1 of the present invention. Figure 6 (a) is a spatial relationship diagram of PCMCI according to an embodiment of the present invention. Figure 6 (b) is a spatiotemporal relationship diagram of PCMCI according to an embodiment of the present invention; Figure 7 This is a causal timing diagram of PCMCI+ before the execution of the MCI stage in Embodiment 1 of the present invention; Figure 8 This is a structural diagram of the J-PCMCI+ and GPDC anomaly classification confusion matrix in Embodiment 1 of the present invention; Figure 9 This is the residual graph attention module of Embodiment 2 of the present invention; Figure 10 This is the MResGAT model architecture of Embodiment 2 of the present invention; Figure 11 This is the confusion matrix for anomaly diagnosis of the MResGAT model in Embodiment 2 of the present invention; Figure 12 This is the weighted GAT structure of Embodiment 2 of the present invention; Figure 13 This is the weighted GCN structure of Embodiment 2 of the present invention; Figure 14 This is the multi-scale GAT structure of Embodiment 2 of the present invention; Figure 15 This is the MinCutPool structure of Embodiment 2 of the present invention. Detailed Implementation

[0022] 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.

[0023] Example 1: This embodiment applies multi-source sensor data fusion to aero-engines to improve the accuracy of anomaly diagnosis and remaining life prediction.

[0024] This embodiment uses a monitoring dataset for turbofan engines, including a 5-class dataset for anomaly diagnosis and CMAPSS and N-CMAPSS datasets for remaining useful life (RUL) prediction. These data were generated by NASA using an advanced simulation system to simulate engine operation in a real flight environment. The datasets exhibit significant time-varying, strong coupling, and nonlinear characteristics, with complex interactions between the various sensor variables.

[0025] The 5-class dataset contains 12 monitored variables, covering key parameters such as fan speed, compressor outlet temperature, and combustion chamber fuel flow rate. Each sample is a time series of length 12. The dataset includes one normal state and four abnormal states (Fan, HPC, HPT, LPT), with the training, validation, and test sets divided in an 8:1:1 ratio.

[0026] The CMAPSS dataset contains four subsets (FD001-FD004), each containing 21 monitored variables and 3 operated variables, with a sample length of 64. The N-CMAPSS dataset expands to 32 variables with a sample length of 32, and contains eight subsets (DS01-DS08), simulating conditions closer to real-world operation.

[0027] Please see Figures 1-8 In this embodiment, an industrial multi-source data fusion method based on causal inference is provided, including the following steps: Step S1: Data preprocessing.

[0028] The raw monitoring data were normalized using z-scores to ensure that the mean of each variable was 0 and the standard deviation was 1, thus eliminating differences in dimensions. The normalization formula is as follows: in, The mean, The standard deviation is denoted as .

[0029] Step S2: Selection and parameter setting of causal inference algorithm To accurately uncover causal relationships among monitored variables, this embodiment selects the improved J-PCMCI+ algorithm as the core causal inference engine, and refines its key parameters and execution steps. This improved algorithm significantly enhances performance in industrial data environments by introducing three mechanisms: pre-screening, dynamic thresholding, and condition set optimization.

[0030] First, a candidate causal set pre-screening is implemented based on information theory. For each target variable... Calculate its relationship with all candidate causal variables. The mutual information is used to assess its generalized correlation, and the calculation formula is as follows: Where x′ and y′ are respectively and The probability distribution of the values ​​in the normalized data X′ is estimated using the histogram method. A quantile K of 50% is set, meaning only the variable pairs with mutual information values ​​in the top 50% are retained for subsequent formal causal testing. This reduces unnecessary calculations by approximately 50%.

[0031] Secondly, configure the key parameters of the dynamic significance threshold adjustment strategy. Set the sliding window length W=50. Within each window, calculate the signal-to-noise ratio (SNR) of the variable as the basis for threshold adjustment: in, One-dimensional Gaussian filtering was applied to... After smoothing, its variance is calculated. This is the variance of the detrended residuals. Dynamic significance threshold. Calculated by the following formula: Finally, the execution details of condition set optimization are clarified. During the MCI verification phase, the condition set... The size is set to M=5, meaning only variables related to the target variable are selected. Five variables with the strongest causal strength (taken from previous test results) were used as a condition set to focus on the core causal path and eliminate irrelevant interference.

[0032] Step S3: Construct the causal relationship strength matrix.

[0033] Based on the causal relationship output by J-PCMCI+ (in the form of...) Construct a symmetric causal strength matrix A, where the elements Defined as: in This represents the strength of the causal relationship, and its value ranges from [−1, 1].

[0034] Step S4: Dimensionality reduction of data based on principal component analysis (PCA).

[0035] Perform eigenvalue decomposition on matrix A and calculate the eigenvalues. and eigenvectors Sort the eigenvectors by contribution rate from highest to lowest, and select the top K eigenvectors to form the projection matrix. Reconstruct the data using the following formula: Where X is the original data matrix, This is the data matrix after dimensionality reduction.

[0036] Step S5: Construction of the abnormal diagnosis model The InceptionTime model is used as the classifier. Its structure includes multiple Inception modules, global average pooling layers, and fully connected layers. It is trained using the AdamW optimizer, and the hyperparameters are optimized using the Optuna algorithm.

[0037] Step S6: Construction of RUL Prediction Model A GRU-Transformer model is used for regression prediction, combining a gated recurrent unit (GRU) and a Transformer encoder, and introducing an attention mechanism to capture key features. Hyperparameters are also optimized using Optuna.

[0038] Step S7: Model Training and Evaluation The model is trained using the training set, hyperparameters are tuned using the validation set, and performance is evaluated using the test set. Anomaly diagnosis is measured by accuracy, while RUL prediction is measured by RMSE and Score.

[0039] To verify the effectiveness of the method of the present invention, a comparative experiment was designed to compare the performance of no dimensionality reduction, PCA dimensionality reduction, KPCA dimensionality reduction, and dimensionality reduction methods based on different causal inference algorithms (PCMCI, PCMCI+, LPCMCI, J-PCMCI+) on anomaly diagnosis and RUL prediction tasks. Figure 1 This demonstrates the causal strength matrix constructed using the J-PCMCI+ algorithm, compared to... Figure 2 The correlation matrix is ​​sparser and has eliminated confounding factors. Figure 3 , Figure 4 The RUL prediction results for engines in the N-CMAPSS DS01 and DS08 subsets are presented respectively. Figure 5 The results of CMAPSS engine RUL prediction are also presented, demonstrating that the method of this invention maintains low prediction error under various operating conditions. Tables 1-4 provide detailed quantitative results. For example, in the anomaly diagnosis task, the multi-source data fusion method based on J-PCMCI+ and GPDC achieves an accuracy of 93.70%, outperforming other methods; in RUL prediction, the FD002 subset has the lowest RMSE of 14.45, significantly better than the comparative methods, and the RMSE of the DS02, DS06, DS07, and DS08 subsets in the N-CMAPSS dataset is also the lowest. These data fully demonstrate the superiority of the method of this invention in the fusion of highly coupled, nonlinear time-series data.

[0040] Table 1. Results of Anomaly Classification Experiment Table 2. RUL Prediction Results from CMAPSS Dataset Table 3. RMSE of RUL predictions in the N-CMAPSS dataset .

[0041] Table 4. Score of RUL prediction in N-CMAPSS dataset .

[0042] This embodiment introduces a pre-screening step based on mutual information into the causal inference algorithm. By calculating the mutual information between the target variable and all candidate causal variables, only variable pairs with mutual information values ​​in the top K percentiles are retained for subsequent testing. This mechanism utilizes information theory metrics to eliminate obviously irrelevant variable pairs in advance, significantly reducing the computational burden of subsequent conditional independence tests. This enables the algorithm to efficiently process high-dimensional industrial sensor data and solves the problem of excessively high computational costs in traditional methods. On the other hand, it abandons the fixed significance level in causal inference and proposes an adaptive threshold adjustment method based on the local signal-to-noise ratio of the data. The signal-to-noise ratio of the data is estimated through a sliding window, and the test threshold is dynamically calculated accordingly: a stricter threshold is used when the data quality is high to improve reliability, and the threshold is appropriately relaxed when the data noise is high to avoid missing weak causal relationships. This strategy enhances the robustness of the algorithm to non-stationary, high-noise industrial data and improves the accuracy of causal discovery. In the MCI conditional independence test stage, this embodiment has optimized the condition set. Instead of considering all candidate condition variables equally, it selects only the finite variables with the strongest causal relationship with the target variable to construct the condition set based on the preliminary causal strength. This effectively reduces the interference of irrelevant variables on the test results and focuses on the core causal path. As a result, it can more accurately identify the true causal relationship in complex systems with potential confounding factors.

[0043] Example 2: This embodiment uses a 5-category dataset for aero-engine anomaly diagnosis, generated by an advanced turbofan engine simulation system to simulate the acquisition process of multi-sensor monitoring data under real flight conditions. The simulation process is based on an aerodynamic-thermodynamic model, considering various operating conditions such as different altitudes, Mach numbers, and throttle angles, and introduces sensor noise and zero-point drift to enhance the realism and complexity of the data. The dataset exhibits significant time-varying characteristics, strong coupling, and nonlinearity, effectively reflecting the dynamic characteristics of the engine during actual operation.

[0044] This embodiment extracts causal relationships between variables from historical monitoring data based on causal inference algorithms (such as J-PCMCI+) and constructs a causal relationship graph (such as...).Figure 6 As shown in the diagram, this graph uses monitored variables as nodes and causal relationships as edges, incorporating causal relationship strength information to guide the construction of a graph neural network, thereby achieving accurate classification of abnormal equipment states. The process includes the following steps: Step 1: Data Input and Preprocessing Input device monitoring data is represented as a multivariate time series matrix. Where N is the number of monitored variables and T is the number of time steps. Each variable is z-score normalized to have a mean of 0 and a standard deviation of 1. ,in and Variables The mean and standard deviation.

[0045] Step 2: Construct a cause-and-effect diagram Causal inference algorithms (such as J-PCMCI+ and GPDC) are used to extract causal relationships between variables from X and construct a causal relationship strength matrix. If the variable and If a causal relationship exists, then This indicates the causal strength; otherwise, it is 0. A directed or undirected graph structure is constructed as the adjacency matrix of the graph neural network.

[0046] Step 3: Construct a multi-receptive-field residual graph attention network (MResGAT) When constructing the Multi-Receptive Field Residual Graph Attention Network (MResGAT), this invention first uses the causal relationship strength matrix obtained in step 2. (Where N is the number of monitored variables, and the elements) The weighted graph attention layer (GAT) is designed to represent the causal strength of variable i on variable j. For each node i, the calculation of its attention coefficient with its neighboring nodes j considers not only the similarity of node features but also the strength of the causal relationship. This allows for a more accurate reflection of the system's underlying mechanisms. Specifically, a multi-head attention mechanism is used. Let the number of attention heads be K. Then, for the k-th head, the similarity coefficient between nodes i and j... The calculation is as follows: in and These are the input feature vectors of nodes i and j. This is a learnable parameter matrix (d and d′ are the input and output feature dimensions, respectively), || denotes the vector concatenation operation, and LeakyReLU is the activation function. Attention weights are normalized using softmax. in This is the set of neighbors of node i. The updated features of node i are obtained by averaging the outputs of each attention head: in This is the activation function.

[0047] To further extract multi-scale spatial features, this invention innovatively introduces a dynamic multi-scale neighbor selection mechanism based on causal relationship strength, replacing the traditional fixed hop count method. This mechanism adaptively defines a threshold using the global strength quantile of the causal relationship matrix A, constructing parallel branches: branch one (strong causal neighborhood) sets a high threshold. For example, to take the 75th quantile of the absolute value of A, only retain those that satisfy... The neighboring nodes form a strong causal neighbor set. A single-layer GAT aggregation feature is applied to this subgraph to capture local core driving patterns; a low threshold is set for branch two (weak causal neighborhood). (e.g., the 50th quantile of A), define a weak causal neighbor set. A single-layer GAT is applied to extract global latent influence features. The output feature vectors of the two branches are denoted as follows: and And through element-level addition and fusion: To mitigate the vanishing gradient problem in deep networks, the model integrates residual connections. Let the... Layer input features are The residual block output is: in This represents the aforementioned multi-scale GAT operation. Subsequently, a MinCutPool graph pooling layer is used to simplify the graph structure while preserving key features. First, the computation is performed through a message-passing layer: in and Let X be the learnable parameter matrix and X be the node feature matrix. A soft assignment matrix is ​​generated using a multilayer perceptron (MLP). (C represents the number of clusters), and the MinCut loss function is optimized to enhance the clustering effect. The graph structure and feature calculation after pooling are as follows: This process progressively compresses the graph size, improving the model's computational efficiency. Ultimately, the MResGAT model achieves deep feature learning by stacking multiple such residual modules. Each module contains parallel multi-scale GAT and residual connections, followed by a MinCutPool layer to hierarchically aggregate information.

[0048] Step 4: Feature Extraction and Classification The final image features are compressed into vectors using a Global Average Pooling (GAP) layer: Input a fully connected layer and a softmax layer, output the probability of the anomaly class: Step 5: Model Training and Optimization To improve the model's generalization ability and align its learning process with prior causal knowledge, we introduce a causal constraint term based on causal relationships into the conventional cross-entropy loss, forming a new composite loss function: a) Main loss: using the standard cross-entropy loss function This is used to ensure the basic prediction accuracy of the model.

[0049] b) Causal constraint: This is a novel regularization term, inspired by the aforementioned causal graph. Instead of requiring the model to learn complex causal variable mappings, we adopt a more intuitive causal-driven contrastive learning approach. Nodes directly connected in the causal graph should also be closer in the representation space learned by the model. We select a set of variable pairs with direct causal relationships from the causal graph, denoted as set P. For each pair of causal variables... We encourage models to use the representations they have learned and It is more similar to the representation of random variables.

[0050] We use a simple triplet loss form: The AdamW optimizer is used to train the composite loss L. The hyperparameter λ is used to balance the accuracy of the main task with causal consistency, and its optimal value is determined by searching using the Optuna automatic hyperparameter optimization framework.

[0051] Example 3: like Figure 4 , Figures 9-15The dataset in this embodiment contains 12 monitoring variables (see Table 5), with a sampling interval of unit time step, and each sample is a multivariate time series of length 12. The dataset covers 5 health states, including 1 normal state (None) and 4 abnormal states: fan anomaly (Fan), high-pressure compressor anomaly (HPC), high-pressure turbine anomaly (HPT), and low-pressure turbine anomaly (LPT). The dataset is divided into training, validation, and test sets in an 8:1:1 ratio, where the training set is used for model training, the validation set is used for hyperparameter tuning, and the test set is used for final performance evaluation.

[0052] This embodiment provides an anomaly diagnosis method based on cause-effect graphs, including the following steps: Step S1: Constructing the causal relationship diagram.

[0053] The J-PCMCI+ algorithm (combined with the GPDC conditional independence test) is used to extract causal relationships between variables from multivariate time series, constructing directed or undirected causal graphs. In these graphs, nodes represent monitored variables, edges represent causal relationships, and edge weights represent causal strength.

[0054] Step S2, Graph Structure Representation The causal graph can be represented as an adjacency matrix A, where the elements are... A represents the causal strength of variable i on variable j. If it is an undirected graph, then A is a symmetric matrix; if it is a directed graph, then A is asymmetric.

[0055] Step S3: Design of Weighted Graph Attention Network (GAT) This step aims to embed prior causal knowledge into the learning process of the graph neural network. The node feature matrix of the layer above the multi-head weighted graph attention layer is designed. The causal relationship strength matrix A is used as input. For each attention head k, the unnormalized attention coefficients eij(k) of node i and its neighboring nodes j are calculated by the following formula: in It is a learnable weight matrix unique to the head k. It is a learnable weight vector for the attention mechanism, and || represents the vector concatenation operation. The causal strength value in the causal relationship matrix A is used as a priori weight to directly modulate the attention score. Subsequently, the softmax function is applied to all neighbors of each node i. Normalize the attention coefficient: The output feature of node i at the k-th attention head is a weighted sum of the features of all its neighboring nodes: Where σ is the ELU nonlinear activation function. Finally, the outputs of the K attention heads are concatenated or averaged to obtain the output feature matrix of the weighted GAT layer.

[0056] Step S4: Construction of Multi-Receptive Field Residual Module To capture anomalous features across different spatial scales and ensure training stability, this step constructs a multi-receptive-field residual module. The core of this module is a dynamic multi-scale neighbor selection mechanism based on causal relationship strength. First, two quantile thresholds are calculated from the global causal strength matrix A, for example... (e.g., 75th percentile) and (e.g., 50th percentile). Based on this, the module adopts a parallel dual-branch structure: Branch 1 (Strong Causal Neighborhood) constructs a neighbor set for each node i. A single-layer weighted GAT is applied to this subgraph to output features. In order to capture the core driving factors in a localized area.

[0057] Branch 2 (weak causal neighborhood) constructs a broader set of neighbors. Similarly, using a single-layer weighted GAT, the output features are... This is done to capture potential global impact. The output features of the two branches are fused by element-wise addition: Finally, the module's input is connected via a residual connection. The features are added to the fused features to avoid gradient vanishing and stabilize deep network training. .

[0058] Step S5: Graph Pooling and Multi-Scale Feature Fusion To perform hierarchical abstraction of the graph structure and fuse multi-scale features, this step introduces a MinCutPool graph pooling layer after the residual module. This layer first preprocesses the node features through a message-passing layer: in and These are learnable parameters. Subsequently, a multilayer perceptron (MLP) is applied to... Generate a soft allocation matrix Where C is the predefined number of clusters, and the matrix elements are... This represents the probability that node i is assigned to cluster c. Pooling operations compress both node features and graph structure using the following two formulas: and This process aggregates strongly connected causal communities, thereby significantly simplifying graph complexity while preserving key structural information. It enables deep fusion and extraction of multi-scale features, providing robust feature representations for the final classification task.

[0059] Step S6, Overall Model Architecture (MResGAT) Model structure as follows Figure 10 As shown, it includes, in sequence: input layer → GAT layer → residual map attention module (×4) → MinCutPool layer → GAP layer → fully connected layer → Softmax classification layer.

[0060] Step S7: Model Training and Optimization The AdamW optimizer is used, and hyperparameters are automatically tuned via Optuna. Key hyperparameters include the number of residual modules, the number of parallel GATs, the learning rate, and the batch size. The loss function is cross-entropy loss, and an early stopping strategy is used during training to prevent overfitting.

[0061] To verify the effectiveness of the method of the present invention, multiple sets of comparative experiments were designed, including comparisons with classic CNN, GCN, GAT models and current advanced temporal classification models (such as temporal Transformer, Perceiver, gMLP, etc.). Figure 11 The confusion matrix of the MResGAT model on the test set is shown, demonstrating that its accuracy in identifying most abnormal states exceeds 96%. In particular, the recognition rate for the most difficult-to-distinguish anomaly, the fan anomaly, improved from 78.36% to 88.54%, with a significant reduction in the false positive rate. Table 2 lists the accuracy comparison results of each model on the 5-class dataset. The MResGAT model proposed in this invention significantly outperforms other models with an accuracy of 96.24%, indicating its significant advantage in highly coupled, nonlinear time-series data classification tasks.

[0062] In summary, this invention effectively improves the accuracy and robustness of anomaly diagnosis in complex systems by introducing a causal graph structure, a multi-receptive field residual attention mechanism, and graph pooling operations, and has strong practical value and prospects for promotion.

[0063] Table 5 Monitoring Variables in the Anomaly Diagnosis Dataset Table 6. Results of the comparative experiment on abnormal diagnosis Table 7 Ablation Experiment Results for Abnormal Diagnosis This embodiment proposes a mechanism for dynamically selecting multi-scale neighbors based on causal relationship strength. It innovatively utilizes the causal relationship strength matrix obtained from causal inference and dynamically constructs a multi-scale neighbor set for each node by setting different quantile thresholds. This mechanism adaptively focuses on core variables that have a direct and strong driving effect on the target node and context variables with broad potential influence, achieving more accurate multi-scale spatial feature extraction that better aligns with the system's intrinsic mechanisms. By designing a weighted multi-head graph attention network (GAT) that integrates causal priors, causal relationship strength is embedded as prior knowledge into the attention mechanism, allowing it to directly participate in the calculation of attention coefficients. By introducing parallel processing of multi-head attention and weighted fusion of causal strengths, the model can more accurately allocate importance weights to neighbor nodes, thereby enhancing the model's ability to model real fault propagation paths and significantly improving diagnostic accuracy. By constructing an end-to-end architecture (MResGAT) integrating multi-scale causal GAT, residual connections, and spectral clustering pooling, the dynamic multi-scale neighbor selection mechanism is combined with the weighted GAT and embedded in the residual module in the form of parallel branches, effectively avoiding the gradient vanishing and feature over-smoothing problems of deep networks. Meanwhile, the MinCutPool graph pooling operation based on spectral clustering is introduced. This operation can be jointly optimized with graph structure learning. While simplifying the graph structure and reducing computational complexity, it better preserves the key community structure information related to anomalies, ultimately forming a stable, efficient and powerful deep anomaly diagnosis model.

[0064] This embodiment significantly improves the accuracy and robustness of anomaly diagnosis in complex systems. Through multi-scale feature extraction guided by causal graphs, the model can more accurately capture comprehensive fault symptoms ranging from strong drivers to weak influences. Experiments show that on a 5-class anomaly dataset for aero-engines, the method achieves an accuracy of 96.24%, approximately 6% higher than traditional correlation graph networks. It achieves superior computational efficiency and engineering applicability. The dynamic multi-scale neighbor selection mechanism avoids the computational overhead of fixed multi-hop traversal of the entire graph. Combined with MinCutPool graph pooling operations, the model adaptively simplifies the graph structure, effectively controlling computational complexity while maintaining high accuracy. This design enables the model to adapt to the modeling needs of systems with varying complexities, making it suitable for anomaly diagnosis tasks in real-time or near-real-time scenarios in industrial settings.

[0065] 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 method for industrial multi-source data fusion based on causal inference, characterized in that, The method is applied to an aero-engine, and the method comprises the following steps: Obtaining original performance data of the aero-engine, and performing normalization processing on the original performance data to obtain target variables, wherein the original performance data comprises rotation speed, exhaust temperature, oil pressure, oil temperature and metal particle composition data; Building a causal inference algorithm to calculate a dynamic threshold value; Calculating a causal strength of each variable pair from a candidate causal set, selecting M variables with the highest causal strength to form an optimization condition set, and building a test algorithm; Building a symmetric causal strength matrix; Based on the target variables and the feature matrix, the product is obtained to obtain a new data set after dimension reduction.

2. The causal inference based industrial multi-source data fusion method according to claim 1, characterized in that, The normalization processing on the original performance data comprises the following steps: The time series data expression of the original performance data is set as: , wherein X is a time series data set, X N is the time series data of the original performance data, T is the time length, and N is the total number of variables; A normalization formula is used: The time series data were normalized using z-score to obtain time series data with a mean of 0 and a standard deviation of 1, where X i ’ X is the target variable. i As a variable, μ i Let σ be the mean of the variable. i is the standard deviation of the variable.

3. The causal inference based industrial multi-source data fusion method according to claim 1, characterized in that, The causal inference algorithm is built to calculate the dynamic threshold value, which comprises the following steps: The causal inference algorithm is built to calculate the mutual information value of the target variable and all candidate cause variables, and a mutual information matrix is obtained; The variable pairs with the mutual information value in the top K percentile are retained to obtain a candidate causal set, and a dynamic threshold value is calculated based on the signal-to-noise ratio characteristics of the data in the sliding window.

4. The method of claim 3, wherein, The causal inference algorithm is built to calculate the mutual information value of the target variable and all candidate cause variables, and a mutual information matrix is obtained; The variable pairs with the mutual information value in the top K percentile are retained to obtain a candidate causal set, and a dynamic threshold value is calculated based on the signal-to-noise ratio characteristics of the data in the sliding window, which comprises the following steps: The causal inference algorithm is built: computing the mutual information value, wherein is a joint probability distribution, and is a marginal distribution, is a candidate cause variable, , is a mutual information value; including variable pairs with mutual information values in the top K percentiles into the candidate causal set , and excluding the rest The normalized data X' is divided into a sliding window with a length of W, and the signal-to-noise ratio of the variables in each window is calculated using a signal-to-noise ratio calculation formula, The formula is built: computing a dynamic threshold, wherein and are upper and lower bounds of a significance level, respectively, is a decay parameter.

5. The causal inference based industrial multi-source data fusion method according to claim 1, characterized in that, The causal strength of each variable pair from the candidate causal set is calculated, M variables with the highest causal strength are selected to form an optimization condition set, and a test algorithm is built, which comprises the following steps: M variables with the highest causal strength are selected to obtain the optimization condition set; The test algorithm is built as: ， wherein .

6. The causal inference based industrial multi-source data fusion method according to claim 5, characterized in that, The symmetric causal strength matrix is built, which comprises the following steps: The causal strength matrix is set as , and principal component analysis is used for data dimension reduction; The maximum causal relationship strength is built as: wherein, are elements, aij = 0 if there is no causal relationship, S is the strength of the causal relationship; The eigenvalue decomposition is performed on the causal strength matrix, the eigenvalues and the corresponding eigenvectors are calculated, the contribution rate of each eigenvalue is calculated, and the eigenvectors corresponding to the K largest contribution rates are selected to form a dimension reduction matrix; The original normalized data matrix is multiplied by the dimension reduction matrix to perform data reconstruction, and a new data set after dimension reduction is obtained.

7. The causal inference based industrial multi-source data fusion method according to claim 6, characterized in that, The eigenvalue decomposition formula is wherein, is an eigenvalue, is an eigenvector, and N is the total number of variables. 8.The industrial multi-source data fusion method based on causal inference of claim 1, wherein, The contribution rate of the eigenvalue is The new data set X' after dimension reduction is XV', wherein X' contains K characteristic variables.

9. The causal inference based industrial multi-source data fusion method according to claim 1, characterized in that, Based on the target variables and the feature matrix, the product is obtained to obtain a new data set after dimension reduction fusion, which comprises the following steps: The original normalized data X' is multiplied by the feature matrix V' to obtain a new data set after dimension reduction fusion: wherein .

10. The causal inference based industrial multi-source data fusion method according to claim 9, characterized in that, The new data set is applied to an abnormal diagnosis model and / or a residual life prediction model.

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