Sodium-ion battery SOC estimation method and system based on PINN-EKF fusion

Abstract

The invention belongs to the technical field of battery management, and particularly relates to a sodium ion battery SOC estimation method and system based on PINN-EKF fusion, and the method comprises the steps: obtaining the operation data of a single battery, and constructing a feature vector; inputting the feature vector into a preposed physical information neural network, and dynamically outputting a second-order RC model parameter and a noise scaling factor; constructing a time-varying adaptive noise matrix based on the model parameters and the noise scaling factor, and executing extended Kalman filtering recursion to obtain an SOC preliminary estimated value; and in response to a standing calibration triggering condition, performing strong calibration updating on the SOC preliminary estimation value based on the open-circuit voltage measurement value and the OCV-SOC mapping relation, and outputting a final SOC estimation value. According to the method, model parameters and noise regulation factors are generated in real time through the PINN, so that the model can adapt to battery working condition changes, and a standing strong calibration mechanism is introduced to effectively inhibit accumulative errors.

Description

Technical Field

[0001] This invention belongs to the field of battery management technology, specifically relating to a method and system for estimating the state of charge (SOC) of sodium-ion batteries based on PINN-EKF fusion. Background Technology

[0002] Sodium-ion batteries, due to their abundant resources, low cost, and high safety, have shown broad application prospects in energy storage power stations, electric transportation, and smart grids in recent years, and are considered an important supplement or even replacement for lithium-ion batteries. The state of charge (SOC) of a battery, as a key parameter characterizing the remaining usable capacity, directly affects the battery's safety, lifespan, and system energy management efficiency. However, the electrochemical characteristics of sodium-ion batteries are complex, and the relationship between SOC and factors such as voltage, current, and temperature exhibits strong nonlinearity and hysteresis, making traditional SOC estimation methods difficult to meet high-accuracy requirements.

[0003] Currently, SOC estimation methods based on the fusion of equivalent circuit models and Kalman filtering have been widely studied and applied. For example, patent application CN119916227A discloses a sodium-ion battery SOC estimation method based on extended Kalman filtering. This method constructs a third-order RC equivalent circuit model, uses offline HPPC test data to fit the open-circuit voltage-state-of-charge (OCV-SOC) function relationship and identify model parameters, and then uses the extended Kalman filtering algorithm to recursively estimate the SOC.

[0004] This method improves the accuracy of SOC estimation to some extent, but still has the following drawbacks: First, the model parameters are obtained through offline testing and remain fixed during actual operation, which cannot adapt to the dynamic characteristics of the battery under different operating conditions and aging stages; Second, the process noise and observation noise matrices use fixed preset values, which makes it difficult to reflect the real changes in model uncertainty and sensor noise under different operating conditions, resulting in limited filter estimation accuracy; In addition, the pure recursive estimation method is prone to error accumulation and lacks an effective error correction mechanism, resulting in a significant decrease in estimation accuracy after long-term operation. Summary of the Invention

[0005] The purpose of this invention is to provide a sodium-ion battery SOC estimation method and system based on PINN-EKF fusion, in order to solve the problems of existing sodium-ion battery SOC estimation methods, such as fixed model parameters, inability to adapt to changes in operating conditions, and lack of error correction methods, resulting in low estimation accuracy and long-term error accumulation.

[0006] The present invention achieves the above objectives through the following technical solutions: Firstly, this invention proposes a method for estimating the state of charge (SOC) of sodium-ion batteries based on PINN-EKF fusion, comprising the following steps: The battery's current operating data is acquired, and a feature vector characterizing the battery's current operating condition is constructed based on the operating data and the SOC estimate from the previous moment; the operating data includes voltage, current, and temperature. The feature vector is input into the pre-physical information neural network, which outputs the second-order RC equivalent circuit model parameters and noise scaling factor at the current moment. Based on the parameters of the second-order RC equivalent circuit model and the noise scaling factor, a time-varying adaptive noise matrix is ​​constructed, and an extended Kalman filter recursion is performed to obtain a preliminary SOC estimate. In response to the detection that the battery meets the preset static calibration trigger condition, the initial SOC estimate is strongly calibrated and updated based on the current open-circuit voltage measurement value and the pre-stored open-circuit voltage-state of charge mapping relationship, and the final SOC estimate is output.

[0007] Furthermore, before acquiring real-time operating data of a single battery cell, the method further includes: Set the initial values ​​of SOC, polarization voltage, error covariance matrix, basic process noise matrix, and basic observation noise matrix as the initial state of the extended Kalman filter; The initial SOC value is obtained by inverse solving based on the open-circuit voltage measurement value at the power-on time and the pre-stored open-circuit voltage-state of charge mapping relationship, or by reading the historically stored SOC value, or by using the system's preset default value.

[0008] Furthermore, the preceding physical information neural network is a multi-layer feedforward neural network, comprising an input layer, several hidden layers, and an output layer connected in sequence. The input layer is used to receive the input feature vector. , is represented as: In the formula, This is the estimated SOC value from the previous time step. The current battery temperature. This is the absolute value of the current. Let k be the rate of change of current and k be the index of the sampling time. The hidden layer is used to perform nonlinear transformation on the feature vector to extract hidden layer features associated with battery polarization effect, ohmic effect and noise characteristics. The output layer generates the current output vector based on the hidden layer features. , is represented as: In the formula, The parameters of the second-order RC model output at time k are... This is the process noise scaling factor. To measure the noise scaling factor; During the offline training phase, the aforementioned pre-physical information neural network uses the terminal voltage from historical operating data as a supervision signal to construct a multi-objective loss function that integrates terminal voltage prediction error constraints, residual constraints of the second-order RC model dynamic equations, and physical range constraints of parameters for training. This enables the network to learn the nonlinear mapping relationship between battery physical characteristics and model parameters and noise characteristics.

[0009] Furthermore, the multi-objective loss function is obtained by the following formula: ; In the formula, For voltage prediction loss; This represents a loss of physical consistency. This is the regularization loss; The voltage prediction loss The mean square error between the predicted terminal voltage and the measured terminal voltage, based on the parameters of the second-order RC model output by the network, is constructed as follows: ; In the formula, The terminal voltage is predicted based on the parameters of a second-order RC model output by the network. Where N is the measured terminal voltage, and N is the number of samples. The physical consistency loss The residuals of the discretized dynamic equations based on the second-order RC equivalent circuit model are constructed as follows: ; In the formula, , The polarization voltage at the current moment. , The polarization voltage is the value at the previous moment, and T is the sampling period. and It is a time constant. and Polarization resistor; The regularization loss The smoothing constraint terms, including the range constraints of the model parameters and the noise scaling factor, are as follows: + ; In the formula, These are the model parameters output by the network. and These are the minimum and maximum values ​​of the corresponding model parameters, respectively. and These are the process noise scaling factors at times k+1 and k, respectively. and These are the observation noise scaling factors at times k+1 and k, respectively.

[0010] Furthermore, the construction of the time-varying adaptive noise matrix is ​​specifically as follows: Based on the preset basic process noise matrix With the basic observation noise matrix The base noise is scaled using the noise scaling factor output by the neural network based on the prior physical information, and the process noise matrix and observation noise matrix at the current moment are constructed as follows: ; In the formula, Let k be the process noise matrix at time k. Let k be the observation noise matrix at time k. This is the process noise scaling factor. To observe the noise scaling factor.

[0011] Furthermore, the process of performing extended Kalman filtering recursion to obtain a preliminary estimate of SOC is as follows: Discretize the second-order RC equivalent circuit model into a state-space expression: ; In the formula, This is the state vector for the next time step. Let this be the current state vector. The state transition coefficient matrix is... For the input coefficient matrix, This refers to the system's controllable input at the current moment. These are actual observed values. The observation coefficient matrix, This is the gain coefficient matrix. For system noise, For measuring noise; The execution state prediction step obtains the prior state estimate. and prior error covariance matrix : ; In the formula, This is the state transition coefficient matrix at the current time. This is the state transition coefficient matrix from the previous time step. This is the transpose of the state transition coefficient matrix at the current moment. The input coefficient matrix is ​​the one from the previous time step. This represents the input from the previous time step. Let be the posterior error covariance matrix of the previous time step. For process noise covariance; Perform the observation update step and calculate the Kalman gain. : ; In the formula, These are predicted measurement values. These are actual measured values. The observation coefficient matrix, This is the gain coefficient matrix. This is the transpose of the observation coefficient matrix. For output value error, To observe the noise covariance; Using Kalman gain The prior estimate is corrected for observation errors to obtain the posterior state estimate. and the posterior error covariance matrix : ; in, It is the identity matrix. The observation coefficient matrix, The prior error covariance matrix; Based on the posterior state estimation Determine the preliminary estimate of SOC at the current moment.

[0012] Furthermore, the static calibration triggering conditions include: Current criterion: The absolute value of the sampled current is continuously lower than the preset resting current threshold, and the duration exceeds the preset minimum resting time; Voltage stability criterion: The standard deviation of the terminal voltage within a preset time window is less than a preset voltage stability threshold; Temperature stability criterion: The rate of temperature change within a preset time window is less than a preset temperature stability threshold. When the current criterion, voltage stability criterion, and temperature stability criterion are all satisfied, the battery is determined to be in a relaxation state, and the current terminal voltage measurement value is taken as the open circuit voltage value.

[0013] Furthermore, the pre-stored open-circuit voltage-state-of-charge mapping relationship is established through the following steps: The sodium-ion battery was charged and discharged at multiple preset temperatures. At each preset temperature, it was charged with a constant current to the cutoff voltage and then charged with a constant voltage until the current dropped to a preset threshold. After being left to stand for a preset time, it was discharged with a constant current. The terminal voltage was recorded as the open circuit voltage value after each preset SOC change. A fourth-order polynomial was used to fit the open-circuit voltage-state-of-charge data at different temperatures: ; in, Open circuit voltage, - The coefficients of the polynomial, This indicates the battery's state of charge.

[0014] Furthermore, the initial SOC estimate is strongly calibrated and updated based on the current open-circuit voltage measurement and the pre-stored open-circuit voltage-state-of-charge mapping relationship, specifically as follows: In response to the detection that the battery meets the preset rest calibration trigger condition, the current terminal voltage is... As open circuit voltage ; Based on the current temperature The fitted curve at the corresponding temperature is retrieved from the pre-stored open-circuit voltage-state of charge mapping relationship; Current terminal voltage Substituting the fitted curve, the calibrated SOC value is obtained by inverse solution; Replace the extended Kalman filter's posterior state estimate at the current time step with the calibrated SOC value. The SOC component in the polarization voltage state. , Reset to zero to obtain the corrected posterior state estimate; The SOC component in the corrected posterior state estimate is output as the final SOC estimate at the current time, and the corrected posterior state estimate and its corresponding posterior error covariance matrix are used as the initial state for the next time step of the extended Kalman filter recursion.

[0015] Secondly, the present invention proposes an estimation system that applies the sodium-ion battery SOC estimation method described above, the system comprising: The data acquisition module is used to acquire the current operating data of a single battery cell, including voltage, current, and temperature. The feature construction module is used to construct a feature vector representing the current operating condition of the battery based on the running data and the final SOC estimate output at the previous moment. The parameter generation module has a built-in pre-physical information neural network, which is used to output the second-order RC equivalent circuit model parameters and noise scaling factor at the current moment based on the feature vector. The filtering estimation module is used to construct a time-varying adaptive noise matrix based on the parameters of the second-order RC equivalent circuit model and the noise scaling factor, and to perform extended Kalman filter recursion to obtain the intermediate estimate of SOC at the current time. The static calibration module is used to detect whether the battery meets the preset static calibration trigger conditions, and when the conditions are met, it performs strong calibration and updates the intermediate SOC estimate based on the current open-circuit voltage measurement value and the pre-stored open-circuit voltage-state of charge mapping relationship, and outputs the final SOC estimate value at the current moment. The initialization module is used to set the initial values ​​of SOC, polarization voltage, error covariance matrix, basic process noise matrix, and basic observation noise matrix when the system starts up, as the initial state of the extended Kalman filter.

[0016] The beneficial effects of this invention are as follows: (1) This invention uses a pre-processed physical information neural network (PINN) to dynamically generate five key parameters (ohmic internal resistance, polarization resistance, polarization capacitance) of a second-order RC equivalent circuit model in real time, as well as two noise scaling factors of an extended Kalman filter. This enables the model parameters to be adaptively adjusted according to changes in battery operating conditions (SOC, temperature, current), solving the problem that traditional methods have fixed model parameters and are difficult to adapt to complex operating conditions.

[0017] (2) In this invention, the multi-objective loss function of PINN integrates voltage prediction error, physical equation residuals, and parameter range constraints, ensuring the physical rationality and generalization ability of the output parameters. Targeting the high linearity of the OCV-SOC curve of sodium-ion batteries, a multi-criteria static detection mechanism and a strong calibration strategy are designed. When the battery is fully relaxed, the SOC value is inversely solved using the open-circuit voltage to forcibly correct the estimation results, effectively suppressing the error accumulation of the pure recursive algorithm. Attached Figure Description

[0018] Figure 1 This is a flowchart of a sodium-ion battery SOC estimation method in one embodiment of the present invention; Figure 2 This is a schematic diagram of a second-order RC equivalent circuit model in one embodiment of the present invention; Figure 3 This is a schematic diagram of the PINN-EKF model structure in one embodiment of the present invention; Figure 4 This is a system block diagram of a sodium-ion battery SOC estimation system in one embodiment of the present invention. Detailed Implementation

[0019] The present application will now be described in further detail with reference to the accompanying drawings. It should be noted that the following specific embodiments are only used to further illustrate the present application and should not be construed as limiting the scope of protection of the present application. Those skilled in the art can make some non-essential improvements and adjustments to the present application based on the above application content.

[0020] Example 1 This embodiment provides a sodium-ion battery SOC estimation method based on PINN-EKF fusion. This method combines a pre-processed Physical Information Neural Network (PINN) with an Extended Kalman Filter (EKF) to achieve high-precision online estimation of the sodium-ion battery's state of charge. This method fully considers the complex dynamic characteristics of sodium-ion batteries and their susceptibility to operating conditions. It generates model parameters and noise information in real time through PINN and incorporates a static strong calibration mechanism, effectively solving the problems of fixed models and easy error accumulation in traditional methods. (See reference...) Figure 1 The present invention proposes a sodium-ion battery SOC estimation method based on PINN-EKF fusion in a specific embodiment, which includes the following steps: S1. Obtain the current operating data of a single battery cell, and construct a feature vector representing the current operating condition of the battery based on the operating data and the SOC estimate of the previous time.

[0021] Specifically, the battery management system (BMS) acquires the current operating data of individual cells, including terminal voltage, load current (positive for charging, negative for discharging), and battery temperature T. The collected raw data is then preprocessed. (1) Remove abnormal data: Set reasonable threshold ranges, such as voltage exceeding 2.5~4.5V, current exceeding ±500A, and temperature exceeding -30~80℃, and judge them as abnormal data, remove them or use the data from the previous moment to replace them; (2) Data interpolation: When the sampling frequency is inconsistent or there is data loss, linear interpolation is used to complete the data sequence; (3) Time synchronization check: Ensure that voltage, current and temperature data are aligned on the timestamp to avoid phase difference causing model misjudgment; (4) Normalization: Scale data of different dimensions to a uniform range (e.g., [0,1]) to improve the stability of neural network training.

[0022] Based on the preprocessed data, construct the feature vector for the current time step. The feature vector contains four key features: the estimated SOC value at the previous time step, the current temperature, the current absolute current value, and the rate of change of current, specifically represented as follows: In the formula, This is the estimated SOC value from the previous time step. The current battery temperature. This is the absolute value of the current. Here, is the rate of change of current, and k is the index of the sampling time. These four features together characterize the current operating condition of the battery. Reflecting the historical state of the battery, Affecting the internal reaction rate and parameter changes of the battery Reflects load strength This reflects the drastic changes in operating conditions. By combining these features, sufficient operating condition information can be provided for subsequent neural networks.

[0023] It should be noted that the "preliminary SOC estimate" mentioned in this embodiment refers to the state variable obtained after EKF recursion but before static calibration. If the static calibration trigger condition is met at the current moment, the preliminary estimate is updated by strong calibration to obtain the "final SOC estimate" and output. If the static calibration trigger condition is not met at the current moment, the preliminary SOC estimate is directly output as the final SOC estimate. Regardless of whether calibration has been performed, the final SOC value output at this moment is used as the "previous moment SOC estimate" for the next moment.

[0024] Before starting the recursive estimation, a reasonable initial state needs to be set for the extended Kalman filter to ensure fast convergence and estimation accuracy. Therefore, this method performs the following initialization settings after acquiring real-time running data and before the first execution of the filter recursion.

[0025] In a preferred embodiment, after acquiring the real-time operating data of a single battery cell, the method further includes: Set the initial values ​​of SOC, polarization voltage, error covariance matrix, basic process noise matrix, and basic observation noise matrix as the initial state of the extended Kalman filter; The initial SOC value is obtained by inverse solving the open-circuit voltage measurement at power-on and the pre-stored open-circuit voltage-state-of-charge mapping relationship, or by reading historically stored SOC values, or by using the system's default value. Proper initialization settings can accelerate filter convergence and improve estimation accuracy in the initial stage. Specifically, the initial polarization voltage value is typically set to 0, the initial error covariance matrix value is set based on the degree of uncertainty regarding the initial state, and the basic process noise matrix and basic observation noise matrix are pre-calibrated based on sensor accuracy and model error empirical values.

[0026] S2. Input the feature vector into the pre-physical information neural network, and output the second-order RC equivalent circuit model parameters and noise scaling factor at the current moment.

[0027] To overcome the limitation of traditional fixed-parameter models in adapting to the time-varying characteristics of batteries, this invention introduces a pre-existing physical information neural network (PINN), see [reference]. Figure 3The aforementioned pre-processing physical information neural network is a multi-layer feedforward neural network, comprising an input layer, several hidden layers, and an output layer connected in sequence. During the offline training phase, the network uses the terminal voltage from historical operating data as a supervisory signal to construct a multi-objective loss function that integrates terminal voltage prediction error constraints, residual constraints of the second-order RC model's dynamic equations, and physical range constraints of the parameters. This allows the network to learn the nonlinear mapping relationship between battery physical characteristics and model parameters and noise characteristics.

[0028] When used in online applications, the feature vector constructed in step S1 will be... The input is fed into a pre-trained neural network containing physical information. This network is a multi-layer feedforward neural network, consisting of an input layer, several hidden layers, and an output layer connected in sequence.

[0029] The input layer is used to receive feature vectors. The number of nodes is the same as the dimension of the input features (4 nodes in this embodiment).

[0030] The hidden layers are used to perform nonlinear transformations on the feature vectors, extracting hidden features associated with battery polarization effects, ohmic effects, and noise characteristics. The number of hidden layers and the number of nodes per layer can be optimized based on the training effect. In this embodiment, three hidden layers are preferably used, with 64 nodes per layer. The ReLU activation function is used to enhance the nonlinear expressive power of the network.

[0031] The output layer generates the output vector at the current time step based on the hidden layer features. , is represented as: In the formula, The parameters of the second-order RC model output at time k are... This is the process noise scaling factor. To observe the noise scaling factor.

[0032] In this embodiment, unlike the traditional method where the model parameters are fixed, the network output parameters of the present invention change dynamically with the operating conditions. For example, during high current discharge, the network may output a larger polarization resistance to reflect the enhanced polarization effect; when the temperature changes, the ohmic internal resistance is also adjusted accordingly, so that the model can adapt to the dynamic characteristics of the battery under different SOC, temperature and current in real time, significantly improving the model's adaptability.

[0033] During the offline training phase, the aforementioned pre-processed physical information neural network uses the terminal voltage from historical operational data as a supervision signal to construct a multi-objective loss function for training. This loss function integrates data-driven and physical constraints, specifically comprising three parts: (1) Voltage prediction loss The mean square error between the predicted terminal voltage and the measured terminal voltage based on the parameters of the second-order RC model output by the network ensures that the network can accurately fit the voltage response characteristics. (2) Loss of physical consistency The discretized dynamic equation residuals based on the second-order RC equivalent circuit model ensure that the parameters output by the network conform to the physical laws of the battery. (3) Regularization loss This includes range constraints for model parameters and smoothing constraints for noise scaling factors, ensuring that the network output parameters are within a reasonable physical range and that noise factor changes smoothly.

[0034] In a preferred embodiment, the multi-objective loss function is obtained by the following equation: ; Voltage prediction loss The mean square error between the predicted terminal voltage and the measured terminal voltage, based on the parameters of the second-order RC model output by the network, is constructed as follows: ; In the formula, The terminal voltage is predicted based on the parameters of a second-order RC model output by the network. Where N is the measured terminal voltage, and N is the number of samples. Physical consistency loss The residuals of the discretized dynamic equations based on the second-order RC equivalent circuit model are constructed as follows: ; In the formula, , The polarization voltage at the current moment. , The polarization voltage is the value at the previous moment, and T is the sampling period. and It is a time constant. and Polarization resistor; Regularization loss The smoothing constraint terms, including the range constraints of the model parameters and the noise scaling factor, are as follows: + ; In the formula, The model parameters output by the network. and These are the minimum and maximum values ​​of the corresponding model parameters, respectively. and These are the process noise scaling factors at times k+1 and k, respectively. and These are the observation noise scaling factors at times k+1 and k, respectively.

[0035] Through joint optimization of multi-objective loss functions, the network incorporates battery physical characteristics while learning from historical data, thereby enabling it to dynamically generate model parameters and noise control factors that conform to physical laws based on real-time operating conditions. After training, the network parameters are fixed and can be directly used for online estimation.

[0036] After obtaining the current-time second-order RC model parameters and noise scaling factor of the PINN network output through step S2, these dynamic parameters need to be effectively applied to the recursive estimation of SOC. Therefore, step S3 designs a specific implementation method for adaptive noise matrix construction and EKF filtering recursion.

[0037] S3. Construct a time-varying adaptive noise matrix based on the parameters of the second-order RC equivalent circuit model and the noise scaling factor, and perform extended Kalman filter recursion to obtain a preliminary estimate of SOC.

[0038] After obtaining the dynamic model parameters and noise factor at the current moment, this step seamlessly embeds them into the EKF framework. Based on the second-order RC model parameters and noise scaling factor output from step S2, a time-varying adaptive noise matrix is ​​constructed, and an extended Kalman filter recursion is performed to obtain a preliminary estimate of the SOC at the current moment.

[0039] First, a time-varying adaptive noise matrix is ​​constructed. The performance of the EKF is highly dependent on the accuracy of the process noise matrix Q and the observation noise matrix R. Traditional methods using fixed Q and R matrices struggle to adapt to complex and variable operating conditions. This invention utilizes the scaling factor output by PINN to dynamically adjust the noise level, enabling the filter to adaptively adjust its weights based on the current operating conditions and model uncertainties. This is based on a preset fundamental process noise matrix. With the basic observation noise matrix The base noise is scaled by combining the noise scaling factor output by the neural network based on the prior physical information, and the process noise matrix and observation noise matrix at the current moment are constructed: ; In the formula, Let k be the process noise matrix at time k. Let k be the observation noise matrix at time k. This is the process noise scaling factor. To measure the noise scaling factor, an exponential function mapping is used to ensure the positive definiteness of the noise matrix, while allowing the scaling factor to be freely adjusted in the logarithmic domain, which is more conducive to the learning and output of the neural network.

[0040] Secondly, a second-order RC equivalent circuit model of the sodium-ion battery is established and discretized, serving as the physical basis for the EKF recursion. Based on Kirchhoff's current law and voltage law, the continuous-time domain expression of the second-order RC equivalent circuit model is as follows: ; ; In the formula, Let be the external load current of the battery at time t. Polarized capacitor, Polarization resistor, Polarization voltage, Let be the external terminal voltage of the battery at time t. It is the internal resistance of the Ohm.

[0041] Figure 2 This is a schematic diagram of the second-order RC equivalent circuit model used in an embodiment of the present invention. The model consists of an open-circuit voltage source. Ohmic internal resistance It consists of two parallel RC networks connected in series. The first RC network is composed of a polarization resistor. and polarization capacitor The first RC network consists of a voltage U1 across its terminals, representing the electrochemical polarization effect of the battery; the second RC network is composed of polarization resistors. and polarization capacitor It is composed of a voltage of U2 across its two ends, which characterizes the concentration polarization effect of the battery. Let I be the battery terminal voltage and I be the load current (negative for charging, positive for discharging). This model achieves a good balance between computational complexity and descriptive accuracy, accurately reflecting the dynamic characteristics of sodium-ion batteries. This invention outputs data in real time via a PINN network. , , , , Five model parameters enable the model to adaptively adjust to changes in operating conditions.

[0042] Discretizing the above continuous model yields the following set of discretized equations: ; In the formula, The terminal voltage at the current moment. and The polarization voltage at the current moment. and This is the polarization voltage at the previous moment. The current state of charge. and It is a time constant. This is the row vector of coefficients for the OCV-SOC curve fitting function.

[0043] Based on the above discretization equations, the battery SOC and two polarization voltages are... As a state variable, current I is the input, and terminal voltage... As observed variables, combined with the dynamic parameters output in real time by the PINN network, a state-space expression suitable for EKF recursion can be obtained: Substituting the second-order RC equivalent circuit model of the battery into the state-space expression of the discrete system, the discretization results in the following set of system state equations and output observation equations: ; In the formula, Represents the nominal capacity.

[0044] Based on the above state-space equations, the EKF recursive process is executed to obtain a preliminary estimate of the SOC. The specific recursive steps are as follows: The discretized equations of the second-order RC equivalent circuit model are rewritten as standard state-space expressions: ; in, This is the state vector for the next time step. Let this be the current state vector. The state transition coefficient matrix is... For the input coefficient matrix, This refers to the system's controllable input at the current moment. These are actual observed values. The observation coefficient matrix, This is the gain coefficient matrix. For system noise, For measuring noise; Specifically, the coefficient matrices are as follows: ; ; ; ; The execution state prediction step obtains the prior state estimate. and prior error covariance matrix : ; in, This is the state transition coefficient matrix at the current time. This is the state transition coefficient matrix from the previous time step. This is the transpose of the state transition coefficient matrix at the current moment. The input coefficient matrix is ​​the one from the previous time step. This represents the input from the previous time step. Let be the posterior error covariance matrix of the previous time step. For process noise covariance; Perform the observation update step and calculate the Kalman gain. : ; in, These are predicted measurement values. These are actual measured values. The observation coefficient matrix, This is the gain coefficient matrix. This is the transpose of the observation coefficient matrix. Indicates the error in the output value. Represents the observation noise covariance. This is the prior error covariance matrix obtained in the previous step; Using Kalman gain The prior estimate is corrected for observation errors to obtain the posterior state estimate. and the posterior error covariance matrix : ; in, It is the identity matrix. Here is the Kalman gain matrix. The observation coefficient matrix, The prior error covariance matrix; This represents the posterior estimate of the state quantity at the current moment. The preliminary estimate of the battery's SOC at the current moment is obtained through the posterior estimate (first component) of the state quantity.

[0045] S4. In response to the detection that the battery meets the preset static calibration trigger condition, based on the current open circuit voltage measurement value and the pre-stored open circuit voltage-state of charge mapping relationship, perform strong calibration update on the preliminary SOC estimate and output the final SOC estimate.

[0046] Considering that the terminal voltage of a sodium-ion battery is very close to the actual open-circuit voltage after sufficient rest, and that its OCV-SOC curve has good linearity and repeatability, this invention designs a rest-based strong calibration mechanism as an effective means of correcting the accumulated error in the EKF recursion process, which can maintain high estimation accuracy even after long-term operation.

[0047] To achieve SOC calibration based on open-circuit voltage, a precise, temperature-varying OCV-SOC mapping library needs to be established beforehand. In a preferred embodiment, the pre-stored open-circuit voltage-state-of-charge mapping is established through the following steps: The sodium-ion battery was subjected to charge-discharge tests at multiple preset temperatures, such as typical temperature points like -20℃, 0℃, 25℃, 45℃, and 60℃, covering the battery's normal operating temperature range. At each preset temperature, the battery was charged to the cutoff voltage with a constant current (e.g., 0.5C), then charged with a constant voltage until the current dropped to a preset threshold (e.g., 0.05C), and left to stand for a preset time (e.g., 2 hours) to ensure the battery reached equilibrium. Then, the battery was discharged with a constant current (e.g., 0.5C), and left to stand at preset SOC changes (e.g., 5%), with the terminal voltage recorded as the open-circuit voltage value. The above steps were repeated until the battery discharged to 0% of its remaining capacity.

[0048] Considering that the OCV-SOC curve of sodium-ion batteries is flatter and more linear than that of lithium-ion batteries, a fourth-order polynomial is used to fit the open-circuit voltage-state-of-charge data at different temperatures: ; in, Open circuit voltage, - The coefficients of the polynomial, This indicates the battery's state of charge. - By conducting charge-discharge tests on sodium-ion batteries at different temperatures, open-circuit voltage data corresponding to each State of Charge (SOC) point were collected, and the experimental data were fitted with a fourth-order polynomial using the least squares method. For temperature points not directly tested, the values ​​could be obtained through linear interpolation of the coefficients of adjacent temperature points, thereby constructing a continuous OCV-SOC mapping relationship covering the entire temperature range, providing an accurate basis for SOC calibration under different environments.

[0049] In a preferred embodiment, the static calibration trigger conditions include: Current criterion: The absolute value of the sampled current is continuously lower than the preset resting current threshold, such as 0.05C (C is the battery rated capacity ratio), and the duration exceeds the preset minimum resting time. For sodium-ion batteries, in order to ensure sufficient relaxation of polarization effect, this time can be set to 2 hours. Voltage stability criterion: Within a preset time window, such as the last 10 minutes, the standard deviation of the terminal voltage is less than the preset voltage stability threshold, such as 5mV, to ensure that the voltage has stabilized and there are no obvious fluctuations. Temperature stability criterion: The rate of temperature change within a preset time window is less than a preset temperature stability threshold, such as 2℃ / h, to eliminate the interference of temperature change on the open circuit voltage measurement value; When the current criterion, voltage stability criterion, and temperature stability criterion are simultaneously satisfied, the battery is determined to be in a fully relaxed state. At this point, the internal polarization voltage of the battery can be considered to have decayed to a negligible level, and the current terminal voltage measurement value is taken as the open-circuit voltage value. This multi-criteria static detection mechanism effectively avoids false calibration triggering when the battery is not truly stable, ensuring the accuracy and reliability of OCV measurement.

[0050] After the above-mentioned static calibration triggering conditions are met, a strong calibration update is performed. In a preferred embodiment, based on the current open-circuit voltage measurement and the pre-stored open-circuit voltage-state-of-charge mapping relationship, a strong calibration update is performed on the preliminary SOC estimate. This is a key step in suppressing error accumulation during the EKF recursion process, and is particularly suitable for systems like sodium-ion batteries that have a good OCV-SOC linear relationship. Specifically: (1) In response to the detection that the battery meets the preset static calibration trigger condition, the current terminal voltage is set. As open circuit voltage ; (2) Based on the current temperature The fitted curve at the corresponding temperature is retrieved from the pre-stored open-circuit voltage-state of charge mapping relationship; (3) Set the current terminal voltage Substitute the fitted curve and inversely solve to obtain the calibrated SOC value; (4) Replace the extended Kalman filter's posterior state estimate at the current time step with the calibrated SOC value. The SOC component in the polarization voltage state. , Reset to zero to obtain the corrected posterior state estimate; (5) Output the SOC component in the corrected posterior state estimate as the final SOC estimate at the current time, and use the corrected posterior state estimate and its corresponding posterior error covariance matrix as the initial state for the next time step of the extended Kalman filter recursion.

[0051] This forced calibration method can completely eliminate the SOC estimation error accumulated during the early dynamic operation, and at the same time reset the polarization voltage state, so that the model can start the recursion again with an accurate initial state after the resting period, thereby significantly improving the estimation accuracy and robustness in long-term operation.

[0052] In an optional approach, to address the model parameter drift caused by aging and degradation during long-term battery use, this method also sets up a periodic recalibration strategy. When the battery's cumulative operating time reaches a set threshold (such as 3 months or 500 equivalent full charge cycles), or when the SOC error during static calibration is detected to continuously exceed a preset threshold (such as three consecutive static calibration errors greater than 3%), the model update process will be automatically triggered.

[0053] The updates include: refitting the OCV-SOC curve using data collected during the recent resting phase to correct for changes in the OCV relationship caused by aging; and freezing most of the PINN network layers, only using the latest running data to perform lightweight fine-tuning of the output layer weights. This transfer learning approach enables the model to quickly adapt to the current aging state of the battery with minimal computational cost, thereby maintaining the estimation accuracy and adaptability of this method throughout the entire battery lifespan.

[0054] Example 2 See Figure 4 Based on the same inventive concept, a specific embodiment of this invention proposes an estimation system that implements the sodium-ion battery SOC estimation method as described in Embodiment 1. This system can be integrated into a battery management system (BMS) as a core functional module of the BMS, enabling high-precision online estimation of the sodium-ion battery's state of charge. The system includes a data acquisition module, a feature construction module, a parameter generation module, a filtering estimation module, a static calibration module, and an initialization module.

[0055] The data acquisition module is used to acquire the current operating data of individual battery cells, including voltage, current, and temperature. This module connects to the sensor interface in the battery management system and collects the battery's terminal voltage, load current (positive for charging, negative for discharging), and battery temperature in real time at a preset sampling frequency (e.g., 1Hz-10Hz). The data acquisition module also integrates a preprocessing unit to filter, remove outliers, and check time synchronization of the raw sampled data, ensuring the quality and consistency of the output data and providing input data for subsequent modules.

[0056] The feature construction module is used to construct a feature vector representing the current operating condition of the battery based on the operating data and the final SOC estimate output from the previous time step. This module receives the current operating data output from the data acquisition module and reads the final SOC estimate output from the previous time step from the system storage unit, constructing the feature vector according to the method described in step S1 of Embodiment 1. This feature vector represents the battery's historical state, current temperature, load intensity, and the degree of drastic change in operating conditions, and serves as the input to the parameter generation module.

[0057] The parameter generation module incorporates a pre-trained physical information neural network (PINN) to output the parameters of the second-order RC equivalent circuit model and the noise scaling factor at the current moment based on the feature vector. The core of this module is a pre-trained physical information neural network (PINN), with a network structure as described in step S2 of Example 1, including an input layer (4 nodes), several hidden layers (preferably 3 layers, 64 nodes per layer, with ReLU activation function), and an output layer (7 nodes). When the feature construction module generates the feature vector... After being input into the network, the network performs forward propagation calculations and outputs the second-order RC model parameters at the current time step in real time. and noise scaling factor , These dynamic parameters can reflect the changes in battery characteristics under different operating conditions in real time.

[0058] The filtering estimation module constructs a time-varying adaptive noise matrix based on the parameters of the second-order RC equivalent circuit model and the noise scaling factor, and performs extended Kalman filtering recursion to obtain the intermediate estimate of the SOC at the current time. This module first generates the noise scaling factor from the parameter generation module output. , The time-varying adaptive process noise matrix and observation noise matrix are constructed according to the formula. Then, based on the second-order RC model parameters output by the parameter generation module, the state-space equation as described in step S3 of Example 1 is established, and EKF recursion is performed, including steps such as state prediction, linearization processing, and observation update, to finally obtain the posterior state estimate at the current time, where the SOC component is the intermediate SOC estimate (i.e., the preliminary estimate). This module realizes the filter's adaptability to complex operating conditions through adaptive noise adjustment and dynamic model update.

[0059] The static calibration module detects whether the battery meets the preset static calibration trigger conditions. When the conditions are met, it performs a strong calibration update on the intermediate SOC estimate based on the current open-circuit voltage measurement and the pre-stored open-circuit voltage-state-of-charge mapping relationship, and outputs the final SOC estimate for the current moment. This module continuously monitors the current, voltage, and temperature data provided by the data acquisition module to determine whether the three static calibration trigger conditions described in step S4 of Example 1 are simultaneously met: current criterion, voltage stability criterion, and temperature stability criterion. When all three conditions are met, the battery is determined to be in a fully relaxed state, and the current terminal voltage is used as the open-circuit voltage. Then, based on the current temperature, the corresponding temperature fitting curve is retrieved from the pre-stored OCV-SOC mapping relationship library, and the calibrated SOC value is obtained through numerical solution. Finally, the calibrated SOC value replaces the SOC component in the posterior state estimate output by the filtering estimation module, and the polarization voltage is adjusted accordingly. , The state is reset to zero, resulting in a corrected posterior state estimate. The SOC component of this estimate is the final SOC estimate for the current time step. Simultaneously, this corrected state estimate and its error covariance matrix are fed back to the filtering estimation module as the initial state for the EKF recursion at the next time step.

[0060] The initialization module sets the initial values ​​of SOC, polarization voltage, error covariance matrix, basic process noise matrix, and basic observation noise matrix during system startup, serving as the initial state for the extended Kalman filter (EKF). This module is triggered upon system power-on or reset and determines the initial SOC value according to a preset strategy: preferentially, it obtains the value through inverse solving of the open-circuit voltage measurement at power-on and the OCV-SOC mapping relationship; if this is not feasible, it reads the historically stored SOC value; if still not feasible, it adopts the system's preset default value (e.g., 50%). Simultaneously, it sets the initial polarization voltage value to 0 and sets the initial values ​​of the error covariance matrix, basic process noise matrix, and basic observation noise matrix based on empirical values. These initial states are loaded into the filter estimation module, ensuring that the EKF is recursively calculated from an accurate initial state, thus accelerating convergence.

[0061] As an optional feature, the system also includes a model maintenance module to monitor the battery's cumulative runtime and static calibration error. When a preset recalibration trigger condition is met, the model update process is initiated. This module records the battery's cumulative runtime (e.g., number of charge-discharge cycles or total runtime) and monitors the error between the intermediate SOC estimate and the OCV inverse solution value during static calibration. The model maintenance module is triggered when the cumulative runtime exceeds a preset threshold (e.g., 3 months or 500 equivalent full-charge cycles), or when the static calibration error exceeds a preset threshold multiple times consecutively (e.g., three consecutive errors greater than 3%).

[0062] The update process includes: refitting the OCV-SOC curve using data collected during the recent resting phase and updating the mapping database; simultaneously, freezing most of the PINN network layers in the parameter generation module and only using the latest running data to perform lightweight fine-tuning of the output layer weights. This maintenance mechanism can effectively address the model drift problem caused by battery aging and maintain the estimation accuracy of the system throughout the entire battery lifespan.

[0063] It should be noted that each module in the above-described sodium-ion battery SOC estimation system corresponds to steps S1 to S4 and subsequent calibration and maintenance steps in the sodium-ion battery SOC estimation method described above. Multiple modules implement the same instances and application scenarios as their corresponding steps, but are not limited to the content disclosed in Embodiment 1 above. In practical applications, these modules can be implemented in software, hardware, or a combination of both. For example, they can run as embedded programs on the main control chip of the BMS, or be integrated as dedicated hardware logic circuits in the BMS's coprocessor. Data interaction between modules is completed through the system bus or shared memory, ensuring the real-time performance and reliability of the entire estimation process.

[0064] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of the present invention are generated.

[0065] The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions may be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions may be transmitted from one website, computer, server, or data center to another via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium may be any available medium that a computer can access, or a data storage device such as a server or data center that integrates one or more available media. The available medium may be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., a solid-state drive (SSD)).

[0066] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0067] In addition, the functional modules in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0068] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A method for estimating the state of charge (SOC) of sodium-ion batteries based on PINN-EKF fusion, characterized in that, Includes the following steps: The battery's current operating data is acquired, and a feature vector characterizing the battery's current operating condition is constructed based on the operating data and the SOC estimate from the previous moment; the operating data includes voltage, current, and temperature. The feature vector is input into the pre-physical information neural network, which outputs the second-order RC equivalent circuit model parameters and noise scaling factor at the current moment. Based on the parameters of the second-order RC equivalent circuit model and the noise scaling factor, a time-varying adaptive noise matrix is ​​constructed, and an extended Kalman filter recursion is performed to obtain a preliminary SOC estimate. In response to the detection that the battery meets the preset static calibration trigger condition, the initial SOC estimate is strongly calibrated and updated based on the current open-circuit voltage measurement value and the pre-stored open-circuit voltage-state of charge mapping relationship, and the final SOC estimate is output.

2. The sodium-ion battery SOC estimation method based on PINN-EKF fusion according to claim 1, characterized in that, Before acquiring real-time operating data of a single battery cell, the method further includes: Set the initial values ​​of SOC, polarization voltage, error covariance matrix, basic process noise matrix, and basic observation noise matrix as the initial state of the extended Kalman filter; The initial SOC value is obtained by inverse solving based on the open-circuit voltage measurement value at the power-on time and the pre-stored open-circuit voltage-state of charge mapping relationship, or by reading the historically stored SOC value, or by using the system's preset default value.

3. The sodium-ion battery SOC estimation method based on PINN-EKF fusion according to claim 1, characterized in that, The preceding physical information neural network is a multi-layer feedforward neural network, including an input layer, several hidden layers and an output layer connected in sequence; The input layer is used to receive the input feature vector. , is represented as: In the formula, This is the estimated SOC value from the previous time step. The current battery temperature. This is the absolute value of the current. Let k be the rate of change of current and k be the index of the sampling time. The hidden layer is used to perform nonlinear transformation on the feature vector to extract hidden layer features associated with battery polarization effect, ohmic effect and noise characteristics. The output layer generates the current output vector based on the hidden layer features. , is represented as: In the formula, The parameters of the second-order RC model output at time k are... This is the process noise scaling factor. To measure the noise scaling factor; During the offline training phase, the aforementioned pre-physical information neural network uses the terminal voltage from historical operating data as a supervision signal to construct a multi-objective loss function that integrates terminal voltage prediction error constraints, residual constraints of the second-order RC model dynamic equations, and physical range constraints of parameters for training. This enables the network to learn the nonlinear mapping relationship between battery physical characteristics and model parameters and noise characteristics.

4. The sodium-ion battery SOC estimation method based on PINN-EKF fusion according to claim 3, characterized in that, The multi-objective loss function is obtained by the following formula: ； In the formula, For voltage prediction loss; This represents a loss of physical consistency. This is the regularization loss; The voltage prediction loss The mean square error between the predicted terminal voltage and the measured terminal voltage, based on the parameters of the second-order RC model output by the network, is constructed as follows: ； In the formula, The terminal voltage is predicted based on the parameters of a second-order RC model output by the network. Where N is the measured terminal voltage, and N is the number of samples. The physical consistency loss The residuals of the discretized dynamic equations based on the second-order RC equivalent circuit model are constructed as follows: ； In the formula, , The polarization voltage at the current moment. , The polarization voltage is the value at the previous moment, and T is the sampling period. and It is a time constant. and Polarization resistor; The regularization loss The smoothing constraint terms, including the range constraints of the model parameters and the noise scaling factor, are as follows: + ； In the formula, These are the model parameters output by the network. and These are the minimum and maximum values ​​of the corresponding model parameters, respectively. and These are the process noise scaling factors at times k+1 and k, respectively. and These are the observation noise scaling factors at times k+1 and k, respectively.

5. The sodium-ion battery SOC estimation method based on PINN-EKF fusion according to claim 2, characterized in that, The construction of the time-varying adaptive noise matrix is ​​specifically as follows: Based on the preset basic process noise matrix With the basic observation noise matrix The base noise is scaled using the noise scaling factor output by the neural network based on the prior physical information, and the process noise matrix and observation noise matrix at the current moment are constructed as follows: ； In the formula, Let k be the process noise matrix at time k. Let k be the observation noise matrix at time k. This is the process noise scaling factor. To observe the noise scaling factor.

6. The sodium-ion battery SOC estimation method based on PINN-EKF fusion according to claim 2, characterized in that, The process of performing extended Kalman filtering recursion to obtain a preliminary estimate of SOC is as follows: Discretize the second-order RC equivalent circuit model into a state-space expression: ； In the formula, This is the state vector for the next time step. Let this be the current state vector. The state transition coefficient matrix is... For the input coefficient matrix, This refers to the system's controllable input at the current moment. These are actual observed values. The observation coefficient matrix, This is the gain coefficient matrix. For system noise, For measuring noise; The execution state prediction step obtains the prior state estimate. and prior error covariance matrix : ； In the formula, This is the state transition coefficient matrix at the current time. This is the state transition coefficient matrix from the previous time step. This is the transpose of the state transition coefficient matrix at the current moment. The input coefficient matrix is ​​the one from the previous time step. This represents the input from the previous time step. Let be the posterior error covariance matrix of the previous time step. For process noise covariance; Perform the observation update step and calculate the Kalman gain. : ； In the formula, These are predicted measurement values. These are actual measured values. The observation coefficient matrix, This is the gain coefficient matrix. This is the transpose of the observation coefficient matrix. For output value error, To observe the noise covariance; Using Kalman gain The prior estimate is corrected for observation errors to obtain the posterior state estimate. and the posterior error covariance matrix : ； in, It is the identity matrix. The observation coefficient matrix, The prior error covariance matrix; Based on the posterior state estimation Determine the preliminary estimate of SOC at the current moment.

7. The sodium-ion battery SOC estimation method based on PINN-EKF fusion according to claim 1, characterized in that, The static calibration trigger conditions include: Current criterion: The absolute value of the sampled current is continuously lower than the preset resting current threshold, and the duration exceeds the preset minimum resting time; Voltage stability criterion: The standard deviation of the terminal voltage within a preset time window is less than a preset voltage stability threshold; Temperature stability criterion: The rate of temperature change within a preset time window is less than a preset temperature stability threshold. When the current criterion, voltage stability criterion, and temperature stability criterion are all satisfied, the battery is determined to be in a relaxation state, and the current terminal voltage measurement value is taken as the open circuit voltage value.

8. The sodium-ion battery SOC estimation method based on PINN-EKF fusion according to claim 1, characterized in that, The pre-stored open-circuit voltage-state of charge mapping relationship is established through the following steps: The sodium-ion battery was charged and discharged at multiple preset temperatures. At each preset temperature, it was charged with a constant current to the cutoff voltage and then charged with a constant voltage until the current dropped to a preset threshold. After being left to stand for a preset time, it was discharged with a constant current. The terminal voltage was recorded as the open circuit voltage value after each preset SOC change. A fourth-order polynomial was used to fit the open-circuit voltage-state-of-charge data at different temperatures: ； in, Open circuit voltage, - The coefficients of the polynomial, This indicates the battery's state of charge.

9. The sodium-ion battery SOC estimation method based on PINN-EKF fusion according to claim 6, characterized in that, The initial SOC estimate is strongly calibrated and updated based on the current open-circuit voltage measurement and the pre-stored open-circuit voltage-state-of-charge mapping relationship, specifically as follows: In response to the detection that the battery meets the preset rest calibration trigger condition, the current terminal voltage is... As open circuit voltage ; Based on the current temperature The fitted curve at the corresponding temperature is retrieved from the pre-stored open-circuit voltage-state of charge mapping relationship; Current terminal voltage Substituting the fitted curve, the calibrated SOC value is obtained by inverse solution; Replace the extended Kalman filter's posterior state estimate at the current time step with the calibrated SOC value. The SOC component in the polarization voltage state. , Reset to zero to obtain the corrected posterior state estimate; The SOC component in the corrected posterior state estimate is output as the final SOC estimate at the current time, and the corrected posterior state estimate and its corresponding posterior error covariance matrix are used as the initial state for the next time step of the extended Kalman filter recursion.

10. An estimation system that implements the sodium-ion battery SOC estimation method as described in any one of claims 1-9, characterized in that, The system includes: The data acquisition module is used to acquire the current operating data of a single battery cell, including voltage, current, and temperature. The feature construction module is used to construct a feature vector representing the current operating condition of the battery based on the running data and the final SOC estimate output at the previous moment. The parameter generation module has a built-in pre-physical information neural network, which is used to output the second-order RC equivalent circuit model parameters and noise scaling factor at the current moment based on the feature vector. The filtering estimation module is used to construct a time-varying adaptive noise matrix based on the parameters of the second-order RC equivalent circuit model and the noise scaling factor, and to perform extended Kalman filter recursion to obtain the intermediate estimate of SOC at the current time. The static calibration module is used to detect whether the battery meets the preset static calibration trigger conditions, and when the conditions are met, it performs strong calibration and updates the intermediate SOC estimate based on the current open-circuit voltage measurement value and the pre-stored open-circuit voltage-state of charge mapping relationship, and outputs the final SOC estimate value at the current moment. The initialization module is used to set the initial values ​​of SOC, polarization voltage, error covariance matrix, basic process noise matrix, and basic observation noise matrix when the system starts up, as the initial state of the extended Kalman filter.

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