Battery capacity degradation prediction method based on parameter identification and neural network joint modeling

Abstract

The invention discloses a battery capacity degradation prediction method based on parameter identification and neural network joint modeling. The method comprises the following steps: firstly, carrying out data preprocessing on voltage and current data of a lithium ion battery to extract more local information; then defining key parameters to be identified; carrying out parameter identification on key parameters in the physical model by adopting a genetic algorithm; generating a high-precision prediction voltage sequence for filtering instantaneous working condition disturbance by using a physical model; and finally, based on a PKA network, time sequence features are extracted, and high-precision capacity degradation trajectory prediction is realized. And evaluating MSE and RMSE indexes on the test set, and supporting uncertainty estimation and visualization. According to the method, the physical model is introduced to predict the voltage to serve as a feature enhancement signal, physical constraint and mechanism interpretation are provided for capacity degradation modeling, and therefore prediction precision, robustness and interpretability are improved, and the method can still operate when a capacity label is lacked in the early stage.

Description

Technical Field

[0001] This invention belongs to the field of battery health status assessment and prediction technology, specifically involving a battery capacity degradation prediction method based on parameter identification and neural network joint modeling. Background Technology

[0002] Capacity degradation in lithium-ion batteries is a key indicator for measuring battery state of health (SOH) and remaining useful life (RUL), and its changes directly affect the battery's energy output capacity and operational safety in applications such as electric vehicles and energy storage systems. Accurately predicting the battery capacity degradation trajectory not only helps in developing maintenance plans in advance and optimizing energy dispatch, but also effectively reduces operation and maintenance costs and extends system life.

[0003] Currently, the mainstream methods for predicting battery capacity degradation mainly include: 1) Physical model-based methods: These methods use equivalent circuit models (ECMs) or electrochemical models (such as P2D models) to estimate capacity changes using data such as current and voltage. These methods offer strong interpretability but rely on precise model parameters, and the parameter identification process is complex and sensitive to experimental conditions and initial information. 2) Data-driven methods: These methods employ machine learning or deep learning algorithms to directly learn degradation patterns from historical capacity data, exhibiting strong nonlinear fitting capabilities. However, model performance significantly degrades in scenarios with scarce capacity labels or early predictions, and the lack of physical constraints limits generalization ability. 3) Hybrid modeling methods: These methods incorporate some physical laws into the data-driven model, attempting to balance interpretability and accuracy. However, most studies only use physical features as input, failing to fully utilize the predictive power of the physical model to guide data modeling.

[0004] While deep learning has demonstrated high accuracy in battery capacity prediction, it largely relies on complete capacity measurement data as training labels. In practical applications, capacity testing is time-consuming, costly, and can interfere with equipment operation, often resulting in a lack of capacity data in the early stages. Furthermore, existing methods often directly use measured voltage and current as input, neglecting the predicted voltage sequence generated by the parameter-optimized physical model—a sequence that reveals the degradation mechanisms at different cycle stages and provides physical constraints and feature enhancements for capacity modeling. Therefore, it is necessary to propose a capacity degradation prediction method that integrates physical model parameter identification and neural network modeling. This method leverages the physical model to enhance the physical meaning and interpretability of features, while utilizing the strong feature extraction and nonlinear fitting capabilities of neural networks to achieve high-accuracy prediction throughout the entire lifespan, maintaining reliability and robustness even in the early stages when capacity labels are unavailable. Summary of the Invention

[0005] The purpose of this invention is to provide a battery capacity degradation prediction method based on joint modeling of parameter identification and neural networks. By introducing the predicted voltage of the physical model as a feature enhancement signal, it provides physical constraints and mechanism explanations for capacity degradation modeling, thereby improving prediction accuracy, robustness and interpretability, and can still operate in the early stage when there is a lack of capacity labels.

[0006] The technical solution adopted in this invention is a battery capacity degradation prediction method based on joint modeling of parameter identification and neural networks, which is implemented according to the following steps: Step 1: Perform data preprocessing on the voltage and current data of the lithium-ion battery to extract more local information; Step 2: Define the key parameters to be identified; Step 3: Use a genetic algorithm to identify key parameters in the physical model; Step 4: Use the physical model to generate a high-precision predicted voltage sequence that filters out instantaneous operating condition disturbances; Step 5: Based on the PKA network, extract temporal features to achieve high-precision capacity degradation trajectory prediction; Step 6: Evaluate MSE and RMSE metrics on the test set to support uncertainty estimation and visualization.

[0007] The invention is further characterized in that, Step 1 is implemented in the following steps: Step 1.1: Collect the current sequence of the lithium-ion battery in the first few cycles. With measured voltage sequence Outlier detection methods are used to remove outliers. The outlier criteria are:

[0008] in, and These are the sequence mean and standard deviation, respectively. For a single sample in the sequence; Step 1.2: Perform Min-Max normalization on the current and voltage data respectively, using the following formula:

[0009] in, For the normalized data, The original data, and These are the minimum and maximum values ​​of the batch of data, respectively. Step 1.3: Using the sliding window method, let the window length be... Step size is The sequence is divided into multiple time segments to form samples:

[0010] in, This represents the nth sample after being cropped using a sliding window.

[0011] Step 2 is implemented in the following steps: Based on the physical mechanism, key parameters reflecting the solid-phase electrochemical kinetics process are selected to form a parameter vector:

[0012] in, Represents a parameter set, including the solid-phase diffusion coefficient. Volume fraction of active materials Maximum lithium-ion concentration The key parameters, with subscripts n and p representing the negative electrode and positive electrode respectively, reflect the characteristics of the solid-phase electrochemical kinetic process and are the main factors affecting the battery capacity decay and voltage response characteristics. Therefore, they are selected as identification objects to improve the accuracy and reliability of subsequent model predictions.

[0013] Step 3 is implemented in the following steps: Step 3.1: Using the input current sequence I(t) and parameter vector φ as inputs, a multiphysics coupling model is adopted. This model includes: a solid-phase diffusion equation describing the diffusion of lithium ions in electrode particles, an electrolyte transport equation characterizing ion migration and concentration distribution in the electrolyte, and a polarization effect equation reflecting the influence of charge transfer and concentration polarization on voltage. This model is used to establish the battery voltage prediction function.

[0014] in, For predicting voltage; It can simulate the voltage response of a battery under given operating conditions, accurately reflecting the dynamic characteristics of the physical process; Step 3.2: To achieve parameter identification, the mean square error (MSE) between the predicted voltage and the measured voltage is defined as the objective function, as shown in the following formula:

[0015] in, The optimal parameters identified are J(θ), which represents the prediction error index; the parameters are implemented using a genetic algorithm (GA). Global optimization; Step 3.3: Conduct sensitivity analysis and uncertainty assessment on key parameters to quantify the impact of each parameter on the prediction results.

[0016] Step 3.3 is implemented in accordance with the following steps: Step 3.3.1, Sensitivity Analysis: For the parameters... Each term in the calculation is perturbed by ±5%, while keeping other parameters constant. The predicted voltages before and after the perturbation are then calculated. The mean square error ΔMSE between the predicted voltage and the reference operating condition, and the relative deviation ΔQ of the predicted capacity retention rate; based on the magnitudes of ΔMSE and ΔQ, the sensitivity of each parameter to the model output is determined. In the middle, when the negative electrode solid-phase diffusion coefficient When the change is ±5%, the increase in ΔMSE is significantly greater than that of other parameters, indicating that this parameter has a high sensitivity to the prediction results; Step 3.3.2, Uncertainty Assessment: Within a preset measurement error range, assess the parameter set... Monte Carlo random sampling was performed, and model simulations were repeated. The confidence intervals of the predicted voltage curve and capacity degradation trajectory were statistically analyzed to quantify the model's robustness under varying operating conditions. In, when the volume fraction of active material When measurement bias exists, the fluctuation range of the prediction results is small, indicating that the parameter has a limited impact on the robustness of the model.

[0017] Step 4 is implemented in the following steps: Step 4.1: Obtain the identified optimal parameters Substituting the above multiphysics coupling model, a predicted voltage sequence is generated that is highly consistent with the measured results, due to the parameters... It can characterize the electrochemical properties of batteries under different operating conditions. The predicted voltage after substitution not only has high accuracy, but also can effectively suppress noise fluctuations in the measured signal, providing reliable physical prior features for subsequent neural network modeling. Step 4.2: Obtain the predicted voltage sequence Measured voltage sequence at corresponding time points Time alignment is performed to ensure data consistency at corresponding time points. Subsequently, a dual-channel fused input vector is constructed:

[0018] in, The dual-channel fused input at time t contains data from two dimensions: measured voltage and voltage predicted by the physical model. Step 4.3: Using the sliding window method, construct multi-channel input samples containing multiple consecutive time points:

[0019] in, Let L be the k-th input sample, and L be the window length.

[0020] Step 5 is implemented in the following steps: Step 5.1: Input the dual-channel sample constructed in Step 4. Compared with the parameter vector identified in step 3 The fusion process employs a parameter adaptive fusion strategy, dynamically encoding physical parameters into time-series context information through linear transformation and gating mechanisms. This achieves the organic enhancement of time-series features by physical knowledge, as shown in the following formula:

[0021] in, For enhanced feature representation after fusion, Let b be the learnable weight matrix, and b be the bias. For the activation function, 1 L Represents a vector of length L consisting entirely of 1s, used to implement time-scaling of physical parameters; Step 5.2: The prediction-knowledge-assisted network PKA is used to predict the capacity degradation trajectory of the fused features. The prediction-knowledge-assisted network PKA consists of three layers of one-dimensional convolutional Conv1D, a bidirectional long short-term memory network Bi-LSTM, and two fully connected layers. The kernel sizes of the one-dimensional convolutional Conv1D are {k1,k2,k3}. Each convolutional layer is followed by a Batch Normalization layer and a ReLU activation function. A MaxPooling1D layer is set after the first convolutional layer to enhance feature selectivity. The Bi-LSTM part consists of two stacked bidirectional LSTM units, which are used to model the bidirectional temporal dependencies of the features extracted by the convolutional layers, thereby capturing global temporal dynamics. A Dropout mechanism is introduced at each Bi-LSTM layer, as shown in the following formula:

[0022] in, This represents the extracted multi-scale temporal features, where ⨁ denotes the concatenation operation of feature channels. Input the fused features; Step 5.3: Utilize the fully connected layer to analyze the features of the Bi-LSTM output. A nonlinear mapping is performed to transform temporal features into capacity degradation curves. Residual connectivity and Dropout regularization mechanisms are introduced. The mapping process formula is as follows:

[0023] in, The predicted capacity degradation value for the k-th sample. This is the weight matrix of the fully connected layer. For activation function, Used to prevent overfitting Corresponding bias term; Step 5.4: Use the weighted mean squared error (MSE) loss function as the optimization objective to achieve end-to-end training of the PKA model. The optimization objective function is:

[0024] in, For the total loss, The total number of training samples, This represents the actual capacity degradation value. The regularization coefficient is . This is the set of network weights.

[0025] Step 6 is implemented in the following steps: For the predicted sequence With the sequence of true capacity degradation values To compare the models, various performance metrics are calculated to quantify model accuracy, including mean squared error (MSE), root mean square error (RMSE), and mean absolute error (MAE). These metrics are used to comprehensively evaluate the model's predictive performance and stability.

[0026] The beneficial effect of this invention is that the battery capacity degradation prediction method based on parameter identification and neural network joint modeling aims to solve the problem in existing technologies that rely solely on measured voltage and current as input, making it difficult to utilize the degradation mechanism information contained in the physical model. This method first collects and preprocesses battery operating data, establishing a thermo-electric coupling model or equivalent circuit model containing key physical parameters. Optimal parameter sets related to degradation characteristics are obtained through parameter identification, and a predicted voltage sequence is generated based on this. The predicted voltage is used as a feature enhancement signal input to the neural network, jointly modeled with the original operating data, extracting multi-scale time-series features and establishing a nonlinear mapping relationship for the capacity degradation curve. This method can achieve high-precision capacity prediction even in the early stages when capacity labels are lacking, exhibiting stronger robustness and interpretability, and is suitable for battery health management throughout its entire life cycle. Attached Figure Description

[0027] Figure 1 This is an overall flowchart of the battery capacity degradation trajectory prediction method of the present invention; Figure 2 This is a diagram illustrating the overall structure of the battery capacity degradation trajectory prediction method of the present invention. Figure 3 This is a flowchart of the physical model in Embodiment 6 of the present invention; Figure 4 This is a flowchart of the data-driven model in Embodiment 6 of the present invention; Figure 5 This is a diagram of the internal structure of the multiphysics model in Embodiment 6 of the present invention. Detailed Implementation

[0028] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0029] This invention relates to a battery capacity degradation prediction method based on joint parameter identification and neural network modeling, combined with... Figure 1 , Figure 2 The specific steps are as follows: Step 1: Perform data preprocessing on the voltage and current data of the lithium-ion battery to extract more local information; Step 1 is implemented in the following steps: Step 1.1: Collect the current sequence of the lithium-ion battery in the first few cycles. With measured voltage sequence Outlier detection methods are used to remove outliers. The outlier criteria are:

[0030] in, and These are the sequence mean and standard deviation, respectively. For a single sample in the sequence; Step 1.2: Perform Min-Max normalization on the current and voltage data respectively, using the following formula:

[0031] in, For the normalized data, The original data, and These are the minimum and maximum values ​​of the batch of data, respectively. Step 1.3: Using the sliding window method, let the window length be... Step size is The sequence is divided into multiple time segments to form samples:

[0032] in, This represents the nth sample after being cropped using a sliding window.

[0033] Step 2: Define the key parameters to be identified; Step 2 is implemented in the following steps: Based on the physical mechanism, key parameters reflecting the solid-phase electrochemical kinetics process are selected to form a parameter vector:

[0034] in, Represents a parameter set, including the solid-phase diffusion coefficient. Volume fraction of active materials Maximum lithium-ion concentration The key parameters, with subscripts n and p representing the negative electrode and positive electrode respectively, reflect the characteristics of the solid-phase electrochemical kinetic process and are the main factors affecting the battery capacity decay and voltage response characteristics. Therefore, they are selected as identification objects to improve the accuracy and reliability of subsequent model predictions.

[0035] Step 3: Use a genetic algorithm to identify key parameters in the physical model; Step 3 is implemented in the following steps: Step 3.1: Using the input current sequence I(t) and parameter vector φ as inputs, a multiphysics coupling model is adopted. This model includes: a solid-state diffusion equation (describing the diffusion of lithium ions in electrode particles), an electrolyte transport equation (characterizing ion migration and concentration distribution in the electrolyte), and a polarization effect equation (reflecting the influence of charge transfer and concentration polarization on voltage), which is used to establish the battery voltage prediction function.

[0036] in, For predicting voltage; It can simulate the voltage response of a battery under given operating conditions, accurately reflecting the dynamic characteristics of the physical process; Step 3.2: To achieve parameter identification, the mean square error (MSE) between the predicted voltage and the measured voltage is defined as the objective function, as shown in the following formula:

[0037] in, The optimal parameters identified are J(θ), which represents the prediction error index; the parameters are implemented using a genetic algorithm (GA). Global optimization; Step 3.3: Conduct sensitivity analysis and uncertainty assessment on key parameters to quantify the impact of each parameter on the prediction results.

[0038] Step 3.3 is implemented in accordance with the following steps: Step 3.3.1, Sensitivity Analysis: For the parameters... Each term in the calculation is perturbed by ±5%, while keeping other parameters constant. The predicted voltages before and after the perturbation are then calculated. The mean square error ΔMSE between the predicted voltage and the reference operating condition, and the relative deviation ΔQ of the predicted capacity retention rate; based on the magnitudes of ΔMSE and ΔQ, the sensitivity of each parameter to the model output is determined. In the middle, when the negative electrode solid-phase diffusion coefficient When the change is ±5%, the increase in ΔMSE is significantly greater than that of other parameters, indicating that this parameter has a high sensitivity to the prediction results; Step 3.3.2, Uncertainty Assessment: Within a preset measurement error range (e.g., ±5% to ±10%), assess the parameter set. Monte Carlo random sampling was performed, and model simulations were repeated. The confidence intervals of the predicted voltage curve and capacity degradation trajectory were statistically analyzed to quantify the model's robustness under varying operating conditions. In, when the volume fraction of active material When measurement bias exists, the fluctuation range of the prediction results is small, indicating that the parameter has a limited impact on the robustness of the model; The above analysis not only identifies the most sensitive parameters that have the greatest impact on the prediction results, thus guiding the setting of parameter constraints, but also reveals the robustness level of the model under parameter uncertainty, providing methodological support for reliability in practical applications.

[0039] Step 4: Use the physical model to generate a high-precision predicted voltage sequence that filters out instantaneous operating condition disturbances; Step 4 is implemented in the following steps: Step 4.1: Obtain the identified optimal parameters Substituting the above multiphysics coupling model, a predicted voltage sequence is generated that is highly consistent with the measured results, due to the parameters... It can characterize the electrochemical properties of batteries under different operating conditions. The predicted voltage after substitution not only has high accuracy, but also can effectively suppress noise fluctuations in the measured signal, providing reliable physical prior features for subsequent neural network modeling. Step 4.2: Obtain the predicted voltage sequence Measured voltage sequence at corresponding time points Time alignment is performed to ensure data consistency at corresponding time points. Subsequently, a dual-channel fused input vector is constructed:

[0040] in, The dual-channel fused input at time t contains data from two dimensions: measured voltage and voltage predicted by the physical model. Step 4.3: Using the sliding window method, construct multi-channel input samples containing multiple consecutive time points:

[0041] in, For the k-th input sample, L is the window length. This multi-channel fusion input effectively integrates the complementary information of physical model prediction and measured data, providing rich and high-quality temporal features for the capacity degradation prediction of the subsequent neural network model.

[0042] Step 5: Based on the PKA network, extract temporal features to achieve high-precision capacity degradation trajectory prediction; Step 5 is implemented in the following steps: Step 5.1: Input the dual-channel sample constructed in Step 4. Compared with the parameter vector identified in step 3 The fusion process employs a parameter adaptive fusion strategy, dynamically encoding physical parameters into time-series context information through linear transformation and gating mechanisms. This achieves the organic enhancement of time-series features by physical knowledge, as shown in the following formula:

[0043] in, For enhanced feature representation after fusion, Let b be the learnable weight matrix, and b be the bias. For the activation function, 1 L Represents a vector of length L consisting entirely of 1s, used to implement time-scaling of physical parameters; Step 5.2: The Prediction-Knowledge-Assisted Network (PKA) is used to predict the capacity degradation trajectory of the fused features. The PKA consists of three layers of one-dimensional convolutional Conv1D, a bidirectional long short-term memory network (Bi-LSTM), and two fully connected layers. The kernel sizes of the one-dimensional Conv1D are {k1, k2, k3}. Each convolutional layer is followed by a Batch Normalization layer and a ReLU activation function. A MaxPooling1D layer is set after the first convolutional layer to enhance feature selectivity. The Bi-LSTM part consists of two stacked bidirectional LSTM units, which are used to model the bidirectional temporal dependencies of the features extracted by the convolutional layers, thereby capturing global temporal dynamics. A Dropout mechanism is introduced at each Bi-LSTM layer to effectively suppress overfitting and improve the generalization ability of the model. The formula is as follows:

[0044] in, This represents the extracted multi-scale temporal features, where ⨁ denotes the concatenation operation of feature channels. Input the fused features; Step 5.3: Utilize the fully connected layer to analyze the features of the Bi-LSTM output. A nonlinear mapping is performed to transform temporal features into capacity degradation curves. To alleviate the gradient vanishing problem and improve the model's generalization ability, residual connections and Dropout regularization mechanisms are introduced. The mapping process formula is as follows:

[0045] in, The predicted capacity degradation value for the k-th sample. This is the weight matrix of the fully connected layer. For activation function, Used to prevent overfitting Corresponding bias term; Step 5.4: Use the weighted mean squared error (MSE) loss function as the optimization objective to achieve end-to-end training of the PKA model. The optimization objective function is:

[0046] in, For the total loss, The total number of training samples, This represents the actual capacity degradation value. The regularization coefficient is . This is the set of network weights.

[0047] The Adam optimization algorithm is used during training to effectively accelerate convergence and improve training stability.

[0048] Step 6: Evaluate MSE and RMSE metrics on the test set to support uncertainty estimation and visualization.

[0049] Step 6 is implemented in the following steps: For the predicted sequence With the sequence of true capacity degradation values To compare the models, various performance metrics are calculated to quantify model accuracy, including mean squared error (MSE), root mean square error (RMSE), and mean absolute error (MAE). These metrics are used to comprehensively evaluate the model's predictive performance and stability.

[0050] Example 1 Following the battery capacity degradation trajectory prediction method of Example 1, the main steps of this Example 2 are: Step 1: Collect current and measured voltage data of lithium-ion batteries during multiple cycles. After preprocessing such as outlier removal and normalization, construct multi-sample time-series data containing time dependencies. Refer to Example 1 for the specific preprocessing process; Step 2: Design a multiphysics coupling model and determine the parameter vector composed of key parameters to be identified, laying the physical foundation for subsequent model identification. (Refer to...) Figure 3 The main process is as described in Example 1.

[0051] Step 3: Use a genetic algorithm to globally optimize the key parameters in the physical model. Refer to Example 1 for the specific process.

[0052] Step 4: Combine the identified optimal parameters with the input current data, and use the physical model to generate a high-precision predicted voltage sequence that filters out instantaneous operating condition disturbances. For details, refer to Example 1.

[0053] Step 5: Time-align the measured voltage sequence with the predicted voltage sequence to construct a fusion input sample containing dual-channel information; based on the PKA network, extract multi-scale time-series features to achieve high-precision nonlinear mapping prediction. The main process is as described in Example 1.

[0054] Step 6: Evaluate the model prediction results on the test dataset. The main process is the same as in Example 1.

[0055] Example 2 Referring to Example 1, the steps of the battery capacity degradation prediction method in this example are as follows: Step 1: Preprocess early data from lithium-ion batteries.

[0056] Step 2: Establish a multiphysics coupling model and determine the parameter vector to be identified.

[0057] Step 3: Use a genetic algorithm to globally optimize the model parameters and improve the accuracy of parameter identification.

[0058] Step 4: Combine the optimal parameters and current data to generate a high-precision predicted voltage sequence.

[0059] Step 5: Fuse the measured voltage with the predicted voltage, input the data into the PKA network to extract time-series features, and realize capacity degradation trajectory prediction.

[0060] Step 6: Evaluate metrics such as MSE and RMSE on the test set to support uncertainty estimation and visualization.

[0061] This embodiment 2 presents a lithium-ion battery capacity degradation prediction method based on joint modeling of parameter identification and neural networks. The method first performs outlier removal and normalization on current and voltage data during battery cycling, and constructs multi-sample time-series data using a sliding window. Based on a multi-physics coupling model of solid-phase diffusion, electrolyte dynamics, and polarization effects, key parameter vectors are selected, and a genetic algorithm is used to achieve global optimization and identification of the parameters. Subsequently, the identified optimal parameters are combined with the input current data to generate a high-precision voltage prediction sequence, which serves as the dual-channel fusion input feature. A knowledge-assisted network (PKA) is designed to achieve deep fusion of physical parameters and multi-scale time-series features. Multi-layer convolutional and bidirectional long short-term memory networks are used to extract complex time-series dependencies, and finally, a fully connected layer completes the nonlinear mapping of capacity degradation. This method combines the advantages of physical mechanisms and data-driven approaches, significantly improving the accuracy and generalization ability of capacity prediction, and is suitable for battery state management under complex operating conditions.

[0062] Example 3 This invention relates to a battery capacity degradation prediction method based on joint parameter identification and neural network modeling, combined with... Figure 1 , Figure 2 The specific steps are as follows: Step 1: Perform data preprocessing on the voltage and current data of the lithium-ion battery to extract more local information; Step 1 is implemented in the following steps: Step 1.1: Collect the current sequence of the lithium-ion battery in the first few cycles. With measured voltage sequence Outlier detection methods are used to remove outliers. The outlier criteria are:

[0063] in, and These are the sequence mean and standard deviation, respectively. For a single sample in the sequence; Step 1.2: Perform Min-Max normalization on the current and voltage data respectively, using the following formula:

[0064] in, For the normalized data, The original data, and These are the minimum and maximum values ​​of the batch of data, respectively. Step 1.3: Using the sliding window method, let the window length be... Step size is The sequence is divided into multiple time segments to form samples:

[0065] in, This represents the nth sample after being cropped using a sliding window.

[0066] Step 2: Define the key parameters to be identified; Step 2 is implemented in the following steps: Based on the physical mechanism, key parameters reflecting the solid-phase electrochemical kinetics process are selected to form a parameter vector:

[0067] in, Represents a parameter set, including the solid-phase diffusion coefficient. Volume fraction of active materials Maximum lithium-ion concentration The key parameters, with subscripts n and p representing the negative electrode and positive electrode respectively, reflect the characteristics of the solid-phase electrochemical kinetic process and are the main factors affecting the battery capacity decay and voltage response characteristics. Therefore, they are selected as identification objects to improve the accuracy and reliability of subsequent model predictions.

[0068] Step 3: Use a genetic algorithm to identify key parameters in the physical model; Step 3 is implemented in the following steps: Step 3.1: Using the input current sequence I(t) and parameter vector φ as inputs, a multiphysics coupling model is adopted. This model includes: a solid-state diffusion equation (describing the diffusion of lithium ions in electrode particles), an electrolyte transport equation (characterizing ion migration and concentration distribution in the electrolyte), and a polarization effect equation (reflecting the influence of charge transfer and concentration polarization on voltage), which is used to establish the battery voltage prediction function.

[0069] in, For predicting voltage; It can simulate the voltage response of a battery under given operating conditions, accurately reflecting the dynamic characteristics of the physical process; Step 3.2: To achieve parameter identification, the mean square error (MSE) between the predicted voltage and the measured voltage is defined as the objective function, as shown in the following formula:

[0070] in, The optimal parameters identified are J(θ), which represents the prediction error index; the parameters are implemented using a genetic algorithm (GA). Global optimization; Step 3.3: Conduct sensitivity analysis and uncertainty assessment on key parameters to quantify the impact of each parameter on the prediction results.

[0071] Step 4: Use the physical model to generate a high-precision predicted voltage sequence that filters out instantaneous operating condition disturbances; Step 5: Based on the PKA network, extract temporal features to achieve high-precision capacity degradation trajectory prediction; Step 6: Evaluate MSE and RMSE metrics on the test set to support uncertainty estimation and visualization.

[0072] Example 4 This invention relates to a battery capacity degradation prediction method based on joint parameter identification and neural network modeling, combined with... Figure 1 , Figure 2 The specific steps are as follows: Step 1: Perform data preprocessing on the voltage and current data of the lithium-ion battery to extract more local information; Step 1 is implemented in the following steps: Step 1.1: Collect the current sequence of the lithium-ion battery in the first few cycles. With measured voltage sequence Outlier detection methods are used to remove outliers. The outlier criteria are:

[0073] in, and These are the sequence mean and standard deviation, respectively. For a single sample in the sequence; Step 1.2: Perform Min-Max normalization on the current and voltage data respectively, using the following formula:

[0074] in, For the normalized data, The original data, and These are the minimum and maximum values ​​of the batch of data, respectively. Step 1.3: Using the sliding window method, let the window length be... Step size is The sequence is divided into multiple time segments to form samples:

[0075] in, This represents the nth sample after being cropped using a sliding window.

[0076] Step 2: Define the key parameters to be identified; Step 2 is implemented in the following steps: Based on the physical mechanism, key parameters reflecting the solid-phase electrochemical kinetics process are selected to form a parameter vector:

[0077] in, Represents a parameter set, including the solid-phase diffusion coefficient. Volume fraction of active materials Maximum lithium-ion concentration The key parameters, with subscripts n and p representing the negative electrode and positive electrode respectively, reflect the characteristics of the solid-phase electrochemical kinetic process and are the main factors affecting the battery capacity decay and voltage response characteristics. Therefore, they are selected as identification objects to improve the accuracy and reliability of subsequent model predictions.

[0078] Step 3: Use a genetic algorithm to identify key parameters in the physical model; Step 3 is implemented in the following steps: Step 3.1: Using the input current sequence I(t) and parameter vector φ as inputs, a multiphysics coupling model is adopted. This model includes: a solid-state diffusion equation (describing the diffusion of lithium ions in electrode particles), an electrolyte transport equation (characterizing ion migration and concentration distribution in the electrolyte), and a polarization effect equation (reflecting the influence of charge transfer and concentration polarization on voltage), which is used to establish the battery voltage prediction function.

[0079] in, For predicting voltage; It can simulate the voltage response of a battery under given operating conditions, accurately reflecting the dynamic characteristics of the physical process; Step 3.2: To achieve parameter identification, the mean square error (MSE) between the predicted voltage and the measured voltage is defined as the objective function, as shown in the following formula:

[0080] in, The optimal parameters identified are J(θ), which represents the prediction error index; the parameters are implemented using a genetic algorithm (GA). Global optimization; Step 3.3: Conduct sensitivity analysis and uncertainty assessment on key parameters to quantify the impact of each parameter on the prediction results.

[0081] Step 3.3 is implemented in accordance with the following steps: Step 3.3.1, Sensitivity Analysis: For the parameters... Each term in the calculation is perturbed by ±5%, while keeping other parameters constant. The predicted voltages before and after the perturbation are then calculated. The mean square error ΔMSE between the predicted voltage and the reference operating condition, and the relative deviation ΔQ of the predicted capacity retention rate; based on the magnitudes of ΔMSE and ΔQ, the sensitivity of each parameter to the model output is determined. In the middle, when the negative electrode solid-phase diffusion coefficient When the change is ±5%, the increase in ΔMSE is significantly greater than that of other parameters, indicating that this parameter has a high sensitivity to the prediction results; Step 3.3.2, Uncertainty Assessment: Within a preset measurement error range (e.g., ±5% to ±10%), assess the parameter set. Monte Carlo random sampling was performed, and model simulations were repeated. The confidence intervals of the predicted voltage curve and capacity degradation trajectory were statistically analyzed to quantify the model's robustness under varying operating conditions. In, when the volume fraction of active material When measurement bias exists, the fluctuation range of the prediction results is small, indicating that the parameter has a limited impact on the robustness of the model; The above analysis not only identifies the most sensitive parameters that have the greatest impact on the prediction results, thus guiding the setting of parameter constraints, but also reveals the robustness level of the model under parameter uncertainty, providing methodological support for reliability in practical applications.

[0082] Step 4: Use the physical model to generate a high-precision predicted voltage sequence that filters out instantaneous operating condition disturbances; Step 5: Based on the PKA network, extract temporal features to achieve high-precision capacity degradation trajectory prediction; Step 6: Evaluate MSE and RMSE metrics on the test set to support uncertainty estimation and visualization.

[0083] Example 5 This invention relates to a battery capacity degradation prediction method based on joint parameter identification and neural network modeling, combined with... Figure 1 , Figure 2 The specific steps are as follows: Step 1: Perform data preprocessing on the voltage and current data of the lithium-ion battery to extract more local information; Step 1 is implemented in the following steps: Step 1.1: Collect the current sequence of the lithium-ion battery in the first few cycles. With measured voltage sequence Outlier detection methods are used to remove outliers. The outlier criteria are:

[0084] in, and These are the sequence mean and standard deviation, respectively. For a single sample in the sequence; Step 1.2: Perform Min-Max normalization on the current and voltage data respectively, using the following formula:

[0085] in, For the normalized data, The original data, and These are the minimum and maximum values ​​of the batch of data, respectively. Step 1.3: Using the sliding window method, let the window length be... Step size is The sequence is divided into multiple time segments to form samples:

[0086] in, This represents the nth sample after being cropped using a sliding window.

[0087] Step 2: Define the key parameters to be identified; Step 2 is implemented in the following steps: Based on the physical mechanism, key parameters reflecting the solid-phase electrochemical kinetics process are selected to form a parameter vector:

[0088] in, Represents a parameter set, including the solid-phase diffusion coefficient. Volume fraction of active materials Maximum lithium-ion concentration The key parameters, with subscripts n and p representing the negative electrode and positive electrode respectively, reflect the characteristics of the solid-phase electrochemical kinetic process and are the main factors affecting the battery capacity decay and voltage response characteristics. Therefore, they are selected as identification objects to improve the accuracy and reliability of subsequent model predictions.

[0089] Step 3: Use a genetic algorithm to identify key parameters in the physical model; Step 3 is implemented in the following steps: Step 3.1: Using the input current sequence I(t) and parameter vector φ as inputs, a multiphysics coupling model is adopted. This model includes: a solid-state diffusion equation (describing the diffusion of lithium ions in electrode particles), an electrolyte transport equation (characterizing ion migration and concentration distribution in the electrolyte), and a polarization effect equation (reflecting the influence of charge transfer and concentration polarization on voltage), which is used to establish the battery voltage prediction function.

[0090] in, For predicting voltage; It can simulate the voltage response of a battery under given operating conditions, accurately reflecting the dynamic characteristics of the physical process; Step 3.2: To achieve parameter identification, the mean square error (MSE) between the predicted voltage and the measured voltage is defined as the objective function, as shown in the following formula:

[0091] in, The optimal parameters identified are J(θ), which represents the prediction error index; the parameters are implemented using a genetic algorithm (GA). Global optimization; Step 3.3: Conduct sensitivity analysis and uncertainty assessment on key parameters to quantify the impact of each parameter on the prediction results.

[0092] Step 3.3 is implemented in accordance with the following steps: Step 3.3.1, Sensitivity Analysis: For the parameters... Each term in the calculation is perturbed by ±5%, while keeping other parameters constant. The predicted voltages before and after the perturbation are then calculated. The mean square error ΔMSE between the predicted voltage and the reference operating condition, and the relative deviation ΔQ of the predicted capacity retention rate; based on the magnitudes of ΔMSE and ΔQ, the sensitivity of each parameter to the model output is determined. In the middle, when the negative electrode solid-phase diffusion coefficient When the change is ±5%, the increase in ΔMSE is significantly greater than that of other parameters, indicating that this parameter has a high sensitivity to the prediction results; Step 3.3.2, Uncertainty Assessment: Within a preset measurement error range (e.g., ±5% to ±10%), assess the parameter set. Monte Carlo random sampling was performed, and model simulations were repeated. The confidence intervals of the predicted voltage curve and capacity degradation trajectory were statistically analyzed to quantify the model's robustness under varying operating conditions. In, when the volume fraction of active material When measurement bias exists, the fluctuation range of the prediction results is small, indicating that the parameter has a limited impact on the robustness of the model; The above analysis not only identifies the most sensitive parameters that have the greatest impact on the prediction results, thus guiding the setting of parameter constraints, but also reveals the robustness level of the model under parameter uncertainty, providing methodological support for reliability in practical applications.

[0093] Step 4: Use the physical model to generate a high-precision predicted voltage sequence that filters out instantaneous operating condition disturbances; Step 4 is implemented in the following steps: Step 4.1: Obtain the identified optimal parameters Substituting the above multiphysics coupling model, a predicted voltage sequence is generated that is highly consistent with the measured results, due to the parameters... It can characterize the electrochemical properties of batteries under different operating conditions. The predicted voltage after substitution not only has high accuracy, but also can effectively suppress noise fluctuations in the measured signal, providing reliable physical prior features for subsequent neural network modeling. Step 4.2: Obtain the predicted voltage sequence Measured voltage sequence at corresponding time points Time alignment is performed to ensure data consistency at corresponding time points. Subsequently, a dual-channel fused input vector is constructed:

[0094] in, The dual-channel fused input at time t contains data from two dimensions: measured voltage and voltage predicted by the physical model. Step 4.3: Using the sliding window method, construct multi-channel input samples containing multiple consecutive time points:

[0095] in, For the k-th input sample, L is the window length. This multi-channel fusion input effectively integrates the complementary information of physical model prediction and measured data, providing rich and high-quality temporal features for the capacity degradation prediction of the subsequent neural network model.

[0096] Step 5: Based on the PKA network, extract temporal features to achieve high-precision capacity degradation trajectory prediction; Step 6: Evaluate MSE and RMSE metrics on the test set to support uncertainty estimation and visualization.

[0097] Example 6 Reference Figure 1 , Figure 2 Based on the battery capacity degradation prediction method proposed in this invention, which combines parameter identification and neural network modeling, the steps for predicting the battery capacity degradation trajectory are as follows: Step 1: Outlier removal and normalization are performed on voltage and current data to ensure data quality consistency. Then, a sliding window and step size strategy is used to generate local time segments, thereby constructing a multimodal input feature sequence with temporal dependence and physical consistency. The specific process is as follows: 1.1) Collect the current sequence of the lithium-ion battery during the first 100 cycles. With measured voltage sequence Outlier detection methods are used to remove values ​​that meet the criteria. Abnormal data points were identified to ensure data quality. Subsequently, the current and voltage sequences were subjected to Min-Max normalization, as shown in the following formula:

[0098] in, The original data, and These are the minimum and maximum values ​​of the data in this batch, respectively. The normalized data has its values ​​scaled to the [0,1] range.

[0099] 1.2) The sliding window method is used, and the window length is set to... =50, step size is The normalized sequence is divided into multiple samples:

[0100] in, .

[0101] Reference Figure 3 , Figure 5 The design of the multiphysics coupling model is as follows: Step 2: A multiphysics coupling model was established. This model combines physical mechanisms with numerical solution methods, enabling high-precision prediction of the dynamic response of battery voltage. The specific process is as follows: 2.1) A multiphysics coupling model is constructed based on solid-state diffusion, electrolyte dynamics, and polarization effects. The parameter vector is defined as follows:

[0102] in, Let be the solid-phase diffusion coefficient. This represents the volume fraction of the active material. The maximum lithium-ion concentration is a key parameter reflecting the solid-phase electrochemical kinetics process.

[0103] 2.2) Using the input current sequence I(t) and parameter vector φ as input, a battery voltage prediction function is established by solving the diffusion equation, electrolyte transport equation, and polarization effect equation:

[0104] in, For predicting voltage.

[0105] 2.3) The mean squared error (MSE) is used as the objective function, and a genetic algorithm (GA) is used for global parameter optimization to obtain the optimal parameters, as shown in the following formula:

[0106] in, The optimal parameters identified are represented by J(θ), which indicates the prediction error index. Substituting the optimal parameters into the model generates a high-precision predicted voltage sequence that filters out instantaneous operating condition disturbances.

[0107] 2.4) Conduct sensitivity analysis on key parameters to quantify the impact of each parameter on the model output, guiding parameter constraints and experimental design. Simultaneously, perform uncertainty analysis to assess the model's robustness under parameter fluctuations, ensuring the model is applicable to varying operating conditions.

[0108] Step 3: Construct a multi-channel fusion input based on the physical model output. The specific process is as follows: The predicted voltage sequence obtained in step 2 Measured voltage sequence at corresponding time points Perform time alignment to construct a dual-channel fused input:

[0109] in, The dual-channel fused input at time t contains data from both measured voltage and physical model predicted voltage.

[0110] Using the sliding window method, with a window length L=50, construct multi-channel input samples:

[0111] in, This is the kth input sample.

[0112] Reference Figure 4 The process of predicting capacity degradation trajectories using the PKA model is as follows: Step 4: Design a knowledge-assisted network (PKA) model based on multi-channel fusion input to achieve nonlinear mapping prediction with capacity degradation. The specific process is as follows: A PKA model, comprising a physical knowledge injection module, a multi-scale temporal feature extraction module, and a nonlinear mapping module, is used to achieve nonlinear mapping prediction with capacity degradation. The physical knowledge injection module inputs samples through two channels. With the optimal parameter vector The fusion and dynamic encoding of physical knowledge is represented by the following formula:

[0113] in, For enhanced feature representation after fusion, Let b be the learnable weight matrix, and b be the bias. Let L be the activation function, and 1L be an all-1 vector of length L.

[0114] Step 5: Based on the multi-channel features obtained in Step 4, further extract multi-scale temporal information during the capacity degradation process, and achieve accurate conversion of features to the capacity degradation state through a nonlinear mapping module. The specific process is as follows: 5.1) Multi-scale temporal features are extracted using a multi-layer convolutional network combined with a bidirectional long short-term memory (Bi-LSTM) network. The formula is as follows:

[0115] in, This represents the extracted multi-scale temporal features, where ⨁ denotes the concatenation operation of feature channels. This is the input of the fused features in step 4.

[0116] 5.2) Nonlinear mapping is performed through several fully connected layers to output the capacity degradation prediction value:

[0117] middle, The predicted capacity degradation value for the k-th sample. This is the weight matrix of the fully connected layer. For activation function, Used to prevent overfitting Corresponding bias term.

[0118] During training, a weighted mean squared error loss function is used, and the Adam optimizer is used for end-to-end training.

[0119] Step 6: Predict and output the capacity degradation trajectory based on the trained PKA network model. The specific process is as follows: 6.1) Fuse the multi-channel input samples in the test set and the corresponding physical parameter vector Input the trained PKA network and obtain the predicted values ​​for capacity degradation:

[0120] in, This is the predicted value for the size degradation of the k-th sample.

[0121] 6.2) For the predicted sequence With the sequence of true capacity degradation values To make comparisons, various performance metrics were calculated to quantify model accuracy, including mean squared error (MSE), root mean square error (RMSE), and mean absolute error (MAE), as shown in the following formulas;

[0122]

[0123]

[0124] The predictive performance and stability of the model are evaluated using the above indicators.

[0125] The definitions and meanings of the key parameters of the physical model involved in this invention are summarized in Table 1 for ease of subsequent description and understanding.

[0126] Table 1. Explanation of Key Parameters of the Physical Model

Claims

1. A battery capacity degradation prediction method based on parameter identification and neural network joint modeling, characterized in that, Specifically, the following steps are implemented: Step 1, data preprocessing of voltage and current data of lithium-ion battery to extract more local information; Step 2, define key parameters to be identified; Step 3, use genetic algorithm to identify key parameters in physical model; Step 4, use physical model to generate high-precision predicted voltage sequence filtered from transient operating condition disturbances; Step 5, based on PKA network, extract time series features, and realize high-precision capacity degradation trajectory prediction; Step 6, evaluate MSE and RMSE indicators on the test set, support uncertainty estimation and visualization.

2. The battery capacity degradation prediction method based on parameter identification and neural network joint modeling according to claim 1, characterized in that, The step 1 is implemented according to the following steps: Step 1.1, Collecting current sequence of lithium-ion battery in previous several cycles with measured voltage sequence , using outlier detection method to eliminate outliers, the condition of outliers is that: wherein, and are the sequence mean and standard deviation, respectively, is a single sample in the sequence; Step 1.2, Min-Max normalization is performed on current and voltage data respectively, and the formula is as follows: wherein, is the normalized data, is the original data, and are the minimum and maximum values of the batch of data, respectively. Step 1.3, divide the sequence into multiple time segments with a sliding window method, with window length , step size , form samples: wherein, represents the jth sample after the sliding window interception.

3. The battery capacity degradation prediction method based on parameter identification and neural network joint modeling according to claim 2, characterized in that, The step 2 is implemented according to the following steps: Based on physical mechanism, select key parameters reflecting solid-phase electrochemical kinetics process to form parameter vector: wherein, denotes the parameter set, containing the solid diffusion coefficient , the volume fraction of active material , the maximum lithium ion concentration key parameters, the subscripts n and p represent the negative and positive electrodes, respectively. These parameters reflect the characteristics of the solid-phase electrochemical kinetic process and are the main factors affecting the capacity attenuation and voltage response characteristics of the battery. Therefore, they are selected as the identification objects to improve the accuracy and reliability of subsequent model predictions.

4. The battery capacity degradation prediction method based on parameter identification and neural network joint modeling according to claim 3, characterized in that, The step 3 is implemented according to the following steps: Step 3.1, use multi-physical field coupling model with input current sequence I(t) and parameter vector θ as input, which includes solid-phase diffusion equation describing lithium ion diffusion in electrode particles, electrolyte transport equation describing ion migration and concentration distribution in electrolyte, and polarization effect equation reflecting charge transfer and concentration polarization effect on voltage, to establish battery voltage prediction function: wherein, is the predicted voltage; The voltage response of the battery can be simulated under a given working condition, and the dynamic characteristics in the physical process are accurately reflected. Step 3.2, to realize parameter identification, define the mean square error MSE between predicted voltage and measured voltage as the objective function, and the formula is as follows: wherein, J(θ) represents a prediction error index for the identified optimal parameters; and a global optimization of the parameters is achieved using a genetic algorithm GA. Step 3.3, sensitivity analysis and uncertainty evaluation are carried out on key parameters to quantify the influence of each parameter on the prediction result.

5. The battery capacity degradation prediction method based on parameter identification and neural network joint modeling according to claim 4, characterized in that, The step 3.3 is implemented according to the following steps: Step 3.3.1, Sensitivity analysis: perturb each item in the parameters by ±5%, keeping other parameters unchanged, calculate the mean square error ΔMSE between the predicted voltage before and after the perturbation, and the relative deviation ΔQ of the predicted capacity retention rate; according to the size of ΔMSE and ΔQ, determine the sensitivity of each parameter to the model output, and the parameter with the highest sensitivity is the negative electrode solid-phase diffusion coefficient When the negative electrode solid-phase diffusion coefficient changes by ±5%, the growth rate of ΔMSE is significantly greater than that of other parameters, indicating that this parameter has high sensitivity to the prediction result. Step 3.3.2, Uncertainty Assessment: Within a preset measurement error range, assess the parameter set... Monte Carlo random sampling was performed, and model simulations were repeated. The confidence intervals of the predicted voltage curve and capacity degradation trajectory were statistically analyzed to quantify the model's robustness under varying operating conditions. In, when the volume fraction of active material When measurement bias exists, the fluctuation range of the prediction results is small, indicating that the parameter has a limited impact on the robustness of the model.

6. The battery capacity degradation prediction method based on parameter identification and neural network joint modeling according to claim 5, characterized in that, The step 4 is implemented according to the following steps: Step 4.1, identifying the optimal parameters The above multi-physics coupling model is substituted to generate a predicted voltage sequence highly consistent with the measured results. Since the parameters are able to characterize the electrochemical characteristics of the battery under different working conditions, the predicted voltage after substitution not only has high accuracy, but also effectively suppresses the noise fluctuations in the measured signal, providing reliable physical prior characteristics for subsequent neural network modeling. Step 4.2, the obtained predicted voltage sequence with the measured voltage sequence at the corresponding time time alignment is performed to ensure that the data at the corresponding time points match, and then a dual-channel fusion input vector is constructed: wherein, Xt= {Vt, Vt} represents the dual-channel fusion input at time t, containing data of two dimensions of measured voltage and physically modeled predicted voltage; Step 4.3, use sliding window method to construct multi-channel input samples containing multiple consecutive time points: wherein, is the kth input sample, and L is the window length.

7. The battery capacity degradation prediction method based on parameter identification and neural network joint modeling according to claim 6, characterized in that, The step 5 is implemented according to the following steps: Step 5.1, inputting the dual-channel samples constructed in step 4 with the parameter vector recognized in step 3 fusion, specifically using a parameter adaptive fusion strategy, dynamically encoding the physical parameters into time series context information through linear transformation and gating mechanism, realizing the organic enhancement of physical knowledge to time series features, as follows: wherein, is the enhanced feature representation after fusion, is a learnable weight matrix, and b is a bias, is an activation function, and 1 L denotes an all-ones vector of length L, implementing a time expansion of the physical parameters; Step 5.2, use prediction-knowledge auxiliary network PKA to predict the capacity degradation trajectory of the fused features, and the prediction-knowledge auxiliary network PKA is composed of three layers of one-dimensional convolution Conv1D, bidirectional long short-term memory network Bi-LSTM and two layers of fully connected layer, where the convolution kernel size of one-dimensional convolution Conv1D is {k1, k2, k3}, and Batch Normalization layer and ReLU activation function are connected after each convolution layer, and a MaxPooling1D layer is set after the first convolution layer to enhance feature selectivity, and the Bi-LSTM part is composed of two layers of stacked bidirectional LSTM units, which are used to model the bidirectional time dependence of the features extracted by the convolution layer, so as to capture the global time series dynamic characteristics, and Dropout mechanism is introduced at the end of each Bi-LSTM layer, and the formula is as follows: wherein, is the extracted multi-scale temporal feature representation, and ⨁ denotes a concatenation operation of feature channels, is the fused feature input; Step 5.

3. Feature of Bi-LSTM output with full connection layer Nonlinear mapping is performed to convert the time series features into the capacity degradation curve. The residual connection and Dropout regularization mechanism are introduced. The mapping process is as follows: wherein, a predicted capacity degradation value for the kth sample, a weight matrix for the fully connected layer, an activation function, for preventing overfitting, a corresponding bias term; Step 5.4, use weighted decay mean square error MSE loss function as the optimization objective to realize end-to-end training of PKA model, and the optimization objective function is: wherein, is the total loss, is the total number of training samples, is the true capacity degradation value, is the regularization coefficient, is the set of network weights.

8. The battery capacity degradation prediction method based on parameter identification and neural network joint modeling according to claim 7, characterized in that, The step 6 is implemented according to the following steps: to the predicted sequence with the real capacity degradation value sequence In comparison, a variety of performance indicators are calculated to quantify the accuracy of the model, including mean square error MSE, root mean square error RMSE and mean absolute error MAE, and the prediction performance and stability of the model are comprehensively evaluated through the above indicators.

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