A Lithium-Ion Battery SOH Estimation Method Based on Impedance Feature Selection and Optimized Support Vector Regression

Abstract

The present invention relates to the technical field of power batteries, and discloses a method for estimating the state of health (SOH) of lithium-ion batteries based on impedance feature selection and optimized support vector regression. First, data collection, data processing and feature extraction, support vector regression model construction, sparrow search algorithm model hyperparameter optimization, and chaos mapping theory optimization of the optimization process are carried out. Finally, the SOH of single cells is calculated. This method, based on electrochemical impedance spectroscopy data, uses a sequential forward search strategy and combines a multi-objective decision-making method to realize the selection of impedance features, and applies the chaotic sparrow search algorithm to the hyperparameter optimization of the support vector regression model to construct an SOH estimation model for single cells. It can effectively track the degradation trajectory of the SOH of lithium-ion batteries, and uses a feature optimization method to greatly reduce the number of features, eliminate the interference of irrelevant features, reduce the EIS feature test time, and establish an optimized support vector regression model to achieve accurate estimation of the battery SOH.

Description

Technical Field

[0001] The present invention relates to the technical field of power batteries, and particularly to a method for estimating the state of health (SOH) of lithium-ion batteries based on impedance feature selection and optimized support vector regression. Background Art

[0002] Lithium batteries have the advantages of long life, fast charging speed, no memory effect, etc., and have now become the first choice for energy storage in pure electric vehicles and hybrid electric vehicles. However, with the increase in the number of charge and discharge cycles, the performance of lithium batteries will gradually decline, mainly manifested as an increase in internal resistance and a decrease in available capacity. Therefore, accurately estimating its state of health (SOH) during battery use is crucial for ensuring the efficient operation and safety of the battery.

[0003] Electrochemical impedance spectroscopy contains rich information about material properties, interfacial phenomena, and electrochemical reactions inside the battery, and reflects the aging state of the battery from multiple angles. It is considered an effective means to accurately estimate the SOH. Data-driven estimation methods do not require the construction of complex battery models and can autonomously learn the non-linear relationship between the battery SOH and external characteristics through measured data such as the real part of impedance, the imaginary part of impedance, and phase angle, with high transferability, robustness, and generalization. However, directly using the full-frequency EIS data as input increases the training difficulty of the model, and the presence of irrelevant features will reduce the accuracy of the model. In addition, conducting full-band EIS measurements requires a large amount of time, making practical applications difficult. Therefore, how to optimally select a feature subset closely related to the battery SOH from the full-band EIS data, significantly reduce the feature measurement time, improve the prediction accuracy of the power battery SOH, and achieve accurate prediction of the SOH of different batteries is an urgent problem to be solved. Summary of the Invention

[0004] (1) Technical Problems to be Solved

[0005] Aiming at the deficiencies of the prior art, the present invention provides a method for estimating the state of health (SOH) of lithium-ion batteries based on impedance feature selection and optimized support vector regression, which has the advantages of accurate estimation of the battery SOH, etc., and solves the above technical problems.

[0006] (2) Technical Solutions

[0007] To achieve the above object, the present invention provides the following technical solution: A method for estimating the state of health (SOH) of lithium-ion batteries based on impedance feature selection and optimized support vector regression, comprising the following steps:

[0008] S1. Data acquisition: Conduct aging impedance experiments on different lithium-ion batteries under different temperature conditions until the discharge capacity of the battery is lower than 70% of the initial capacity. Record the charge-discharge and electrochemical impedance spectroscopy data in real time, including charge-discharge cycle data and impedance under different aging states.

[0009] S2. Data processing and feature extraction: Preprocess the charge-discharge data and electrochemical impedance spectroscopy data obtained in step S1; analyze the relationship between electrochemical impedance and battery aging, select impedance features based on the sequential forward search algorithm, and optimize the feature subset obtained by sequential forward search using the multi-objective decision-making method to obtain impedance features and SOH data.

[0010] S3. Based on the radial basis kernel function, select the penalty coefficient, insensitive loss function parameter, and kernel function parameter to construct a support vector regression model.

[0011] S4. Sparrow search algorithm model hyperparameter optimization: Apply the sparrow search algorithm to the hyperparameter optimization of the support vector regression model to optimize the support vector regression model.

[0012] S5. Use the chaos of the Sine chaotic map to replace the random initialization process of the initial value of the sparrow algorithm, and based on the dataset obtained in step S2, train the optimized support vector regression model to obtain the trained Sine-SSA-SVR model.

[0013] S6. Estimation of the SOH of a single battery: Based on the Sine-SSA-SVR model obtained in step S5, input the impedance features to estimate the SOH of the lithium-ion battery.

[0014] As a preferred technical solution of the present invention, the process of charging and discharging the battery in the data collection of step S1 is as follows: In the charging stage, first charge at a constant current of 1C to the cut-off voltage of 4.2V, then charge at a constant voltage to 0.1C, and finally stand for 15 minutes. In the discharging stage, discharge at a constant current of 2C to the lower cut-off voltage of 3V, and then stand for 15 minutes.

[0015] As a preferred technical solution of the present invention, the specific expression of the support vector regression model in step S3 is as follows:

[0016]

[0017] Among them, ω and b respectively represent the weight vector and bias term of the support vector regression model, x represents the input variable, is the prediction output function corresponding to the input x, and by introducing Lagrange multipliers, the above formula can be transformed into a convex quadratic optimization problem, where the dual function and constraint conditions are:

[0018]

[0019] Among them, is the optimization objective function of SVR, ||ω|| 2 is the regularization term, n represents the number of training sample sets, c represents the penalty parameter, ξ j and respectively represent two different relaxation factors, s.t. represents the constraint, x j represents the input feature vector of the j-th sample, y j the true target value of the j-th sample, and the training data set is ε represents the insensitive loss function, and solving the above formula gives the following expression:

[0020]

[0021] Among them, nsv is the number of support vectors, K(x j , x) represents the kernel function, which is used to calculate the inner product between the support vector x j and the current input vector x, α j , are the Lagrange multipliers corresponding to the j-th sample, and the specific expressions are as follows:

[0022]

[0023] Among them, exp(*) represents the exponential function with the natural constant e as the base, g represents the radial basis kernel function parameter, ||x - x j || 2 is the square of the Euclidean distance between the input vector x and the support vector x j .

[0024] As a preferred technical solution of the present invention, the hyperparameter optimization of the sparrow search algorithm model in step S4 is carried out through the following expressions, specifically:

[0025] Position update of the discoverer:

[0026]

[0027] Position update of the joiner:

[0028]

[0029] Position update of the vigilant:

[0030]

[0031] Among them, i represents the index of the current individual, that is, the i-th group of SVR parameters, d represents the dimension of the SVR parameters, respectively represent the position of the \(i\)-th (discoverer, joiner, or sentinel) in the \(d\)-th dimension at time \(t + 1\). represents the position of the \(i\)-th (discoverer, joiner, or sentinel) in the \(d\)-th dimension at time \(t\). \(\alpha\) is a positive constant used to control the step size and the rate of exponential decay in position update. \(\exp(*)\) represents the exponential function with the base of the natural constant \(e\). \(itermax\) represents the maximum number of iterations. \(Q\) is a random number following a normal distribution \(Q\sim N(0, 1)\). \(L\) is a random number with a Laplace distribution used to simulate the raiding behavior of the discoverer. \(R\) 2 is a random number following a uniform distribution \(R\) 2 \(\sim U(0, 1)\). \(ST\) represents the warning value. represents the position of the worst individual in the \(d\)-th dimension in the \(t\)-th generation of the population. \(m\) represents the population size, which is the number of individuals participating in the optimization process. represents the position of the randomly selected \(p\)-th individual in the \(d\)-th dimension at time \(t + 1\). represents the distance between the current individual and the randomly selected individual in the \(d\)-th dimension. \(A\) is a random number following a uniform distribution \(A\sim U(-1, 1)\). \(l\) is a constant used to control the step size. is the position of the best individual in the current population. represents the distance between the sentinel and the best individual. represents the distance between the sentinel and the worst individual. \(\beta\) is a random number following a uniform distribution \(\beta\sim U(0, 1)\). \(K\) is a random number following a normal distribution \(K\sim N(0, 1)\). \(\delta\) is a very small value used to prevent the denominator from being zero. \(f\) i represents the fitness value of the \(i\)-th individual. \(f\) g and \(f\) w respectively represent the fitness values of the global best and the worst individuals.

[0032] Compared with the prior art, the present invention provides a method for estimating the state of health (SOH) of a lithium-ion battery based on impedance feature selection and optimized support vector regression, having the following beneficial effects:

[0033] Based on electrochemical impedance spectroscopy (EIS) data, the present invention uses a sequential forward search strategy and combines a multi-objective decision-making method to select impedance features, and applies the chaotic sparrow search algorithm to optimize the hyperparameters of the support vector regression model, thereby constructing a single-cell SOH estimation model. This model can effectively track the degradation trajectory of the SOH of a lithium-ion battery. Based on full-frequency EIS data, a feature optimization method is adopted to significantly reduce the number of features, eliminate the interference of irrelevant features, reduce the EIS feature test time, and establish an optimized support vector regression model to accurately estimate the SOH of the battery. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 Schematic diagram of the process of the present invention;

[0035] Figure 2 Diagram showing the relationship between different SOHs and electrochemical impedance spectra;

[0036] Figure 3 Diagram of the optimal result of the SFS - MOOA feature subset;

[0037] Figure 4 Diagram showing the estimated results and errors of the same battery by different methods;

[0038] Figure 5 Diagram comparing the results and errors of different batteries at different temperatures. Specific implementation manner

[0039] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0040] Please refer to Figures 1 - 5 , a method for estimating the SOH of a lithium - ion battery based on impedance feature selection and optimized support vector regression, comprising the following steps:

[0041] S1. Data acquisition: Aging impedance experiments are carried out at 25°C, 35°C, and 45°C respectively. The experiment follows the same charge - discharge process, and each cycle includes two parts: charging and discharging. In the charging stage, first, constant - current charging is carried out at a rate of 1C until the cut - off voltage of 4.2V, then constant - voltage charging is carried out until 0.1C, and finally, it is left standing for 15 minutes. In the discharging stage, constant - current discharging is carried out at a rate of 2C until the lower cut - off voltage of 3V, and then it is left standing for 15 minutes. Electrochemical impedance spectroscopy tests and capacity tests are carried out on even - numbered charge - discharge cycles. And the battery impedance spectrum is measured when the battery is full and left standing for 15 minutes. In the frequency range from 0.02Hz to 20KHz, a total of 60 frequencies are selected, and the amplitude of the excitation current is 5mA. When the battery capacity decays to 70% of the initial capacity, the aging experiment is terminated;

[0042] S2. Data processing and feature extraction: The charge - discharge data and electrochemical impedance spectrum data obtained in step S1 are pre - processed. The electrochemical impedance spectra under different SOHs are as Figure 2As shown, as the battery SOH decreases, the overall EIS curve in the high-frequency region moves to the right. There are two arcs in the mid-high and mid-low frequency regions, and as the battery SOH decreases, they show an expanding trend. As the battery undergoes cyclic aging, the oxide deposition on the electrode surface becomes thicker, resulting in a decrease in the rate of the electrochemical reaction. At the same time, lithium deposition occurs at the negative electrode, causing the real and imaginary parts of the impedance in the low-frequency region to generally increase. By analyzing the EIS curve of the battery, it can be found that it contains rich information about battery aging. Based on the battery test data, the impedance at 60 frequencies measured in each cycle is split into the real part and the imaginary part of the impedance, obtaining 120 impedance features. Considering the influence of model accuracy and the number of features on the model, with the lowest comprehensive score as the optimization goal, the sequential forward search algorithm (SFS) is applied to select impedance features, and the feature subset obtained by SFS search is optimized based on the multi-objective decision-making method to obtain impedance features and SOH data. The feature optimization process is as Figure 3 shown;

[0043] S3. Based on the radial basis kernel function, select the penalty coefficient, the parameter of the insensitive loss function, and the parameter of the kernel function to construct a support vector regression model (SVR model);

[0044] The specific expression of the support vector regression model is as follows:

[0045]

[0046] where ω and b represent the weight vector and the bias term of the support vector regression model respectively, and x represents the input variable, is the prediction output function corresponding to the input x, and by introducing the Lagrange multiplier, the above formula can be transformed into solving a convex quadratic optimization problem, where the dual function and the constraint conditions are:

[0047]

[0048]

[0049] where, is the optimization objective function of SVR, ||ω|| 2 is the regularization term, n represents the number of the training sample set, c represents the penalty parameter, ξ j and represent two different relaxation factors respectively, s.t. represents the constraint, x j represents the input feature vector of the j-th sample, y j is the true target value of the j-th sample, and the training data set is ε represents the insensitive loss function, and solving the above formula gives the following expression:

[0050]

[0051] Among them, nsv is the number of support vectors, and K(x j , x) represents the kernel function, which is used to calculate the inner product between the support vector x j and the current input vector x, and α j , is the Lagrange multiplier corresponding to the j-th sample, and the specific expression is as follows:

[0052]

[0053] Among them, exp(*) represents the exponential function with the natural constant e as the base, g represents the radial basis kernel function parameter, and ||x - x j || 2 is the square of the Euclidean distance between the input vector x and the support vector x j .

[0054] S4. Hyperparameter optimization of the sparrow search algorithm model: Apply the sparrow search algorithm to the hyperparameter optimization of the support vector regression model to optimize the support vector regression model;

[0055] Hyperparameter optimization of the sparrow search algorithm model: To solve the problems of long time and poor effect in the optimization of SVR hyperparameters c, ε, and g, the SSA method is selected to optimize the hyperparameter optimization process of SVR, and improve the optimization speed and accuracy of hyperparameters c, ε, and g. First, generate a random hyperparameter combination, calculate the fitness value on the validation set using the SVR model and the initial hyperparameter combination, and adjust the hyperparameter combination of the sparrow individuals according to the update rules of SSA. Through iterative optimization, repeatedly calculate the fitness and position update until the convergence condition is met. Finally, select the hyperparameter combination with the optimal fitness to train the SVR model to obtain the final SSA-SVR model, thereby improving the prediction performance of the model.

[0056] The hyperparameter optimization process of the sparrow search algorithm can be specifically abstracted into a discoverer-joiner model and a detection and early warning mechanism is added;

[0057] Position update of the discoverer:

[0058]

[0059] Position update of the joiner:

[0060]

[0061] Position update of the vigilant:

[0062]

[0063] Among them, i represents the index of the current individual, that is, the i-th group of SVR parameters, and d represents the dimension of the SVR parameters. They respectively represent the position of the i-th (discoverer, joiner, vigilant) in the d-th dimension at the (t + 1)-th moment. represents the position of the i-th (discoverer, joiner, vigilant) in the d-th dimension at the t-th moment. α is a positive constant used to control the step size and the rate of exponential decay in position update. exp(*) represents the exponential function with the natural constant e as the base, and iter max represents the maximum number of iterations. Q is a random number following a normal distribution Q ∼ N(0, 1). L is a random number with a Laplace distribution, used to simulate the raiding behavior of the discoverer, and R 2 is a random number following a uniform distribution R 2 ∼ U(0, 1). ST represents the early warning value. represents the position of the worst individual in the d-th dimension in the t-th generation population. m represents the population size, that is, the number of individuals participating in the optimization process. represents the position of the p-th randomly selected individual in the d-th dimension at the (t + 1)-th generation. represents the distance between the current individual and the randomly selected individual in the d-th dimension. A is a random number following a uniform distribution A ∼ U(-1, 1). l is a constant used to control the step size. is the position of the best individual in the current population. represents the distance between the vigilant and the best individual. represents the distance between the vigilant and the worst individual. β is a random number following a uniform distribution β ∼ U(0, 1). K is a random number following a normal distribution K ∼ N(0, 1). δ is a very small value used to prevent the denominator from being 0, and f i represents the fitness value of the i-th individual, and f g and f w respectively represent the fitness values of the global best and worst individuals.

[0064] S5. Use the chaos of the Sine chaotic map to replace the random initialization process of the initial value of the sparrow algorithm, and based on the dataset obtained in step S2, train the optimized support vector regression model to obtain the trained Sine-SSA-SVR model.

[0065] S6. Estimation of the SOH of a single battery: Based on the optimized Sine-SSA-SVR model obtained in step S5, extract all the health characteristics and SOH of a certain battery obtained from the impedance test after cyclic charge and discharge in step S2 as the model training set. After repeating steps S3 - S5, input the health characteristics of other batteries into the optimized model, and the estimation of the SOH of lithium-ion batteries can be realized.

[0066] The performance of the proposed method is evaluated using R-squared (R 2 2 ), maximum absolute error (MAE), average absolute error (AAE), and root mean square error (RMSE), and the calculation formulas are as follows:

[0067]

[0068] As Figure 4 shown, the SOH estimation results of different data-driven methods are compared and analyzed, and the comparison results are shown in Table 1. In addition, it can be seen from the figure that the trained Sine-SSA-SVR model can accurately estimate the SOH of the battery during its entire life cycle, and the predicted values can be well distributed near the true values. The model can better track the decline trajectory of the battery health state, and the prediction effect of the battery SOH is good. Further, as Figure 5 shown, the model is verified on different batteries at different temperatures, showing that the proposed method has good prediction accuracy and generalization ability, indicating the strong estimation performance of the method, making it show broad application prospects in the field of battery health state prediction.

[0069] Table 1 Estimation results and errors of different methods

[0070]

[0071] Although the embodiments of the present invention have been shown and described, for those of ordinary skill in the art, it can be understood that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A lithium-ion battery SOH estimation method based on impedance feature selection and optimized support vector regression model, characterized in that: The following steps are involved: S1. Data collection: Perform aging impedance experiments on different lithium-ion batteries under different temperature conditions until the battery discharge capacity is less than 70% of the initial capacity, and record the battery charge and discharge and electrochemical impedance spectrum data in real time, including charge and discharge cycle data and impedance under different aging conditions; S2, data processing and feature extraction: pre-processing the charge-discharge cycle data and electrochemical impedance spectrum data obtained in step S1; analyzing the relationship between electrochemical impedance and battery aging, selecting impedance features based on a sequential forward search algorithm, and applying a multi-objective decision method to optimize the feature subset obtained by the sequential forward search algorithm to obtain impedance features and SOH data; S3, based on the radial basis kernel function, select the penalty coefficient, insensitive loss function parameters and kernel function parameters to build a support vector regression model; S4. Sparrow search algorithm model hyperparameter optimization: Apply the sparrow search algorithm to the support vector regression model hyperparameter optimization to optimize the support vector regression model; S5, applying the chaos of Sine chaotic mapping to replace the random initialization process of the initial value of the sparrow search algorithm, and training the optimized support vector regression model based on the impedance characteristics and SOH data obtained in step S2 to obtain a trained Sine-SSA-SVR model; S6. Single cell SOH estimation: Based on the Sine-SSA-SVR model obtained in step S5, the impedance characteristics are input to estimate the SOH of the lithium-ion battery.

2. The method for estimating SOH of a lithium-ion battery based on impedance feature selection and optimized support vector regression model according to claim 1, characterized in that: The battery charging and discharging process in the step S1 data collection is as follows: in the charging stage, first charge at a constant current of 1C to an upper cut-off voltage of 4.2V, then charge at a constant voltage of 0.1C, and finally stand for 15 minutes; in the discharging stage, discharge at a constant current of 2C to a lower cut-off voltage of 3V, and then stand for 15 minutes.

3. The method for estimating SOH of a lithium-ion battery based on impedance feature selection and optimized support vector regression model according to claim 1, characterized in that: The specific expression of the support vector regression model in step S3 is as follows: Among them, ω and b represent the weight vector and bias term of the support vector regression model respectively, x represents the input variable, is the predicted output function corresponding to the input x, and by introducing the Lagrange multiplier, the above formula can be transformed into a convex quadratic optimization problem, including the dual function and constraints: in, is the optimization objective function of SVR, ||ω|| 2 is the regularization term, n represents the number of training sample sets, c represents the penalty parameter, ξ j and Represent two different relaxation factors, st represents constraint, x j represents the input feature vector of the jth sample, y j The true target value of the jth sample, the training data set is ε represents the insensitive loss function, and solving the above formula gives the following expression: Among them, nsv is the number of support vectors, K(x j ,x) represents the kernel function, which is used to calculate the support vector x in high-dimensional space. j The inner product between the current input vector x, α j , is the Lagrange multiplier corresponding to the jth sample, and the specific expression is as follows: K(x j ,x)=exp(-g||x-x j || 2 ) Among them, exp(*) represents the exponential function with the natural constant e as the base, g represents the radial basis kernel function parameter, ||xx j || 2 is the input vector x and the support vector x j The square of the Euclidean distance between them.

4. The method for estimating SOH of a lithium-ion battery based on impedance feature selection and optimized support vector regression model according to claim 3 is characterized in that: In step S4, the hyperparameter optimization of the sparrow search algorithm model is performed by the following expression: Finder's location update: Location update for joiners: Vigilante Location Update: Among them, i represents the index of the current individual, that is, the i-th group of SVR parameters, d represents the dimension of the SVR parameters, They represent the positions of the i-th discoverer, joiner, and vigilant on the d-th dimension at time t+1, respectively. represents the position of the ith discoverer, joiner, or vigilant in the dth dimension at time t. α is a positive constant used to control the step size and exponential decay rate in position updates. exp(*) represents an exponential function with the natural constant e as the base. max represents the maximum number of iterations, Q is a random number Q~N(0,1) that obeys a normal distribution, L is a random number with a Laplace distribution, which is used to simulate the raid behavior of the discoverer, R2 is a random number R2~U(0,1) that obeys a uniform distribution, ST represents the warning value, It indicates the position of the worst individual in the t-th generation population on the d-th dimension, m indicates the population size, and indicates the number of individuals involved in the optimization process. represents the position of the pth randomly selected individual in the dth dimension at the t+1th generation, It represents the distance between the current individual and the randomly selected individual in the dth dimension. A is a random number A~U(-1,1) that obeys a uniform distribution. l is a constant used to control the step length. is the position of the best individual in the current population, represents the distance between the vigilant and the optimal individual, represents the distance between the vigilant and the worst individual, β is a uniformly distributed random number β~U(0,1), K is a normally distributed random number K~N(0,1), δ represents the value to prevent the denominator from being 0, and f i represents the fitness value of the i-th individual, f g and f w Represent the fitness values ​​of the global optimal and worst individuals respectively.

Images