A method for estimating the state of health of lithium batteries based on an improved gray wolf optimization algorithm (IBWO) and a physical information neural network (PINN).

Abstract

This invention proposes a method for estimating the State of Health (SOH) of lithium batteries based on a Physical Information Neural Network (PINN) using an Improved Gray Wolf Optimization Algorithm (IBWO). The method includes: acquiring and preprocessing multi-source monitoring data such as voltage, current, and temperature during the charging and discharging process of the lithium battery; establishing a fractional-order equivalent circuit model (FO-ECM) of the lithium battery, and using IBWO to perform high-dimensional and physically reasonable identification of the FO-ECM model parameters; constructing an identification pattern using the proposed PINN network as the backbone network, and building an SOH prediction model by adding physical constraints; training the model using a training set, and validating the model performance using a test set. Experimental results show that this method can effectively improve the accuracy, robustness, and interpretability of lithium battery health estimation.

Description

Technical Field

[0001] This invention relates to the field of lithium battery state monitoring and health management technology, specifically a lithium battery SOH estimation method that integrates mechanism models and data-driven features. Background Technology

[0002] In lithium-ion battery health management and state assessment, accurate estimation of battery state of health (SOH) is a core element in ensuring the safe and reliable operation of the battery system. Accurate SOH prediction allows for timely assessment of battery performance degradation, leading to optimized usage strategies and extended battery life. In recent years, many researchers have attempted to apply PINN (Physical Induction Neural Network) to lithium-ion battery SOH estimation, aiming to combine the advantages of mechanistic models and data-driven approaches. However, existing methods often rely on relatively simple input features from PINN, failing to fully integrate parameters with clear electrochemical significance identified from high-fidelity physical models as strong physical priors. This results in the ineffective utilization of physical constraints within the model, limiting its generalization ability under data-scarce or complex operating conditions. Furthermore, the parameters of FO-ECM (Focused Optimal-Oriented Model) are high-dimensional and strongly coupled, making it easy for traditional optimization algorithms to get trapped in local optima during parameter identification and difficult to guarantee the physical rationality of the parameters. This further restricts the accuracy of subsequent SOH estimation. Therefore, efficiently and accurately identifying physically reasonable model parameters from battery operating data and embedding them as effective physical information into neural networks is crucial for improving the accuracy, robustness, and interpretability of SOH estimation models. Summary of the Invention

[0003] This invention proposes a lithium battery SOH estimation method based on IBWO and PINN, which can effectively solve the problems of insufficient accuracy and lack of physical rationality in fractional-order model parameter identification, and improve the accuracy and interpretability of SOH estimation.

[0004] This invention is implemented as follows: a method for estimating the state of health of a lithium battery based on IBWO and PINN, the method comprising the following steps:

[0005] S1: Acquire multi-source monitoring data during the charging and discharging process of the lithium battery, and preprocess the data;

[0006] S2: Establish the FO-ECM of the lithium battery and determine the parameters to be identified in the model, including 12 parameters to be identified, such as ohmic internal resistance, polarization resistance, polarization capacitance and fractional order.

[0007] S3: IBWO is used to identify the parameters of the fractional-order model to obtain a parameter set with electrochemical and physical significance;

[0008] S4: Using PINN as the core framework, a SOH prediction model is constructed with IBWO identification parameters as input;

[0009] S5: Train the SOH prediction model using the training set and evaluate the model's performance using the test set.

[0010] Furthermore, the multi-source monitoring data in step S1 includes voltage, current, and temperature parameters; the preprocessing method is a data normalization method.

[0011] Furthermore, step S3, parameter identification using IBWO, includes: designing a grouped collaborative search mechanism based on the FO-ECM physical topology to decompose the high-dimensional parameter space into multiple functional subspaces for parallel optimization; introducing a high-dimensional dynamic weight strategy based on the exploration and development capabilities of the parameter sensitivity difference balancing algorithm; embedding electrochemical physical constraints in the fitness function to ensure the rationality of the identification results; the specific steps of parameter identification using IBWO include:

[0012] S21: Population Initialization: Generate an initial population by grouping parameters according to their functions, and verify the physical constraints of the parameters: The parameter grouping mapping, based on the physical topology and parameter function characteristics of FO-ECM, divides the 12-dimensional parameters into four subspace vectors according to their functional correlation, resulting in an overall parameter vector. for:

[0013]

[0014] in, For ohmic internal resistance, corresponding to the instantaneous response branch of the model; To characterize the double-layer capacitance and charge transfer process in the fast polarization branch; The slow polarization branch is used to characterize the lithium-ion diffusion process; The parameters are nonlinear fitting parameters for OCV-SOC, reflecting the characteristics of the electrode electrochemical potential.

[0015] S22: Stratified fitness calculation and dominant wolf selection: Determine the dominant wolf within the group based on in-group fitness; determine α, β, and δ wolves based on global fitness;

[0016] S23: Group Collaborative Update and Physical Constraint Verification: The global dominant wolf and the dominant wolf within the group jointly guide the position update of ordinary individuals in the population; during the update process, the group coupling constraints and parameter physical boundary constraints are embedded for real-time verification and correction to ensure the physical rationality of the newly generated parameters;

[0017] S24: Iterative convergence judgment, update algorithm control parameters, and determine whether the maximum number of iterations or the global fitness convergence threshold has been reached; if the convergence condition is not met, return to step S22 to continue iterative optimization; if it is met, output the current optimal parameter identification result.

[0018] Furthermore, in step S22, when using hierarchical fitness calculation to select dominant wolves, the model construction for fitness calculation and dominant wolf selection is as follows:

[0019] S31: Within-group fitness function:

[0020]

[0021] in, The parameter vector representing group 2, This is the measured value of the fast polarization voltage at the k-th sampling point. The fast polarization voltage prediction is calculated using the group 2 parameters through the discretized recursive equation of FO-ECM. Its calculation depends on the recursive formula of the fractional-order model:

[0022]

[0023] s is the sampling time. The length of the GL derivative is used for memory. Penalty coefficient

[0024] S32: Global fitness function:

[0025]

[0026] in, This is the measured value of the battery terminal voltage at the k-th sampling point. The predicted value is calculated using the complete parameter set θ through the FO-ECM terminal voltage equation:

[0027]

[0028] S33: In-group dominant wolf selection: Within each parameter subspace, based on in-group fitness... Sort the wolves in ascending order and select the two individuals with the best fitness as the dominant wolves in that group. , It is responsible for guiding the fine-grained search of parameters within the group;

[0029] S34: Global Dominance Wolf Selection: Selecting wolves based on global fitness across the entire population. Sort the wolves in ascending order and select the top 3 individuals (α, β, δ) with the best fitness as the global dominant wolves, responsible for guiding the global search direction of the population.

[0030] Furthermore, the step S4, which involves constructing a SOH prediction model using PINN, includes:

[0031] S41: Construction of Physics Prior Inputs:

[0032] The parameter set of the fractional-order equivalent circuit model (FO-ECM) identified by the IBWO algorithm: , , As the physical prior input of the PINN network.

[0033] S42: Physical Constraint Embedding and Loss Function Design

[0034] By embedding the core physical equations of FO-ECM as hard constraints into the loss function of PINN, an optimization objective that combines data-driven learning capabilities with physical constraints is constructed. Total loss function. Loss due to data fitting and physical constraint loss Weighted composition:

[0035]

[0036] The above formula, It is a balancing hyperparameter used to adjust the weight between the data fitting accuracy and the constraints of physical laws.

[0037] Among them, data fitting loss Mean squared error (MSE) is used to measure the deviation between the SOH value predicted by the network and the actual SOH value:

[0038]

[0039] Physical constraint loss Based on the terminal voltage equation of FO-ECM, the error between the model-predicted voltage and the measured voltage is calculated to ensure that the network prediction results conform to the battery electrochemical mechanism.

[0040]

[0041] in, It can be calculated using the following formula:

[0042]

[0043] In the formula, OCV(SOC) is determined by the identification parameters. to Fitting, and Contains The fractional differential equation is obtained by discretization. This physical constraint term directly injects the physical meaning of the parameters identified by IBWO into the learning process of the neural network.

[0044] S43: Model Training and SOH Prediction:

[0045] The constructed PINN model was trained using the training dataset. The total loss function was minimized using the backpropagation algorithm and Adam. The network's internal weights are optimized. During training, physical constraints guide the network's learning direction, ensuring that its output not only fits the data but also strictly adheres to the electrochemical laws described by FO-ECM. After training, the model can receive new FO-ECM parameter inputs and output high-precision, physically reasonable SOH predictions.

[0046] Compared with the prior art, the beneficial effects of this invention are as follows:

[0047] This invention treats lithium battery state of health (SOH) estimation as a prediction problem and employs a combination of IBWO and PINN to construct a battery health state estimation model. The algorithm introduces a grouped collaborative search mechanism and a high-dimensional dynamic weight strategy to optimize the identification of fractional-order model parameters. Compared to traditional optimization algorithms, IBWO can adaptively handle high-dimensional, strongly coupled parameter spaces, effectively solving complex optimization challenges such as high parameter dimensionality, strong coupling, and strict physical constraints in fractional-order equivalent circuit models. Furthermore, through the structural design of PINN, identified parameters with clear physical meaning are embedded as prior knowledge into the network input, and physical constraint terms are added to the loss function. This not only avoids the "black box" defect of purely data-driven models but also enhances the model's interpretability and extrapolation ability. Experiments show that the IBWO-based PINN method proposed in this invention can effectively improve the accuracy and efficiency of parameter identification, significantly improving the accuracy and robustness of lithium battery health state estimation under complex operating conditions and small sample scenarios. Attached Figure Description

[0048] Figure 1 This is a flowchart illustrating the overall process of the method described in this invention.

[0049] Figure 2 This is the IBWO flowchart used in this invention;

[0050] Figure 3 This is a graph showing the error distribution and convergence curve of the improved IBWO algorithm described in this invention. Detailed Implementation

[0051] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0052] See Figure 1 As shown, a method for estimating the state of harm (SOH) of a lithium battery based on modified IBWO and PINN is presented. This method includes the following steps:

[0053] S1: Acquire multi-source monitoring data during the charging and discharging process of lithium batteries, and preprocess the data using a normalization method;

[0054] S2: Establish the FO-ECM of the lithium battery and determine the parameters to be identified in the model, including 12 parameters to be identified, such as ohmic internal resistance, polarization resistance, polarization capacitance and fractional order.

[0055] S3: IBWO is used to identify the parameters of the fractional-order model to obtain a parameter set with electrochemical and physical significance;

[0056] S4: Using PINN as the core framework, a SOH prediction model is constructed with IBWO identification parameters as input;

[0057] S5: Train the SOH prediction model using the training set and evaluate the model's performance using the test set.

[0058] The multi-source monitoring data in step S1 includes voltage, current, and temperature parameters; the pre-method is a data normalization processing method.

[0059] Furthermore, step S3 uses IBWO for parameter identification, such as... Figure 2 As shown, it includes: designing a grouped collaborative search mechanism based on the FO-ECM physical topology, decomposing the high-dimensional parameter space into multiple functional subspaces for parallel optimization; introducing a high-dimensional dynamic weight strategy, based on the exploration and development capabilities of the parameter sensitivity difference balancing algorithm; embedding electrochemical physical constraints in the fitness function to ensure the rationality of the identification results; the parameter identification by IBWO specifically includes the following steps:

[0060] S21: Population Initialization: Generate an initial population by grouping parameters according to their functions, and verify the physical constraints of the parameters: The parameter grouping mapping, based on the physical topology and parameter function characteristics of FO-ECM, divides the 12-dimensional parameters into four subspace vectors according to their functional correlation, resulting in an overall parameter vector. for:

[0061]

[0062] in, For ohmic internal resistance, corresponding to the instantaneous response branch of the model; To characterize the double-layer capacitance and charge transfer process in the fast polarization branch; The slow polarization branch is used to characterize the lithium-ion diffusion process; The parameters are nonlinear fitting parameters for OCV-SOC, reflecting the characteristics of the electrode electrochemical potential.

[0063] S22: Stratified fitness calculation and dominant wolf selection: Determine the dominant wolf within the group based on in-group fitness; determine α, β, and δ wolves based on global fitness;

[0064] S23: Group Collaborative Update and Physical Constraint Verification: The global dominant wolf and the dominant wolf within the group jointly guide the position update of ordinary individuals in the population; during the update process, the group coupling constraints and parameter physical boundary constraints are embedded for real-time verification and correction to ensure the physical rationality of the newly generated parameters;

[0065] S24: Iterative convergence judgment, update algorithm control parameters, and determine whether the maximum number of iterations or the global fitness convergence threshold has been reached; if the convergence condition is not met, return to step S22 to continue iterative optimization; if it is met, output the current optimal parameter identification result.

[0066] Furthermore, in step S22, when using hierarchical fitness calculation to select dominant wolves, the model construction for fitness calculation and dominant wolf selection is as follows:

[0067] S31: Within-group fitness function:

[0068]

[0069] in, The parameter vector representing group 2, This is the measured value of the fast polarization voltage at the k-th sampling point. The fast polarization voltage prediction is calculated using the group 2 parameters through the discretized recursive equation of FO-ECM. Its calculation depends on the recursive formula of the fractional-order model:

[0070]

[0071] s is the sampling time. The length of the GL derivative is used for memory. This is the penalty coefficient.

[0072] S32: Global fitness function:

[0073]

[0074] in, This is the measured value of the battery terminal voltage at the k-th sampling point. The predicted value is calculated using the complete parameter set θ through the FO-ECM terminal voltage equation:

[0075]

[0076] S33: In-group dominant wolf selection: Within each parameter subspace, based on in-group fitness... Sort the wolves in ascending order and select the two individuals with the best fitness as the dominant wolves in that group. , It is responsible for guiding the fine-grained search of parameters within the group;

[0077] S34: Global Dominance Wolf Selection: Selecting wolves based on global fitness across the entire population. Sort the wolves in ascending order and select the top 3 individuals (α, β, δ) with the best fitness as the global dominant wolves, responsible for guiding the global search direction of the population.

[0078] Furthermore, the step S4, which involves constructing a SOH prediction model using PINN, includes:

[0079] S41: Construction of Physics Prior Inputs:

[0080] The FO-ECM parameter set obtained by the IBWO algorithm: , , As the physical prior input of the PINN network.

[0081] S42: Physical Constraint Embedding and Loss Function Design

[0082] By embedding the core physical equations of FO-ECM as hard constraints into the loss function of PINN, an optimization objective that combines data-driven learning capabilities with physical constraints is constructed. Total loss function. Loss due to data fitting and physical constraint loss Weighted composition:

[0083]

[0084] The above formula, It is a balancing hyperparameter used to adjust the weight between the data fitting accuracy and the constraints of physical laws.

[0085] Among them, data fitting loss MSE is used to measure the deviation between the network-predicted SOH value and the actual SOH value:

[0086]

[0087] Physical constraint loss Based on the terminal voltage equation of FO-ECM, the error between the model-predicted voltage and the measured voltage is calculated to ensure that the network prediction results conform to the battery electrochemical mechanism.

[0088]

[0089] in, It can be calculated using the following formula:

[0090]

[0091] In the formula, OCV(SOC) is determined by the identification parameters. to Fitting, and Contains The fractional differential equation is obtained by discretization. This physical constraint term directly injects the physical meaning of the parameters identified by IBWO into the learning process of the neural network.

[0092] S43: Model Training and SOH Prediction:

[0093] The constructed PINN model was trained using the training dataset. The total loss function was minimized using the backpropagation algorithm and Adam. The network's internal weights are optimized. During training, physical constraints guide the network's learning direction, ensuring that its output not only fits the data but also strictly adheres to the electrochemical laws described by FO-ECM. After training, the model can receive new FO-ECM parameter inputs and output high-precision, physically reasonable SOH predictions.

[0094] This invention treats State of Health (SOH) estimation as a prediction problem, constructing a battery SOH estimation model based on the proposed improved Grey Wolf optimization algorithm and a physical information neural network (PIN) structure. The proposed IBWO uses a grouped collaborative search mechanism and a high-dimensional dynamic weight strategy to optimize and identify the parameters of the fractional-order model. Compared to traditional optimization algorithms, it can adaptively handle high-dimensional, strongly coupled parameter spaces, effectively solving complex optimization problems such as high parameter dimensionality, strong coupling, and strict physical constraints in fractional-order equivalent circuit models. Simultaneously, using the PINN structure design, the fitted parameters with clear physical meaning are embedded as prior knowledge into the network input. By adding a physical constraint term to the loss function, the "black box" defect of purely data-driven models is avoided, and the interpretability and extrapolation ability of the model are enhanced. Experiments show that the proposed improved Grey Wolf optimization PSN can effectively improve the accuracy and efficiency of parameter identification, and significantly improve the accuracy and robustness of lithium battery state of health estimation under complex operating conditions and small sample scenarios.

[0095] The invention will be further explained in detail below using a specific lithium battery MIT dataset as an example. The above-mentioned lithium battery SOH estimation method can be described as follows:

[0096] Step 1: Obtain the MIT dataset for lithium batteries and perform data preprocessing to construct the model input dataset. The preprocessing step includes the following steps:

[0097] Obtain the MIT dataset for lithium batteries, which includes time series data of parameters such as voltage, current, and temperature.

[0098] The original data is normalized to the range [-1, 1]. The normalization formula is as follows:

[0099]

[0100] The preprocessed dataset is randomly divided into a training set and a test set according to a preset ratio of 7:3, which are used for model training and performance evaluation, respectively.

[0101] Step 2: Based on the PyTorch 1.7.1 framework, use Python to design IBWO to identify the parameters of the fractional-order model and obtain a parameter set with electrochemical physical significance. This specifically includes the following computational steps:

[0102] S21: Population Initialization: Generate an initial population by grouping parameters according to their functions, and verify the physical constraints of the parameters: The parameter grouping mapping, based on the physical topology and parameter function characteristics of FO-ECM, divides the 12-dimensional parameters into four subspace vectors according to their functional correlation, resulting in an overall parameter vector. for:

[0103]

[0104] in, For ohmic internal resistance, corresponding to the instantaneous response branch of the model; To characterize the double-layer capacitance and charge transfer process in the fast polarization branch; The slow polarization branch is used to characterize the lithium-ion diffusion process; The parameters are nonlinear fitting parameters for OCV-SOC, reflecting the characteristics of the electrode electrochemical potential.

[0105] S22: Stratified fitness calculation and dominant wolf selection: Determine the dominant wolf within the group based on in-group fitness; determine α, β, and δ wolves based on global fitness;

[0106] S23: Group Collaborative Update and Physical Constraint Verification: The global dominant wolf and the dominant wolf within the group jointly guide the position update of ordinary individuals in the population; during the update process, the group coupling constraints and parameter physical boundary constraints are embedded for real-time verification and correction to ensure the physical rationality of the newly generated parameters;

[0107] S24: Iterative convergence judgment, update algorithm control parameters, and determine whether the maximum number of iterations or the global fitness convergence threshold has been reached; if the convergence condition is not met, return to step S22 to continue iterative optimization; if it is met, output the current optimal parameter identification result.

[0108] S41: Construction of Physics Prior Inputs:

[0109] The FO-ECM parameter set obtained by the IBWO algorithm: , , As the physical prior input of the PINN network.

[0110] S42: Physical Constraint Embedding and Loss Function Design

[0111] By embedding the core physical equations of FO-ECM as hard constraints into the loss function of PINN, an optimization objective that combines data-driven learning capabilities with physical constraints is constructed. Total loss function. Loss due to data fitting and physical constraint loss Weighted composition:

[0112]

[0113] The above formula, It is a balancing hyperparameter used to adjust the weight between the data fitting accuracy and the constraints of physical laws.

[0114] Among them, data fitting loss MSE is used to measure the deviation between the network-predicted SOH value and the actual SOH value:

[0115]

[0116] Physical constraint loss Based on the terminal voltage equation of FO-ECM, the error between the model-predicted voltage and the measured voltage is calculated to ensure that the network prediction results conform to the battery electrochemical mechanism.

[0117]

[0118] in, It can be calculated using the following formula:

[0119]

[0120] In the formula, OCV(SOC) is determined by the identification parameters. to Fitting, and Contains The fractional differential equation is obtained by discretization. This physical constraint term directly injects the physical meaning of the parameters identified by IBWO into the learning process of the neural network.

[0121] S43: Model Training and SOH Prediction:

[0122] The constructed PINN model was trained using the training dataset. The total loss function was minimized using the backpropagation algorithm and Adam. The network's internal weights are optimized. During training, physical constraints guide the network's learning direction, ensuring that its output not only fits the data but also strictly adheres to the electrochemical laws described by FO-ECM. After training, the model can receive new FO-ECM parameter inputs and output high-precision, physically reasonable SOH predictions.

[0123] Figure 3 The performance verification results of the IBWO model proposed in this invention are presented in summary. The voltage identification curve in the upper left shows that the model fitting curve highly coincides with the real data, with an RMSE of only 0.0578V. The error distribution histogram in the upper right shows that the model estimation error is extremely low, with an MAE of 0.0351V and concentrated near the value of 0. The current and SOC estimation results in the lower left verify the model's accurate tracking ability of dynamic operating conditions. The convergence curve in the lower right reflects the excellent characteristics of the algorithm, which decreases rapidly in the early stage of iteration and converges stably in the later stage. Overall, the model exhibits extremely high accuracy and stability in the field of lithium-ion battery parameter identification and state estimation, fully demonstrating the effectiveness and superiority of this invention.

[0124] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention.

Claims

1. A method for estimating the State of Health (SOH) of lithium batteries based on an improved gray wolf optimization algorithm (IBWO) and a physical information neural network (PINN), characterized in that, The method includes the following steps: S1: Acquire multi-source monitoring data during the charging and discharging process of the lithium battery, and preprocess the data; S2: Establish a fractional-order equivalent circuit model (FO-ECM) for the lithium battery and determine the parameters to be identified in the model, including 12 parameters to be identified, such as ohmic internal resistance, polarization resistance, polarization capacitance and fractional order. S3: IBWO is used to identify the parameters of the fractional-order model to obtain a parameter set with electrochemical and physical significance; S4: Using PINN as the core framework, a SOH prediction model is constructed with IBWO identification parameters as input; S5: Train the SOH prediction model using the training set and evaluate the model's performance using the test set.

2. The method according to claim 1, characterized in that, The multi-source monitoring data in step S1 includes voltage, current, and temperature parameters; the preprocessing method is a data normalization method.

3. The method according to claim 1, characterized in that, Step S3, parameter identification using IBWO, includes: designing a grouped collaborative search mechanism based on the FO-ECM physical topology to decompose the high-dimensional parameter space into multiple functional subspaces for parallel optimization; introducing a high-dimensional dynamic weight strategy based on the exploration and development capabilities of the parameter sensitivity difference balancing algorithm; embedding electrochemical physical constraints in the fitness function to ensure the rationality of the identification results; the specific steps of parameter identification using IBWO include: S21: Population Initialization: Generate an initial population by grouping parameters according to their functions, and verify the physical constraints of the parameters: The parameter grouping mapping, based on the physical topology and parameter function characteristics of FO-ECM, divides the 12-dimensional parameters into four subspace vectors according to their functional correlation, resulting in an overall parameter vector. for: in, For ohmic internal resistance, corresponding to the instantaneous response branch of the model; To characterize the double-layer capacitance and charge transfer process in the fast polarization branch; The slow polarization branch is used to characterize the lithium-ion diffusion process; The parameters are nonlinear fitting parameters for OCV-SOC, reflecting the characteristics of the electrode electrochemical potential. S22: Stratified fitness calculation and dominant wolf selection: Determine the dominant wolf within the group based on in-group fitness; determine α, β, and δ wolves based on global fitness; S23: Group Collaborative Update and Physical Constraint Verification: The global dominant wolf and the dominant wolf within the group jointly guide the position update of ordinary individuals in the population; during the update process, the group coupling constraints and parameter physical boundary constraints are embedded for real-time verification and correction to ensure the physical rationality of the newly generated parameters; S24: Iterative convergence judgment, update algorithm control parameters, and determine whether the maximum number of iterations or the global fitness convergence threshold has been reached; if the convergence condition is not met, return to step S22 to continue iterative optimization; if it is met, output the current optimal parameter identification result.

4. The method according to claim 3, characterized in that, In step S22, when using hierarchical fitness calculation to select dominant wolves, the model construction for fitness calculation and dominant wolf selection is as follows: S31: Within-group fitness function: in, The parameter vector representing group 2, This is the measured value of the fast polarization voltage at the k-th sampling point. The fast polarization voltage prediction is calculated using the group 2 parameters through the discretized recursive equation of FO-ECM. Its calculation depends on the recursive formula of the fractional-order model: s is the sampling time. The length of the GL derivative is used for memory. This is the penalty coefficient. S32: Global fitness function: in, This is the measured value of the battery terminal voltage at the k-th sampling point. The predicted value is calculated using the complete parameter set θ through the FO-ECM terminal voltage equation: S33: In-group dominant wolf selection: Within each parameter subspace, based on in-group fitness... Sort the wolves in ascending order and select the two individuals with the best fitness as the dominant wolves in that group. , It is responsible for guiding the fine-grained search of parameters within the group; S34: Global Dominance Wolf Selection: Selecting wolves based on global fitness across the entire population. Sort the wolves in ascending order and select the top 3 individuals (α, β, δ) with the best fitness as the global dominant wolves, responsible for guiding the global search direction of the population.

5. The method according to claim 1, characterized in that, The step S4, which involves constructing the SOH prediction model using PINN, includes: S41: Construction of Physics Prior Inputs: The FO-ECM parameter set obtained by the IBWO algorithm: , , As the physical prior input of the PINN network. S42: Physical Constraint Embedding and Loss Function Design By embedding the core physical equations of FO-ECM as hard constraints into the loss function of PINN, an optimization objective that combines data-driven learning capabilities with physical constraints is constructed. Total loss function. Loss due to data fitting and physical constraint loss Weighted composition: The above formula, It is a balancing hyperparameter used to adjust the weight between the data fitting accuracy and the constraints of physical laws. Among them, data fitting loss Mean squared error (MSE) is used to measure the deviation between the SOH value predicted by the network and the actual SOH value: Physical constraint loss Based on the terminal voltage equation of FO-ECM, the error between the model-predicted voltage and the measured voltage is calculated to ensure that the network prediction results conform to the battery electrochemical mechanism. in, It can be calculated using the following formula: In the formula, OCV(SOC) is determined by the identification parameters. to Fitting, #imgpt40# is obtained by discretizing the fractional differential equation containing #imgpt41#. This physical constraint term directly injects the physical meaning of the parameters identified by IBWO into the learning process of the neural network. S43: Model Training and SOH Prediction: The constructed PINN model was trained using the training dataset. The total loss function was minimized using the backpropagation algorithm and the gradient descent optimizer (Adam) to optimize the network's internal weights. During training, physical constraints guided the network's learning direction, ensuring that its output not only fits the data but also strictly adheres to the electrochemical laws described by FO-ECM. After training, the model can accept new FO-ECM parameter inputs and output high-precision, physically reasonable SOH predictions.

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