Method for modeling spatial relationship of oil well sensor based on centrality guided graph convolution

Abstract

The application belongs to the technical field of oil well fault detection, and particularly relates to an oil well sensor spatial relationship modeling method based on centrality guided graph convolution, which comprises the following steps: firstly, valid nodes are reserved through node integrity maintenance, and state and trend features are extracted by using a double-view feature generation method; secondly, a weighted hybrid adjacency matrix is constructed by fusing prior physical connection and data-driven correlation; then, based on the weighted hybrid adjacency matrix and the node centrality score, a weight parameter for guiding spatial information aggregation is generated; finally, based on the weight parameter, centrality guided graph convolution operation is performed on a two-dimensional feature vector of the sensor node to update the node feature, and spatial relationship modeling is completed. The application introduces and optimizes a physical graph topology in oil well fault detection for the first time, effectively models the complex spatial dependence between sensors, significantly improves the interpretability, accuracy and robustness of a subsequent fault detection task, and is particularly suitable for identifying long-time evolving faults.

Description

Technical Field

[0001] This invention relates to the field of oil well fault detection technology, and in particular to a method for modeling the spatial relationships of oil well sensors based on centrality-guided graph convolution. Background Technology

[0002] Oil and gas production is a complex and high-risk industrial process that relies on continuous monitoring by multiple sensors (such as pressure, temperature, and flow sensors) deployed downhole. Accurate and timely fault detection is crucial for ensuring safe production. Existing deep learning-based oil well fault detection methods, such as Long Short-Term Memory networks and Transformers, typically treat multiple sensor data as independent time series. These methods primarily model the relationships between different sensor variables implicitly through fully connected layers or channel attention mechanisms, lacking explicit modeling of the inherent physical connections and spatial topology between sensors.

[0003] An oil well system is a physically defined entity. Sensors are installed in specific locations such as the tubing, casing, and annulus, and the coupling relationships between them are determined by physical laws such as fluid dynamics and thermodynamics. For example, the readings of the bottom hole pressure gauge (P-PDG) and the top hole pressure gauge (P-TPT) are connected through a fluid column and exhibit a strong correlation. Ignoring this prior spatial dependency makes it difficult for the model to capture the propagation path and evolution mode of faults in the physical system, limiting detection accuracy, robustness, and model interpretability.

[0004] Graph Neural Networks (GNNs) offer the possibility of modeling such relationships, but their direct application to oil well scenarios faces challenges: 1) Sensor data is largely missing or frozen, resulting in incomplete predefined graph structures; 2) Simple graph convolutions (such as GCNs) treat all neighboring nodes equally and cannot identify the importance of key hub sensors in the topology; 3) How to effectively combine explicit physical knowledge with the implicit relationships in the data to construct a reliable and interpretable graph structure is an urgent problem to be solved. Summary of the Invention

[0005] This invention proposes a spatial relationship modeling method for oil well sensors based on centrality-guided graph convolution, aiming to solve the technical problem that existing oil well fault detection methods ignore the spatial topological relationship of sensors.

[0006] In a first aspect, the present invention provides a method for modeling the spatial relationships of oil well sensors based on centrality-guided graph convolution, including:

[0007] S1, adaptive preprocessing and feature generation are performed on the raw time series data of the oil well multi-sensor system to obtain the two-dimensional feature vector of each sensor node;

[0008] S2, based on the prior physical connection relationship between sensors and the correlation driven by data, construct a weighted hybrid adjacency matrix;

[0009] S3, calculate the centrality score of each sensor node in the weighted hybrid adjacency matrix;

[0010] S4. Based on the weighted hybrid adjacency matrix and the node centrality score, generate weight parameters to guide spatial information aggregation.

[0011] S5. Based on the weight parameters, perform a centrality-guided graph convolution operation on the two-dimensional feature vector of the sensor node to update the node features and complete the spatial relationship modeling.

[0012] The technical advantages of the spatial relationship modeling method for oil well sensors based on centrality-guided graph convolution disclosed in this invention are as follows: For the first time, a physical graph topology is systematically introduced and constructed in oil well fault detection, giving the spatial reasoning process of the model clear physical meaning, facilitating engineer understanding and verification, and meeting the stringent interpretability requirements of industrial safety scenarios. The method combines determinism and data adaptability through hybrid graph construction, and distinguishes node importance through centrality-guided graph convolution. This method can more effectively capture the nonlinear and heterogeneous spatial coupling relationships between sensors. Experiments demonstrate that in long-term fault detection relying on multi-sensor collaborative evolution, its performance is significantly superior to traditional time-series models and ordinary graph neural network models.

[0013] Further, S1 specifically includes: S1 specifically includes:

[0014] S11, Node Integrity Maintenance: For sensor nodes with missing or frozen data, screening and filling are performed based on the proportion of sample quantity and statistics of frozen samples to retain valid sensor nodes and data.

[0015] S12, Dual-view combined feature generation: For the time series data of each retained sensor node, the tail-cutting mean and slope are calculated within the sliding time window to form a two-dimensional feature vector representing the state and trend.

[0016] Furthermore, in S11, the screening is based on the proportion of sample size, specifically as follows:

[0017] If the number of samples of the sensor node with the largest sample size is N base For other sensor nodes, if their sample size N i Satisfying N i / N base If the value is greater than τ, it is retained; otherwise, it is discarded; where τ is a preset proportional threshold.

[0018] Furthermore, in S11, the filtering and filling based on the statistics of the frozen samples are performed as follows:

[0019] For a given sensor node, count the number N of frozen sample rows across all monitored wells. frozen and the number of normal sample rows N normal If N frozen =N total If N frozen <N total And N frozen >N normal If N frozen <N total And N frozen ≤N normal If the corresponding sensor node is retained, the frozen outliers will be replaced with the average feature value of all normal wells on that sensor for filling and repair, where N total This represents the total number of all monitored wells.

[0020] Furthermore, the tail-cutting mean in S12 and slope The calculation formula is as follows:

[0021] For a sensor node in a time window First, remove the maximum and minimum values ​​from the data within the window to obtain a new sequence. ;

[0022] ;

[0023] in, and These are the time index sequence and the mean of the data, respectively. It is a time series.

[0024] Furthermore, in S2, a weighted hybrid adjacency matrix A is constructed. hybrid Specifically:

[0025] A hybrid =A prior +α∙A learned ;

[0026] The range of the hyperparameter α is [0-1), A prior A is a binary prior adjacency matrix constructed based on the relationship between the oil well tubing structure and the physical installation positions of sensors. learned It is a sparse data-driven adjacency matrix calculated based on two-dimensional eigenvectors.

[0027] Furthermore, the sparse data between node i and node j drives the adjacency matrix. The construction method is as follows:

[0028] Calculate the cosine similarity between the feature vectors of all sensor nodes. For each node i, only retain the node with the highest similarity. , forming a sparse matrix, where:

[0029] ;

[0030] ;

[0031] in, and These are the feature vectors of node i and node j, respectively.

[0032] Furthermore, in step S3, the calculation of node centrality scores employs the PageRank algorithm, with the following iterative formula:

[0033] ;

[0034] in, For the first The node centrality score vector of the next iteration. The damping coefficient is... The total number of nodes. It is a vector consisting entirely of 1s; The weighted mixed adjacency matrix is ​​iterated until convergence to obtain the final centrality fraction vector. .

[0035] Furthermore, in step S4, weight parameters are generated to guide the aggregation of spatial information. Specifically:

[0036] ;

[0037] in, It represents the Hadamah accumulation. Let be the node centrality score vector. It is a vector of all 1s. It is a weighted mixed adjacency matrix.

[0038] Furthermore, the formula for the graph convolution operation in S5 is:

[0039] ;

[0040] in, For the first The node feature matrix of layer graph convolution; for The degree matrix; For the first The trainable parameter matrix of the layer; It is a non-linear activation function. Attached Figure Description

[0041] Figure 1 This is a schematic diagram of the overall process of the oil well sensor spatial relationship modeling method based on centrality-guided graph convolution proposed in an embodiment of the present invention;

[0042] Figure 2 This is a schematic diagram of the data preprocessing process provided in an embodiment of the present invention;

[0043] Figure 3 This is a schematic diagram of the hybrid graph construction process provided in an embodiment of the present invention;

[0044] Figure 4 This is a schematic diagram of the graph convolution operation process provided in an embodiment of the present invention;

[0045] Figure 5 This is a schematic diagram comparing the performance of different spatial propagation models provided in the embodiments of the present invention, wherein the arrows indicate the direction of optimal performance. Detailed Implementation

[0046] 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.

[0047] The graph neural network (GNN) mentioned in the background technology provides the possibility for modeling the relationship in oil well detection, but its direct application to oil well scenarios faces challenges: 1) There are a lot of missing or frozen sensor data, resulting in incomplete predefined graph structures; 2) Simple graph convolution (such as GCN) treats all neighbor nodes equally and cannot identify the importance of key hub sensors in the topology; 3) How to effectively combine explicit physical knowledge with the implicit relationships in the data to construct a reliable and interpretable graph structure is an urgent problem to be solved.

[0048] This invention provides a method for modeling the spatial relationships of oil well sensors based on centrality-guided graph convolution, referencing... Figures 1 to 4 As shown, the specific steps include:

[0049] This embodiment uses offshore oil well production monitoring as an application scenario and employs sensor data from the publicly available 3W dataset (version 2.0) to demonstrate the implementation process of the method described in this invention.

[0050] Step S1: Adaptive Preprocessing and Feature Generation. Assume there are N wells (i.e., the total number of nodes), and each well is equipped with C types of sensors. The raw data of the multi-sensor variable signals are represented as follows: , where T is the total time length. Specifically, it includes the following sub-steps:

[0051] S11, Node Integrity Maintenance: Assume there are 10 types of sensors. First, count the total number of valid samples for each type of sensor across all wells and all time points. Assume sensor A1 has the largest number of samples, N... base =1,000,000. Set the proportional threshold τ=0.8.

[0052] Sensor A2 has 250,000 samples, and 250k / 1000k = 0.25 < 0.3, therefore all data for sensor A2 is deleted. Sensor A3 has 850,000 samples, and 850k / 1000k = 0.85 > 0.3, therefore sensor A3 is retained. Next, the frozen data issue is addressed. Taking sensor D as an example, its data across all 100 wells is examined:

[0053] If the data from 90 wells remains constant (frozen), then the data from 10 wells are normal. N frozen >N normal Therefore, sensor D is removed.

[0054] If 20 wells freeze, the remaining 80 wells will remain normal. N frozen <N normal Therefore, sensor D is retained, and the frozen values ​​of those 20 wells are filled with the characteristic mean of the normal data of the remaining 80 wells.

[0055] Finally, all the retained sensor data were aligned along the time axis, and samples from time points that were missing due to the removal of some sensors were directly deleted without interpolation, resulting in cleaned data. Where C' represents the number of sensor categories retained.

[0056] S12, Dual-view combined feature generation: For each retained sensor e, at each time point t, take a sliding window W of length L=90 (representing 15 minutes). t e =[x t-89 e ,...,x t e ].

[0057] (1) Calculate the tail-cutting mean: Remove W t e The maximum and minimum values ​​in the range are averaged over the remaining 88 data points to obtain m. t eThis value is not sensitive to abnormal fluctuations and can stably reflect the average level within the time period. The calculation method is as follows:

[0058] ;

[0059] Where, x max and x min Window W t c The maximum and minimum values ​​in the range.

[0060] 2. Calculate the slope: For the 90 original data points within the window [x t-89 c ,...,x t c A straight line is fitted using the least squares method, and the slope of this line is s. t c This value reflects the upward or downward trend of the data within this time period. The calculation method is as follows:

[0061] ;

[0062] in, The average of time indices. This represents the average value of the data within the window.

[0063] Ultimately, each original one-dimensional time series point x t c Replaced with a two-dimensional feature vector [m t c ,s t c ] T The features of all sensors at all points in time constitute a new feature tensor. To perform graph modeling, sensors of the same type from different wells are treated as the same graph node, thus reshaping the features into... Each node (sensor) has a characteristic that is The sequence. When performing graph convolution, we typically take the two-dimensional features of a time slice (such as the current time) as the initial features of that node. .

[0064] This step effectively addresses common quality issues in industrial data, ensuring data authenticity while retaining the maximum number of physical nodes. Dual-view features compress high-dimensional sparse time-series signals into low-dimensional, information-dense features, significantly reducing subsequent computational complexity and providing the model with crucial information that directly reflects the dynamics (trends) of fault evolution.

[0065] Step S2, construct the weighted mixed adjacency matrix. This specifically includes the following steps:

[0066] S21, Construct the prior physical adjacency matrix A prior Based on the well tubing design drawings and sensor installation manual, determine the physical connections between sensors. For example, if pressure sensor P-TPT and temperature sensor T-TPT installed on adjacent tubing sections have a direct physical connection, then in section A... prior Set the corresponding position in the middle to 1, otherwise set it to 0. A prior It is a C'×C' symmetric binary matrix.

[0067] S22, Construct the data-driven adjacency matrix A learned : Take the average feature vector of all nodes over a certain time period as its embedding representation. Calculate the cosine similarity S between the embeddings of any two nodes i and j. ij The calculation formula is as follows:

[0068] ;

[0069] For node i, find the k=3 nodes with the highest similarity to it, and connect these nodes to node A. learned The corresponding value in is set to The remaining connections are set to 0. This results in a sparse adjacency matrix that reflects the inherent correlations within the data.

[0070] S23, Weighted fusion, set the fusion weight α=0.7. Calculate the mixed adjacency matrix A. hybrid Specifically:

[0071] A hybrid =A prior +α∙A learned ;

[0072] The range of the hyperparameter α is [0-1), A prior A is a binary prior adjacency matrix constructed based on the relationship between the oil well tubing structure and the physical installation positions of sensors. learned This is a sparse data-driven adjacency matrix calculated based on two-dimensional eigenvectors. The hyperparameter α represents the dominance of prior physical knowledge, and its value is not fixed.

[0073] This step creatively combines deterministic engineering knowledge with data-driven statistical correlations. A prior It provides a stable, interpretable skeleton, A learned It makes up for implicit dependencies that may not be covered by prior knowledge, making the constructed graph structure both reliable and possessing a certain degree of adaptability.

[0074] Step S3: Calculate the node centrality score. The PageRank algorithm is used to calculate A. hybrid Importance score vector of each node Set the damping coefficient β = 0.85 and initialize. ,in The vector is composed entirely of 1s. Iterate using the following formula until convergence (e.g., when the Euclidean distance between the result vectors of two consecutive iterations is less than 10). −6 hour):

[0075] ;

[0076] The final result In the graph, nodes with high scores correspond to sensors that occupy key positions in the hybrid graph topology (such as pressure sensors located at the intersection of multiple flow paths).

[0077] The PageRank algorithm can globally evaluate the influence of nodes in a network. The identified key sensor nodes are often crucial hubs for fault propagation or performance, providing a basis for subsequent discriminative information dissemination.

[0078] Step S4: Based on the weighted hybrid adjacency matrix and the node centrality scores, generate weight parameters to guide spatial information aggregation. Then, convert the node centrality score vector... A C'×1 column vector is broadcast to all its outgoing edges. The specific calculation of the centrality-guided weight parameters is then performed. :

[0079] ;

[0080] in, This represents the Hadamard product (element-by-element multiplication). Let be the node centrality score vector. It is a vector of all 1s. It is a weighted mixed adjacency matrix.

[0081] This step transforms the "importance of nodes" into the "importance of edges." This allows information from important nodes to be more effectively transmitted during graph convolution, and the information aggregation process no longer treats all neighbors equally, but instead focuses on key paths.

[0082] Step S5: Based on the weight parameters, perform a center-guided graph convolution operation on the two-dimensional feature vectors of the sensor nodes to update the node features and complete the spatial relationship modeling. The formula for the graph convolution operation is:

[0083] ;

[0084] in, For the first The node feature matrix H of layer graph convolution. 0 The two-dimensional feature vector matrix output in step S1; for The degree matrix; For the first The trainable parameter matrix of the layer; It is a non-linear activation function, such as the ReLU function.

[0085] After several layers (optimally 3 layers) of such centrally guided graph convolutions, the output features of each sensor node are... It not only includes its own state trend information, but also integrates information from its physically connected and data-related neighbors, which is weighted according to the importance of the nodes, thus completing a deep modeling of the spatial dependency of the oil well sensor system.

[0086] On the one hand, characteristic signals from highly central nodes (whether as senders or receivers) are amplified; on the other hand, the edges connecting highly central nodes also become the "main arteries" for information flow. This mechanism is more in line with the reality that key sensors (nodes) and their key connections (edges) in the physical network of oil wells jointly dominate the transmission of system state, thus achieving more accurate and robust spatial relationship modeling than simply modifying edge weights or focusing only on node characteristics.

[0087] This step enables focused information propagation within the specific physical topology constraints of the oil well. Experiments show that this method outperforms standard GCN and GAT in modeling complex spatial relationships. For example, when detecting faults such as "pipeline hydrate formation" that involve slow evolution across multiple sensors, introducing this spatial modeling module can improve the overall detection performance's MCC index by more than 13%.

[0088] The following is a comparative experimental analysis:

[0089] 1. Extracted experimental data.

[0090] Ablation experiment data (proving the necessity of spatial modeling): When faced with Class-8 faults that have a long evolutionary cycle, contain 10 topological nodes, and have complex relationships, if the spatial modeling module is removed, the model's F1-Score drops sharply from 0.9696 to 0.9210, the MCC index, which reflects classification balance, decreases by about 10% (from 0.9397 to 0.8419), and the false positive rate increases significantly.

[0091] Comparative experimental data (demonstrating the superiority of the centrality-guided mechanism): such as Figure 5As shown, the performance test results of short-cycle faults (Class-2, average evolution period of approximately 1.12 hours) and long-cycle faults (Class-8, average evolution period of approximately 72.53 hours) under different spatial relationship propagation models are comprehensively presented. The baseline models for comparison include mainstream graph models: Graph Convolutional Networks (GCN), Graph Attention Networks (GAT), Graph Isomorphic Networks (GIN), and Approximate Personalized Propagation Neural Networks (APPNP). Figure 5 Specifically, it is divided into four sub-graphs:

[0092] • Figure (a): Shows the comparison of the models in terms of three positive metrics (higher is better) under Class-2 faults: accuracy (ACC), F1 score (F1) and Matthews correlation coefficient (MCC).

[0093] • Figure (b): shows the comparison of the models in terms of two negative indicators (lower is better) – false negative rate (FNR) and false positive rate (FPR) – under Class-2 fault conditions;

[0094] • Figure (c): Shows the comparison of the three positive indicators of ACC, F1 and MCC for each model under Class-8 fault;

[0095] • Figure (d): Shows the comparison of the two negative indices, FNR and FPR, for each model under Class-8 fault;

[0096] As can be seen from Figures (c) and (d), the method of this invention demonstrates absolute superiority when facing the complex evolution of Class-8 faults. For example, in terms of positive indicators, the method of this invention achieves an ACC of 0.9781, an F1 score of 0.9696, and an MCC of 0.9397. In terms of negative indicators, the method of this invention controls the FNR at 2.23% and the FPR at 2.08%. In contrast, the GAT model, which also has the ability to calculate dynamic weights, exhibits a false negative rate (FNR) of 5.24% and a lower MCC (0.83) for Class-8 faults, which is not as effective as the method of this invention.

[0097] As can be seen from Figures (a) and (b), for the rapidly evolving short-cycle fault Class-2, all the baseline models can achieve a high level of detection. Therefore, the performance gap between the method of this invention and other models is not as significant as in the case of long-cycle faults (Class-8). However, even with the already high baseline performance, the method of this invention still shows further superior performance. Specifically, in terms of positive indicators, the ACC (0.9990), F1 (0.9990), and MCC (0.9979) of this invention remain the highest among all tested models. In terms of negative indicators, the false positive rate (FPR) of this invention is reduced to an extremely small 0.0002, which is the lowest among all models. Its false negative rate (FNR) is 0.0017, which is basically on par with the best-performing GCN model in the baseline.

[0098] Node importance analysis data (proving interpretability): In Class-8 faults, this method accurately identified four nodes—T-MON-CKP, QGL, ESTADO-SDV-GL, and P-JUS-CKGL—that not only have high node centrality but also contribute the most to fault identification features. In Class-2 faults, the T-TPT node was accurately identified as a topology hub and a direct fault indicator.

[0099] Beneficial effects:

[0100] Effectively capturing complex spatial dependencies and improving long-cycle fault identification rates: When facing complex industrial scenarios with multiple coupled sensors (such as Class-8 faults with multiple topological connections), relying solely on time-series features will miss a large amount of spatial correlation information, leading to increased false negative and false positive rates. This method successfully quantifies the spatial relationships of multiple sensors at the system level through centrality-guided graph convolution, significantly improving the identification accuracy of complex faults and the stability of the system.

[0101] The centrality fusion mechanism overcomes the limitations of traditional graph algorithms: traditional strategies based on single-neighborhood aggregation (such as GAT) are unable to reliably capture effective spatial dependencies in complex fault evolution scenarios due to class imbalance, resulting in extremely high false negative rates. The "joint modeling of edge weights and node centrality (centrality-guided)" mechanism proposed in this invention can provide aggregation weights with richer information and stronger interpretability, thus comprehensively surpassing traditional graph network models.

[0102] High industrial interpretability: This method can jointly quantify and analyze the node centrality and feature importance of sensors, accurately locate physical sensors (such as T-TPT sensors) that play a key role in the fault, and provide clear data support and physical interpretability for prioritizing the monitoring and maintenance of core sensors in actual engineering.

[0103] This invention has disclosed exemplary embodiments, and although specific terminology has been used, it is for illustrative purposes only and should be interpreted in a general descriptive sense only, and is not intended to be limiting. In some instances, it will be apparent to those skilled in the art that features, characteristics, and / or elements described in conjunction with particular embodiments may be used alone, or in combination with features, characteristics, and / or elements described in conjunction with other embodiments, unless otherwise expressly indicated. Therefore, those skilled in the art will understand that various changes in form and detail may be made without departing from the scope of the invention as set forth by the appended claims.

Claims

1. A method for modeling the spatial relationship of oil well sensors based on centrality-guided graph convolution, characterized in that, include: S1, adaptive preprocessing and feature generation are performed on the raw time series data of the oil well multi-sensor system to obtain the two-dimensional feature vector of each sensor node; S2, based on the prior physical connection relationship between sensors and the correlation driven by data, construct a weighted hybrid adjacency matrix; S3, calculate the centrality score of each sensor node in the weighted hybrid adjacency matrix; S4. Based on the weighted hybrid adjacency matrix and the node centrality score, generate weight parameters to guide spatial information aggregation. S5. Based on the weight parameters, perform a centrality-guided graph convolution operation on the two-dimensional feature vector of the sensor node to update the node features and complete the spatial relationship modeling. In S2, a weighted hybrid adjacency matrix A is constructed. hybrid Specifically: A hybrid =A prior +α∙A learned ; The range of the hyperparameter α is [0-1), A prior A is a binary prior adjacency matrix constructed based on the relationship between the oil well tubing structure and the physical installation positions of sensors. learned The adjacency matrix is ​​driven by sparse data calculated based on two-dimensional feature vectors; The PageRank algorithm is used to calculate the node centrality score in S3, and its iterative formula is as follows: ； in, For the first The node centrality score vector of the next iteration. The damping coefficient is... The total number of nodes. It is a vector consisting entirely of 1s; The weighted mixed adjacency matrix is ​​iterated until convergence to obtain the final centrality fraction vector. ; In step S4, weight parameters are generated to guide the aggregation of spatial information. Specifically: ； in, It represents the Hadamah accumulation. Let be the node centrality score vector. It is a vector of all 1s. It is a weighted mixed adjacency matrix.

2. The method for modeling the spatial relationship of oil well sensors based on centrality-guided graph convolution according to claim 1, characterized in that, S1 specifically includes: S11, Node Integrity Maintenance: For sensor nodes with missing or frozen data, screening and filling are performed based on the proportion of sample quantity and statistics of frozen samples to retain valid sensor nodes and data. S12, Dual-view combined feature generation: For the time series data of each retained sensor node, the tail-cutting mean and slope are calculated within the sliding time window to form a two-dimensional feature vector representing the state and trend.

3. The method for modeling the spatial relationship of oil well sensors based on centrality-guided graph convolution according to claim 2, characterized in that, The filtering in S11 based on the proportion of sample size is as follows: If the number of samples of the sensor node with the largest sample size is N base For other sensor nodes, if their sample size N i Satisfying N i / N base If the value is greater than τ, it is retained; otherwise, it is discarded; where τ is a preset proportional threshold.

4. The method for modeling the spatial relationship of oil well sensors based on centrality-guided graph convolution according to claim 2, characterized in that, The filtering and filling process in S11 based on frozen sample statistics is as follows: For a given sensor node, count the number N of frozen sample rows across all monitored wells. frozen and the number of normal sample rows N normal If N frozen =N total If N frozen <N total And N frozen >N normal If N frozen <N total And N frozen ≤N normal If the corresponding sensor node is retained, the frozen outliers will be replaced with the average feature value of all normal wells on that sensor for filling and repair, where N total This represents the total number of all monitored wells.

5. The method for modeling the spatial relationship of oil well sensors based on centrality-guided graph convolution according to claim 2, characterized in that, The tail-cutting mean in S12 and slope The calculation formula is as follows: For a sensor node in a time window First, remove the maximum and minimum values ​​from the data within the window to obtain a new sequence. ; ； in, and These are the time index sequence and the mean of the data, respectively. It is a time series.

6. The method for modeling the spatial relationship of oil well sensors based on centrality-guided graph convolution according to claim 1, characterized in that, Sparse data-driven adjacency matrix between node i and node j The construction method is as follows: Calculate the cosine similarity between the feature vectors of all sensor nodes. For each node i, only retain the node with the highest similarity. , forming a sparse matrix, where: ； ； in, and These are the feature vectors of node i and node j, respectively.

7. The method for modeling the spatial relationship of oil well sensors based on centrality-guided graph convolution according to claim 1, characterized in that, The formula for the graph convolution operation in S5 is: ； in, For the first The node feature matrix of layer graph convolution; for The degree matrix; For the first The trainable parameter matrix of the layer; It is a non-linear activation function.

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