SOH Estimation Method and System for Lithium-Ion Batteries Based on Electrochemical Impedance Spectroscopy

Abstract

The present invention belongs to the field of electronic technology, and relates to a method and system for estimating the state of health (SOH) of a lithium-ion battery based on electrochemical impedance spectroscopy. By using an improved relaxation time distribution algorithm to interpret and extract features from electrochemical impedance spectroscopy data, the robustness to noise and the ability to detect abnormal data are enhanced. The constructed neural network model adopts an improved joint loss convolutional neural network to perform end-to-end estimation of the SOH of a lithium-ion battery using electrochemical impedance spectroscopy. The neural network model fuses the DRT features calculated based on the relaxation time with the DRT features automatically extracted by the neural network model, avoiding the loss of feature information, effectively improving the performance of the neural network model, and enhancing the accuracy of the neural network model. Furthermore, through the improved neural network model, the SOH of a lithium-ion battery can be estimated quickly and accurately.

Description

Technical Field

[0001] The present invention belongs to the field of electronic technology and relates to a lithium battery SOH measurement technology, and in particular to a lithium ion battery SOH estimation method and system based on electrochemical impedance spectroscopy. Background Art

[0002] As a necessary condition and material basis for developing the marine economy and exploring marine resources, the importance of marine instrument research equipment is self-evident. The normal operation of marine instrument equipment is inseparable from a safe and stable energy system. Considering the complexity of marine environment operations (low temperature, high pressure, etc.), the reliability requirements for the energy system are also further improved. Lithium-ion batteries can be recycled, the battery reaction is reversible, the internal resistance is smaller than that of lithium primary batteries, and the load capacity is higher. Compared with lead-acid batteries and nickel-cadmium batteries, lithium-ion batteries have many advantages such as light weight, high specific energy, low self-discharge rate, and long cycle life. Therefore, lithium-ion batteries have become an indispensable part of the energy system of marine instrument research equipment such as submarines, ships, and underwater robots. Lithium-ion batteries will gradually age with the continuous increase of the use cycle, and the reduction of internal electron energy and number is the main factor causing the battery capacity to decline at the microscopic level. The capacity decay of lithium-ion batteries is a complex nonlinear process that couples physical and chemical reactions, mainly including the decomposition of electrolytes, changes in the mechanical structure of electrode materials, and the formation of lithium dendrites. It can be summarized as lithium ion loss (Loss of Lithium Inventory, LLI), active material loss (Loss of Active Material, LAM), and thickening of the solid electrolyte interface membrane (SEI). In order to quantify the capacity decay of lithium-ion batteries, researchers introduced the indicator of state of health (SOH). SOH is calculated by the ratio of actual battery capacity to nominal capacity, expressed as:

[0003] SOH=C present / C initial ×100%

[0004] In the formula, C present is the maximum capacity of the battery available under current conditions, C initial is the initial capacity of a new battery.

[0005] When the State of Health (SOH) of a lithium-ion battery decays to 80%, it is considered to reach the End of Life (EOL). At this time, the lithium-ion battery needs to be replaced and the waste lithium-ion battery needs to be recycled. Recycling waste lithium-ion batteries, as the last link in the use process of lithium-ion batteries, is conducive to realizing resource recycling and the cascade utilization of lithium-ion batteries, and can avoid environmental pollution caused by harmful substances in lithium-ion batteries. When the performance of a lithium-ion battery deteriorates to a certain extent, various accidents such as leakage and short circuit may occur.

[0006] Currently, there are mainly three methods for estimating the SOH of lithium-ion batteries: model-based methods, experimental feature analysis methods, and data-driven methods.

[0007] The model-based SOH estimation method can be divided into: Equivalent Circuit Model (ECM) and electrochemical model according to different models. The equivalent circuit model does not consider the specific electrochemical reactions inside the battery, but uses basic electrical components such as resistors, capacitors, and voltage sources to simulate the polarization reaction and self-discharge reaction inside the battery. Commonly used equivalent circuit models mainly include the Rint model (see Figure 1 ), the PNGV model (see Figure 2 ), the first-order RC model (i.e., the Thevenin model, see Figure 3 ), the second-order RC model (see Figure 4 ), and the second-order fractional-order model (see Figure 5 ). The model-based SOH estimation method mainly models the complex electrochemical dynamic system inside the lithium-ion battery. The method is complex and difficult to implement. Researchers need to have sufficient understanding of the electrochemical reactions and failure mechanisms inside the battery. Battery health-related parameters (internal resistance and capacity) can be obtained from the battery model using methods such as parameter identification and state estimation. However, due to the uncertainty of the model and the limitation of measured parameters, it is difficult to obtain reliable estimation results with clear physical meanings.

[0008] The experimental feature analysis method is a method based on electrochemistry analysis technology and signal processing technology. Its basic principle is to analyze the experimental data such as the collected current, voltage, and temperature to obtain some characteristic parameters (capacity, impedance, or custom health factor, etc.) that can reflect battery degradation, so as to achieve the calibration of SOH. The experimental feature analysis method can be divided into the time-domain working condition analysis method (such as: incremental curve analysis method, differential voltage curve analysis method, differential thermal voltammetry analysis method, etc.) and the frequency-domain impedance analysis method (such as: electrochemical impedance spectroscopy analysis method, etc.). The incremental curve (English: Incremental Curve, abbreviation: IC) analysis method focuses on analyzing the change of battery capacity Q with battery voltage V. By using the shape change of the IC curve, the decline trend of battery capacity can be analyzed, so as to estimate the capacity. The differential voltage (English: Differential Voltage, abbreviation: DV) curve analysis method describes the relationship between battery voltage V and battery capacity Q during charge and discharge. The capacity estimation of the DV curve is similar to that of the IC curve. By using the characteristics of the curve combined with the regression model, the battery capacity decline is estimated. The two have good consistency and reliability in battery capacity decline analysis. The differential thermal voltammetry (English: Differential Thermal Voltammetry, abbreviation: DTV) analysis method describes the relationship between temperature T and voltage V during battery charge and discharge. Compared with the DV curve and the IC curve, the DTV curve is more suitable for high-current charge and discharge (the temperature change is more obvious). The differential analysis method requires a complete charge and discharge test and a very low current (C / 25) to obtain available data to accurately evaluate the health state of the battery. Too large a current will lead to a decrease in measurement accuracy. At the same time, due to the very slow charge and discharge rate, noise will inevitably be introduced during the test, increasing the difficulty of data processing. It is not suitable for online SOH estimation and is only suitable for offline estimation of the battery. The electrochemical impedance spectroscopy (English: Electrochemical Impedance Spectroscopy, abbreviation: EIS) analysis method applies a small-amplitude sinusoidal current (constant current mode) or voltage (constant voltage mode) within a certain frequency range to the battery, measures the voltage or current response of the battery to obtain the complex impedance of the battery, and characterizes it on the complex plane to obtain the electrochemical impedance spectrum of the battery. The electrochemical impedance spectroscopy analysis method can apply a perturbation signal during battery cycling to achieve in-situ dynamic measurement, and can provide information on the internal electrochemical process of the battery without damaging the battery. However, the acquisition of the electrochemical impedance spectrum is relatively difficult, and the measurement time at low frequencies is relatively long. Summary of the Invention

[0009] In view of the above problems existing in the prior art, the present invention provides a method and system for estimating the SOH of a lithium-ion battery based on electrochemical impedance spectroscopy, which can accurately and quickly estimate the SOH of the lithium-ion battery.

[0010] To achieve the above object, a first aspect of the present invention provides a method for estimating the SOH of a lithium-ion battery based on electrochemical impedance spectroscopy, and the steps are as follows:

[0011] S1. Data acquisition step: Obtain the historical EIS data of the lithium-ion battery;

[0012] S2. Data processing step: Perform quality evaluation on the historical EIS data to obtain the original EIS data with qualified quality;

[0013] S3. DRT calculation step: Calculate the peak area of the DTR curve of the original EIS data according to the peak relaxation time, and use the peak area of the DTR curve as the DRT feature P DRT ;

[0014] S4. Model construction step: Construct a neural network model, and the neural network model includes an impedance spectrum information extraction layer, a feature fusion layer, and an SOH estimation layer; the impedance spectrum information extraction layer is used to extract the impedance feature P in the historical EIS data Z ; the feature fusion layer is used to fuse the DRT feature P DRT and the impedance feature P Z for feature fusion, and jointly splice them into a new impedance feature P new ; the SOH estimation layer takes the impedance feature P new as input and outputs the SOH estimation result;

[0015] S5. Actual data measurement step: Measure the actual EIS data of the lithium-ion battery in real time, and calculate the peak area of the DTR curve of the actual EIS data according to the peak relaxation time;

[0016] S6. SOH estimation step: Input the EIS data of the lithium-ion battery measured in real time and the peak area of the DTR curve of the actual EIS data into the neural network model to obtain the SOH of the lithium-ion battery.

[0017] In some embodiments, the data processing step includes:

[0018] S21. Error test step: Calculate the error of each frequency point in the historical EIS data;

[0019] S22. Evaluation step: Use the root mean square value of the overall frequency error of the historical EIS data as the evaluation index of the EIS quality. If the root mean square value is less than the set threshold, obtain the original EIS data and directly enter step S3, otherwise enter step S23;

[0020] S23, data cleaning step: based on the discontinuity between adjacent frequency points in the historical EIS data, remove the point with the largest discontinuity, repeat steps S21 to S23 until the original EIS data is obtained, and directly enter step S3.

[0021] In some embodiments, in step S2, before step S21, the data processing step further includes a screening step: eliminating abnormal data in the historical EIS data whose measurement error is greater than the set error.

[0022] In some embodiments, the neural network model further includes an EIS secondary synthesis layer, wherein the EIS secondary synthesis layer is based on the impedance characteristic P new The original EIS data are synthesized to obtain synthetic EIS data to evaluate the extracted impedance feature P. Z Whether the original EIS data can be fully described.

[0023] In some embodiments, after step S4, a model training step is also included: comparing the synthetic EIS data and the original EIS data, if the error between the synthetic EIS data and the original EIS data is greater than the minimum error, back propagation is performed to update the weights of the neural network model until the error between the synthetic EIS data and the original EIS data reaches the minimum error.

[0024] In order to achieve the above-mentioned object, the second aspect of the present invention provides a lithium-ion battery SOH estimation system based on electrochemical impedance spectroscopy, which is used to implement the lithium-ion battery SOH estimation method based on electrochemical impedance spectroscopy described in the first aspect of the present invention, and the system comprises:

[0025] Data acquisition module, to obtain historical EIS data of lithium-ion batteries;

[0026] EIS measurement device, used to measure the actual EIS data of lithium-ion batteries in real time;

[0027] The data processing module evaluates the quality of historical EIS data to obtain qualified original EIS data; the DRT calculation module calculates the peak area of ​​the DTR curve of the original EIS data according to the peak relaxation time, and uses the peak area as the DRT characteristic P DRT ; And calculate the peak area of ​​the DTR curve of the actual EIS data based on the peak relaxation time;

[0028] The model building module is used to build a neural network model, which includes an impedance spectrum information extraction layer, a feature fusion layer and a SOH estimation layer; the impedance spectrum information extraction layer is used to extract the impedance feature P in the historical EIS data. Z ; The feature fusion layer is used to combine the DRT feature P DRT And the impedance characteristic P ZPerform feature fusion and splice them together into a new impedance feature P new The SOH estimation layer is based on the impedance characteristic P new As input, output SOH estimation result;

[0029] The SOH estimation module inputs the real-time measured EIS data of the lithium-ion battery and the peak area of ​​the DTR curve of the actual EIS data into the neural network model to obtain the SOH of the lithium-ion battery.

[0030] In some embodiments, the data processing module includes:

[0031] Error test module, calculates the error of each frequency point in the historical EIS data;

[0032] The evaluation module uses the root mean square value of the overall frequency error of the historical EIS data as the evaluation index of the EIS quality. If the root mean square value is less than the set threshold, the original EIS data is obtained, otherwise it is unqualified EIS data. The data cleaning module removes the points with the largest discontinuity in the unqualified EIS data based on the discontinuity between adjacent frequency points in the historical EIS data.

[0033] In some embodiments, the data processing module further includes a screening module, and the screening module is used to eliminate abnormal data in the historical EIS data whose measurement error is greater than a set error.

[0034] In some embodiments, the neural network model further includes an EIS secondary synthesis layer, wherein the EIS secondary synthesis layer is based on the impedance characteristic P new The original EIS data are synthesized to obtain synthetic EIS data to evaluate the extracted impedance feature P. Z Whether the original EIS data can be fully described.

[0035] In some embodiments, the system further comprises a model training module for training the neural network model based on the synthetic EIS data and the original EIS data.

[0036] Compared with the prior art, the advantages and positive effects of the present invention are:

[0037] (1) Based on Electrochemical Impedance Spectroscopy (EIS), the present invention interprets and extracts features from EIS data through an improved relaxation time distribution algorithm, enhancing the robustness to noise and the ability to detect abnormal data. The constructed neural network model uses an improved combined loss convolutional neural network to perform end-to-end estimation of the State of Health (SOH) of lithium-ion batteries using EIS. The neural network model fuses the DRT features calculated based on the relaxation time with the DRT features automatically extracted by the neural network model, avoiding the loss of feature information, effectively improving the performance of the neural network model, enhancing the accuracy of the neural network model, and thus enabling the rapid and accurate estimation of the SOH of lithium-ion batteries through this neural network model.

[0038] (2) The present invention expands the available range of EIS data through EIS secondary synthesis, trains the neural network model in an unsupervised learning manner, and uses unlabeled data for training the neural network model, reducing the data annotation cost, alleviating feature overfitting, increasing the utilization rate of EIS data, and further improving the accuracy of the neural network model.

[0039] (3) For the two different functional layers of the SOH estimation layer and the EIS secondary synthesis layer in the neural network model constructed by the present invention, different loss functions are designed respectively, improving the prediction accuracy and stability of the neural network model. Description of the Drawings

[0040] Figures 1-5 is a common equivalent circuit model for lithium-ion batteries;

[0041] Figure 6 is a flowchart of the data processing steps described in the embodiment of the present invention;

[0042] Figure 7 is a schematic diagram of the original simulated impedance spectrum with artificial noise added in the embodiment of the present invention;

[0043] Figure 8 is a schematic diagram of the impedance spectrum after abnormal points are removed in the embodiment of the present invention;

[0044] Figure 9 is an EIS curve diagram of the cyclic aging of lithium-ion battery 1 described in the embodiment of the present invention;

[0045] Figure 10 is an EIS curve diagram of the cyclic aging of lithium-ion battery 2 described in the embodiment of the present invention;

[0046] Figure 11 is an EIS curve diagram of the cyclic aging of lithium-ion battery 3 described in the embodiment of the present invention;

[0047] Figure 12EIS curve of the cyclic aging of the lithium-ion battery 4 according to the embodiment of the present invention;

[0048] Figure 13 DRT change trend diagram of the cyclic aging of the lithium-ion battery 1 according to the embodiment of the present invention;

[0049] Figure 14 DRT change trend diagram of the cyclic aging of the lithium-ion battery 2 according to the embodiment of the present invention;

[0050] Figure 15 DRT change trend diagram of the cyclic aging of the lithium-ion battery 3 according to the embodiment of the present invention;

[0051] Figure 16 DRT change trend diagram of the cyclic aging of the lithium-ion battery 4 according to the embodiment of the present invention;

[0052] Figure 17 DRT plan view of the cyclic aging of the lithium-ion battery 1 according to the embodiment of the present invention;

[0053] Figure 18 DRT plan view of the cyclic aging of the lithium-ion battery 2 according to the embodiment of the present invention;

[0054] Figure 19 DRT plan view of the cyclic aging of the lithium-ion battery 3 according to the embodiment of the present invention;

[0055] Figure 20 DRT plan view of the cyclic aging of the lithium-ion battery 4 according to the embodiment of the present invention;

[0056] Figure 21 Schematic diagram of the convolution operation process of the one-dimensional convolution kernel according to the embodiment of the present invention;

[0057] Figure 22 Schematic diagram of the maximum pooling process of the maximum pooling layer according to the embodiment of the present invention;

[0058] Figure 23 Schematic diagram of the average pooling process of the average pooling layer according to the embodiment of the present invention;

[0059] Figure 24 Schematic diagram of the structure of the SOH estimation layer according to the embodiment of the present invention;

[0060] Figure 25 Structure block diagram of the SOH estimation system of the lithium-ion battery based on electrochemical impedance spectroscopy according to the embodiment of the present invention;

[0061] Figure 26 Schematic diagram of the EIS and its DRT simulated by the first set of parameters according to the embodiment of the present invention;

[0062] Figure 27Schematic diagram of EIS and DRT simulated with the second set of parameters in the embodiments of the present invention;

[0063] Figure 28 Schematic diagram of EIS and DRT simulated with the third set of parameters in the embodiments of the present invention;

[0064] Figure 29 Schematic diagram of EIS and DRT simulated with the fourth set of parameters in the embodiments of the present invention;

[0065] Figure 30 Schematic diagram of EIS and DRT of the second - order RC model in the embodiments of the present invention;

[0066] Figure 31 Schematic diagram of EIS and DRT of the equivalent circuit model containing two ZARC elements in the embodiments of the present invention;

[0067] Figure 32 Schematic diagram of the electrochemical impedance spectrum of the lithium - ion battery at 80% SOC in the embodiments of the present invention;

[0068] Figure 33 Schematic diagram of DRT comparison calculated by the DRT calculation method of the present invention, the traditional DRT algorithm and the unprocessed regularization algorithm in the embodiments of the present invention;

[0069] Figure 34 Schematic diagram of the EIS data and DRT calculation results of all sampling points in the full - frequency range in the embodiments of the present invention;

[0070] Figure 35 Schematic diagram of the EIS data and DRT calculation results of half of the sampling points in the full - frequency range in the embodiments of the present invention;

[0071] Figure 36 Schematic diagram of the EIS data and DRT calculation results of shortening the measurement frequency range and reducing the number of sampling points in the embodiments of the present invention;

[0072] Figure 37 Schematic diagram of the comparison result of the secondary - synthesized EIS and the real EIS at two different aging periods in the embodiments of the present invention;

[0073] Figure 38 Schematic diagram of the EIS synthesis error at different SOHs in the embodiments of the present invention;

[0074] Figure 39 Schematic diagram of the performance comparison of neural network models with different capacity annotation ratios in the embodiments of the present invention;

[0075] Figure 40 Schematic diagram of the comparison result of the SOH estimation of the neural network model of the present invention and the traditional CNN in the embodiments of the present invention;

[0076] Figure 41 Schematic diagram of the comparison of SOH estimation results with and without feature fusion in the neural network model of the present invention for the embodiments of the present invention;

[0077] Figure 42 Schematic diagram of the comparison of absolute errors of three models, namely Model 1, Model 2, and Model 3, described in the embodiments of the present invention.

[0078] In the figure, A, early stage of aging; B, late stage of aging; C, maximum error point; 1, data acquisition module; 2, EIS measurement device; 3, data processing module; 31, error test module; 32, evaluation module; 33, data cleaning module; 34, screening module; 4, DRT calculation module; 5, model construction module; 6, SOH estimation module; 7, model training module. Detailed implementation manners

[0079] Next, the present invention will be specifically described through exemplary implementation manners. However, it should be understood that, without further narration, the elements, structures, and features in one implementation manner can also be beneficially combined into other implementation manners.

[0080] Accurately and quickly obtaining the health status of lithium-ion batteries is crucial for ensuring the normal operation of marine instrument research equipment, the stable acquisition of data, and the successful completion of tasks. As an important part of the energy system of marine instrument research equipment, if the health status of lithium-ion batteries is not good, it may lead to failures of marine instrument research equipment, data loss, or task failures, etc., bringing serious impacts to aspects such as marine surveys, scientific research, and resource development. At the same time, accurate health status assessment provides an information basis for the task scheduling and equipment maintenance of marine instrument research equipment, avoiding waste of time and cost caused by unnecessary equipment maintenance. By real-time monitoring and analyzing the health status of lithium-ion batteries, faults or potential problems in lithium-ion batteries can be discovered in time, and they can be effectively maintained and managed, extending the service life of lithium-ion batteries, reducing losses and wastes caused by lithium-ion battery failures, and enhancing the reliability and stability of marine instrument research equipment while improving the utilization rate and economic benefits of marine instrument research equipment. In order to accurately and quickly obtain the health status of lithium-ion batteries, the present invention provides a method and system for estimating the SOH of lithium-ion batteries based on electrochemical impedance spectroscopy. Based on electrochemical impedance spectroscopy data, the electrochemical impedance spectroscopy data is interpreted and feature-extracted by a DRT calculation method based on relaxation time, and an improved joint loss convolutional neural network (i.e., the neural network model constructed by the present invention) is used for end-to-end estimation of the SOH of lithium-ion batteries. Through the method and system for estimating the SOH of lithium-ion batteries based on electrochemical impedance spectroscopy of the present invention, the SOH of lithium-ion batteries can be accurately and quickly estimated, and the accuracy of the estimated SOH of lithium-ion batteries is high.

[0081] In the first aspect of the present invention, an embodiment provides a method for estimating the SOH of a lithium-ion battery based on electrochemical impedance spectroscopy, and the steps are as follows:

[0082] S1. Data acquisition step: Obtain the historical EIS data of the lithium-ion battery.

[0083] S2. Data processing step: Perform quality evaluation on the historical EIS data to obtain qualified original EIS data.

[0084] In some embodiments, referring to Figure 6 , the data processing step further includes:

[0085] S21. Error test step: Calculate the error of each frequency point in the historical EIS data.

[0086] Specifically, the specific steps for calculating the error of each frequency point in the historical EIS data are as follows:

[0087] Use the time constants of different RC elements to fit the impedance in the frequency domain from the time domain and express it as:

[0088]

[0089] In the formula, represents the impedance in the frequency domain fitted from the time domain, N represents the number of measured frequency points in the impedance spectrum, R ∞ , L respectively represent the magnitudes of the series-connected resistance and capacitance; τ k = R k C k represents the time constant of the kth RC element, R k , C k respectively represent the magnitudes of the resistance and capacitance in the kth RC element.

[0090] The error of each frequency point can be expressed as:

[0091]

[0092] In the formula, Error i represents the error of the frequency point, Z(ω i ) represents the actual impedance in the frequency domain.

[0093] The equivalent minimization error of the time-domain fitting of the impedance is expressed as Error = ∑ i |w(ω i )·Error i | 2 , w(ω i ) is the weight of different frequency points, and it is rewritten in matrix form as:

[0094] Error = (Ax - Z) H W T W(Ax - Z) (3)

[0095] where the superscripts T and H represent ordinary transpose and conjugate transpose respectively, the specific values of matrices A and B are given by equations (4) and (5), W = diag(w) is a diagonal matrix of weights ω as shown in equation (6), where the default value of the elements is 1, and Z represents the matrix of impedance in the frequency domain.

[0096]

[0097] B = [R ∞ L R1 R2 … R N T (5)

[0098]

[0099] Equation (3) is rewritten as equation (7) to transform it into a quadratic programming problem with element constraints.

[0100]

[0101] In the formula, A r represents the real part of the complex matrix, A i represents the imaginary part of the complex matrix, Z r represents the real part of the impedance, Z i represents the imaginary part of the impedance;

[0102] After obtaining the minimized error the estimated value of the impedance spectrum is represented by equation (8):

[0103]

[0104] The error at a single frequency point is expressed as:

[0105]

[0106] S22. Evaluation step: Using the root mean square value ε kk of the overall frequency error of the historical EIS data as the evaluation index of the EIS quality. If the root mean square value ε kk is less than the set threshold ε1, it is considered that the quality of the EIS data meets the requirements, and this EIS data is used as the original EIS data and directly enters step S3; otherwise, it enters step S23.

[0107] ​S23. Data cleaning step: Based on the discontinuity between adjacent frequency points in the historical EIS data, remove the point with the largest discontinuity. Repeat steps S21 to S23 until the historical EIS data meets the quality requirements to obtain the original EIS data, and directly proceed to step S3.

[0108] Specifically, calculate the discontinuity ε between adjacent frequency points in the historical EIS data kk2 , if the discontinuity ε of the current frequency point i kk2 is greater than the set threshold ε2, and the current frequency point i is the point i with the largest discontinuity max , then delete this frequency point, and recalculate the discontinuity ε between adjacent frequency points in the historical EIS data after deleting this frequency point i kk2 , and repeat the judgment on whether the discontinuity ε kk2 is greater than the set threshold ε2, and whether the current frequency point i is the point i with the largest discontinuity max , until the discontinuity ε kk2 is less than the set threshold ε2, and the current frequency point i is not the point i with the largest discontinuity max , and the historical EIS data meets the quality requirements to obtain the original EIS data, and directly proceed to step S3.

[0109] It should be noted that in the EIS data, the abnormality degree of the data is defined as the discontinuity between adjacent frequencies. The discontinuity is defined as the difference between the smoothed impedance curve and the unsmoothed impedance curve, and the mathematical definition is:

[0110] ε(ω) = |Z(ω) - Z 平滑 (ω)| (10)

[0111] In the formula, ε(ω) represents the difference between the smoothed impedance curve and the unsmoothed impedance curve, Z(ω) represents the unsmoothed impedance curve, and Z 平滑 (ω) represents the smoothed impedance curve.

[0112] The present invention uses a Savitzky-Golay filter (hereinafter referred to as: S-G filter) for smoothing the impedance curve. The Savitzky-Golay filter is a digital signal processing technology proposed by Schafer and is widely used for smoothing digital signals. The S-G filter has characteristics that other filters (such as FIR filters, IIR filters, etc.) do not have. For example, the S-G filter has a smoother response and fewer amplitude mutations in the frequency domain, and it can filter out noise while keeping the shape and width of the signal unchanged. The S-G filter uses the least squares to determine the weighted coefficients of the polynomial and cooperates with a moving window for local polynomial approximation to achieve signal smoothing. The S-G filter can directly process time-domain signals, avoiding the conversion between the time domain and the frequency domain of traditional filters and improving the calculation speed.

[0113] The smoothed EIS data can be fitted with a polynomial shown in Equation (11), expressed as:

[0114]

[0115] where a k represents the coefficient of the fitted polynomial.

[0116] Introduce an auxiliary matrix C to transform the coefficient matrix into:

[0117]

[0118] where C = {a n,i}, a n,i = n i , -M ≤ n ≤ M, 0 ≤ i ≤ N, and x represents the value corresponding to the original data point within the sliding window. To prevent normal data from being screened out, only one point with the largest discontinuity is deleted each time. After deleting the abnormal data, the discontinuities of the points around the deleted point will be recalculated.

[0119] Figure 7 and Figure 8 are the original simulated impedance spectrum with added artificial noise and the impedance spectrum after removing abnormal points respectively. It can be seen from Figure 7 and Figure 8 that data cleaning has successfully removed the red artificial noise points, ensuring the accuracy of the data.

[0120] In some embodiments, in the step S2, before the step S21, the data processing step further includes a screening step: removing abnormal data in the historical EIS data with a measurement error greater than the set error. Using the historical EIS data with abnormal data removed as the basic data for DRT calculation improves the robustness to abnormal points.

[0121] S3. DRT calculation step: Calculate the peak area of the DTR curve of the original EIS data according to the peak relaxation time, and use the peak area of the DTR curve as the DRT feature P DRT .

[0122] Specifically, the specific method for calculating the peak area of the DTR curve of the original EIS data according to the peak relaxation time is:

[0123] The peak area of the DTR curve is defined as:

[0124]

[0125] where S represents the peak area of the DTR curve, τ1 is the relaxation time at the start of the peak, and τ2 is the relaxation time at the end of the peak;

[0126] After discretization, it becomes:

[0127]

[0128] In the formula, n represents the number of peaks.

[0129] It should be noted that the use of the EIS and DRT comparison diagrams can highlight the impedance changes of batteries in different aging states. For example: Refer to Figures 9 to 12 , and select the EIS curves of 4 lithium-ion batteries (i.e., lithium-ion battery 1, lithium-ion battery 2, lithium-ion battery 3, and lithium-ion battery 4) at different cycle periods in the aging experiment. The peak heights of the DRT curves in different health states are not the same. Refer to Figures 13 to 16 The DRT peaks of the four batteries shown in Figures 17 to 20 all increase with the increase of the cycle period. To facilitate the analysis of the positional change relationship between the peaks, they are plotted on a plane graph, as shown in

[0130] Figures 17 to 19 Each peak shown in Figure 20 represents a different electrochemical process. The P1 peak and the P2 peak correspond to the charge transfer effect and the double-layer capacitance respectively. In the later stage of the aging process (with a larger number of cycles), the P2 peak shows a certain upward trend compared to the initial cycle. The peak value of the P3 peak increases most significantly and continuously moves to the right, which explains the increase in the radius of the mid-frequency arc in the EIS curve.

[0131] The present invention proposes to use the relaxation time distribution function to interpret complex EIS data. Aiming at the noise sensitivity problem of traditional regularization methods, a new calculation method for calculating the peak area of the DRT curve based on the peak relaxation time is given, which has high noise robustness. Using the DRT peak area as a feature of the EIS data provides a corresponding data basis for battery health estimation.

[0132] S4, model construction step: construct a neural network model, the neural network model includes an impedance spectrum information extraction layer, a feature fusion layer and a SOH estimation layer; the impedance spectrum information extraction layer is used to extract the impedance feature P in the historical EIS data Z ; The feature fusion layer is used to combine the DRT feature P DRT And the impedance characteristic P Z Perform feature fusion and splice them together into a new impedance feature P new The SOH estimation layer is based on the impedance characteristic P new is input and outputs SOH estimation result.

[0133] S5, actual data measurement step: measuring the actual EIS data of the lithium-ion battery in real time, and calculating the peak area of ​​the DTR curve of the actual EIS data according to the peak relaxation time.

[0134] S6, SOH estimation step: inputting the real-time measured EIS data of the lithium-ion battery and the peak area of ​​the DTR curve of the actual EIS data into the neural network model to obtain the SOH of the lithium-ion battery.

[0135] In some embodiments, the neural network model further includes an EIS secondary synthesis layer, wherein the EIS secondary synthesis layer is based on the impedance characteristic P new The original EIS data are synthesized to obtain synthetic EIS data to evaluate the extracted impedance feature P. Z Whether the original EIS data can be fully described. Expand the available range of EIS data through EIS secondary synthesis.

[0136] Specifically, in some embodiments, the impedance spectrum information extraction layer is composed of four convolution modules and two fully connected layers, wherein each convolution module is composed of a convolution layer and a pooling layer, and is passed to the next layer after the activation function. The convolution layer uses convolution and convolution with the impedance data to extract local features (i.e., impedance features P Z ). Considering that the information contained in the impedance spectrum in the high, medium and low frequency bands is different, in order to retain this information to the greatest extent, the average pooling layer is selected for pooling operation. The Leaky ReLU activation function is used to introduce nonlinearity into the convolution module to accelerate the convergence speed of the neural network model. Through the cooperation between four convolution modules, two fully connected layers and the Leaky ReLU activation function, the high-dimensional impedance features are extracted and the feature vector is formed. The impedance feature description of the entire historical EIS data is as follows:

[0137] P Z =f1([Z real Z imag ] T ) (15)

[0138] In the formula, f1(·) represents the non - linear model generated by the impedance spectrum information extraction layer, and P Z is an N×1 vector of extracted impedance features, where N is the length of the impedance spectrum sequence, and Z real and Z imag are the real and imaginary parts of the impedance spectrum sequence, respectively.

[0139] It should be noted that the convolution module in the impedance spectrum information extraction layer is one of the important core components for the neural network model to achieve the function of automatic feature extraction. Its main design purpose is to learn the features of the input data. Specifically, the convolutional layer is usually composed of multiple convolutional kernels, and the convolutional kernels are used to calculate and generate different feature maps. First, through the convolution operation between the input data and the convolutional kernels, and then taking the operation result of the convolution as the input of the non - linear activation function, a new feature map is obtained. Different from traditional two - dimensional image recognition operations, EIS data is one - dimensional sequence data, and two - dimensional convolutional kernels cannot be used for feature extraction. Instead, one - dimensional convolutional kernels are used for convolution operations. One - dimensional convolutional kernels only slide in one direction. For each position, the convolutional kernel only considers the information of the current position and its adjacent positions, as Figure 21 shown in the convolution operation process of the one - dimensional convolutional layer.

[0140] To ensure that the feature map can correctly reflect different features of the input, the convolutional kernels use the same weights at all positions of the input data. The feature value of the k - th feature map of the l - th layer at the position (i, j) is obtained from Equation (16).

[0141]

[0142] In the formula, is the weight of the k - th convolutional kernel of the l - th layer, is the bias of the k - th convolutional kernel of the l - th layer, is the input data.

[0143] In the convolutional layer, each neuron used to generate the feature map is only connected to a small area of adjacent neurons in the previous layer. The receptive field of the neuron is this adjacent area. By changing the size and stride of the convolutional kernel, the size of the receptive field can be controlled. If you want to capture local features of the input data, a smaller receptive field is required. On the contrary, if you want to capture global features, the receptive field needs to be increased. The size of the receptive field determines the performance of the entire neural network model and needs to be adjusted according to specific data to achieve the best feature extraction effect.

[0144] It should also be noted that the pooling layer is another important component in the impedance information extraction layer. By downsampling the feature map, it aggregates each region of the feature map and compresses the information within that region into a single value, reducing the size of the feature map and also the number of parameters in the neural network model. Since the pooling operation only involves information within a local region, the pooling operation has translational invariance, that is, the translation of the input sequence does not change the output result of the neural network model. The pooling operation is usually performed after the convolution operation, which can further reduce the data dimension, reduce the amount of computation, and improve the robustness and generalization ability of the neural network model. The pooling function can be expressed as pool(·), for each feature value The pooled feature value is shown in Equation (17):

[0145]

[0146] where is the pooled feature value, and R i,j is a partial region around the position (i, j).

[0147] Commonly used pooling operations include two types: average pooling and max pooling. Refer to Figure 22 , the max pooling layer divides the input feature map into several non-overlapping regions according to the size of the pooling window. In each pooling window, the max pooling layer takes the maximum value within the window as the feature output. Increasing the pooling window can quickly reduce the size of the feature map, but it may also lead to the loss of more feature information. Therefore, the size of the pooling window needs to be specifically determined according to the size of the input feature map and the stride of the convolutional layer. Refer to Figure 23 , average pooling uses a sliding window, slides on the feature map and calculates the average value within each window. The average pooling layer can increase the translational invariance of the model because the average pooling operation is not affected by the change in the position of the input feature map.

[0148] After comprehensively considering the advantages and disadvantages of max pooling and average pooling, the impedance information extraction layer of the present invention selects average pooling as the pooling layer, which can reduce the loss of feature information and suppress overfitting.

[0149] It should also be noted that the activation function is an important means to introduce non-linearity into the entire neural network model. For different tasks, it is crucial to select an appropriate activation function. Different activation functions have different advantages and disadvantages when dealing with the non-linear transformation of input data. Some can alleviate the problem of gradient disappearance, and some can improve the stability and robustness of the network, etc.

[0150] Using an activation function to perform a non - linear transformation on the output after the convolutional layer can increase the expressive power of the neural network model. Commonly used activation functions usually have special properties such as non - linearity, monotonic increase, and continuous differentiability. These special properties enable the neural network model to have a stronger fitting ability when dealing with complex non - linear problems. At the same time, they can also make the neural network model better adapt to complex data distributions and, to a certain extent, prevent the occurrence of overfitting phenomena. The activation function used in this invention is the Leaky ReLU function.

[0151] The definition of the Leaky ReLU function is:

[0152]

[0153] The Leaky ReLU function is an improved version of the ReLU function. Different from the ReLU function, the Leaky ReLU function introduces a slope of size α when less than 0, and its value range is between (0, 1). In this way, the part less than 0 is only compressed instead of being completely discarded, avoiding the occurrence of the "neuron death" phenomenon when the input value is less than 0.

[0154] Specifically, the feature fusion layer fuses the DRT feature P DRT and the impedance feature P Z to jointly splice them into a new impedance feature P new , expressed as:

[0155] P new = f2(P Z , P DRT ) (19)

[0156] In the formula, f2(·) represents the feature splicing function of the feature fusion layer.

[0157] It should be noted that in the new impedance feature P new , the impedance feature P Z extracted by the convolutional layer and the DRT feature P DRT both come from the same impedance spectrum sequence. There is a strong correlation and mutual dependence between them. Simply fusing the two parts of features by splicing or weighted summation may not be able to capture the complex correlation inside the feature sequence. Therefore, to improve the performance of feature extraction, a self - attention mechanism is introduced into the feature fusion layer network.

[0158] The self - attention mechanism can adaptively calculate the relative importance between features at different positions and dynamically adjust the weights of features according to the calculation results. By introducing the self - attention mechanism, the neural network model can better capture the correlation inside the feature sequence, thereby improving the prediction performance and generalization ability of the neural network model.

[0159] In the network structure of the feature fusion layer, the DRT feature P DRT is only used for updating the neuron weights of the SOH estimation layer and the EIS secondary synthesis layer, and does not participate in the gradient backpropagation of the impedance information extraction layer. This is because the DRT feature P DRT is pre-determined and does not need to be updated through backpropagation. Only the weights of the neurons in its corresponding layer need to be updated. On the contrary, backpropagation is mainly for the impedance feature P Z extracted by the impedance information extraction layer to update the weights to optimize the feature extraction performance.

[0160] Specifically, in some embodiments, the SOH estimation layer is a module composed of two fully connected layers, which receives the new impedance feature P new from the feature fusion layer as input and outputs the estimated result of the SOH. Its mathematical expression is:

[0161]

[0162] In the formula, is the estimated value of the true battery health y, and f3(·) represents the SOH estimation function of the SOH estimation layer. It should be noted that to implement the SOH estimation function, the first fully connected layer maps the input feature vector to an intermediate feature space, and the second fully connected layer maps the intermediate feature space to the final SOH estimated value. These mapping relationships are trained through supervised learning, that is, using the true SOH value as the supervision signal during the training process to optimize the network parameters so that it can accurately estimate the health state of the battery. The SOH estimation layer uses the fused feature signal, which can effectively avoid the problem of information loss during the feature extraction process, enabling the neural network model to better utilize the information contained in the original data and improving the prediction accuracy and the generalization performance of the model.

[0163] See Figure 24 the structural schematic diagram of the SOH estimation layer shown. It is one of the key layers that determine the output result of the entire network. The connection method of the neurons in the SOH estimation layer is the same as that of the traditional ANN, where each neuron is connected to the corresponding neuron in the previous layer. Its function is to flatten the feature output result and convert it into the form of a one-dimensional vector. By changing the weights and biases between the neurons, the features extracted after convolution and pooling are further combined and transformed to generate a higher-level feature representation in the form of global semantic information, and then output. The specific mathematical definition is shown in Equation (20):

[0164] Y = W T X + b (20)

[0165] Wherein, W is the weight vector of each neuron; b is the bias, and its length is the same as that of the output feature map Y. Each neuron in the SOH estimation layer has a learnable weight and bias, which are used to control the propagation and transformation of signals. The final result can be used for tasks such as classification and regression. The parameter information such as the weights and biases of the SOH estimation layer is optimized using the backpropagation algorithm to minimize the neural network model error and improve the generalization ability of the neural network model.

[0166] Specifically, in some embodiments, the EIS secondary synthesis layer consists of two fully connected layers. Its main purpose is to use the fused feature information to perform secondary synthesis on the original impedance signal to evaluate whether the impedance features extracted by the impedance spectrum information extraction layer can completely describe the original EIS sequence, so that the impedance features obtained by the impedance spectrum information extraction layer are more meaningful. The impedance sequence obtained by the secondary synthesis of the EIS secondary synthesis layer is expressed as:

[0167] Z C = f4(P new ) (20)

[0168] Wherein, f4(·) represents the secondary synthesis function of the EIS secondary synthesis layer, and Z C is the impedance sequence after secondary synthesis, specifically expressed as:

[0169] Z C = [Z Creal1 , Z Creal2 , …, Z CrealN , Z Cimag1 , …, Z CimagN (21)

[0170] Wherein, Z Creali , i = 1, ..., N represents the real part of the impedance feature P new , and Z Cimagi , i = 1, ..., N represents the imaginary part of the impedance feature P new .

[0171] It should be noted that different from the SOH estimation layer, the EIS secondary synthesis layer uses the unsupervised learning method to train the neural network model, that is, it does not use labeled data for training, but conducts error analysis by comparing the impedance sequence after secondary synthesis with its own original impedance sequence. Training in the unsupervised learning method helps to reduce the data annotation cost and alleviate the phenomenon of feature overfitting.

[0172] In some embodiments, after the step S4, a model training step is further included: comparing the synthesized EIS data with the original EIS data. If the error between the synthesized EIS data and the original EIS data is greater than the minimum error, backpropagation is performed to update the weights of the neural network model until the error between the synthesized EIS data and the original EIS data reaches the minimum error. Training in an unsupervised learning manner helps reduce the data annotation cost and alleviate the phenomenon of feature overfitting.

[0173] Specifically, in some embodiments, for two different functional layers, namely the SOH estimation layer and the EIS secondary synthesis layer, the total loss function of the neural network model is obtained by weighted summation of the loss function of the SOH estimation layer and the loss function of the EIS secondary synthesis layer.

[0174] The goal of the SOH estimation layer is to minimize the error between the estimated battery capacity value output by the SOH estimation layer and the true battery capacity value corresponding to the impedance spectrum, so as to achieve accurate SOH estimation. Therefore, the loss function of the SOH estimation layer is expressed as:

[0175]

[0176] In the formula, m is the sample size of the SOH annotation of the lithium-ion battery, is the estimated battery capacity value of the i-th sample output by the SOH estimation layer, and y i is the true battery capacity value of the i-th sample corresponding to the impedance spectrum.

[0177] The optimization goal of the EIS secondary synthesis layer is to minimize the error between the re-synthesized impedance spectrum and the true impedance spectrum. Then the loss function of the EIS secondary synthesis layer is expressed as:

[0178]

[0179] In the formula, is the impedance of the i-th sample synthesized by the EIS secondary synthesis layer, is the real part of the impedance of the i-th sample synthesized by the EIS secondary synthesis layer, is the imaginary part of the impedance of the i-th sample synthesized by the EIS secondary synthesis layer, Z′ i is the real part of the true impedance of the i-th sample, and Z″ is the imaginary part of the true impedance of the i-th sample.

[0180] Then the total loss function of the neural network model is expressed as:

[0181] L total =α·L1(δ1)+(1 - α)·L2(δ2) (22)

[0182] In the formula, δ1 is the parameter set used by the SOH estimation layer, δ2 is the parameter set used by the EIS synthesis layer, α is used to balance the contributions of the two loss functions, and the value of α ranges from 0 to 1. When α = 0, only the loss function of the EIS secondary synthesis layer is considered; when α = 1, only the loss function of the SOH estimation layer is considered, and the loss function of the EIS secondary synthesis layer is ignored. In actual training, α needs to be adjusted according to the specific situation of the data set and the task to achieve the best training effect.

[0183] Specifically, in some embodiments, the gradient descent method is used for backpropagation of the loss to optimize the parameter set of the neural network model and improve the performance of the neural network model.

[0184] Specifically, in some embodiments, the neural network model is constructed based on the PyTorch package (version 1.10) in Python 3.6 and trained using an NVIDIA GeForce GTX 1080 graphics processing unit. To achieve the above object, the second aspect of the present invention provides a lithium-ion battery SOH estimation system based on electrochemical impedance spectroscopy for implementing the lithium-ion battery SOH estimation method based on electrochemical impedance spectroscopy described in the first aspect of the present invention. Refer to Figure 25 , the system includes:

[0185] A data acquisition module 1 for acquiring historical EIS data of the lithium-ion battery;

[0186] An EIS measurement device 2 for real-time measurement of the actual EIS data of the lithium-ion battery;

[0187] A data processing module 3 for evaluating the quality of the historical EIS data to obtain qualified original EIS data; a DRT calculation module 4 for calculating the peak area of the DTR curve of the original EIS data based on the peak relaxation time and taking the peak area as the DRT feature P DRT ; and calculating the peak area of the DTR curve of the actual EIS data based on the peak relaxation time;

[0188] A model construction module 5 for constructing a neural network model, the neural network model including an impedance spectrum information extraction layer, a feature fusion layer, and an SOH estimation layer; the impedance spectrum information extraction layer is used for extracting the impedance feature P in the historical EIS data Z ; the feature fusion layer is used for fusing the DRT feature P DRT and the impedance feature P Z for feature fusion and jointly splicing them into a new impedance feature P new ; the SOH estimation layer takes the impedance feature P new as input and outputs the SOH estimation result;

[0189] The SOH estimation module 6 inputs the real-time measured EIS data of the lithium-ion battery and the peak area of ​​the DTR curve of the actual EIS data into the neural network model to obtain the SOH of the lithium-ion battery.

[0190] In some embodiments, see Figure 25 , the data processing module 3 includes:

[0191] An error testing module 31 calculates the error of each frequency point in the historical EIS data;

[0192] The evaluation module 32 uses the root mean square value of the overall frequency error of the historical EIS data as the evaluation index of the EIS quality. If the root mean square value is less than the set threshold, the original EIS data is obtained, otherwise it is unqualified EIS data; the data cleaning module 33 removes the point with the largest discontinuity in the unqualified EIS data based on the discontinuity between adjacent frequency points in the historical EIS data.

[0193] In some embodiments, see Figure 25 The data processing module 3 also includes a screening module 34, which is used to eliminate abnormal data in the historical EIS data whose measurement error is greater than the set error.

[0194] In some embodiments, the neural network model further includes an EIS secondary synthesis layer, wherein the EIS secondary synthesis layer is based on the impedance characteristic P new The original EIS data are synthesized to obtain synthetic EIS data to evaluate the extracted impedance feature P. Z Whether the original EIS data can be fully described. The structure of the EIS secondary synthesis layer is the same as the structure of the EIS secondary synthesis layer described in the above method, and will not be repeated here.

[0195] In some embodiments, see Figure 25 The system also includes a model training module 7, which is used to train the neural network model based on the synthetic EIS data and the original EIS data.

[0196] Specifically, the model training module trains the neural network model in the following specific method: comparing the synthetic EIS data and the original EIS data, if the error between the synthetic EIS data and the original EIS data is greater than the minimum error, then back propagation is performed to update the weight of the neural network model until the error between the synthetic EIS data and the original EIS data reaches the minimum error. Training in an unsupervised learning manner helps reduce data annotation costs and alleviate the phenomenon of feature overfitting.

[0197] Specifically, in some embodiments, the EIS measurement device is an electrochemical workstation, such as BioLogic MPG-205 electrochemical workstation.

[0198] Specifically, the method for calculating the DRT by the DRT calculation module is the same as the method described in the above method, and will not be elaborated here.

[0199] Specifically, in the neural network model, the structures of the impedance spectrum information extraction layer, the feature fusion layer, and the SOH estimation layer are the same as those of the impedance spectrum information extraction layer, the feature fusion layer, and the SOH estimation layer described in the above method, and will not be elaborated here again. The total loss function of the neural network model is the same as the total loss function described in the above method, and will not be elaborated here either.

[0200] The following combines specific embodiments to verify the effectiveness of the DRT calculation method in the above-mentioned method and system for estimating the SOH of lithium-ion batteries based on electrochemical impedance spectroscopy, and to evaluate the accuracy of the constructed neural network model.

[0201] 1. Verification of the effectiveness of the DRT calculation method

[0202] (1) Use the simulated impedance spectrum generated by a fractional-order RC equivalent circuit model containing one impedance arc (ZARC element) to verify the effectiveness of the DRT calculation method of the present invention. The fractional-order RC equivalent circuit model consists of an ohmic internal resistance R ∞ and an R-CPE link. The R-CPE link contains a resistor and a constant phase element (i.e., CPE element), and its impedance value is expressed as:

[0203]

[0204] In the formula, R ∞ , R is the resistance, τ is the equivalent time constant of the R-CPE link, and β represents the order of the fractional-order RC equivalent circuit model, and its value range is between 0.5 and 1.

[0205] Correspondingly, the DRT numerical expression of the fractional-order RC equivalent circuit model is:

[0206]

[0207] In the formula, τ0 is the initial equivalent time constant of the R-CPE link.

[0208] The simulated impedance spectrum data is determined by pre-determined circuit parameters. The generated simulated impedance spectrum data is all corrupted by random Gaussian noise ζ to simulate various accidental noises generated in real experiments, ζ = ζ re + ζ im . Among them, ζ re and ζ imThey are independent normal random variables with a mean of 0 and a variance of σ2n. By changing the magnitude of the noise coefficient, the overall noise level can be controlled. In addition, several artificially generated error points are added to the simulated impedance spectrum data to increase the interference to the data. See Table 1 for the relevant parameters of the equivalent circuit model.

[0209] Table 1

[0210] Group <![CDATA[R ∞ (Ω)]]> R (Ω) τ β Noise First group 10 50 1 0.73 0.1 Second group 10 50 1 0.73 0.5 Third group 10 50 1 0.73 1 Fourth group 8 30 1 0.85 1

[0211] By adding different levels of noise to the simulated impedance spectra with four groups of different parameters, the robustness of the DRT calculation method proposed in the present invention is verified. Figures 26 to 29 The results of the four groups of experiments are shown respectively. Table 2 shows the relative errors between the peak areas of the curves of each group and the true values.

[0212] Table 2

[0213] Group Calculated area value True area value Relative error First group 49.931 49.924 0.014％ Second group 49.955 49.924 0.062％ Third group 49.960 49.924 0.072％ Fourth group 29.986 29.964 0.073％

[0214] The first group, the second group, and the third group are control groups for each other. The model parameters of their fractional-order RC equivalent circuit models are the same, and different levels of Gaussian random noise are applied respectively. It can be seen that: at a low noise level (noise coefficient of 0.1), the positions and widths of the DRT peaks calculated by the DRT calculation algorithm of the present invention are basically the same as the true DRT; at a medium noise level (noise coefficient of 0.5), the positions of the peaks and relaxation times are slightly shifted; at a high noise level (noise coefficient of 1), the peak position has a greater shift compared with the second group, but the overall peak width can still maintain the same level as the true value, and the relative error of the peak area is only 0.073% at most. The third group and the fourth group are control groups for each other. They have the same noise level, but the parameters of the fractional-order RC equivalent circuit model are different. The DRT calculation results of both show consistency, indicating that the parameters of the fractional-order RC equivalent circuit model do not affect the results of the DRT calculation algorithm. In summary, the DRT calculation algorithm proposed in the present invention can accurately recover the DRT of the simulated impedance spectrum containing a single ZARC element under the influence of different levels of noise. Although the shapes of the DRT curves are slightly different, the error between the area enclosed by the peaks and the theoretical value is very small.

[0215] (2) For the DRT calculation of complex impedance spectra containing multiple time constants, two different equivalent circuit models are used to verify the effectiveness of the DRT calculation method of the present invention. The first equivalent circuit model is a second-order RC model with similar time constants; the second equivalent circuit model is an equivalent circuit model containing two ZARC elements. Both of the above two equivalent circuit models include the ohmic internal resistance R∞, and the same low noise intensity is used to interfere with the impedance spectrum data.

[0216] Figure 30 andFigure 31 The EIS data with a small amount of noise added to two equivalent circuits respectively and the calculated DRT are shown. It can be seen from the figure that the width of the calculated DRT curve almost completely matches the true value, only the height of the peak is slightly different. For the overlapping EIS data in the frequency domain, the DRT calculation method proposed by the present invention can clearly identify two separated peaks.

[0217] (3) Use the real EIS data of commercial lithium-ion batteries to verify the effectiveness of the DRT calculation method of the present invention. The EIS data was measured by a BioLogic MPG-205 electrochemical workstation under a constant temperature condition of 23°C. The measured EIS data is the electrochemical impedance spectrum of a lithium-ion battery of model 18650 at 80% SOC, as shown in 32. Since the equivalent circuit parameters of the real EIS data are unknown and accurate DRT data cannot be used as a reference, the traditional DRT algorithm and the regularization algorithm without data processing are used for comparative verification.

[0218] The verification of the real EIS data is carried out in two items.

[0219] The first verification: Use the DRT calculation method of the present invention, the traditional DRT algorithm and the regularization algorithm without data processing to calculate the DRT of the original EIS data, Figure 33 which is a comparison of the DRT calculated by the three methods. Compared with the traditional DRT algorithm, the regularization algorithm without data processing cannot handle the influence of noise, and there are many bifurcated pseudo-peaks in the peak of its DRT distribution function, and its calculation effect is very unsatisfactory. The position of the DRT is shifted and the peak size of the time constant is also inaccurate. Compared with the traditional DRT algorithm, the DRT calculation method of the present invention has better pseudo-peak suppression ability, and the recognition of the main peak is also very close between the two.

[0220] The second verification: Select the impedance spectrum with complex frequency domain to verify whether the DRT calculation method of the present invention can distinguish the coupled relaxation time and its distribution. There are 60 sampling points in the frequency range of the EIS data used. For the real EIS data, the following three different processing means are adopted: (1) Do not process the original EIS data, that is, use the EIS data of all sampling points in the full frequency range; (2) Use the EIS data of half of the sampling points in the full frequency range; (3) Shorten the measurement frequency range and reduce the number of sampling points. Figures 34 to 36Shows the processed three EIS data and their DRT results. For the original EIS data, its DRT consists of a total of three main peaks (where the rightmost main peak represents negligible Warburg impedance), and their relaxation times are 0.0003 s, 0.0024 s, and 0.029 s respectively. It can be seen from the figure that reducing the number of sampling points has little effect on the DRT calculation and reduces the interference of Warburg impedance on the calculation of the relaxation time distribution. The DRT calculation results are very close to the EIS data without data processing. For the data with a reduced frequency range, the DRT peak is reduced to one, and its relaxation time distribution is quite different from the original data, which cannot reflect the true impedance state inside the battery and causes truncation error. Therefore, when conducting EIS tests, the excitation range of the frequency should be expanded as much as possible to achieve wide-frequency sampling, so as to obtain more accurate DRT data.

[0221] 2. Accuracy Evaluation of Neural Network Model

[0222] (1) Accuracy Evaluation of EIS Secondary Synthesis Layer

[0223] The mean squared error (abbreviation: MSE), root mean square error (abbreviation: RMSE), and mean absolute error (abbreviation: MAE) are used to evaluate the accuracy of different models, and their mathematical definitions are shown in Equations (25), (26), and (27) respectively.

[0224]

[0225]

[0226]

[0227] Where N is the number of test samples, y is the actual value of SOH, is the estimated value of SOH.

[0228] The EIS secondary synthesis layer plays a crucial role in the unsupervised learning performance of the entire neural network model. To evaluate the role of the EIS secondary synthesis layer, the performance is evaluated by comparing the secondary synthesized EIS with the real EIS.

[0229] Such as Figure 37As shown, the comparison between the secondary synthesized EIS and the true EIS at two different aging stages (pre-aging stage A and post-aging stage B) is presented. The synthesized EIS uses the feature vectors after feature fusion, whose dimension is much smaller than the original dimension of the input EIS. The feature vectors can describe the high-dimensional impedance spectrum with sufficiently refined information, excluding redundant information and preventing the occurrence of overfitting. To specifically evaluate its synthesis quality, the RMSE at different SOH levels is calculated, as Figure 38 shown.

[0230] Analysis Figure 38 shows that its maximum root mean square error is only 0.023, which means that the feature vectors after feature fusion can completely represent the original EIS, further verifying the role of the feature fusion layer in the neural network model. This experiment can also reflect the complex aging mechanism of the battery from the Figure 38 fact that when the SOH is small, the corresponding synthesis error is large, indicating that as the battery ages, the aging characteristics gradually become more complex, making the error of the secondary synthesized EIS larger.

[0231] Due to the existence of the EIS secondary synthesis layer, the neural network model proposed in the present invention can realize the combination of unsupervised learning and supervised learning. The advantage of this network structure is that it can use impedance spectrum data without capacity annotation, reducing the cost of dataset annotation and expanding the available range of the dataset. By changing the proportion of capacity annotation of the original dataset to verify the performance of the proposed neural network model, its absolute error is as Figure 39 shown. The SOH estimation errors of datasets with different annotation proportions are shown in Table 3.

[0232] Table 3

[0233] Annotation scale 10％ 30％ 50％ 70％ 90％ Neural network model 0.026 0.025 0.017 0.016 0.01 Traditional CNN 0.06 0.047 0.026 0.023 0.020

[0234] From Figure 39 and Table 3, it can be seen that when using a 90% capacity annotation ratio for training, both have high accuracy, but as the annotation ratio decreases, the estimation errors of both increase. At the same annotation ratio, the neural network model of the present invention has better performance than the traditional CNN, which is all due to the unsupervised learning ability provided by the EIS secondary synthesis layer to the entire neural network model, enabling the J-CNN to still show better stability even in the absence of annotated data.

[0235] 2. Accuracy evaluation of the SOH estimation layer and the feature fusion layer

[0236] All impedance spectrum data with capacity annotation are used as the training set, which is simultaneously used for the training of the traditional CNN and the neural network model of the present invention, ensuring that the hyperparameters are the same except for the network structure.Figure 40 The comparison between the true and estimated values of SOH for the neural network model of the present invention and the traditional CNN is given in [reference], and the error results are shown in Table 4.

[0237] Table 4

[0238] Model MSE RMSE MAE Neural network model 0.00017 0.013 0.0094 Traditional CNN 0.001 0.032 0.025

[0239] From Figure 40 and the joint analysis of Table 4, it can be found that under the condition of the same hyperparameters, the neural network model of the present invention performs better than the traditional CNN in SOH estimation. This difference benefits from the improved network structure, which enables it to better capture the temporal characteristics of impedance spectrum data, thereby improving the accuracy of SOH estimation. In contrast, the traditional CNN only uses convolutional layers, max-pooling layers, and fully connected layers for SOH estimation, lacking the feature fusion layer and the EIS secondary synthesis layer compared with the neural network model of the present invention. Given that the training set data are all data with capacity annotations, therefore, compared with the traditional CNN, the advantage of the neural network model of the present invention mainly comes from the existence of the feature fusion layer.

[0240] To verify the role of the feature fusion layer, a neural network model that only retains the EIS secondary synthesis layer is used for neural network training, and it is compared with the complete neural network model. The comparison results are as Figure 41 shown, and the error results are shown in Table 5.

[0241] Table 5

[0242]

[0243] Analyzing Table 4, Table 5 and Figure 41 it can be seen that the SOH estimation effect of the neural network model of the present invention without using the feature fusion layer is slightly inferior to that of the complete neural network model of the present invention. This is because the feature fusion layer uses the attention mechanism to fuse the DRT features calculated based on the relaxation time with the DRT features automatically extracted by the neural network model, avoiding the phenomenon of feature loss.

[0244] The box plots are used to compare the performance of the complete neural network model, the neural network model that only retains the EIS secondary synthesis layer, and the traditional CNN in the estimation of battery health state, as Figure 42 shown. In the figure, the complete neural network model is denoted as Model 1, the neural network model that only retains the EIS secondary synthesis layer is denoted as Model 2, and the traditional CNN is denoted as Model 3. From Figure 42It can be seen that the error distribution of the complete neural network model is relatively concentrated, and its outliers are not scattered, showing a more stable estimation ability; the neural network model that only retains the EIS secondary synthesis layer performs poorly in SOH estimation, but compared with the traditional CNN, due to having a certain unsupervised learning ability, its overall error distribution is relatively small; the traditional CNN has neither the feature fusion ability of the feature fusion layer nor the unsupervised learning ability provided by the EIS secondary synthesis layer, so its performance in SOH estimation is the worst among the three models. These results all indicate that the feature fusion layer and the EIS secondary synthesis layer play an important role in improving the performance of the neural network model, and the mutual cooperation between different layers enables the neural network model to estimate SOH with high precision.

[0245] The above embodiments are used to explain the present invention rather than limit the present invention. Any modifications and changes made to the present invention within the spirit and scope of the claims of the present invention fall within the protection scope of the present invention.

Claims

1. A method for estimating the state of health (SOH) of a lithium-ion battery based on electrochemical impedance spectroscopy, characterized in that, The steps are: S1. Data acquisition step: obtaining historical EIS data of lithium-ion batteries; S2, data processing step: perform quality evaluation on historical EIS data to obtain original EIS data of qualified quality; S3, DRT calculation steps: Calculate the peak area of the DRT curve of the original EIS data based on the peak relaxation time, and use the peak area of the DRT curve as the DRT feature P DRT ; S4. Model construction step: Construct a neural network model, which includes an impedance spectrum information extraction layer, a feature fusion layer, and an SOH estimation layer; the impedance spectrum information extraction layer is used to extract the impedance feature P from historical EIS data Z ; the feature fusion layer is used to fuse the DRT feature P DRT and the impedance feature P Z for feature fusion and jointly splice them into a new impedance feature P new ; the SOH estimation layer takes the impedance feature P new as the input and outputs the SOH estimation result; the neural network model also includes an EIS secondary synthesis layer, which performs secondary synthesis on the original EIS data according to the impedance feature P new to obtain synthesized EIS data, so as to evaluate whether the extracted impedance feature P Z can completely describe the original EIS data; The loss function of the SOH estimation layer is expressed as: where m is the sample size of the SOH annotation of the lithium-ion battery, is the estimated value of the capacity of the i-th sample battery output by the SOH estimation layer, y i is the true value of the capacity of the i-th sample battery corresponding to the impedance spectrum; The loss function of the EIS secondary synthesis layer is expressed as: Wherein, is the impedance of the i-th sample synthesized by the EIS secondary synthesis layer, is the real part of the impedance of the i-th sample synthesized by the EIS secondary synthesis layer, is the imaginary part of the impedance of the i-th sample synthesized by the EIS secondary synthesis layer, Z i ' is the real part of the true impedance of the i-th sample, Z i '' is the imaginary part of the true impedance of the i-th sample; The total loss function of the neural network model is expressed as: L total = α·L1(δ1)+(1 - α)·L2(δ2) Where δ1 is the parameter set used by the SOH estimation layer, δ2 is the parameter set used by the EIS synthesis layer, and α is used to balance the contribution of the two loss functions; S5, actual data measurement step: measuring the actual EIS data of the lithium-ion battery in real time, and calculating the peak area of ​​the DRT curve of the actual EIS data according to the peak relaxation time; S6, SOH estimation step: inputting the real-time measured EIS data of the lithium-ion battery and the peak area of ​​the DRT curve of the actual EIS data into the neural network model to obtain the SOH of the lithium-ion battery.

2. The method for estimating the SOH of a lithium-ion battery based on electrochemical impedance spectroscopy according to claim 1, wherein The data processing steps include: S21, error test step: calculate the error of each frequency point in the historical EIS data; S22, evaluation step: taking the root mean square value of the overall frequency error of the historical EIS data as the evaluation index of the EIS quality, if the root mean square value is less than the set threshold, the original EIS data is obtained and the process directly proceeds to step S3, otherwise it proceeds to step S23; S23, data cleaning step: based on the discontinuity between adjacent frequency points in the historical EIS data, remove the point with the largest discontinuity, repeat steps S21 to S23 until the original EIS data is obtained, and directly enter step S3.

3. The method for estimating the SOH of a lithium-ion battery based on electrochemical impedance spectroscopy according to claim 2, wherein In the step S2, before the step S21, the data processing step further includes a screening step: eliminating abnormal data in the historical EIS data whose measurement error is greater than the set error.

4. The method for estimating the SOH of a lithium-ion battery based on electrochemical impedance spectroscopy according to claim 1, wherein After step S4, a model training step is also included: comparing the synthetic EIS data and the original EIS data, if the error between the synthetic EIS data and the original EIS data is greater than the minimum error, back propagation is performed to update the weights of the neural network model until the error between the synthetic EIS data and the original EIS data reaches the minimum error.

5. A state of health (SOH) estimation system for a lithium-ion battery based on electrochemical impedance spectroscopy, which is used to implement the SOH estimation method for a lithium-ion battery based on electrochemical impedance spectroscopy according to any one of claims 1 to 4, characterized in that, The system comprises: Data acquisition module, to obtain historical EIS data of lithium-ion batteries; EIS measurement device, used to measure the actual EIS data of lithium-ion batteries in real time; The data processing module evaluates the quality of historical EIS data to obtain original EIS data of qualified quality; The DRT calculation module calculates the peak area of the DRT curve of the original EIS data based on the peak relaxation time, and uses the peak area as the DRT feature P DRT ; and calculates the peak area of the DRT curve of the actual EIS data based on the peak relaxation time; A model construction module for constructing a neural network model, the neural network model including an impedance spectrum information extraction layer, a feature fusion layer, and an SOH estimation layer; the impedance spectrum information extraction layer is used to extract the impedance feature P from historical EIS data Z ; the feature fusion layer is used to fuse the DRT feature P DRT and the impedance feature P Z for feature fusion and jointly splice them into a new impedance feature P new ; the SOH estimation layer takes the impedance feature P new as input and outputs the SOH estimation result; The SOH estimation module inputs the real-time measured EIS data of the lithium-ion battery and the peak area of ​​the DRT curve of the actual EIS data into the neural network model to obtain the SOH of the lithium-ion battery.

6. The SOH estimation system for a lithium-ion battery based on electrochemical impedance spectroscopy according to claim 5, characterized in that The data processing module comprises: Error test module, calculates the error of each frequency point in the historical EIS data; The evaluation module uses the root mean square value of the overall frequency error of the historical EIS data as the evaluation index of the EIS quality. If the root mean square value is less than the set threshold, the original EIS data is obtained, otherwise it is unqualified EIS data; The data cleaning module removes the points with the largest discontinuity in the unqualified EIS data based on the discontinuity between adjacent frequency points in the historical EIS data.

7. The SOH estimation system of a lithium-ion battery based on electrochemical impedance spectroscopy according to claim 6, characterized in that, The data processing module further includes a screening module, and the screening module is used to eliminate abnormal data with a measurement error greater than a set error in the historical EIS data.

8. The SOH estimation system for lithium-ion batteries based on electrochemical impedance spectroscopy according to claim 5, wherein The neural network model further includes an EIS secondary synthesis layer, which performs secondary synthesis on the original EIS data according to the impedance feature P new to obtain synthesized EIS data for evaluating whether the extracted impedance feature P Z can completely describe the original EIS data.

9. The SOH estimation system for lithium-ion batteries based on electrochemical impedance spectroscopy according to claim 8, wherein The system further includes a model training module for training the neural network model according to the synthetic EIS data and the original EIS data.

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