A sodium-ion battery state of charge prediction method based on a PINN-LSTM dual-channel residual network
Patent Information
- Application Number
- CN202611288162.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-08-24
- Publication Date
- 2026-10-20
AI Technical Summary
此外，不同于磷酸铁锂电池具有平坦的电压平台，钠离子电池的开路电压（OCV）与SOC之间呈现近乎线性的映射关系，现有深度学习算法多直接套用锂电池方案，未能有效利用钠电池该物理特性
[0043]1.本发明可以增强模型可解释性，提升鲁棒性：提出一种‘物理基准+数据微调’的双通道架构。物理分支确保预测趋势的合理性，残差分支负责拟合极化引起的微小偏差，有效避免极端工况下的发散预测。
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Abstract
Description
Technical Field
[0001] This invention relates to the field of battery state estimation and deep learning technologies, and more specifically, to a method for predicting the state of charge of sodium-ion batteries based on a PINN-LSTM dual-channel residual network. Background Technology
[0002] Sodium-ion batteries, with their advantages of high cost-effectiveness, excellent low-temperature performance, abundant sodium resources, and high safety, are gradually becoming an important energy storage medium in large-scale energy storage systems and low-speed electric vehicles. Accurately estimating the state of charge (SOC) of sodium-ion batteries is crucial for optimizing battery management systems, preventing overcharging and over-discharging, and extending battery life.
[0003] Currently, traditional SOC estimation methods mainly include the ampere-hour integration method and filtering algorithms based on equivalent circuit models (such as extended Kalman filtering). The ampere-hour integration method suffers from significant current accumulation error; while filtering algorithms require complex parameter identification and are prone to distortion under battery aging or extreme operating conditions. In recent years, purely data-driven deep learning methods (such as Long Short-Term Memory networks LSTM) have become a hot topic.
[0004] However, traditional deep learning models are typically data-driven black-box models, lacking physical mechanisms. When encountering extreme dynamic driving conditions not covered in the training set, they are prone to outputting abnormal results that violate physical laws (such as sudden changes in SOC or exceeding the physical extreme range of 0 to 1). Furthermore, unlike lithium iron phosphate batteries which have a flat voltage plateau, sodium-ion batteries exhibit a near-linear mapping relationship between open-circuit voltage (OCV) and SOC. Existing deep learning algorithms often directly apply lithium battery solutions, failing to effectively utilize this physical characteristic of sodium batteries.
[0005] Meanwhile, under continuous dynamic operating conditions, the battery internal resistance includes ohmic internal resistance and polarization internal resistance. Traditional models are unable to separate the dynamic internal resistance in real time under continuous operating conditions and reflect the transient impact of polarization effect on SOC.
[0006] Therefore, there is an urgent need for a method for predicting the state of charge of sodium-ion batteries based on a PINN-LSTM dual-channel residual network to solve the above problems. Summary of the Invention
[0007] To overcome the aforementioned deficiencies of the prior art, embodiments of the present invention provide a method for predicting the state of charge (SOC) of sodium-ion batteries based on a PINN-LSTM dual-channel residual network. The present invention has the advantages of reducing dependence on full-condition data and improving the model's prediction stability under unknown extreme conditions. It has the function of accurately estimating the SOC in real time over a wide temperature range (e.g., -5℃ to 45℃) and under complex dynamic stress. It is suitable for sodium-ion battery management system (BMS) environments in energy storage power stations and electric vehicles, thereby solving the problems mentioned in the background art.
[0008] To achieve the above objectives, the present invention provides the following technical solution: a method for predicting the state of charge of sodium-ion batteries based on a PINN-LSTM dual-channel residual network, comprising the following steps:
[0009] Step 1: Obtain historical operating data of sodium-ion batteries as a training set, as well as real-time operating data to be predicted. The operating data includes voltage, current and temperature time series within a specific time window. In terms of historical operating data acquisition, standard dynamic operating condition tests and pulse charge-discharge tests are performed on sodium-ion batteries using a battery testing platform under a set wide temperature range environment. During the test, the battery terminal voltage, operating current and surface temperature are continuously collected at a set sampling frequency to form historical operating data containing multiple complex polarization states.
[0010] Step 2: Perform sequence interpolation alignment and global normalization on the historical operating data, and calculate the true state of charge at each time step based on the ampere-hour integration method. This result is used as the training label, and the calculation formula is as follows:
[0011] ;
[0012] in: This indicates the initial fully charged anchor point's state of charge, typically set to 1.0. This represents the real-time charging and discharging current; discharging is negative and charging is positive. Indicates the nominal capacity of the sodium-ion battery;
[0013] To ensure that the true value conforms to physical reality, the calculated values are... A limiting operation is performed to restrict the data to the range of [0, 1]. For historical operating data and real-time operating data collected by the vehicle-side BMS, a fixed-length sliding time window is used to extract the continuous data stream. For cases where the sampling frequency may fluctuate, a one-dimensional linear interpolation algorithm is used to uniformly align the extracted data sequence to the preset standard time step, thereby forming a standard voltage, current and temperature time series feature matrix that conforms to the input dimension of the long short-term memory network branch.
[0014] Step 3: Extract the dynamic internal resistance of the battery from the voltage and current time series of the operating data, and calculate the estimated open-circuit voltage based on the current voltage, current, and dynamic internal resistance. Within the time window, calculate the first-order difference of the current series. and the corresponding first-order voltage difference Find the current abrupt change point with the largest absolute value of the difference, when this abrupt change point satisfies At that time, extract the dynamic internal resistance:
[0015] ;
[0016] Based on the sampled voltage at the current moment Sampling current and the dynamic internal resistance Strip the ohmic voltage drop and calculate the estimated open-circuit voltage:
[0017] ;
[0018] in: This represents the estimated open-circuit voltage after removing transient ohmic polarization;
[0019] Step 4: Construct a PINN-LSTM dual-channel network model, which includes a physical perception branch, a long short-term memory network branch, and a residual compensation module.
[0020] Step 5: The physical perception branch uses a single-layer linear fully connected network to extract... Construct a fully connected network with three-dimensional physical feature vectors as input, and directly map the output to the reference state of charge. :
[0021] ;
[0022] The voltage, current, and temperature time series are input into the Long Short-Term Memory network branch, and the time series hidden layer features are output. ;
[0023] Step 6: Concatenate the temporal hidden layer features with the dynamic internal resistance and the current temperature to form a joint feature vector, input it into the residual compensation module, and calculate the compensated state of charge caused by the polarization effect. :
[0024] ;
[0025] Step 7: Construct a physical information loss function that includes physical boundary constraints and core physical constraints:
[0026] ;
[0027] in:
[0028] The mean squared error between the total network prediction and the true label;
[0029] This is a physical boundary penalty term used to constrain the predicted value from exceeding the theoretical limit.
[0030] ;
[0031] For the physical backbone constraints, calculate separately. The error compared to the true label ensures that the overall direction is guided by physical laws;
[0032] For the residual regularization term, calculate The sum of squares limits the output amplitude of the LSTM branch, making it suitable for calculating small-amplitude compensations for the baseline state.
[0033] The error between the model's predicted output and the training labels is calculated, and the parameters of the PINN-LSTM dual-channel network model are updated using the backpropagation algorithm.
[0034] Step 8: After extracting the dynamic internal resistance and estimating the open-circuit voltage from the real-time running data to be predicted in Step 3, input the trained PINN-LSTM dual-channel network model, add the reference state of charge and the compensated state of charge output by the model to obtain the final state of charge prediction result.
[0035] In a preferred embodiment, the change in ampere-hours at each time step is calculated and accumulated to obtain the cumulative capacity. The actual state of charge at the current moment is then calculated by combining the initial state of the battery with the nominal capacity.
[0036] In a preferred embodiment, the specific process of extracting the dynamic internal resistance of the battery includes: calculating the first-order difference of the current sequence within a set time window, identifying abrupt changes where the absolute value of the current difference is greater than a preset current threshold; when the absolute value of the current difference corresponding to the abrupt change is greater than the preset current threshold, calculating the dynamic internal resistance of the current time window using the ratio of the corresponding voltage difference to the current difference.
[0037] In a preferred embodiment, the residual compensation module adopts a multilayer perceptron structure, including a first linear layer, a ReLU activation function layer, and a second linear layer connected in sequence. Its input layer dimension is composed of the temporal hidden layer feature dimension, internal resistance dimension, and temperature dimension, enabling the residual compensation module to perform compensation calculations in conjunction with the current dynamic internal resistance and temperature changes.
[0038] In a preferred embodiment, the physical information loss function is composed of a weighted sum of four parts, including the total prediction mean square error, the physical boundary penalty term, the physical backbone constraint mean square error, and the L2 regularization term for the output of the residual compensation module.
[0039] In a preferred embodiment, the physical boundary penalty term is used to constrain the model output to conform to the actual physical range. It is calculated by applying the ReLU activation function to the model prediction values less than 0 and the model prediction values greater than 1 respectively and taking the mean. The mean is then used as the penalty term and included in the total loss.
[0040] In a preferred embodiment, the mean square error of the physical backbone constraint is the mean square error between the reference state of charge output by the physical sensing branch and the training label, which is used to constrain the prediction benchmark of the physical sensing branch.
[0041] In a preferred embodiment, the L2 regularization term is used to limit the amplitude of the output of the residual compensation module, so that the residual compensation module only fine-tunes the reference state of charge, avoiding overfitting or output divergence of the long short-term memory network branches in the overall model prediction.
[0042] The technical effects and advantages of this invention are as follows:
[0043] 1. This invention enhances model interpretability and robustness by proposing a dual-channel architecture of 'physical baseline + data fine-tuning'. The physical branch ensures the rationality of the predicted trend, while the residual branch is responsible for fitting the small biases caused by polarization, effectively avoiding divergent predictions under extreme conditions.
[0044] 2. This invention can make full use of the characteristics of sodium batteries: by utilizing the approximately linear relationship between the open-circuit voltage and the state of charge (SOC) of sodium-ion batteries, the fitting pressure and complexity of deep learning models are significantly reduced.
[0045] 3. This invention enables online physical feature extraction: by using the current mutation differential method within a sliding window to track dynamic internal resistance in real time, it reduces the reliance of traditional methods on offline HPPC test tables and has good engineering applicability.
[0046] 4. The physical information loss function designed in this invention introduces a boundary penalty term to avoid going out of bounds, and introduces backbone constraints and residual L2 regularization to effectively limit the output amplitude of the long short-term memory network branches, prevent the pure data-driven model from overcompensating and masking the physical benchmark, and constrain the model to follow physical prior knowledge. Attached Figure Description
[0047] Figure 1 This is an overall schematic diagram of the sodium battery SOC prediction method based on the PINN-LSTM dual-channel residual network of the present invention.
[0048] Figure 2 This is a schematic diagram of the PINN-LSTM dual-channel network model structure and the principle of residual forward propagation.
[0049] Figure 3 This is a schematic diagram illustrating the principle of the dynamic internal resistance extraction algorithm within a sliding time window. Figure 4 This is a comparison chart of the continuous dynamic SOC prediction performance of the model of this invention under a nominal ambient temperature (25℃).
[0050] Figure 5 This is a comparison chart of the continuous dynamic SOC prediction performance of the model of this invention in an extremely cold environment (-5℃).
[0051] Figure 6 This is a comparison chart of the continuous dynamic SOC prediction performance of the model of this invention in a high-temperature environment (45℃). Detailed Implementation
[0052] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0053] As attached Figure 1 Appendix Figure 2 Appendix Figure 3 Appendix Figure 4 Appendix Figure 5 and attached Figure 6 As shown, this invention provides a method for predicting the state of charge of sodium-ion batteries based on a PINN-LSTM dual-channel residual network. The specific implementation steps are as follows:
[0054] S1: Sodium-ion battery operation data acquisition and preprocessing
[0055] The application of the model in this invention is divided into two stages: offline training and online prediction. Therefore, the running data includes historical running data for offline training and real-time running data for online evaluation.
[0056] Regarding the acquisition of historical operating data: Under a set wide temperature range (e.g., preferably -5℃ to 45℃), the sodium-ion battery is subjected to standard dynamic operating condition tests (e.g., Dynamic Stress Test, DST) and pulse charge-discharge tests using a battery testing platform. During the test, the battery's terminal voltage, operating current, and surface temperature are continuously collected at a set sampling frequency to form historical operating data containing various complex polarization states.
[0057] Regarding the construction of ground truth labels: For the collected historical operational data, the ampere-hour integration method is used to calculate the true state of charge at each time step, which is then used as the ground truth label for training the dual-channel residual network. The calculation formula is as follows:
[0058]
[0059] in: This indicates the initial fully charged anchor point's state of charge (usually set to 1.0). This indicates the real-time charging and discharging current (negative for discharging, positive for charging). This indicates the nominal capacity (Ah) of the sodium-ion battery.
[0060] To ensure that the true value conforms to physical reality, the calculated values are... Perform a limiting operation to restrict it to the range [0, 1].
[0061] In terms of time series construction (this step is shared by training and real-time prediction): For the historical operation data and the real-time operation data collected by the vehicle-side BMS, a fixed-length sliding time window (preferably 51 time steps in this embodiment) is used to extract the continuous data stream; for cases where the sampling frequency may fluctuate, a one-dimensional linear interpolation algorithm is used to uniformly align the extracted data sequence to the preset standard time step, thereby forming a standard voltage, current and temperature time series feature matrix that conforms to the input dimension of the Long Short-Term Memory (LSTM) network branch.
[0062] S2: Dynamic Physical Feature Extraction
[0063] Traditional data-driven models directly input raw data, lacking awareness of the battery's internal polarization state. This invention extracts the battery's dynamic internal resistance and estimates the open-circuit voltage in real time within a sliding time window.
[0064] Within the time window, calculate the first difference of the current sequence. and the corresponding first-order voltage difference Find the current abrupt change point with the largest absolute value of the difference, when this abrupt change point satisfies... (In this embodiment) When set to 0.1A, extract the dynamic internal resistance:
[0065]
[0066] Based on the sampled voltage at the current moment Sampling current and the dynamic internal resistance Strip the ohmic voltage drop and calculate the estimated open-circuit voltage:
[0067]
[0068] in: This represents the estimated open-circuit voltage after removing transient ohmic polarization.
[0069] S3: Construction and Forward Derivation of PINN-LSTM Dual-Channel Residual Network
[0070] A dual-channel network is constructed, comprising a physical perception branch, a long short-term memory network branch, and a residual compensation module.
[0071] Physical perception branch: This branch uses a single-layer linear fully connected network to extract... Construct a fully connected network with three-dimensional physical feature vectors as input, and directly map the output to the reference state of charge. :
[0072]
[0073] Long Short-Term Memory (LSTM) branch: The temporal feature matrix within the sliding window (in this embodiment, the input dimension is 3, i.e., voltage, current, and temperature; the time step size is 51) is input into the LSTM network. To extract complex historical polarization accumulation effects, this embodiment uses a 2-layer LSTM structure, with the number of hidden layer neurons preferably set to 64. The output of the last time step of the LSTM network is taken as the extracted temporal hidden layer features. This feature is a one-dimensional 64-element vector.
[0074] Residual compensation module: This module processes the 64-dimensional hidden layer features mentioned above. 1-dimensional dynamic internal resistance And the current temperature in 1D. The features are spliced and fused along the feature dimension to form a joint feature vector with a length of 66 dimensions.
[0075] The joint feature vector is input into a residual compensation network composed of a multilayer perceptron (MLP). In this embodiment, the residual compensation network sequentially includes: a first linear layer with an input dimension of 66 and an output dimension of 32; a ReLU activation function layer; and a second linear layer with an input dimension of 32 and an output dimension of 1. Through this residual module, a compensated state of charge caused by concentration polarization and electrochemical polarization is output. :
[0076]
[0077] Finally, the baseline value of the physical branch is added to the compensation value of the residual branch to obtain the prediction result:
[0078]
[0079] S4: Model Training Based on Four-Dimensional Physical Information Loss Function
[0080] During the model training phase, to prevent overfitting of the black-box network and to constrain predicted outputs that do not conform to actual physical meaning, this invention constructs a physical information loss function:
[0081] in:
[0082] This represents the mean squared error between the network's total predicted value and the true label.
[0083] This is a physical boundary penalty term used to constrain the predicted value from exceeding the theoretical limit.
[0084]
[0085] For the physical backbone constraints, calculate separately. The error compared to the true label ensures that the overall direction is guided by physical laws.
[0086] For the residual regularization term, calculate The sum of squares limits the output amplitude of the LSTM branch, enabling it to be used for small-amplitude compensation calculations for the baseline state.
[0087] The model employs the Adam optimization algorithm and is configured with a ReduceLROnPlateau learning rate decay strategy based on validation set loss for backpropagation training.
[0088] S5: Online Real-Time Prediction and Application of Models
[0089] The real-time running data to be predicted is processed through steps S1 and S2 above, and then fed into the trained dual-channel residual network model in real time. The model directly outputs a high-precision SOC prediction value for the current moment, achieving end-to-end online prediction without historical iterations or accumulated errors.
[0090] Experimental verification and result analysis
[0091] To verify the effectiveness and high environmental robustness of the PINN-LSTM dual-channel residual network proposed in this invention, this embodiment was tested under various temperature conditions (-5℃, 25℃, 45℃) using the DST (Dynamic Stress Test) condition.
[0092] The experiment included a visual comparison of the prediction results. (See attached...) Figure 4 To be continued Figure 6In the diagram, the solid black line represents the true state of charge, the dashed blue line represents the baseline state of charge obtained solely from the physical perception branch, and the solid red line represents the final predicted value output by the model of this invention.
[0093] Under nominal ambient temperature (25℃): as shown in the attached document. Figure 4 As shown, the polarization effect is relatively small at room temperature, and the physical baseline curve (blue line) already has a certain degree of accuracy, but fluctuations still exist. After adding residual compensation, the prediction curve (red line) of this invention closely matches the true curve, with a prediction root mean square error (RMSE) as low as 0.72%. This demonstrates that this invention has high prediction accuracy under nominal operating conditions.
[0094] In extreme low temperature environments (-5℃): see attached. Figure 5 As shown, low temperatures slow down ion conduction within the battery, leading to a sharp amplification of concentration polarization and electrochemical polarization. At this point, estimations based solely on physical formulas (blue line) show significant deviations, resulting in a systematic downward shift of approximately 10% to 20%. However, the Long Short-Term Memory (LSTM) network branch of this invention accurately captures temporal polarization characteristics and effectively compensates for the shift through the residual module. The final prediction curve (red line) maintains high-precision tracking of the true trajectory even under harsh, cold conditions, with an RMSE of only 1.33%. Experimental results validate the effectiveness of the dual-channel residual compensation architecture.
[0095] In high-temperature active environments (45℃): see attached. Figure 6 As shown, the model also exhibits good stability in high-temperature environments, with smooth and divergent SOC tracking throughout its lifecycle, and the RMSE further reduced to 0.62%.
[0096] In summary, the experimental results show that this invention effectively improves the shortcomings of pure data-driven models, which are prone to divergence and have poor robustness under complex dynamic conditions and wide temperature ranges, by deeply integrating the linear OCV physical characteristics of sodium batteries with the time-series mining capabilities of deep learning. This provides a SOC prediction scheme with good engineering application value for the commercial application of sodium-ion batteries.
[0097] In conclusion, the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.
Claims
1. A method for predicting the state of charge (SOC) of sodium-ion batteries based on a PINN-LSTM dual-channel residual network, characterized in that, Includes the following steps: Step 1: Obtain historical operating data of sodium-ion batteries as a training set, as well as real-time operating data to be predicted. The operating data includes voltage, current and temperature time series within a specific time window. In terms of historical operating data acquisition, standard dynamic operating condition tests and pulse charge-discharge tests are performed on sodium-ion batteries using a battery testing platform under a set wide temperature range environment. During the test, the battery terminal voltage, operating current and surface temperature are continuously collected at a set sampling frequency to form historical operating data containing multiple complex polarization states. Step 2: Perform sequence interpolation alignment and global normalization on the historical operating data, and calculate the true state of charge at each time step based on the ampere-hour integration method. This result is used as the training label, and the calculation formula is as follows: ； in: This indicates the initial fully charged anchor point's state of charge, typically set to 1.
0. This represents the real-time charging and discharging current; discharging is negative, and charging is positive. Indicates the nominal capacity of the sodium-ion battery; To ensure that the true value conforms to physical reality, the calculated values are... A limiting operation is performed to restrict the data to the [0,1] interval. For historical operating data and real-time operating data collected by the vehicle-side BMS, a fixed-length sliding time window is used to intercept the continuous data stream. For cases where the sampling frequency may fluctuate, a one-dimensional linear interpolation algorithm is used to uniformly align the intercepted data sequence to the preset standard time step, thereby forming a standard voltage, current and temperature time series feature matrix that conforms to the input dimension of the long short-term memory network branch. Step 3: Extract the dynamic internal resistance of the battery from the voltage and current time series of the operating data, and calculate the estimated open-circuit voltage based on the current voltage, current, and dynamic internal resistance. Within the time window, calculate the first-order difference of the current series. and the corresponding first-order voltage difference Find the current abrupt change point with the largest absolute value of the difference, when this abrupt change point satisfies At that time, extract the dynamic internal resistance: ； Based on the sampled voltage at the current moment Sampling current and the dynamic internal resistance Strip the ohmic voltage drop and calculate the estimated open-circuit voltage: ； in: This represents the estimated open-circuit voltage after removing transient ohmic polarization; Step 4: Construct a PINN-LSTM dual-channel network model, which includes a physical perception branch, a long short-term memory network branch, and a residual compensation module. Step 5: The physical perception branch uses a single-layer linear fully connected network to extract... Construct a fully connected network with three-dimensional physical feature vectors as input, and directly map the output to the reference state of charge. : ； The voltage, current, and temperature time series are input into the Long Short-Term Memory network branch, and the time series hidden layer features are output. ; Step 6: Concatenate the temporal hidden layer features with the dynamic internal resistance and the current temperature to form a joint feature vector, input it into the residual compensation module, and calculate the compensated state of charge caused by the polarization effect. : ； Step 7: Construct a physical information loss function that includes physical boundary constraints and core physical constraints: ； in: The mean squared error between the total network prediction and the true label; This is a physical boundary penalty term used to constrain the predicted value from exceeding the theoretical limit. ； For the physical backbone constraints, calculate separately. The error compared to the true label ensures that the overall direction is guided by physical laws; For the residual regularization term, calculate The sum of squares limits the output amplitude of the LSTM branch, making it suitable for calculating small-amplitude compensations for the baseline state. The error between the model's predicted output and the training labels is calculated, and the parameters of the PINN-LSTM dual-channel network model are updated using the backpropagation algorithm. Step 8: After extracting the dynamic internal resistance and estimating the open-circuit voltage from the real-time running data to be predicted in Step 3, input the trained PINN-LSTM dual-channel network model, add the reference state of charge and the compensated state of charge output by the model to obtain the final state of charge prediction result.
2. The method for predicting the state of charge of sodium-ion batteries based on a PINN-LSTM dual-channel residual network according to claim 1, characterized in that: The change in ampere-hours at each time step is calculated and accumulated to obtain the cumulative capacity. The actual state of charge at the current moment is calculated by combining the initial state of the battery with the nominal capacity.
3. The method for predicting the state of charge of sodium-ion batteries based on a PINN-LSTM dual-channel residual network according to claim 1, characterized in that: The specific process of extracting the dynamic internal resistance of the battery includes: calculating the first-order difference of the current sequence within a set time window, identifying abrupt changes where the absolute value of the current difference is greater than a preset current threshold; when the absolute value of the current difference corresponding to the abrupt change is greater than the preset current threshold, calculating the dynamic internal resistance of the current time window using the ratio of the corresponding voltage difference to the current difference.
4. The method for predicting the state of charge of sodium-ion batteries based on a PINN-LSTM dual-channel residual network according to claim 1, characterized in that: The residual compensation module adopts a multilayer perceptron structure, including a first linear layer, a ReLU activation function layer and a second linear layer connected in sequence. Its input layer dimension is composed of the temporal hidden layer feature dimension, internal resistance dimension and temperature dimension, so that the residual compensation module can perform compensation calculations in combination with the current dynamic internal resistance and temperature changes.
5. The method for predicting the state of charge of sodium-ion batteries based on a PINN-LSTM dual-channel residual network according to claim 1, characterized in that: The physical information loss function consists of a weighted sum of four parts: total prediction mean square error, physical boundary penalty term, physical backbone constraint mean square error, and L2 regularization term for the output of the residual compensation module.
6. The method for predicting the state of charge of sodium-ion batteries based on a PINN-LSTM dual-channel residual network according to claim 5, characterized in that: The physical boundary penalty term is used to constrain the model output to conform to the actual physical range. It is calculated by applying the ReLU activation function to the model prediction values less than 0 and the model prediction values greater than 1 respectively and taking the mean. The mean is then used as the penalty term and included in the total loss.
7. The method for predicting the state of charge of sodium-ion batteries based on a PINN-LSTM dual-channel residual network according to claim 5, characterized in that: The mean square error of the physical backbone constraint is the mean square error between the reference state of charge output by the physical sensing branch and the training label, and is used to constrain the prediction benchmark of the physical sensing branch.
8. The method for predicting the state of charge of sodium-ion batteries based on a PINN-LSTM dual-channel residual network according to claim 5, characterized in that: The L2 regularization term is used to limit the magnitude of the output of the residual compensation module, so that the residual compensation module only fine-tunes the reference charge state, avoiding overfitting or output divergence of the long short-term memory network branches in the overall model prediction.