A full-time sequence missing data imputation and prediction method based on a double-branch graph network

Abstract

The application discloses a kind of based on double branch graph network's full time sequence incomplete data interpolation and prediction method, it is related to industrial data completion and prediction technical field, this method is first obtained and pre-processes visible node time series monitoring data and equipment operating condition characteristic data, according to preset proportion division training set, verification set and test set;Full node space relation adjacency graph is constructed, the double branch interpolation prediction model based on graph convolution gate recurrent neural network is built, data missing scene is simulated by dynamic masking strategy, model training optimization is completed in combination with multidimensional weighted global loss function, finally output full node time series prediction result.This method can accurately capture node space correlation characteristics, enhance the robustness of the model to full time series missing data, improve prediction accuracy and stability through double branch collaborative learning, effectively solve the problem of key position monitoring missing caused by limited deployment of industrial equipment sensors and long-term failure, adapt to real-time monitoring needs of industrial scene.

Description

Technical Field

[0001] This application relates to the field of industrial data completion and prediction technology, and in particular to a method for full-time incomplete data interpolation and prediction based on a bi-branch graph network. Background Technology

[0002] In the long-term operation of complex industrial equipment, monitoring and predicting critical operating states are core aspects of ensuring system safety and reliability. When critical state variables evolve abnormally or remain inaccurate for extended periods, it can accelerate equipment aging, shorten service life, and even induce serious safety risks. Large industrial systems typically exhibit significant spatial gradients and dynamic coupling characteristics; their internal states are influenced by both changes in operating conditions and external environmental disturbances. Continuous monitoring and accurate prediction of critical operating signals enable preventative maintenance, reduce the risk of sudden failures, improve system operating efficiency, and provide decision-making support for operational strategy optimization and lifespan management.

[0003] In real-world engineering scenarios, limitations imposed by factors such as the number of sensors, installation locations, communication conditions, and cost constraints often prevent industrial equipment from achieving comprehensive sensing of all key locations and state variables. In cases of sensor damage, communication interruption, or prolonged failure, some monitoring nodes may fail to acquire valid data throughout the entire observation period, resulting in a complete lack of corresponding features over time—a phenomenon known as full-time-series feature loss. This lack of full-time-series feature loss provides no historical context, rendering traditional signal completion and prediction methods that rely on temporal continuity ineffective, posing a significant challenge to the comprehensiveness and reliability of industrial monitoring systems.

[0004] To alleviate the observation gaps caused by insufficient monitoring points and sensor failures, related research has gradually explored multiple directions, including mechanism modeling, sensor deployment optimization, and data-driven modeling. Mechanism-based modeling methods typically construct multi-physics or coupled models to characterize the transmission paths and dynamic evolution of the system. However, these methods heavily rely on precise boundary conditions and parameter settings, resulting in high computational complexity and difficulty in meeting real-time prediction requirements. Sensor topology optimization methods improve system observability by rationally configuring a limited number of monitoring points, but in practical industrial environments, they are often limited by structural layout, maintenance costs, and deployment conditions, still resulting in insufficient information coverage. Data-driven methods, which have emerged in recent years, learn the temporal evolution of system states directly from historical operating data, exhibiting stronger adaptability under complex operating conditions. However, existing research mainly focuses on scenarios with local or random discrete time-series missing data, paying insufficient attention to the structural and long-term full-time-series feature loss problems commonly found in industrial systems, and failing to achieve accurate interpolation and prediction of temporal features under conditions without historical observation data.

[0005] Furthermore, the operating status of industrial equipment typically exhibits significant time-varying, non-stationary, and cross-variable coupling characteristics, with potential physical correlations and dynamic constraints often existing between different types of monitoring signals. How to fully exploit the intrinsic correlations between multi-source monitoring signals, model dynamic spatiotemporal dependency structures, and achieve highly reliable reconstruction of missing features under conditions of sensor sparsity and long-term failure of critical nodes is a key problem that urgently needs to be solved in the field of industrial condition sensing and health assessment. Summary of the Invention

[0006] The purpose of this application is to provide a method for interpolating and predicting time-series incomplete data based on a bi-branch graph network. This method can utilize multi-source operational monitoring data collected by a small number of effective sensors as observable constraints, thereby improving the stability and reliability of predicting the temporal characteristics of target locations under conditions without historical observations.

[0007] To achieve the above objectives, this application provides the following solution: A method for full-time incomplete data imputation and prediction based on bi-branch graph networks includes the following steps: Based on the node layout and operating conditions of industrial equipment, the locations where sensors are installed are marked as visible nodes, and the predicted target locations where no sensors are installed are marked as missing nodes. The location information of all nodes is recorded.

[0008] The system acquires time-series monitoring data and industrial equipment operating condition characteristic data from visible nodes over several historical periods. After preprocessing the acquired data, it divides the data into training, validation, and test sets according to a preset ratio.

[0009] Based on the location information of all nodes and the operating condition characteristics data of industrial equipment, a spatiotemporal adjacency graph of all nodes is constructed.

[0010] Based on spatiotemporal adjacency graphs and graph convolutional gated recurrent neural networks, a full-time incomplete data imputation prediction model is constructed. The full-time incomplete data imputation prediction model includes teacher branches and student branches with identical structures. The input of the teacher branch only includes the time-series monitoring data of each visible node in the historical period, and the output is the time-series prediction data of each visible node in the future period. The input of the student branch includes the time-series monitoring data of all nodes in the historical period, and the output is the time-series prediction data of all nodes in the future period. The time-series monitoring data of missing nodes are all set to zero.

[0011] A dynamic masking strategy is adopted to randomly mask the monitoring data of a specified number of visible nodes in the input of the student branch, resulting in masked nodes and unmasked nodes.

[0012] Using training, validation, and test sets, the full-time incomplete data imputation prediction model is trained, validated, and tested sequentially according to a weighted global loss function to obtain an optimized full-time incomplete data imputation prediction model. The weighted global loss function includes imputation loss generated based on the prediction results of each masked node by the student branch, reconstruction loss generated based on the prediction results of each visible node by the teacher branch, and cross-branch consistency loss generated based on the prediction results of the student branch and the teacher branch for the same non-masked node or the same masked node.

[0013] The time-series monitoring data of all nodes in several historical periods are input into the student branch of the optimized full-time incomplete data imputation prediction model to obtain the time-series prediction data of all nodes in several future periods.

[0014] Optionally, locations in industrial equipment that have operational and maintenance value but cannot accommodate sensors can be selected as missing nodes, and locations in the spatial topology adjacent to the missing node or on adjacent components where sensors can be accommodated can be selected as visible nodes.

[0015] Optionally, the time-series monitoring data collected from visible nodes can be divided into time windows, and the divided time segments can be used as input data for model training; the operating condition feature data and the time-series monitoring data are synchronous data collected at the same time, and the operating condition feature data is used to supplement the spatiotemporal correlation features between nodes.

[0016] Optionally, based on the location information of all nodes and the operating condition characteristic data of industrial equipment, a spatiotemporal adjacency graph of all nodes is constructed, specifically including the following steps: The spatial topological distance between nodes is calculated using Euclidean distance and then normalized to obtain the spatial adjacency matrix.

[0017] The correlation degree of working condition characteristic data between each node is calculated by using the Pearson correlation coefficient, and the working condition adjacency relationship matrix is ​​obtained.

[0018] The heat transfer correlation degree between each node is calculated using the Gaussian decay model, and the heat transfer adjacency relationship matrix is ​​obtained.

[0019] The spatial adjacency matrix, the operating condition adjacency matrix, and the heat transfer adjacency matrix are weighted and summed, and the summed matrix is ​​then sparsified to obtain the spatiotemporal adjacency graph.

[0020] Optionally, the spatial topological distance between nodes can be calculated using the following formula: .

[0021] in, For nodes and nodes Spatial topological distance between them For nodes The three-dimensional coordinates For nodes The three-dimensional coordinates.

[0022] The Pearson correlation coefficient between nodes is calculated using the following formula: .

[0023] in, For nodes and nodes The Pearson correlation coefficient between them and They are nodes and nodes From 0 The standard deviation of the time-of-flight operating condition characteristic data For nodes and nodes The covariance.

[0024] The heat transfer correlation between nodes is calculated using the following formula: .

[0025] in, For nodes and nodes The heat transfer correlation between them Used to control attenuation sensitivity.

[0026] Optionally, both the teacher branch and the student branch adopt an encoder and decoder structure. Both the encoder and decoder are constructed based on a graph convolutional gated recurrent neural network. The graph convolutional gated recurrent neural network is a single-layer GRU network. In the GRU network, all matrix multiplication operations of the update gate, reset gate and candidate hidden state are replaced by graph convolution operators. The encoder encodes the input data and outputs a hidden state tensor. The decoder receives the hidden state tensor output by the encoder and decodes it. The output of the decoder is flattened to obtain the prediction result of the corresponding branch.

[0027] Optionally, a dynamic masking strategy can be executed by initializing the masking function. The input to the initializing masking function includes the spatiotemporal adjacency graph, the index of missing nodes, and the number of masked nodes. The output of the initializing masking function includes the sub-adjacency graph corresponding to the visible nodes, and performs a specified number of random masks on the visible nodes using Boolean masks, outputting the global index of the masked nodes.

[0028] Optionally, the imputation loss, reconstruction loss, and cross-branch consistency loss are all constructed using the mean squared error function. The imputation loss, reconstruction loss, and cross-branch consistency loss are weighted and summed using preset weighting parameters to obtain the weighted global loss function.

[0029] Optionally, the interpolation loss can be calculated using the following formula: .

[0030] in, To compensate for the loss, For the true value, For the student branch, the predicted value for the masked node. For the masking indication matrix, the first i The indicator value of each node, Indicates the predicted time series length.

[0031] The reconstruction loss is calculated using the following formula: .

[0032] Among them, To reconstruct the loss, For the teacher branch, the predicted value for the visible nodes. For the missing indicator matrix, the first... i The indicator value of each node.

[0033] The cross-branch consistency loss is calculated using the following formula: .

[0034] in, This results in cross-branch consistency loss.

[0035] The weighted global loss function is calculated using the following formula: .

[0036] in, For the weighted global loss function, These are the weights for interpolation loss, reconstruction loss, and cross-branch consistency loss, respectively.

[0037] Optionally, when training the full-time incomplete data imputation prediction model, the Adam optimization algorithm is used to optimize the network weights and biases, with an initial learning rate of 0.001 and a decay rate of 0.95 every 10 cycles.

[0038] According to the specific embodiments provided in this application, the following technical effects are disclosed: This application provides a method for full-time missing data imputation and prediction based on a bi-branch graph network. The method acquires time-series monitoring data of visible nodes and equipment operating condition feature data from several historical time periods. After preprocessing, the data is divided into training, validation, and test sets according to a preset ratio, effectively improving data quality and providing a hierarchical and standardized data source for model training, validation, and testing, ensuring the model training effect. Based on the location information of all nodes and equipment operating condition feature data, a spatiotemporal adjacency graph of all nodes is constructed, fully exploring the spatial topology and operating condition correlation features between nodes, providing structural support for the model to capture the spatiotemporal dependencies of nodes. Based on the spatiotemporal adjacency graph and a graph convolutional gated recurrent neural network, a full-time missing data imputation and prediction model with teacher and student branches having identical structures is constructed. The teacher branch only inputs historical time-series monitoring data of visible nodes and outputs their future time-series prediction data, while the student branch inputs historical time-series monitoring data of all nodes (missing node data is set to zero) and outputs the future time-series prediction data of all nodes. The branch structure enables decoupled modeling of the visible and prediction domains, simultaneously capturing the spatial correlation and temporal evolution characteristics between nodes. A dynamic masking strategy is then employed to randomly mask a specified number of visible node monitoring data points in the student branch input, resulting in masked and unmasked nodes. This simulates a scenario with missing full-time data, enhancing the model's adaptability and robustness to missing data. Using training, validation, and test sets, and based on a weighted global loss function including imputation loss, reconstruction loss, and cross-branch consistency loss, the model is sequentially trained, validated, and tested to obtain an optimized model. This weighted optimization approach with multiple losses enables collaborative learning between the two branches, effectively improving the model's prediction accuracy and stability. By inputting the temporal monitoring data of all nodes from several historical time periods into the optimized model's student branch, temporal prediction data for all nodes in future time periods is obtained. Based on the trained and optimized model, accurate imputation and prediction of the full-time features of missing nodes are achieved, solving the problem of missing key location monitoring caused by limited or failed sensor deployment in industrial equipment. Attached Figure Description

[0039] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0040] Figure 1 This is a flowchart illustrating a full-time incomplete data interpolation and prediction method based on a bi-branch graph network, provided as an embodiment of this application.

[0041] Figure 2This is a schematic diagram illustrating the principle of the full-time incomplete data interpolation and prediction model in a full-time incomplete data interpolation and prediction method based on a bi-branch graph network provided in an embodiment of this application.

[0042] Figure 3 This is a schematic diagram illustrating the application of a full-time incomplete data interpolation and prediction method based on a dual-branch graph network in a stacked battery pack, as provided in an embodiment of this application.

[0043] Figure 4 This diagram illustrates a comparison of interpolation prediction results for a full-time incomplete data interpolation and prediction method based on a dual-branch graph network, as provided in an embodiment of this application, applied to a stacked battery pack. Detailed Implementation

[0044] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0045] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0046] This application provides a method for full-time incomplete data imputation and prediction based on a dual-branch graph network. In an exemplary embodiment, such as... Figure 1 As shown, it includes the following steps: S1. Based on the node layout and operating conditions of industrial equipment, mark the locations where sensors are installed as visible nodes, mark the target prediction locations where no sensors are installed as missing nodes, and record the location information of all nodes.

[0047] Specifically, missing nodes are selected from locations in industrial equipment that have operational and maintenance value but where sensors cannot be installed. These locations are typically core locations for monitoring the equipment's operational status, but due to limitations in equipment structure space, deployment costs, and harsh operating conditions such as high temperature and high pressure, sensors cannot be installed, or the sensors are prone to long-term failure. Visible nodes are selected from the spatial topology locations adjacent to the missing nodes or from locations on adjacent components where sensors can be installed. The placement of visible nodes must ensure that monitoring data with strong spatiotemporal correlation with the missing nodes can be collected, providing observable constraints for the prediction of missing nodes.

[0048] S2. Acquire time-series monitoring data and industrial equipment operating condition characteristic data from visible nodes in several historical time periods, and after preprocessing the acquired data, divide it into training set, validation set and test set according to a preset ratio.

[0049] The time-series monitoring data consists of continuous time-series signals collected by sensors at visible nodes at a preset sampling frequency, including but not limited to industrial equipment operating status parameters such as temperature, pressure, vibration, and strain. The operating condition feature data consists of equipment operating condition parameters collected at the same time as the time-series monitoring data, including but not limited to voltage, current, power, speed, and flow rate, used to supplement the spatiotemporal correlation features between nodes. Preprocessing of the time-series monitoring data includes outlier removal, data smoothing, and time window division. In this embodiment, time-series segments of the past five time steps are used as input data for model training, and time-series segments of the next one time step are used as training labels.

[0050] After acquiring the time-series monitoring data collected from visible nodes, the data is divided into time windows, and the divided time segments are used as input data for model training. The operating condition feature data and the time-series monitoring data are synchronous data collected at the same time. The operating condition feature data is used to supplement the spatiotemporal correlation features between nodes.

[0051] S3. Based on the location information of all nodes and the operating condition characteristic data of the industrial equipment, construct a spatiotemporal adjacency graph of all nodes. In this embodiment, step S3 specifically includes the following steps: S31. Calculate and normalize the spatial topological distance between nodes using Euclidean distance to obtain the spatial adjacency matrix. The spatial topological distance between nodes is calculated using the following formula: .

[0052] in, For nodes and nodes Spatial topological distance between them For nodes The three-dimensional coordinates For nodes The three-dimensional coordinates.

[0053] The min-max normalization method was used to calculate the spatial topological distance. Normalization is performed: .

[0054] This represents the normalized spatial topological distance.

[0055] S32. Calculate the correlation degree of the operating condition characteristic data between each node using the Pearson correlation coefficient to obtain the operating condition adjacency matrix. Calculate the Pearson correlation coefficient between each node according to the following formula: .

[0056] in, For nodes and nodes The Pearson correlation coefficient between them and They are nodes and nodes From 0 The standard deviation of the time-of-flight operating condition characteristic data For nodes and nodes The covariance can be calculated using the following formula: .

[0057] in, and They are nodes and nodes From 0 The mean of the time-varying operating condition characteristic data. m To determine the number of nodes, calculate the number of nodes using the following formula. From 0 Mean and standard deviation of time-varying condition characteristic data: , .

[0058] in, For nodes From 0 to Operating condition characteristic data at any given time.

[0059] S33. Calculate the heat transfer correlation degree between each node using the Gaussian decay model to obtain the heat transfer adjacency matrix. Calculate the heat transfer correlation degree between each node according to the following formula: .

[0060] in, For nodes and nodes The heat transfer correlation between them Used to control attenuation sensitivity, in this embodiment The value is 0.5.

[0061] S34. The spatial adjacency matrix, the working condition adjacency matrix, and the heat transfer adjacency matrix are weighted and summed, and the summed matrix is ​​sparsified to obtain the spatiotemporal adjacency graph.

[0062] The spatial adjacency matrix, the operating condition adjacency matrix, and the heat transfer adjacency matrix are weighted and summed according to preset weights to obtain a comprehensive adjacency matrix. The comprehensive adjacency matrix is ​​then sparsified, retaining the k nearest neighbors with the strongest adjacency weights for each node, and setting the remaining weights to zero. Finally, a spatiotemporal adjacency graph containing spatial topology, operating condition coupling, and local heat transfer information is obtained.

[0063] S4. Based on the spatiotemporal adjacency graph and graph convolutional gated recurrent neural network, a full-time incomplete data imputation prediction model is constructed. This model includes teacher and student branches with identical structures. The teacher branch's input consists only of the historical time-series monitoring data for each visible node, and its output is the future time-series prediction data for each visible node. The student branch's input includes the historical time-series monitoring data for all nodes, and its output is the future time-series prediction data for all nodes. The time-series monitoring data for missing nodes is set to zero. Specifically, the teacher and student branches use identical encoder-decoder structures, differing only in the dimension of the input data: the student branch's input data dimension is N×T×F, where N is the total number of nodes (visible nodes + missing nodes), T is the time window length, and F is the feature dimension; the teacher branch's input data dimension is M×T×F, where M is the number of visible nodes, M... <N。

[0064] Both the encoder and decoder are constructed based on a graph convolutional gated recurrent neural network (GC-GRU). The GC-GRU is a single-layer GRU network. All matrix multiplication operations in the GRU network, including update gate, reset gate, and candidate hidden states, are replaced with graph convolution (GCN) operators. After encoding the input data, the encoder extracts spatiotemporal features through the GC-GRU layer and performs a nonlinear transformation on the output of the GC-GRU using the ReLU activation function, ultimately outputting a hidden state tensor. The decoder receives the hidden state tensor output by the encoder and decodes it. The output of the decoder is flattened to obtain the prediction result of the corresponding branch.

[0065] S5. A dynamic masking strategy is adopted to randomly mask the monitoring data of a specified number of visible nodes in the student branch input, resulting in masked and unmasked nodes. Specifically, the dynamic masking strategy is executed by initializing a masking function. The input to the initialization masking function includes the spatiotemporal adjacency graph, the missing node index, and the number of masked nodes. The output of the initialization masking function includes the sub-adjacency graph corresponding to the visible nodes, and performs a specified number of random maskings on the visible nodes using Boolean masks, outputting the global index of the masked nodes. The dynamic masking strategy is re-executed before each round of training, randomly generating new masked nodes to simulate the scenario of missing features throughout the entire time series, enhancing the model's adaptability and robustness to missing data.

[0066] For example, the spatiotemporal adjacency graph contains the spatiotemporal prior information of all nodes, with dimensions (22, 22). The sub-adjacency graph of visible points extracts the adjacency relationships between visible points from the spatiotemporal adjacency graph, with dimensions (19, 19). The global index of missing nodes is expressed by the missing node indicator matrix I, which is a (22×1) matrix composed of 0s and 1s, where 0 indicates that it is a visible node and 1 indicates that it is a missing node. For example, I=[0,0,0,0,0,0,0,1,1,0,...,0,1,0,0] means that the node with the label [8,9,20] is an inherent missing node. Correspondingly, the missing node [8,9,20] will not become a candidate for a masking node. The position of a masking node is expressed by the masking indicator matrix M, which is a (22×1) matrix composed of 0s and 1s, where 0 indicates that the point is a non-masked node in this round and 1 indicates that the point is selected as a masked node in this round. For example, M=[1,0,0,1,1,0,...,0] means that the visible node with the label [1,4,5] is randomly selected as the masking node in this round.

[0067] S6. Using training, validation, and test sets, the full-time incomplete data imputation prediction model is trained, validated, and tested sequentially according to a weighted global loss function to obtain an optimized full-time incomplete data imputation prediction model. The weighted global loss function includes the imputation loss generated based on the prediction results of each masked node by the student branch, the reconstruction loss generated based on the prediction results of each visible node by the teacher branch, and the cross-branch consistency loss generated based on the prediction results of the student and teacher branches for the same non-masked node or the same masked node. The overall process of training the full-time incomplete data imputation prediction model is as follows: Figure 2 As shown.

[0068] In this embodiment, the imputation loss, reconstruction loss, and cross-branch consistency loss are all constructed using the mean squared error function. The imputation loss, reconstruction loss, and cross-branch consistency loss are weighted and summed using preset weighting parameters to obtain the weighted global loss function.

[0069] Specifically, in this embodiment, the interpolation loss is calculated according to the following formula: .

[0070] in, To compensate for the loss, For the true value, For the student branch, the predicted value for the masked node. For the masking indication matrix, the first i The indicator value of each node, Indicates the predicted time series length.

[0071] The reconstruction loss is calculated using the following formula: .

[0072] in, To reconstruct the loss, For the teacher branch, the predicted value for the visible nodes. For the missing indicator matrix, the first... i The indicator value of each node.

[0073] The cross-branch consistency loss is calculated using the following formula: .

[0074] in, This results in cross-branch consistency loss.

[0075] The weighted global loss function is calculated using the following formula: .

[0076] in, For the weighted global loss function, These are the weights for interpolation loss, reconstruction loss, and cross-branch consistency loss, respectively.

[0077] When training the full-time incomplete data imputation prediction model, the min-max normalization method is used to globally normalize the masked input data, mapping the data to the [0,1] interval to eliminate the influence of differences in feature dimensions on model training. In this embodiment, the Adam optimization algorithm is selected to optimize the network weights and biases of the model. The initial learning rate is set to 0.001, the learning rate decay coefficient is 0.95, and the learning rate decay is performed once every 10 training cycles. The preprocessed dataset is divided into training set, validation set, and test set in a 6:2:2 ratio. Early stopping is used to avoid model overfitting. When the loss value of the validation set does not decrease by more than a preset threshold within 10 consecutive training cycles, training is stopped, and the model of the current cycle is selected as the final trained model. The maximum training cycle of the model is set to 100.

[0078] S7. Input the time series monitoring data of all nodes in several historical time periods into the student branch of the optimized full-time incomplete data imputation prediction model to obtain the time series prediction data of all nodes in several future time periods.

[0079] Specifically, the full data containing all visible and missing nodes is input into the student branch of the trained model, where the feature values ​​of the missing nodes are set to zero, and the model outputs the temporal feature prediction results of the missing nodes; the prediction results are then subjected to an inverse normalization operation, which is the opposite of the training process, to restore them to the values ​​of actual physical quantities, and finally the full temporal feature interpolation and prediction results of the key positions of industrial equipment are obtained.

[0080] In a specific application embodiment, this method is applied to, for example... Figure 3 The temperature monitoring scenario of stacked battery packs in the new energy storage cabinet shown is implemented to interpolate and predict the full-time temperature characteristics for key locations in the battery pack where temperature sensors cannot be placed (in this embodiment, it is assumed that the nodes with indices 8, 9, and 20 are key locations where temperature sensors cannot be placed).

[0081] The dataset used in this embodiment comes from temperature and voltage monitoring data of stacked battery packs in a new energy storage cabinet. The data records the temperature (T-00~T-21) of 20 battery cells and 2 terminal interfaces, as well as the voltage (B-01~B-10, B12~B-21) of the 20 battery cells. The temperature monitoring range is 17℃ to 36℃, and the voltage monitoring range is 3.19V to 3.50V. The data sampling interval is 5 minutes, and the recording period is from 14:40 on March 21st to 04:09 on March 24th. Each feature contains 13536 time steps. The specific process in this embodiment includes the following steps: A1. Node labeling: Three key locations in the battery pack that have thermal runaway monitoring value but cannot accommodate temperature sensors are selected as missing nodes, with a global index of [8,9,20]. The remaining 19 locations where temperature sensors are located are selected as visible nodes, and the three-dimensional spatial location information of all 22 nodes is recorded.

[0082] A2. Data Preprocessing: Acquire temperature time-series monitoring data from 19 visible nodes and voltage condition characteristic data from 20 battery cells. Remove outliers from the data. Divide the temperature time-series data into time windows. Select temperature data from the past 5 time steps as input and temperature data from the next time step as labels to construct samples. Divide several samples into training set, validation set, and test set. Voltage data and temperature data are synchronous data from the same moment to supplement the condition correlation characteristics between nodes.

[0083] A3. Spatiotemporal Adjacency Graph Construction: The spatial topological distance of 22 nodes is calculated and normalized using Euclidean distance to obtain a spatial adjacency matrix; the correlation degree of voltage characteristics of each node is calculated using Pearson correlation coefficient to obtain a working condition adjacency matrix; the thermal conduction correlation degree between nodes is calculated using Gaussian decay model to obtain a heat transfer adjacency matrix; after weighting and summing the three matrices according to preset weights, the comprehensive matrix is ​​sparsified, and the 6 nearest neighbors with the strongest adjacency weights for each node are retained to obtain a 22×22 spatiotemporal adjacency graph, while extracting the 19×19 sub-adjacency graph corresponding to the visible nodes.

[0084] A4. Dual-branch model construction: A dual-branch GC-GRU model with consistent teacher and student branch structures is constructed. The student branch has an input dimension of 22×5×1, corresponding to 22 nodes, 5 time steps, and 1 temperature feature; the teacher branch has an input dimension of 19×5×1, corresponding to 19 visible nodes, 5 time steps, and 1 temperature feature; both the encoder and decoder adopt a single-layer GC-GRU structure, with the hidden layer dimension set to 64 and the activation function used being ReLU.

[0085] A5. Dynamic masking strategy execution: Before each round of training, the masking function is initialized to randomly mask 3 of the 19 visible nodes in the student branch input, a Boolean mask is generated to set the temperature value of the masked node to zero, and the global index of the masked node is output to simulate the full-time temperature missing scenario.

[0086] A6. Loss Function Construction and Model Training: Weighting parameters α=1, β=1, and γ=0.5 were set. Imputation loss, reconstruction loss, and cross-branch consistency loss were constructed based on the mean squared error function, and weighted summation was performed to obtain the global loss function. Global min-max normalization was applied to the masked temperature data. The Adam optimizer was used to train the model based on the global loss function, with an initial learning rate of 0.001, a learning rate decay of 0.95 times every 10 epochs, and a maximum training epoch of 100. Early stopping was used to avoid overfitting.

[0087] A7. Model Application Prediction: Input the full dataset containing 22 nodes into the trained model, set the feature values ​​of missing nodes to zero, and output the temperature prediction results for the three missing nodes at future times. After inverse normalization, the actual temperature value is obtained.

[0088] like Figure 4 As shown, the predicted values ​​of the student branches in this embodiment have a very high degree of fit with the actual values. The median prediction error of missing node 8 is 0.1898℃ and the mean error is 0.2111℃, the median prediction error of missing node 9 is 0.1603℃ and the mean error is 0.2041℃, and the median prediction error of missing node 20 is 0.4188℃ and the mean error is 0.4468℃, which verifies the high prediction accuracy of this method.

[0089] The method provided in the above embodiments of this application addresses the scenario of missing full-time-series features of industrial equipment. It constructs a spatiotemporal adjacency graph incorporating spatial topology, operating condition coupling, and heat transfer correlation to comprehensively characterize the intrinsic relationships between nodes, providing reliable spatial constraints for predicting missing nodes without historical observation data. A dual-branch graph convolutional gated recurrent network model decouples the visible and prediction domains, simultaneously capturing the spatial relationships and temporal evolution characteristics between nodes, achieving in-depth mining of spatiotemporal features. A dynamic masking strategy simulates the full-time-series-missing scenario, enhancing the model's robustness to missing data. By constructing a weighted global loss function including imputation loss, reconstruction loss, and cross-branch consistency loss, collaborative learning between the two branches is achieved, effectively improving the accuracy and stability of predicting the temporal features of missing nodes. This application does not rely on complex physical mechanism modeling, has high computational efficiency, and strong scalability. It can achieve accurate imputation and prediction of the temporal features of missing nodes even without any historical observation features. It is suitable for real-time or near-real-time operational status monitoring and health assessment of various industrial equipment, effectively solving the problem of limited sensor deployment and long-term failure leading to the inability to monitor the status of key locations in industrial scenarios.

[0090] The full-time-series incomplete data interpolation and prediction method based on bi-branch graph networks provided in this application can be applied to various industrial equipment monitoring scenarios where sensor deployment is limited or sensor failures lead to the loss of full-time-series features, including but not limited to the operation status monitoring and health assessment of new energy storage equipment, power equipment, chemical equipment, rail transit equipment, etc.

[0091] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0092] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for full-time incomplete data interpolation and prediction based on a bi-branch graph network, characterized in that, include: Based on the node layout and operating conditions of industrial equipment, the locations where sensors are installed are marked as visible nodes, and the predicted locations of targets without sensors are marked as missing nodes, and the location information of all nodes is recorded. Acquire time-series monitoring data collected from visible nodes in several historical time periods, as well as operating condition characteristic data of industrial equipment. After preprocessing the acquired data, divide it into training set, validation set, and test set according to a preset ratio. Based on the location information of all nodes and the operating condition characteristic data of industrial equipment, a spatiotemporal adjacency graph of all nodes is constructed. A full-time incomplete data interpolation prediction model is constructed based on spatiotemporal adjacency graphs and graph convolutional gated recurrent neural networks. The full-time incomplete data interpolation prediction model includes teacher branches and student branches with identical structures. The input of the teacher branch includes only the time-series monitoring data of each visible node in the historical period, and the output is the time-series prediction data of each visible node in the future period. The input of the student branch includes the time series monitoring data of all nodes in the historical period, and the output is the time series prediction data of all nodes in the future period; the time series monitoring data of missing nodes are all set to zero. A dynamic masking strategy is adopted to randomly mask the monitoring data of a specified number of visible nodes in the input of the student branch, resulting in masked nodes and unmasked nodes. Using the training set, the validation set, and the test set, the full-time incomplete data imputation prediction model is sequentially trained, validated, and tested according to a weighted global loss function to obtain an optimized full-time incomplete data imputation prediction model. The weighted global loss function includes imputation loss generated based on the prediction results of each masked node by the student branch, reconstruction loss generated based on the prediction results of each visible node by the teacher branch, and cross-branch consistency loss generated based on the prediction results of the student branch and the teacher branch for the same non-masked node or the same masked node. The time-series monitoring data of all nodes in several historical periods are input into the student branch of the optimized full-time incomplete data imputation prediction model to obtain the time-series prediction data of all nodes in several future periods.

2. The method for full-time incomplete data interpolation and prediction based on a bi-branch graph network according to claim 1, characterized in that, Locations in industrial equipment that have operational and maintenance value but cannot be equipped with sensors are selected as missing nodes. Locations in the spatial topology adjacent to the missing nodes or on adjacent components where sensors can be installed are selected as visible nodes.

3. The method for full-time incomplete data interpolation and prediction based on a bi-branch graph network according to claim 1, characterized in that, The time-series monitoring data collected from visible nodes is divided into time windows, and the divided time segments are used as input data for model training; the operating condition feature data and the time-series monitoring data are synchronous data collected at the same time, and the operating condition feature data is used to supplement the spatiotemporal correlation features between nodes.

4. The method for full-time incomplete data interpolation and prediction based on a bi-branch graph network according to claim 1, characterized in that, Based on the location information of all nodes and the operating condition characteristic data of industrial equipment, a spatiotemporal adjacency graph of all nodes is constructed, specifically including: The spatial topological distance between nodes is calculated using Euclidean distance and then normalized to obtain the spatial adjacency matrix. The correlation degree of working condition characteristic data between each node is calculated by Pearson correlation coefficient to obtain the working condition adjacency matrix; The heat transfer correlation degree between each node is calculated using the Gaussian decay model, and the heat transfer adjacency relationship matrix is ​​obtained. The spatial adjacency matrix, the operating condition adjacency matrix, and the heat transfer adjacency matrix are weighted and summed, and the summed matrix is ​​then sparsified to obtain a spatiotemporal adjacency graph.

5. The method for full-time incomplete data interpolation and prediction based on a bi-branch graph network according to claim 4, characterized in that, The spatial topological distance between nodes is calculated using the following formula: ； in, For nodes and nodes Spatial topological distance between them For nodes The three-dimensional coordinates For nodes 3D coordinates; The Pearson correlation coefficient between nodes is calculated using the following formula: ； in, For nodes and nodes The Pearson correlation coefficient between them and They are nodes and nodes From 0 The standard deviation of the time-of-flight operating condition characteristic data For nodes and nodes covariance; The heat transfer correlation between nodes is calculated using the following formula: ； in, For nodes and nodes The heat transfer correlation between them Control the attenuation sensitivity.

6. The method for full-time incomplete data interpolation and prediction based on a bi-branch graph network according to claim 1, characterized in that, Both the teacher branch and the student branch adopt an encoder and decoder structure; the encoder and decoder are both constructed based on a graph convolutional gated recurrent neural network, which is a single-layer GRU network. In the GRU network, all matrix multiplication operations of update gate, reset gate and candidate hidden state are replaced by graph convolution operators; the encoder encodes the input data and outputs a hidden state tensor, the decoder receives the hidden state tensor output by the encoder and decodes it, and the output of the decoder is flattened to obtain the prediction result of the corresponding branch.

7. The method for full-time incomplete data interpolation and prediction based on a bi-branch graph network according to claim 1, characterized in that, The dynamic masking strategy is executed by initializing the masking function. The input of the initializing masking function includes the spatiotemporal relationship adjacency graph, the missing node index, and the number of masked nodes. The output of the initializing masking function includes the sub-adjacency graph corresponding to the visible nodes, and performs a specified number of random maskings on the visible nodes through Boolean masking, and outputs the global index of the masked nodes.

8. The method for full-time incomplete data interpolation and prediction based on a bi-branch graph network according to claim 1, characterized in that, The imputation loss, reconstruction loss, and cross-branch consistency loss are all constructed using the mean squared error function. The imputation loss, reconstruction loss, and cross-branch consistency loss are weighted and summed using preset weighting parameters to obtain the weighted global loss function.

9. The method for full-time incomplete data interpolation and prediction based on a bi-branch graph network according to claim 8, characterized in that, The interpolation loss is calculated using the following formula: ； in, To compensate for the loss, For the true value, For the student branch, the predicted value for the masked node. For the masking indication matrix, the first i The indicator value of each node, Indicates the predicted time series length; The reconstruction loss is calculated using the following formula: ； in, To reconstruct the loss, For the teacher branch, the predicted value for the visible nodes. For the missing indicator matrix, the first... i The indicator value of each node; The cross-branch consistency loss is calculated using the following formula: ； in, This results in cross-branch consistency loss. The weighted global loss function is calculated using the following formula: ； in, For the weighted global loss function, These are the weights for interpolation loss, reconstruction loss, and cross-branch consistency loss, respectively.

10. The method for full-time incomplete data interpolation and prediction based on a bi-branch graph network according to claim 1, characterized in that, When training the full-time incomplete data imputation prediction model, the Adam optimization algorithm is used to optimize the network weights and biases. The initial learning rate is set to 0.001 and decays every 10 cycles at a rate of 0.95.

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