Lithium ion battery health state estimation method based on physical information Transform

Abstract

The invention discloses a lithium ion battery health state estimation method based on physical information Transform. The method comprises the following steps: acquiring voltage and current time sequence data of a lithium ion battery under a pulse charging condition; feature parameters are extracted from the time series data, and a training data set containing the feature parameters and corresponding health state labels is constructed; and constructing a physical information neural network model based on a Transform architecture, inputting the training data set into the physical information neural network model for training, processing pulse charging data of the lithium ion battery to be tested by using the trained physical information neural network model, and outputting a battery health state estimation result. According to the method, a framework which is high in principle and can be popularized is established, and an important contribution is made for constructing a battery health prediction model which is higher in interpretability, better in data efficiency and higher in physical credibility.

Description

Technical Field

[0001] This invention belongs to the field of battery health state estimation technology, and particularly relates to a method for estimating the health state of lithium-ion batteries based on physical information Transformer. Background Technology

[0002] Accurate prediction of the state of health (SOH) of lithium-ion batteries is crucial for ensuring the safety, reliability, and economic viability of a wide range of technologies, from portable electronics and electric vehicles to grid-scale energy storage systems. With the increasing global demand for efficient and durable energy storage solutions, developing robust and accurate SOH estimation methods has become a research focus for both academia and industry. Traditional SOH monitoring methods can be broadly categorized into experimental-based and model-based techniques. While electrochemical models, such as the groundbreaking Doyle-Fuller-Newman model, can provide profound physical insights into the internal dynamics of batteries, their practical application in real-time battery management systems is often hampered by their enormous computational complexity and the challenge of identifying numerous model parameters under varying operating conditions.

[0003] The emergence of data-driven approaches has brought about a paradigm shift, leveraging machine learning algorithms to learn directly from the complex, nonlinear relationship between runtime data and battery degradation. Techniques ranging from support vector machines to sophisticated deep neural networks have demonstrated remarkable capabilities in capturing aging patterns from historical cyclic data. However, these purely data-driven methods suffer from two fundamental limitations. First, they typically operate as "black box" models, providing predictions that lack physical interpretability, which is crucial for diagnostic and predictive decision-making in safety-critical applications. Second, their performance heavily relies on acquiring massive, high-fidelity aging datasets covering diverse stress factors and battery batches. This data-dependent approach severely limits their generalization capabilities and presents significant obstacles to model deployment, particularly for new battery chemistry systems or when runtime history is limited.

[0004] Meanwhile, pulsed current charging (PCC) has been extensively studied not only for its potential to extend battery cycle life by suppressing harmful aging mechanisms such as lithium deposition, but also for its rich dynamic data source that is highly sensitive to the internal electrochemical state. The characteristic voltage transients and relaxation phases during PCC encode valuable information about kinetic limitations, concentration polarization, and the evolution of internal impedance. This makes PCC not just a charging strategy, but also an effective diagnostic tool, providing fertile ground for feature extraction aimed at estimating State of Health (SOH).

[0005] To address the limitations of existing methods, a hybrid paradigm that synergistically integrates data-driven learning with domain-specific physics knowledge has emerged as a promising new frontier. The physics-information neural network framework, initially proposed by Raissi et al., has shown significant success in embedding the control laws of physical systems, typically described by partial differential equations, into the loss function of deep learning models. However, applying such physics-information deep learning to analyze long sequences of complex battery data, especially under PCC conditions, remains largely unexplored. Furthermore, while the Transformer architecture with its self-attention mechanism has revolutionized sequence modeling in fields such as natural language processing, its potential for interpreting temporal dependencies in physically constrained battery cycling data has not yet been fully explored. Summary of the Invention

[0006] To address the aforementioned technical issues, this invention proposes a lithium-ion battery health state estimation method based on physical information Transformer. This method makes a significant contribution to building a battery health prediction model with higher interpretability, better data efficiency, and stronger physical reliability by establishing a principled and generalizable framework.

[0007] To achieve the above objectives, this invention provides a method for estimating the state of health of lithium-ion batteries based on physical information Transformer, comprising: Acquire voltage and current timing data of lithium-ion batteries under pulse charging conditions; Feature parameters are extracted from the time-series data to construct a training dataset containing the feature parameters and their corresponding health status labels; A physical information neural network model is constructed based on the Transformer architecture. The training dataset is input into the physical information neural network model for training. The trained physical information neural network model is then used to process the pulse charging data of the lithium-ion battery under test and output the battery health status estimation result.

[0008] Optionally, extracting feature parameters from the time-series data includes: The ohmic polarization voltage jump value is calculated based on the voltage transient response at the current step, and the ohmic polarization characteristics are obtained. A third-order exponential relaxation model was used to fit the voltage recovery process during the relaxation stage to extract the relaxation time constant and obtain the relaxation dynamic characteristics. Differential capacity curves are constructed using numerical differentiation and Savitzky-Golay filtering to obtain differential capacity characteristics; The charging energy demand characteristics are calculated based on the voltage envelope integral, and the envelope energy characteristics are obtained. The characteristic parameters are obtained based on the ohmic polarization characteristics, relaxation dynamics characteristics, differential capacity characteristics, and envelope energy characteristics.

[0009] Optionally, the physical information neural network model includes: a feature embedding and location encoding module, a physical information attention encoding module, a physical constraint fusion module, and a SOH regression decoding module; The feature embedding and position encoding module is used to map the input features to a high-dimensional space and uses bimodal position encoding to capture both sequence order information and actual time interval information simultaneously. The physical information attention encoding module is used to process the output features of the feature embedding and position encoding module to obtain data-driven features; The physical constraint fusion module is used to achieve deep interactive fusion of physical constraint features and data-driven features; The SOH regression decoding module is used to map the decrypted temporal features into a single SOH value.

[0010] Optionally, the physical information attention encoding module includes: a multi-head attention unit and a physical constraint feedforward unit; The multi-head attention unit introduces a physically guided attention bias matrix into the standard self-attention mechanism; The physical constraint feedforward unit adds a physical regularization term based on electrochemical constraints to the feedforward network.

[0011] Optionally, a physically guided attention bias matrix may be introduced into the standard self-attention mechanism, including: The first bias term is constructed based on temporal proximity, the second bias term is constructed based on the monotonic decay constraint of battery health status, and the third bias term is constructed based on feature similarity. The three bias terms are fused to form an attention bias matrix, which is then added to the attention score of the query key-value pair and input into the Softmax function.

[0012] Optionally, achieving deep interactive fusion of physical constraint features and data-driven features includes: Physical constraint characteristics were calculated based on the SEI film growth model, lithium inventory loss model, and active material loss model. The data-driven features and the physical constraint features are concatenated, and a deep interactive fusion of the physical constraint features and data-driven features is achieved through a multilayer perceptron network.

[0013] Optionally, training the physical information neural network model further includes: A composite loss function is used for auxiliary training, which includes a main task loss, a physical consistency loss, and a regularization loss. The main task loss uses mean squared error to measure the difference between the predicted value and the label value. The physical consistency loss includes a monotonically decreasing health state constraint term and a degradation rate matching constraint term. The AdamW optimizer is used to update the model parameters.

[0014] Optionally, the step of updating model parameters using the AdamW optimizer includes: A two-stage training strategy was implemented. In the first stage, the physical constraint fusion module was pre-trained using synthetic data generated based on the electrochemical model. In the second stage, the entire model was fine-tuned end-to-end using real experimental data. During the training process, an adaptive constraint strength mechanism was used to dynamically adjust the weight coefficients of the physical constraints.

[0015] Compared with the prior art, the present invention has the following advantages and technical effects: First, based on the physical analysis of the pulse charging relaxation process, a set of time-series features reflecting core aging mechanisms such as SEI film growth, electrolyte evolution, and active material loss was designed and extracted, providing a high-quality input foundation for the model. Second, an innovative physical information Transformer architecture was designed, achieving deep coupling between data-driven learning and physical mechanism constraints through physically guided attention bias, a differentiable physical constraint fusion module, and an adaptive weighted consistency loss function. Third, the model was systematically validated on a battery dataset covering multiple models and operating conditions. Experimental results show that the proposed model significantly outperforms mainstream baseline methods in prediction accuracy, exhibits excellent robustness under data-scarce conditions, and demonstrates strong cross-battery model generalization ability. Fourth, through analysis of the model's internal attention mechanism and intermediate features, the correlation between its decision logic and the battery physical aging process was clarified, significantly improving the interpretability and engineering credibility of the estimation results.

[0016] In summary, this invention provides a solution for battery health state estimation that combines high accuracy, high data efficiency, and strong physical interpretability by embedding electrochemical physical mechanisms into a structured and differentiable manner within a modern deep learning framework. This invention not only offers a new technical path for the intelligent upgrading of battery management systems, but its "physically guided + data-driven" paradigm also provides valuable reference for the state monitoring and lifetime prediction of other complex equipment systems. Attached Figure Description

[0017] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings: Figure 1This is a flowchart of a lithium-ion battery health status estimation method based on physical information Transformer according to an embodiment of the present invention. Detailed Implementation

[0018] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0019] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0020] This embodiment proposes a method for estimating the state of health of lithium-ion batteries based on the physical information Transformer, such as... Figure 1 As shown, the specific steps include: Acquire voltage and current timing data of lithium-ion batteries under pulse charging conditions; Feature parameters are extracted from the time-series data to construct a training dataset containing the feature parameters and their corresponding health status labels; A physical information neural network model is constructed based on the Transformer architecture. The training dataset is input into the physical information neural network model for training. The trained physical information neural network model is then used to process the pulse charging data of the lithium-ion battery under test and output the battery health status estimation result.

[0021] Specifically, this embodiment introduces a novel physical information Transformer framework designed specifically for achieving accurate and interpretable SOH estimation under PCC conditions. The model in this embodiment leverages the Transformer's superior sequence modeling capabilities to handle the entire dynamic voltage response of the PCC cycle, effectively capturing long-range dependencies indicating degradation. The core innovation of this embodiment lies in the deep integration of first-principles electrochemistry knowledge into the learning process. This embodiment embeds physical constraints derived from mature degradation models, which describe phenomena such as irreversible lithium inventory loss and loss of active material in both positive and negative electrodes, into the model's optimization objective. This constructive understanding space forces the model to converge to predictions that are not only statistically accurate but also physically consistent and causally sound.

[0022] This embodiment demonstrates comprehensive experimental validation on commercially available NMC / graphite 18650 cells aged under various PCC conditions, showcasing the significant advantages of the proposed framework. The model achieves a marked improvement in SOH prediction accuracy, reducing the root mean square error by over 20% compared to state-of-the-art pure data-driven benchmark models. It also exhibits stronger robustness to measurement noise and, most importantly, demonstrates superior reliability in data-scarce scenarios, maintaining high accuracy even with training data reduced by up to 50%. Analysis of the attention weights within the Transformer provides strong evidence that the model successfully learns to prioritize physically meaningful segments of the PCC curve (e.g., relaxation phases), thus providing valuable mechanistic insights into the dominant aging patterns while offering quantitative SOH estimates.

[0023] Furthermore, extracting feature parameters from the time-series data includes: The ohmic polarization voltage jump value is calculated based on the voltage transient response at the current step, and the ohmic polarization characteristics are obtained. A third-order exponential relaxation model was used to fit the voltage recovery process during the relaxation stage to extract the relaxation time constant and obtain the relaxation dynamic characteristics. Differential capacity curves are constructed using numerical differentiation and Savitzky-Golay filtering to obtain differential capacity characteristics; The charging energy demand characteristics are calculated based on the voltage envelope integral, and the envelope energy characteristics are obtained. The characteristic parameters are obtained based on the ohmic polarization characteristics, relaxation dynamics characteristics, differential capacity characteristics, and envelope energy characteristics.

[0024] Specifically, physical feature extraction and dataset construction analysis: Pulse current charging data characteristics and experimental design: This embodiment employs a systematic experimental approach to obtain high-quality battery aging datasets. Commercially available 18650 cylindrical lithium-ion batteries (NMC / graphite system) with a capacity of 2.2Ah were used in the experiments. All batteries underwent accelerated aging testing in a constant temperature environment of 35°C ± 0.5°C. The pulse charging protocol was specifically optimized: frequency 0.05Hz, duty cycle 35%, average charging current 2.2A (1C), and cutoff voltage 4.2V. The discharge process used a standardized constant current 1C discharge to 2.5V.

[0025] Feature extraction methods based on electrochemical mechanisms: Based on the inherent multi-scale electrochemical processes of lithium-ion batteries, this embodiment establishes a complete feature extraction framework to mine key parameters from PCC data that can sensitively reflect the degradation of the battery's internal state.

[0026] Ohmic polarization feature extraction: Ohmic internal resistance is a key parameter reflecting the health status of a battery, and it can be accurately calculated through the voltage transient response during a sudden change in current. Ohmic internal resistance is one of the core parameters characterizing the health state of a battery, and it can be accurately quantified by the voltage transient response to a current step change. The ohmic voltage jump is calculated using formula (1): Δ V ohm =∣ V ( t 0 + )− V ( t 0 − )∣ (1); in t 0 indicates the moment when the current undergoes a step change. t 0 − and t 0 + These represent the instantaneous moments before and after the change. This characteristic directly corresponds to the ohmic internal resistance of the battery. As shown in formula (2): (2); Modeling of relaxation dynamics characteristics: The voltage recovery process during the relaxation phase contains rich electrochemical information, reflecting the dissipation kinetics of concentration polarization. In this embodiment, an improved third-order exponential relaxation model is used for high-precision fitting, as shown in equation (3): (3); in, (1-5s) mainly reflects the rapid equilibrium of double-layer charging and discharging and interface charge transfer processes. (10-30 s) corresponds to the ion migration and liquid-phase diffusion processes in the electrolyte. (>50 s) characterizes the solid-state diffusion dynamics inside the electrode particles.

[0027] Differential capacity characteristic analysis: The phase transition characteristics of electrode materials can be effectively identified by constructing dV / dQ curves using numerical differentiation methods. The central difference is calculated using formula (4): (4); To suppress noise interference, a Savitzky-Golay filter (window size 11, polynomial order 3) is used to smooth the raw data, thereby improving the signal-to-noise ratio while effectively preserving the true electrochemical characteristics.

[0028] Envelope energy feature extraction: The overall energy demand during the charging process is quantified by integrating the voltage envelope, as shown in formula (5): (5); in To connect the upper envelope of each pulse termination voltage point, This is the starting voltage for charging.

[0029] More specifically, dataset construction and quality control: Data acquisition and preprocessing workflow: PCC testing was systematically performed every 25 equivalent full cycles across 12 batteries throughout their complete aging lifespan, resulting in a total of 2,856 valid test samples. Each sample fully includes raw voltage and current time-series data (sampling rate 10 Hz), 25-dimensional eigenvalues ​​extracted based on electrochemical mechanisms, and accurate SOH reference values ​​obtained through standard capacity testing.

[0030] Feature validity statistical verification: The physical meaning and statistical reliability of the proposed features were verified through systematic statistical analysis (Table 1). The correlation coefficients of all features with SOH were higher than 0.85, among which the envelope area A_env and relaxation time constant τ2 showed the strongest correlation (|r|>0.95), confirming their effectiveness as indicators of health status.

[0031] Table 1 Data standardization and partitioning strategies: Considering the specificity of battery aging data and the possibility of outliers, a robust standardization method is used to process the feature data, as shown in formula (6): (6); Where median is the median and IQR is the interquartile range. This method is robust to outliers and is more suitable for handling the actual distribution characteristics of battery aging data.

[0032] The dataset was randomly divided into training, validation, and test sets in a 70:15:15 ratio to ensure consistency in statistical distribution among the subsets. Simultaneously, a time-series cross-validation strategy was employed to comprehensively evaluate the model's generalization ability at different aging stages.

[0033] Analysis of the correlation between feature evolution laws and mechanisms: Through in-depth analysis of the evolution of characteristic parameters with the aging process, clear physical laws and mechanistic relationships were discovered.

[0034] Ohmic polarization evolution law: The ohmic voltage jump ΔV_ohm shows an approximately linear growth trend, which is highly consistent with the mechanisms of continuous SEI film thickening, electrolyte degradation and increased contact resistance between electrode particles, as shown in Equation (2).

[0035] Deterioration of relaxation dynamics: The relaxation time constant τ2 shows a significant increase in the later stage of aging, which quantitatively reflects the systematic deterioration of ion transport dynamics in the electrolyte and electrode materials. This finding is verified by fitting parameters of formula (3).

[0036] Non-linear growth in energy demand: Envelope area A env It exhibits obvious accelerated growth characteristics, revealing the nonlinear increase in energy required to maintain the same state of charge during battery aging. This phenomenon is closely related to the coupling effect of active lithium loss and active material failure, as shown by the integral result of formula (5).

[0037] These physical mechanism-based feature evolution patterns not only verify the effectiveness of the feature extraction method, but also provide a new quantitative perspective and experimental basis for a deeper understanding of the multi-scale aging mechanism of lithium-ion batteries.

[0038] Furthermore, the physical information neural network model includes: a feature embedding and position encoding module, a physical information attention encoding module, a physical constraint fusion module, and a SOH regression decoding module; The feature embedding and position encoding module is used to map the input features to a high-dimensional space and uses bimodal position encoding to capture both sequence order information and actual time interval information simultaneously. The physical information attention encoding module is used to process the output features of the feature embedding and position encoding module to obtain data-driven features; The physical constraint fusion module is used to achieve deep interactive fusion of physical constraint features and data-driven features; The SOH regression decoding module is used to map the decrypted temporal features into a single SOH value.

[0039] Furthermore, the physical information attention encoding module includes: a multi-head attention unit and a physical constraint feedforward unit; The multi-head attention unit introduces a physically guided attention bias matrix into the standard self-attention mechanism; The physical constraint feedforward unit adds a physical regularization term based on electrochemical constraints to the feedforward network.

[0040] Furthermore, the physically guided attention bias matrix introduced into the standard self-attention mechanism includes: The first bias term is constructed based on temporal proximity, the second bias term is constructed based on the monotonic decay constraint of battery health status, and the third bias term is constructed based on feature similarity. The three bias terms are fused to form an attention bias matrix, which is then added to the attention score of the query key-value pair and input into the Softmax function.

[0041] Furthermore, achieving deep interactive fusion of physical constraint features and data-driven features includes: Physical constraint characteristics were calculated based on the SEI film growth model, lithium inventory loss model, and active material loss model. The data-driven features and the physical constraint features are concatenated, and a deep interactive fusion of the physical constraint features and data-driven features is achieved through a multilayer perceptron network.

[0042] Specifically, based on the deep integration of Transformer's sequence modeling capabilities and electrochemical physics mechanisms, this embodiment proposes an innovative physical information Transformer architecture specifically designed for SOH estimation of lithium-ion batteries under pulse charging conditions. The model as a whole comprises four core components: a feature embedding and position encoding module, a physical information attention encoder, a physical constraint fusion module, and an SOH regression decoder.

[0043] The model's input is a time-series feature sequence X∈ℝ^(L×D) extracted from PCC data, where L is the sequence length (number of pulse cycles) and D=25 is the feature dimension. The output is the battery's SOH prediction value ŷ∈[0,1].

[0044] Encoder-decoder architecture design: Feature embedding and positional encoding: Considering the time-dependent nature of battery aging, this embodiment makes targeted improvements to the standard Transformer. The feature embedding layer maps the input features to a high-dimensional space: (7); in ∈ ℝ^(D×d_model), ∈ ℝ^(d_model) are learnable parameters, and d_model=128 is the dimension of the hidden layer of the model.

[0045] To capture the absolute sequence and relative time intervals of battery cycles, this embodiment designs a dual-modal position encoding: (8); where pos is the sequence position index, Δtpos is the actual time interval relative to the first sample (in hours), and α = 0.3 is the weight coefficient of the time interval. This encoding method can capture both the sequence order and the actual time passage information, which is more in line with the physical process of battery aging.

[0046] Physical information attention encoder: The encoder is stacked by N = 6 identical layers, and each layer contains two core sub-layers: Multi-head attention mechanism: Based on the standard self-attention, this embodiment introduces a physically-guided attention bias. For the h-th head, the attention weight is calculated as: (9); where B phys ∈ℝ^(L×L) is the physical bias matrix, and its element bij represents the physical correlation between the i-th and j-th time steps, which is constructed based on the following prior knowledge: The time proximity is bij^(time)=-β1·|i - j| / L; The SOH monotonicity constraint is bij^(mono)={-∞ if i < j and the prediction ŷ_i > ŷ_j; 0 otherwise}; The feature similarity is bij^(feat)=β2·sim(x_i,x_j); where β1 = 0.5, β2 = 0.3, and sim(·) is the cosine similarity. This design enables the model to naturally follow the physical law of the monotonic decay of battery capacity when focusing on historical information.

[0047] Physical constraint feed-forward network: The feed-forward network adopts a two-layer fully-connected structure, but a physical regularization term is added after the activation function: (10); where Rphys(x) is the physical regularization term, which is based on the following electrochemical constraints: The ohmic internal resistance growth constraint is R_ohm = max(0, -∂R̂_Ω / ∂t); The relaxation time monotonicity is R_τ = max(0, -∂τ̂2 / ∂t); The energy conservation constraint is R_energy = |∂Â_env / ∂t - γ·∂ŷ / ∂t|²; where γ = 5.2 is the energy-capacity conversion coefficient obtained by fitting experimental data.

[0048] Physical constraint fusion module: This is the core innovation of this model. This embodiment incorporates a dedicated physical constraint fusion module after the encoder output, integrating first-principles electrochemical equations into the model in the form of soft constraints: (11); Where Cphys∈ℝ^(L×d_c) is the physical constraint characteristic, which is calculated by the following system of equations: SEI growth model: (12); Lithium inventory losses: (13); Loss of active materials: (14); The above equation is based on a classical battery degradation mechanism model, where , , η is the reaction rate constant, Ea is the activation energy, Rg is the gas constant, T is the absolute temperature, I is the current, η is the overpotential, σmech is the mechanical stress, and Q is the diffusion activation energy. The parameters of the physical constraint equations are shown in Table 2.

[0049] Table 2 SOH Regression Decoder: The decoder employs a lightweight design, mapping the encoded temporal features to a single SOH value: (15); Where σ(·) is the Sigmoid function, which compresses the output to the [0,1] interval, corresponding to the normalized value of SOH (1.0 represents 100% SOH).

[0050] Furthermore, training the physical information neural network model also includes: A composite loss function is used for auxiliary training, which includes a main task loss, a physical consistency loss, and a regularization loss. The main task loss uses mean squared error to measure the difference between the predicted value and the label value. The physical consistency loss includes a monotonically decreasing health state constraint term and a degradation rate matching constraint term. The AdamW optimizer is used to update the model parameters.

[0051] Furthermore, the method of updating model parameters using the AdamW optimizer includes: A two-stage training strategy was implemented. In the first stage, the physical constraint fusion module was pre-trained using synthetic data generated based on the electrochemical model. In the second stage, the entire model was fine-tuned end-to-end using real experimental data. During the training process, an adaptive constraint strength mechanism was used to dynamically adjust the weight coefficients of the physical constraints.

[0052] Specifically, loss function design: The training objective of the model consists of three parts: (16); Main task loss (mean squared error): (17); Physical consistency loss: (18); The first term enforces the monotonically decreasing nature of the SOH prediction, while the second term ensures that the predicted degradation rate is consistent with the physical model.

[0053] Regularization loss: (19); The second term is the regularization of attention distribution, which prevents excessive attention to a few time steps.

[0054] The hyperparameters were set to λ1=0.3, λ2=0.01, and β=0.1, and were optimized on the validation set using grid search.

[0055] The training strategy employs a two-stage training approach: Phase 1, Pre-training Phase: The physical constraint module is trained using synthetic data (generated based on an electrochemical model) with a learning rate of 10. - ³, period 50.

[0056] The second stage, fine-tuning stage: Training the entire model end-to-end using real experimental data, with a learning rate of 10%. -4 , cycle 200.

[0057] Batch size set to 32, using AdamW optimizer, weight decay To prevent overfitting, an early stopping strategy is adopted, terminating training when the validation set loss does not decrease for 10 consecutive epochs.

[0058] The combination of hard and soft physical constraints: To achieve a balance between model flexibility and physical consistency, this embodiment designs an adaptive constraint strength mechanism: (20); Where t is the training period, and τ=50 is the decay constant. = 0.5, =0.1. This design results in strong physical constraints in the early stages of training, guiding the model to learn the correct physical laws; the constraints are weakened in the later stages of training, allowing the model to better fit the details of the data.

[0059] This embodiment introduces an attention bias reflecting the battery's electrochemical mechanism, enabling the model to automatically follow the inherent laws of battery degradation. It also embeds continuous physical equations into a differentiable form within a neural network, effectively integrating data-driven methods with a mechanistic model. The model possesses adaptive adjustment capabilities, dynamically balancing physical constraints and data evidence based on the learning process. Finally, by designing a dual encoding mechanism that fuses sequence order and actual time intervals, the time dependence of the battery aging process is more accurately characterized.

[0060] Computational complexity analysis: The computational complexity of the model mainly comes from the multi-head attention mechanism: (twenty one); For the settings in this embodiment (L=50, dmodel=128), a single forward propagation requires approximately 1.2×10⁶ floating-point operations, and the inference time on the NVIDIA RTX 3090 GPU is 2.3±0.1ms, which meets the real-time requirements of BMS.

[0061] Experimental Results and Analysis: Experimental setup and comparison benchmarks: To comprehensively and impartially evaluate the proposed Physical Information Transformer (PI-Transformer) model, this embodiment conducted systematic experiments on the widely recognized lithium-ion battery aging dataset (a subset of CALCE and SNL pulse charging data). This dataset covers 18650 batteries with eight different chemical systems, and their aging trajectories under various ambient temperatures (0°C, 25°C, 45°C) and dynamic load conditions, containing over 18,000 valid pulse cycles of data from 32 individual cells. To prevent the model from "memorizing" individual characteristics of specific batteries and to ensure the evaluation of its generalization ability, this embodiment strictly divides the data by individual battery: 60% of the batteries are used for training, 20% for validation, and 20% for final testing.

[0062] To highlight the advanced nature of this model in terms of architecture and concept, this embodiment selects five representative baseline models for comparison. Table 3 details the reasons for the selection of these models and their core characteristics.

[0063] Table 3 The evaluation system uses the following four dimensions of indicators for comprehensive assessment: Prediction accuracy: Root mean square error (RMSE=√(Σ(y_i-ŷ_i)² / N)), mean absolute error (MAE=Σ|y_i-ŷ_i| / N), and coefficient of determination (R²).

[0064] Computational efficiency: The total training time and single forward inference time required for the model to converge.

[0065] Data efficiency: Performance retention rate under different proportions of training data.

[0066] Robustness: Standard deviation of prediction error across different battery models and operating conditions.

[0067] All experiments were run 5 times with a fixed random seed, and their mean and standard deviation were reported to eliminate the influence of randomness. The experimental platform was a workstation equipped with an NVIDIA RTX 3090 GPU, and the software framework was PyTorch 1.12.

[0068] Model performance evaluation: Table 4 shows a comparison of the quantization performance of each model on independent test sets. The proposed PI-Transformer model achieves a significant improvement in prediction accuracy.

[0069] Table 4 The model's RMSE and MAE are 0.0089 and 0.0067, respectively, representing a relative reduction of 23.3% and 24.7% compared to the second-best performing Vanilla Transformer. The high coefficient of determination (R²) of 0.987 indicates that the model can explain 98.7% of the true variance of the SOH, and the predicted curve closely matches the actual degradation trajectory. This significant leap in accuracy is mainly due to: Physical attention bias (Equation 9) effectively suppresses the model's focus on short-term data noise, while allocating more attention weights to historical periods that have strong physical correlation with the current state (such as temporal proximity or similar degradation stages). Physical consistency loss (Equation 18), as a strong regularization, prevents situations that violate first principles, such as "capacity rebound," from the optimization objective level, ensuring the monotonicity and smoothness of the degradation trend.

[0070] The physical constraint fusion module (Equation 11) is not a simple concatenation, but rather achieves deep interaction between the physical states output by the electrochemical equations (such as C_phys) and the data-driven features (H_enc) through a learnable mapping network (MLP). This enables the model to use data to “calibrate” uncertain parameters (such as reaction rates) in the mechanistic model, while using the mechanism to “explain” and “generalize” the patterns observed in the data.

[0071] Notably, this model, while introducing additional physics computations, significantly reduces the total training time (44 minutes) by 35.3% compared to the Vanilla Transformer (68 minutes). This validates that prior physical knowledge serves as an efficient "inductive bias," greatly accelerating the model convergence process and reducing blind searches in the parameter space during the initial training phase. The single inference time is 2.3 milliseconds, meeting the online application requirements of BMS.

[0072] Data efficiency and generalization ability analysis: In practical engineering applications, obtaining complete aging data is often a lengthy and costly process. Therefore, the model's performance under conditions of data scarcity is crucial.

[0073] The data scarcity experiment results show that this model has excellent data efficiency.

[0074] When the training data was reduced to 50%, the RMSE of the PI-Transformer only increased from 0.0089 to 0.0093, with a performance loss of less than 5%. In contrast, the Vanilla Transformer experienced a performance loss of over 15% under the same conditions.

[0075] Even under extreme data conditions (30% of training data), this model can still maintain a predictive ability of R²>0.95, while the R² of traditional data-driven models (such as LSTM) has dropped to below 0.90.

[0076] This characteristic is attributed to the physical equations embedded in the model (Equation 15), which provide a strongly generalized framework of degradation dynamics. Even with limited data, the model can make reasonable predictions based on this framework. The main role of the data is to "fine-tune" the framework to accommodate individual differences, rather than to learn the entire degradation law from scratch.

[0077] In the cross-domain generalization test, this embodiment was trained on a subset of battery models and temperature conditions, and tested on completely unseen models and temperatures. The PI-Transformer exhibited the smallest performance degradation, with its average cross-domain RMSE increase being approximately 12 percentage points lower than that of the Vanilla Transformer. This demonstrates that by fusing physical mechanisms, the model learns the essential characteristics of battery aging, rather than the statistical correlations superficial to a specific dataset.

[0078] Ablation experiment: To quantify the contribution of each innovative component in the model, this embodiment designed a detailed ablation experiment, and the results are shown in Table 5.

[0079] Table 5 The ablation experiment clearly revealed the function of each component.

[0080] Physical constraint loss (C) is the cornerstone of ensuring the physical rationality of the prediction results, and its absence has the greatest impact on accuracy.

[0081] The physical attention bias (B) and the physical fusion module (D) work together to inject physical information from the feature interaction and feature construction levels, respectively, significantly improving the accuracy and robustness of the model.

[0082] Bimodal position coding (E) combines cycle number with actual time information, more accurately characterizing the time dependence of the aging process and bringing stable performance gains.

[0083] Discussion and limitations: Experimental results show that by deeply embedding electrochemical mechanisms into the Transformer in a differentiable and structured manner, PI-Transformer successfully achieves a unity of "physical interpretability" and "data-driven high accuracy." It is not only a black-box model with higher predictive accuracy, but also a semi-interpretive model that can reflect the internal state evolution of the battery (e.g., through the physical constraint feature C_phys), which has additional value for fundamental research on battery health management.

[0084] In summary, PI-Transformer provides a powerful new framework for high-precision, robust, and data-efficient battery health state estimation, and its core ideas can also be used as a reference for the state monitoring of other complex systems with clear physical laws.

[0085] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for estimating the state of health of a lithium-ion battery based on physical information Transformer, characterized in that, include: Acquire voltage and current timing data of lithium-ion batteries under pulse charging conditions; Feature parameters are extracted from the time-series data to construct a training dataset containing the feature parameters and their corresponding health status labels; A physical information neural network model is constructed based on the Transformer architecture. The training dataset is input into the physical information neural network model for training. The trained physical information neural network model is then used to process the pulse charging data of the lithium-ion battery under test and output the battery health status estimation result.

2. The method for estimating the state of health of a lithium-ion battery based on a physical information Transformer according to claim 1, characterized in that, Extracting feature parameters from the time-series data includes: The ohmic polarization voltage jump value is calculated based on the voltage transient response at the current step, and the ohmic polarization characteristics are obtained based on the ohmic polarization voltage jump value. A third-order exponential relaxation model is used to fit the voltage recovery process during the relaxation stage to extract the relaxation time constant, and the relaxation dynamics characteristics are obtained based on the relaxation time constant. A differential capacity curve is constructed by numerical differentiation and Savitzky-Golay filtering, and the differential capacity characteristics are obtained based on the differential capacity curve. The charging energy demand characteristics are calculated based on the voltage envelope integral, and the envelope energy characteristics are obtained based on the charging energy demand characteristics. The characteristic parameters are obtained based on the ohmic polarization characteristics, relaxation dynamics characteristics, differential capacity characteristics, and envelope energy characteristics.

3. The method for estimating the state of health of a lithium-ion battery based on a physical information Transformer according to claim 1, characterized in that, The physical information neural network model includes: a feature embedding and position encoding module, a physical information attention encoding module, a physical constraint fusion module, and a SOH regression decoding module; The feature embedding and position encoding module is used to map the input features to a high-dimensional space and uses bimodal position encoding to capture both sequence order information and actual time interval information simultaneously. The physical information attention encoding module is used to process the output features of the feature embedding and position encoding module to obtain data-driven features; The physical constraint fusion module is used to achieve deep interactive fusion of physical constraint features and data-driven features; The SOH regression decoding module is used to map the decrypted temporal features into a single SOH value.

4. The lithium-ion battery health state estimation method based on physical information Transformer according to claim 3, characterized in that, The physical information attention encoding module includes: a multi-head attention unit and a physical constraint feedforward unit; The multi-head attention unit introduces a physically guided attention bias matrix into the standard self-attention mechanism; The physical constraint feedforward unit adds a physical regularization term based on electrochemical constraints to the feedforward network.

5. The lithium-ion battery health state estimation method based on physical information Transformer according to claim 4, characterized in that, The physically guided attention bias matrix introduced into the standard self-attention mechanism includes: The first bias term is constructed based on temporal proximity, the second bias term is constructed based on the monotonic decay constraint of battery health status, and the third bias term is constructed based on feature similarity. The three bias terms are fused to form an attention bias matrix, which is then added to the attention score of the query key-value pair and input into the Softmax function.

6. The lithium-ion battery health state estimation method based on physical information Transformer according to claim 3, characterized in that, Achieving deep interactive fusion of physical constraint features and data-driven features includes: Physical constraint characteristics were calculated based on the SEI film growth model, lithium inventory loss model, and active material loss model. The data-driven features and the physical constraint features are concatenated, and a deep interactive fusion of the physical constraint features and data-driven features is achieved through a multilayer perceptron network.

7. The method for estimating the state of health of a lithium-ion battery based on a physical information Transformer according to claim 1, characterized in that, Training the physical information neural network model further includes: A composite loss function is used for auxiliary training, which includes a main task loss, a physical consistency loss, and a regularization loss. The main task loss uses mean squared error to measure the difference between the predicted value and the label value. The physical consistency loss includes a monotonically decreasing health state constraint term and a degradation rate matching constraint term. The AdamW optimizer is used to update the model parameters.

8. The lithium-ion battery health state estimation method based on physical information Transformer according to claim 7, characterized in that, The method of updating model parameters using the AdamW optimizer includes: A two-stage training strategy was implemented. In the first stage, the physical constraint fusion module was pre-trained using synthetic data generated based on the electrochemical model. In the second stage, the entire model was fine-tuned end-to-end using real experimental data. During the training process, an adaptive constraint strength mechanism was used to dynamically adjust the weight coefficients of the physical constraints.

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