An AUV lithium ion battery thermal state prediction method

Abstract

This invention relates to the field of battery thermal management, specifically to a method for predicting the thermal state of lithium-ion batteries in AUVs. The method includes the following steps: constructing an electrothermal coupled reduced-order thermal model to generate a physically consistent initial temperature estimate; constructing a physics-guided spatiotemporal dynamic graph convolutional network (PG-STDGCN) as an error correction model, which embeds physical priors such as battery topology and circuit characteristics into dynamic graph learning to construct a static and dynamic fusion adjacency matrix and outputs a correction amount for the initial temperature estimate; and adding the initial temperature estimate to the correction amount to obtain the final battery thermal state prediction result. This method achieves an organic integration from physical modeling to data-driven correction, balancing interpretability, accuracy, and adaptability under AUV dynamic operating conditions, and significantly improving the multi-cell temperature prediction performance at the battery pack level.

Description

Technical Field

[0001] This invention relates to the field of battery thermal management, specifically to a method for predicting the thermal state of an AUV lithium-ion battery. Background Technology

[0002] Autonomous underwater vehicles (AUVs), as a core branch of unmanned underwater vehicles, have become key equipment for complex underwater missions due to their autonomous operation capabilities. Lithium-ion battery systems, with their advantages of high energy density and long cycle life, have become the preferred power source for pure electric AUVs. However, the inherently limited space in the AUV's battery compartment restricts heat dissipation, making it difficult to quickly release the heat generated by the battery modules. Furthermore, the installation of the battery cells within an insulating structure further exacerbates heat accumulation, potentially leading to catastrophic failures such as thermal runaway when the temperature exceeds a safe threshold.

[0003] As AUVs evolve towards higher speeds, miniaturization, and lower costs, the dynamic uncertainty of the battery system's thermal state has significantly increased. On the one hand, the compact cabin space leads to poor heat dissipation conditions; on the other hand, the drastic fluctuations in load current during missions are coupled with the heat dissipation of other power devices within the cabin, making the battery temperature field more complex. Therefore, establishing a high-precision dynamic model of the battery's thermal state to achieve real-time temperature prediction is of significant engineering value for ensuring AUV operational safety, optimizing battery performance output, and extending battery life.

[0004] Existing thermal state estimation methods fall into three categories: (1) impedance and resistance-based estimation, (2) thermal model-based estimation, and (3) data-driven estimation. In impedance and resistance-based estimation, the relationship between battery temperature and electrochemical impedance or DC resistance is first established, and then the battery temperature is inferred based on online impedance / resistance measurements. Thermal model-based estimation relies on a physics-based model describing battery thermodynamics (i.e., heat generation, heat accumulation, and heat dissipation). This model typically consists of a set of algebraic or differential equations. Thermal models used for temperature estimation can be further categorized into full-order models, reduced-order lumped models, and reduced-order distributed models. In data-driven estimation, machine learning algorithms are used to derive the estimation model to map the nonlinear relationship between measured data and battery temperature. Both pure data-driven methods and hybrid methods are included in data-driven estimation. The former uses only machine learning algorithms without considering battery thermodynamics, while the latter combines machine learning algorithms with domain knowledge of battery thermodynamics.

[0005] However, existing methods for data-driven models of battery temperature mostly focus on a small number of cells, and researchers can generally only obtain the surface temperature or core temperature of the battery in a laboratory environment, without considering the multi-heat source coupling and temperature inconsistency issues at the battery pack level. Although some studies have attempted to combine multi-scale long short-term memory artificial neural networks (LSTM) with bistable thermoelectric coupling models to improve the accuracy of surface temperature prediction, the cell load conditions are singular, and the dynamic changes in heat dissipation conditions and loads in actual operation are not adequately considered.

[0006] Therefore, to achieve accurate thermal prediction during the operation of autonomous underwater vehicle (AUV) batteries, the following key challenges need to be addressed: First, the ambient temperature inside the AUV cabin is not constant but is significantly affected by the operating conditions of other heat source devices within the cabin, resulting in strong time-varying thermal boundary conditions. Second, battery pack-level thermal prediction needs to consider the thermal coupling and heat conduction between individual cells within the battery pack, as well as the heat transfer characteristics of various materials such as the battery pack casing and module support, which places higher demands on the physical representation of the model, parameter identification, and computational feasibility. Third, the load conditions of the AUV batteries change dynamically with mission conditions, increasing the nonlinearity, time-varying nature, and multi-physics coupling intensity of the battery system, while also increasing the complexity of modeling and the difficulty of prediction. Summary of the Invention

[0007] To address the aforementioned technical problems, this invention proposes a method for predicting the thermal state of AUV lithium-ion batteries. This method aims to overcome the shortcomings of existing methods for estimating the thermal state of AUV lithium-ion batteries during operation, such as the strong time-varying nature of thermal boundary conditions, insufficient modeling of multi-cell thermal coupling at the battery pack level, and weak adaptability to nonlinear time-varying characteristics under dynamic loads.

[0008] To achieve the above objectives, the present invention provides a method for predicting the thermal state of an AUV lithium-ion battery, which specifically includes the following steps:

[0009] (1) Construct an electrothermal coupled reduced-order thermal model to generate an initial temperature estimate with physical consistency;

[0010] (2) Construct a Physically Guided Spatiotemporal Dynamic Graph Convolutional Network PG-STDGCN as an error correction model, and output the correction amount for the initial temperature estimate;

[0011] (3) Add the initial temperature estimate to the correction amount to obtain the final battery thermal state prediction result.

[0012] This invention combines a physically consistent electrothermal coupling reduced-order thermal model with a data-driven PG-STDGCN error correction model: the former provides a general initial temperature estimate, while the latter, by fusing battery physical topology and dynamic spatiotemporal graph learning, accurately models the time-varying thermal boundary, multi-cell coupling, and load nonlinearity using multi-scale sparse graph convolution, effectively correcting errors caused by environmental and operating condition disturbances, and finally achieving high-precision thermal state prediction through residual fusion.

[0013] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0014] This invention proposes a battery thermal state prediction model that integrates an electrothermal coupled reduced-order thermal model and an error correction model PG-STDGCN, achieving an organic fusion from physical modeling to data-driven correction. Under the dynamic operating conditions of AUVs, it balances interpretability, accuracy, and adaptability, significantly improving the temperature prediction performance of multi-cell batteries at the pack level.

[0015] This invention proposes a physics-guided spatiotemporal dynamic modeling method: embedding prior physical knowledge such as battery topology and circuit characteristics into a graph convolutional network to construct a static and dynamic fusion adjacency matrix, solving the problem of missing physical meaning in traditional data-driven models, and achieving high-precision prediction of multi-cell temperature at the battery pack level. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating the design of the battery thermal state prediction model for this invention.

[0017] Figure 2 This is a diagram of the electrothermal coupling reduced-order thermal model of the present invention;

[0018] Figure 3 This is a diagram of the Physically Guided Spatiotemporal Dynamic Graph Convolutional Network (PG-STDGCN) of the present invention;

[0019] Figure 4 This is a static diagram of the physical information of the battery pack of the present invention.

[0020] Figure 5 This is a current data graph for the first cruise mission of the present invention;

[0021] Figure 6 This is a current data graph for the second cruise mission of the present invention.

[0022] In the diagram: 1. Power node; 2. Ambient temperature node; 3. Cell temperature node. Detailed Implementation

[0023] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0024] like Figure 1As shown, an AUV lithium-ion battery thermal state prediction method includes the following specific implementation steps:

[0025] S1: Constructing a reduced-order electrothermal coupled thermal model

[0026] Due to its computational efficiency and simple structure, LTI-ROM is widely used to quickly obtain the transient temperature response under a given input power, which can significantly accelerate the simulation process and effectively predict the dynamic thermal behavior in forced convection cooling. However, under time-varying boundary conditions, traditional LTI-ROM has certain limitations in temperature prediction accuracy; despite this, it still has good physical meaning and strong interpretability, providing a solid foundation for building high-fidelity and efficient battery thermal management models.

[0027] Based on the aforementioned LTI-ROM, this invention proposes an electrothermal coupling reduced-order thermal model. This model improves computational speed while preserving physical meaning by reasonably simplifying the degrees of freedom of the physical model. The specific process is shown in Figure 2. First, the current, SOC, and ambient temperature are input into the equivalent circuit model. In the equivalent circuit model, the cell equivalent circuit is based on the cell hybrid pulse power characteristic (HPPC) data. The parameters of the second-order equivalent circuit model (ECM) are identified by the least squares method to accurately characterize the voltage response of the battery in transient and steady-state conditions, thereby achieving accurate calculation of the battery's heat generation power. The battery pack equivalent model integrates the multi-cell series-parallel structure, connection resistance, and inconsistencies, outputting the total heat generation power at the pack level, providing a high-fidelity heat source input for the thermal model. Second, a conjugate heat transfer model of the battery pack is constructed, defining the overall geometry, material properties (density, specific heat capacity, thermal conductivity), and boundary / initial conditions. The model is linearized and reduced to LTI-ROM order through step thermal response, balancing computational efficiency and dynamic fidelity. Ultimately, an electro-thermal closed-loop coupled simulation is achieved: the heat generation power output by the electrical model drives the thermal model to predict the temperature, while the temperature fed back by the thermal model is used to correct the temperature-related polarization and internal resistance parameters in the electrical model, forming a self-consistent multi-physics co-simulation model, laying the foundation for high-precision, real-time thermal management.

[0028] S2: Establish a Physically Guided Spatiotemporal Dynamic Graph Convolutional Network (PG-STDGCN)

[0029] Due to unmodeled dynamic characteristics, environmental disturbances, and other factors, purely physics-driven predictions often suffer from systematic biases. To correct these errors, this invention designs PG-STDGCN as an error correction model to revise the initial prediction results. Its core idea is to integrate prior physical knowledge with a data-driven dynamic graph learning mechanism to achieve efficient and robust spatiotemporal joint modeling. The specific process is as follows: Figure 3 As shown.

[0030] First, the original multivariate time series input X∈ is placed in the data embedding layer. Transform into a four-dimensional feature tensor Xs∈ Where B is the batch size, T is the time step length of the input temperature sequence, C is the number of feature channels, and N is the total number of nodes. This tensor structure can explicitly separate the node dimensions, providing a foundation for subsequent graph operations.

[0031] The reconstructed four-dimensional feature tensor Xs is fed into a binary tree structure composed of multiple Spatiotemporal Graph Convolutional (STDGCN) modules. Within each STDGCN module, the input feature sequence is divided into two sub-sequences along the temporal dimension based on their parity indices. These two sub-sequences fully preserve the temporal structure of the current level and serve as the two branches of spatiotemporal interaction learning. Through continuous cross-branch information interaction and mutual enhancement, the implicit contextual features are fully explored, thereby more effectively modeling global spatiotemporal dependencies and significantly improving the module's ability to represent complex spatiotemporal dynamics. Each STDGCN module contains three key components: a temporal correlation capture module, a spatial correlation capture module, and a spatiotemporal interaction learning strategy. The temporal correlation capture module is responsible for modeling the historical dynamics of a single node; the spatial correlation capture module is responsible for modeling the thermal coupling relationships between nodes; and the spatiotemporal interaction learning strategy, by promoting information interaction between the temporal and spatial modules, synergistically enhances the model's joint representation ability of spatiotemporal dependencies. By stacking multiple STDGCN modules and downsampling the time dimension layer by layer, this binary tree structure can effectively capture multi-scale spatiotemporal correlations from global coarse-grained to local fine-grained, thereby accurately characterizing the dynamic characteristics at different time scales during the thermal evolution of the battery.

[0032] (1) Temporal correlation modeling: Convolutional module

[0033] The temporal module uses convolutional modules (Conv) to capture temporal correlations. For example... Figure 3 As shown, a total of four Conv modules are used, each containing two Conv2d layers with convolutional kernel sizes of (1, k1) and (1, k2) respectively. Since the input tensor dimension is (C, N, T) and the convolutional kernel size in dimension N is 1, operations are performed only on the time dimension of the battery temperature data. This design ensures that the time series of each cell is modeled independently and effectively, accurately capturing its transient and steady-state thermal responses during charging and discharging.

[0034] (2) Spatial correlation modeling: dynamic graph convolutional network

[0035] The spatial module is implemented based on a Graph Convolutional Network (GCN). Its core function is to simultaneously construct a dynamic graph structure and model the spatial relationships between nodes based on the physical prior graph (i.e., a static graph constructed based on the battery pack structure, encoding the heat transfer paths between cells, the driving relationship between power nodes and cells, and the heat dissipation connection between cells and the environment). To achieve this goal, the module consists of two key components: a graph generator and a diffusion-based GCN.

[0036] The graph generator is responsible for constructing a dynamically evolving fused adjacency matrix to characterize the dynamic thermal coupling relationships between nodes under different operating conditions. This generator employs a hybrid graph construction method that integrates prior physical knowledge with a data-driven mechanism. It can dynamically adjust the graph structure based on cell temperature data, ensuring that the reconstructed graph accurately reflects the dynamic correlation of cell temperature changes.

[0037] Specifically, the graph adjacency matrix consists of three parts:

[0038] 1) Static graph structure based on the physical characteristics of the battery pack, such as Figure 4 As shown in the diagram, there are 22 nodes, including power node 1, ambient temperature node 2, and 20 cell temperature nodes 3. The connection relationships follow these rules: power node 1 is directed to each cell temperature node 3; cell temperature nodes 3 are undirected if they are adjacent; and all of them are undirected to ambient temperature node 2. The corresponding adjacency matrix is ​​constructed based on this structure. .

[0039] 2) The global mode memory adjacency matrix is ​​generated as follows:

[0040] ,

[0041] in It is the weight between the i-th node and the j-th memory template in batch b. It is the feature value of the i-th node in batch b at channel c and time t. The weight of the j-th memory template in channel c, The weight of the k-th memory template in channel c, The number of feature channels is represented by T, the number of time steps is T, and the number of memory templates is M.

[0042] 3) Node similarity adjacency matrix, the generation process of which is defined as:

[0043] ,

[0044] ,

[0045] in, It is the feature value of the i-th node in batch b at channel c and time t. It is the mean of the feature values ​​of the i-th node in batch b at channel c and time t along the time step dimension. It is the mean of the feature values ​​of the j-th node in batch b at channel c and time t along the time step dimension. It is the mean of the feature values ​​of the k-th node in batch b at channel c and time t along the time step dimension, where T is the number of time steps. It is the weight of the association strength between the i-th node and the j-th node in batch b. The number of feature channels is represented by N, which represents the number of nodes.

[0046] The above Includes potential spatial relationships between nodes. It performs similarity calculations with itself and generates dynamic associations between nodes within the current time period. These two types of dynamic adjacency matrices together support the data-driven evolution of graph structures during the operation of graph neural networks, characterizing the dynamic spatial associations between nodes from different perspectives.

[0047] Subsequently, the three adjacency matrices are concatenated along the feature dimension and adaptively fused through a fully connected layer to generate the initial fused adjacency matrix A.

[0048] To further improve the computational efficiency and robustness of the model, this invention performs sparsification on the graph structure. Specifically, a learnable mask matrix is ​​introduced. ∈ This is used to sparsify the adjacency matrix A. Based on the correlation strength between each node and other nodes, this mask identifies the top K most important elements at each specific position in the input tensor A. The sparsification operation is defined as follows:

[0049] ,

[0050] ,

[0051] in, , This represents element-wise multiplication, where K is the threshold of the TopKMask function, and represents the maximum number of neighbors of a node. Let b be the mask tensor, i be the query node, and j be the candidate node; Indicates an indicator function, This represents the row vector corresponding to the i-th query node in the b-th batch of the fusion matrix. Sort the nodes in descending order to obtain the sorted index sequence, and take the first K indices of the sequence, which are the indices of the K candidate neighbor nodes with the highest similarity to node i.

[0052] Finally, the sparsed adjacency matrix As a priori graph structure, this is input into the diffusion-based GCN to effectively capture dynamic spatial correlations. This GCN treats the dynamic change in cell temperature as a diffusion process: the state of a target node depends not only on its own history but also on the temperature information of its neighboring nodes at the previous time step. Through multi-step message passing, the model can aggregate contextual information from multi-order neighborhoods, thereby characterizing complex heat conduction and coupling effects. Specifically, the diffusion-based GCN is defined as follows:

[0053] ;

[0054] ;

[0055] ;

[0056] ;

[0057] ;

[0058] in, For the initialized node features, This represents the node feature matrix after the k-th step of graph diffusion propagation. ; H represents the graph convolution operation, where H is the comprehensive feature matrix formed by concatenating the diffusion features of each order along the channel dimension. represents the concatenation of channel dimensions, K represents the diffusion step size, and Z is the enhanced representation obtained by performing feature transformation on H. This indicates the output of GCN.

[0059] GCN dynamic graph convolution constructs a dynamic fusion graph structure from two perspectives: first, the potential heat transfer patterns exhibited by nodes due to spatiotemporal heterogeneity; and second, the dynamic correlations between nodes as operating conditions evolve. Based on this graph structure, the model effectively aggregates neighborhood information, thereby accurately modeling complex dynamic spatial dependencies. Performing dynamic graph construction within each GCN module adaptively captures multi-granularity dynamic associations from global to local levels at different levels, thus revealing deeper spatiotemporal coupling characteristics.

[0060] The concatenated and reconstructed adjacency matrix is ​​input into a linear gated unit (GLU), which uses a gating mechanism to select and fuse spatiotemporal representations. In this process, the GLU not only effectively fuses and explores global spatiotemporal representations but also filters and corrects them. Subsequently, the enhanced representations output by the GLU are mapped through a fully connected regression layer to generate a temperature prediction sequence for future time windows; the final prediction result uses only the first point of the prediction sequence as the output.

[0061] S3: Establish a battery thermal state prediction model that integrates an electrothermal coupling reduced-order thermal model with PG-STDGCN.

[0062] To systematically address key challenges at multiple levels, from fundamental physical modeling to fine spatiotemporal characterization, this invention organically combines physics-based modeling with data-driven correction methods to construct a high-precision battery thermal state prediction model, thereby enhancing the accuracy and robustness of temperature estimation.

[0063] First, a reduced-order thermal model of electrothermal coupling is constructed to provide physically consistent initial temperature estimates and ensure good model versatility. This system consists of an equivalent circuit model and a thermal model. The equivalent circuit model calculates the electrochemical heat generation power of the battery, while the thermal model predicts the battery temperature distribution based on this heat source input. However, due to unmodeled kinetics and environmental disturbances, purely physical-driven predictions often suffer from systematic biases. To correct these errors, this invention designs PG-STDGCN to perform data-driven fine-tuning of the initial prediction results. PG-STDGCN constructs a spatiotemporal graph convolutional architecture that integrates battery physical topology priors with data-driven dynamic graph learning, and introduces multi-scale hierarchical modeling and sparse graph structures. This effectively captures the complex spatiotemporal correlation characteristics within the battery system caused by heat conduction, electrothermal coupling, and time-varying operating conditions.

[0064] By connecting the electrothermal coupled reduced-order thermal model with PG-STDGCN through a residual structure, a closed-loop process of "physical prior modeling - data-driven correction" can be realized, taking into account accuracy, interpretability and adaptability. The final output is the predicted temperature of the battery cell, and the error is controlled within ±1% in the multi-cell temperature prediction.

[0065] S4: Detailed Implementation

[0066] The dataset used in this invention comes from two routine cruise missions performed by the AUV. The current data from these two cruise missions are as follows: Figure 5 and Figure 6 As shown, the training set consists of all the data from the first task and a portion of the data from the second task, containing 69,161 consecutive data points. The validation set consists of the first 20% of the data from the second task, totaling 5,518 consecutive data points. The test set consists of 20%-40% of the data from the second task, totaling 5,518 consecutive data points.

[0067] During training, the model employs a sequence-to-sequence input-output format. This is because battery temperature changes exhibit significant temporal continuity, and this strategy can more effectively learn the dynamic evolution patterns within the time series. Compared to direct sequence-to-single-point prediction, sequence-to-sequence training better captures the long-term dependencies in the temperature evolution process, thereby significantly improving prediction accuracy and robustness. The Huber function is used to calculate the loss during training, and its mathematical formula is as follows:

[0068] ,

[0069] in, It is the actual value. It is a predicted value. This is a hyperparameter that controls the limits of the error magnitude. This loss function combines the advantages of mean squared error (MSE) and mean absolute error (MAE): it uses a squared term to ensure smoothness when the error is small, while switching to a linear term when the error is large, thereby effectively reducing the sensitivity to outliers.

[0070] The battery pack used in the experiment consisted of 20 cells arranged in a rectangular symmetrical layout, numbered sequentially from 1 to 20 starting from the negative terminal. Based on the symmetry of the cell array in the XY plane, five representative cells (cells 2, 3, 5, 10, and 14) were selected for in-depth analysis, denoted as Cell2, Cell3, Cell5, Cell10, and Cell14, respectively. The battery thermal state prediction model (physical model + PG-STDGCN) proposed in this invention and the various comparison methods (physical model + other error correction algorithms) all adopted the same experimental settings: the simulated output of the physical model served as the input to their respective correction modules, and training and testing were performed based on data from two tasks. Specifically, all correction algorithms were trained on the exact same simulated error sequence and evaluated on a unified test set, thereby ensuring the fairness of the experimental setup and the comparability of the results.

[0071] The comparison results of the calibration algorithms are shown in Tables 1 and 2. In the tests of five battery cells, PG-STDGCN achieved the best or near-best results in both MSE and MAE, especially in Cell10 and Cell14, where the MSE was as low as 0.007 and 0.013 respectively, significantly outperforming other comparative methods. This result fully demonstrates that PG-STDGCN possesses robust predictive capabilities for battery cells in different locations and under different thermal environments, effectively overcoming individual differences and exhibiting excellent generalization performance.

[0072] In terms of overall performance, PG-STDGCN also performed best: its average MSE was 0.0132, about 70% lower than the second-place STIDGCN (0.0444); its average MAE was 0.0958, more than 35% lower than the second-place (0.1480). The significant lead in MSE indicates that its predicted values ​​are very close to the actual temperature with minimal bias; while the significant advantage in MAE reflects the model's excellent predictive stability and robustness.

[0073] Therefore, PG-STDGCN significantly outperforms other cutting-edge models in error correction performance, validating its advanced nature and engineering applicability as a core correction module in battery digital twin systems.

[0074] Table 1 Comparison of losses in multi-cell thermal state prediction using different error correction methods.

[0075]

[0076] Table 2 Comparison of average losses of different error correction methods in multi-cell thermal state prediction.

[0077]

[0078] The foregoing has provided a detailed description of one embodiment of the present invention, but this description is merely a preferred embodiment and should not be construed as limiting the scope of the invention. All equivalent variations and modifications made within the scope of the claims of this invention should still fall within the patent coverage of this invention.

Claims

1. A method for predicting the thermal state of an AUV lithium-ion battery, characterized in that, Includes the following steps: S1: Construct an electrothermal coupled reduced-order thermal model to generate an initial temperature estimate with physical consistency; The specific steps are as follows: First, the current, SOC, and ambient temperature are input into the equivalent circuit model; in the equivalent circuit model, the cell equivalent circuit is based on the cell's hybrid pulse power characteristic data, and the parameters of the second-order equivalent circuit model are identified by the least squares method to accurately characterize the battery's voltage response under transient and steady-state conditions, thereby realizing the accurate calculation of the battery's heat generation power; the battery pack equivalent model then integrates the multi-cell series-parallel structure, connection resistance, and inconsistencies on this basis, and outputs the total heat generation power at the pack level. Secondly, a conjugate heat transfer model of the battery pack is constructed, defining the overall geometry, material properties and boundary / initial conditions. The model is linearized and reduced to LTI-ROM through step thermal response. Finally, an electro-thermal closed-loop coupled simulation is achieved. S2: Construct a Physically Guided Spatiotemporal Dynamic Graph Convolutional Network PG-STDGCN as an error correction model, connect the electrothermal coupled reduced-order thermal model with PG-STDGCN through a residual structure, and output the correction amount for the initial temperature estimate; S3: Add the initial temperature estimate to the correction amount to obtain the final battery thermal state prediction result; The PG-STDGCN in S2 includes the following steps: S2.1: The original multivariate time series input data is embedded into a layer and converted into a four-dimensional feature tensor; S2.2: Feed the four-dimensional feature tensor into a binary tree structure composed of multiple spatiotemporal graph convolution STDGCN modules to generate several target enhancement representations; S2.3: After splicing and adjusting the target enhancement representation, it is input into the linear gating unit (GLU) for filtering and correction; S2.4: The enhanced representation of the GLU output is mapped through a fully connected regression layer to generate a temperature prediction sequence, and the first point of the prediction sequence is selected as the prediction result. The STDGCN module in S2.2 includes: a temporal correlation capture module, a spatial correlation capture module, and a spatiotemporal interaction learning strategy; The time correlation capture module operates on the time dimension of battery temperature data and models the historical dynamic dependencies of nodes through convolution operations along the time dimension. The spatial correlation capture module is implemented based on a graph convolutional network. Based on the static graph constructed by the battery pack structure, it encodes the heat transfer path between cells, the driving relationship of power nodes to cells, and the heat dissipation connection between cells and the environment. It simultaneously completes the construction of the dynamic graph structure and the modeling of the spatial correlation between nodes. The spatiotemporal interactive learning strategy is used to fuse the output features of the temporal and spatial branches; The graph convolutional network includes the following steps: S2.2.1: The graph generator adopts a hybrid graph construction method that integrates physical prior knowledge and data-driven mechanism, and dynamically adjusts the graph structure according to the cell temperature data; the graph generator is used to construct a static adjacency matrix based on the physical characteristics of the battery pack, a global pattern memory adjacency matrix, and a node similarity adjacency matrix, and then merges them to obtain a fused adjacency matrix; A static graph structure based on the physical characteristics of the battery pack includes power nodes, ambient temperature nodes, and 20 cell temperature nodes. The connection relationships follow these rules: power nodes to each cell temperature node are directed connections, adjacent cell temperature nodes are undirected connections, and all of them are undirected connections to the ambient temperature nodes. A corresponding adjacency matrix is ​​constructed based on this structure. ; S2.2.2: Perform sparsification processing on the fused adjacency matrix to obtain a sparse fused adjacency matrix; S2.2.3: Input the sparse fusion critical matrix into a graph convolutional network (GCN) based on a diffusion mechanism for multi-step message passing, aggregate multi-order neighborhood information and model dynamic spatial correlation; The global pattern memory adjacency matrix in S2.2.1 The generation process is defined as follows: ， in, It is the feature value of the i-th node in batch b at channel c and time t. No. The weights of each memory template in channel c, No. The weights of each memory template in channel c, The number of feature channels is represented by T, the number of time steps is T, and the number of memory templates is M. The node similarity adjacency matrix in S2.2.1 The generation process is defined as follows: ， ， in, It is the feature value of the i-th node in batch b at channel c and time t. It is the mean of the feature values ​​of the i-th node in channel c across the time step dimension. It is the mean of the feature values ​​of the j-th node in channel c along the time step dimension. It is the mean of the feature values ​​of the k-th node in channel c in batch b, along the time step dimension, where T is the number of time steps. The number of feature channels is represented by N, which represents the number of nodes.

2. The method for predicting the thermal state of an AUV lithium-ion battery according to claim 1, characterized in that, The sparsity operation in S2.2.2 is defined as follows: ， ， in, , This represents element-wise multiplication, where K is the threshold of the TopKMask function, and represents the maximum number of neighbors of a node. Let b be the mask tensor, and b be the batch size. For querying nodes, Candidate nodes; Indicates an indicator function, This indicates that for the b-th batch of the fusion matrix, the... The row vector corresponding to each query node Sort the data in descending order, obtain the sorted index sequence, and take the first K indices of this sequence, which are related to the nodes. The index of the K most similar candidate neighbor nodes.

3. The method for predicting the thermal state of an AUV lithium-ion battery according to claim 1, characterized in that, The graph convolutional network (GCN) based on the diffusion mechanism in S2.2.3 is defined as follows: ； ； ； ； ； in, For the initialized node features, Indicates after the first The node feature matrix after step-by-step propagation. ; H represents the graph convolution operation, where H is the comprehensive feature matrix formed by concatenating the diffusion features of each order along the channel dimension. Represents the splicing of channel dimensions. Z represents the diffusion step size, and is an enhanced representation obtained by performing a feature transformation on H. This indicates the output of GCN.

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