A two-stage lithium-ion battery capacity degradation trajectory prediction method based on residual life and knee point

Abstract

The application discloses a two-stage lithium ion battery capacity degradation trajectory prediction method based on residual life and knee point, and belongs to the technical field of lithium ion battery health state evaluation and life prediction. The method firstly constructs a feature set by using the capacity-cycle data obtained through a cycle test, and realizes joint prediction of RUL and knee point based on a hybrid network of convolution-gated recurrent unit; the capacity curve is divided into a slow degradation stage and an accelerated degradation stage by taking the knee point as a boundary, LOESS smoothing fitting and a double exponential model are respectively used for modeling, and a continuous and derivable fusion of the two curve sections is realized in the knee point neighborhood through a splicing function with a smoothing coefficient; global parameter solving is carried out by taking the minimum full-life error as a criterion, and network hyperparameters and stage model parameters are adaptively determined through a melolontha optimization method. The application can simultaneously capture the differential degradation mechanism before and after the knee point, ensure the smoothness and consistency of the full-life capacity trajectory, and significantly improve the prediction accuracy of the accelerated degradation stage.

Description

Technical Field

[0001] This invention belongs to the field of lithium-ion battery health status assessment and lifespan prediction technology, specifically involving a two-stage lithium-ion battery capacity degradation trajectory prediction method based on remaining lifespan and knee point. Background Technology

[0002] Capacity degradation is the core manifestation of battery performance decline in lithium-ion batteries. As the number of battery uses increases, battery capacity typically exhibits a non-linear degradation characteristic. Especially in the early stages of degradation, capacity decreases relatively slowly, but after the knee point, the battery enters an accelerated degradation phase. The knee point is the inflection point in the battery capacity degradation curve, marking a significant acceleration in the degradation rate. Accurately predicting the knee point location not only provides early performance warnings but also significantly improves the accuracy of RUL (Recovery Limiting Life) and capacity prediction, enabling battery management systems to more accurately assess the battery's health status.

[0003] Data-driven battery health assessment methods primarily rely on historical and real-time data, employing techniques such as machine learning and statistical analysis to analyze the battery's capacity degradation process and thus assess its health status. However, most current battery health assessment methods focus on predicting RUL (Range Limit Up) and fitting the capacity degradation trajectory, neglecting the accurate prediction of the knee point. This results in inaccurate fitting of the capacity degradation trajectory, failing to comprehensively reflect the dynamic changes in battery health. While deep learning-based prediction methods can provide relatively accurate results in some scenarios, these methods typically rely on large amounts of data for training, requiring significant computational power. Furthermore, most mainstream prediction methods focus on single-task prediction, lacking joint prediction from multiple aspects. Consequently, the degradation characteristics at different stages of battery capacity degradation are not fully captured, especially in the accelerated degradation phase before and after the knee point.

[0004] Current research on joint prediction of RUL and knee point, as well as high-precision prediction and fitting of the two-stage capacity degradation trajectory, is relatively scarce. Establishing methods that conform to practical application scenarios and developing technologies for accurately fitting the capacity degradation trajectory of lithium batteries based on joint prediction of RUL and knee point are of great significance for improving the accuracy of battery health status assessment. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a two-stage lithium-ion battery capacity degradation trajectory prediction method based on remaining lifespan and knee point.

[0006] To achieve the above technical solution, the steps include:

[0007] S1. Cyclic data acquisition and capacity decay sequence construction;

[0008] Under constant temperature conditions, multiple charge-discharge tests were conducted on different batteries of the same model until the discharge capacity decayed to 80% of the rated capacity. Different charging strategies were used during the test, including constant current-constant voltage (CC-CV) and multi-stage constant current-constant voltage (C1-C2-CV) modes. When the SOC reached 80%, the multi-stage constant current was cut off, the battery was left to rest for 10 seconds, and the charging state changed from multi-stage constant current charging to constant voltage charging. The charging voltage, number of cycles, and discharge capacity were recorded.

[0009] S2, Data Preprocessing and Feature Construction;

[0010] Wavelet denoising and smoothing were performed on the voltage and capacity data collected during multiple charge-discharge cycles of lithium-ion batteries to remove abnormal cycle points.

[0011] Voltage characteristics are constructed by extracting voltage characteristic parameters during the charging and discharging phases. And combined with the capacity decay feature matrix This forms the comprehensive input matrix: ;

[0012] Using belt The linear regression model with regularization terms imposes sparse constraints on the importance of features in the comprehensive input matrix, and its optimization objective function is:

[0013]

[0014] In the formula, For the intercept term; This is a vector of regression coefficients; The regularization coefficient is used. The target variable; This represents the total number of battery cycle samples. An index representing the total number of battery cycle samples; Represents the total number of features. An index representing the total number of features; Indicates the first The first sample of the battery cycle One eigenvalue; Indicates the first The absolute values ​​of the regression coefficients of each feature;

[0015] Determining the optimal method through cross-validation And retain the subset of key voltage and capacity features with non-zero coefficients; define feature importance indices based on the correlation between feature variance and target variable:

[0016]

[0017] In the formula, Indicates the first The overall importance score of each feature; Indicates the first Variance of features For this feature and the target variable of this feature The correlation coefficient between them; For weighting coefficients, according to Sort the data in descending order and select the first four relevant features to form the final input matrix. ,right Perform standardization and construct multi-channel timing features:

[0018]

[0019] In the formula, This represents the first-order difference, that is, the... The cycle and the first The amount of change between cycles; Indicates data type identifier, , Represents a capacity sequence, Represents a voltage sequence; Representing different data types The value of the cycle; Representing different data types The value of the cycle; It represents the first-order difference, that is, the change in the quantity, in order to capture velocity information; Representing different data types The value of the cycle; Represents the moving average; Indicates a circular index; Indicates the length of the sliding window; For lagging indexes within the window;

[0020] Capacity sequence First-order difference Second-order difference With moving average Align and concatenate the data according to time steps to form a capacity sequence multi-channel input matrix. :

[0021]

[0022] in, Indicates a time step;

[0023] voltage sequence First-order difference Second-order difference With moving average Align and concatenate the data according to time steps to form a multi-channel input matrix for the voltage sequence. :

[0024]

[0025] The two types of time series blocks are concatenated along the channel dimension to obtain a multi-channel input matrix. .

[0026] S3.1 Input serialization and tag alignment;

[0027] The multi-channel input matrix obtained in step S2 As time series samples for the model, each sample consists of continuous... It consists of 1 time step, each time step contains 10 time steps. There are 8 channels, and samples are acquired by sliding along the time axis with a step size of 1. The starting anchor point is denoted as . , terminated The total number of samples is The label represents the remaining lifetime cycle count. Knee point cycle number All samples are stacked in chronological order to form the input tensor samples of the model and their corresponding supervision labels, with the center anchor points of the time-series samples. Align the sequences to obtain the input sequence;

[0028] S3.2 Convolutional Feature Extraction Layer (CNN): The input sequence first passes through a one-dimensional convolutional layer to extract local temporal features. The convolution calculation formula is:

[0029]

[0030] In the formula, This represents a convolution operation along the time dimension; Represents the convolution kernel weight matrix; Represents the bias vector; Represents the input sequence; For non-linear activation functions, ReLU is preferred;

[0031] This layer is used to automatically extract local trend information from capacity decay features. The extraction results are then passed into the recurrent layer after batch normalization and Dropout operations.

[0032] S3.3 Gated Recurrent Unit (GRU) Layer: Convolutional Layer Output Sequence The system is sent to the Gate Control Recurrent Unit (GRU) layer, where the GRU operates at time steps. The state update process is as follows:

[0033]

[0034] In the formula, Indicates at time step The feature vector input to the GRU unit; This is the Sigmoid activation function, and its output value is in the range of 0-1. To update the activation value of the gate, which is used to control the proportion of the state maintained in the previous moment; To reset the activation value of the gate, used to adjust the degree of forgetting of the previous state; Represents a candidate hidden state, indicating a short-term memory update under the combined effect of the current input and the previous hidden state; For time steps The output is hidden; Indicates element-wise product; , , These are the weight matrices corresponding to the inputs; , , These are the weight matrices for the recursive connection of the hidden states; , , These are the bias terms for each gate and candidate state, respectively; The hyperbolic tangent activation function is used to constrain candidate hidden states within a nonlinear region. This structure retains key decay information and suppresses redundant memory through a gating mechanism, thus obtaining the final hidden state. ;

[0035] S3.4 Output Mapping Layer and Joint Prediction: The Final Hidden State of the GRU Output The fully connected layer maps the result to the prediction space, and the calculation formula is as follows:

[0036]

[0037] In the formula, This is the weight matrix. For bias vectors, Use the ReLU activation function; output correspond or ;

[0038] S3.5 Adaptive Hyperparameter Optimization Based on Dung Beetle Optimization (DBO): Before model training, the Dung Beetle Optimization (DBO) algorithm is introduced to adaptively optimize the key hyperparameters of the network structure.

[0039] The set of hyperparameters to be optimized is:

[0040]

[0041] In the formula, This represents the number of convolutional kernels; The kernel time length; This refers to the Dropout ratio; Mini-Batch size; This represents the number of GRU units;

[0042] Hyperparameters are encoded as real-valued vectors in the DBO algorithm. During the iterative update process of the dung beetle optimization algorithm, the position change of an individual in the search space is determined by four behaviors: rolling, obstacle avoidance, boundary correction, and cooperative update. The mathematical expression for its position update is:

[0043]

[0044] In the formula, Indicates the first Individuals at time step The iterative position vector at time, ∈ ; The individual's position at the previous moment; The inertia coefficient; This is the offset coefficient; This represents the displacement increment; For random perturbation angles; Indicates the disturbance term; , These are the lower and upper bounds of the search space, respectively; , These are the upper and lower limits after boundary correction; This represents the current globally optimal individual position. This is a random correction factor; For the position of the partner individual; This is the proportionality coefficient; It is the gravitational factor;

[0045] For the remaining lifetime and knee point of the joint output, the mean squared error (MSE) is used as the training objective:

[0046]

[0047] In the formula, The total number of samples, This represents the true RUL value or knee value. To predict RUL values ​​or knee values;

[0048] The root mean square error (RMSE) of the validation set is used as the fitness function for DBO, defined as:

[0049]

[0050] In the formula, To verify the total number of samples; To verify the true RUL value or knee value in the set; To verify the predicted RUL value or knee value in the set;

[0051] After the DBO hyperparameter search is completed, the hyperparameters are fixed, and then... Update the weights on the training set and on the validation set. Implementing early shutdown and model selection;

[0052] The constructed CNN-GRU hybrid neural network completes the joint prediction of RUL and knee: the data is first passed through one-dimensional convolution to capture local temporal dependencies. The one-dimensional convolution CNN is set with two levels of convolutional blocks, each containing two layers of convolution, batch normalization and ReLU. Then, GRU is used to model long-term dependencies. The number of hidden units is searched by DBO. The tail is mapped to two regression outputs through fully connected layers, which give the cycle number of RUL and the cycle number of knee, respectively.

[0053] S4. Remaining life and knee point prediction, the steps are as follows:

[0054] S4.1 Define the knee point as the inflection point in the capacity-cycle curve where the capacity transitions from a slow decline phase to an accelerated decline phase, corresponding to the location where the rate of capacity change increases significantly. Calculate the capacity curve. The curvature function, represented based on the smooth transition model, is expressed as follows:

[0055]

[0056] In the formula, For the first, second, and third parameters of the smoothing model, ,in, , These represent the local linear slopes before and after the knee point, respectively. For intermediate parameters, The parameter is the turning point center parameter; This is the transition smoothing coefficient; This represents the number of loop iterations. For capacity;

[0057] Based on the local linear slope before and after the knee point, a knee point is obtained by calculating the slope of the angle bisector, as shown in the following expression:

[0058]

[0059] In the formula, The slope of the angle bisector;

[0060] The knee point is determined by calculating the number of iterations at the knee point, as shown in the following expression:

[0061]

[0062] In the formula, Indicates the adjustment parameter; The number of cycles at the knee point;

[0063] S4.2 Model Training and Output: The first 20% of the input sequences from the target battery are used as input. The samples are divided into training and test sets in an 8:2 ratio. The target battery data is included in the test set. A CNN-GRU model with the optimal hyperparameter configuration determined by the DBO algorithm is used for training. The test set is then input into the model to obtain predictions. and .

[0064] S5. Two-stage capacity decay curve modeling based on RUL and knee point;

[0065] Specifically, based on the knee point, the capacity decay curve is divided into a slow decay stage and an accelerated decay stage; before the knee point (slow decay stage), LOESS (locally weighted regression) is used for smooth fitting, and after the knee point (accelerated decay stage), a double exponential function model is used; through iterative optimization, continuous splicing of curves between stages and overall consistent modeling are achieved. The specific steps are as follows:

[0066] S5.1, Perform phase division and data input; according to The number of termination cycles corresponding to the remaining lifespan The battery capacity degradation curve is divided into a slow degradation stage and an accelerated degradation stage; the input data includes capacity sequences. Knee point x and y coordinates and the end points of the cycle (horizontal and vertical) ;

[0067] S5.2. For the slow decline phase before the knee, the Locally Weighted Regression (LOESS) method is used to smoothly fit the volume data. The fitting function is:

[0068]

[0069] In the formula, It is a fitted curve for the slow decline phase; The total number of samples in the locally weighted regression method. Indicates the index of the sample; In the first The capacity value of a local sample point; These are the weighting coefficients. In the sample of the locally weighted regression method, the first... Number of iterations for each local sample point;

[0070] The definition of is:

[0071]

[0072] In the formula, For smoothing bandwidth parameters;

[0073] S5.3, Modeling the Accelerated Decay Phase; In the accelerated decay phase after the knee point, the cycle number and capacity are normalized to unify the scale of different lifetime intervals:

[0074]

[0075]

[0076] In the formula, For normalized cycle number, Normalized capacity; This is the actual number of cycles; This is the actual capacity value;

[0077] Based on the similarity of battery aging mechanisms, transfer learning is introduced: aging knowledge fitted during the slow degradation phase is transferred to the accelerated degradation phase through transfer learning. The transfer mapping relationship is defined as follows:

[0078]

[0079] In the formula, Represents the transfer function; Let be the set of migration parameters, where, This is the capacity amplitude adjustment coefficient. As a time scale factor, This is a horizontal translation term. This is the vertical offset;

[0080] The specific form of the transfer function is:

[0081]

[0082] In the formula, This represents the capacity magnitude adjustment factor of the transfer function; This represents the time scale factor of the transfer function; This represents the horizontal shift term of the transfer function; This represents the vertical offset of the transfer function; Normalized cycle number;

[0083] The migration parameters are determined by minimizing the following formula:

[0084]

[0085] In the formula, This represents the objective function for transfer learning; To accelerate the sample size during the recession phase; Indicates the first Migration prediction capacity for each sample; To accelerate capacity data during the decline phase; Indicates the first Number of iterations for each sample;

[0086] S5.4, Double-Exponential Enhanced Modeling: After transfer learning correction, an improved double-exponential function is used to enhance the fitting of capacity decay in the accelerated decay phase. Its expression is:

[0087]

[0088] In the formula, and These are the amplitude coefficients for the slow and accelerated decay components, respectively. and Parameters for slow and fast decay rates are defined, and boundary constraints are applied; Normalized cyclic number; parameters obtained through transfer learning Used to correct the initial values ​​of the amplitude coefficient and the decay rate parameter;

[0089] S5.5 Curve Fusion and Parameter Optimization; The fitting functions of the first and second stages are concatenated to establish the overall capacity decay prediction function, the expression of which is:

[0090]

[0091] In the formula, This is the transition smoothing coefficient; The number of cycles at the knee point; This represents the fitting function for the slow decay phase. This is the actual number of cycles; This represents the fitting function for the accelerated decline phase;

[0092] By minimizing the objective function: ,in, Indicates the first The overall model prediction value for each sample cycle point. Indicates the first Experimental observations at each sample cycle point; combined with parameter constraints from transfer learning output, to achieve global optimization of the overall curve;

[0093] The DBO optimization algorithm is used to solve the problem and obtain the optimal parameter combination. The optimized full-lifetime capacity prediction function is as follows:

[0094]

[0095] In the formula, This is the transition smoothing coefficient; The number of cycles at the knee point; This represents the optimized fitting function for the slow decay phase. This is the actual number of cycles; This represents the optimized fitting function for the accelerated decay phase.

[0096] S6. Output capacity decay trajectory prediction results;

[0097] Specifically, the overall fitting curve obtained in step S5 Compared with measured capacity data Interpolation in the same number of iterations The Euclidean distance between each sampling point is calculated by comparing the samples at each sampling point. The formula for calculating the distance is as follows:

[0098]

[0099] In the formula, in the formula, Indicates the optimized first... The fit capacity value for each sample; Indicates the first Experimental observations at each sample cycle point; For the first The cycle point of each sample;

[0100] Define the integral form of capacity deviation:

[0101]

[0102] in, This represents the number of cycles to terminate the current lifetime.

[0103] The fitted curve that minimizes the integral of the Euclidean distance and the capacity deviation is selected as the final prediction curve.

[0104] Beneficial effects of the present invention

[0105] This invention achieves joint prediction of RUL and knee point by inputting 20% ​​of the sequence data during the battery's life cycle, and accurately fits the capacity degradation trajectory, significantly improving prediction accuracy.

[0106] By inputting only a small amount of data, this invention can comprehensively reflect the dynamic changes in battery health status, successfully achieving early performance warning and providing important support for the fine management of the entire battery life cycle.

[0107] Experimental results show that the RMSE of this invention is 21.735 in RUL prediction and 24.727 in knee position prediction, which is 15% more accurate than existing prediction methods. The fitting error (IAE) of capacity decay trajectory is 2.62, achieving a good fitting effect. Attached Figure Description

[0108] Figure 1 This is a flowchart of the method of the present invention;

[0109] Figure 2 This is a model structure diagram of the present invention, wherein, Figure 2 (a) is the structural flowchart of the hybrid model. Figure 2 (b) is a schematic diagram of the structure of a convolutional neural network (CNN); Figure 2 (c) is a schematic diagram of the gated loop unit (GRU);

[0110] Figure 3 These are the prediction results and error results of RUL obtained from the implementation of this invention; wherein, Figure 3 (a) is a graph showing the prediction results for RUL. Figure 3 (b) is a graph showing the error and error rate results of RUL;

[0111] Figure 4 These are the prediction results and error results of the knee point obtained from the implementation of this invention; wherein, Figure 4 (a) is a graph showing the predicted knee point. Figure 4 (b) is a graph showing the error and error rate at the knee point;

[0112] Figure 5 These are the knee point prediction and stage division results obtained from the implementation of this invention;

[0113] Figure 6 This is a graph showing the integral result of the absolute error of a single constant current 4.8C test in this invention;

[0114] Figure 7 This is a graph showing the integral result of the absolute error of the second constant current 6C-3C implementation of the present invention;

[0115] Figure 8 This is a graph showing the integral result of the absolute error of the second constant current 6C-3.6C implementation of the present invention. Detailed Implementation

[0116] The present invention will be further described in detail below with reference to specific embodiments.

[0117] like Figure 1 As shown, a two-stage lithium-ion battery capacity degradation trajectory prediction method based on remaining lifetime and knee point includes the following steps:

[0118] S1. Cyclic data acquisition and capacity decay sequence construction;

[0119] Specifically, under constant temperature conditions, multiple charge-discharge tests were conducted on different batteries of the same model until the discharge capacity decayed to 80% of the rated capacity. Different charging strategies were used during the test, including constant current-constant voltage (CC-CV) and multi-stage constant current-constant voltage (C1-C2-CV) modes. When the SOC reached 80%, the multi-stage constant current was cut off, the battery was left to rest for 10 seconds, and the charging state changed from multi-stage constant current charging to constant voltage charging. The charging voltage, number of cycles, and discharge capacity were recorded.

[0120] In this embodiment, the commercial lithium iron phosphate battery cycle life dataset from MIT was used. This dataset was divided into two batches, containing a total of 92 batteries that cycled to the end of their lifespan under different charging conditions. Batteries that experienced experimental accidents or malfunctions were removed, and the remaining 77 batteries were numbered sequentially. The nominal capacity of the batteries was 1.1 Ah, and the upper and lower cutoff voltages were 3.6V and 2.0V, respectively. The ambient temperature was set to a constant 30°C during the experiment. Different charging rates were used for different batteries, with the highest charging rate ranging from 4C to 8C, until the cycle life decreased to 80% of the nominal capacity, i.e., 0.88 Ah.

[0121] S2, Data Preprocessing and Feature Construction;

[0122] Wavelet denoising and smoothing were performed on the voltage and capacity data collected during multiple charge-discharge cycles of lithium-ion batteries to remove abnormal cycle points.

[0123] Voltage characteristics are constructed by extracting voltage characteristic parameters during the charging and discharging phases. And combined with the capacity decay feature matrix This forms the comprehensive input matrix:

[0124]

[0125] Using belt The linear regression model with regularization terms imposes sparse constraints on the importance of features in the comprehensive input matrix, and its optimization objective function is:

[0126]

[0127] In the formula, For the intercept term; This is a vector of regression coefficients; The regularization coefficient is used. The target variable; This represents the total number of battery cycle samples. The index represents the total number of battery cycle samples. The total number of cycle samples for the 77 batteries in this dataset ranges from 532 to 1933. Represents the total number of features. An index representing the total number of features; Indicates the first The first sample of the battery cycle One eigenvalue; Indicates the first The absolute values ​​of the regression coefficients of each feature;

[0128] Determining the optimal method through cross-validation And retain the subset of key voltage and capacity features with non-zero coefficients; define feature importance indices based on the correlation between feature variance and target variable:

[0129]

[0130] In the formula, Indicates the first The overall importance score of each feature; Indicates the first Variance of features For this feature and the target variable of this feature The correlation coefficient between them; For weighting coefficients, according to Sort the data in descending order and select the first four relevant features to form the final input matrix. ,right Perform standardization and construct multi-channel timing features:

[0131]

[0132] In the formula, This represents the first-order difference, that is, the... The cycle and the first The amount of change between cycles; Indicates data type identifier, , Represents a capacity sequence, Represents a voltage sequence; Representing different data types The value of the cycle; Representing different data types The value of the cycle; It represents the first-order difference, that is, the change in the quantity, in order to capture velocity information; Representing different data types The value of the cycle; Represents the moving average; Indicates a circular index; Indicates the length of the sliding window; This is the lag index within the window, with a value range of 0-63;

[0133] Capacity sequence First-order difference Second-order difference With moving average Align and concatenate the data according to time steps to form a capacity sequence multi-channel input matrix. :

[0134]

[0135] in, Indicates a time step;

[0136] voltage sequence First-order difference Second-order difference With moving average Align and concatenate the data according to time steps to form a multi-channel input matrix for the voltage sequence. :

[0137]

[0138] The two types of time series blocks are concatenated along the channel dimension to obtain a multi-channel input matrix. The number of input channels is 8. The size is 8× The constructed multi-channel input matrix is ​​shown in Table 1.

[0139] Table 1: Constructing the multi-channel input matrix

[0140]

[0141] S3. Construction of a joint prediction model for remaining lifetime and knee point based on CNN-GRU, the steps are as follows:

[0142] S3.1 Input serialization and tag alignment;

[0143] The multi-channel input matrix obtained in step S2 As time series samples for the model, each sample consists of continuous... It consists of 1 time step, each time step contains 10 time steps. There are 8 channels, and samples are acquired by sliding along the time axis with a step size of 1. The starting anchor point is denoted as . , terminated The total number of samples is The label represents the remaining lifetime cycle count. Knee point cycle number All samples are stacked in chronological order to form the input tensor samples of the model and their corresponding supervision labels, with the center anchor points of the time-series samples. Align the sequences to obtain the input sequence;

[0144] S3.2 Convolutional Feature Extraction Layer (CNN): The input sequence first passes through a one-dimensional convolutional layer to extract local temporal features. The convolution calculation formula is:

[0145]

[0146] In the formula, This represents a convolution operation along the time dimension; Represents the convolution kernel weight matrix; Represents the bias vector; Represents the input sequence; For non-linear activation functions, ReLU is preferred;

[0147] This layer is used to automatically extract local trend information from capacity decay features. The extraction results are then passed into the recurrent layer after batch normalization and Dropout operations.

[0148] S3.3 Gated Recurrent Unit (GRU) Layer: Convolutional Layer Output Sequence The system is sent to the Gate Control Recurrent Unit (GRU) layer, where the GRU operates at time steps. The state update process is as follows:

[0149]

[0150] In the formula, Indicates at time step The feature vector input to the GRU unit; This is the Sigmoid activation function, and its output value is in the range of 0-1. To update the activation value of the gate, which is used to control the proportion of the state maintained in the previous moment; To reset the activation value of the gate, used to adjust the degree of forgetting of the previous state; Represents a candidate hidden state, indicating a short-term memory update under the combined effect of the current input and the previous hidden state; For time steps The output is hidden; Indicates element-wise product; , , These are the weight matrices corresponding to the inputs; , , These are the weight matrices for the recursive connection of the hidden states; , , These are the bias terms for each gate and candidate state, respectively; The hyperbolic tangent activation function is used to constrain candidate hidden states within a nonlinear region. This structure retains key decay information and suppresses redundant memory through a gating mechanism, thus obtaining the final hidden state. ;

[0151] S3.4 Output Mapping Layer and Joint Prediction: The Final Hidden State of the GRU Output The fully connected layer maps the result to the prediction space, and the calculation formula is as follows:

[0152]

[0153] In the formula, This is the weight matrix. For bias vectors, Use the ReLU activation function; output correspond or ;

[0154] S3.5 Adaptive Hyperparameter Optimization Based on Dung Beetle Optimization (DBO): Before model training, the Dung Beetle Optimization (DBO) algorithm is introduced to adaptively optimize the key hyperparameters of the network structure.

[0155] The set of hyperparameters to be optimized is:

[0156]

[0157] In the formula, This represents the number of convolutional kernels; The kernel time length; This refers to the Dropout ratio; Mini-Batch size; This represents the number of GRU units;

[0158] Hyperparameters are encoded as real-valued vectors in the DBO algorithm. During the iterative update process of the dung beetle optimization algorithm, the position change of an individual in the search space is determined by four behaviors: rolling, obstacle avoidance, boundary correction, and cooperative update. The mathematical expression for its position update is:

[0159]

[0160] In the formula, Indicates the first Individuals at time step The iterative position vector at time, ∈ ; The individual's position at the previous moment; The inertia coefficient; This is the offset coefficient; This represents the displacement increment; For random perturbation angles; Indicates the disturbance term; , These are the lower and upper bounds of the search space, respectively; , These are the upper and lower limits after boundary correction; This represents the current globally optimal individual position. This is a random correction factor; For the position of the partner individual; This is the proportionality coefficient; It is the gravitational factor;

[0161] For the remaining lifetime and knee point of the joint output, the mean squared error (MSE) is used as the training objective:

[0162]

[0163] In the formula, The total number of samples, This represents the true RUL value or knee value. To predict RUL values ​​or knee values;

[0164] The root mean square error (RMSE) of the validation set is used as the fitness function for DBO, defined as:

[0165]

[0166] In the formula, To verify the total number of samples; To verify the true RUL value or knee value in the set; To verify the predicted RUL value or knee value in the set;

[0167] After the DBO hyperparameter search is completed, the hyperparameters are fixed, and then... Update the weights on the training set and on the validation set. Implementing early shutdown and model selection;

[0168] The constructed CNN-GRU hybrid neural network completes the joint prediction of RUL and knee point;

[0169] One-dimensional convolution is used to capture local temporal dependencies. Two-level convolutional blocks are set, each containing two convolutional layers, batch normalization, and ReLU. The time step is 1, and the padding method keeps the sequence length unchanged. The kernel size is searched by DBO, and commonly used values ​​are 3 to 9. The number of channels ranges from 32 to 256. Dropout is applied after the convolutional block to suppress overfitting, with an overall ratio between 0.05 and 0.30. The convolutional branch uses half of the global ratio.

[0170] Long-term dependencies are modeled using GRU, with the number of hidden units searched by DBO, typically ranging from 64 to 256, and the output is taken from the last time step. The tail is mapped to two regression outputs through a fully connected layer, giving the loop number of the RUL and the loop number of the knee point, respectively. The structure and training hyperparameters are uniformly optimized by DBO, with search variables including the number of two-level convolution channels, convolution kernel size, Dropout ratio, batch size, and number of GRU units. The population size is adaptive with the number of available cores, and the iteration is performed for 35 rounds. The fitness is the root mean square error of the validation set. Feasibility constraints are also set for the convolution kernel length, effective sequence length, batch size, and sample size.

[0171] The initial learning rate for final training is between 0.001 and 0.005, decreasing by a factor of 0.6 every 10 cycles, with a maximum of 120 training cycles and a tolerance of 15 cycles for early stopping;

[0172] The training model uses a pre-built training set. The parameters saved after model training include: the kernel weights, bias terms, and batch normalization statistics of the convolutional neural network part; the update gate, reset gate, and weights and biases corresponding to candidate hidden states of the gated recurrent unit part; the fully connected weights and biases of the output head; as well as the mean and variance of feature standardization, the index set of feature selection, and the optimal configuration obtained by hyperparameter search; the hyperparameter configuration includes the number of convolution channels, kernel size, dropout ratio, batch size, and number of recurrent units.

[0173] Furthermore, such as Figure 2 As shown, Figure 2 (a) is a schematic diagram of the hybrid structure, showing that the convolutional branch and the recurrent branch are connected in parallel and then merged into the multi-task regression head; Figure 2 (b) is a schematic diagram of the structure of a convolutional neural network, showing the connection between two levels of convolutional blocks, activation and regularization; Figure 2 (c) is a schematic diagram of the gated loop unit, showing the calculation process and output path of the update gate, reset gate and candidate state;

[0174] The training data consists only of the same battery cell operating data under different rates and different charging and discharging strategies. During the model training process, different battery samples and data from multiple environmental temperature conditions such as low temperature, normal temperature and high temperature can be included at the same time to improve the model's generalization ability in cross-cell and cross-temperature scenarios.

[0175] Furthermore, the training samples are based on the first 20% of the sequences throughout the lifetime as the input ratio, and "to complete joint prediction with a lower data ratio" is the continuous optimization goal, so as to maintain effective representation and output of remaining lifetime, knee point and capacity decay trajectory under the condition of limited availability.

[0176] Furthermore, the training adopts a "training-test" organization method and supports rolling updates. Battery samples can be added or data quality improved at any time or periodically to refresh model parameters. When new battery cells or new operating conditions are introduced, samples are directly added and fine-tuned or retrained to update model parameters.

[0177] S4. Remaining life and knee point prediction, the steps are as follows:

[0178] S4.1 Define the knee point as the inflection point in the capacity-cycle curve where the capacity transitions from a slow decline phase to an accelerated decline phase, corresponding to the location where the rate of capacity change increases significantly. Calculate the capacity curve. The curvature function, represented based on the smooth transition model, is expressed as follows:

[0179]

[0180] In the formula, For the first, second, and third parameters of the smoothing model, ,in, , These represent the local linear slopes before and after the knee point, respectively. For intermediate parameters, The parameter is the turning point center parameter; This is the transition smoothing coefficient, with a value range of 5-30; This represents the number of loop iterations. For capacity;

[0181] Based on the local linear slope before and after the knee point, a knee point is obtained by calculating the slope of the angle bisector, as shown in the following expression:

[0182]

[0183] In the formula, The slope of the angle bisector;

[0184] The knee point is determined by calculating the number of iterations at the knee point, as shown in the following expression:

[0185]

[0186] In the formula, Indicates the adjustment parameter; The number of cycles at the knee point;

[0187] S4.2 Model Training and Output: The first 20% of the input sequences from the target battery are used as input. The samples are divided into training and test sets in an 8:2 ratio. The target battery data is included in the test set. A CNN-GRU model with the optimal hyperparameter configuration determined by the DBO algorithm is used for training. The test set is then input into the model to obtain predictions. and .

[0188] S5. Two-stage capacity decay curve modeling based on RUL and knee point;

[0189] Specifically, based on the knee point, the capacity decay curve is divided into a slow decay stage and an accelerated decay stage; before the knee point (slow decay stage), LOESS (locally weighted regression) is used for smooth fitting, and after the knee point (accelerated decay stage), a double exponential function model is used; through iterative optimization, continuous splicing of curves between stages and overall consistent modeling are achieved. The specific steps are as follows:

[0190] S5.1, Perform phase division and data input; according to The number of termination cycles corresponding to the remaining lifespan The battery capacity degradation curve is divided into a slow degradation stage and an accelerated degradation stage; the input data includes capacity sequences. Knee point x and y coordinates and the end points of the cycle (horizontal and vertical) ;

[0191] S5.2. For the slow decline phase before the knee, the Locally Weighted Regression (LOESS) method is used to smoothly fit the volume data. The fitting function is:

[0192]

[0193] In the formula, It is a fitted curve for the slow decline phase; The total number of samples in the locally weighted regression method. Indicates the index of the sample; In the first The capacity value of a local sample point; These are the weighting coefficients. In the sample of the locally weighted regression method, the first... Number of iterations for each local sample point;

[0194] The definition of is:

[0195]

[0196] In the formula, For smoothing bandwidth parameters;

[0197] S5.3, Modeling the Accelerated Decay Phase; In the accelerated decay phase after the knee point, the cycle number and capacity are normalized to unify the scale of different lifetime intervals:

[0198]

[0199]

[0200] In the formula, For normalized cycle number, Normalized capacity; This is the actual number of cycles; This is the actual capacity value;

[0201] Based on the similarity of battery aging mechanisms, transfer learning is introduced: aging knowledge fitted during the slow degradation phase is transferred to the accelerated degradation phase through transfer learning. The transfer mapping relationship is defined as follows:

[0202]

[0203] In the formula, Represents the transfer function; Let be the set of migration parameters, where, This is the capacity amplitude adjustment coefficient. As a time scale factor, This is a horizontal translation term. This is the vertical offset;

[0204] The specific form of the transfer function is:

[0205]

[0206] In the formula, This represents the capacity magnitude adjustment factor of the transfer function; This represents the time scale factor of the transfer function; This represents the horizontal shift term of the transfer function; This represents the vertical offset of the transfer function; Normalized cycle number;

[0207] The migration parameters are determined by minimizing the following formula:

[0208]

[0209] In the formula, This represents the objective function for transfer learning; To accelerate the sample size during the recession phase; Indicates the first Migration prediction capacity for each sample; To accelerate capacity data during the decline phase; Indicates the first Number of iterations for each sample;

[0210] S5.4, Double-Exponential Enhanced Modeling: After transfer learning correction, an improved double-exponential function is used to enhance the fitting of capacity decay in the accelerated decay phase. Its expression is:

[0211]

[0212] In the formula, and These are the amplitude coefficients for the slow and accelerated decay components, respectively. and Parameters for slow and fast decay rates are defined, and boundary constraints are applied; Normalized cyclic number; parameters obtained through transfer learning Used to correct the initial values ​​of the amplitude coefficient and the decay rate parameter;

[0213] S5.5 Curve Fusion and Parameter Optimization; The fitting functions of the first and second stages are concatenated to establish the overall capacity decay prediction function, the expression of which is:

[0214]

[0215] In the formula, This is the transition smoothing coefficient; The number of cycles at the knee point; This represents the fitting function for the slow decay phase. This is the actual number of cycles; This represents the fitting function for the accelerated decline phase;

[0216] By minimizing the objective function: ,in, Indicates the first The overall model prediction value for each sample cycle point. Indicates the first Experimental observations at each sample cycle point; combined with parameter constraints from transfer learning output, to achieve global optimization of the overall curve;

[0217] The DBO optimization algorithm is used to solve the problem and obtain the optimal parameter combination. The optimized full-lifetime capacity prediction function is as follows:

[0218]

[0219] In the formula, This is the transition smoothing coefficient; The number of cycles at the knee point; This represents the optimized fitting function for the slow decay phase. This is the actual number of cycles; This represents the optimized fitting function for the accelerated decay phase.

[0220] S6. Output capacity decay trajectory prediction results;

[0221] Specifically, the overall fitting curve obtained in step S5 Compared with measured capacity data Interpolation in the same number of iterations The Euclidean distance between each sampling point is calculated by comparing the samples at each sampling point. The formula for calculating the distance is as follows:

[0222]

[0223] In the formula, in the formula, Indicates the optimized first... The fit capacity value for each sample; Indicates the first Experimental observations at each sample cycle point; For the first The cycle point of each sample;

[0224] Define the integral form of capacity deviation:

[0225]

[0226] in, This represents the number of cycles to terminate the current lifetime.

[0227] The fitted curve that minimizes the integral of the Euclidean distance and the capacity deviation is selected as the final prediction curve.

[0228] The RUL and knee prediction results obtained in this embodiment are as follows: Figure 3 and Figure 4 As shown, from Figure 3 As shown in (a), the RMSE predicted by RUL is 22.104 cycles, from Figure 3 As shown in (b), the MAE is 20.142 cycles, the maximum error is 39 cycles, and the mean absolute error rate is 2.31%. Figure 4 It can be seen that, from Figure 4 As shown in (a), the RMSE for knee prediction is 22.984 cycles. Figure 4 As shown in (b), the MAE is 19.169 cycles, the maximum error is 45 cycles, and the average absolute error rate is 3.5%. Under the condition of using the first 20% of the data in the whole life, the model can maintain high accuracy and stability for both RUL and knee point.

[0229] The knee prediction and stage division results obtained in this embodiment are as follows: Figure 5 As shown in the figure, the capacity decay curve changes from slow decay to accelerated decay at the knee point. The intersection of the angle bisector and the fitted curve is the knee point. Based on this, the trajectory is divided into a slow decay stage before the knee point and an accelerated decay stage after the knee point.

[0230] The capacity decay trajectory prediction result obtained in this embodiment is as follows: Figure 6 , Figure 7 and Figure 8 As shown, by Figure 6 It can be seen that this corresponds to a constant current (4.8C) charging mode, and the integral of absolute error (IAE) is 1.508822; Figure 7 This corresponds to the secondary constant current (6C-3C) charging mode, with an IAE of 2.615846; Figure 8 The corresponding charging mode is constant current (6C-3.6C), with an IAE of 1.827746; this proves that the capacity degradation trajectory prediction method proposed in this invention still has high accuracy under different charging conditions.

[0231] It should be noted that the above are merely preferred embodiments of this application and do not limit the scope of patent protection of this application. Any equivalent structural or procedural changes made using the content of this application's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the scope of patent protection of this application.

Claims

1. A two-stage lithium-ion battery capacity degradation trajectory prediction method based on remaining lifetime and knee point, characterized in that, Includes the following steps: S1. Cyclic data acquisition and capacity decay sequence construction; Under constant temperature conditions, multiple charge-discharge tests were conducted on different batteries of the same model until the discharge capacity decayed to 80% of the rated capacity. Different charging strategies were used during the test, including constant current-constant voltage and multi-stage constant current-constant voltage modes. When the SOC reached 80%, the multi-stage constant current was cut off, the battery was left to stand for 10 seconds, and the charging state was set to constant voltage charging. The charging voltage, number of cycles, and discharge capacity were recorded. S2. Perform data preprocessing on the data obtained in S1 and construct features to obtain a multi-channel input matrix; S3. Based on the multi-channel input matrix, construct a joint prediction model for the remaining lifetime and knee point of CNN-GRU; In the CNN-GRU remaining lifetime and knee joint prediction model, hyperparameter adaptive optimization is performed through the Dung Beetle Optimization (DBO) algorithm. S4. Perform Remaining Life (RUL) and Knee Point Prediction; S4 operations include: S4.1 Define the knee point as the inflection point in the capacity-cycle curve where the capacity transitions from a slow decline phase to an accelerated decline phase, corresponding to the location where the rate of capacity change increases significantly. Calculate the capacity curve. The curvature function, represented based on the smooth transition model, is expressed as follows: ； In the formula, For the first, second, and third parameters of the smoothing model, ,in, , These represent the local linear slopes before and after the knee point, respectively. For intermediate parameters, The parameter is the turning point center parameter; This is the transition smoothing coefficient; This represents the number of loop iterations. Based on the local linear slope before and after the knee point, a knee point is obtained by calculating the slope of the angle bisector, as shown in the following expression: ； In the formula, The slope of the angle bisector; The knee point is determined by calculating the number of iterations at the knee point, as shown in the following expression: ； In the formula, Indicates the adjustment parameter; The number of cycles at the knee point; S4.2 Model Training and Output: The first 20% of the input sequences from the target battery are used as input. The samples are divided into training and test sets in an 8:2 ratio. The target battery data is included in the test set. A CNN-GRU model with the optimal hyperparameter configuration determined by the DBO algorithm is used for training. The test set is then input into the model to obtain predictions. and ; S5. Modeling a two-stage capacity decay curve based on remaining lifetime RUL and knee point; The two-stage capacity decay curve modeling includes: before the knee point, a local weighted regression LOESS smoothing fit is used, and after the knee point, a double exponential function model is used. S6. Output capacity decay trajectory prediction results; The fitted curve that minimizes the integral of the Euclidean distance and the capacity deviation is selected as the final prediction curve.

2. The method for predicting the capacity degradation trajectory of a two-stage lithium-ion battery based on remaining lifetime and knee point as described in claim 1, characterized in that: The operations of S2 include: Wavelet denoising and smoothing were performed on the voltage and capacity data collected during multiple charge-discharge cycles of lithium-ion batteries to remove abnormal cycle points. Voltage characteristics are constructed by extracting voltage characteristic parameters during the charging and discharging phases. And combined with the capacity decay feature matrix This forms the comprehensive input matrix: ； Using belt The linear regression model with regularization terms imposes sparse constraints on the importance of features in the comprehensive input matrix, and its optimization objective function is: ； In the formula, For the intercept term; This is a vector of regression coefficients; The regularization coefficient is used. The target variable; This represents the total number of battery cycle samples. An index representing the total number of battery cycle samples; Represents the total number of features. An index representing the total number of features; Indicates the first The first sample of the battery cycle One eigenvalue; Indicates the first The absolute values ​​of the regression coefficients of each feature; Determining the optimal method through cross-validation And retain the subset of key voltage and capacity features with non-zero coefficients; define feature importance indices based on the correlation between feature variance and target variable: ； In the formula, Indicates the first The overall importance score of each feature; Indicates the first Variance of features For this feature and the target variable of this feature The correlation coefficient between them; For weighting coefficients, according to Sort the data in descending order and select the first four relevant features to form the final input matrix. ,right Perform standardization and construct multi-channel timing features: ； In the formula, This represents the first-order difference, that is, the... The cycle and the first The amount of change between cycles; Indicates data type identifier, , Represents a capacity sequence, Represents a voltage sequence; Representing different data types The value of the cycle; Representing different data types The value of the cycle; It represents the first-order difference, that is, the change in the quantity, in order to capture velocity information; Representing different data types The value of the cycle; Represents the moving average; Indicates a circular index; Indicates the length of the sliding window; For lagging indexes within the window; Capacity sequence First-order difference Second-order difference With moving average Align and concatenate according to time steps to form a capacity sequence multichannel input matrix. : ； in, Indicates a time step; voltage sequence First-order difference Second-order difference With moving average Align and concatenate the data according to time steps to form a multi-channel input matrix for the voltage sequence. : ； The two types of time series blocks are concatenated along the channel dimension to obtain a multi-channel input matrix. .

3. The method for predicting the capacity degradation trajectory of a two-stage lithium-ion battery based on remaining lifetime and knee point as described in claim 1, characterized in that: S3 operations include: S3.1 Input serialization and tag alignment; The multi-channel input matrix obtained in step S2 As time series samples for the model, each sample consists of continuous... It consists of 1 time step, each time step contains 10 time steps. There are 8 channels, and samples are acquired by sliding along the time axis with a step size of 1. The starting anchor point is denoted as . , terminated The total number of samples is The label represents the remaining lifetime cycle count. Knee point cycle number All samples are stacked in chronological order to form the input tensor samples of the model and their corresponding supervision labels, with the center anchor points of the time-series samples. Align the sequences to obtain the input sequence; S3.2 Convolutional Feature Extraction Layer (CNN): The input sequence first passes through a one-dimensional convolutional layer to extract temporal local features. The convolution calculation formula is: ； In the formula, This represents a convolution operation along the time dimension; Represents the convolution kernel weight matrix; Represents the bias vector; Represents the input sequence; ReLU is a non-linear activation function. This layer is used to automatically extract local trend information from capacity decay features. The extraction results are then passed into the recurrent layer after batch normalization and Dropout operations. S3.3 Gated Recurrent Unit (GRU) Layer: Convolutional Layer Output Sequence It is sent to the GRU layer of the gate control loop unit, and the GRU is in time step The state update process is as follows: ； In the formula, Indicates at time step The feature vector input to the GRU unit; Use the Sigmoid activation function; To update the activation value of the gate; To reset the door's activation value; Indicates the candidate hidden state; For time step The output is hidden; Indicates element-wise product; , , These are the weight matrices corresponding to the inputs; , , These are the weight matrices for the recursive connection of the hidden states; , , These are the bias terms for each gate and candidate state, respectively; It is the hyperbolic tangent activation function; S3.4 Output Mapping Layer and Joint Prediction: The Final Hidden State of the GRU Output The fully connected layer maps the result to the prediction space, and the calculation formula is as follows: ； In the formula, This is the weight matrix. For bias vectors, Use the ReLU activation function; output correspond or ; S3.5 Adaptive Hyperparameter Optimization Based on Dung Beetle Optimization Algorithm (DBO): Before model training, the dung beetle optimization algorithm is introduced to adaptively optimize the key hyperparameters of the network structure. The set of hyperparameters to be optimized is: ； In the formula, This represents the number of convolutional kernels; The kernel time length; This refers to the Dropout ratio; Mini-Batch size; This represents the number of GRU units; For the remaining lifetime and knee point of the joint output, the mean squared error (MSE) is used as the training target: ； In the formula, The total number of samples, This represents the true RUL value or knee value. To predict RUL values ​​or knee values; The root mean square error (RMSE) of the validation set is used as the fitness function for DBO, defined as: ； In the formula, To verify the total number of samples; To verify the true RUL value or knee value in the set; To verify the predicted RUL or knee value, the hyperparameters are fixed after the DBO hyperparameter search is completed, and then... Update the weights on the training set and on the validation set. Implement early shutdown and model selection.

4. The method for predicting the capacity degradation trajectory of a two-stage lithium-ion battery based on remaining lifetime and knee point as described in claim 1, characterized in that: S5 operations include: S5.1, Perform phase division and data input; according to The number of termination cycles corresponding to the remaining lifespan The battery capacity degradation curve is divided into a slow degradation stage and an accelerated degradation stage; the input data includes capacity sequences. Knee point x and y coordinates and the end points of the cycle (horizontal and vertical) ; S5.

2. For the slow decline phase before the knee, the LOESS method of local weighted regression is used to smoothly fit the volume data. The fitting function is: ； In the formula, It is a fitted curve for the slow decline phase; The total number of samples in the locally weighted regression method. Indicates the index of the sample; In the first The capacity value of a local sample point; These are the weighting coefficients. In the sample of the locally weighted regression method, the first... Number of iterations for each local sample point; S5.3, Modeling the Accelerated Decay Phase; In the accelerated decay phase after the knee point, the cycle number and capacity are normalized to unify the scale of different lifetime intervals: ； ； In the formula, For normalized cycle number, Normalized capacity; This is the actual number of cycles; This is the actual capacity value; Transfer learning is introduced based on the similarity of battery aging mechanisms: The specific form of the transfer function is: ； In the formula, This represents the capacity magnitude adjustment factor of the transfer function; The time scale factor representing the transfer function; This represents the horizontal shift term of the transfer function; This represents the vertical offset of the transfer function; Normalized cycle number; The migration parameters are determined by minimizing the following formula: ； In the formula, This represents the objective function for transfer learning; To accelerate the sample size during the recession phase; Indicates the first Migration prediction capacity for each sample; To accelerate capacity data during the decline phase; Indicates the first Number of iterations for each sample; S5.4, Double-Exponential Enhanced Modeling: After transfer learning correction, an improved double-exponential function is used to enhance the fitting of capacity decay in the accelerated decay phase. Its expression is: ； In the formula, and These are the amplitude coefficients for the slow and accelerated decay components, respectively. and Parameters for slow and accelerated decay rates; Normalized cyclic number; parameters obtained through transfer learning Used to correct the initial values ​​of the amplitude coefficient and the decay rate parameter; S5.5 Curve Fusion and Parameter Optimization; The fitting functions of the first and second stages are concatenated to establish the overall capacity decay prediction function, the expression of which is: ； In the formula, This is the transition smoothing coefficient; The number of cycles at the knee point; This represents the fitting function for the slow decay phase. This is the actual number of cycles; This represents the fitting function for the accelerated decline phase; By minimizing the objective function: ,in, Indicates the first The overall model prediction value for each sample cycle point. Indicates the first Experimental observations at each sample cycle point; combined with parameter constraints from transfer learning output, to achieve global optimization of the overall curve; The DBO optimization algorithm is used to solve the problem and obtain the optimal parameter combination. The optimized full-lifetime capacity prediction function is as follows: ； In the formula, This is the transition smoothing coefficient; The number of cycles at the knee point; This represents the optimized fitting function for the slow decay phase. This is the actual number of cycles; This represents the optimized fitting function for the accelerated decay phase.

5. The method for predicting the capacity degradation trajectory of a two-stage lithium-ion battery based on remaining lifetime and knee point as described in claim 1, characterized in that: The calculation methods for Euclidean distance and capacity deviation integrals in S6 are as follows: The overall fitting curve obtained in step S5 Compared with measured capacity data Interpolation in the same number of iterations The Euclidean distance between each sampling point is calculated by comparing the samples at each sampling point. The formula for calculating the distance is as follows: ； In the formula, in the formula, Indicates the optimized first... The fit capacity value for each sample; Indicates the first Experimental observations at each sample cycle point; For the first The cycle point of each sample; Define the integral form of capacity deviation: ； in, This represents the number of termination cycles corresponding to the remaining lifespan.

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