EIS-based field adaptive retired battery state-of-health estimation method

Abstract

The invention discloses a field self-adaptive retired battery health state estimation method based on an EIS. The method comprises the following steps: firstly, extracting electrochemical impedance spectroscopy data of a retired aged battery; and then a fractional order battery equivalent circuit model is constructed, and the characterization capability of dynamic degradation of an electrode interface is enhanced through a constant phase element. Fractional order battery equivalent circuit model parameters are extracted from electrochemical impedance spectroscopy data based on nonlinear least square fitting, Pearson correlation analysis is adopted to screen parameters having a significant relationship with SOH, then a recursive feature elimination method is used for further screening, and an optimal parameter subset strongly associated with the state of health is extracted from a high-dimensional parameter set. And finally, constructing a decommissioned battery state-of-health estimation method of a field adaptive method, modeling the influence of different operation conditions on battery aging through knowledge migration, and realizing cross-working-condition decommissioned battery state-of-health estimation with both physical interpretability and working condition robustness.

Description

Technical Field

[0001] The present invention relates to the field of performance evaluation of retired batteries, and particularly to a method for estimating the state of health of retired batteries based on EIS with domain adaptation. Background Art

[0002] With the rapid development of electric vehicles and large-scale energy storage systems, the estimation of the state of health (SOH) of lithium-ion batteries has become a key technology for ensuring system safety and enhancing economic value. As a core indicator for measuring the degree of battery aging, SOH directly determines the remaining life and potential for secondary use of the battery.

[0003] Although traditional methods such as capacity fade monitoring or internal resistance measurement are widely used, capacity testing is time-consuming and difficult to implement online, while the internal resistance model is sensitive to operating condition fluctuations and cannot resolve the microscopic degradation of the internal electrochemical mechanism of the battery. In recent years, Electrochemical Impedance Spectroscopy (EIS) technology has attracted much attention due to its non-invasive and high information density characteristics. It captures the battery's dynamic response through a wide-frequency domain excitation signal, and the characteristics of ohmic impedance, charge transfer impedance, and diffusion impedance contained in its Nyquist plot are deeply coupled with the aging mechanisms of side reactions at the electrode interface and loss of active materials. However, existing SOH estimation based on EIS still faces multiple challenges: traditional integer-order equivalent circuit models are difficult to accurately describe the fractional-order characteristics of battery polarization behavior, resulting in fitting errors in the diffusion process in the high-frequency region; impedance spectrum testing is vulnerable to interference from the state of charge (SOC), temperature, and historical operating conditions, leading to insufficient generalization ability of the SOH estimation model in cross-operating condition scenarios.

[0004] In response to the above problems, the introduction of a fractional-order equivalent circuit model provides a new idea for mechanism modeling. By using a Constant Phase Element (CPE) to replace the traditional capacitor, its impedance characteristics can more accurately characterize the non-ideal capacitive behavior at the electrode-electrolyte interface and the diffusion process, and model the degradation mechanisms of lithium deposition and thickening of solid electrolyte interface films. However, existing research mainly focuses on new battery modeling. The variable operating conditions experienced by retired batteries in practical applications lead to distribution shifts between batteries, and there is no systematic understanding of the non-linear mapping relationship between the fractional-order parameters of retired batteries and SOH. How to deeply integrate electrochemical mechanisms with data-driven methods to construct an interpretable and strongly generalized cross-operating condition SOH estimation framework is still a blank in current research. Summary of the Invention

[0005] Aiming at the deficiencies of the existing technology, the present invention proposes a method for estimating the state of health of retired batteries based on EIS. By non-linearly least-squares fitting of the electrochemical impedance spectrum of the fractional-order equivalent model, Pearson correlation analysis and recursive feature elimination are used to obtain the best health factors, and a domain-adaptive state of health estimation model for batteries is constructed to achieve interpretable and strongly generalized cross-condition state of health (SOH) estimation of retired batteries.

[0006] A method for estimating the state of health of retired batteries based on EIS includes the following steps:

[0007] Step 1: Charge in a constant current-constant voltage mode until the cut-off current of 0.05 A is reached to ensure uniform distribution of lithium ions in the electrode and eliminate the influence of SOC differences on the electrochemical impedance spectrum. After charging is completed, disconnect the circuit and let it stand still to allow the polarization effect to fully relax; in the frequency range from 0.02 Hz to 20 kHz, with 10 frequency points per decade, set the excitation signal amplitude to 10 mV to obtain electrochemical impedance spectrum data M represents the number of frequency points.

[0008] Step 2: Construct a fractional-order equivalent circuit model of the retired battery:

[0009] L1+R1+(R2 / / CPE1)+(R3 / / CPE2)+W

[0010] Among them, + represents series connection, and / / represents parallel connection. CPE represents a constant phase element, R represents resistance, L represents capacitance, and W represents a Warburg diffusion element.

[0011] Preferably, construct a fractional-order equivalent circuit model of the retired battery as follows:

[0012] L1+R1+(R2 / / CPE1)+(R3 / / C1)+((R4+W) / / CPE2)

[0013] Among them, L1 represents the parasitic inductance of the lead wire, R1 represents the ohmic impedance, R2 represents the ion transport resistance of the SEI film, R3 is the charge transfer resistance, R4 is the contact resistance of the bulk material, and C1 is the double-layer capacitance. CPE1 represents the non-ideal capacitance behavior of the SEI film, CPE2 quantifies the low-frequency non-ideal polarization behavior caused by the aging of the electrode pore structure, and the impedance of the constant phase element CPE a is: For:

[0014]

[0015] Among them, a = 1, 2, 0 < n a < 1, reflecting the heterogeneity of the film layer structure, Q a is the constant phase element CPE aThe conductance, which is the reciprocal of impedance.

[0016] The impedance of the Warburg diffusion element W is expressed as a frequency-dependent impedance Z w , in the following form:

[0017]

[0018] where Z w is the impedance of the Warburg diffusion element W. σ w is the Warburg coefficient, which is related to the diffusion coefficient, electrode area, and diffusion layer thickness. τ W is the Warburg time constant, which is related to the diffusion layer thickness and diffusion coefficient.

[0019] The total impedance Z of the fractional-order equivalent circuit model model is:

[0020]

[0021] Step 3: Fit the electrochemical impedance spectrum and extract the parameters of the fractional-order equivalent circuit model.

[0022] Step 4: For the parameters of the fractional-order equivalent circuit model extracted in Step 3, calculate the Pearson linear correlation coefficient r between each parameter and the battery SOH p :

[0023]

[0024] where θ c represents the model parameter of the c-th cycle, represents the average value of the parameter, SOH c represents the health state of the c-th cycle, represents the average value of SOH for all cycles, and C is the number of cycles. For the model parameters with |r p | > 0.7, they are considered significant parameters and are retained. Other parameters are excluded to eliminate the noise interference terms.

[0025] Step 5: Calculate the mean square error MSE of the model, and use recursive feature elimination and support vector regression to perform a secondary fine screening on the model parameters retained in Step 4.

[0026] Step 6: Construct a domain adaptation model for the health state of retired batteries based on correlation alignment, and effectively transfer the mapping relationship between the main aging mechanisms of the operating conditions in the source domain and the capacity attenuation to the target domain. Specifically:

[0027] Obtain the features X t of the source domain and the target domain through the common feature extractor F s and Xt The source domain is the battery aging electrochemical impedance spectroscopy data collected under laboratory controllable conditions, including complete SOH tags; the target domain is the battery operation data under actual complex working conditions of dynamic temperature, variable load, and random charge and discharge. Obtain the covariance matrices C s and C t of the source domain and the target domain features:

[0028]

[0029] where X s and X t represent the features of the source domain and the target domain respectively, and μ s and μ t represent the average values of the source domain and the target domain features respectively, and n s and n t represent the feature dimensions of the source domain and the target domain respectively.

[0030] Reduce the distribution difference between the source domain and the target domain features by adjusting the covariance matrices of the source domain and the target domain features through correlation alignment Map the source domain feature distribution to the target domain feature distribution space to improve the generalization ability of the model in the target domain:

[0031]

[0032] where ||·|| F is the F-norm and d is the feature dimension. Subsequently, match the source domain feature covariance matrix to the target domain through a linear transformation:

[0033]

[0034] Input the aligned target domain features into a multi-layer perceptron for SOH estimation.

[0035] Step 7: Use the retired batteries in the source domain working conditions to train the model, use the mean square error loss as the loss function, Adam as the optimizer, and update the parameters of the model through the gradient backpropagation algorithm. Use the trained model to estimate the SOH of retired batteries.

[0036] The present invention has the following beneficial effects:

[0037] The domain adaptation method for estimating the health state of retired batteries based on electrochemical impedance spectroscopy overcomes the industry problems of low accuracy, poor generalization, and weak interpretability in the SOH estimation of retired batteries through the triple fusion of electrochemical mechanism - big data analysis - domain adaptation, realizes high-precision and cross-scenario robust estimation of the SOH of retired batteries under complex working conditions, and provides a reliable technical tool for the intelligent operation and maintenance of electric vehicles and large-scale energy storage systems. Description of the Drawings

[0038] Figure 1 is the workflow diagram of the present invention;

[0039] Figure 2 is the fractional-order equivalent circuit model constructed in Example 1;

[0040] Figure 3 is the fractional-order equivalent circuit model constructed in Example 2;

[0041] Figure 4 is the result of the electrochemical impedance spectrum fitting in the embodiment. Detailed implementation manners

[0042] The present invention will be further explained below with reference to the accompanying drawings;

[0043] Example 1

[0044] A method for estimating the health state of retired batteries based on EIS, as Figure 1 shown, specifically includes the following steps:

[0045] Step 1: Charge in a constant current-constant voltage mode to a cut-off current of 0.05C to ensure uniform distribution of lithium ions in the electrode and eliminate the influence of SOC difference on the impedance spectrum; after charging is completed, disconnect the circuit and let it stand still to fully relax the polarization effect; in the frequency range from 0.02 Hz to 20 kHz, with 10 frequency points per decade, set the amplitude of the excitation signal to 10 mV to obtain electrochemical impedance spectrum data.

[0046] Step 2: Construct a fractional-order equivalent circuit model of the retired battery as Figure 2 shown:

[0047] L1 + R1 + (R2 / / CPE1) + (R3 / / CPE2) + W

[0048] where, + represents series connection, and / / represents parallel connection. CPE represents a constant phase element, R represents a resistor, L represents a capacitor, and W represents a Warburg diffusion element.

[0049] Step 3: Fit the electrochemical impedance spectrum and extract the parameters of the fractional-order equivalent circuit model.

[0050] Step 4: Calculate the Pearson linear correlation coefficient r p between each parameter in the fractional-order equivalent circuit model and the battery SOH p . For the model parameters with |r

[0051] p |>0.7, they are considered significant parameters and are retained. Other parameters are excluded to eliminate noise interference terms.Step 5: Calculate the mean squared error (MSE) of the model, and perform secondary fine screening on the model parameters retained in Step 4 using recursive feature elimination and support vector regression.

[0052] Step 6: Construct a domain adaptation model for the state of health of retired batteries based on correlation alignment, effectively transfer the mapping relationship between the main aging mechanisms of the operating conditions in the source domain and capacity decay to the target domain, and input the aligned target domain features into a multi-layer perceptron for SOH estimation.

[0053] Step 7: Use retired batteries in the source domain working conditions to train the model, use the mean squared error loss as the loss function, Adam as the optimizer, and the gradient backpropagation algorithm to update the model parameters. Use the trained model to estimate the SOH of retired batteries.

[0054] Example 2

[0055] Step 1: Collect electrochemical impedance spectroscopy data.

[0056] Step 2: Considering that in practice, the accumulation of ions at the interface of the electrode will cause the double capacitance effect, Figure 2 the circuit model structure shown in [reference] cannot effectively model this phenomenon, and thus cannot accurately fit the electrochemical impedance spectroscopy data. On the basis of Example 1, construct a fractional-order equivalent circuit model as shown in Figure 3 the following:

[0057] L1 + R1 + (R2 / / CPE1) + (R3 / / C1) + ((R4 + W) / / CPE2)

[0058] where, L1 represents the parasitic inductance of the lead wire, describing the electromagnetic interference characteristics in the high-frequency band; R1 represents the ohmic impedance, corresponding to the pure resistive loss of electrolyte ion conduction and collector contact resistance; R2 / / CPE1 describes the impedance characteristics of the solid electrolyte interface film, R2 represents the SEI film ion transport resistance, which is positively correlated with the film thickness. R3 / / C1 describes the kinetic response of the charge transfer process, R3 is the charge transfer resistance, which is related to the activation energy of the electrode reaction, and C1 is the double-layer capacitance; (R4 + W) / / CPE2 describes the diffusion process, R4 is the bulk material contact resistance, reflecting the deterioration of the connection between active particles; the Warburg diffusion element W = σ W (jωτ W ) -0.5 , used to describe the lithium-ion solid-phase diffusion impedance. The constant phase element CPE1 characterizes the non-ideal capacitance behavior of the SEI film, and CPE2 quantifies the low-frequency non-ideal polarization behavior caused by the aging of the electrode pore structure:

[0059]

[0060] where, Represents the constant phase element CPE a impedance, where a = 1, 2, 0 < n a < 1, reflecting the heterogeneity of the film structure. Q a is the conductance of the CPE.

[0061] The impedance Z of the Warburg diffusion element W w is frequency-dependent:

[0062]

[0063] where σ W is the Warburg coefficient, τ W is the Warburg time constant.

[0064] The total impedance Z of the fractional-order equivalent circuit model model is:

[0065]

[0066] Step 3. Define the residual vector r(θ) of the impedance data as:

[0067]

[0068] where M represents the number of frequency points of the impedance data, θ represents the equivalent circuit model parameters, Re(·) represents the real part, and Re(·) represents the imaginary part.

[0069] Minimize the weighted sum of squared residuals:

[0070] WRSS(θ) = r(θ) T Wr(θ)

[0071] where the superscript T represents matrix transpose. W is the weight matrix:

[0072]

[0073] Set physical constraint terms: R1 > 0, R2 > 0, R3 > 0, R4 > 0, Q1 > 0, Q2 > 0, 0 < n1 < 1, 0 < n2 < 1, σ W > 0, τ W > 0. Let the initial value of the equivalent circuit parameter θ be [1e - 7, 0.1, 1.0, 0.06, 0.1, 0.1, 0.1, 0.001, 0.01, 0.01, 3.0, 0.1]. Update the parameter θ iteratively to minimize the weighted sum of squared residuals WRSS(θ):

[0074] θ (k+1) = θ (k) + Δθ

[0075] Among them, k represents the number of iterations, and Δθ represents the iteration increment, which is obtained by solving the following linear equations:

[0076]

[0077] Among them, λ is the damping factor that controls the step size, J is the Jacobian matrix of dimension 2M×P, and the odd-row elements J 2m-1,p and the even-row elements J 2m,p are respectively:

[0078]

[0079] Among them, p = 1, 2, …, P, P represents the number of parameters in the equivalent circuit model. When the relative parameter change or the change rate of WRSS converges, the updated fractional-order equivalent circuit model parameters θ = [4e-7, 2.3e-1, 1.12, 6e-2, 4.5e-1, 0.22, 0.11, 3e-3, 2e-2, 4.5e-2, 3.25, 4.5e-1], and the fitted electrochemical impedance spectrum is as Figure 4 shown.

[0080] Step 4: Calculate the Pearson linear correlation coefficient r between each parameter and SOH p :

[0081]

[0082] Among them, θ c represents the model parameters of the c-th cycle, represents the average value of the parameters, SOH c represents the health state of the c-th cycle, represents the average value of SOH for all cycles, and C is the number of cycles. The results are shown in Table 1:

[0083] Table 1

[0084]

[0085] Retain the significant parameters with the correlation coefficient |r p | > 0.7.

[0086] Step 5: Train the support vector regression function, calculate the mean square error MSE of the model through cross-validation, and after removing the α-th model parameter, calculate the change in the model performance through cross-validation as the importance score γ of the α-th parameter α :

[0087]

[0088] Delete the parameter with the minimum importance evaluation. Repeat this process to recursively eliminate redundant parameters until the remaining four key parameters that contribute the most to the SOH estimation are left.

[0089] Step 6. Through the common feature extractor F t Obtain the features X s and X t , where the source domain is the labeled battery aging electrochemical impedance spectroscopy data collected under laboratory controllable conditions, and the target domain is the unlabeled battery operation data under actual complex working conditions of dynamic temperature, variable load, and random charge and discharge. Calculate the average values μ s and μ t of the source domain and target domain features, and obtain the covariance matrices C s and C t :

[0090]

[0091] Adjust the covariance matrices of the source domain and target domain features through Correlation Alignment (CORAL) to reduce the distribution difference between the two.

[0092]

[0093] where ||·|| F is the F-norm and d is the feature dimension. Subsequently, match the source domain feature covariance matrix to the target domain through a linear transformation:

[0094]

[0095] Input the aligned target domain features into the multi-layer perceptron for SOH estimation.

[0096] Step 7. Use the retired batteries in the source domain working conditions for training, with the mean squared error loss as the loss function and Adam as the optimizer, and update the parameters of the model using the gradient backpropagation algorithm. The error results of the SOH estimation at three different temperatures are shown in Table 2:

[0097] Table 2

[0098]

[0099] The results show that the SOH estimation method for batteries based on the modified circuit structure in Example 2 has a mean absolute error of less than 1.4%, a root mean square error of less than 1.5%, and a mean absolute percentage error of less than 1.5% at three different temperatures. Compared with the commonly used circuit structure, the mean absolute error is increased by about 1.4%, the root mean square error is increased by about 1.6%, and the mean absolute percentage error is increased by about 1.6%. The proposed method realizes more accurate SOH estimation of retired batteries, more effectively identifies the internal health status of batteries, and provides a strong basis for the subsequent cascade utilization and recycling of retired batteries.

Claims

1. A method for estimating the health state of retired batteries based on EIS, characterized in that: It includes the following steps: Step 1, collect the electrochemical impedance spectroscopy data of retired batteries M represents the number of frequency points; Step 2, construct a fractional-order equivalent circuit model of the retired battery; Step 3, fit the electrochemical impedance spectrum and extract the parameters of the fractional-order equivalent circuit model; Step 4: Calculate the Pearson linear correlation coefficient r between each parameter and battery SOH for the fractional-order equivalent circuit model parameters. p ; retain the Pearson linear correlation coefficient r p Model parameters greater than a threshold; Step 5, calculate the mean square error MSE of the model, and perform secondary fine screening on the model parameters retained in Step 4 using recursive feature elimination and support vector regression; Step 6, construct a domain adaptation model for the state of health of retired batteries based on correlation alignment, and transfer the mapping relationship between the main aging mechanisms of the operating conditions in the source domain and the capacity attenuation to the target domain; Step 7, use the retired batteries under the source domain conditions to train the model, set the mean square error loss as the loss function, and update the parameters of the model; use the trained model to estimate the SOH of the retired batteries.

2. The method for estimating the health state of retired batteries based on EIS for domain adaptation according to claim 1, characterized in that: Charge in constant current-constant voltage mode until the cut-off current of 0.05C; disconnect the circuit and let it stand still after charging is completed; in the frequency range from 0.02 Hz to 20 kHz, with 10 frequency points per decade, set the amplitude of the excitation signal to 10 mV to obtain the electrochemical impedance spectrum data.

3. The method for estimating the health state of a retired battery based on EIS for domain adaptation according to claim 1, wherein: The fractional-order equivalent circuit model of the retired battery is: L1+R1+(R2 / / CPE1)+(R3 / / CPE2)+W Among them, + represents series connection, / / represents parallel connection; CPE represents a constant phase element, R represents resistance, L represents capacitance, and W represents a Warburg diffusion element.

4. The method for estimating the health state of a retired battery based on EIS for domain adaptation according to claim 1, wherein: The fractional-order equivalent circuit model of the retired battery is: L1+R1+(R2 / / CPE1)+(R3 / / C1)+((R4+W) / / CPE2) Among them, + represents series connection, / / represents parallel connection; L1 represents the parasitic inductance of the lead wire, R1 represents the ohmic impedance, R2 represents the ion transport resistance of the SEI film, R3 is the charge transfer resistance, R4 is the contact resistance of the bulk material, and C1 is the double-layer capacitance; CPE1 represents the non-ideal capacitance behavior of the SEI film, and CPE2 quantifies the low-frequency non-ideal polarization behavior caused by the aging of the electrode pore structure.

5. The method for estimating the health state of a retired battery based on EIS for domain adaptation according to claim 1, wherein: The method for extracting the parameters of the fractional-order equivalent circuit model is: Define the residual vector r(θ) of impedance data as follows: Among them, θ represents the parameters of the equivalent circuit model, Re(·) represents the real part, and Re(·) represents the imaginary part; Minimize the weighted residual sum of squares: WRSS(θ) = r(θ) T Wr(θ) Among them, the superscript T represents the matrix transpose; W is the weight matrix: Set the physical constraint relationship and initial value of the fractional-order equivalent circuit model parameter θ, and minimize the weighted residual sum of squares WRSS(θ) by iteratively updating the parameter θ: θ (k+1) = θ (k) + Δθ where k represents the number of iterations, and Δθ represents the iteration increment; when the relative parameter change or the change rate of WRSS converges, update the parameters of the fractional-order equivalent circuit model obtained, and fit the electrochemical impedance spectrum obtained.

6. The method for estimating the health state of a retired battery based on EIS for domain adaptation according to claim 5, characterized in that: The iterative increment Δθ is obtained by solving the following linear equations: where λ is the damping factor for controlling the step size, J is the Jacobian matrix of dimension 2M×P, and the elements in the odd rows and even rows of the matrix J 2m-1,p and J 2m,p are respectively: Among them, p = 1, 2, … P, and P represents the number of parameters in the equivalent circuit model.

7. The method for estimating the health state of retired batteries based on EIS for domain adaptation according to claim 1, characterized in that: Using the labeled battery aging electrochemical impedance spectroscopy data collected under laboratory-controlled conditions as the source domain, and the unlabeled battery operation data under the actual complex working conditions of dynamic temperature, variable load, and random charge and discharge as the target domain; through the common feature extractor F t Obtain the features X of the source domain and the target domain s and X t ,Calculate the mean values μ representing the features of the source domain and the target domain s and μ t ,Obtain the covariance matrices C of the features of the source domain and the target domain s and C t : Adjust the covariance matrices of the source domain and target domain features through relevant alignment to reduce the distribution difference between the two where ||·|| F is the F-norm and d is the feature dimension; subsequently, the source domain feature covariance matrix is matched to the target domain through a linear transformation: Input the aligned target domain features into a multi-layer perceptron for SOH estimation.

8. The method for estimating the health state of a retired battery based on EIS for domain adaptation according to claim 1, wherein: Use Adam as the optimizer and update the parameters of the model through the gradient backpropagation algorithm.

9. A computer-readable storage medium, on which a computer program is stored. When the computer program is executed in a computer, the computer is made to execute the method according to any one of claims 1 to 8.

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