Battery health state estimation method based on physical constraint network

Abstract

The invention provides a battery health state estimation method based on a physical constraint network, and the method comprises the steps: extracting an input feature vector from the standard operation data of a battery charging process without depending on an additional sensor; constructing an update candidate network; each unit of the network comprises an update gate branch for generating a feature adaptive weight and a candidate branch for generating a nonlinear feature, and outputs of the two branches are fused through element-level multiplication; the candidate network is trained and updated by adopting a loss function containing physical constraints, and the physical constraints comprise partial differential equation residual constraints based on a battery degradation kinetic equation and physical consistency regularization adapted to degradation characteristics of different chemical systems; the partial differential equation residual constraint is used for enabling the network predicted state-of-health evolution to conform to a battery degradation kinetic equation and to be consistent with a degradation rate estimated value; and inputting the input feature vector of the to-be-tested battery into the trained updated candidate network, and directly outputting a battery health state estimation value through single forward propagation.

Description

Technical Field

[0001] This invention belongs to the field of battery management and state estimation technology, specifically relating to a battery health state estimation method based on physical constraint networks. Background Technology

[0002] Lithium-ion batteries are widely used in electric vehicles, renewable energy storage systems, and distributed microgrids. Accurate estimation of their State of Health (SOH) is crucial for ensuring system safety, reliability, and lifecycle management. During long-term charge and discharge, batteries are affected by various electrochemical factors, including solid electrolyte interphase (SEI) growth, lithium deposition, loss of active materials, and increased internal resistance, leading to capacity degradation and power performance decline. Therefore, timely and accurate estimation of battery SOH is a key technology for predictive maintenance, fault warning, and secondary utilization.

[0003] Existing battery health estimation methods mainly fall into two categories: model-driven and data-driven. Model-driven methods include electrochemical models (ECM) and equivalent circuit models (EECM). Electrochemical models (such as the Doyle-Fuller-Newman model) can characterize the solid-state diffusion, kinetic reactions, and polarization effects of the battery through partial differential equations, possessing strong physical interpretability. However, these models are high-dimensional, have many parameters, and are highly sensitive to temperature and operating conditions, often requiring extensive experimental calibration in practical applications, making them difficult to apply in real-time battery management systems. Equivalent circuit models simulate the dynamic characteristics of the battery through a combination of resistance and capacitance, with low computational cost and easy embedding into battery management systems. However, their parameters change significantly with the aging process and cannot effectively reflect internal degradation mechanisms, easily leading to estimation errors across operating conditions and lifespan stages.

[0004] With the improvement of sensing, computing, and data acquisition capabilities, data-driven methods have become a research hotspot in recent years. Traditional machine learning methods, such as support vector regression, random forests, and Gaussian process regression, can learn capacity and degradation patterns from measurable signals such as voltage, current, and temperature. However, these methods are heavily reliant on feature engineering and have limited generalization ability under complex conditions. Deep learning models (such as convolutional networks, long short-term memory networks, and Transformer structures) have further improved the modeling ability of nonlinear features and have shown good performance in capacity estimation tasks. However, many deep learning models focus on sequence prediction or multi-step time series tasks and are not suitable for single-step SOH regression. In addition, purely data-driven methods lack physical constraints, are prone to producing non-physical, non-monotonic, or fluctuating predictions, and have insufficient generalization ability in noisy environments, across temperature ranges, and across chemical systems.

[0005] To compensate for the lack of physical consistency in data-driven methods, Physical Information Neural Networks (PINNs) have emerged in recent years. By introducing physical equation residuals, energy conservation constraints, and monotonicity constraints into the loss function, PINNs make model predictions more physically consistent. PINNs have been applied to tasks such as battery state estimation, capacity prediction, and degradation modeling. However, existing PINNs mostly use fixed fully connected networks as the backbone structure, making it difficult to effectively characterize the complex and diverse degradation modes under different chemical systems, current rates, and temperature conditions. Furthermore, their physical constraint expression capabilities are limited, and they are still prone to performance degradation and insufficient robustness under noisy data or cross-dataset conditions. Therefore, designing a unified network structure that simultaneously possesses high flexibility, high generalization ability, and strong physical consistency remains a key technical problem that urgently needs to be solved in the field of battery health estimation. Summary of the Invention

[0006] To address the shortcomings and deficiencies of existing technologies, this invention provides a battery state of health (SOH) estimation method and system based on physical constraint networks. It aims to solve the problems of pure data-driven methods being prone to non-physical predictions, having weak generalization ability across operating conditions and chemical systems, and the fixed structure and insufficient robustness of traditional physical information neural networks (PINNs). Furthermore, some solutions rely on additional hardware sensors, resulting in high costs and high failure rates.

[0007] This method first extracts input feature vectors from standard operational data (including voltage, current, and temperature data) during the battery charging process without relying on additional hardware sensors. The feature types cover statistical features, time-domain features, and derived features related to battery state. Then, an update candidate network (UCBNet) is constructed. This network consists of multiple stacked units (UCB-Units). The core is used to output the battery SOH estimate, and it can also be extended to generate degradation rate estimates. Each unit contains an update gate branch that generates adaptive weights for the generated features and a candidate branch that generates nonlinear features. The outputs of the two branches are processed through... Element-level multiplication is used to achieve fusion, and the extended degradation rate prediction branch shares low-level feature parameters with the network backbone feature extraction part. During the model training phase, a loss function with multi-level physical constraints is used to train UCBNet. The physical constraints include partial differential equation (PDE) residual constraints based on the battery degradation kinetic equation and physical consistency regularization adapted to the degradation characteristics of different chemical systems. The PDE residual constraints ensure that the network's predicted SOH evolution conforms to the actual battery degradation kinetics and is consistent with the degradation rate estimate by abstracting battery degradation into a kinetic equation and combining automatic differentiation to calculate relevant derivatives and minimize residuals. The computational consistency and physical consistency regularization include directional consistency constraints (supervising the consistency between the predicted SOH change direction and the actual direction through weighted operations, with weighting coefficients correlated to the actual SOH change amplitude, and a specific activation function used to ensure differentiability) and smoothness constraints (suppressing high-frequency oscillations in the predicted trajectory through second-derivative squared penalties). These two constraints work together to adapt the network to different chemical systems such as nickel-cobalt-manganese (NCM), nickel-cobalt-aluminum (NCA), and lithium iron phosphate (LFP), without requiring structural adjustments or retraining for a single system. During training, a parameter optimization algorithm is also employed to perform differentiated learning on the network backbone and the degradation rate prediction branch. The degradation rate branch has a relatively smaller learning rate, and stability is improved by combining gradient pruning, weight decay, and batch training mechanisms. For scenarios with insufficient labeled samples, high-precision estimation can be achieved by freezing the degradation rate branch and only fine-tuning the backbone parameters, or by using only a small number of labeled samples to train the backbone. Finally, for the battery under test, its input feature vector only needs to be input into the trained UCBNet, and the SOH estimate can be directly output through a single forward propagation without relying on time series or recursive calculations. After the output, post-processing steps such as smoothing filtering, outlier removal, historical record correlation analysis, or health alarms can be performed as needed.

[0008] Corresponding to the above method, the present invention also provides a battery health state estimation system. The system includes a feature extraction module, a network construction module, a model training module, and a SOH estimation module. The functions of each module correspond one-to-one with the input feature extraction, UCBNet construction, model training with physical constraints, and single-step SOH inference steps in the method. It can be stably deployed in scenarios such as electric vehicle battery management systems, energy storage power stations or microgrid battery management systems, communication base station backup power systems, and portable energy storage devices. While ensuring high accuracy and physical consistency of SOH estimation, it significantly reduces hardware costs and failure risks, and improves the flexibility and reliability of engineering applications.

[0009] The specific technical solution adopted by this invention to solve its technical problem is as follows:

[0010] A battery health state estimation method based on physical constraint networks includes:

[0011] Without relying on additional sensors, an input feature vector is extracted from standard operating data of the battery charging process, including voltage, current, and temperature data.

[0012] An update candidate network is constructed, which consists of multiple stacked units, for outputting battery health state estimates and can be extended to generate degradation rate estimates; each unit includes an update gate branch that generates adaptive weights for generating features and a candidate branch that generates nonlinear features, and the outputs of the two branches are fused through element-wise multiplication;

[0013] The updated candidate network is trained using a loss function with physical constraints. The physical constraints include partial differential equation residual constraints based on the battery degradation kinetic equation and physical consistency regularization adapted to the degradation characteristics of different chemical systems. The partial differential equation residual constraints are used to make the health state evolution predicted by the network conform to the battery degradation kinetic equation and consistent with the degradation rate estimate.

[0014] The input feature vector of the battery to be tested is input into the trained update candidate network, and the battery health status estimate is directly output through a single forward propagation.

[0015] Furthermore, the features corresponding to the input feature vector include statistical features, time-domain features, and derived features related to battery state; the statistical features include statistical parameters of voltage fluctuations during charging, the time-domain features include the duration of the voltage plateau, and the derived features include polarization-related parameters calculated based on the voltage-current curve.

[0016] Furthermore, each unit of the updated candidate network is a UCB-Unit, and the degradation rate estimate is generated by the degradation rate prediction branch extended by the updated candidate network. The degradation rate prediction branch shares the underlying feature parameters with the backbone feature extraction part of the updated candidate network.

[0017] Furthermore, the method for constructing the partial differential equation residual constraint is as follows: the battery degradation process is abstracted into a kinetic equation to characterize the correlation between the derivative of the degradation state function with respect to cycle time and the estimated degradation rate; the derivative of the health state predicted by the updated candidate network with respect to the input features and cycle number is calculated by automatic differentiation, and the residual is obtained by substituting it into the kinetic equation; the partial differential equation residual constraint is achieved by minimizing the residual obtained from the kinetic equation.

[0018] Furthermore, the physical consistency regularization includes directional consistency constraints and smoothness constraints; the directional consistency constraints are achieved by weighting the deviation of the predicted health status from the actual health status in terms of direction of change, with the weighting coefficient being the absolute value of the actual health status change amplitude, and the calculation process uses the Softplus function to ensure differentiability; the smoothness constraints are achieved by squaring the second derivative of the predicted health status with respect to the input features, with the penalty coefficient being a preset smoothness adjustment constant.

[0019] Furthermore, when training the updated candidate network, a parameter optimization algorithm is used, and a differential learning rate is applied to the backbone feature extraction part and the degradation rate prediction branch of the updated candidate network, with the learning rate of the degradation rate prediction branch being less than that of the backbone feature extraction part; the training process also includes gradient pruning, weight decay, and batch training mechanisms to improve training stability.

[0020] Furthermore, before inputting the input feature vector of the battery to be tested into the update candidate network, the input feature vector is further subjected to normalization or standardization preprocessing, and the preprocessing operation does not change the physical meaning of the features.

[0021] Furthermore, when the number of labeled samples in the scene where the battery under test is located is insufficient, the training of the updated candidate network includes: freezing the parameters of the degradation rate prediction branch and only fine-tuning the parameters of the backbone feature extraction part; or training the backbone feature extraction part using only 1-2 labeled battery samples under test.

[0022] Furthermore, after outputting the battery health status estimate, a post-processing step is also included. The post-processing step includes smoothing filtering, outlier removal, correlation analysis with historical health status records, or comparison with a preset health threshold to trigger a health alarm.

[0023] And, a battery health state estimation system based on physical constraint networks, comprising:

[0024] The feature extraction module is used to extract input feature vectors from standard operating data during the battery charging process. The standard operating data includes voltage, current and temperature data, without relying on additional hardware sensors.

[0025] The network construction module is used to construct an update candidate network, which is composed of multiple stacked units and is used to output a battery health state estimate and can be extended to generate a degradation rate estimate. Each unit includes an update gate branch that generates adaptive weights for features and a candidate branch that generates nonlinear features. The outputs of the two branches are fused through element-wise multiplication.

[0026] The model training module is used to train the updated candidate network using a loss function with physical constraints. The physical constraints include partial differential equation residual constraints based on the battery degradation kinetic equation and physical consistency regularization adapted to the degradation characteristics of different chemical systems. The partial differential equation residual constraints are used to make the health state evolution predicted by the network conform to the battery degradation kinetic equation and consistent with the degradation rate estimate.

[0027] The SOH estimation module is used to input the input feature vector of the battery under test into the trained update candidate network, and directly output the battery health state estimate through a single forward propagation.

[0028] And a computer device including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the method described above.

[0029] A non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method described above.

[0030] Compared with the prior art, the present invention and its preferred embodiments have at least the following beneficial effects:

[0031] This invention significantly reduces hardware dependence and system costs while improving operational reliability. It eliminates the need for additional hardware sensors (such as expansion sensors or deformation probes), estimating health status solely based on standard operating data such as voltage, current, and temperature that can be routinely collected by the battery management system during charging. This not only eliminates the material and manufacturing costs of additional deformation sensors but also avoids the risk of failure due to temperature drift, mechanical loosening, or aging of these components. It reduces system maintenance complexity and improves long-term operational stability and cost-effectiveness from a hardware perspective.

[0032] Improve the physical consistency and predictive reliability of health status estimates. By introducing multi-level physical constraints during model training, including partial differential equation residual constraints based on battery degradation kinetics equations and physical consistency regularization adapted to different chemical systems, this effectively suppresses common non-physical predictions in pure data-driven methods (such as unexpected growth or abrupt changes in health status), ensuring that the prediction results conform to the actual electrochemical mechanism of battery aging. At the same time, smoothness constraints avoid high-frequency oscillations in the prediction trajectory caused by noise, making the health status estimates closer to the actual degradation patterns of batteries, and providing a more reliable decision-making basis for subsequent safe operation and lifespan management.

[0033] Enhance the model's generalization ability and scenario adaptability. The updated candidate network (UCBNet) constructed in this invention adopts a unified dual-branch gating structure, combined with physical consistency constraints, which can adapt to batteries with different chemical systems such as nickel-cobalt-manganese, nickel-cobalt-aluminum, and lithium iron phosphate, without the need to adjust the network structure or retrain for a single chemical system. At the same time, for scenarios with insufficient labeled samples, by freezing the degradation rate branch and only fine-tuning the backbone parameters or using a small number of labeled samples for training, high-precision health state estimation can be achieved, which greatly improves the model's transferability in heterogeneous operating conditions and cross-dataset scenarios, and reduces the dependence on a large amount of labeled data.

[0034] This invention improves computational efficiency and engineering deployment flexibility. It employs a single-step forward propagation inference method, eliminating the need for time-series data or recursive computation, and rapidly outputs health status estimates to meet the real-time requirements of battery management systems. Furthermore, its small network structure parameters and lack of complex stacking design make it easy to embed into battery management systems across various scenarios, including electric vehicles, energy storage power stations, microgrids, and portable energy storage devices. It requires minimal modification to existing system hardware or structure, resulting in low engineering difficulty and wide applicability.

[0035] To ensure the stability and estimation accuracy of model training, a differentiated learning rate strategy is adopted for updating the candidate network backbone and degradation rate prediction branch. Combined with gradient pruning, weight decay, and batch training mechanisms, gradient oscillation and overfitting problems during training are effectively avoided, improving the convergence quality and numerical stability of model training. Finally, through the synergistic optimization of data fitting loss and physical constraint loss, physical consistency is ensured while maintaining high accuracy in health state estimation, enabling the model to maintain stable performance under different loop protocols and different scaling factors. Attached Figure Description

[0036] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0037] Figure 1 This is a schematic diagram of the overall framework of the PIUN, a core component of an embodiment of the present invention.

[0038] Figure 2 This is a structural diagram of UCBNet according to an embodiment of the present invention;

[0039] Figure 3 This is a schematic diagram of the loss function in an embodiment of the present invention;

[0040] Figure 4 This is a flowchart illustrating the model training process in an embodiment of the present invention.

[0041] Figure 5 This is a flowchart illustrating the SOH inference process in an embodiment of the present invention. Detailed Implementation

[0042] To make the features and advantages of the present invention more apparent and understandable, specific embodiments are described below in detail:

[0043] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used in this specification have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0044] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0045] This invention provides a network structure with a physical constraint mechanism and a method for estimating the state of health (SOH) of a battery. This method is applicable to various types of rechargeable batteries, including but not limited to lithium-ion batteries, lithium iron phosphate (LFP) batteries, nickel-cobalt-manganese (NCM) batteries, and nickel-cobalt-aluminum (NCA) batteries.

[0046] This method constructs an updated candidate network structure (UCBNet) to model key health characteristics and degradation patterns of batteries within a single-step inference framework. To ensure that the prediction results conform to the basic physical laws of battery aging, this invention introduces multi-level physical consistency constraints during network training, including partial differential equation (PDE) type physical residual constraints to characterize end-stage dynamic behavior, and physical consistency regularization (PCL) oriented towards degradation mechanisms. This limits the reasonable relationship between key feature changes and SOH evolution, reducing non-physical predictions and cross-condition instability problems commonly found in traditional data-driven methods. This invention, through joint optimization of data fitting loss and the aforementioned physical constraint loss, enables the network to learn key information reflected by battery degradation behaviors such as capacity decay, polarization changes, end-stage voltage evolution, and load effects, thereby improving the ability to characterize different degradation mechanisms. For ease of explanation, the embodiments of this invention are illustrated using lithium-ion batteries as an example. The unified network structure constructed maintains stable prediction performance under different chemical systems (such as NCM, NCA, LFP), different cycling protocols, and different rate conditions, achieving high-precision SOH estimation across datasets and experimental conditions. This invention employs a single-step estimation strategy, eliminating the need for recursive inference or long sequence inputs. It boasts advantages such as high computational efficiency, strong generalization ability, and flexible deployment. It can be applied to battery management systems for electric vehicles, grid energy storage systems, microgrids, and portable electronic devices, providing reliable support for battery safety operation, lifespan management, and health assessment.

[0047] The specific solution of this embodiment is described below:

[0048] 1. Technical problems to be solved

[0049] The degradation process of lithium-ion batteries is influenced by multiple electrochemical mechanisms, including solid electrolyte interfacial film growth, intensified polarization, and loss of active materials, exhibiting characteristics such as strong nonlinearity, multivariate coupling, and significant differences across chemical systems. Existing data-driven methods lack physical constraints, easily producing non-physical or unstable prediction results, and have limited generalization ability across temperature, operating conditions, and chemical systems. Furthermore, existing PINNs generally employ fixed fully connected networks as the backbone structure, resulting in limited expressive power and insufficient robustness to noisy environments or non-monotonic degradation data. Therefore, a unified network structure is needed that simultaneously possesses physical consistency, high expressive power, high robustness, and cross-dataset generalization ability to achieve accurate and stable single-step estimation of SOH in lithium-ion batteries.

[0050] 2. Technical Solution

[0051] The overall implementation process of the embodiment of the present invention can be referred to the following steps:

[0052] Step 1: Construct input features and establish network input interface. Extract statistical features, time-domain features, and other physically relevant features from the battery charging process or measurement signals to form the input feature vector x∈ In this embodiment, the feature dimension available for reference is 17, but the present invention is not limited thereto, and those skilled in the art can select and set it according to the actual situation.

[0053] Step 2: Constructing a Unified Update Candidate Network (UCBNet). This invention constructs an update candidate network (UCBNet), as follows: Figure 2 As shown, it consists of multiple stacked UCB-Units, used for adaptive weighting, nonlinear transformation, and physical constraint fusion representation of input features. Each UCB-Unit receives the output features from the previous layer. And it is processed through two parallel branches:

[0054] (1) Update Branch

[0055] The update gate branch is used to generate an adaptive weighted vector along the feature dimension, and its expression is:

[0056]

[0057] in, (·) represents the Sigmoid activation function. Represents the weight matrix. This is a bias term.

[0058] (2) Candidate Branch

[0059] The candidate branch performs a non-linear mapping on the input features, and its expression is as follows:

[0060]

[0061] in, This represents the hyperbolic tangent activation function.

[0062] (3) Feature fusion

[0063] The vectors generated by the two branches are fused together using element-wise multiplication to obtain the output features of the UCB-Unit:

[0064]

[0065] in, This indicates element-wise multiplication.

[0066] Multiple UCB-Units are stacked to form a complete UCBNet, whose final output features are mapped to SOH predicted values ​​through a regression head.

[0067]

[0068] UCBNet can also extend the degradation rate prediction branch r^ as an approximation of the degradation dynamics function g(·), thus enabling its use in conjunction with PDE physical constraints to achieve approximate modeling of the degradation equation.

[0069] Step 3: Introduce physical consistency constraints and construct the total loss function.

[0070] like Figure 3 As shown, this invention introduces multiple types of physical consistency constraints based on the data fitting objective and constructs a unified loss function for training optimization. The data loss, degradation dynamics residual loss, and physical consistency loss introduced in this step together constitute the overall optimization objective of the Physics-Informed Unified Network (PIUN), as follows: Figure 1 As shown.

[0071] (1) Data fitting loss

[0072] The data fitting loss is used to constrain the deviation between the predicted values ​​and the true SOH, ensuring that the model has basic regression accuracy. Its form is:

[0073]

[0074] in: It is the true SOH of the i-th sample. is the SOH predicted by the network, and N is the number of training samples. This loss ensures that the model can accurately reflect the statistical regularities of the observable data.

[0075] (2) Degradation kinetic residual loss

[0076] To ensure that the prediction results conform to the physical dynamics of battery degradation, this invention introduces physical residual constraints based on the degradation equation. Battery degradation can be described as follows:

[0077]

[0078] θ is the degradation state function; g(·) is the degradation rate function, approximated by the degradation rate branch in UCBNet; and θ is the model parameter. Based on the above dynamic relationship, this invention constructs the following PDE residual term:

[0079]

[0080] and The input samples are assigned cycle numbers and features. To predict the derivative of SOH with respect to the corresponding variable, it is obtained by automatic differentiation. The degradation rate estimation function is parameterized by the network. This residual term is used to constrain the prediction results to be consistent with the degradation dynamics, thereby avoiding anomalous behaviors such as non-physical growth or abrupt changes.

[0081] (3) Loss of physical consistency

[0082] To enhance the model's stability, smoothness, and compatibility with different degradation modes (including regeneration), this invention introduces a physical consistency loss, consisting of two parts: directional consistency constraint and smoothness constraint. The directional consistency constraint is used to ensure that the predicted SOH change direction remains consistent with the actual change direction, and its form is as follows:

[0083]

[0084] Specifically, when the actual SOH decreases, the prediction should show a downward trend; when local regeneration (actual growth) exists, the prediction should allow for slight growth. =∣ - |: Samples with larger degradation amplitudes are assigned higher weights. The softplus function ensures the differentiability of the constraints and training stability. This design can adapt to the degradation characteristics of different chemical systems and the non-strictly monotonic SOH variation patterns. For smoothness constraints, to avoid high-frequency oscillations caused by noise in the predicted trajectory, this invention introduces a second derivative penalty term:

[0085]

[0086] in, To predict the second derivative of SOH with respect to the input, κ is a smoothness adjustment coefficient, which is a constant. This term encourages the predicted sequence to exhibit a continuous, gradual degradation trend. The overall expression for the physical consistency loss is:

[0087] In summary, the overall form of the physical consistency loss can be expressed as:

[0088]

[0089] Total loss function To achieve comprehensive optimization of data accuracy, physical consistency, and cross-domain robustness, this invention combines the above three types of losses into a unified total loss function:

[0090]

[0091] in, , To balance the adjustment coefficients for data fitting and physical constraints, gradient descent is used to optimize parameters during model training, achieving a balance between accuracy and physical consistency in the prediction results. Through these physical consistency constraints, this invention effectively suppresses non-physical predictions and improves the robustness and generalization performance of the model under different chemical systems, temperatures, and operating conditions.

[0092] Step 4: Model Training Process

[0093] After completing the network structure construction and physical consistency constraint design, this invention trains the Unified Update Candidate Network (UCBNet) and its extended branches, enabling the model to simultaneously satisfy the consistency of data fitting accuracy and degradation dynamics. For example... Figure 4 As shown, the model training process includes the following steps:

[0094] (1) Initialization and Optimizer Setup: The model parameters are updated using a gradient descent-based optimization algorithm. The optimizer can be an adaptive moment estimation method to achieve stable convergence in the multidimensional parameter space. In the initial training phase, a learning rate warm-up mechanism can be set to gradually increase the learning rate from a low value, improving the stability of early training. Subsequently, a learning rate decay strategy can be used to gradually decrease the learning rate during training to improve the convergence quality in later stages. This invention does not limit the specific optimization algorithm, learning rate range, or scheduling method.

[0095] (2) Differentiated learning rate strategy between the main network and the degenerate branch: Considering the sensitivity of the degenerate dynamics branch g(·) and its role in the PDE loss, a relatively small learning rate can be adopted for the parameters of this branch to improve the numerical stability during training and reduce gradient oscillations. The learning rates between the data regression backbone and the degenerate modeling branch can be set independently, and this invention does not limit their specific ratio.

[0096] (3) Training Stability Enhancement Mechanism: To improve the stability of the model during training, the present invention may adopt the following measures: Gradient clipping: Limiting the gradient magnitude before updating network parameters to avoid excessively large gradients leading to training divergence. Weight decay (regularization): Suppressing overfitting and enhancing the model's generalization ability by adding a weight penalty term to the loss function. Batch training mechanism: Using batch training to improve training efficiency and reduce the impact of noise; the batch size is not limited. The above mechanisms can be adjusted according to actual deployment and data characteristics; the present invention does not limit their specific form.

[0097] (4) Division of training set, validation set and test set: In order to ensure the generalization ability of the model and the controllability of the training process, the dataset can be divided into training set, validation set and test set according to the sample level: the training set is used for main parameter optimization; the validation set is used to monitor the training process, evaluate the hyperparameters of the model and prevent overfitting; the specific division ratio is not limited and can be flexibly adjusted according to the actual scenario.

[0098] (5) Model training process: During the training process, the input features are fed into the network in batches, the predicted values ​​are obtained through forward propagation, and the total loss is calculated as follows. The gradient is then calculated using the backpropagation algorithm, and the model parameters are updated. This process is repeated until the termination condition is met. The number of training iterations can be set according to actual needs; this invention does not limit the specific number of training rounds.

[0099] (6) Model performance evaluation: After training, the model performance is measured using preset evaluation metrics (such as root mean square error, relative error, etc.). To verify the model stability, repeated training and evaluation can be performed using multiple independent trials or different random partitioning methods. This invention does not limit the number of repetitions or the randomization method.

[0100] Step 5: SOH Inference Process. After model training is complete, the trained Unified Update Candidate Network (UCBNet) and its physical consistency constraint mechanism can be used to predict the health status of the battery sample in a single step. This step describes the complete process of the SOH inference stage, as follows: Figure 5 As shown.

[0101] (1) Input data collection and feature construction

[0102] The charging process, voltage-current records, temperature changes, or other measurable signals of the battery to be estimated are sampled, and an input feature vector x is generated according to a preset feature extraction method.

[0103] Features include, but are not limited to: statistical features, time-domain features, and derived features related to battery state.

[0104] This invention does not limit the specific number and type of features; those skilled in the art can select features based on the actual situation, in conjunction with the technical framework disclosed in this invention.

[0105] (2) Feature normalization and input processing: For input features, normalization, standardization, or other preprocessing operations that do not change the physical meaning of the data can be performed to improve the robustness of the model to features at different scales. The preprocessing steps can be adjusted according to the actual application requirements, and this invention does not limit them.

[0106] (3) Forward inference of UCBNet

[0107] The constructed input feature vector x is input into the trained UCBNet and sequentially processed through multiple UCB-Unit processes, including:

[0108] Update the gate calculation to generate feature dimension weights;

[0109] Candidate branch computation is used to generate nonlinear representations;

[0110] Element-by-element fusion output generates a unified feature representation;

[0111] The regression head output generates the corresponding SOH predicted value. .

[0112] The entire inference process is a single forward propagation, requiring no time series dependence, recursion, or multi-step prediction.

[0113] (4) Inference phase retention of physical consistency constraints

[0114] Although the loss function is no longer calculated during the inference phase, the model naturally retains its characteristics during inference due to the PDE constraints, directional consistency constraints, and smoothness constraints introduced during the training phase.

[0115] The physically consistent degradation trend is nothing more than physical decomposition or mutation, as well as stability and generalization ability across operating conditions.

[0116] Even if the inferred samples come from different chemical systems or operating conditions than the training samples, the predicted trends still remain physically plausible.

[0117] (5) SOH output and scalable post-processing

[0118] generated This represents the single-step SOH estimate for the corresponding battery sample, which can be directly used as input to the battery management system (BMS). Depending on the application scenario, the following optional steps can be further performed:

[0119] Smoothing filtering;

[0120] Outlier removal;

[0121] Perform correlation analysis with historical records;

[0122] Comparison with a threshold is used for health alerts;

[0123] This invention does not limit the above post-processing procedure.

[0124] (6) Application scenario description

[0125] Based on the above inference process, the model of this invention can be deployed in:

[0126] Electric vehicle battery management system (EV-BMS);

[0127] Energy storage power stations or microgrid BMS;

[0128] Backup power system for communication base stations;

[0129] Portable energy storage devices;

[0130] Or, other scenarios that require real-time SOH assessment;

[0131] In the above applications, the SOH estimation process provided by this invention has significant advantages such as single-step inference, fast response, high accuracy and robustness, strong physical consistency, and easy embedded deployment.

[0132] Compared to existing technologies that rely on additional hardware such as deformation sensors and structural expansion measurements, this invention estimates SOH solely based on standard operating data such as voltage and current during normal charging, without relying on external sensors or additional data acquisition channels. Therefore, this invention has the following further advantages:

[0133] (1) No additional hardware sensors are required, which significantly reduces the system material and manufacturing costs.

[0134] Existing solutions using deformation sensors require additional strain gauges, expansion probes, or complex coupling measurement structures to be placed on the battery surface or in the module structure, which not only increases processing steps but also raises overall manufacturing costs. This invention is entirely based on voltage / current charging data obtainable from existing BMS systems, requiring no additional hardware and can be directly embedded into existing systems, significantly reducing hardware costs.

[0135] (2) The system is more reliable and avoids the risk of failure caused by additional components.

[0136] Deformation sensors are susceptible to temperature drift, mechanical loosening, installation errors, and aging failures in actual operating conditions, increasing the failure rate and maintenance complexity of the BMS. This invention employs a data-driven, sensorless solution that incorporates physical constraints, eliminating the need for any mechanical structures or auxiliary devices. This approach removes the risks of sensor failure, structural detachment, and signal distortion at the source, thereby improving the long-term reliability of the system.

[0137] (3) It is easier to deploy and has a wider range of applications.

[0138] Because it requires no additional hardware, this invention can be seamlessly deployed on most mass-produced battery platforms and existing BMS systems, and is applicable to battery products from different manufacturers, with different specifications and chemical systems, without requiring modifications to the structure or module. Compared to the expansion measurement schemes in the comparative literature, this invention is more universally applicable in engineering implementation.

[0139] (4) It has better long-term stability and does not have problems such as structural fatigue or human installation error.

[0140] The accuracy of deformation detection solutions is highly dependent on the sensor bonding method, fixing structure and long-term stability, while the present invention only relies on the statistical characteristics of the charging curve, and is not affected by mechanical assembly, changes in contact interface or module structure stress changes, and has higher stability in the long-term degradation process.

[0141] The main innovative designs of this invention include:

[0142] Candidate Update Structure (UCBNet)

[0143] UCBNet unifies the candidate update mechanisms in various deep structures, implementing parameter updates in a unified form of Linear + Sigmoid + gating.

[0144] This unified structure has unique advantages such as: a single structure can be adapted to multiple data sources, small parameter size (no need for complex stacking), stable response to degradation features, and easy embedding of physical constraints.

[0145] Physical Consistency Constraints (PINN)

[0146] include:

[0147] 1. Monotonic physical constraint (SOH decreases with cycling);

[0148] 2. PDE Degradation Constraints (based on Degradation Differential Equations);

[0149] 3. Data consistency constraints (physical consistency of the same battery sample);

[0150] These constraints belong to a fusion mechanism of explicit physical equations and physical a priori knowledge, which is completely absent in existing technologies.

[0151] A consistent modeling and unified feature fusion framework across chemical systems

[0152] This invention proposes a consistent modeling approach across chemical systems, which includes physical consistency integration and a unified fusion strategy based on UCBNet. This approach enables unified modeling and stable generalization of different chemical systems such as NCM, NCA, and LFP, achieving good transferability and cross-data consistency.

[0153] To verify the effectiveness of the Physically Consistent Constraint-Based Update Candidate Network (PIUN) proposed in this invention, this embodiment further conducts an exemplary performance comparison on four publicly available battery aging datasets (XJTU, TJU, MIT, and HUST). The comparison methods include pure data-driven models (MLP, CNN) and Physically Information Neural Networks (PINN). Under the same experimental settings, the comparison results show a consistent performance trend.

[0154] (1) Overall performance improvement trend

[0155] In six batch tests on the XJTU dataset, this invention achieved the best or tied-best SOH prediction accuracy. Regarding error metrics MAPE and RMSE, the average error of this invention is lower than PINN and significantly lower than MLP and CNN. For example, in these six batches, this invention reduced the average MAPE by approximately 11% and the average RMSE by approximately 7% compared to PINN. Only in a very few batches did some baseline methods slightly outperform this invention, but this did not affect the overall trend. On the TJU dataset, this invention also achieved a lower average error, showing a significant advantage over PINN, while the data-driven methods MLP and CNN showed significantly higher errors. On the MIT and HUST datasets, the error of this invention was lower than the comparison models in all batches, demonstrating a clear performance lead. Considering all sub-experiments on the four datasets, this invention achieved the lowest MAPE and lowest RMSE in most cases, indicating that the proposed physical consistency constraints and unified gating structure can consistently improve the accuracy of SOH estimation.

[0156] (2) Robustness under noise enhancement conditions

[0157] To simulate measurement noise, sensor anomalies, and system offsets that may occur in real-world operating environments, this embodiment introduces three types of noise into the training data: small-amplitude Gaussian perturbations (amplitude 0.01), random feature loss (proportion 0.1), and systematic offsets (offset 0.02). The validation and test sets are kept clean.

[0158] Even under noise enhancement conditions, this invention still achieves optimal or near-optimal prediction performance. Taking the XJTU dataset as an example, the average MAPE and RMSE of this invention are still lower than PINN under noisy conditions and far below the error range of purely data-driven models. Compared with the best baseline model, the average MAPE of this invention is reduced by about 16% and the RMSE is reduced by about 16% under noise, demonstrating a significant robustness advantage. In noisy scenarios at TJU, MIT, and HUST, this invention also maintains a performance trend superior to the three types of baseline models, indicating that physical consistency constraints and unified gating structures have a substantial effect on improving stable predictions under noise.

[0159] (3) Transfer ability under cross-dataset and small sample conditions

[0160] To verify the cross-domain generalization ability of this invention in heterogeneous chemical systems and under different capacities and temperatures, this embodiment further conducted two types of migration experiments:

[0161] 1. Source Only: Freeze the degradation dynamics branch and fine-tune only the feature map branch to adapt to new data;

[0162] 2. Target Only: This method does not use source domain data at all, relying only on 1-2 labeled battery samples from the target domain for training with a small number of samples.

[0163] Test results show that this invention significantly outperforms PINN in most transfer scenarios. For example, in the XJTU→MIT transfer, the error of this invention is significantly lower than that of PINN, demonstrating strong zero-shot transfer capability; in more challenging scenarios such as TJU→MIT, this invention still maintains a significant advantage. In target-only scenarios, using only 1-2 target batteries, this invention still achieves a low RMSE. For example, in the XJTU and TJU datasets, using a single labeled battery can achieve near-full-data training performance, while PINN shows greater fluctuations under few-sample conditions. This invention demonstrates more efficient data processing capabilities.

[0164] Based on the same inventive concept, this invention also provides a computer device, comprising: one or more processors, and a memory for storing one or more computer programs; the programs include program instructions, and the processor executes the program instructions stored in the memory. The processor may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, used to implement one or more instructions, specifically for loading and executing one or more instructions stored in a computer storage medium to implement the above-described method.

[0165] It should be further explained that, based on the same inventive concept, the present invention also provides a computer storage medium storing a computer program, which, when executed by a processor, performs the above-described method. This storage medium can be any combination of one or more computer-readable media. A computer-readable medium can be a computer-readable signal medium or a computer-readable storage medium. A computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of computer-readable storage media (a non-exhaustive list) include: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In the present invention, a computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0166] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0167] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

[0168] This invention is not limited to the preferred embodiment described above. Anyone inspired by this invention can derive other forms of battery health state estimation methods based on physical constraint networks. All equivalent variations and modifications made within the scope of the claims of this invention shall fall within the scope of this invention.

Claims

1. A battery health state estimation method based on physical constraint networks, characterized in that, include: Without relying on additional sensors, an input feature vector is extracted from standard operating data of the battery charging process, including voltage, current, and temperature data. An update candidate network is constructed, which consists of multiple stacked units, for outputting battery health state estimates and can be extended to generate degradation rate estimates; each unit includes an update gate branch that generates adaptive weights for generating features and a candidate branch that generates nonlinear features, and the outputs of the two branches are fused through element-wise multiplication; The updated candidate network is trained using a loss function with physical constraints. The physical constraints include partial differential equation residual constraints based on the battery degradation kinetic equation and physical consistency regularization adapted to the degradation characteristics of different chemical systems. The partial differential equation residual constraints are used to make the health state evolution predicted by the network conform to the battery degradation kinetic equation and consistent with the degradation rate estimate. The input feature vector of the battery to be tested is input into the trained update candidate network, and the battery health status estimate is directly output through a single forward propagation.

2. The battery health state estimation method based on physical constraint networks according to claim 1, characterized in that: The features corresponding to the input feature vector include statistical features, time-domain features, and derived features related to battery state; The statistical features include statistical parameters of voltage fluctuations during charging, the time-domain features include the duration of the voltage plateau, and the state-derived features include polarization-related parameters calculated based on the voltage-current curve.

3. The battery health state estimation method based on physical constraint networks according to claim 1, characterized in that: Each unit of the updated candidate network is a UCB-Unit, and the degradation rate estimate is generated by the degradation rate prediction branch extended by the updated candidate network. The degradation rate prediction branch shares the underlying feature parameters with the backbone feature extraction part of the updated candidate network.

4. The battery health state estimation method based on physical constraint networks according to claim 1, characterized in that: The method for constructing the partial differential equation residual constraint is as follows: the battery degradation process is abstracted into a dynamic equation to characterize the correlation between the derivative of the degradation state function with respect to cycle time and the estimated degradation rate; the derivative of the health state predicted by the updated candidate network with respect to the input features and cycle number is calculated by automatic differentiation, and the residual is obtained by substituting it into the dynamic equation; the partial differential equation residual constraint is achieved by minimizing the residual obtained from the dynamic equation.

5. The battery health state estimation method based on physical constraint networks according to claim 1, characterized in that: The physical consistency regularization includes directional consistency constraints and smoothness constraints. The directional consistency constraint is achieved by weighting the deviation of the predicted health status from the actual health status, with the weighting coefficient being the absolute value of the actual health status change amplitude, and the calculation process uses the Softplus function to ensure differentiability. The smoothness constraint is achieved by squaring the second derivative of the predicted health status with respect to the input features, with the penalty coefficient being a preset smoothness adjustment constant.

6. The battery health state estimation method based on physical constraint networks according to claim 3, characterized in that: When training the updated candidate network, a parameter optimization algorithm is used, and a differential learning rate is applied to the backbone feature extraction part and the degradation rate prediction branch of the updated candidate network, wherein the learning rate of the degradation rate prediction branch is less than the learning rate of the backbone feature extraction part. The training process also includes gradient clipping, weight decay, and batch training mechanisms to improve training stability.

7. The battery health state estimation method based on physical constraint networks according to claim 1, characterized in that: Before inputting the input feature vector of the battery to be tested into the update candidate network, the input feature vector is further subjected to normalization or standardization preprocessing. The preprocessing operation does not change the physical meaning of the features.

8. The battery health state estimation method based on physical constraint networks according to claim 1, characterized in that: When the number of labeled samples in the scene where the battery under test is located is insufficient, the methods for training the updated candidate network include: freezing the parameters of the degradation rate prediction branch and only fine-tuning the parameters of the backbone feature extraction part; or training the backbone feature extraction part using only 1-2 labeled battery samples under test.

9. The battery health state estimation method based on physical constraint networks according to claim 1, characterized in that: After outputting the battery health status estimate, a post-processing step is also included. The post-processing step includes smoothing filtering, outlier removal, correlation analysis with historical health status records, or comparison with a preset health threshold to trigger a health alarm.

10. A battery health state estimation system based on physical constraint networks, characterized in that, include: The feature extraction module is used to extract input feature vectors from standard operating data during the battery charging process. The standard operating data includes voltage, current and temperature data, without relying on additional hardware sensors. The network construction module is used to construct an update candidate network, which is composed of multiple stacked units and is used to output a battery health state estimate and can be extended to generate a degradation rate estimate. Each unit includes an update gate branch that generates adaptive weights for features and a candidate branch that generates nonlinear features. The outputs of the two branches are fused through element-wise multiplication. The model training module is used to train the updated candidate network using a loss function with physical constraints. The physical constraints include partial differential equation residual constraints based on the battery degradation kinetic equation and physical consistency regularization adapted to the degradation characteristics of different chemical systems. The partial differential equation residual constraints are used to make the health state evolution predicted by the network conform to the battery degradation kinetic equation and consistent with the degradation rate estimate. The SOH estimation module is used to input the input feature vector of the battery under test into the trained update candidate network, and directly output the battery health state estimate through a single forward propagation.

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