Lithium battery SOH estimation method based on time sequence diagram neural network under physical constraint

Abstract

The invention provides a lithium battery SOH estimation method based on a time sequence diagram neural network under physical constraints. The method comprises the following steps: collecting battery charge-discharge cycle data; time-related statistical characteristics and IC curve characteristics are extracted from the battery charge-discharge cycle data, and analysis characteristics are obtained after PCC analysis; calculating a time sequence distance between analysis features based on a sliding window and multi-channel collaborative dynamic time warping, and constructing a graph structure; constructing a time sequence diagram neural network, firstly extracting spatial features through diagram convolution, and then modeling a degradation law through time convolution to obtain a preliminary SOH predicted value; defining a physical residual error loss and a monotonicity regular term, and performing weighted combination on the physical residual error loss and the monotonicity regular term and data fitting loss to construct a joint optimization objective function; based on the optimization target, a final constrained SOH predicted value is obtained through a back propagation training model; therefore, in combination with a physical information constraint mechanism, high-precision and physically consistent SOH prediction is realized.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of battery state of health intelligent evaluation, in particular to a lithium battery SOH estimation method based on a time series graph neural network under physical constraints. BACKGROUND

[0002] With the rapid development of new energy vehicles, energy storage systems and portable devices, the safety and service life of lithium ion batteries as the core energy storage unit have attracted increasing attention. The state of health (SOH) of the battery, as an important indicator reflecting the degree of battery performance degradation, is of great significance to ensure the safe operation of the system and optimize energy management. Therefore, accurate estimation of SOH has become a core task in intelligent battery management systems (BMS).

[0003] In recent years, data-driven methods based on artificial intelligence have gradually become the mainstream. However, the existing SOH estimation methods rely too much on static neural network modeling, ignoring the dynamic evolution of feature dependency relationships in the battery aging process and the capacity regeneration phenomenon, resulting in distortion when predicting SOH across cycles. In addition, the traditional constraint mechanism is rigid and cannot adapt to the needs of different training stages, requiring repeated trials to determine the constraint strength, resulting in waste of training resources. Moreover, the traditional estimation method has a gradient decay problem when processing long sequence data of the battery, affecting the model's ability to capture short-term patterns and long-term degradation trends of the battery. Therefore, it is an important challenge to establish a dynamic modeling, good generalization and efficient lithium battery SOH estimation method. SUMMARY

[0004] In view of the needs in the prior art, the present application provides a lithium battery SOH estimation method based on a time series graph neural network under physical constraints, aiming to combine a physical information constraint mechanism to achieve high-precision and physically consistent SOH prediction.

[0005] The lithium battery SOH estimation method based on a time series graph neural network under physical constraints comprises the following steps:

[0006] Step 1: Collecting battery charge-discharge cycle data;

[0007] Step 2: Extracting time-dependent statistical features and IC curve features from the battery charge-discharge cycle data, and obtaining analysis features after PCC analysis;

[0008] Step 3: Calculating the time series distance between the analysis features based on a sliding window and multi-channel collaborative dynamic time warping, and constructing a graph structure;

[0009] Step 4: Constructing and training a time series graph neural network model, performing spatial feature extraction on the graph structure, and performing time series modeling on the graph-level feature vector representation of multiple cycles, thereby obtaining a preliminary SOH prediction value;

[0010] Step 5: Construct a joint optimization objective function, combining the physical residual loss, monotonicity regularization term and data fitting error, and optimize the parameters of the timing graph neural network model during the training process to guide the TGNN to learn the battery degradation law and obtain the final SOH prediction value with physical consistency.

[0011] Further: Step 5 is specifically as follows:

[0012] Step 5.1: From the perspective of differentiation, ensure that the continuous derivative of SOH prediction over time is non-positive, that is, , is the preliminary SOH prediction value, that is, the prediction sequence, and its time step is: , through automatic differentiation;

[0013]

[0014] in, is the SOH value predicted by the time series graph neural network at the i-th time step, For the The time index of the time step, is the continuous derivative of the predicted SOH value with respect to time;

[0015] Step 5.2: Introduce the physical residual loss term to suppress The upward trend:

[0016]

[0017] in, Physical residual loss, N is the sequence length of the predicted SOH value; If the derivative is greater than 0, it means that the SOH is rising, and the positive value is retained and penalized. Otherwise, it means that the prediction result conforms to the physical law of monotony and no penalty is required;

[0018] Step 5.3: Get the data fitting loss from training the temporal graph neural network ;

[0019]

[0020] in, is the true SOH value of the i-th sample, is the SOH value predicted by the time series graph neural network, and N is the sequence length of the predicted SOH value;

[0021] Step 5.4: Define the monotonicity loss function , used to penalize local rises within the tolerance range:

[0022]

[0023] wherein, represents a penalty only when , if , the term is 0; is set to the maximum rising range of ; , i.e. the change amount of adjacent SOH values is calculated by difference operation;

[0024] Step 5.5: weight coefficients of physical residual loss and monotonicity loss and are defined as follows, respectively:

[0025]

[0026]

[0027] wherein, is the current training round, is the maximum training round epoch = 500; and are both the maximum constraint weights;

[0028] Step 5.6: constructing a joint optimization objective function , and optimizing the time series graph neural network:

[0029]

[0030] Step 5.7: input feature sequence , input the optimized time series graph neural network, and obtain the predicted output :

[0031]

[0032] wherein, represents a set of parameters to be learned by the time series graph neural network, represents the time series graph neural network based on the parameters ;

[0033] Step 5.8: updating the set of parameters of the time series graph neural network to obtain an updated set of parameters , to obtain an updated time series graph neural network;

[0034]

[0035] wherein, is the set of parameters of the time series graph neural network, is the optimized set of parameters, To optimize , so that the joint optimization objective function obtains the minimum value;

[0036] Step 5.9: predicting the final SOH prediction value after constraint by the updated time series graph neural network ;

[0037]

[0038] wherein, is the updated time series graph neural network, is the input feature sequence.

[0039] Further, step 4 is specifically:

[0040] Step 4.1: updating the node features layer by layer through a 3-layer graph convolutional network on the input graph structure:

[0041]

[0042] wherein, is the normalized adjacency matrix (including self-loop); is the initial node feature, is the node feature matrix of the graph structure; is the node feature matrix of the L-th layer, L=3, is the learnable weight; is the ReLU activation function; After three-layer graph convolution processing, the node-level representation is obtained, and then the graph-level feature vector representation is obtained by global average pooling operation on all node feature vectors

[0043] :

[0044]

[0045] wherein, is the feature vector of the i-th node in , is the number of nodes in the graph is 8, used to realize the global average pooling;

[0046] Step 4.2: concatenating the graph-level feature vectors obtained in multiple consecutive periods in time sequence to construct a graph-level feature time sequence with length T ;

[0047]

[0048] wherein, is the graph-level feature vector of the t-th time step, and T is the length of the graph-level feature sequence, determined by the sliding window; ​​

[0049] Input to the time convolution module, the degradation evolution law modeling, time convolution network is composed of dilated convolution, weight normalization (WeightNorm), activation function (ReLU) and Dropout, initialization , each layer operation:

[0050]

[0051] Among them, is the output feature of the first layer, is the output feature of the first layer, L=3, a total of 3 layers, is the dilated convolution operation, the dilated coefficient , is the weight normalization operation, is the activation function, is the random inactivation operation;

[0052] Step 4.3: the graph level feature vector is aggregated into the current cycle graph level feature vector input Convolution module, linear mapping, used to extract local dimensional features, and output as residual path And the results of the time convolution module are fused;

[0053]

[0054]

[0055] Among them, is the fusion feature;

[0056] Step 4.4: the fusion feature Input into the fully connected layer, output the predicted value , that is, the preliminary SOH prediction value;

[0057]

[0058] Among them, is the fully connected layer.

[0059] Further, step 3 is specifically:

[0060] Step 3.1: construct a sliding time window, specifically: for the rth cycle of the ith feature channel, extract the data of the w periods before and after the cycle, and construct a sliding time window with a length of T=2w+1 with the cycle as the center, select the time range as [r-w, r+w]; define the time series of the ith feature channel in the rth cycle as:

[0061]

[0062] where, represents the value of the i-th feature channel in the r-w-th cycle, forming a one-dimensional time series of each feature channel, r is the current charge and discharge cycle index, taking the value range 1 to 10000;

[0063] Stacking the sequences of all feature channels forms the feature matrix of the node ;

[0064]

[0065] where, is the number of feature channels, is the feature matrix of the node;

[0066] Step 3.2: For any two feature channels i and j, take their time series , , calculate the basic distance matrix :

[0067]

[0068] where, is the basic distance between the i-th feature channel and the j-th feature channel between time points p, q, is the value of the i-th feature channel at the p-th time point in the window, is the value of the j-th feature channel at the q-th time point in the window, ;

[0069] For each pair of feature channels, its cumulative distance matrix is calculated recursively from the lower left corner to the upper right corner as follows:

[0070]

[0071] where the initial condition is:

[0072] C(T,1)=D(T,1)

[0073] The multi-channel collaborative dynamic time warping distance is calculated as:

[0074]

[0075] where, is the minimum cumulative distance from the starting point (T, 1) to the current point , is the basic distance of the current alignment point, To select the path direction with the smallest cumulative distance from three feasible directions; 、 、 They represent the three directions recursively derived from the bottom, left, and lower left corners respectively; T is the length of the sliding time window 2w+1, is the feature channel With feature channels Minimum collaborative dynamic time alignment distance within the current sliding window; , are the numbers of the two feature channels involved in the comparison; C(T,1) is the starting point of the recursion; C(1,T) is the end point, indicating the cumulative distance of the shortest path;

[0076] Step 3.3: According to , construct the adjacency matrix of the graph :

[0077]

[0078] in, and Respectively represent feature channels and feature channels, For the feature channels and The temporal similarity distance of feature channels in the sliding time window, is the distance threshold;

[0079] Adjacency Matrix Perform symmetric normalization:

[0080]

[0081] in, Introduce self-connection for the identity matrix, for The degree matrix of (diagonal elements are the sum of each row), is the normalized adjacency matrix, is the adjacency matrix ;

[0082] Step 3.4: Graph Structure for:

[0083]

[0084] in, is the feature matrix of the node ; is the normalized adjacency matrix.

[0085] Further, the process of PCC analysis is as follows: the Pearson correlation coefficient between each feature and SOH is calculated, and features with PCC>0.7 are selected as analysis features.

[0086] Further:

[0087] Step 2 specifically includes the following steps:

[0088] Step 2.1: Extract the average value, standard deviation, peak value, skewness, and root mean square (RMS) features of the current and voltage curves obtained during battery charge and discharge.

[0089] Step 2.2: Extract charge and discharge IC curve features;

[0090] Step 2.3: Use Pearson correlation coefficient to analyze the linear relationship between feature data and SOH;

[0091] The calculation formula for the correlation coefficient is as follows:

[0092]

[0093] in, is the Pearson correlation coefficient between variables x and y; x and y represent the feature and SOH variables respectively, and The variables x and y are The value of the sample points; and are the means of variables x and y respectively;

[0094] Step 2.4: Select feature data with a Pearson correlation coefficient greater than 0.7 as analysis features.

[0095] The beneficial effects of the present invention are as follows: a graph structure between features is constructed through multi-channel collaborative dynamic time warping, and multi-channel collaborative dynamic time warping can be combined with graph convolution to capture the dynamic dependencies of multiple channels such as voltage, current, and IC features, thereby improving feature expression capabilities; and then dilated convolution is used to enhance long-term time series modeling capabilities, avoid the gradient vanishing problem, and improve training efficiency and prediction stability; on this basis, through the partial differential equation residual loss and the SOH monotonically decreasing regularization term, non-physical behaviors in the prediction are suppressed, and the credibility and interpretability of the results are enhanced, thereby achieving high-precision, physically consistent SOH predictions. BRIEF DESCRIPTION OF THE DRAWINGS

[0096] Figure 1 is a flow chart of the present invention;

[0097] Figure 2 Construct a schematic diagram for the graph structure;

[0098] Figure 3 This is a structural diagram of the timing graph neural network. DETAILED DESCRIPTION

[0099] The present invention will be described in detail below with reference to the accompanying drawings. The embodiments of the present invention are described in detail below, and examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements with the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and are not to be construed as limiting the present invention. The directional terms such as left, center, right, top, and bottom in the embodiments of the present invention are merely relative concepts or are based on the normal use state of the product, and should not be considered as restrictive.

[0100] Lithium battery SOH estimation method based on time series graph neural network under physical constraints, combined with Figure 1 As shown, the following steps are included:

[0101] Step 1: Collect battery charge and discharge cycle data;

[0102] A self-built laboratory test platform was built: the test equipment was Neware BTS-5V12A, with a measurement error of ±0.05%; the batteries used were 7 Prospower ICR18650P cylindrical lithium batteries from the same batch, numbered NP-11, NP-12, NP-14, NP-15, NP-16, NP-17, and NP-18; each battery contained 1000 complete charge and discharge cycles; the experiment was carried out at a constant temperature of 25°C±1°C, with charge and discharge rates of 1C and 3C, respectively, using a constant current-constant voltage charging strategy; in terms of data division, NP-11, NP-14, NP-16, and NP-18 were used for training, and NP-12, NP-15, NP-16, and NP-17 were used for training. 5. NP-17 was used for verification and testing. During the experiment, all batteries followed the same cycling procedure, including 5 pre-conditioning cycles, 50 aging cycles, and 20 capacity calibration cycles. The specific charge and discharge strategy was as follows: first, charge to 4.2V at a constant current of 1C, then enter the constant voltage stage, maintain 4.2V until the current drops to 0.1C; then discharge at a constant current of 3C to a cutoff voltage of 2.5V. After each charge and discharge, the battery was allowed to rest for 1 hour to recover the battery state, and the voltage, current, and capacity data of the entire process were collected.

[0103] The present invention uses the ratio of the current available capacity of the battery to the rated capacity to express the SOH of the battery, which is expressed as follows:

[0104]

[0105] here, Indicates the current maximum discharge capacity (remaining capacity) of the battery. Indicates the initial capacity;

[0106] Step 2: Extract time-related statistical features and IC curve features from battery charge-discharge cycle data, and obtain analysis features after PCC analysis; the process of PCC analysis is: calculate the Pearson correlation coefficient of each feature and SOH, and select the features with PCC>0.7 as analysis features, which includes the following steps:

[0107] Step 2.1: Extract average value, standard deviation, peak value, skewness, and root mean square features from the current and voltage curves obtained during the battery charging and discharging process; traditional feature extraction methods often ignore the details of time series and charging process, resulting in incomplete characterization of battery health status; this paper extracts multiple time-related statistical quantities and morphological features, which can more accurately reflect the battery degradation characteristics and improve the accuracy and robustness of SOH estimation;

[0108] Step 2.2: Extract average value, standard deviation, peak value, skewness, and root mean square features for the selected charging current and voltage curves, and extract charge-discharge IC curve features; charge-discharge IC curve features: IC curve peak value, left peak slope, right peak slope, and peak area;

[0109] Extract average value, standard deviation, peak value, skewness, and root mean square features from the current and voltage curves obtained during the battery charging and discharging process, the formulas are as follows:

[0110] Mean value (Mean):

[0111]

[0112] Where, is each data point in the time series data, is the total number of data;

[0113] Standard deviation (Standard Deviation):

[0114]

[0115] Where, is each data point in the time series data;

[0116] Peak value (Peak): the maximum value in the data sequence, representing the peak value of current or voltage;

[0117] Skewness (Skewness): measures the skewness of data distribution, the formula is as follows:

[0118]

[0119] Root mean square (Root Mean Square, RMS):

[0120]

[0121] Charge-discharge IC curve feature extraction;

[0122] IC curve refers to the relationship curve between current and voltage during battery charging and discharging. Feature extraction of IC curve can include:

[0123] IC curve peak value: represents the maximum current or voltage value in the IC curve;

[0124]

[0125] where, is the derivative of capacity Q and voltage V during battery charging and discharging;

[0126] Left slope of peak: calculate the slope of the curve on the left side of the peak, that is, the negative slope region;

[0127]

[0128] where, is the voltage on the left side of the peak, is the voltage corresponding IC value, is the voltage corresponding to the peak value of IC curve;

[0129] Right slope of peak: calculate the slope of the curve on the right side of the peak, that is, the positive slope region;

[0130]

[0131] where, is the voltage on the right side of the peak, is the voltage corresponding IC value;

[0132] Peak area: near the peak value of IC curve, calculate the area under the curve, representing the energy change during charging and discharging;

[0133]

[0134] where, and are the voltages on the left and right sides of the peak, respectively;

[0135] Step 2.3: Use Pearson correlation coefficient to analyze the linear relationship between feature data and SOH; Pearson correlation coefficient ranges from -1 to 1, where the larger the absolute value indicates the greater the linear impact of the feature on SOH;

[0136] The formula for calculating the correlation coefficient is as follows:

[0137]

[0138] wherein, is the Pearson correlation coefficient between variables x and y; x and y represent the feature and SOH variable, respectively, and are the values of variables x and y at the th sample point; and are the mean values of variables x and y, respectively;

[0139] Step 2.4: Select feature data with a Pearson correlation coefficient greater than 0.7 as analysis features, which have high explanatory power in the SOH prediction model;

[0140] Step 3: Calculate the time series distance between analysis features based on the sliding window and multi-channel collaborative dynamic time warping, and construct a graph structure; specifically:

[0141] As shown in Figure 2 , 8 features are extracted from the battery charging and discharging data, and each feature generates a local time series in the time dimension through a sliding window; for example, the window covers data in the range of r-w to r+w, capturing the dynamic changes of the feature over time; then, the MC-DTW algorithm is used to calculate the time series similarity between different feature channels: by dynamic programming to align the feature sequences, the cumulative distance matrix is calculated, and finally the MC-DTW distance between features is obtained; this distance reflects the nonlinear dependence relationship of the features in the time evolution, such as the collaborative change pattern of voltage and current with battery degradation; according to the preset threshold, select the feature pairs with smaller distance, construct an adjacency matrix, and form an undirected graph structure, where the nodes are features and the edges represent strong time series correlation;

[0142] Step 3.1: Construct a sliding time window, which is commonly used in time series analysis to capture data changes within a local time range, and can handle the continuity and local characteristics of time series; specifically: for the rth period of the ith feature channel, extract data from the previous and subsequent w periods, where w=30 in this embodiment, which helps to capture the dynamic changes of the feature over time, rather than relying on data at a single time point; In addition, the sliding window can also handle time series with different speeds or phase shifts, which is particularly important for battery degradation, which may be influenced by multiple factors; construct a sliding time window with a length of T=2w+1 centered on the period, and select the time range [r-w, r+w]; define the feature channel The time series constructed in the rth period is:

[0143]

[0144] where, represents the value of the ith feature channel in the r-wth cycle, forming a one-dimensional time series of each feature channel, r is the current charge and discharge cycle index, taking the value range 1 to 10000;

[0145] Stacking the sequences of all feature channels forms the feature matrix of the node :

[0146]

[0147] where, is the number of feature channels, is the feature matrix of the node;

[0148] Step 3.2: For any two feature channels i and j, take their time series , , calculate the basic distance matrix :

[0149]

[0150] where, is the basic distance between the ith feature channel and the jth feature channel between time points p, q, is the value of the ith feature channel at the pth time point in the window, is the value of the jth feature channel at the qth time point in the window, ;

[0151] For each pair of feature channels, its cumulative distance matrix is calculated recursively from the lower left to the upper right as follows:

[0152]

[0153] where the initial condition is:

[0154] C(T,1)=D(T,1)

[0155] In dynamic programming, multi-channel collaborative dynamic time warping realizes the collaborative optimization of feature channels by calculating the minimum cumulative distance between each time point, considers the collaborative relationship between multiple channels, and comprehensively considers the dynamic dependence between all feature channels in the calculation of the minimum cumulative distance at each time point. The MC-DTW distance between the ith feature channel and the jth feature channel is defined as the minimum cumulative distance corresponding to the path from the starting point (T,1) to the ending point (1,T):

[0156]

[0157] in, From the starting point (T, 1) to the current point The minimum cumulative distance, is the base distance of the current alignment point, To select the path direction with the smallest cumulative distance from three feasible directions; 、 、 They represent the three directions recursively derived from the bottom, left, and lower left corners respectively; T is the length of the sliding time window 2w+1, is the feature channel With feature channels Minimum collaborative dynamic time alignment distance within the current sliding window; , are the numbers of the two feature channels involved in the comparison; C(T,1) is the starting point of the recursion; C(1,T) is the end point, indicating the cumulative distance of the shortest path;

[0158] In the battery state of health (SOH) estimation task, traditional methods are used to calculate the similarity between two time series, mainly by aligning the two time series point by point and calculating their distance or similarity, which is usually applicable to single-channel sequence alignment problems; however, the battery degradation process involves multiple feature channels, and the data of each channel reflects the degradation state of the battery in different dimensions. There are often complex temporal dependencies between these channels; for such multi-dimensional feature data, traditional methods cannot fully capture the co-evolution pattern between these feature channels; the proposed multi-channel collaborative dynamic time warping effectively reduces unnecessary calculations by co-optimizing the similarity between feature channels, thereby improving the computational efficiency of multi-channel data processing, especially when training on large-scale data sets, the efficiency and stability are significantly improved; in the multi-channel collaborative dynamic time warping distance (MC-DTW) algorithm The design of limiting the path search direction to up, right, and right-up is based on the following core principles: First, the battery degradation process has strict temporal unidirectionality (such as a unidirectional increase in the cycle period). The path direction constraint ensures that time alignment relies only on historical data, avoiding reverse interference from future information, which conforms to the physical causal relationship of battery aging. Second, the recursive logic of dynamic programming requires that the path gradually advance from the starting point to the end point. By restricting the direction (up, right, and right-up), the controllability and computational efficiency of the cumulative distance calculation are optimized, avoiding the exponential complexity growth of redundant directions. Finally, the sliding window already covers the bidirectional timing information before and after the current cycle, eliminating the need for additional path direction expansion. The direction constraint can suppress non-physical associations and ensure that the edges of the adjacency matrix reflect the true dynamic dependency of features. This design deeply integrates the battery degradation mechanism with the efficiency requirements of the algorithm, providing a physically consistent structural foundation for the robust modeling of time-series graph neural networks.

[0159] Step 3.3: According to , construct the adjacency matrix of the graph :

[0160]

[0161] in, and Respectively represent feature channels and feature channels, For the feature channels and The temporal similarity distance of feature channels in the sliding time window, is the distance threshold ( );

[0162] Adjacency Matrix Perform symmetric normalization:

[0163]

[0164] in, Introduce self-connection for the identity matrix, for The degree matrix of (diagonal elements are the sum of each row), is the normalized adjacency matrix, is the adjacency matrix ;

[0165] Step 3.4: Graph Structure for:

[0166]

[0167] in, is the feature matrix of the node ; is the normalized adjacency matrix;

[0168] Step 4: Build and train a time series graph neural network model, extract spatial features from the graph structure, and perform time series modeling on the graph-level feature vector representations of multiple periods to obtain preliminary SOH prediction values; Figure 3As shown in the figure, the TGNN backbone network path: the bottom input is a multi-channel feature sequence, which first passes through the convolution layer to extract node-level dependencies, and then is compressed into a graph-level representation through ReLU activation and node-level graph pooling operations; the middle time modeling adopts the dilated causal convolution structure, combined with weight normalization (WeightNorm), ReLU activation and Dropout mechanism, to explore the evolution law of SOH in the time dimension layer by layer. Residual fusion path: The right side of the figure is a 1×1 convolution module, which is used to capture local information not modeled in the backbone path. The final output is formed by adding it to the backbone output residual, enhancing the model's feature expression and fitting capabilities; physical consistency guidance module: Among them, the simulated SOH degradation derivative is used, and the residual loss term and monotonicity regularization term are constructed. Together with the main loss term, it constitutes the total loss for end-to-end training to improve the physical rationality of the prediction curve; the specific processing process is as follows:

[0169] Step 4.1: Update the node features layer by layer through a 3-layer graph convolutional network on the input graph structure:

[0170]

[0171] in, is the normalized adjacency matrix (including self-loops); Initially it is node feature, is the node feature matrix of the graph structure; It is The node feature matrix of the layer, L=3, are learnable weights; is the ReLU activation function;

[0172] After three layers of graph convolution processing, the node-level representation is obtained. Then, the feature vectors of all nodes are globally averaged through the graph pooling operation to obtain the graph-level feature vector representation. :

[0173]

[0174] in, yes The eigenvector of the i-th node in , The number of nodes in the graph is 8, which is used to implement global average pooling;

[0175] Step 4.2: Concatenate the graph-level feature vectors obtained from multiple consecutive periods in chronological order to construct a graph-level feature time series of length T. ;

[0176]

[0177] wherein, is the graph-level feature vector of the t-th time step, and T is the length of the graph-level feature sequence, determined by the sliding window;

[0178] is input into the time convolution module to model the degradation evolution law. The time convolution network is composed of dilated convolution, weight normalization (WeightNorm), activation function (ReLU) and Dropout. The initial layer operation:

[0179]

[0180] wherein, is the output feature of the t-th time step, is the output feature of the t-th time step, L=3, and there are 3 layers, is the dilated convolution operation, and the dilated coefficient , is the weight normalization operation, is the activation function, is the random inactivation operation; Step 4.3: The graph-level feature vector is aggregated into the graph-level feature vector of the current period by the pooling operation and input into the convolution module to perform linear mapping, which is used to extract local inter-dimensional features and output as a residual path

[0181] and the result of the time convolution module is fused;

[0182]

[0183] wherein, is the fusion feature;

[0184] Step 4.4: The fusion feature is input into the fully connected layer to output the prediction value

[0185] , i.e. the preliminary SOH prediction value

[0186]

[0187] wherein, is the fully connected layer;

[0188] ​​In practical applications, SOH data is often accompanied by local fluctuations or outliers, making it difficult for a single-path time series model to account for both global trends and local disturbances. The convolutional residual path is introduced to compensate for shallow local features and fuse them with the main path features, thereby improving the model's robustness to complex conditions such as noise disturbances and nonlinear changes.

[0189] Step 5: Construct a joint optimization objective function, combining the physical residual loss, monotonicity regularization term, and data fitting error. Optimize the parameters of the timing graph neural network model during training to guide the TGNN to learn the battery degradation law and obtain the final SOH prediction value with physical consistency. Specifically:

[0190] Step 5.1: From the perspective of differentiation, ensure that the continuous derivative of SOH prediction over time is non-positive, that is, , is the preliminary SOH prediction value, that is, the prediction sequence, and its time step is: , through automatic differentiation;

[0191]

[0192] in, is the SOH value predicted by the time series graph neural network at the i-th time step, For the The time index of the time step, is the continuous derivative of the predicted SOH value with respect to time; if , indicating that the predicted SOH value increases with time, violating the laws of physics;

[0193] Step 5.2: Introduce the physical residual loss term to suppress The upward trend:

[0194]

[0195] in, Physical residual loss, N is the sequence length of the predicted SOH value; If the derivative is greater than 0, it means that the SOH is rising, and the positive value is retained and penalized. Otherwise, it means that the prediction result conforms to the physical law of monotony and no penalty is required;

[0196] Step 5.3: Get the data fitting loss from training the temporal graph neural network ;

[0197]

[0198] in, is the true SOH value of the i-th sample, is the SOH value predicted by the time series graph neural network, and N is the sequence length of the predicted SOH value;

[0199] Step 5.4: Define monotonicity loss function , to punish local rising parts within the tolerance range, retain a certain degree of freedom through "soft constraint", and improve the generalization ability of the model in real scenarios:

[0200]

[0201] wherein, represents that only when penalty is generated, if , the item is 0; is the maximum rising range of , that is, the change amount of adjacent SOH values is calculated by difference operation;

[0202] Step 5.5: Weight coefficient of physical residual loss and weight coefficient of monotonicity loss are defined as follows, respectively:

[0203]

[0204]

[0205] wherein, is the current training round, is the maximum training round epoch=500; and are both the maximum constraint weight, and linearly increase with the training round to prevent the physical constraint from interfering with the ability of the model to fit the data too early and too strongly;

[0206] Step 5.6: Construct joint optimization objective function , and optimize the time series graph neural network:

[0207]

[0208] Step 5.7: Input the input feature sequence into the optimized time series graph neural network to obtain the predicted output :

[0209]

[0210] wherein, represents the parameter set to be learned by the time series graph neural network, represents the time series graph neural network based on the parameter ;

[0211] ​Step 5.8: updating the parameter set of the time series graph neural network to obtain an updated parameter set , to obtain an updated time series graph neural network

[0212]

[0213] wherein, is the parameter set of the time series graph neural network, is the optimized parameter set, is optimized to make the joint optimization objective function reach a minimum value;

[0214] Step 5.9: predicting the final SOH prediction value after constraint by the updated time series graph neural network ;

[0215]

[0216] wherein, is the updated time series graph neural network, is the input feature sequence.

[0217] In order to improve the physical consistency and explainability of SOH prediction, the application introduces a dynamic feedback physical information enhanced neural network (DF-EPINN) constraint mechanism on the basis of a data-driven model; the application innovatively introduces a degenerate dynamics model based on a partial differential equation (PDE) as physical prior information, and through the physical information neural network idea, the derivative constraint of SOH with respect to time is embedded in the network training, a physical residual loss function is constructed, the physical violation behavior in model prediction is effectively inhibited, and the explainability and credibility of the prediction result are enhanced; the final loss function of the model is composed of three parts: data fitting loss, physical residual loss and monotonicity regularization loss, which jointly optimize the model performance and physical consistency.

[0218] The proposed method is comprehensively evaluated by six evaluation indexes, namely mean square error (MSE), root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), determination coefficient (R2) and maximum error (MAXE).

[0219]

[0220]

[0221]

[0222]

[0223] ​

[0224]

[0225] As shown in Table 1, the performance of the physical constraint-based time series graph neural network (PI-TGNN) is compared with existing models (Transformer, GAT-TCN, CNN-LSTM, CNN-KAN, and CNN-TCN). The selected test objects are four batteries of laboratory dataset NP-12, NP-15 and public dataset CS2-36, CS2-38, and the remaining batteries are used for model training. The laboratory dataset is the battery charge and discharge cycle data collected by the laboratory test platform in step 1. The public dataset is the CS2 battery dataset published by the University of Maryland, which contains four LiCoO2 (lithium cobalt oxide) positive electrode material batteries numbered CS2-35, CS2-36, CS2-37 and CS2-38, with a rated capacity of 1100 mAh. During the battery cycle process, the standard constant current-constant voltage (CC-CV) charging protocol is used: first, charge at 0.5C (550 mA) constant current to 4.2V, and then enter the constant voltage stage to maintain the current below 0.05A. The discharge cutoff voltage is set to 2.7V. The evaluation indicators include MSE, RMSE, MAE, MAPE, R² and MAXE.

[0226] The results show that the physical constraint-based time series graph neural network (PI-TGNN) performs best in all evaluation indicators, with better prediction accuracy, stability and robustness than other comparison models. For example, the R² of PI-TGNN on NP-12 battery reaches 0.995985, and the MAXE is 1.1365, which is better than GAT-TCN (R² is 0.9932, MAXE is 1.9949) and Transformer (R² is 0.9913, MAXE is 1.4537); in NP-15 battery samples, the R² of PI-TGNN is as high as 0.9938, the MSE is only 0.1720, and the maximum error is controlled at 1.1449, which is significantly better than the MSE (0.6373) and MAXE (1.8590) of GAT-TCN, effectively suppressing error fluctuations. The R² of PI-TGNN on CS2-36 and CS2-38 batteries is 0.9969 and 0.9846 respectively, both of which are the highest, and the maximum error is the smallest, verifying its generalization ability across samples. The above results fully demonstrate that PI-TGNN not only has better prediction accuracy, but also effectively integrates physical prior constraints to improve the model's estimation ability of lithium-ion battery health status, and is suitable for actual life prediction and health management scenarios.

[0227] Table 1 results of comparison experiments

[0228]

[0229] To verify the robustness of the health state estimation method of the application under noise interference, two batteries NP-12 and NP-15 in the laboratory data set were selected as test objects, and the remaining batteries were used for training. In the experiment, Gaussian noise with amplitudes of 50 mV, 100 mV and 150 mV was superimposed on the original data to simulate the disturbance environment in the actual measurement process.

[0230] The experimental results are shown in Table 2. With the increase of noise amplitude, the error indicators slightly increase, but the overall level remains low. For example, on the NP-12 battery, the MAXE under 150 mV noise is 1.6694, and the R² is still 0.9876; on the NP-15 battery, the R² is always higher than 0.969, indicating that the model has good anti-interference ability.

[0231] In addition, compared with the traditional method after adding different noise, the PI-TGNN model proposed in the application shows better prediction accuracy under all noise levels. For example, the MAXE of NP-12 under the PI-TGNN model is only 1.1365, which is significantly better than the comparative result under 150 mV noise (1.6694); the RMSE of NP-15 is also reduced from 0.9259 to 0.4147. Further verification of the method of the application under various noise disturbance conditions shows that it maintains high accuracy and stability, indicating that it has good robustness and error adaptation ability in practical applications.

[0232] In addition, similar trends are also shown in the CS2-36 and CS2-38 battery experiments in the CS2 battery data set published by the University of Maryland; for example, the RMSE of CS2-36 under 150 mV noise is as high as 2.8197, while under the PI-TGNN model it is only 0.5230, and the R² is increased to 0.9969; the MAE of CS2-38 under 150 mV noise is 1.6908, while under the PI-TGNN it is reduced to 0.4918, further proving that the method has strong generalization ability and prediction accuracy under different data sources and noise disturbances.

[0233] Table 2 Results of noise experiment

[0234]

[0235] The experimental results show that the application has better prediction accuracy (MSE is reduced by about 30-40% on average) under cross-dataset and multi-condition environment, and still maintains stable performance under different noise levels, significantly better than traditional methods. Its lightweight structure and multi-source data compatibility support efficient deployment in intelligent battery management systems (BMS), and can provide reliable health state evaluation solutions for electric vehicles, energy storage systems and other scenarios, with both technical innovation and engineering practicality.

[0236] The foregoing merely illustrates the principles of the application and application of its more prominent features. Various modifications and enhancements are possible without departing from the spirit and scope of the application. Accordingly, what has been described above and illustrated in the accompanying drawings is a broad exposition of the more notable and principle features of the application. It is the intention of the inventors that what has been described above and that will be claimed below is a complete description of the inventive principles of the application and that the application is defined by the following claims and their equivalents.

Claims

1. A lithium battery SOH estimation method based on a time series graph neural network under physical constraints, characterized by: The following steps are involved: Step 1: Collect battery charge and discharge cycle data; Step 2: Extract time-related statistical features and IC curve features from the battery charge and discharge cycle data, and obtain analysis features after PCC analysis; Step 3: Calculate the temporal distance between analysis features based on sliding window and multi-channel collaborative dynamic time warping, and construct a graph structure; Step 4: Build and train a time-series graph neural network model, extract spatial features from the graph structure, and perform time series modeling on the graph-level feature vector representations of multiple periods to obtain preliminary SOH prediction values. Step 5: Construct a joint optimization objective function, combining the physical residual loss, monotonicity regularization term and data fitting error, and optimize the parameters of the timing graph neural network model during the training process to guide the TGNN to learn the battery degradation law and obtain the final SOH prediction value with physical consistency.

2. The lithium battery SOH estimation method based on a time series graph neural network under physical constraints according to claim 1 is characterized in that: Step 5 is as follows: Step 5.1: From the perspective of differentiation, ensure that the continuous derivative of SOH prediction over time is non-positive, that is, , is the preliminary SOH prediction value, that is, the prediction sequence, and its time step is: , through automatic differentiation; ； in, is the SOH value predicted by the time series graph neural network at the i-th time step, For the The time index of the time step, is the continuous derivative of the predicted SOH value with respect to time; Step 5.2: Introduce the physical residual loss term to suppress The upward trend: ； in, Physical residual loss, N is the sequence length of the predicted SOH value; If the derivative is greater than 0, it means that the SOH is rising, and the positive value is retained and penalized. Otherwise, it means that the prediction result conforms to the physical law of monotony and no penalty is required; Step 5.3: Get the data fitting loss from training the temporal graph neural network ; ； in, is the true SOH value of the i-th sample, is the SOH value predicted by the time series graph neural network, and N is the sequence length of the predicted SOH value; Step 5.4: Define the monotonicity loss function , used to penalize local rises within the tolerance range: ； in, ) means only in Penalty occurs when Then the item is 0; To set The maximum rise range, , that is, the change of adjacent SOH values ​​is calculated by differential operation; Step 5.5: Weight coefficient of physical residual loss and the weight coefficient of monotonicity loss They are defined as: ； ； in, is the current training round, The maximum training round epoch=500; and Both are maximum constraint weights; Step 5.6: Construct joint optimization objective function , and optimize the time series graph neural network: ； Step 5.7: Input feature sequence Input the optimized time series graph neural network to get the predicted output : ； in, Represents the set of parameters that the temporal graph neural network needs to learn, Indicates that the parameters Based on the temporal graph neural network; Step 5.8: Update the parameter set of the timing graph neural network and obtain the updated parameter set , get the updated temporal graph neural network; ； in, is the parameter set of the temporal graph neural network, is the optimized parameter set, For Optimize so that the joint optimization objective function achieves the minimum value; Step 5.9: Use the updated time series graph neural network to predict the final constrained SOH prediction value ; ； in, is the updated temporal graph neural network, is the input feature sequence.

3. The lithium battery SOH estimation method based on a time series graph neural network under physical constraints according to claim 1 is characterized in that: Step 4 is as follows: Step 4.1: Update the node features layer by layer through a 3-layer graph convolutional network on the input graph structure: ； in, is the normalized adjacency matrix (including self-loops); Initially it is node feature, is the node feature matrix of the graph structure; It is The node feature matrix of the layer, L=3, are learnable weights; is the ReLU activation function; After three layers of graph convolution processing, the node-level representation is obtained. Then, the feature vectors of all nodes are globally averaged through the graph pooling operation to obtain the graph-level feature vector representation. : ； in, yes The eigenvector of the i-th node in , The number of nodes in the graph is 8, which is used to implement global average pooling; Step 4.2: Concatenate the graph-level feature vectors obtained from multiple consecutive periods in chronological order to construct a graph-level feature time series of length T. ; ； in, is the graph-level feature vector at the t-th time step, T is the length of the graph-level feature sequence, which is determined by the sliding window; Input to the time convolution module to model the degradation evolution law. The time convolution network consists of dilated convolution, weight normalization (WeightNorm), activation function (ReLU) and Dropout. Initialization , each layer operation: ； in, For the The output features of the layer, For the The output features of the layer, L=3, there are 3 layers in total, For the dilated convolution operation, the dilation coefficient , is the weight normalization operation, for activation function, It is a random deactivation operation; Step 4.3: Aggregate the graph-level feature vector into the graph-level feature vector input of the current cycle through pooling operation Convolution module, which performs linear mapping to extract local inter-dimensional features and outputs them as residual paths Fuse with the results of the temporal convolution module; ； ； in, It is a fusion feature; Step 4.4: Fusion features Input the fully connected layer and output the predicted value , which is the preliminary SOH prediction value; ； in, is a fully connected layer.

4. The lithium battery SOH estimation method based on a time series graph neural network under physical constraints according to claim 1 is characterized in that: Step 3 is as follows: Step 3.1: Construct a sliding time window. Specifically, for the r-th period of the i-th feature channel, extract the data of w periods before and after the period, construct a sliding time window with a length of T=2w+1 centered on the period, and select the time range as [rw,r+w]. Define the time series constructed by the i-th feature channel in the r-th period as: ； in, Represents the value of the i-th feature channel in the rw-th cycle, forming a one-dimensional time series for each feature channel. r is the index of the current charge and discharge cycle, ranging from 1 to 10000; Stack the sequences of all feature channels to form the feature matrix of the node : ； in, is the number of feature channels, is the feature matrix of the node; Step 3.2: For any two feature channels i and j, take their time series 、 , calculate the basic distance matrix : ； in, is the basic distance between the i-th feature channel and the j-th feature channel at time point p, q, is the value of the i-th feature channel at the p-th time point in the window, is the value of the j-th feature channel at the q-th time point in the window, ; For each pair of feature channels, the cumulative distance matrix is ​​recursively calculated from the lower left corner to the upper right corner as follows: ； The initial conditions are: C(T,1)=D(T,1); The MC-DTW distance between the i-th feature channel and the j-th feature channel is defined as the minimum cumulative distance corresponding to the path from the starting point (T, 1) to the end point (1, T): ； in, From the starting point (T, 1) to the current point The minimum cumulative distance, is the base distance of the current alignment point, To select the path direction with the smallest cumulative distance from three feasible directions; 、 、 They represent the three directions recursively derived from the bottom, left, and lower left corners respectively; T is the length of the sliding time window 2w+1, is the feature channel With feature channels Minimum collaborative dynamic time alignment distance within the current sliding window; , are the numbers of the two feature channels involved in the comparison; C(T,1) is the starting point of the recursion; C(1,T) is the end point, indicating the cumulative distance of the shortest path; Step 3.3: According to , construct the adjacency matrix of the graph : ； in, and Respectively represent feature channels and feature channels, For the feature channels and The temporal similarity distance of feature channels in the sliding time window, is the distance threshold; Adjacency Matrix Perform symmetric normalization: ； in, Introduce self-connection for the identity matrix, for The degree matrix of (diagonal elements are the sum of each row), is the normalized adjacency matrix, is the adjacency matrix ; Step 3.4: Graph Structure for: ； in, is the feature matrix of the node ; is the normalized adjacency matrix.

5. The lithium battery SOH estimation method based on a time series graph neural network under physical constraints according to claim 1 is characterized in that: The process of PCC analysis is as follows: calculate the Pearson correlation coefficient between each feature and SOH, and select features with PCC>0.7 as analysis features.

6. The lithium battery SOH estimation method based on a time series graph neural network under physical constraints according to claim 1 or 5, characterized in that: Further: Step 2 specifically includes the following steps: Step 2.1: Extract the average value, standard deviation, peak value, skewness, and root mean square (RMS) features of the current and voltage curves obtained during battery charge and discharge. Step 2.2: Extract charge and discharge IC curve features; Step 2.3: Use Pearson correlation coefficient to analyze the linear relationship between feature data and SOH; The calculation formula for the correlation coefficient is as follows: ； in, is the Pearson correlation coefficient between variables x and y; x and y represent the feature and SOH variables respectively, and are the values ​​of variables x and y at the 𝑖th sample point respectively; and are the means of variables x and y respectively; Step 2.4: Select feature data with a Pearson correlation coefficient greater than 0.7 as analysis features.

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