Lithium battery state of health estimation method based on multi-feature fusion and improved HKELM

Abstract

This invention provides a lithium-ion battery health state estimation method based on multi-feature fusion and an improved HKELM model. It extracts multiple features reflecting the state of health (SOH) of lithium-ion batteries from a selected battery aging dataset, including charge / discharge time, incremental capacity curves, and differential voltage curves. The correlation between these health features and the health state is evaluated using the Pearson correlation coefficient. Multi-scale decomposition of the health state signal is performed using VMD. The Black-winged Kite Algorithm (BKA) is improved by combining mixed chaotic mapping, dynamic parameter adjustment mechanisms, Cauchy-Gaussian mixed variability perturbation, and adaptive spiral position update. The improved BKA optimization algorithm is then used to optimize the key parameters of the HKELM model, constructing an IBKA-HKELM-Adaboost lithium-ion battery health state estimation sub-model. The integrated model estimation results of each modal component are superimposed to obtain the final SOH estimate. This invention improves the accuracy and real-time performance of the model in estimating the health state of lithium-ion batteries, providing an important basis for battery energy management and periodic replacement.

Description

Technical Field

[0001] This invention relates to the field of electric vehicle and lithium battery state estimation technology, specifically to a lithium battery health state estimation method based on multi-feature fusion and improved HKELM. Background Technology

[0002] With the continuous increase in the number of gasoline-powered vehicles worldwide, humanity will face serious problems such as fossil fuel shortages and environmental pollution. Developing new energy vehicles has become an important way to alleviate the energy and environmental crisis. Lithium batteries, due to their advantages such as long cycle life, high power density, and low self-discharge rate, can be widely used in the field of distributed energy storage and have become the main energy storage device in the field of new energy electric vehicles.

[0003] However, during continuous cycling, lithium batteries experience performance degradation and permanent capacity decline. Continuing to use a battery beyond its maximum lifespan can lead to serious safety incidents. Therefore, accurate health assessment of lithium batteries is crucial for ensuring their operational safety and reliability. Summary of the Invention

[0004] To address the problems mentioned in the background art, this invention provides a lithium battery health state estimation method based on multi-feature fusion and improved HKELM. It extracts multiple battery health state features, mines the inherent information of the data through correlation analysis and VMD decomposition, constructs an IBKA-HKELM model, and employs an Adaboost weighted ensemble weak learner to improve the accuracy and real-time performance of the model in estimating the lithium battery health state, providing an important basis for battery energy management and periodic replacement.

[0005] Technical solution: This invention discloses a lithium battery health state estimation method based on multi-feature fusion and improved HKELM, including the following steps:

[0006] Step 1: Obtain the lithium battery aging dataset, extract multi-dimensional health features from the lithium battery charge and discharge data, and screen features that are strongly correlated with battery capacity degradation using the Pearson correlation coefficient;

[0007] Step 2: Use VMD technology to decompose the original SOH sequence into multiple modal components;

[0008] Step 3: Improve the Black-winged Kite optimization algorithm (BKA algorithm). The specific improvement strategy is as follows:

[0009] Step 3.1: Initialize the population position using an elite initialization strategy that combines oppositional learning with Tent chaotic mapping;

[0010] Step 3.2: In the attack phase, an adaptive weighting factor is introduced to dynamically adjust the search step size;

[0011] Step 3.3: Introduce Cauchy-Gaussian hybrid variation perturbation and adaptive spiral position update during the migration phase;

[0012] Step 4: Optimize the parameters in the HKELM model using the improved BKA algorithm from Step 3;

[0013] Step 5: For each modal component, construct the IBKA-HKELM-Adaboost model using the Adaboost ensemble algorithm. Use the health features selected in Step 1 as the model input and the modal components as the target estimates. Superimpose the estimates of each modal component to obtain the final SOH estimate.

[0014] Furthermore, step 1 extracts multi-dimensional health features, including:

[0015] The analysis is conducted from four aspects: voltage interval time, capacity integration, incremental capacity, and temperature monitoring. Specifically, the voltage interval time is used to extract constant current charging time HF1, constant voltage charging time HF2, optimal interval constant voltage rise charging time HF3, and optimal interval constant voltage drop discharging time HF4; the capacity integration is used to extract total charging capacity HF5, constant current charging capacity HF6, and constant voltage charging capacity HF7; the incremental capacity analysis is used to extract the peak value of the incremental capacity curve HF8 and the corresponding voltage HF9; and the temperature characteristics are used to extract the maximum temperature during the discharge process HF10.

[0016] Furthermore, step 2, which uses VMD technology to decompose the original SOH sequence into multiple modal components, includes:

[0017] Preset the number of modes, penalty factor, noise tolerance, and convergence accuracy, and use the comprehensive sample entropy value as the fitness evaluation standard to perform a global optimal combination search for the number of modes and penalty factor in the VMD decomposition method;

[0018] The original SOH sequence is decomposed into j components, with the constraint that the sum of all modes equals the input signal, and a variational model is constructed.

[0019] By introducing a penalty factor and Lagrange multipliers, the constrained variational problem is transformed into an unconstrained variational problem;

[0020] The variational problem is solved by an alternating direction multiplier iterative algorithm, which updates the modal components, the corresponding center frequencies and Lagrange multipliers until the convergence accuracy is met, and finally generates j IMF components of SOH.

[0021] Furthermore, an elite initialization strategy combining hybrid oppositional learning and Tent chaotic mapping is employed to initialize the population positions:

[0022] The mathematical expression for the Tent chaotic mapping is shown in (1). The chaotic variables are mapped to the search space to obtain the initial solution of the population:

[0023]

[0024] X u,v =UB+γ u,v+1 (UB-IB) (2)

[0025] In the formula, γ u,v γ represents the chaotic variable value in the u-th population and the v-th iteration; u,v+1 X represents the chaotic variable value obtained after iteration through the Tent mapping; u is the population size; v is the chaotic variable index; a is a random number within (0,1); X u,v The initial solution for the population is generated based on the Tent mapping; UB and IB are the upper and lower bounds of the search space, respectively.

[0026] The elite-opposition learning strategy generates an inverse population, and the corresponding opposite solution is:

[0027]

[0028] In the formula, The elite individual is the extreme point corresponding to a general individual in the population. The solution is the opposite of the elite individual; rand is a random number between [0,1].

[0029] Furthermore, an adaptive weighting factor is introduced into the attack behavior to dynamically adjust the search step size, and its formula is shown below:

[0030]

[0031] In the formula, w(t) is the adaptive weight; t is the current iteration number; T is the maximum iteration number. After introducing the adaptive weight factor, the Black-winged Kite position update formula during the attack phase is:

[0032]

[0033] In the formula, X(t+1) and X(t) represent the positions of the black-winged kite in the (t+1)th and tth iterations, respectively, r is a random number between (0,1), p is a constant 0.9, and n is a nonlinear convergence factor.

[0034] Furthermore, a Cauchy-Gaussian mixed mutation perturbation is introduced during the migration phase. In the early stages of iteration, the Cauchy perturbation dominates the global exploration, while in the later stages, the Gaussian perturbation dominates the local development. The Cauchy-Gaussian mixed mutation formula is shown below:

[0035] Mutation=β1·C(0,σ 2 )+β2·G(0,σ 2 (7)

[0036] In the formula, Mutation is the mixed variation perturbation factor; β1=(1-t) / T and β2=t / T are dynamic parameters; C(0,σ 2 G(0,σ) is a Cauchy distributed random variable; 2 Let be a Gaussian distributed random variable. When the fitness of an individual is less than the fitness of the random individual, a perturbation update position formula is used:

[0037] X(t+1)=X(t)+Mutation·(X(t)-X best (t)) (8)

[0038] In the formula, X best X(t) represents the current global optimal solution, and X(t+1) and X(t) represent the positions of the Black-winged Kite in the (t+1)th and tth iterations, respectively.

[0039] Furthermore, the migration phase borrows the spiral path from the whale optimization algorithm. When the fitness of an individual is greater than that of a random individual, an adaptive spiral position update with a step size is introduced. The formulas for the spiral path and the adaptive step size are as follows:

[0040] X(t+1)=X best (t)+|X best (t)-X(t)|·e bl ·cos(2πl) (9)

[0041]

[0042] In the formula, X best (t) represents the current global optimal solution, X(t+1) and X(t) represent the positions of the Black-winged Kite in the (t+1)th and tth iterations, respectively, b is the adaptive step size parameter, and l is a random number controlling the direction of the spiral, with a value between [-1, 1].

[0043] Furthermore, for each IMF component, the Adaboost-integrated HKELM modeling steps include:

[0044] Initialize training sample weights and set the number of iterations; train the HKELM weak learner and optimize the kernel and regularization parameters of the current HKELM model using an improved BKA algorithm; calculate the model error and weights, and update the sample weights; combine the strong learners and superimpose the IMF prediction results to output the SOH estimate; its mathematical model is:

[0045]

[0046] In the formula, ε kThe weighted error is denoted by m; m is the number of training samples, i = 1, 2, ..., m; K is the number of iterations to train the weak classifier, k = 1, 2, ..., K; D k (i) represents the weight of the i-th sample in the k-th round of training of the Adaboost ensemble algorithm; y i h k (x i ) represent the actual output and predicted output of the weak classifier, respectively; x i α is the input feature of the i-th sample. k The weights of the weak learners in the ensemble model; D k+1 (i) represents the updated sample weights; sign(·) is the sign function, which expresses whether there is an error in the prediction; H(x) is the final prediction output of the Adaboost ensemble model.

[0047] Beneficial effects:

[0048] (1) Pearson correlation coefficient analysis was performed on the extracted multidimensional health features to screen out key health features; Variational Mode Decomposition (VMD) was introduced to decompose the original noisy and non-stationary SOH signal into multiple intrinsic mode components, effectively separating degradation information at different frequency scales. These two data processing perspectives significantly improved feature quality and robustness, and reduced noise interference and data dependence.

[0049] (2) An elite initialization strategy of hybrid opposition learning and Tent chaotic mapping is adopted to enhance population diversity and improve the quality of the initial population. In the attack phase, an adaptive weight factor is introduced to dynamically adjust the search step size, improve the population's ability to escape local optima and accelerate the convergence speed. In the migration phase, Cauchy-Gaussian hybrid mutation perturbation and adaptive spiral position update are introduced to balance global exploration and local development and improve the optimization efficiency of the algorithm.

[0050] (3) For each modal component obtained by VMD decomposition, an independent hybrid kernel extreme learning machine (HKELM) sub-model is constructed, along with an Adaboost dynamic weighted weak classifier. Then, the IBKA algorithm with multiple improved strategies is used to optimize the parameters of the Adaboost-HKELM model to improve the classification accuracy and generalization ability of the model. Each sub-model captures the degradation mode in a specific frequency domain, thereby improving the model's ability to capture nonlinear degradation features and its prediction accuracy. Attached Figure Description

[0051] Figure 1 This is the overall flowchart of the present invention.

[0052] Figure 2 This is a flowchart of the improved black-winged kite optimization algorithm in this invention.

[0053] Figure 3 This is a comparison chart of the convergence performance of IBKA and several other algorithms in this invention.

[0054] Figure 4 This is a comparison curve of the estimated SOH value and the actual value of lithium battery using the method proposed in this invention. Detailed Implementation

[0055] The embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and specific examples.

[0056] like Figure 1 As shown, this invention discloses a lithium battery health state estimation method based on multi-feature fusion and improved HKELM, specifically including the following steps:

[0057] Step 1: Obtain the lithium battery aging dataset, extract multi-dimensional health features from the lithium battery charge and discharge data, and screen features that are strongly correlated with battery capacity degradation using the Pearson correlation coefficient.

[0058] Multi-dimensional health features were extracted, including analysis from four aspects: voltage range time, capacity integral, incremental capacity, and temperature monitoring. Ten feature factors related to battery performance degradation were extracted. Among them, the voltage range time feature extraction included constant current charging time HF1, constant voltage charging time HF2, optimal range isobaric ramp-up charging time HF3, and optimal range isobaric drop discharging time HF4.

[0059] Capacity integral feature extraction uses the trapezoidal numerical integration method to calculate three types of capacity features, including total charging capacity HF5, constant current charging capacity HF6, and constant voltage charging capacity HF7.

[0060]

[0061] In the formula, Q total s is the total charging capacity, s0 is the charging start time, s end Let I(s) be the charging end time, I(s) be the charging current at time s, and Q be the charging current at time s. CC For constant current charging capacity; s 4.2 When the voltage reaches 4.2V, I con Q represents the current during the constant current phase. CV This refers to the constant voltage charging capacity.

[0062] Incremental capacity analysis extracts the peak value HF8 and corresponding voltage HF9 of the incremental capacity curve by differentiating the charge-discharge curve. The specific calculation formula for the capacity increment IC is as follows:

[0063]

[0064] In the formula, IC is the capacity increment; ΔQ is the capacity change; and ΔV is the voltage change.

[0065] The maximum temperature HF10 during the discharge process is extracted by directly reading the timing data from the temperature sensor.

[0066] Step 2: The process of decomposing the original SOH sequence into multiple modal components using VMD technology includes:

[0067] The algorithm presets the number of modes, penalty factor, noise tolerance, and convergence accuracy, and uses the comprehensive sample entropy value as the fitness evaluation criterion to perform a global optimal combination search for the number of modes and penalty factor in the VMD decomposition method.

[0068] The original SOH sequence is decomposed into j components, with the constraint that the sum of all modes equals the input signal, and a variational model is constructed.

[0069] By introducing a penalty factor and Lagrange multipliers, the constrained variational problem is transformed into an unconstrained variational problem.

[0070] The variational problem is solved by an alternating direction multiplier iterative algorithm, which updates the modal components, the corresponding center frequencies and Lagrange multipliers until the convergence accuracy is met, and finally generates j IMF components of SOH.

[0071] Step 3: As Figure 2 As shown, the Blackwing Kite Algorithm BKA is improved by combining hybrid chaotic mapping, dynamic parameter adjustment mechanism, Cauchy-Gaussian hybrid mutation perturbation and adaptive spiral position update, resulting in IBKA.

[0072] Step 3.1 Initialize the population position using an elite initialization strategy that combines hybrid oppositional learning and Tent chaotic mapping. The mathematical expression for Tent chaotic mapping is shown in (1). Map the chaotic variables to the search space to obtain the initial solution for the population:

[0073]

[0074] X u,v =UB+γ u,v+1 (UB-IB)

[0075] In the formula, γ u,v γ represents the chaotic variable value in the u-th population and the v-th iteration; u,v+1 X represents the chaotic variable value obtained after iteration through the Tent mapping; u is the population size; v is the chaotic variable index; a is a random number within (0,1); X u,v is the initial solution for the population generated based on the Tent mapping; UB and IB are the upper and lower bounds of the search space, respectively.

[0076] The elite-opposition learning strategy generates an inverse population, and the corresponding opposite solution is:

[0077]

[0078] In the formula, The elite individual is the extreme point corresponding to a general individual in the population. The solution is the opposite of the elite individual; rand is a random number between [0,1].

[0079] Step 3.2 In the Black-winged Kite attack behavior, an adaptive weight factor is introduced to dynamically adjust the search step size, and the formula is as follows:

[0080]

[0081] In the formula, w(t) is the adaptive weight; t is the current iteration number; and T is the maximum iteration number. After introducing the adaptive weight factor, the Black-winged Kite position update formula during the attack phase is:

[0082]

[0083] In the formula, X(t+1) and X(t) represent the positions of the black-winged kite in the (t+1)th and tth iterations, respectively, r is a random number between (0,1), p is a constant 0.9, and n is a nonlinear convergence factor.

[0084] Step 3.3 In the migration phase of the Black-winged Kite, a Cauchy-Gaussian mixed mutation perturbation is introduced. In the early stage of the iteration, the Cauchy perturbation dominates the global exploration, while in the later stage, the Gaussian perturbation dominates the local development. The Cauchy-Gaussian mixed mutation formula is shown below:

[0085] Mutation=β1·C(0,σ 2 )+β2·G(0,σ 2 )

[0086] In the formula, Mutation is the mixed variation perturbation factor; β1=(1-t) / T and β2=t / T are dynamic parameters; C(0,σ 2 G(0,σ) is a Cauchy distributed random variable; 2 Let be a Gaussian distributed random variable. When the fitness of an individual is less than the fitness of a random individual, a perturbation update position formula is used:

[0087] X(t+1)=X(t)+Mutation·(X(t)-X best (t))

[0088] In the formula, X best (t) represents the current global optimal solution.

[0089] Simultaneously, the migration phase borrows the spiral path from the whale optimization algorithm. When the fitness of an individual is greater than that of a random individual, an adaptive spiral position update with a step size is introduced. The spiral path and adaptive step size formulas are as follows:

[0090] X(t+1)=X best (t)+|X best (t)-X(t)|·e bl ·cos(2πl)

[0091]

[0092] In the formula, b is the adaptive step size parameter; l is a random number that controls the direction of the spiral, and its value ranges from [-1, 1].

[0093] Step 4: Optimize the parameters in the HKELM model using the improved BKA algorithm. Specific steps include:

[0094] Step 4.1 Determine the parameters to be optimized: regularization coefficient, RBF kernel coefficient, polynomial kernel coefficients poly1 and poly2, and kernel weight coefficient.

[0095] Step 4.2 Set the search range of the parameters (regularization coefficient ∈ [1, 20], RBF kernel coefficient ∈

[10] ). -3 10 3 ]、poly1∈[10 -3 10 3 ]、poly2∈[10 -3 10 3 The population size and maximum number of iterations of IBKA are defined, along with the kernel weight coefficients (∈[0,1]) and the IBKA population size. A fitness function is defined with the prediction error of HKELM as the objective, and the smaller the value, the better the parameters.

[0096] Step 4.3 Initialize the black-winged kite population positions, calculate the fitness value of each black-winged kite, determine the current optimal solution, and update the individual positions according to the improved black-winged kite algorithm rules in each iteration. Check if the maximum number of iterations has been reached. If not, return to continue comparing fitness values. If the maximum number of iterations has been reached, output the parameter combination that achieves the optimal performance.

[0097] Step 4.4 Use the optimal parameters obtained by IBKA optimization to initialize the Adaboost sample weights, iteratively train multiple HKELM weak learners, and finally integrate all weak learners and combine the SO H estimation results according to their respective weights.

[0098] Step 5: For each IMF component, perform the HKELM modeling steps integrated with Adaboost, including: initializing training sample weights and setting the number of iterations; training the HKELM weak learner and optimizing the kernel and regularization parameters of the current HKELM model using IBKA; calculating the model error and weights, and updating the sample weights; combining the strong learners and superimposing the IMF prediction results to output the SOH estimate. The mathematical model is as follows:

[0099]

[0100] In the formula, ε k The weighted error is denoted by m; m is the number of training samples, i = 1, 2, ..., m; K is the number of iterations to train the weak classifier, k = 1, 2, ..., K; D k (i) represents the weight of the i-th sample in the k-th round of training of the Adaboost ensemble algorithm; y i h k (x i ) represent the actual output and predicted output of the weak classifier, respectively; x i α is the input feature of the i-th sample. k The weights of the weak learners in the ensemble model; D k+1 (i) represents the updated sample weights; sign(·) is the sign function, which expresses whether there is an error in the prediction; H(x) is the final prediction output of the Adaboost ensemble model.

[0101] In one specific embodiment of the present invention, a lithium-ion battery degradation dataset published by NASA was used. The selected lithium-ion batteries were numbered B0005, B0006, B0007, and B0018. These four lithium batteries underwent three different operating conditions (charging, discharging, and impedance testing) at room temperature. The charging process was initially performed in a constant current (CC) mode of 1.5A until the battery voltage reached 4.2V, then switched to a constant voltage (CV) mode to continue charging until the charging current dropped to 20mA. The discharging process was performed in a constant current (CC) mode of 2A. For batteries numbered 5, 6, 7, and 18, discharging was performed until the battery voltage dropped to 2.7V, 2.5V, 2.2V, and 2.5V, respectively. The relevant battery parameters are shown in Table 1.

[0102] Table 1. Parameters related to four NASA lithium battery degradation datasets.

[0103]

[0104] The Pearson correlation coefficient is commonly used to measure the linear correlation between variables. The closer the absolute value of the coefficient is to 1, the stronger the linear correlation between the two samples. The table below shows the Pearson correlation coefficients of four battery health characteristics from NASA. As can be seen from the table, there is a high correlation between different health factors. This paper selects HF2, HF6, and HF8 as input variables from the 10 characteristics.

[0105] Table 210 Pearson coefficients for health factors

[0106]

[0107] Variational Mode Decomposition (VMD) is an adaptive, fully non-recursive signal processing method. By decomposing variables using VMD, the Intrinsic Mode Components (IMFs) can be effectively separated, and the signal can be rationally divided into frequency domains, thus obtaining the effective decomposed components of a given signal and ultimately achieving the optimal solution to the variational problem. VMD decomposes the original State of Harmonic Oscillator (SOH) signal into multiple IMFs. Low-frequency components capture the overall SOH decay trend, mid-frequency components reflect staged capacity decay, and high-frequency components extract short-term capacity regeneration. Too few IMFs may lead to information loss, while too many may cause frequency aliasing. This invention, for the B0005 battery, selects a mode decomposition number of 5.

[0108] Figure 3 To compare the improved Black-winged Kite Algorithm (IBKA) with the Grey Wolf Algorithm (GWO), Whale Algorithm (WOA), Particle Swarm Optimization (PSO), and the original Black-winged Kite Algorithm in the test function The results are shown in the graph below. The population size was uniformly set to 30, the maximum number of iterations to 500, and each function was run independently 30 times. As can be seen from the graph, the improved Black-winged Kite optimization algorithm converges faster than other optimization algorithms.

[0109] To verify the effectiveness of the model proposed in this invention, the coefficient of determination R is used in this embodiment. 2 Mean absolute error (MAE) and root mean square error (RMSE) were used as performance indicators for the model. The evaluation indicators are shown in Table 3. In the experiment of the battery state of health (SOH) estimation model, four battery types—B0005, B0006, B0007, and B0018—were analyzed.

[0110] Table 3 Evaluation Indicators for the 60% Predicted Starting Point Assessment Results of Four NASA Batteries

[0111]

[0112] Figure 4 This is a graph showing the estimated starting point for 60% prediction of battery B0005 in the NASA dataset. The horizontal axis represents the number of lithium battery cycles, and the vertical axis represents the state of harmonics (SOH) of the lithium battery. From... Figure 4 As can be seen from the SOH decay curves of lithium-ion batteries during charge-discharge cycles, the SOH of lithium-ion batteries does not decrease smoothly and uniformly with the number of cycles, and the decay is inconsistent among different batteries. During the charge-discharge cycle, the battery undergoes a period of rest, during which capacity regeneration occurs. This paper combines charge-discharge standards with battery aging mechanisms when processing battery charge-discharge data to extract health factors that characterize battery aging capacity decay and intermittent capacity recovery. Then, using an improved Blackwing Kite optimization algorithm, an IBKA-HKELM-Adaboost lithium-ion battery health state estimation model is constructed. This model can not only fit the overall trend of battery SOH decay but also effectively capture the intermittent capacity recovery phenomenon.

[0113] The above embodiments are only for illustrating the technical concept and features of the present invention, and are intended to enable those skilled in the art to understand the content of the present invention and implement it accordingly. They should not be construed as limiting the scope of protection of the present invention. All equivalent transformations or modifications made in accordance with the spirit and essence of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A lithium battery health state estimation method based on multi-feature fusion and improved HKELM, characterized in that, Includes the following steps: Step 1: Obtain the lithium battery aging dataset, extract multi-dimensional health features from the lithium battery charge and discharge data, and screen features that are strongly correlated with battery capacity degradation using the Pearson correlation coefficient; Step 2: Use VMD to decompose the original SOH sequence into multiple modal components; Step 3: Improve the Black-winged Kite optimization algorithm (BKA algorithm). The specific improvement strategy is as follows: Step 3.1: Initialize the population position using an elite initialization strategy that combines oppositional learning with Tent chaotic mapping; Step 3.2: In the attack phase, an adaptive weighting factor is introduced to dynamically adjust the search step size; Step 3.3: Introduce Cauchy-Gaussian hybrid variation perturbation and adaptive spiral position update during the migration phase; Step 4: Optimize the parameters in the HKELM model using the improved BKA algorithm from Step 3; Step 5: For each modal component, construct the IBKA-HKELM-Adaboost model using the Adaboost ensemble algorithm. Use the health features selected in Step 1 as the model input and the modal components as the target estimates. Superimpose the estimates of each modal component to obtain the final SOH estimate.

2. The lithium battery health state estimation method based on multi-feature fusion and improved HKELM according to claim 1, characterized in that, Step 1 extracts multi-dimensional health features, including: The analysis is conducted from four aspects: voltage interval time, capacity integration, incremental capacity, and temperature monitoring. Specifically, the voltage interval time is used to extract constant current charging time HF1, constant voltage charging time HF2, optimal interval constant voltage rise charging time HF3, and optimal interval constant voltage drop discharging time HF4; the capacity integration is used to extract total charging capacity HF5, constant current charging capacity HF6, and constant voltage charging capacity HF7; the incremental capacity analysis is used to extract the peak value of the incremental capacity curve HF8 and the corresponding voltage HF9; and the temperature characteristics are used to extract the maximum temperature during the discharge process HF10.

3. The lithium battery health state estimation method based on multi-feature fusion and improved HKELM according to claim 1, characterized in that, Step 2, which uses VMD to decompose the original SOH sequence into multiple modal components, includes: Preset the number of modes, penalty factor, noise tolerance, and convergence accuracy, and use the comprehensive sample entropy value as the fitness evaluation standard to perform a global optimal combination search for the number of modes and penalty factor in the VMD decomposition method; The original SOH sequence is decomposed into j components, with the constraint that the sum of all modes equals the input signal, and a variational model is constructed. By introducing a penalty factor and Lagrange multipliers, the constrained variational problem is transformed into an unconstrained variational problem; The variational problem is solved by an alternating direction multiplier iterative algorithm, which updates the modal components, the corresponding center frequencies and Lagrange multipliers until the convergence accuracy is met, and finally generates j IMF components of SOH.

4. The lithium battery health state estimation method based on multi-feature fusion and improved HKELM according to claim 1, characterized in that, The population positions are initialized using an elite initialization strategy that combines hybrid oppositional learning with Tent chaotic mapping: The mathematical expression for the Tent chaotic mapping is shown in (1). The chaotic variables are mapped to the search space to obtain the initial solution of the population: X u,v = UB + γ u,v+1 (UB - IB) (2) In the formula, γ u,v γ represents the chaotic variable value in the u-th population and the v-th iteration; u,v+1 The chaotic variable value is obtained at the next time step after iteration through the Tent mapping; u is the population size; v is the chaotic variable index; a is a random number in (0,1); X u,v The initial solution for the population is generated based on the Tent mapping; UB and IB are the upper and lower bounds of the search space, respectively. The elite-opposition learning strategy generates an inverse population, and the corresponding opposite solution is: In the formula, The elite individual is the extreme point corresponding to a general individual in the population. The solution is the opposite of the elite individual; rand is a random number between [0,1].

5. The lithium battery health state estimation method based on multi-feature fusion and improved HKELM according to claim 1, characterized in that, An adaptive weighting factor is introduced into the attack behavior to dynamically adjust the search step size, and its formula is shown below: In the formula, w(t) is the adaptive weight; t is the current iteration number; T is the maximum iteration number. After introducing the adaptive weight factor, the Black-winged Kite position update formula during the attack phase is: In the formula, X(t+1) and X(t) represent the positions of the black-winged kite in the (t+1)th and tth iterations, respectively, r is a random number between (0,1), p is a constant 0.9, and n is a nonlinear convergence factor.

6. The lithium battery health state estimation method based on multi-feature fusion and improved HKELM according to claim 1, characterized in that, During the migration phase, a Cauchy-Gaussian mixed mutation perturbation is introduced. In the early stages of iteration, the Cauchy perturbation dominates the global exploration, while in the later stages, the Gaussian perturbation dominates the local development. The Cauchy-Gaussian mixed mutation formula is shown below: Mutation=β1·C(0,σ 2 )+β2·G(0,σ 2 ) (7) In the formula, Mutation is the mixed variation perturbation factor; β1=(1-t) / T and β2=t / T are dynamic parameters; C(0,σ 2 G(0,σ) is a Cauchy distributed random variable; 2 Let be a Gaussian distributed random variable. When the fitness of an individual is less than the fitness of the random individual, a perturbation update position formula is used: X(t+1)=X(t)+Mutation·(X(t)-X best (t)) (8) In the formula, X best X(t) represents the current global optimal solution, and X(t+1) and X(t) represent the positions of the Black-winged Kite in the (t+1)th and tth iterations, respectively.

7. The lithium battery health state estimation method based on multi-feature fusion and improved HKELM according to claim 1, characterized in that, The migration phase borrows the spiral path from the whale optimization algorithm. When the fitness of an individual is greater than that of a random individual, an adaptive spiral position update with a step size is introduced. The spiral path and adaptive step size formulas are as follows: X(t+1)=X best (t)+|X best (t)-X(t)|·e bl ·cos(2πl) (9) In the formula, X best (t) represents the current global optimal solution, X(t+1) and X(t) represent the positions of the Black-winged Kite in the (t+1)th and tth iterations, respectively, b is the adaptive step size parameter, and l is a random number controlling the direction of the spiral, with a value between [-1, 1].

8. The lithium battery health state estimation method based on multi-feature fusion and improved HKELM according to claim 1, characterized in that, The improved BKA algorithm optimizes the parameters in the HKELM model, including regularization coefficients, RBF kernel coefficients, polynomial kernel coefficients poly1 and poly2, and kernel weight coefficients.

9. The lithium battery health state estimation method based on multi-feature fusion and improved HKELM according to claim 1, characterized in that, For each IMF component, the Adaboost integrated HKELM modeling steps include: Initialize training sample weights and set the number of iterations; train the HKELM weak learner and optimize the parameters of the current HKELM model using the improved BKA algorithm; calculate the model error and weights, and update the sample weights; combine the strong learners and superimpose the IMF prediction results to output the SOH estimate; its mathematical model is: In the formula, ε k The weighted error is denoted by m; m is the number of training samples, i = 1, 2, ..., m; K is the number of iterations to train the weak classifier, k = 1, 2, ..., K; D k (i) represents the weight of the i-th sample in the k-th round of training of the Adaboost ensemble algorithm; y i h k (x i ) represent the actual output and predicted output of the weak classifier, respectively; x i α is the input feature of the i-th sample. k The weights of the weak learners in the ensemble model; D k+1 (i) represents the updated sample weights; sign(·) is the sign function, which expresses whether there is an error in the prediction; H(x) is the final prediction output of the Adaboost ensemble model.

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