Battery state of health estimation method based on improved graph neural network and hybrid pinn

Abstract

This invention relates to the field of lithium-ion battery state monitoring and health management technology, and proposes a battery health state estimation method based on an improved graph neural network and a hybrid PINN. The method includes constructing a hybrid graph structure containing time edges and similarity edges based on weighted multidimensional health features and time series information, and inputting it into an improved graph sampling aggregation network. High-dimensional spatiotemporal features of each battery charge-discharge cycle node are extracted and embedded through multi-layer graph convolution operations. A hybrid physical prior model is constructed and combined with a residual correction module to form a physical constraint dynamic equation. The high-dimensional spatiotemporal feature embeddings are input into a prediction network to obtain a preliminary prediction of the battery health state. A loss weight annealing strategy is used to dynamically weight the data-driven loss and the physical constraint loss, and the improved graph sampling aggregation network, prediction network, hybrid physical prior model, and residual correction module are collaboratively trained to finally output the estimated battery health state.

Description

Technical Field

[0001] This invention relates to the field of lithium-ion battery state monitoring and health management technology, and in particular to a battery health state estimation method based on an improved graph neural network and a hybrid PINN. Background Technology

[0002] Currently, the state of health (SOH) estimation of lithium-ion batteries mainly employs two types of methods: physics / empirical model-based and data-driven approaches. Model-based methods estimate SOH by establishing electrochemical or equivalent circuit models and combining them with algorithms such as Kalman filtering. While possessing physical interpretability, these methods suffer from high model complexity, difficulty in parameter identification, and a challenge in balancing real-time performance and accuracy. Data-driven methods, such as deep learning, directly utilize historical charge-discharge data to construct mapping relationships. Although they can capture time-series dependencies, they ignore battery degradation kinetic constraints, and the prediction results may violate physical principles, lacking interpretability.

[0003] While the emerging Physical Information Machine Learning (PIML) method can integrate the advantages of physical priors and data-driven approaches, it still faces three key challenges: First, traditional graph neural network methods rely solely on voltage segments to construct static linear topologies, neglecting multi-dimensional electrochemical features such as current and temperature. Furthermore, the standard GCN stacking suffers from "oversmoothing," failing to uncover long-distance, high-order dependencies. Second, existing physical models, such as the Verhulst model, make simplistic assumptions, making it difficult to describe the multi-stage degradation characteristics of batteries throughout their entire lifecycle, from SEI film formation to accelerated aging, resulting in insufficient generalization ability. Third, simple FNN / MLP architectures ignore the spatiotemporal correlations between cycles, relying on "monotonicity constraints" to characterize non-monotonic fluctuations such as capacity recovery. Moreover, the "secondary training" correction mechanism is computationally expensive and lacks real-time performance, making it difficult to meet the online application requirements of battery management systems (BMS). Summary of the Invention

[0004] To address the aforementioned shortcomings, the present invention aims to propose a battery state of health estimation method based on an improved graph neural network and a hybrid PINN. This method aims to improve the accuracy, robustness, and physical interpretability of SOH estimation by constructing a hybrid graph structure with dual temporal-state correlations, integrating a Weibull-power-law hybrid physical prior model that combines reliability theory and electrochemical mechanisms, and employing a residual correction module based on a Kolmogorov-Arnold network and a loss weight annealing strategy. This will meet the real-time application requirements of battery management systems.

[0005] To achieve this objective, the present invention adopts the following technical solution: A battery health state estimation method based on improved graph neural networks and hybrid PINN includes the following steps: S1: Collect and process battery life cycle monitoring data, extract multidimensional health features, and weight the multidimensional health features based on feature importance; S2: Based on the weighted multidimensional health features and time series information, a hybrid graph structure including time edges and similarity edges is constructed. The time edges are used to connect adjacent battery charge-discharge cycle nodes to characterize temporal evolution, and the similarity edges are used to connect cycle nodes with similar states in the weighted feature space to characterize state association. S3: Input the hybrid graph structure into the improved graph sampling aggregation network, and extract the high-dimensional spatiotemporal feature embedding of each battery charge-discharge cycle node through multi-layer graph convolution operation that integrates residual connections and layer normalization; S4: Construct a hybrid physical prior model that integrates reliability theory and electrochemical mechanism, and combine it with a residual correction module based on a learnable network to form a physical constraint dynamic equation for describing the evolution of battery health state. S5: High-dimensional spatiotemporal features are embedded into the prediction network to obtain a preliminary prediction of the battery health status. The preliminary prediction is then constrained and corrected using the physical constraint dynamics equation. Simultaneously, a loss weight annealing strategy is used to dynamically weight the data-driven loss and the physical constraint loss. The improved graph sampling aggregation network, the prediction network, the hybrid physical prior model, and the residual correction module are then trained collaboratively to finally output the estimated battery health status.

[0006] Preferably, step S1 includes: Extracting data reflecting battery aging status from battery lifecycle monitoring data across a specific charge-discharge cycle. Initial health feature vector; For the first 3D features Normalization is performed, and the normalized features are... Satisfying the relation: ; in, Indicates the first The original numerical values ​​of the dimensional features. and They represent Minimum and maximum values ​​in the training dataset; A hybrid strategy combining mutual information and random forest is used for computation. Feature importance weight vector of initial health features , among which, the Mutual information weights of dimensional features For based on Initial health characteristics and battery health status labels mutual information The mutual information is calculated and normalized. Satisfying the relation: ; in, Representation of features With tags The joint probability density function, and This represents the corresponding marginal probability density function; The feature importance weight vector It is obtained by weighted averaging the mutual information weight vector and the feature importance weight vector obtained based on the random forest algorithm.

[0007] Preferably, step S2 includes: Based on the normalized health feature vector and the feature importance weight vector Build a battery information map , where the node set Each node in the set corresponds to a battery charge / discharge cycle, and the edge set Including time edges and similarity edges; The time edge represents the connection node. and nodes An edge, any two nodes and Weighted distance between Satisfying the relation: ; in, Represents the feature importance weight vector The Middle Weights of dimensional features and Representing nodes respectively and The Normalized health eigenvalues; For each node Apply the k-nearest neighbor algorithm to connect nodes Weighted Euclidean distance to all other nodes A predetermined number of nodes, sorted from smallest to largest, are connected to form the similarity edge.

[0008] Preferably, step S3 includes: Let the feature matrix of the input nodes be... The improved graph sampling aggregation network includes Graph convolutional layer, for the th layer layer( ), perform the following operations: For each node Aggregation node Its own information and neighboring nodes Generate intermediate features The intermediate features Satisfying the relation: ; in, Indicates the first The learnable weight matrix of the layer, The function represents the mean aggregation function. Indicates the first Layer nodes Feature representation, Represents a node The set of neighboring nodes; The intermediate features Input features By adding elements one by one, the residual characteristics are obtained. The residual features Satisfying the relation: ; Wherein, when the intermediate feature Input features When the dimensions are inconsistent, first process the input features. Perform a linear projection to align the dimensions; For the residual features Layer normalization is performed, followed by a nonlinear activation function, and some neurons are randomly discarded to obtain the th... Layer Node Feature Representation The node feature representation Satisfying the relation: ; in, Presentation layer normalization operation, Represents a non-linear activation function. This indicates an operation that randomly discards some neurons; go through After processing by the graph convolutional layer, the final embedded representation of each node is obtained. , as the high-dimensional spatiotemporal feature embedding.

[0009] Preferably, step S4 includes: By Weibull's recession term Power-law decay term Linear superposition yields a Weibull-power-law hybrid physical prior model The Satisfying the relation: ; Wherein, the Weibull decimation term Used to describe the accelerated wear characteristics in the later stages of battery aging. Satisfying the relation: ; in, This indicates the current predicted State of Health (SOH) value of the battery. Indicates the current loop count or normalized time. The scale parameter of the Weibull distribution is denoted by . This represents the shape parameter of the Weibull distribution. and All are learnable parameters that are ensured to be non-negative through exponential transformation; The power-law decay term Used to describe the capacity decay in the early stages of battery aging, which is dominated by the growth of a solid electrolyte interface film. Satisfying the relation: ; in, Represents the power-law exponent. Indicates the recession coefficient. and All of these are learnable parameters that are guaranteed to be positive through nonlinear functions; Constructing a residual correction module based on a learnable network The residual correction module takes the current health characteristics, time, SOH prediction value and its gradient as input, and outputs the decay rate residuals not covered by the physical model. From the hybrid physics prior model and the residual correction module Adding them together, we obtain the physical constraint dynamic equations, which satisfy the following relationship: ; in, This represents the derivative of the SOH prediction value with respect to time.

[0010] Preferably, a residual correction module based on a learnable network is constructed. include: The input vector of the residual correction module Satisfying the relation: ; in, Indicates the health characteristics of the current cycle. With normalized timestamp features The concatenated vector This represents the current predicted SOH value. This indicates that SOH is related to the input health characteristics. gradient, Indicates SOH versus time The gradient; To be based on the input vector The activation function was calculated using the Kolmogorov-Arnold network, which replaces the fixed activation function in the multilayer perceptron with a learnable univariate activation function. Satisfying the relation: ; in, Represents the input vector The One portion, This represents a learnable univariate activation function. Represents the input vector Dimensions This represents a linear combination or activation function.

[0011] Preferably, step S5 includes: Construct the total loss function The total loss function Satisfying the relation: ; in, This represents data-driven loss, used to measure the error between the model's predicted value and the actual battery state of health (SOH) label. Represents the physical and dynamic constraint loss. This represents the monotonicity constraint loss. Indicates the regularization loss. The fixed weighting coefficients represent the data-driven loss. The fixed weight coefficients represent the regularization loss. and The physical dynamics constraint loss and monotonicity constraint loss respectively represent the changes in the number of training rounds. Dynamically changing weighting coefficients; The data-driven loss Satisfying the relation: ; in, and These represent the prediction network's predictions for two adjacent time steps. and Predicted State of Health (SOH) value for the battery. and These represent the corresponding true SOH labels, and MSE represents the mean squared error function. The monotonic constraint loss Satisfying the relation: ; Execute the loss-weighted annealing strategy to make and During the preset annealing cycle The value increases linearly from the initial value to the preset maximum value for each training epoch. , and Satisfying the relation: ; ; in, and They represent and The initial weights, and They represent and The maximum weight after annealing, when the number of training rounds... season , ; In each training epoch, according to the total loss function and dynamic weighting coefficients and The gradient is calculated, and all learnable parameters in the improved graph sampling aggregation network, the prediction network, the hybrid physics prior model, and the residual correction module are updated and optimized synchronously.

[0012] One of the above technical solutions has the following advantages or beneficial effects: This invention overcomes the shortcomings of traditional methods, such as single feature dimensions and unreasonable weighting of key information, by employing a hybrid strategy of mutual information and random forest to calculate feature importance and weight multidimensional health features. This allows subsequent modeling to focus on electrochemical features that significantly affect the aging process. By constructing a hybrid graph structure including time edges and similarity edges, where time edges connect adjacent charge-discharge cycles to represent temporal evolution and similarity edges connect nodes with similar states based on the k-nearest neighbor algorithm in the weighted feature space, this invention addresses the limitations of traditional static linear graph structures that fragment temporal information and cannot represent nonlinear state relationships. It achieves dual capture of natural temporal characteristics and implicit state similarities during battery degradation. Furthermore, by integrating an improved graph sampling aggregation network with residual connections and layer normalization for multi-layer graph convolution, this architecture allows initial feature information to flow directly to deep networks, effectively mitigating the oversmoothing and gradient vanishing problems that occur after standard GCN stacking. This enables the model to mine data across the entire battery lifecycle. The system establishes long-range, high-order spatiotemporal dependencies and outputs robust high-dimensional feature embeddings. Addressing the challenge of insufficient universality of single physical models, step S4 constructs a hybrid physical prior model integrating Weibull distribution and power-law mechanisms. The Weibull term adaptively describes accelerated wear in the later stages of aging through learnable parameters, while the power-law term characterizes early capacity decay based on the electrochemical SEI film growth mechanism, effectively achieving precise kinetic constraints on the entire battery aging process from linear degradation to nonlinear accelerated aging. Finally, the high-dimensional features are embedded into the prediction network to obtain preliminary SOH estimates, which are then corrected using physical constraint kinetic equations. A loss weight annealing strategy dynamically balances the contributions of data-driven loss and physical constraint loss. The graph network, prediction network, physical prior, and residual correction module based on the Kolmogorov-Arnold network are trained simultaneously. This collaborative training mechanism avoids the computational delay and multi-objective optimization conflicts caused by traditional secondary correction, achieving efficient and stable end-to-end learning. Attached Figure Description

[0013] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0014] Figure 1 This is a flowchart of a battery health state estimation method based on an improved graph neural network and hybrid PINN provided in an embodiment of the present invention. Detailed Implementation

[0015] Embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0016] In this invention, the terms "comprising," "including," or any other variations thereof are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0017] Battery health state estimation methods based on improved graph neural networks and hybrid PINN, such as Figure 1 As shown, a preferred embodiment of the present invention includes the following steps: S1: Collect and process battery life cycle monitoring data, extract multidimensional health features, and weight the multidimensional health features based on feature importance; It should be noted that battery lifecycle monitoring data refers to the electrochemical signals continuously collected by sensors from the initial use of lithium-ion batteries to capacity degradation and failure threshold, mainly including time series such as terminal voltage, loop current, and surface temperature during the charging and discharging stages. Multidimensional health features are numerical indicators derived from the raw monitoring data that quantify the degree of battery aging, including but not limited to the peak value of the incremental capacity curve, constant current charging time, and average temperature. Feature importance refers to the quantitative measure of the contribution of each health feature to the prediction of the battery's state of health (SOH). It is calculated using a hybrid strategy combining mutual information and random forest. Mutual information measures the nonlinear dependence between features and SOH, while random forest assesses the contribution of features in decision tree splitting using the Gini index or mean squared error reduction. The two are weighted and fused to obtain a comprehensive weight vector. This weight vector is used to distinguish between key and secondary features, guiding similarity measurement in subsequent graph construction, ensuring that highly important features dominate node distance calculations.

[0018] Understandably, by collecting complete battery operation data and extracting multi-dimensional health indicators, a data foundation reflecting the battery degradation pattern can be established. Through a weighted mechanism combining mutual information and random forests, the electrochemical features most sensitive to capacity decay can be identified, noise interference can be suppressed, and high-quality feature representations can be provided for subsequent graph structure construction. This feature selection mechanism ensures that key aging information is preserved while reducing the impact of irrelevant variables on model training, thus improving the robustness and specificity of feature representation.

[0019] S2: Based on the weighted multidimensional health features and time series information, a hybrid graph structure including time edges and similarity edges is constructed. The time edges are used to connect adjacent battery charge-discharge cycle nodes to characterize temporal evolution, and the similarity edges are used to connect cycle nodes with similar states in the weighted feature space to characterize state association. It should be noted that the hybrid graph structure is a topological data structure composed of a set of nodes and a set of edges. Each node uniquely corresponds to a battery charge-discharge cycle, and the node feature is the weighted health feature vector of that cycle. Temporal edges are unidirectional edges connecting nodes in consecutive cycles, used to convey the temporal continuity information of the battery aging process and reflect the natural evolution path of capacity decay. Similarity edges are undirected edges based on feature-weighted distance metrics. The k-nearest neighbor algorithm connects each node in the feature space to its k closest neighbor nodes, allowing the model to learn from degradation patterns under similar historical operating conditions. Weighted Euclidean distance is a distance metric improved by incorporating feature importance weights.

[0020] Understandably, by constructing a hybrid graph structure containing temporal edges and similarity edges, a comprehensive representation of the battery degradation process can be achieved. Temporal edges preserve the natural temporal evolution characteristics of battery aging, ensuring that the model learns the continuous pattern of capacity decay; similarity edges, on the other hand, uncover the nonlinear state correlations between different cycle periods in the multidimensional feature space, enabling the model to utilize historically similar but non-adjacent cycle data to assist current predictions, enhancing its ability to capture complex aging patterns. This dual correlation mechanism overcomes the shortcomings of traditional single graph structures that fragment temporal information or ignore state similarity, providing rich topological semantic information for subsequent deep feature extraction.

[0021] S3: Input the hybrid graph structure into the improved graph sampling aggregation network, and extract the high-dimensional spatiotemporal feature embedding of each battery charge-discharge cycle node through multi-layer graph convolution operation that integrates residual connections and layer normalization; It's important to note that the improved graph sampling aggregation network is a deep graph neural network that integrates residual connections and layer normalization mechanisms on top of the standard GraphSAGE. GraphSAGE generates node embeddings through a sampling-aggregation mechanism, where each node in each layer samples a fixed number of nodes from its neighbor set and aggregates their features, avoiding the computational overhead of processing the entire graph required by GCN. Residual connections are cross-layer identity mapping mechanisms that directly add layer inputs to the output, allowing initial feature information to flow directly into the deep network and mitigating the gradient vanishing problem. Layer normalization standardizes the output of single-layer neurons, stabilizing feature distribution and accelerating convergence. The high-dimensional spatiotemporal feature embedding is a condensed node representation obtained after multi-layer graph convolution, fusing node features, temporal neighbor information, and information from state-similar neighbors. Its dimensionality is typically higher than the original features, resulting in stronger representational capabilities.

[0022] Understandably, the purpose of using an improved GraphSAGE network to perform deep information aggregation on the hybrid graph structure is to capture the complex spatiotemporal dependencies throughout the battery's lifespan. Standard graph neural networks are prone to oversmoothing after stacking multiple layers, leading to convergence of node features and loss of discriminative information. By integrating residual connections, the output of each layer retains the original input components, ensuring that key aging features are not submerged in the deep network; layer normalization stabilizes the training process, enabling the model to effectively stack multiple layers to expand the receptive field and aggregate multi-hop neighbor information. This architectural design allows the model to learn both local degradation patterns and capture long-range dependencies, significantly improving the depth and robustness of feature extraction and providing high-quality feature representations for subsequent SOH prediction.

[0023] S4: Construct a hybrid physical prior model that integrates reliability theory and electrochemical mechanism, and combine it with a residual correction module based on a learnable network to form a physical constraint dynamic equation for describing the evolution of battery health state. It should be noted that the hybrid physical prior model is a mathematical equation constructed by combining statistical failure laws with electrochemical principles to describe the theoretical rate of SOH decay. The residual correction module is a learnable component based on the Kolmogorov-Arnold network. Its inputs include health features, timestamps, predicted SOH values ​​and their gradients, and its output is the decay rate residual not covered by the physical model. The physical constraint kinetic equation adds the theoretical decay rate to the data-driven residual, forcing the neural network's predicted trajectory to conform to physical laws.

[0024] Understandably, by constructing a hybrid physical prior model, the statistical regularities of battery aging are deeply integrated with the electrochemical mechanisms, providing strong physical constraints for SOH prediction. In actual operating conditions, factors such as temperature fluctuations and static recovery prevent the physical model from fully capturing all dynamics. By introducing a KAN network to learn residuals, it is possible to accurately fit nonlinear fluctuations such as capacity recovery, without requiring secondary training during the testing phase.

[0025] S5: High-dimensional spatiotemporal features are embedded into the prediction network to obtain a preliminary prediction of the battery health status. The preliminary prediction is then constrained and corrected using the physical constraint dynamics equation. Simultaneously, a loss weight annealing strategy is used to dynamically weight the data-driven loss and the physical constraint loss. The improved graph sampling aggregation network, the prediction network, the hybrid physical prior model, and the residual correction module are then trained collaboratively to finally output the estimated battery health status.

[0026] It should be noted that the prediction network is a multilayer perceptron structure that receives high-dimensional feature embeddings extracted by the graph neural network and outputs preliminary SOH predictions. It typically includes 2-3 fully connected layers, each followed by an activation function and Dropout. The loss weight annealing strategy is a training technique that dynamically adjusts the proportion of physical constraint loss in the total loss function. In the early stages of training, a smaller weight is set to allow the model to learn data features first, and the weight is linearly increased to a preset maximum with the number of iterations, preventing physical constraints from interfering with feature learning too early. Co-training refers to simultaneously optimizing the data-driven part, the physical model part, and the residual correction part end-to-end using a composite loss function. The Adam optimizer is used to synchronously update all learnable parameters, including GraphSAGE weights, MLP weights, and physical model parameters. And the learnable activation function coefficients of the KAN network. The total loss function includes data-driven loss, physical dynamics constraint loss, monotonicity constraint loss, and regularization loss, which are weighted and fused using dynamic weights and fixed weights.

[0027] Understandably, the prediction network generates initial SOH values ​​based on spatiotemporal feature embeddings, while the physical constraint kinetic equations impose physical constraints on the predicted trajectory through PDE residuals, ensuring the results conform to the electrochemical mechanism. The loss weight annealing strategy divides the training process into two stages: initially focusing on data fitting to quickly establish an understanding of the degradation trend; and later gradually strengthening physical constraints to correct non-physical fluctuations. This smooth transition from data-driven to physics-data collaborative training effectively avoids excessive gradient noise introduced by physical constraints in the early stages of training, which could lead to optimization difficulties. The collaborative training mechanism enables each module to promote mutual improvement: GraphSAGE provides high-quality features, the physical model provides an interpretable framework, and the KAN network supplements dynamic corrections, ultimately outputting SOH estimation results with both high accuracy and physical consistency, meeting the real-time online application requirements of battery management systems.

[0028] Preferably, step S1 includes: Extracting data reflecting battery aging status from battery lifecycle monitoring data across a specific charge-discharge cycle. Initial health feature vector; For the first 3D features Normalization is performed, and the normalized features are... Satisfying the relation: ; in, Indicates the first The original numerical values ​​of the dimensional features. and They represent Minimum and maximum values ​​in the training dataset; A hybrid strategy combining mutual information and random forest is used for computation. Feature importance weight vector of initial health features , among which, the Mutual information weights of dimensional features For based on Initial health characteristics and battery health status labels mutual information The mutual information is calculated and normalized. Satisfying the relation: ; in, Representation of features With tags The joint probability density function, and This represents the corresponding marginal probability density function; The feature importance weight vector It is obtained by weighted averaging the mutual information weight vector and the feature importance weight vector obtained based on the random forest algorithm.

[0029] It should be noted that, The initial health feature vector refers to the vector extracted from monitoring data of a single charge-discharge cycle. A mathematical vector composed of numerical indicators, each component corresponding to an electrochemical characteristic, is used to quantify the degree of battery aging during that cycle. Normalization is a data preprocessing technique that maps the original feature values ​​to a uniform numerical range through linear transformation. The formula... For the first Measured values ​​of 3D features and These represent the minimum and maximum observed values ​​of this feature in the training set, respectively. The transformed feature distribution is... Intervals are used to eliminate dimensional differences and stabilize model training. Mutual information, in information theory, is a measure of the degree of nonlinear dependence between two random variables, calculated by determining their joint probability distribution. Product with marginal probability distribution The KL divergence is used to implement this, with larger values ​​indicating a stronger statistical association between the feature and the SOH label. The Random Forest algorithm is an ensemble learning method that constructs multiple decision trees and aggregates their predictions. It uses the Gini index or mean squared error reduction to evaluate the contribution of each feature to node splitting, and the resulting importance score reflects the marginal impact of the feature on the prediction target. Feature importance weight vector. It is a length of The numerical vector, where each element represents the relative contribution weight of the corresponding health feature in the SOH estimation, is used to guide the similarity calculation in the subsequent graph structure, so that the key features dominate the distance metric.

[0030] Understandably, a high-quality data representation foundation is established through systematic feature engineering. Extraction The health feature transforms the original voltage and current curves into numerical indicators reflecting the battery aging mechanism, avoiding computational redundancy and noise interference caused by directly using high-dimensional time-series signals. Normalization processing ensures comparability of features at different physical scales, preventing large numerical features from dominating model training. Distribution is beneficial for gradient propagation in neural networks. The hybrid strategy of mutual information and random forest complements each other: mutual information captures the nonlinear correlation between features and SOH (Solar Occurrence of Harmony), compensating for complex dependencies that linear correlation coefficients cannot identify; random forest evaluates feature interaction effects, revealing the marginal contribution of individual features in joint decision-making. Weighted averaging, fusing the two weights, suppresses evaluation bias from single methods, generating a robust feature importance metric. This weight vector not only filters key aging indicators but also weights distance calculations in subsequent graph construction, allowing highly important features to dominate similarity judgments, thereby constructing a more semantically accurate topology and improving the model's ability to capture key battery degradation patterns.

[0031] Preferably, step S2 includes: Based on the normalized health feature vector and the feature importance weight vector Build a battery information map , where the node set Each node in the set corresponds to a battery charge / discharge cycle, and the edge set Including time edges and similarity edges; The time edge represents the connection node. and nodes An edge, any two nodes and Weighted distance between Satisfying the relation: ; in, Represents the feature importance weight vector The Middle Weights of dimensional features and Representing nodes respectively and The Normalized health eigenvalues; For each node Apply the k-nearest neighbor algorithm to connect nodes Weighted Euclidean distance to all other nodes A predetermined number of nodes, sorted from smallest to largest, are connected to form the similarity edge.

[0032] It should be noted that the battery information diagram It is a topological data structure that represents the inter-cycle relationships throughout the battery's entire life cycle, in which For a set of nodes, each node Corresponding to the Each node has a charge / discharge cycle, and its attribute is the normalized health feature vector for that cycle. E represents a set of edges, including temporal edges and similarity edges. Temporal edges connect adjacent cycle nodes. With point The directed edges are used to encode the natural temporal evolution path of battery aging, conveying the continuity information of capacity decay. Weighted Euclidean distance. It is a distance function that measures the difference in physical states between two nodes in the feature space, where The k-nearest neighbor algorithm assigns weights based on feature importance, ensuring that key aging features dominate distance calculations and suppressing interference from low-importance noise features. This algorithm is a non-parametric clustering method that assigns weights based on the importance of each node. Calculate the weighted distances from it to all other nodes and sort them in ascending order. Select the k nearest neighbors to establish undirected connections, forming similarity edges, thereby linking cycles with similar states in history but not adjacent in time, and mining cross-cycle hidden patterns.

[0033] Understandably, by constructing a hybrid graph structure containing temporal edges and similarity edges, a comprehensive topological representation of the battery degradation process can be achieved. Temporal edges preserve the sequential evolutionary characteristics of aging, ensuring that the model learns the irreversible trend of capacity decay; similarity edges break through temporal limitations, mining discontinuous but similar cyclical associations in the weighted feature space, enabling the model to learn from degradation patterns in similar historical states to assist current predictions. Feature importance weights are introduced into the weighted distance calculation, allowing high-weight features to dominate similarity judgments, ensuring the semantic accuracy of connections and avoiding erroneous associations caused by low-weight noise fluctuations such as temperature. The k-nearest neighbor algorithm automatically selects a fixed number of similar neighbors for each node, ensuring the sparsity of the graph structure to reduce computational overhead while constructing rich cross-cycle connections, providing sufficient non-local information aggregation paths for the graph neural network. This hybrid graph design overcomes the shortcomings of traditional single graph structures that fragment temporal sequences or ignore state similarity, laying a high-quality topological foundation for deep spatiotemporal feature extraction, enabling subsequent networks to effectively capture long-range dependencies and complex aging patterns.

[0034] Preferably, step S3 includes: Let the feature matrix of the input nodes be... The improved graph sampling aggregation network includes Graph convolutional layer, for the th layer layer( ), perform the following operations: For each node Aggregation node Its own information and neighboring nodes Generate intermediate features The intermediate features Satisfying the relation: ; in, Indicates the first The learnable weight matrix of the layer, The function represents the mean aggregation function. Indicates the first Layer nodes Feature representation, Represents a node The set of neighboring nodes; The intermediate features Input features By adding elements one by one, the residual characteristics are obtained. The residual features Satisfying the relation: ; Wherein, when the intermediate feature Input features When the dimensions are inconsistent, first process the input features. Perform a linear projection to align the dimensions; For the residual features Layer normalization is performed, followed by a nonlinear activation function, and some neurons are randomly discarded to obtain the th... Layer Node Feature Representation The node feature representation Satisfying the relation: ; in, Presentation layer normalization operation, Represents a non-linear activation function. This indicates an operation that randomly discards some neurons; go through After processing by the graph convolutional layer, the final embedded representation of each node is obtained. , as the high-dimensional spatiotemporal feature embedding.

[0035] It should be noted that the input node feature matrix It is a tensor containing the initial features of all nodes in the hybrid graph, with each row corresponding to a normalized health feature vector of a battery charge-discharge cycle node. The improved graph sampling aggregation network is a deep neural network architecture that integrates cross-layer residual connections and layer normalization mechanisms on top of the standard GraphSAGE, overcoming the over-smoothing bottleneck of traditional GCNs by optimizing the message passing mechanism. An L-layer graph convolutional layer refers to a cascaded structure with a network depth of L, where each layer performs an aggregation-transformation-residual-normalization process. Increasing the number of layers expands the receptive field to L hop neighbors. The SAGEConv layer is the core computational unit of GraphSAGE, through... The function collects neighbor information and concatenates it with the node's own features, then processes it using a learnable weight matrix. Linear transformation generates intermediate representations. When the function uses mean aggregation, it calculates the arithmetic mean of the feature vectors of each node's neighbors, capturing the typical feature distribution of the local neighborhood. Residual connections are a cross-layer identity mapping mechanism that directly superimposes input features onto the output by element-wise addition, allowing original information to propagate across network layers and preventing feature dilution caused by deep stacking. Layer normalization standardizes the mean and variance of all feature dimensions of a single sample without relying on batch statistics, stabilizing the training process of deep networks. The ELU activation function is an exponential linear unit; it outputs non-zero negative values ​​in the negative input interval, keeping the mean of neuron activation close to zero and alleviating gradient vanishing. Dropout is a regularization technique that randomly zeros some neuron outputs with a preset probability during training, forcing the network to learn redundant representations and enhancing generalization ability. High-dimensional spatiotemporal feature embedding is a condensed node representation obtained after L layers of processing. Its dimension is usually higher than the original features, deeply integrating node information, temporal neighbor evolution patterns, and cross-period associations of state-similar neighbors, providing rich spatiotemporal semantics for downstream SOH prediction.

[0036] Understandably, step S3 aims to extract higher-order spatiotemporal dependencies from the hybrid graph structure using a deep graph neural network, addressing the over-smoothing problem of feature convergence after multiple layers of stacked GNNs. In traditional GraphSAGE, when stacked deeply, node features gradually lose individual distinctiveness after multiple aggregations, making it difficult to capture long-distance dependencies. Introducing residual connections explicitly preserves the identity mapping of input components in the output of each layer, allowing initial feature information to flow losslessly to deeper layers, ensuring that key aging signals are not submerged. Simultaneously, the existence of skip paths during gradient backpropagation effectively alleviates gradient vanishing. Layer normalization stabilizes the feature distribution of each layer, accelerating convergence and improving training stability. The mean aggregation function calculates the average of neighboring features, smoothing local noise and capturing common patterns in the neighborhood. ELU activation introduces a non-linear transformation, enhancing the network's expressive power; Dropout randomly masks some neurons to prevent overfitting. By stacking L layers, each node ultimately embeds spatiotemporal information within the fusion L-hop range, including both long-term trends on the time-series chain and cross-cycle patterns connected by similar edges. This achieves a highly robust characterization of the complex degradation patterns throughout the battery's entire life cycle, laying a solid foundation for subsequent accurate SOH prediction.

[0037] Preferably, step S4 includes: By Weibull's recession term Power-law decay term Linear superposition yields a Weibull-power-law hybrid physical prior model The Satisfying the relation: ; Wherein, the Weibull decimation term Used to describe the accelerated wear characteristics in the later stages of battery aging. Satisfying the relation: ; in, This indicates the current predicted State of Health (SOH) value of the battery. Indicates the current loop count or normalized time. The scale parameter of the Weibull distribution is denoted by . This represents the shape parameter of the Weibull distribution. and All are learnable parameters that are ensured to be non-negative through exponential transformation; The power-law decay term Used to describe the capacity decay in the early stages of battery aging, which is dominated by the growth of a solid electrolyte interface film. Satisfying the relation: ; in, Represents the power-law exponent. Indicates the recession coefficient. and All of these are learnable parameters that are guaranteed to be positive through nonlinear functions; Constructing a residual correction module based on a learnable network The residual correction module takes the current health characteristics, time, SOH prediction value and its gradient as input, and outputs the decay rate residuals not covered by the physical model. From the hybrid physics prior model and the residual correction module Adding them together, we obtain the physical constraint dynamic equations, which satisfy the following relationship: ; in, This represents the derivative of the SOH prediction value with respect to time.

[0038] It should be noted that the hybrid physics prior model It is a mathematical equation formed by linearly superimposing Weibull decay terms and power-law decay terms, used to describe the theoretical rate of battery SOH decay, serving as a core constraint of the physical information neural network. Weibull decay term Derived from the Weibull risk rate function in reliability engineering, where the scale parameter Through exponential transformation Achieving nonnegativity constraints to characterize battery lifetime characteristics; shape parameters pass Constraints, when The risk rate increases monotonically over time, accurately depicting the accelerated aging phenomenon at the end of life. (Power-law decay term) Based on the diffusion-limited mechanism of SEI growth in solid electrolyte interphase (SEI) films, the power-law exponent pass Functional constraints To bring it close to 0.5, corresponding to the SEI thickness The physical laws of decay; the coefficient of decay pass Constraints ensure positive values, characterizing the magnitude of the SEI growth rate. Residual correction module. A Kolmogorov-Arnold network structure is used, and health features are concatenated from the input vector. Normalized timestamp SOH Predicted Value and its gradient , By approximating complex dynamics not covered by the physical model using a learnable B-spline activation function, scalar residual values ​​are output. The physical constraint dynamic equations add the theoretical decay rate to the data-driven residuals, forcing the neural network to predict the derivative of the trajectory with respect to time. It conforms to the dynamic law after superposition, and calculates the derivative and constructs the PDE residual loss through the automatic differentiation mechanism during the training process.

[0039] Understandably, step S4 constructs a Weibull-power-law hybrid physical prior model, integrating statistical failure patterns and electrochemical mechanisms to achieve adaptive coverage of the battery's full lifecycle degradation trajectory. A single physical model struggles to simultaneously describe the slow degradation during SEI film formation and the accelerated aging at the end of the lifespan. The Weibull term excels at characterizing later wear effects, while the power-law term accurately fits the early diffusion-limiting process. Their linear superposition forms strong physical constraints, replacing traditional simplified models and significantly improving physical interpretability and generalization ability. In real-world operating conditions, factors such as temperature fluctuations and static recovery prevent theoretical models from capturing all dynamics. Introducing a KAN network to learn residuals allows for proactive fitting of non-monotonic fluctuations such as capacity recovery, eliminating the need for secondary training during the testing phase. The physical constraint dynamic equations automatically differentiate to calculate the time derivative of the predicted trajectory, comparing it with the superposition of the hybrid model and residual terms to construct the PDE residual. Minimizing this residual during training ensures the prediction results intrinsically follow electrochemical laws. This architecture, combining physical anchors and data correction, ensures model physical consistency while flexibly adapting to complex dynamics, overcoming the shortcomings of traditional methods such as excessively strong constraints or high computational costs, and achieving efficient and stable end-to-end SOH estimation.

[0040] Preferably, a residual correction module based on a learnable network is constructed. include: The input vector of the residual correction module Satisfying the relation: ; in, Indicates the health characteristics of the current cycle. With normalized timestamp features The concatenated vector This represents the current predicted SOH value. This indicates that SOH is related to the input health characteristics. gradient, Indicates SOH versus time The gradient; To be based on the input vector The activation function was calculated using the Kolmogorov-Arnold network, which replaces the fixed activation function in the multilayer perceptron with a learnable univariate activation function. Satisfying the relation: ; in, Represents the input vector The One portion, This represents a learnable univariate activation function. Represents the input vector Dimensions This represents a linear combination or activation function.

[0041] It should be noted that the residual correction module It is a learnable component built on the Kolmogorov-Arnold network, designed to capture complex nonlinear dynamics that hybrid physics prior models fail to cover. Input vector Integrating multi-source information through splicing: Based on the health characteristics of the current cycle It is formed by concatenating the normalized timestamp t along the feature dimension, providing the working condition context; This is the current predicted SOH value, characterizing the battery's aging state; and These represent the first-order partial derivatives of SOH with respect to health characteristics and time, respectively, obtained through automatic differentiation calculation, reflecting the instantaneous sensitivity of SOH to each input variable. The Kolmogorov-Arnold network is a novel neural network structure based on the superposition theorem of functions, using a learnable univariate activation function. (This can be a B-spline basis function) to replace the fixed activation function of a traditional MLP, each Independent learning input components The nonlinear mapping, the outer layer through By performing linear combination or secondary activation, a double-nested structure is formed, which significantly improves parameter efficiency and approximation ability compared to traditional networks. represent The total dimension This is the width of the hidden layers in the KAN network. Theoretically, this structure can achieve... The complexity approaches that of any A continuous function.

[0042] Understandably, the purpose of designing the residual correction module is to compensate for the shortcomings of pure physical models in covering complex dynamics such as temperature fluctuations, resting recovery, and capacity recovery in actual operating conditions. Traditional methods use fixed monotonicity constraints or secondary training during the testing phase. The former over-smooths and loses key fluctuation information, while the latter has high computational costs and is difficult to apply in real time. The KAN network utilizes the powerful nonlinear fitting capability of learnable activation functions to actively learn the residuals between physical priors and real data, accurately capturing local non-monotonic fluctuations. The input vector integrates health features, timestamps, predicted values, and their gradients, providing KAN with a comprehensive state description: health features reflect the current operating condition, timestamps encode the cycle position, predicted values ​​provide the baseline aging level, and gradient information reveals dynamic change trends. This multi-dimensional input design enables KAN to identify specific combinations of factors that lead to capacity recovery, such as the interaction effect of high temperature and long resting time. Compared to traditional MLPs, KAN's spline activation function has local support characteristics, which can accurately model drastic changes in residuals within a specific input range. At the same time, the double-layer nested structure enables efficient parameter sharing, significantly improving the accuracy and computational efficiency of capturing complex dynamics, and achieving end-to-end training without an additional correction stage.

[0043] Preferably, step S5 includes: Construct the total loss function The total loss function Satisfying the relation: ; in, This represents data-driven loss, used to measure the error between the model's predicted value and the actual battery state of health (SOH) label. Represents the physical and dynamic constraint loss. This represents the monotonicity constraint loss. Indicates the regularization loss. The fixed weighting coefficients represent the data-driven loss. The fixed weight coefficients represent the regularization loss. and The physical dynamics constraint loss and monotonicity constraint loss respectively represent the changes in the number of training rounds. Dynamically changing weighting coefficients; The data-driven loss Satisfying the relation: ; in, and These represent the prediction network's predictions for two adjacent time steps. and Predicted State of Health (SOH) value for the battery. and These represent the corresponding true SOH labels, and MSE represents the mean squared error function. The monotonic constraint loss Satisfying the relation: ; Execute the loss-weighted annealing strategy to make and During the preset annealing cycle The value increases linearly from the initial value to the preset maximum value for each training epoch. , and Satisfying the relation: ; ; in, and They represent and The initial weights, and They represent and The maximum weight after annealing, when the number of training rounds... season , ; In each training epoch, according to the total loss function and dynamic weighting coefficients and The gradient is calculated, and all learnable parameters in the improved graph sampling aggregation network, the prediction network, the hybrid physics prior model, and the residual correction module are updated and optimized synchronously.

[0044] It should be noted that the total loss function It is a composite multi-objective optimization function, composed of a weighted average of four parts: data-driven loss, physics and dynamics constraint loss, monotonicity constraint loss, and regularization loss. Data-driven loss... Mean squared error is used to calculate the difference between predicted values ​​and true labels at adjacent time steps, ensuring that the model closely matches the observed data. Physical and dynamic constraint loss. The residual norm of the physical constraint dynamics equations is used to measure the forced predicted trajectory's conformity to the theoretical laws resulting from the superposition of the Weibull-power-law hybrid model and the KAN correction term. Monotonic constraint loss. pass The function penalizes non-physical capacity regeneration when This generates a positive loss, suppressing abnormal fluctuations. Regularization loss. Sparseness penalties are applied to the learnable activation function of the KAN network to control model complexity. and For fixed weights, and The weights are dynamic and change linearly with the number of training epochs, e. The loss weight annealing strategy refers to reducing the weights of physical constraints in the early stages to allow the model to learn data features first, and then gradually increasing them to the maximum value in the later stages to strengthen physical consistency and avoid gradient conflicts in the early stages of training.

[0045] Understandably, by designing a composite loss function and a dynamic weight annealing strategy, the gradient conflict and convergence instability issues in multi-objective collaborative training are addressed. Data-driven loss ensures the model captures the overall decay trend of SOH (Solar Oxygen Optimization), while physical dynamics constraint loss embeds mixed physical priors and KAN corrections into the optimization process, giving the prediction results a clear electrochemical meaning. Monotonicity constraints suppress abnormal rebounds that violate physical laws, and regularization loss prevents overfitting of the KAN network. In the early stages of training, if the physical constraint weights are too large, their gradients may conflict with the data loss gradient direction, leading to optimization oscillations or getting stuck in local optima. The loss weight annealing mechanism smoothly increases the physical constraint weights from 0 or a minimum value. Initially, the model focuses on data fitting to quickly learn the overall trend, while later, physical constraints strongly intervene to correct details, forming a smooth transition from data-driven to physical-data collaborative training. The Adam optimizer effectively handles the problem of large gradient scale differences between different modules by adaptively adjusting the learning rate of each parameter. For example, the gradient of the KAN network activation function and the gradient of the GraphSAGE convolution kernel have different magnitudes. Adam can adapt to the optimal stride for each, achieving stable and efficient end-to-end joint optimization, with each module mutually promoting and improving overall performance. The Adam optimizer is an adaptive learning rate optimization algorithm based on first-order moment estimation and second-order moment estimation. It calculates the first-order moment of the gradient. and second moment The learning step size of each parameter is dynamically adjusted to achieve stable convergence.

[0046] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "illustrative embodiment," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0047] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims

1. A battery health state estimation method based on improved graph neural networks and hybrid PINN, characterized in that, Includes the following steps: S1: Collect and process battery life cycle monitoring data, extract multidimensional health features, and weight the multidimensional health features based on feature importance; S2: Based on the weighted multidimensional health features and time series information, a hybrid graph structure including time edges and similarity edges is constructed. The time edges are used to connect adjacent battery charge-discharge cycle nodes to characterize temporal evolution, and the similarity edges are used to connect cycle nodes with similar states in the weighted feature space to characterize state association. S3: Input the hybrid graph structure into the improved graph sampling aggregation network, and extract the high-dimensional spatiotemporal feature embedding of each battery charge-discharge cycle node through multi-layer graph convolution operation that integrates residual connections and layer normalization; S4: Construct a hybrid physical prior model that integrates reliability theory and electrochemical mechanism, and combine it with a residual correction module based on a learnable network to form a physical constraint dynamic equation for describing the evolution of battery health state. S5: High-dimensional spatiotemporal features are embedded into the prediction network to obtain a preliminary prediction of the battery health status. The preliminary prediction is then constrained and corrected using the physical constraint dynamics equation. Simultaneously, a loss weight annealing strategy is used to dynamically weight the data-driven loss and the physical constraint loss. The improved graph sampling aggregation network, the prediction network, the hybrid physical prior model, and the residual correction module are then trained collaboratively to finally output the estimated battery health status.

2. The battery health state estimation method based on improved graph neural network and hybrid PINN according to claim 1, characterized in that, Step S1 includes: Extracting data reflecting battery aging status from battery lifecycle monitoring data across a specific charge-discharge cycle. Initial health feature vector; For the first 3D features Normalization is performed, and the normalized features are... Satisfying the relation: ； in, Indicates the first The original numerical values ​​of the dimensional features. and They represent Minimum and maximum values ​​in the training dataset; A hybrid strategy combining mutual information and random forest is used for computation. Feature importance weight vector of initial health features , among which, the Mutual information weights of dimensional features For based on Initial health characteristics and battery health status labels mutual information The mutual information is calculated and normalized. Satisfying the relation: ； in, Representation of features With tags The joint probability density function, and This represents the corresponding marginal probability density function; The feature importance weight vector It is obtained by weighted averaging the mutual information weight vector and the feature importance weight vector obtained based on the random forest algorithm.

3. The battery health state estimation method based on improved graph neural network and hybrid PINN according to claim 2, characterized in that, Step S2 includes: Based on the normalized health feature vector and the feature importance weight vector Build a battery information map , where the node set Each node in the set corresponds to a battery charge / discharge cycle, and the edge set Including time edges and similarity edges; The time edge represents the connection node. and nodes An edge, any two nodes and Weighted distance between Satisfying the relation: ； in, Represents the feature importance weight vector The Middle Weights of dimensional features and Representing nodes respectively and The Normalized health eigenvalues; For each node Apply the k-nearest neighbor algorithm to connect nodes Weighted Euclidean distance to all other nodes A predetermined number of nodes, sorted from smallest to largest, are connected to form the similarity edge.

4. The battery health state estimation method based on improved graph neural network and hybrid PINN according to claim 1, characterized in that, Step S3 include: Let the input node feature matrix be The improved graph sampling aggregation network includes Graph convolutional layer, for the th layer layer( ), perform the following operations: For each node Aggregation node Its own information and neighboring nodes Generate intermediate features The intermediate features Satisfying the relation: ； in, Indicates the first The learnable weight matrix of the layer, The function represents the mean aggregation function. Indicates the first Layer nodes Feature representation, Represents a node The set of neighboring nodes; The intermediate features Input features By adding elements one by one, the residual characteristics are obtained. The residual features Satisfying the relation: ； Wherein, when the intermediate feature Input features When the dimensions are inconsistent, first process the input features. Perform a linear projection to align the dimensions; For the residual features Layer normalization is performed, followed by a nonlinear activation function, and some neurons are randomly discarded to obtain the th... Layer Node Feature Representation The node feature representation Satisfying the relation: ； in, Presentation layer normalization operation, Represents a non-linear activation function. This indicates an operation that randomly discards some neurons; go through After processing by the graph convolutional layer, the final embedded representation of each node is obtained. , as the high-dimensional spatiotemporal feature embedding.

5. The battery health state estimation method based on improved graph neural network and hybrid PINN according to claim 1, characterized in that, Step S4 includes: By Weibull's recession term Power-law decay term Linear superposition yields a Weibull-power-law hybrid physical prior model The Satisfying the relation: ； Wherein, the Weibull decimation term Used to describe the accelerated wear characteristics in the later stages of battery aging. Satisfying the relation: ； in, This indicates the current predicted State of Health (SOH) value of the battery. Indicates the current loop count or normalized time. The scale parameter of the Weibull distribution is denoted by . This represents the shape parameter of the Weibull distribution. and All are learnable parameters that are ensured to be non-negative through exponential transformation; The power-law decay term Used to describe the capacity decay in the early stages of battery aging, which is dominated by the growth of a solid electrolyte interface film. Satisfying the relation: ； in, Represents the power-law exponent. Indicates the recession coefficient. and All of these are learnable parameters that are guaranteed to be positive through nonlinear functions; Constructing a residual correction module based on a learnable network The residual correction module takes the current health characteristics, time, SOH prediction value and its gradient as input, and outputs the decay rate residuals not covered by the physical model. From the hybrid physics prior model and the residual correction module Adding them together, we obtain the physical constraint dynamic equations, which satisfy the following relationship: ； in, This represents the derivative of the SOH prediction value with respect to time.

6. The battery health state estimation method based on improved graph neural network and hybrid PINN according to claim 5, characterized in that, Constructing a residual correction module based on a learnable network include: The input vector of the residual correction module Satisfying the relation: ； in, Indicates the health characteristics of the current cycle. With normalized timestamp features The concatenated vector This represents the current predicted SOH value. This indicates that SOH is related to the input health characteristics. gradient, Indicates SOH versus time The gradient; To be based on the input vector The activation function was calculated using the Kolmogorov-Arnold network, which replaces the fixed activation function in the multilayer perceptron with a learnable univariate activation function. Satisfying the relation: ； in, Represents the input vector The One portion, This represents a learnable univariate activation function. Represents the input vector Dimensions This represents a linear combination or activation function.

7. The battery health state estimation method based on improved graph neural network and hybrid PINN according to claim 6, characterized in that, Step S5 includes: Construct the total loss function The total loss function Satisfying the relation: ； in, This represents the data-driven loss, used to measure the error between the model's predicted value and the actual battery state of health (SOH) label. Represents the physical and dynamic constraint loss. This represents the monotonicity constraint loss. Indicates the regularization loss. The fixed weighting coefficients represent the data-driven loss. The fixed weight coefficients represent the regularization loss. and The physical dynamics constraint loss and monotonicity constraint loss respectively represent the changes in the number of training rounds. Dynamically changing weighting coefficients; The data-driven loss Satisfying the relation: ； in, and These represent the prediction network's predictions for two adjacent time steps. and Predicted State of Health (SOH) value for the battery. and These represent the corresponding true SOH labels, and MSE represents the mean squared error function. The monotonic constraint loss Satisfying the relation: ； Execute the loss-weighted annealing strategy to make and During the preset annealing cycle The value increases linearly from the initial value to the preset maximum value for each training epoch. , and Satisfying the relation: ； ； in, and They represent and The initial weights, and They represent and The maximum weight after annealing, when the number of training rounds... season , ; In each training epoch, according to the total loss function and dynamic weight coefficients and The gradient is calculated, and all learnable parameters in the improved graph sampling aggregation network, the prediction network, the hybrid physics prior model, and the residual correction module are updated and optimized synchronously.

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