Construction and application method of lithium ion battery health state prediction model

Abstract

The invention provides a construction and application method of a lithium ion battery health state prediction model, the lithium ion battery health state prediction model comprises a double-branch solution network and a dynamic network, and the solution network comprises an encoder and a predictor which are connected in sequence. The method comprises the following steps: inputting battery operation data into an encoder for encoding to obtain potential features, outputting an SOH predicted value through a predictor according to the potential features, calculating a time gradient and a space gradient of the SOH predicted value, and splicing the battery operation data, the time gradient, the SOH predicted value and the space gradient to obtain spliced features; the splicing features are input into a dynamic network to output a nonlinear function item, a PDE residual error is constructed based on the difference value of the time gradient and the nonlinear function item, and a loss function of the lithium ion battery health state prediction architecture is a weighted value of PDE residual error loss, data loss and physical monotonicity loss and can be used for predicting the SOH of the lithium ion battery.

Description

Technical Field

[0001] This application relates to the field of energy storage, and in particular to a method for constructing and applying a health status prediction model for lithium-ion batteries. Background Technology

[0002] Lithium-ion batteries, with their advantages of high energy density and long cycle life, have become the core energy storage unit in key fields such as new energy vehicles and energy storage power stations. However, during long-term service, lithium batteries are affected by irreversible mechanisms such as electrochemical corrosion, SEI film growth, and lithium dendrite deposition, which gradually lead to capacity decay and internal resistance increase. Their State of Health (SOH) directly determines the operational safety, range, and residual value of the energy storage system. Therefore, how to achieve stable, accurate, and physically reliable estimation of SOH under complex operating conditions (such as dynamic charge and discharge rates and extreme temperature fluctuations) and limited observation conditions (such as sparse sampling and sensor noise) has become a core scientific and engineering problem that battery management systems urgently need to solve.

[0003] Currently, numerous data-driven models have been proposed for predicting the state of health (SOH) of lithium batteries. These models achieve high prediction accuracy by exploring the statistical relationship between voltage, current, and their derived features and SOH. However, these methods essentially treat SOH estimation as a black-box regression problem, lacking explicit modeling of the physical constraints of the degradation process. Their generalization ability is highly dependent on the distribution of training data. Once the operating conditions change or the amount of data is insufficient, the model performance often degrades significantly. The prediction results may even exhibit non-monotonic recovery phenomena that violate physical common sense, severely limiting their application in safety-critical systems.

[0004] To address the limitations of generalization in lithium-ion battery state of health prediction tasks when data is scarce or noise is high, existing solutions employ Physically Informed Neural Networks (PINNs) to introduce physical constraints into the data-driven learning process. While PINNs have significant potential in battery modeling, their application in practical SOH prediction tasks still faces a series of key challenges: First, the multi-objective optimization conflict problem: Traditional PINN usually adopts a joint training method in which the solution function and the dynamic function share the same optimizer. This leads to gradient conflicts and training instability in complex degradation scenarios, which manifests as slow convergence speed, high sensitivity of results to initialization and loss weights, and even significant performance degradation under different charging and discharging protocols.

[0005] Second, low sensitivity to key features of degradation dynamics: Existing methods still utilize physical information to a limited extent. Most studies only introduce the residuals of partial differential equations as a soft constraint into the loss function, without fully exploring higher-order physical information such as the rate of state change. This results in the model lacking sufficient physical sensitivity when facing degradation inflection points or abrupt changes in degradation rate. Traditional PINN only uses (x, t, u) as dynamic input and is insensitive to the rate of change of state OH.

[0006] Third, weak constraints on fundamental physical laws and engineering unreliability: The fundamental physical law that SOH decreases monotonically over time is not explicitly constrained in many PINN models, and the prediction results may still show local rebound phenomena that violate physical common sense, which seriously restricts the usability of the model in engineering practice.

[0007] Further analysis by our team revealed that the root cause of the aforementioned problem is not insufficient complexity of the physical information neural network structure, but rather that traditional PINN implicitly treats SOH prediction as a single-objective optimization problem. However, PINN actually undertakes multiple tasks: ensuring the accuracy of fitting the observed data, satisfying the physical consistency of unknown degradation dynamics, and adhering to the fundamental physical constraints of battery degradation. Simply superimposing these objectives onto the same loss function and training through a single optimization path often leads to interference between different objectives, thereby weakening the actual role of physical constraints in model learning. Summary of the Invention

[0008] This application provides a method for constructing and applying a lithium-ion battery health state prediction model. It systematically solves three major problems in physical information neural networks: optimization conflict, insufficient physical sensitivity, and weakened constraints, and achieves high-precision, strong physical consistency, and engineering-deployable battery health state prediction.

[0009] In a first aspect, embodiments of this application provide a method for constructing a lithium-ion battery health status prediction model, comprising the following steps: The full-cycle battery operation data of lithium-ion batteries under different operating conditions is obtained as training data. The battery operation data includes voltage characteristic data, current characteristic data, temperature characteristic data, and time cycle number characteristic data. Training data is input into a lithium-ion battery health state prediction architecture to train a lithium-ion battery health state prediction model. The lithium-ion battery health state prediction architecture includes a two-branch solution network and a kinetic network. The solution network includes an encoder and a predictor connected in sequence. Battery operating data is input into the encoder to encode latent features. The latent features are then passed through the predictor to output SOH prediction values. The temporal and spatial gradients of the SOH prediction values ​​are calculated. The battery operating data, temporal gradient, SOH prediction values, and spatial gradients are concatenated to obtain concatenated features. The concatenated features are input into the kinetic network to output a nonlinear function term. The PDE residual is constructed based on the difference between the temporal gradient and the nonlinear function term. The loss function of the lithium-ion battery health state prediction architecture is a weighted value of the PDE residual loss, data loss, and physical monotonicity loss.

[0010] Secondly, embodiments of this application provide a method for predicting the state of health (SOH) of a lithium-ion battery, comprising: collecting operational data of the lithium-ion battery; inputting the operational data into the lithium-ion battery state of health prediction model constructed by the method described above, and outputting a predicted SOH value.

[0011] The main contributions and innovations of this invention are as follows: First, the lithium-ion battery health state prediction model constructed in this scheme adopts the sub-objective decoupling optimization (SDO) paradigm, which decouples the decoupling network and the dynamic network. The essence of lithium-ion battery SOH prediction is a prediction problem with strong physical constraints and weak data signals. The data is often sparse and noisy, while physical laws (degradation dynamics) dominate. To address the gradient conflict problem, this scheme is the first to achieve complete decoupling of the parameter update paths of the solution function network and the dynamic network in the framework of physical information neural network. Each network is equipped with an independent optimizer and is coupled only at the functional level through physical residuals, thus avoiding training instability caused by multi-objective gradient conflicts from the root.

[0012] Secondly, this scheme explicitly inputs the state gradient of the SOH prediction value of the solution network into the dynamic network to realize the gradient-enhanced physical modeling mechanism (GEI). Lithium battery degradation also has a key characteristic: it does not decrease smoothly. These rates of change are the key to errors. To address the problem of physical insensitivity, the scheme innovatively injects the gradient information of the state gradient of the solution function as an explicit input into the dynamic network, enabling the model to directly sense and respond to the rate of change of SOH, thereby achieving accurate capture of the degradation inflection point. This achieves "high-precision prediction under scarce data": battery aging data is often sparse and expensive, but high accuracy is maintained even with limited data, reducing data acquisition costs.

[0013] Third. This scheme also introduces a Physics-Guided Constrained Learning Framework (PGCL) with physical monotonicity loss: different lithium-ion battery packs have different training methods, resulting in different battery complexities. To address the constraint softening problem, this framework includes two collaborative designs: (a) introducing physical monotonicity loss, which transforms non-differentiable inequality constraints into differentiable hinge-type penalty terms through constraint relaxation techniques, "actively preventing" non-physical rebounds during training; (b) an adaptive weight loss balancing strategy, which dynamically adjusts the adaptive weights of different loss terms based on the loss, achieving an intelligent balance between data fitting and physical constraints, and improving the model's generalization ability.

[0014] Details of one or more embodiments of this application are set forth in the following drawings and description to make other features, objects and advantages of this application more readily apparent. Attached Figure Description

[0015] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments of this application and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings: Figure 1 This is an architecture diagram of a lithium-ion battery health status prediction model according to an embodiment of this application.

[0016] Figure 2 This is a violin distribution plot of MAE, MAPE, and R² for the four models on the dataset.

[0017] Figure 3 These are the SOH prediction results of the PR-PINN model for 6 batches.

[0018] Figures 4 to 6 These are ablation experiment diagrams for various model variants.

[0019] Figure 7 This is a schematic diagram of the hardware structure of an electronic device according to an embodiment of this application. Detailed Implementation

[0020] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numerals in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with one or more embodiments of this specification. Rather, they are merely examples of apparatuses and methods consistent with some aspects of one or more embodiments of this specification as detailed in the appended claims.

[0021] It should be noted that the steps of the corresponding methods are not necessarily performed in the order shown and described in this specification in other embodiments. In some other embodiments, the methods may include more or fewer steps than described in this specification. Furthermore, a single step described in this specification may be broken down into multiple steps in other embodiments; and multiple steps described in this specification may be combined into a single step in other embodiments.

[0022] Example 1 Figure 1 This is an architecture diagram of the lithium-ion battery health status prediction model proposed in this solution, as shown below. Figure 1 As shown, this scheme proposes a method for constructing a lithium-ion battery health state prediction model, including the following steps: The full-cycle battery operation data of lithium-ion batteries under different operating conditions is obtained as training data. The battery operation data includes voltage characteristic data, current characteristic data, temperature characteristic data, and time cycle number characteristic data. Training data is input into a lithium-ion battery health state prediction architecture to train a lithium-ion battery health state prediction model. The lithium-ion battery health state prediction architecture includes a two-branch solution network and a kinetic network. The solution network includes an encoder and a predictor connected in sequence. Battery operating data is input into the encoder to encode latent features. The latent features are then passed through the predictor to output SOH prediction values. The temporal and spatial gradients of the SOH prediction values ​​are calculated. The battery operating data, temporal gradient, SOH prediction values, and spatial gradients are concatenated to obtain concatenated features. The concatenated features are input into the kinetic network to output a nonlinear function term. The PDE residual is constructed based on the difference between the temporal gradient and the nonlinear function term. The loss function of the lithium-ion battery health state prediction architecture is a weighted value of the PDE residual loss, data loss, and physical monotonicity loss.

[0023] From a systems theory perspective, the state-of-the-art (SOH) evolution of lithium-ion batteries can be abstracted as a controlled degradation dynamic system. Its state updates are dominated by unknown degradation dynamics and influenced by both external operating conditions and intrinsic material properties. This controlled degradation dynamic system corresponding to SOH evolution possesses three core properties: irreversibility, weak observability, and strong physical prior constraints. In other words, SOH evolution is a physically constrained system identification problem, not a simple function fitting problem. Although physical information neural networks (PINs) introduce physical control equation residuals into the loss function to ensure that the prediction model simultaneously satisfies data fitting and physical consistency constraints during training, traditional PINs still exhibit problems such as training instability, slow convergence, and even failure of physical constraints when applied to SOH prediction scenarios.

[0024] Our team delved into the mechanisms of traditional physical information neural networks (PINs), discovering that they typically use a single optimizer to jointly train data loss, physical residual loss, and regularization terms with linear weights. This approach implicitly assumes that the gradient directions of each loss term in the parameter space are roughly consistent. However, in SOH degradation modeling of lithium-ion batteries, the data fitting objective often tends to capture local statistical fluctuations, while the physical residual objective attempts to constrain the overall dynamic structure. These two objectives frequently conflict in the gradient space. When gradient directions cancel each other out or oscillate, the optimization process becomes highly unstable and extremely sensitive to the setting of loss weights. Furthermore, in traditional PINs, the solution function network and the dynamics network usually share parameter update paths, forcing the PIN to learn degradation dynamics while fitting state variables. This strongly coupled structure may be feasible when data is plentiful, but in the small-sample, high-noise scenarios of SOH prediction for lithium-ion batteries, it easily leads to the dynamics learning being dominated by data noise, thus weakening the actual effect of physical constraints.

[0025] Based on the problems existing in the application of traditional physical information neural networks to predict the state of health (SOH) of lithium-ion batteries, this solution specifically designs a lithium-ion battery health state prediction model suitable for predicting the SOH of lithium-ion batteries. This lithium-ion battery health state prediction model abandons the single architecture of the traditional physical information neural network and instead adopts a dual network structure in which the decoupling network and the dynamic network are independent yet logically coupled, thereby decoupling and optimizing the traditional physical information neural network and applying physical guidance constraints.

[0026] Specifically, the lithium-ion battery health state prediction model of this scheme adopts a dual-branch structure of solution network and kinetic network. The time gradient of the SOH prediction value output by the solution network and the difference of the nonlinear function term are used to construct the PDE residual, and then the solution network and kinetic network are optimized in a coordinated manner.

[0027] Regarding the training data for this scheme: This solution acquires full-cycle battery operation data of multiple lithium-ion batteries under different operating conditions as training data. The full-cycle battery operation data covers the entire process of lithium-ion batteries from initial service state to capacity decay to failure threshold.

[0028] In some embodiments, the failure threshold refers to the threshold at which a lithium-ion battery fails, typically 80% of its capacity.

[0029] In some embodiments, different operating conditions refer to operating conditions with different ambient temperatures and discharge rates. That is, the core variables of the different operating conditions selected in this scheme for the training data are ambient temperature and discharge rate. These two types of factors are key coupled factors affecting the degradation rate of lithium-ion batteries, and are also the core scenarios for verifying the model's ability to generalize across operating conditions.

[0030] Full-cycle battery operation data includes voltage characteristic data, current characteristic data, temperature characteristic data, and time cycle number characteristic data for the entire charge-discharge cycle. Specifically, the voltage characteristic data consists of the voltage sample values ​​of the lithium-ion battery at various time points during the full-cycle charge-discharge process; the current characteristic data consists of the charge-discharge current data of the lithium-ion battery at various time points during the full-cycle charge-discharge process; the temperature characteristic data consists of the real-time data of the ambient temperature or battery surface temperature of the lithium-ion battery at various time points during the full-cycle charge-discharge process; and the time cycle number characteristic data includes time-series information including cumulative operating time and the number of charge-discharge cycles.

[0031] The training data is converted into feature vectors and then input into the lithium-ion battery health state prediction architecture for training. In some embodiments, the full-cycle battery operation data of this scheme is a 17-dimensional feature vector, specifically including mean, standard deviation, peak value, marginality, charging time corresponding to the voltage (current) curve segment, cumulative charging amount corresponding to the voltage (current) curve segment, slope of the voltage (current) curve, entropy of the voltage (current) curve, and number of cycles.

[0032] It is worth reiterating that the lithium-ion battery health state prediction model in this scheme decouples the solution network and the kinetic network. This decoupling optimization paradigm, through sub-objective decoupling, explicitly distinguishes the parameter update paths for different physical objectives at the optimization structure level, preventing data fitting and physical constraints from directly competing in the same parameter space. From a system identification perspective, this lithium-ion battery health state prediction model treats "state estimation" and "kinetic learning" as two mutually synergistic but independently optimized subproblems. This design is not merely a simple engineering technique, but a structural response to the non-cooperative nature of multi-objective degradation system optimization in SOH prediction.

[0033] Regarding the solution network of this scheme: The architecture of the solution network is designed as an "encoder-predictor" structure, that is, the solution network includes an encoder and a predictor connected in sequence. The encoder contains multiple encoding nodes to map the input training data to the latent space to obtain latent features. The predictor maps the latent features to SOH prediction values ​​and outputs the latent space representation of the SOH prediction values, where the latent space is the temporal gradient and spatial gradient of the SOH prediction values.

[0034] In some embodiments, the encoder in the solution network is used to capture latent features in the training data, wherein the latent features are used to represent smooth nonlinear and periodic changes in battery degradation.

[0035] In some embodiments, the encoder of the decryption network uses an activation function. Preferably, the encoder uses a sinusoidal activation function.

[0036] In some embodiments, the encoder contains three hidden layers, each containing 60 nodes. The 17-dimensional feature vector input to the encoder is mapped to a 32-dimensional latent space through three encoder layers, each containing 60 nodes, to obtain latent features.

[0037] In some embodiments, the predictor in the solution network remaps latent features to SOH predictions.

[0038] In some embodiments, the predictor includes a 64-node hidden layer and performs feature transformation and nonlinear fitting through a 64-node intermediate layer to output SOH prediction values.

[0039] In some embodiments, the predictor uses the Softplus activation function. The advantage of this activation function is that the output is always positive and the gradient is smooth, which can avoid gradient vanishing and is suitable for modeling continuous processes with clear physical boundaries such as battery degradation.

[0040] Regarding the dynamic network of this scheme: Although the decoupling of the solution network and the dynamic network in this scheme alleviates the instability at the optimization level to some extent, the dynamic network, which relies solely on state inputs, still struggles to accurately perceive changes in the degradation rate. To address the problem of insufficient utilization of physical information, this scheme further proposes a gradient enhancement physical input mechanism, which explicitly introduces the gradient information of the temporal gradient and spatial gradient of the solution network output with respect to time or cycle number into the dynamic network.

[0041] The dynamics network in this scheme is tasked with discovering physical laws, specifically learning the nonlinear function terms of the partial differential equation (PDE) controlling battery degradation. This scheme explicitly uses the temporal and spatial gradients of the solution network output as inputs to the dynamics network. By introducing nonlinear function terms into the PDE residuals, it's equivalent to adding first-order derivative information to the weak formal constraints, allowing the model to perceive the "intensity" of degradation rather than just its "state." This is a gradient-level enhancement of traditional physical information neural networks that only constrain function values, a natural extension of variational modeling. Gradient-enhanced modeling improves the model's physical sensitivity to degradation dynamics.

[0042] In some embodiments, battery operating data, temporal gradient, SOH prediction value and spatial gradient are concatenated to obtain concatenated features, and the spatial gradient in the concatenated features is L2 normalized and then input into the dynamic network to output nonlinear function terms.

[0043] In some embodiments, the dynamic network is a sin activation function.

[0044] In degradation dynamic systems, the state gradient, including temporal and spatial gradients, directly reflects the degradation rate and its changing trend, and is a key physical quantity describing the intensity of state-of-the-art (SOH) evolution. By using the state gradient as an input feature of the dynamic network, the lithium-ion battery health state prediction architecture can explicitly perceive the "speed changes" of the degradation process during training, thereby improving the discriminability of the dynamic function. Unlike traditional methods that only use gradient information at the loss function level, this scheme treats the state gradient as a first-class physical input, allowing it to participate in the construction of the dynamic mapping. This design essentially expands the physical information utilization level of the physical information neural network, enabling the lithium-ion battery health state prediction architecture to no longer be limited to state consistency constraints, but to directly learn the degradation rate structure.

[0045] Regarding the loss function of this scheme: Even with optimized decoupling and enhanced dynamic discriminability, the lithium-ion battery health state prediction architecture may still converge to a solution that violates physical priors if no explicit structural constraints are imposed on the solution space. Therefore, addressing the fundamental principle that the state-of-health (SOH) degradation process of lithium batteries is monotonically irreversible, this scheme employs constraint relaxation to transform this non-differentiable physical prior into a differentiable penalty term. A physical monotonicity loss is introduced into the loss function. This loss does not introduce additional constraints when the prediction satisfies the physical prior, but provides a stable gradient signal when monotonicity is violated, thus being equivalent to a hinge-type penalty function approximation of the original inequality constraints. Through this design, the optimization process of the lithium-ion battery health state prediction architecture is confined to a feasible solution subspace consistent with the physical degradation mechanism, rather than an unconstrained search across the entire function space, achieving physical guidance of the solution space structure. That is, this scheme systematically transforms non-differentiable physical constraints into differentiable optimization objectives, introduces physical monotonicity loss during training to directly constrain the function space, ensures that non-physical behaviors are avoided from the source, and thus realizes physical prior-driven function space constraint learning within the framework of physical information neural networks.

[0046] Furthermore, to avoid excessive constraints suppressing data fitting ability, this scheme designs an adaptive loss weight adjustment mechanism, so that the strength of physical constraints is dynamically adjusted during the training phase. That is, in order to dynamically balance the data and physical data, the PDE residual loss and physical monotonicity loss in the loss function of this scheme are weighted with adaptive weights.

[0047] Specifically, the loss function of this scheme is a weighted sum of PDE residual loss, data loss, and physical monotonicity loss. The data loss is the loss between the predicted SOH value and the actual SOH value, used to ensure the fitting ability of the lithium-ion battery health state prediction architecture to the observed SOH data. The PDE residual loss is the loss of the difference between the time gradient and the nonlinear function term, used to satisfy the physical dynamic relationship, and to ensure numerical stability through gradient normalization. The physical monotonicity loss is a penalty for the opposite direction of the actual change in battery capacity and the predicted change in SOH value, used to suppress non-physical phenomena such as the "rebound" of SOH, and to ensure that the predicted capacity change trend is consistent with the physical observation.

[0048] The loss function of this scheme is expressed as:

[0049] in For loss function, For data loss, For the adaptive weights of the PDE residual loss, It is the PDE residual loss. These are adaptive weights for physical monotonicity loss. It is a loss of physical monotonicity.

[0050] Specifically, the data loss in this scheme is used to ensure the fitting ability of the lithium-ion battery health state prediction model to the observed SOH data. The formula for the data loss is as follows:

[0051] in This is the predicted SOH value. This is the true value of SOH, and MSE() is the mean squared error. This results in data loss.

[0052] The PDE residual loss in this scheme is used to satisfy the physical dynamic relationship by minimizing the PDE residual constraint model. Gradient normalization ensures numerical stability. The formula for the PDE residual loss is as follows:

[0053]

[0054]

[0055] in For PDE residuals, Represents the time gradient, Represents a nonlinear function term. To solve for the SOH prediction value of the network, For the input training data, SolutionNetwork() To solve the network, It is the PDE residual loss.

[0056] The physical monotonicity loss in this scheme is used to consider the physical law that SOH decreases monotonically with time, which can effectively suppress the non-physical phenomenon of SOH rebound. The formula for the physical monotonicity loss is as follows:

[0057] in RELU() It is the ReLU function. It is the predicted SOH value at time t+Δt. This is the predicted SOH value at time t, where Δt is the time interval. It is the battery capacity at time t+Δt. It is the battery capacity observed at time t. It is a loss of physical monotonicity.

[0058] The formula for the adaptive weights of the PDE residual loss is as follows:

[0059] The formula for the adaptive weights of the physical monotonicity loss is as follows:

[0060] in For data loss, For the adaptive weights of the PDE residual loss, It is the PDE residual loss. These are adaptive weights for physical monotonicity loss. It is a loss of physical monotonicity. and All are set to the minimum weight value. and These are all set to the maximum weight. It is a restriction function.

[0061] It should be noted that in SOH prediction, there are actually at least three conflicting objectives: data fitting (statistical consistency), PDE residuals (physical consistency), and physical monotonicity constraints (engineering feasibility). Multi-objective optimization theory points out that when the optimal solutions of multiple objectives are inconsistent, forcibly using linear weighting with fixed weights often fails to converge to a stable Pareto solution. Therefore, this scheme dynamically adjusts the adaptive weights of different loss terms based on the magnitude of the loss to achieve an adaptive balance between data fitting and physical constraints. This makes the final trained lithium-ion battery health state prediction model more robust, that is, the weights of the lithium-ion battery health state prediction model adapt to different batches of data, and the model performance is more stable.

[0062] Regarding the training method of this lithium-ion battery health status prediction architecture: The solution network and kinetic network in the lithium-ion battery health state prediction architecture of this scheme use independent optimizers.

[0063] In some embodiments, the solution network and the dynamic network independently employ the Adam optimizer. The Adam optimizer for the solution network is used to optimize the parameters of the solution network, while the Adam optimizer for the dynamic network is used to optimize the parameters of the dynamic network.

[0064] In some embodiments, the training of the lithium-ion battery health state prediction architecture employs the Adam optimizer combined with learning rate and cosine annealing decay, and uses validation data identical to the training data to validate the lithium-ion battery health state prediction model. Early stopping is performed based on the loss of the validation data, and the model parameters with the best validation performance are saved.

[0065] Example 2 This embodiment provides a test example of the lithium-ion battery health status prediction model of this solution: Test Example 1: Predictive Performance Evaluation Experiment To systematically verify the effectiveness of the proposed lithium-ion battery health state prediction model in real-world battery degradation scenarios, this paper uses the publicly available lithium-ion battery life degradation dataset from Xi'an Jiaotong University (XJTU) as the experimental platform. This dataset contains 55 batteries across 6 batches (batch 1-6) under 6 different charge-discharge protocols, covering their entire lifecycle. Under constant current-constant voltage (CC-CV) charge-discharge strategies, this dataset performs complete lifecycle tests on multiple lithium-ion batteries under different ambient temperatures and discharge rates, covering the entire process from initial service state to capacity decay to the failure threshold. Specifically, this dataset covers 6 different charge-discharge protocol batches, enabling a comprehensive evaluation of the model's generalization performance under complex conditions such as different rates and cutoff voltages. The model input dimension is set to 17, the training epochs are 1000, the base learning rate is set to 0.01, and Dropout technology is applied to prevent overfitting.

[0066] Unlike ideal laboratory data, the XJTU dataset exhibits significant nonlinear degradation characteristics during long-term cycling: in the early stages of life, the SOH decay rate is relatively slow and fluctuates significantly, while in the later stages, the degradation process accelerates and is accompanied by a significant inflection point. This non-stationary degradation characteristic places higher demands on modeling methods, especially testing the model's ability to physically perceive changes in the degradation rate. Furthermore, due to manufacturing differences and environmental perturbations, the degradation trajectories of different battery samples differ significantly at local scales, but they all follow the same irreversible degradation law in their overall trend. This characteristic makes this dataset highly suitable for validating the generalization ability and physical consistency of physical information learning methods.

[0067] In the experiment, the battery SOH was defined as the ratio of the current usable capacity to the rated capacity. The model input features included the voltage, current and their statistical characteristics during the charging and discharging process. The output was the predicted SOH value for the corresponding cycle. The test conditions were at ambient temperatures of 25°C, 35°C and 45°C, with each battery undergoing approximately 500-1000 complete cycles. Voltage, current and temperature were recorded for each cycle, and the failure threshold was set to 80%.

[0068] To comprehensively evaluate the performance advantages of PR-PINN, this paper selects several representative SOH prediction methods as benchmarks, including pure data-driven models and typical physical information models.

[0069] Specifically, the comparison methods include: Multilayer Perceptron (MLP), Convolutional Neural Network (CNN), Traditional PINN, and PR-PINN. All comparison methods adopt the same data preprocessing process and training-test split strategy. PR-PINN represents the lithium-ion battery health status prediction model of this solution, PINN represents the benchmark physical information neural network, MLP represents the multilayer perceptron network, and CNN represents the convolutional neural network.

[0070] In terms of experimental setup, all models were trained on the same training set and evaluated on test batteries that were not used for training to examine their cross-battery generalization ability. For PINN-type methods, the physical residual terms were all constructed based on the same degradation dynamics assumptions to ensure that performance differences mainly stemmed from differences in the optimization structure and the way physical information was utilized. The Adam optimizer was used during model training, and the hyperparameter range was determined through cross-validation. The input dimension was set to 17, and the output dimension to 1. The network layers and hidden units were: Solution_u Encoder 3 layers with 60 nodes, Predictor Head 64 nodes, and the Dynamical F layer was adjustable. Dropout was 0.1 (Solution_u) and 0.2 (Dynamical F). The optimizer was Adam. The epoch was 1000. The learning rates were: warmup_lr 0.001, base_lr 0.01, and final_lr 0.0001.

[0071] In terms of evaluation metrics, this scheme not only adopts conventional statistical metrics such as mean absolute error (MAE), root mean square error (RMSE), mean absolute prediction error (MAPE), and coefficient of determination (R²), but also introduces a physical consistency metric to measure the monotonicity and physical rationality of the predicted SOH curve. This setting allows experimental evaluation to be no longer limited to numerical accuracy, but to comprehensively measure the model performance from the perspective of engineering applications.

[0072] To verify the statistical significance of the proposed method, a systematic experiment was conducted on data from six battery batches. The method was compared with three typical approaches: the traditional Physical Information Neural Network (PINN) and two purely data-driven models (MLP and CNN). All models employed a uniform data partitioning strategy (training / validation / testing ≈ 6:2:2), and independent training and testing were repeated 10 times on each dataset to ensure the reliability of the statistical results. The MAE, MAPE, and R² violin distributions of the four models on the datasets are shown below. Figure 2 As shown.

[0073] The statistical results for batch 1 are shown in Table 1. The lithium-ion battery health status prediction model performed well under all operating conditions.

[0074] Taking a representative batch 1 as an example, the MAE of PR-PINN is stably distributed within the range of approximately 0.0037–0.0050, with minimal fluctuations. In contrast, the traditional PINN method exhibits a wider distribution range, indicating that its training process is more susceptible to the influence of initialization and optimization paths. Furthermore, although MLP and CNN can achieve low errors in some experiments, their overall distribution is highly discrete, indicating insufficient generalization ability and susceptibility to interference from changes in data distribution.

[0075] On the more challenging batches 2 and 5, the error distribution of the comparative methods further expands, especially with CNN and MLP showing significant performance degradation. PR-PINN, however, maintains a relatively compact distribution, with RMSE generally kept low, demonstrating its good robustness across operating conditions. This result shows that the proposed method can effectively capture the common dynamic characteristics of battery degradation, rather than relying on a specific data distribution.

[0076] Table 1 Comparison Results of Different Model Methods in Batch 1 .

[0077] The PR-PINN model's prediction results for SOH in 6 batches are as follows: Figure 3 As shown, in all six batches, the prediction results of PR-PINN closely approximate the ideal diagonal, indicating that the model can accurately recover the true degradation trend of SOH. Furthermore, compared to other methods, PR-PINN's point cloud distribution is denser, with a significant reduction in outliers, maintaining good fitting ability even in low SOH regions. This characteristic is particularly crucial for predicting later stages of battery life. From a physical consistency perspective, PR-PINN's prediction results maintain a strictly monotonically decreasing trend throughout the entire lifespan, without any non-physical local rebound phenomena. In contrast, the comparative methods exhibit significant fluctuations that violate physical laws in some batches, further demonstrating the important role of physical constraints in improving model reliability.

[0078] In summary, PR-PINN outperforms existing methods in terms of accuracy, stability, and physical consistency, validating the effectiveness and advancement of the proposed framework in battery SOH prediction.

[0079] Test Example 2: Ablation Experiment This approach employs ablation experiments on batch 1 of the XJTU dataset, using 10 independent replicates to ensure statistical significance. Five model variants were designed, each corresponding to the removal of a specific component from the PR-PINN framework. To accurately quantify and evaluate the independent contributions and synergistic effects of various innovative designs within the PR-PINN framework, a systematic ablation experiment was designed. Using the complete PR-PINN model as a baseline, five comparative model variants were constructed by progressively removing its core components. These variants are: variant "– w / o SDO", "-w / o GEI", "-w / o DML", "-w / o ALB", and "baseline PINN". The "– w / o SDO" variant removes the decoupled optimization of the sub-objectives, restoring the traditional PINN single-optimizer joint training paradigm, used to verify the crucial role of decoupled training in stability. The variant "– w / o GEI" simplifies the input of the dynamical network to the traditional form [x, t, u], removing the gradient information u. x Explicit injection of 'ux' is used to evaluate the improvement of gradient boosting's ability to capture degradation inflection points. The variant "– w / o DML" removes the physical monotonicity loss term L from the loss function. phys This is used to test the indispensability of the constraint in preventing non-physical rebound phenomena. The variant "– w / o ALB" replaces the adaptive crowd with fixed loss weights to explore the impact of dynamic weight adjustment on the model's generalization ability. The "baseline PINN" is the baseline PINN model, which adopts a common monolithic network structure and joint optimization strategy, without including any improvements proposed in this paper, and represents the current mainstream method level.

[0080] All model variants were trained and tested on batch 1 of the XJTU dataset using the same set of hyperparameters (learning rate, batch size, training epochs, etc.) to ensure fairness in the comparison. Each experiment was repeated 10 times to calculate the mean and standard deviation of the performance metrics, thus ensuring the reliability of the statistical conclusions. Through this "controlled variable" experimental design, we can clearly attribute the final performance gain to specific algorithmic improvements, rather than hyperparameter tuning or random factors. Ablation experiment figures for each model variant are shown below. Figures 4-6 As shown.

[0081] Experimental results show that when the SDO mechanism is removed and the traditional joint optimization method is adopted (corresponding to "-w / o SDO"), the model training process exhibits significant oscillations, is highly sensitive to the setting of loss weights, and ultimately the prediction error increases significantly. This result verifies the hypothesis that "multi-objective gradient conflict is the main root cause of instability of PINN in SOH prediction." When SDO is retained but the GEI mechanism is removed (corresponding to "-w / o GEI"), the model can still fit the data well in the early stages of its lifetime, but the prediction error increases significantly in the degradation acceleration stage, making it difficult to accurately capture the degradation inflection point. This indicates that relying solely on state input is insufficient to support dynamic discriminability, and gradient information plays a crucial role in characterizing the changes in degradation rate. Furthermore, when the PGCL constraint is removed (corresponding to "-w / o DML"), although the model's numerical indicators do not change much, local non-monotonicity still occasionally appears in the prediction curve, especially in areas with high data noise. This phenomenon suggests that if physical constraints are not explicitly embedded during the training phase, relying solely on data and dynamic residuals is insufficient to fundamentally limit the solution space structure.

[0082] Systematic ablation experiments revealed that multi-objective gradient conflict is the main bottleneck of PINN in battery SOH prediction. Our proposed solution effectively addresses this issue by decoupling the parameter update path, contributing the largest performance improvement (+48.6%). Gradient information is crucial for degradation dynamics modeling. Our solution explicitly introduces gradient signals, enabling the model to directly perceive changes in degradation rate, contributing a significant additional gain (+32.4%). Similarly, physical constraints require a systematic embedding strategy. Our solution achieves optimized dynamic balance while ensuring physical rationality, with synergistic effects among components. The performance advantage of the complete PR-PINN(d) stems from the organic combination of innovative components, rather than simple superposition. Compared to the baseline PINN, our solution achieves a relative reduction of 40.3% in MAE (a) and an absolute improvement of 0.047 in R² (b).

[0083] Test Example 3: Small Sample Experiment To verify the capabilities of the proposed lithium-ion battery health status prediction model in data-scarce scenarios, a small-sample experiment was conducted. The experimental results are shown in Table 2. Specifically, the model was trained and its performance was tested using data from only 1, 2, 3, and 4 batteries, respectively. It can be seen that when trained using only 1 battery, the performance of the lithium-ion battery health status prediction model trained by this method is comparable to that of MLP and CNN trained using 3-4 batteries, demonstrating its advantage in small-sample scenarios.

[0084] Table 2. Results of Small Sample Experiment .

[0085] Example 3 Based on the same concept, this application also proposes an application method for a lithium-ion battery health state prediction model, namely, providing a lithium-ion battery health state prediction method, including: Collect operational data from lithium-ion batteries; The running data is input into the lithium-ion battery health state prediction model trained in Example 1, which outputs the SOH prediction value.

[0086] In some embodiments, the 17-dimensional full-cycle operating data of the lithium-ion battery specifically includes the mean, standard deviation, peak value, marginality, charging time corresponding to the voltage (current) curve segment, cumulative charging amount corresponding to the voltage (current) curve segment, slope of the voltage (current) curve, entropy of the voltage (current) curve, and number of cycles.

[0087] Example 4 This embodiment also provides an electronic device, see reference. Figure 7 It includes a memory 404 and a processor 402, the memory 404 storing a computer program and the processor 402 being configured to run the computer program to perform the steps in any of the embodiments of the method for constructing and applying a lithium-ion battery health status prediction model.

[0088] Specifically, the processor 402 may include a central processing unit (CPU), or an application-specific integrated circuit (ASIC), or one or more integrated circuits that can be configured to implement the embodiments of this application.

[0089] The memory 404 may include a large-capacity memory 404 for data or instructions. The processor 402 reads and executes the computer program instructions stored in the memory 404 to implement any of the methods for constructing and applying the lithium-ion battery health status prediction model in the above embodiments.

[0090] Optionally, the electronic device may further include a transmission device 406 and an input / output device 408, wherein the transmission device 406 is connected to the processor 402 and the input / output device 408 is connected to the processor 402.

[0091] The transmission device 406 can be used to receive or send data via a network. Specific examples of the network described above may include wired or wireless networks provided by the communication provider of the electronic device. In one example, the transmission device includes a Network Interface Controller (NIC), which can connect to other network devices via a base station to communicate with the Internet. In another example, the transmission device 406 may be a Radio Frequency (RF) module used for wireless communication with the Internet.

[0092] The input / output device 408 is used to input or output information. In this embodiment, the input information may be training data, etc., and the output information may be a lithium-ion battery health status prediction model, etc.

[0093] Optionally, in this embodiment, the processor 402 can be configured to perform the following steps via a computer program: The full-cycle battery operation data of lithium-ion batteries under different operating conditions is obtained as training data. The battery operation data includes voltage characteristic data, current characteristic data, temperature characteristic data, and time cycle number characteristic data. Training data is input into a lithium-ion battery health state prediction architecture to train a lithium-ion battery health state prediction model. The lithium-ion battery health state prediction architecture includes a two-branch solution network and a kinetic network. The solution network includes an encoder and a predictor connected in sequence. Battery operating data is input into the encoder to encode latent features. The latent features are then passed through the predictor to output SOH prediction values. The temporal and spatial gradients of the SOH prediction values ​​are calculated. The battery operating data, temporal gradient, SOH prediction values, and spatial gradients are concatenated to obtain concatenated features. The concatenated features are input into the kinetic network to output a nonlinear function term. The PDE residual is constructed based on the difference between the temporal gradient and the nonlinear function term. The loss function of the lithium-ion battery health state prediction architecture is a weighted value of the PDE residual loss, data loss, and physical monotonicity loss.

[0094] It should be noted that the specific examples in this embodiment can refer to the examples described in the above embodiments and optional implementations, and will not be repeated here.

[0095] Generally, various embodiments can be implemented in hardware or dedicated circuitry, software, logic, or any combination thereof. Some aspects of the invention can be implemented in hardware, while others can be implemented by firmware or software executed by a controller, microprocessor, or other computing device, but the invention is not limited thereto. Although various aspects of the invention may be shown and described as block diagrams, flowcharts, or using some other graphical representation, it should be understood that, by way of non-limiting example, these blocks, apparatuses, systems, techniques, or methods described herein can be implemented in hardware, software, firmware, dedicated circuitry or logic, general-purpose hardware or controllers or other computing devices, or some combination thereof.

[0096] Embodiments of the present invention can be implemented by computer software, which may be executable by a data processor of a mobile device, such as a processor entity, or by hardware, or by a combination of software and hardware. Computer software or programs (also referred to as program products), including software routines, applets, and / or macros, can be stored in any device-readable data storage medium, and they include program instructions for performing specific tasks. A computer program product may include one or more computer-executable components configured to perform embodiments when the program is run. One or more computer-executable components may be at least one piece of software code or a portion thereof. Additionally, it should be noted that any block in the logical flow of the figures may represent a program step, or interconnected logical circuitry, blocks and functions, or a combination of program steps and logical circuitry, blocks and functions. The software may be stored on physical media such as memory chips or blocks of storage implemented within a processor, magnetic media such as hard disks or floppy disks, and optical media such as, for example, DVDs and their data variants, CDs, etc. The physical medium is a non-transient medium.

[0097] Those skilled in the art should understand that the technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments have been described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0098] The above embodiments are merely illustrative of several implementation methods of this application, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of this application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A method for constructing a predictive model for the health status of a lithium-ion battery, characterized in that, Includes the following steps: The full-cycle battery operation data of lithium-ion batteries under different operating conditions is obtained as training data. The battery operation data includes voltage characteristic data, current characteristic data, temperature characteristic data, and time cycle number characteristic data. Training data is input into a lithium-ion battery health state prediction architecture to train a lithium-ion battery health state prediction model. The lithium-ion battery health state prediction architecture includes a two-branch solution network and a kinetic network. The solution network includes an encoder and a predictor connected in sequence. Battery operating data is input into the encoder to encode latent features. The latent features are then passed through the predictor to output SOH prediction values. The temporal and spatial gradients of the SOH prediction values ​​are calculated. The battery operating data, temporal gradient, SOH prediction values, and spatial gradients are concatenated to obtain concatenated features. The concatenated features are input into the kinetic network to output a nonlinear function term. The PDE residual is constructed based on the difference between the temporal gradient and the nonlinear function term. The loss function of the lithium-ion battery health state prediction architecture is a weighted value of the PDE residual loss, data loss, and physical monotonicity loss.

2. The method for constructing a lithium-ion battery health status prediction model according to claim 1, characterized in that, Full-cycle battery operation data covers the entire lifecycle of a lithium-ion battery, from its initial service state to capacity decay to the failure threshold. The full-cycle battery operation data includes voltage characteristic data, current characteristic data, temperature characteristic data, and time cycle number characteristic data for the entire charge and discharge process.

3. The method for constructing a lithium-ion battery health status prediction model according to claim 1, characterized in that, The encoder of the solution network uses an activation function, and latent features are used to represent smooth nonlinear and periodic changes in battery degradation.

4. The method for constructing a lithium-ion battery health status prediction model according to claim 1, characterized in that, Battery operating data, temporal gradient, SOH prediction, and spatial gradient are concatenated to obtain a concatenated feature. The spatial gradient in the concatenated feature is then L2 normalized and input into the dynamic network to output a nonlinear function term.

5. The method for constructing a lithium-ion battery health status prediction model according to claim 1, characterized in that, Data loss is the loss between the predicted SOH value and the actual SOH value; PDE residual loss is the loss of the difference between the time gradient and the nonlinear function term; physical monotonicity loss is the penalty for the actual change direction of battery capacity change being opposite to the predicted change direction of SOH value.

6. The method for constructing a lithium-ion battery health status prediction model according to claim 1, characterized in that, The formula for the physical monotonicity loss is as follows: Where RELU() is the RELU function. It is the predicted SOH value at time t+Δt. This is the predicted SOH value at time t, where Δt is the time interval. It is the battery capacity at time t+Δt. It is the battery capacity at time t.

7. The method for constructing a lithium-ion battery health status prediction model according to claim 1, characterized in that, The formula for the adaptive weights of the PDE residual loss is as follows: The formula for the adaptive weights of the physical monotonicity loss is as follows: in For data loss, For the adaptive weights of the PDE residual loss, It is the PDE residual loss. These are adaptive weights for physical monotonicity loss. It is a loss of physical monotonicity. and All are set to the minimum weight value. and These are all set to the maximum weight. It is a restriction function.

8. The method for constructing a lithium-ion battery health status prediction model according to claim 1, characterized in that, The solution network and the dynamic network use independent optimizers during the training phase, and are trained by combining the learning rate and cosine annealing decay.

9. A method for predicting the health status of a lithium-ion battery, characterized in that, include: Collect operational data from lithium-ion batteries; The lithium-ion battery health state prediction model constructed by inputting the running data into the construction method of any one of claims 1 to 8 outputs the SOH prediction value.

10. A readable storage medium, characterized in that, The readable storage medium stores a computer program, the computer program including program code for controlling a process to execute the process, the process including a method for constructing a lithium-ion battery health state prediction model according to any one of claims 1 to 8 or a lithium-ion battery health state prediction method according to claim 9.

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