Lithium battery SOH fault monitoring method based on electrochemical impedance spectroscopy

Abstract

The invention relates to the technical field of lithium ion testing, and discloses an electrochemical impedance spectroscopy-based lithium battery SOH fault monitoring method, which comprises the following steps of: firstly, acquiring a reference interface roughness parameter and a reference area amplification coefficient in a fault-free state under a set testing condition; applying an alternating current excitation signal to the lithium battery to be detected and collecting original impedance data; obtaining a de-noised interface impedance spectrum after high-frequency parasitic impedance stripping and de-noising reconstruction; a target frequency band with constant phase angle response is locked by calculating a derivative value of an impedance phase angle changing along with frequency; extracting an evolution slope of an imaginary part value in the frequency band, calculating a current interface roughness parameter and converting the current interface roughness parameter into a current area amplification coefficient; and finally, calculating a deviation value with a reference coefficient, and comparing the deviation value with a judgment threshold to output a monitoring result.

Description

Technical Field

[0001] This invention relates to the field of lithium-ion testing technology, and more specifically, to a fault monitoring method for the state of oxygen (SOH) of lithium batteries based on electrochemical impedance spectroscopy. Background Technology

[0002] Lithium-ion batteries are widely used in new energy vehicles and energy storage systems, and accurate assessment of their State of Health (SOH) is crucial for ensuring the safe operation of these systems. During long-term cycling and service, lithium plating on the negative electrode is one of the core failure mechanisms leading to drastic capacity decay and internal short circuits, posing safety hazards. With increased usage time or under harsh charge-discharge conditions, the negative electrode surface undergoes complex morphological evolution, exhibiting an inherent evolutionary pattern from initial needle-like whiskers to moss-like and even dense columnar morphologies. This extreme microscopic morphological evolution fundamentally alters the roughness of the electrode interface, porosity distribution, and the connectivity of the internal microstructure. Currently, electrochemical impedance spectroscopy (EIS), as an in-situ non-destructive testing method, is commonly used to monitor the internal health evolution of batteries. Existing monitoring schemes typically rely on impedance spectrum analysis under full-cell testing scenarios, such as extracting the real part of impedance drift, changes in the Nyquist radius, or utilizing the peak position and peak area evolution of the relaxation time distribution (DRT) to assess the degree of failure. However, existing monitoring methods based on electrochemical impedance spectroscopy suffer from insurmountable attribution ambiguity in practical applications. In in-situ non-destructive testing of full cells, localized lithium plating not only alters the surface morphology of the negative electrode but also causes severe shifts in the state of charge (SOC) of the positive electrode due to the continuous consumption of active lithium. Because the polarization processes of the positive and negative electrodes are highly coupled within the full cell, traditional impedance spectral parameters (such as the aforementioned impedance real part shift, arc variation, and DRT peak shift) are easily confused with other interfacial side reactions within the battery (such as the normal growth and thickening of the solid electrolyte interfacial film). Existing analytical parameters inherently possess attribution non-uniqueness, making misjudgment extremely easy and failing to identify negative electrode lithium plating faults, thus severely hindering the reliability and accuracy of fault monitoring. Summary of the Invention

[0003] This invention provides a fault monitoring method for SOH of lithium batteries based on electrochemical impedance spectroscopy, which solves the technical problems mentioned in the background art.

[0004] This invention provides a fault monitoring method for the state of oxygen (SOH) of lithium batteries based on electrochemical impedance spectroscopy, comprising: S1, under the set state of charge, test temperature and resting time, obtain the reference interface roughness parameter and reference area magnification factor of the lithium battery under test in a fault-free state. S2, apply an AC excitation signal to the lithium battery under test and collect raw impedance data at multiple test frequencies; S3, using the high-frequency values ​​in the original impedance data to strip away parasitic impedance and extract the effective interface impedance of the lithium battery under test. S4. Filter out the measurement noise in the effective interface impedance and reconstruct it to obtain the denoised interface impedance spectrum. S5, extract the derivative value based on the impedance phase angle of the denoised interface impedance spectrum as the test frequency changes, and determine the target frequency band with constant phase angle response based on the derivative value; S6, within the target frequency band, extract the evolution slope of the imaginary part of the impedance spectrum of the denoised interface as a function of the test frequency, calculate the current interface roughness parameter of the lithium battery under test based on the evolution slope, and convert the current interface roughness parameter into the current area magnification factor. S7, calculate the deviation between the current area magnification factor and the reference area magnification factor, and compare the deviation with a preset judgment threshold to output the fault monitoring result.

[0005] The beneficial effects of this invention are as follows: by extracting the evolution slope of the constant phase angle frequency band of the denoised interface impedance spectrum and converting it into interface roughness parameters and area amplification coefficient, the attribution ambiguity caused by full-cell polarization coupling and internal resistance drift is bypassed; this invention can map the drastic changes in surface morphology caused by lithium plating on the negative electrode, avoiding the defect that traditional judgment parameters are easily confused with conventional battery aging phenomena, thereby significantly improving the accuracy and reliability of early internal abnormal state monitoring of lithium batteries. Attached Figure Description

[0006] Figure 1 This is a flowchart of the fault monitoring method for SOH of lithium batteries based on electrochemical impedance spectroscopy of the present invention. Detailed Implementation

[0007] The subject matter described herein will now be discussed with reference to exemplary embodiments. It should be understood that these embodiments are discussed only to enable those skilled in the art to better understand and implement the subject matter described herein, and changes may be made to the function and arrangement of the elements discussed without departing from the scope of this specification. Various processes or components may be omitted, substituted, or added as needed in the examples. Furthermore, features described in some examples may be combined in other examples.

[0008] It should be noted that, unless otherwise defined, the technical or scientific terms used in one or more embodiments of the present invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in one or more embodiments of the present invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" indicate that the element or object preceding the term encompasses the elements or objects listed following the term and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0009] like Figure 1 As shown, a fault monitoring method for SOH of lithium batteries based on electrochemical impedance spectroscopy includes: S1, under the set state of charge, test temperature and resting time, obtain the reference interface roughness parameter and reference area magnification factor of the lithium battery under test in a fault-free state. S2, apply an AC excitation signal to the lithium battery under test and collect raw impedance data at multiple test frequencies; S3, using the high-frequency values ​​in the original impedance data to strip away parasitic impedance and extract the effective interface impedance of the lithium battery under test. S4. Filter out the measurement noise in the effective interface impedance and reconstruct it to obtain the denoised interface impedance spectrum. S5, extract the derivative value based on the impedance phase angle of the denoised interface impedance spectrum as the test frequency changes, and determine the target frequency band with constant phase angle response based on the derivative value; S6, within the target frequency band, extract the evolution slope of the imaginary part of the impedance spectrum of the denoised interface as a function of the test frequency, calculate the current interface roughness parameter of the lithium battery under test based on the evolution slope, and convert the current interface roughness parameter into the current area magnification factor. S7, calculate the deviation between the current area magnification factor and the reference area magnification factor, and compare the deviation with a preset judgment threshold to output the fault monitoring result.

[0010] Preferably, under the set state of charge, test temperature, and resting time, the reference interface roughness parameter and reference area magnification factor of the lithium battery under test in a fault-free state are obtained, including: The temperature change rate of the lithium battery under test was determined to meet the thermal steady-state requirements, and the recorded actual temperature was used as the test temperature. And the remaining power of the lithium battery under test Discretization is performed according to a preset step size to obtain the set state of charge. : ; in, It is a rounding function; The time interval from the end of charging to the current moment of the lithium battery under test is determined. When the time interval is within a preset time tolerance range, the time interval is taken as the resting time. ; Within a specified cycle range when the lithium battery under test is in the fault-free state, reference impedance data is collected, and the temperature shift factor is calculated. : ; in, The equivalent kinetic activation energy, Let be the ideal gas constant. The preset reference temperature, It is an exponential function; Using the temperature translation factor For preset frequency Perform translation and conversion to obtain the temperature-compensated frequency. : ; Based on the temperature compensation frequency The reference interface roughness parameter is obtained by extracting the reference impedance data. And according to the preset lower limit of the microscale range and the upper limit of the microscale range The roughness parameter of the reference interface Converted to the reference area magnification factor : ; The test temperature is the actual temperature recorded after the lithium battery under test reaches thermal steady state. It can be obtained through the thermistor in the cell casing or the temperature sampling module of the battery management system.

[0011] Remaining charge is the proportion of the current remaining charge of the lithium battery under test to its total capacity, which can be collected in real time through the coulomb counter or equivalent coulomb counter module of the battery management system.

[0012] The preset step size is a fixed interval for discretizing the remaining power, preferably 5%, in order to balance suppressing the remaining power estimation error of 1 to 2% and keeping the size of the reference library controllable, so as to avoid peak drift artifacts caused by estimation errors.

[0013] The time tolerance is the range of allowable settling time deviation from the preset value, preferably ±5 seconds, to balance the stability of the settling time and the operability of actual testing, and to avoid the impact of small time deviation on the stability of the interface impedance.

[0014] The specified cycle range is the number of cycles the lithium battery under test can cycle in a fault-free state. It is preferably the 5th to 20th cycle after the first power-on after the battery is manufactured, in order to avoid the unstable stage in the early stage of solid electrolyte phase interface film formation and the non-lithium plating impedance interference caused by later aging, so as to ensure the validity of the reference data.

[0015] The equivalent kinetic activation energy is a parameter characterizing the temperature sensitivity of the electrochemical reaction kinetic rate of a lithium battery. It is preferably 35,000 joules per mole. This value is a commonly used engineering empirical value in the field of lithium batteries, and it can ensure the consistency of frequency shift at different temperatures without offline calibration.

[0016] The ideal gas constant R is a universal constant characterizing the properties of an ideal gas. Its value is fixed at 8.314 joules per mole Kelvin and is an internationally accepted constant.

[0017] The preset reference temperature is a reference temperature used for temperature compensation, preferably 298.15 Kelvin, or 25 degrees Celsius. This temperature is a commonly used reference for room temperature testing and can effectively offset the influence of different test temperatures on electrochemical reaction kinetics.

[0018] The lower limit of the microscale range is the lower limit value for characterizing the scale of lithium plating structure, preferably 0.1 micrometers. This value matches the typical diameter order of lithium plating needle whiskers and can accurately reflect the microscale range of lithium plating structure.

[0019] The upper limit of the microscale range is the upper limit value characterizing the scale of lithium plating structures, preferably 10 micrometers. This value matches the cluster scale of lithium plating moss-like structures and covers the main microscale range of lithium plating structures.

[0020] The preset frequency is a set of frequencies for electrochemical impedance spectroscopy testing. The preferred range is 48 logarithmically equidistant frequency points from 0.5 Hz to 5000 Hz. This frequency range can stably cover the constant phase power-law dispersion frequency band caused by lithium plating structure, thus meeting the requirements of impedance spectroscopy testing.

[0021] The temperature change rate threshold is the critical value for determining whether a lithium battery has reached a thermal steady state. Preferably, the temperature change rate is no more than 0.02 Kelvin per second within 60 consecutive seconds. This threshold can effectively eliminate the influence of transient processes such as electrolyte redistribution and ensure the stability of the test temperature.

[0022] The implementation method for discretizing the remaining charge in 5% increments is as follows: multiply the remaining charge value collected by the battery management system by 20, round it down, and then divide it by 20 to obtain the discretized state of charge (SOC). For example, if the remaining charge is 73%, multiplying by 20 gives 146, rounding it down gives 146, and dividing by 20 gives 75%, which is the discretized SOC of 75%. This process can control the estimation error of the remaining charge within 5%, avoiding misinterpretation of impedance changes caused by lithium plating due to a small estimation error of 1 to 2%, and ensuring the consistency of the reference data.

[0023] The criterion for determining the end of charging is as follows: The end of charging does not simply refer to the moment the charging current reaches zero. Rather, it is determined when the absolute value of the charging current is less than 0.02 times the battery's rated capacity and this state persists for 10 seconds. For example, if the battery's rated capacity is 10 amps, the end of charging is determined when the absolute value of the charging current is less than 0.2 amps for 10 seconds. This standard avoids misjudging the start of the resting period due to current fluctuations during charging, ensuring the accuracy of the resting time.

[0024] The selection method for the fault-free cycle range is as follows: After the lithium battery is manufactured, the solid electrolyte interphase film is in a rapid growth phase during the first 5 cycles, and the interfacial impedance is unstable. After 20 cycles, the battery may begin to show slight aging, which will introduce impedance changes not related to lithium plating. Therefore, the 5th to 20th cycles are selected as the fault-free range, which can collect stable reference impedance data that is not affected by non-lithium plating factors, ensuring the accuracy of the reference interface roughness parameter and the reference area magnification factor.

[0025] Engineering Application of the Temperature Shift Factor: The temperature shift factor is calculated using the Arrhenius equation, converting test frequencies at different test temperatures into temperature-compensated frequencies at a reference temperature. For example, if the test temperature is 303 Kelvin (30 degrees Celsius), the equivalent kinetic activation energy is 35,000 J / mol, and the reference temperature is 298.15 Kelvin, substituting these values ​​into the equation yields the temperature shift factor. Multiplying each test frequency by this factor gives the temperature-compensated frequency. This process counteracts the influence of temperature on electrochemical reaction kinetics, ensuring the comparability of impedance spectra acquired at different temperatures and guaranteeing the stability of subsequent power-law slope estimation.

[0026] The storage strategy for self-reference fingerprints is as follows: Self-reference fingerprints store only two scalars—the reference interface roughness parameter and the reference area magnification factor—rather than the complete electrochemical impedance spectroscopy data. This is because the core of this method utilizes the scale-invariant power-law slope characteristic; the redundant information contained in the complete impedance spectroscopy data has no additional value for subsequent fault diagnosis. Storing only two scalars significantly reduces storage costs and data transmission pressure, without affecting detection accuracy.

[0027] The implementation details of the thermal steady-state criterion are as follows: The thermal steady-state criterion requires that the temperature change rate of the lithium battery does not exceed 0.02 Kelvin per second within 60 consecutive seconds. In actual testing, temperature data needs to be collected once per second using a temperature sensor, and the temperature change between two consecutive data collections needs to be calculated. If the temperature change rate calculated for 60 consecutive times does not exceed the threshold, the battery is determined to have reached thermal steady state. This criterion can take into account both test aging and transient process elimination, reduce the interference of factors such as electrolyte redistribution on interface impedance, and ensure the stability of the test temperature.

[0028] The preset step size is 5%, meaning that when discretizing the remaining power, the remaining power is divided into 21 levels, from 0% to 10% in 5% intervals. For example, when the remaining power is 37%, it is discretized and assigned to the 40% level; when the remaining power is 62%, it is discretized and assigned to the 60% level, ensuring the consistency of the state of charge.

[0029] The specific range of the time tolerance is ±5 seconds. That is, the preset settling time is 300 seconds, and the actual settling time is considered valid if it is between 295 seconds and 305 seconds. If the actual settling time exceeds this range, it must be marked as invalid sampling and the timing must be restarted until the settling time falls within the valid range to ensure the stability of the settling time.

[0030] The specific range of the specified cycle number interval is from the 5th to the 20th cycle after the first power-on following the battery's formation at the factory. For example, after the battery completes its formation process at the factory, reference impedance data can be collected during the 5th cycle after the first power-on. Impedance data collected after the 20th cycle is no longer used as reference data to avoid interference from non-lithium plating factors.

[0031] The thermal steady-state threshold for the rate of temperature change is a temperature change rate that is no greater than 0.02 Kelvin per second over 60 consecutive seconds. In actual testing, a temperature sensor with an accuracy of no less than 0.1 Kelvin should be used to collect the battery temperature once per second. The difference between two adjacent temperatures should be calculated and divided by the time interval of 1 second to obtain the rate of temperature change. If 60 consecutive temperature change rate values ​​are all ≤0.02 Kelvin per second, then thermal steady state is determined to have been reached.

[0032] The preset frequency range is from 0.5 Hz to 5000 Hz, with a total of 48 logarithmically equidistant frequency points. The frequency points are generated sequentially from 0.5 Hz according to a logarithmically equidistant pattern up to 5000 Hz, ensuring sufficient resolution in both high and low frequency bands to cover the constant-phase power-law dispersive frequency band of lithium plating structures.

[0033] The equivalent kinetic activation energy is taken as 35,000 joules per mole.

[0034] The specific values ​​for the microscale range are a lower limit of 0.1 micrometers and an upper limit of 10 micrometers, which perfectly matches the typical scale of lithium plating structures. The diameter of lithium plating needle-like whiskers is usually between 0.1 micrometers and 1 micrometer, while the cluster size of moss-like structures is usually between several micrometers and 10 micrometers. This range can fully cover the microscale range of lithium plating structures, ensuring the accuracy of the area magnification factor calculation.

[0035] Preferably, an AC excitation signal is applied to the lithium battery under test, and raw impedance data at multiple test frequencies are collected, including: Using the preset minimum test frequency Maximum test frequency and the total number of frequency points Each test frequency is generated using a logarithmic equidistant distribution. : ; in, This is the current frequency point number; Based on the estimated internal resistance of the lithium battery under test Preset upper limit of current disturbance and the preset upper limit of voltage response. Determine the amplitude of the AC excitation signal. So that the peak-to-peak value of the voltage response excited by the AC excitation signal is not greater than the upper limit of the voltage response. : ; in, For functions that take the minimum value, the absolute value sign indicates taking the modulus of a complex number; At each of the aforementioned test frequencies Next, using the amplitude of the excitation signal A constant current sinusoidal disturbance is constructed as the AC excitation signal and injected into the lithium battery under test, and the corresponding voltage sampling sequence is acquired within a set integration window length. With current sampling sequence ; For the voltage sampling sequence and the current sampling sequence Perform Discrete Fourier Transform on each component to extract the corresponding fundamental voltage complex amplitude. and fundamental current complex amplitude : ; ; in, The total number of data points in the sampling sequence. The sampling point number, The sampling time interval, The imaginary unit, It is a natural constant; The fundamental voltage complex amplitude Divide by the fundamental current complex amplitude Obtain each of the aforementioned test frequencies The original impedance data below : ; The minimum test frequency is the lowest frequency value for electrochemical impedance spectroscopy testing, preferably 0.5 Hz. This frequency can cover the low-frequency end of constant phase power-law dispersion caused by lithium plating structure, ensuring the integrity of the impedance spectrum.

[0036] The maximum test frequency is the highest frequency value of the electrochemical impedance spectroscopy test, preferably 5000 Hz. This frequency can avoid the serious interference of high-frequency parasitic impedance, while covering the power-law dispersion high-frequency end of the lithium plating structure.

[0037] The total number of frequency points is the number of frequency points for electrochemical impedance spectroscopy testing, preferably 48. With 48 frequency points under logarithmic equidistant distribution, the resolution of high and low frequency bands can be taken into account, which meets the accuracy requirements of power law slope extraction.

[0038] The estimated internal resistance value is an empirical estimate of the internal resistance of a lithium battery, preferably 30 milliohms. This value is the typical internal resistance range of commercial lithium batteries, and its use can ensure the rationality of the excitation amplitude calculation when no actual measurement data is available.

[0039] The preset upper limit of current disturbance is the maximum current limit of the AC excitation signal, preferably 0.02 times the rated capacity of the battery. This value can prevent large current disturbances from damaging the internal structure of the battery, while satisfying the small signal linearity constraint.

[0040] The preset upper limit of voltage response is the critical value for determining whether the excitation signal is in the linear region, preferably 10 millivolts. This threshold can ensure that the electrode response is in the linear range and avoid nonlinear effects from distorting the power-law characteristics of the impedance spectrum.

[0041] The integration window length is the time length for acquiring voltage and current sampling sequences. It is preferably set according to frequency ranges: 10 cycles are taken when the frequency is less than 2 Hz, 6 cycles are taken between 2 Hz and 20 Hz, and 4 cycles are taken when the frequency is greater than or equal to 20 Hz. Taking more cycles in the low frequency range ensures measurement accuracy, while reducing the number of cycles in the high frequency range controls the total test time.

[0042] The sampling rate is the frequency at which voltage and current signals are acquired. It is preferably no less than 250 kHz and the sampling rate must be no less than 50 times the highest test frequency to ensure accurate reproduction of the fundamental component of the sinusoidal excitation signal.

[0043] The sampling time interval is the time difference between two adjacent signal acquisitions, preferably the reciprocal of the sampling rate. This interval ensures that the sampling sequence satisfies the Nyquist sampling theorem and avoids signal aliasing.

[0044] The total number of data points in the sampling sequence is the number of voltage or current signal points collected within each integration window. Preferably, it is the product of the number of cycles included in the integration window and the test frequency, divided by the sampling rate. This number can completely cover the signal within the integration window and ensure the accuracy of the Fourier transform.

[0045] The amplitude of the excitation signal is determined by taking the smaller of the ratios of the upper limit of the current perturbation and the upper limit of the voltage response to twice the estimated internal resistance. For example, when the battery's rated capacity is 10 amps, the upper limit of the current perturbation is 0.2 amps, the estimated internal resistance is 30 milliohms, the upper limit of the voltage response is 10 millivolts, and twice the estimated internal resistance is 60 milliohms. The ratio of the upper limit of the voltage response to this value is approximately 0.167 amps, and the final excitation signal amplitude is taken as 0.167 amps. This calculation method ensures that the peak-to-peak value of the voltage response generated by the excitation signal does not exceed 10 millivolts, avoiding nonlinear reactions that could damage the power-law dispersion characteristics of the lithium plating structure.

[0046] The tiered design of the integration window length is as follows: different integration window periods are used for different frequencies. Low-frequency signals change slowly, so 10 periods can reduce noise interference. For example, the period of a 0.5 Hz signal is 2 seconds, and the integration window length of 10 periods is 20 seconds, which can fully collect signal characteristics. High-frequency signals change rapidly, so 4 periods are sufficient to ensure measurement accuracy. For example, the period of a 5000 Hz signal is 0.2 milliseconds, and 4 periods only require 0.8 milliseconds, which can effectively control the total test time.

[0047] The power frequency interference suppression strategy is as follows: when the test frequency is close to the 50 Hz or 60 Hz power frequency, integer period sampling combined with Hanning window processing is used. For example, when the test frequency is 50 Hz, the integration window length is taken as an integer number of periods to ensure that the sampling sequence is synchronized with the power frequency signal. Then, the data is weighted by Hanning window to suppress the interference of power frequency signal leakage on the extraction of fundamental frequency complex amplitude.

[0048] Synchronous sampling requires that the current injection module and the voltage sampling module share the same clock source, such as by using the same analog-to-digital converter chip or clock synchronization circuit. This avoids phase deviation between the current and voltage signals and ensures the accuracy of phase information in impedance calculations.

[0049] The Discrete Fourier Transform (DFT) is implemented as follows: The fundamental complex amplitude is extracted from the acquired voltage and current sampling sequences using the DFT. For example, if the total number of data points in the sampling sequence is 1024, after performing a Fast Fourier Transform (FFT), the fundamental component with the same frequency as the excitation signal is selected, and the fundamental voltage and current complex amplitudes are calculated. The original impedance data is then obtained by comparing the ratio of these two values.

[0050] The specific value of the minimum test frequency is 0.5 Hz, which can cover the low frequency range of power-law dispersion of lithium plating structures.

[0051] The maximum test frequency is 5000 Hz. This frequency can balance high-frequency resolution and parasitic impedance interference, and avoid impedance spectrum distortion caused by excessively high frequency.

[0052] The total number of frequency points is 48. The frequency points are generated in a logarithmic equidistant manner, that is, starting from 0.5 Hz, each subsequent frequency point is the previous frequency point multiplied by (5000 / 0.5) to the power of (1 / 47), to ensure that the frequency points of high and low frequency bands are evenly distributed.

[0053] The estimated internal resistance is 30 milliohms.

[0054] The preset upper limit for current disturbance is 0.02 times the rated capacity of the battery. For example, for a battery with a rated capacity of 20 amp-hours, the upper limit for current disturbance is 0.4 amp-hours.

[0055] The integration window length is divided into three levels according to the test frequency: 10 cycles for frequencies less than 2 Hz, 6 cycles for frequencies between 2 Hz and 20 Hz, and 4 cycles for frequencies greater than or equal to 20 Hz. For example, when the test frequency is 1 Hz, the integration window length is 10 cycles, or 20 seconds; when the test frequency is 10 Hz, the integration window length is 6 cycles, or 0.6 seconds.

[0056] The specific lower limit of the sampling rate is 250 kHz. In engineering, a higher value can be used, such as 500 kHz, depending on the actual hardware conditions, to ensure accurate acquisition of high-frequency excitation signals.

[0057] The specific implementation method for power frequency interference suppression is as follows: when the test frequency is between 45 Hz and 65 Hz, integer period sampling is used, and a Hanning window weighting is applied to the sampling sequence. The calculation formula for the Hanning window is that the sampling point weight is equal to 0.5 minus 0.5 multiplied by 2π multiplied by the sampling point number divided by the cosine value of the total number of sampling points. This processing reduces the interference of power frequency signals on the fundamental frequency extraction.

[0058] Preferably, the parasitic impedance is stripped from the high-frequency values ​​in the original impedance data to extract the effective interface impedance of the lithium battery under test, including: selecting a predetermined number of consecutive test frequencies located at the highest frequency end as a high-frequency test set. Extract the high-frequency test set The corresponding original impedance data The imaginary part of the value The imaginary part value is fitted using the least squares method. Corresponding to the test frequency The linear proportional relationship is used to calculate the equivalent parasitic inductance. : ; ; in, To take the complex imaginary part function; when the equivalent parasitic inductance At that time, the equivalent parasitic inductance The value is forcibly set to Extract the high-frequency test set The corresponding original impedance data The real part of the value is used to calculate the average and variance of the real part. When the variance value When the variance is not greater than a preset variance threshold, the average value is used as the equivalent series ohmic resistance. : ; in, For the high-frequency test set The number of test frequencies in To take the real part of the complex function; when the variance value When the variance exceeds the preset threshold, the minimum real part value is extracted from the original impedance data corresponding to all the test frequencies and used as the equivalent series ohmic resistance. : ; in, A function that finds the minimum value across all frequency points; from the original impedance data Subtract the equivalent series ohmic resistance from the middle and subtract the test frequency With the equivalent parasitic inductance The product of these components corresponds to the pure imaginary impedance component, which is used to strip away the parasitic impedance and obtain the effective interface impedance. : ; in, It is the imaginary unit.

[0059] The preset number of high-frequency test sets is the number of consecutive high-frequency points used to fit the equivalent parasitic inductance and equivalent series ohmic resistance, preferably 6. Multi-data-point fitting can cancel high-frequency noise interference, is more robust than single-point estimation, and improves the accuracy of parasitic quantity extraction.

[0060] The preset variance threshold is a critical value for judging the stability of the real part of the original impedance data corresponding to the high-frequency test set. It is preferably the square of 2 milliohms. This threshold can effectively distinguish between the stable and fluctuating states of the high-frequency real part and avoid distortion of the equivalent series ohm resistance estimation due to high-frequency instability.

[0061] The high-frequency parasitic inductance fitting method is implemented as follows: Six consecutive frequency points from the highest frequency end of the original impedance data are selected as the high-frequency test set. The imaginary part of the original impedance corresponding to each frequency point is extracted. The linear relationship between the imaginary part and the test frequency is fitted using the least squares method, and the slope is the equivalent parasitic inductance. For example, the high-frequency test set includes six highest frequency points such as 5000 Hz and 4500 Hz. After extracting the imaginary part values ​​of each point, a linear equation is obtained through fitting, and the slope of the equation is the equivalent parasitic inductance. Compared with single-point estimation, this multi-frequency fitting method can effectively suppress high-frequency noise and improve the estimation accuracy of parasitic inductance.

[0062] Equivalent parasitic inductance is a physical quantity characterizing the parasitic properties of a circuit, and theoretically should be non-negative. When the fitted result is less than zero, it indicates that the phase in the high-frequency band is affected by noise or instrument calibration error. In this case, the equivalent parasitic inductance is forcibly set to zero. For example, if the fitted equivalent parasitic inductance is -0.1 microhenries, it does not conform to the rule and should be directly corrected to zero.

[0063] The process for determining the series resistance is as follows: First, calculate the average and variance of the real part of the original impedance corresponding to the high-frequency test set. If the variance is no greater than 2 milliohms squared, it indicates that the high-frequency real part is stable, and the average value is used as the equivalent series resistance. If the variance is greater than this threshold, it indicates that the high-frequency real part fluctuates greatly. In this case, the minimum value of the real impedance corresponding to all test frequencies is extracted as the equivalent series resistance. For example, if the average value of the high-frequency real part is 30 milliohms and the variance is 3 milliohms squared, which is greater than the preset threshold, then the minimum real part of 28 milliohms is extracted by iterating through the real parts of all frequency points, and this is the equivalent series resistance.

[0064] The calculation logic for effective interface impedance is as follows: Effective interface impedance is the impedance data after removing series parasitic impedance, reflecting only the interface characteristics between the lithium battery electrode and the electrolyte. During calculation, the original impedance data at each frequency point is subtracted from the equivalent series resistance, and then the purely imaginary impedance component corresponding to the product of the test frequency and the equivalent parasitic inductance is subtracted. For example, if the original impedance at a certain frequency is 50 milliohms plus j20 milliohms, the equivalent series resistance is 30 milliohms, the equivalent parasitic inductance is 1 microhenry, and the purely imaginary component corresponding to the test frequency is j6.28 milliohms, then the effective interface impedance is 20 milliohms plus j13.72 milliohms.

[0065] The preset number of high-frequency test sets is 6. This number can achieve a balance between ensuring fitting accuracy and computational efficiency. The 6 consecutive high-frequency points can cover high-frequency parasitic characteristics without introducing interference from non-parasitic characteristics due to too many data points.

[0066] The preset variance threshold is 2 milliohms squared, or 4 milliohms squared. This value is determined based on the typical fluctuation range of the real part of the high-frequency impedance of commercial lithium batteries, and can effectively filter out stable high-frequency real part data.

[0067] The trigger condition for the parasitic inductance non-physical value processing rule is that the fitted equivalent parasitic inductance value is less than zero. When this occurs, there is no need to refit; the equivalent parasitic inductance is directly forced to zero to ensure the physical rationality of subsequent effective interface impedance calculations. For example, if the fitted result is -0.5 microhenries, the trigger condition is met, and it is directly corrected to zero.

[0068] Preferably, the reconstruction of the effective interface impedance by filtering out measurement noise includes: using the preset maximum test frequency. With the preset minimum test frequency The reciprocal of the product is used to determine the minimum relaxation time constant. With the maximum relaxation time constant : ; ; Based on the minimum relaxation time constant The maximum relaxation time constant and the total number of preset relaxation branches Each relaxation time constant is generated by a logarithmic equidistant distribution. : ; in, The relaxation branch number is used; the high-frequency test set is extracted. The corresponding effective interface impedance The imaginary part value is given, and the standard deviation of the imaginary part value is calculated. and the standard deviation The product of the square of the product and the preset regularization factor is used as the smoothing regularization coefficient. : ; ; in, To calculate the standard deviation function, To take the imaginary part of a complex number, For the test frequency sequence number; construct a high-frequency resistor with a limiting frequency. With multiple branch resistance weights Equivalent circuit representation model of series-connected relaxor branches : ; in, The imaginary unit is used; a non-negative constraint condition is set to ensure that the limiting high-frequency resistance is... With all the branch resistance weights All are not less than zero: ; Construct an objective function, and iteratively minimize the objective function under the non-negativity constraints: ; in, The total number of preset frequency points, To minimize the solution operator; if the iterative minimization solution fails to converge within the set maximum number of iterations, then the smoothing regularization coefficient is adjusted. After amplifying the solution by a set magnification, the solution is solved again; the calculated impedance value output by the equivalent circuit representation model after convergence is used as the impedance spectrum of the denoised interface. : ; The total number of relaxation branches is the number of relaxation branches that constitute the equivalent circuit representation model. It is preferably 80. This number can cover all possible relaxation processes within the test frequency band, taking into account both fitting accuracy and computational efficiency, and avoiding fitting distortion due to too few branches.

[0069] The preset regularization factor is a fixed coefficient used to calculate the smoothing regularization coefficient, preferably 10. This value can effectively balance the smoothness of impedance approximation error and branch resistance weight, and suppress spikes caused by noise.

[0070] The maximum number of iterations is set as the upper limit of the number of iterations to minimize the objective function, preferably 2000. This number can meet the convergence requirements in most scenarios and avoid insufficient solutions due to insufficient iterations.

[0071] The smoothing regularization coefficient amplification factor is the factor by which the regularization coefficient is adjusted when the iteration fails to converge, preferably by a factor of 10. This factor can quickly enhance the smoothing constraint and increase the convergence probability of the objective function.

[0072] The implementation method of Voigt network time constant grid design is as follows: the minimum relaxation time constant is taken as the reciprocal of the maximum test frequency, and the maximum relaxation time constant is taken as the reciprocal of the minimum test frequency. Then, 80 relaxation time constants are generated in a logarithmically equidistant manner. For example, if the maximum test frequency is 5000 Hz, the minimum relaxation time constant is 0.2 microseconds; if the minimum test frequency is 0.5 Hz, the maximum relaxation time constant is 2 seconds. The 80 time constants are distributed logarithmically between 0.2 microseconds and 2 seconds to ensure relaxation characteristics covering the entire test frequency band.

[0073] The logic for applying the non-negativity constraint is as follows: the weights of the limiting high-frequency resistance and the branch resistance are both resistances, and theoretically should be non-negative. Setting this constraint can avoid non-physical results with negative resistance in the optimization solution. For example, it can prevent negative relaxation of the equivalent circuit due to negative branch resistance weights, thereby avoiding the generation of spurious constant phase intervals.

[0074] The adaptive regularization coefficient is calculated as follows: the smoothing regularization coefficient is equal to the square of the standard deviation of the imaginary part of the effective interface impedance corresponding to the high-frequency test set multiplied by 10. For example, if the standard deviation of the imaginary part of the high-frequency band is 0.5 milliohms and the square of the standard deviation is 0.25 milliohms squared, the smoothing regularization coefficient is 2.5 milliohms squared. This calculation method can dynamically adjust the regularization strength according to the test noise.

[0075] The strategy for handling non-convergence during iteration is as follows: if the objective function fails to converge within 2000 iterations, the smoothing regularization coefficient is increased by a factor of 10 and the solution is recalculated. For example, if the original regularization coefficient is 2.5 milliohms squared, it is increased to 25 milliohms squared to strengthen the smoothing constraint and reduce the difficulty of solving the problem. If convergence still fails, an anomaly is forcibly output according to the rules.

[0076] The matrix-based solution is implemented by transforming the impedance calculation of the equivalent circuit into a system of linear equations with separate real and imaginary parts. The unknown vector includes the limiting high-frequency resistance and the weights of all branch resistances. The objective function is the sum of the approximation error term and the regularization penalty term. This is solved using non-negative Tikhonov least squares under non-negative constraints. For example, the resistance parameters can be obtained by calling this system of linear equations through readily available non-negative least squares or quadratic programming solvers.

[0077] The total number of relaxation branches is 80, which achieves an optimal balance between fitting accuracy and computational efficiency, and fully covers the relaxation process within the test frequency band.

[0078] The preset regularization factor is 10, which is a commonly used engineering value in the field of lithium battery impedance denoising and can effectively suppress the interference of noise on the fitting results.

[0079] The maximum number of iterations is set to 2000, which can meet the convergence requirements of most scenarios. If convergence is not achieved after exceeding this number, the solution is considered to have failed.

[0080] The specific value of the smoothing regularization coefficient amplification factor is 10 times. This factor can quickly enhance the smoothing constraint and effectively solve the problem of non-convergence caused by excessive noise.

[0081] The limiting high-frequency resistance is the equivalent resistance of the electrode interface in the high-frequency band, reflecting the electronic conduction characteristics inside the electrode. Its constraint boundary is not less than 0, which is consistent with the non-negative constraint of the branch resistance weight, ensuring the rationality of the equivalent circuit.

[0082] The specific algorithm for solving the objective function is the non-negative Tikhonov least squares algorithm. This algorithm can suppress the oscillation of the solution result by regularization term while satisfying the non-negativity constraint. It is suitable for denoising and reconstructing impedance spectrum and can be implemented by calling existing solvers.

[0083] Preferably, calculating the derivative of the impedance phase angle of the denoised interface impedance spectrum with respect to the test frequency, and determining the target frequency band with a constant phase angle response based on the derivative, includes: Calculate each of the test frequencies The corresponding denoised interface impedance spectrum The original impedance phase angle : ; in, To find the argument function of a complex number; Compare the original impedance phase angles corresponding to adjacent test frequencies, based on pi. The original impedance phase angle is subjected to phase dewinding processing to obtain a continuous impedance phase angle, specifically: while satisfying... At the current frequency, the original impedance phase angle is subtracted by twice pi. In order to satisfy At the current frequency, the original impedance phase angle is increased by twice pi. ; The continuous impedance phase angle is averaged and smoothed using a preset sliding window to obtain a smoothed impedance phase angle. : ; Extract the difference between adjacent smoothed impedance phase angles, convert the test frequency to a natural logarithmic value, calculate the logarithmic difference between adjacent natural logarithmic values, and divide the difference by the logarithmic difference to obtain the derivative value. : ; in, It is the natural logarithm function; Determine the derivative value Is the absolute value not greater than the preset phase drift upper limit threshold? The test frequencies that meet the conditions are selected to form a set of constant phase frequency points. : ; In the set of constant phase frequency points In the process, extract the frequency points with the largest number of consecutive frequency points that are not less than the preset minimum threshold number of consecutive points. The continuous frequency band is used as the target frequency band ; When the set of constant phase frequency points The number of frequency points that do not exist is not less than the minimum consecutive point threshold. When dealing with continuous frequency bands, the test frequency corresponding to the preset intermediate frequency sequence interval is extracted and forcibly used as the target frequency band. : ; ; ; ; in, The total number of preset frequency points, This is the starting frequency number of the target frequency band. This is the termination frequency number of the target frequency band. It is a rounding function. This is the floor function.

[0084] The upper limit threshold of phase drift is the critical value for judging whether the impedance phase angle changes smoothly with frequency. It is preferably 0.08 radians per natural logarithmic radian per second. This value can filter out the constant phase angle response range caused by lithium plating structure and avoid misjudging the effective frequency band due to small phase fluctuations.

[0085] The minimum number of consecutive points threshold is the minimum number of frequency points required to constitute an effective target frequency band, preferably 10. Ten consecutive frequency points can ensure the statistical reliability of the power law slope extraction and avoid a small number of noise points from forming a false constant phase frequency band.

[0086] The sliding window size is the length of the window used to smooth the phase angle of the continuous impedance. It is preferably 3 points. The 3-point sliding average can effectively suppress phase noise without destroying the true trend of phase angle change.

[0087] The intermediate frequency sequence range is the fallback frequency range when there is no effective constant phase frequency band. It is preferably between 0.35 times the total number of frequency points and 0.65 times the total number of frequency points. This range covers the main distribution frequency band of constant phase power-law dispersion of lithium plating structure, ensuring process continuity.

[0088] The combined strategy for phase preprocessing is implemented as follows: First, the original impedance phase angle is unwound, and then smoothed using a three-point sliding average. During unwinding, if the difference between the current frequency phase angle and the previous frequency phase angle is greater than pi, the current phase angle is subtracted by twice pi; if the difference is less than negative pi, the current phase angle is added by twice pi. For example, if the previous frequency phase angle is 3 radians and the current one is 0.5 radians, the difference is -2.5 radians, which is less than -3.14 radians, so the current phase angle is adjusted to 0.5 plus 6.28, which equals 6.78 radians. During smoothing, each phase angle is averaged with its own value and the values ​​of its immediate and adjacent phase angles. Endpoint frequencies directly copy the smoothed values ​​of their adjacent frequencies to avoid endpoint distortion.

[0089] The selection logic for constant-phase frequencies is as follows: phase stability is determined by calculating the phase derivative, which is the difference between adjacent smooth phase angles divided by the difference in the natural logarithm of the corresponding frequency. When the absolute value of the derivative is not greater than 0.08, the frequency is included in the set of constant-phase angles. This selection does not rely on any equivalent circuit priors, but is directly based on the characteristics of the impedance spectrum itself, bypassing the peak attribution process.

[0090] The rule for determining the effective target frequency band is as follows: traverse the set of constant phase angle frequency points, find all continuous frequency band subsets, and select the subset with the most continuous points and no less than 10 as the target frequency band. For example, if there are 15 and 8 continuous frequency points in the constant phase angle set, the frequency band consisting of 15 frequency points is selected first to ensure that there is sufficient data to support the extraction of the power law slope.

[0091] The fallback solution for no effective frequency band is as follows: when there is no frequency band in the set of constant phase angles that satisfies a consecutive number of points ≥ 10, the intermediate frequency (IF) interval is forcibly used as the target frequency band. For example, if the total number of frequency points is 48, 0.35 times is 16.8, rounded up to 17, and 0.65 times is 31.2, rounded down to 31. The target frequency band is the 17th to 31st frequency points. This interval is a typical distribution area for the CPE behavior of lithium plating structures. Although it is marked as low confidence, it does not affect subsequent calculations and result output.

[0092] The phase derivative is calculated using the central difference method. This method utilizes the difference between the smoothed phase angle and the logarithmic difference between two frequencies before and after the current frequency. Compared to single-sided difference, this reduces endpoint errors and noise interference, improving the accuracy of the derivative calculation. For example, to calculate the derivative at the k-th frequency, the difference between the smoothed phase angle of the (k+1)-k-1 frequency points is used, divided by the corresponding logarithmic difference of the frequencies, ensuring that the derivative accurately reflects the rate of change of the phase angle.

[0093] The specific value of the upper limit threshold for phase drift is 0.08 radians per natural logarithmic radians per second. This value can effectively distinguish between constant phase angle and fluctuating phase angle, and is suitable for the power-law dispersion characteristics of lithium plating structures.

[0094] The minimum consecutive point threshold is 10. This number strikes a balance between ensuring computational accuracy and noise immunity, and avoids distortion of slope estimation due to too few frequency points.

[0095] The sliding window has a specific number of points: 3. The 3-point sliding mean is a common method in impedance signal processing, which can suppress noise while preserving the key features of the signal.

[0096] The specific proportion of the mid-frequency sequence interval is from 0.35 times the total number of frequency points to 0.65 times the total number of frequency points. When the total number of frequency points is 48, the corresponding frequency point sequence number is 17 to 31. This interval can cover the normal phase response frequency band of most commercial lithium battery lithium plating structures.

[0097] The specific criteria for determining phase dewinding are as follows: When the difference in the original impedance phase angle between two adjacent frequency points is greater than 3.14 radians, the phase angle of the current frequency point is reduced by 6.28 radians; when the difference is less than -3.14 radians, the phase angle of the current frequency point is increased by 6.28 radians. For example, if the previous frequency point phase angle was 3.0 radians and the current one is 0.2 radians, the difference is -2.8 radians, which is greater than -3.14 radians, so no adjustment is needed; if the current phase angle is -3.0 radians and the difference is -6.0 radians, which is less than -3.14 radians, the current phase angle is adjusted to -3.0 plus 6.28, which equals 3.28 radians.

[0098] The smoothed impedance phase angle is calculated as follows: for the 2nd to K-1th frequency points, the smoothed phase angle is equal to the average of the original unwinding phase angles of the previous, current, and next frequency points; the smoothed phase angle of the 1st frequency point is equal to the average of the original unwinding phase angles of the 1st and 2nd frequency points; the smoothed phase angle of the last frequency point is equal to the average of the original unwinding phase angles of the last two frequency points, ensuring the continuity of the entire phase angle sequence.

[0099] Preferably, within the target frequency band, the evolution slope of the imaginary part of the impedance spectrum of the denoised interface as a function of the test frequency is extracted; the current interface roughness parameter of the lithium battery under test is calculated based on the evolution slope; and the current interface roughness parameter is converted into a current area magnification factor, including: within the target frequency band Within, extract the temperature compensation frequency corresponding to each of the test frequencies. Calculate the temperature compensation frequency The natural logarithm of the value is used as the independent variable. : ; Extract the target frequency band The corresponding noise-reducing interface impedance spectrum absolute value of the imaginary part The absolute value of the imaginary part With the preset minimum constant Compare the values, select the larger one, convert it to its natural logarithm, and use it as the dependent variable. : ; in, To take the imaginary part of a complex number, To extract the target frequency band, a function for finding the maximum value is used. The corresponding noise-reducing interface impedance spectrum absolute value of the real part The absolute value of the real part Divide by the absolute value of the imaginary part With the minimum constant The ratio is obtained by summing the terms, based on a constant. The weighting coefficients are constructed using the reciprocal of the sum of the squares of the ratios. : ; in, To extract the real part of the complex function; based on the weighting coefficients For the independent variable With the dependent variable Perform weighted least squares regression to obtain the independent variables. With the dependent variable The negative of the linear fit slope is used as the evolution slope. : ; ; in, The weighted average of the independent variables. The weighted average of the dependent variables; expressed as a constant. Subtract the evolution slope Obtain the initial interface roughness and limit the initial interface roughness to a preset lower roughness limit value. Compared with the preset roughness upper limit value Between these points, the current interface roughness parameter is obtained. : ; in, To find the minimum value function; calculate the upper limit of the microscale interval. With the lower limit of the microscale interval The scale ratio, and the scale ratio is taken from the current interface roughness parameter. Subtract constant The current area magnification factor is obtained by raising the power of the product. : ; The minimum constant is a protective constant set to avoid numerical calculation crashes caused by zero or minimum values ​​in logarithmic calculations. It is preferably 10 to the power of negative 6 ohms. This value is much smaller than the conventional imaginary part of the lithium battery interface impedance, so it does not interfere with normal impedance calculations and can effectively avoid numerical anomalies in logarithmic operations.

[0100] The roughness lower limit is the lower critical value of the current interface roughness parameter, preferably 2.0. This value corresponds to the fractal characteristic limit of the smooth interface of the lithium battery electrode, which conforms to the physical meaning of fractal dimension. When there is no lithium plating fault, the battery interface roughness parameter is close to this value.

[0101] The roughness upper limit is the physical upper limit critical value of the current interface roughness parameter, preferably 2.9. This value corresponds to the characteristic limit of the extremely strong fractal rough interface after lithium plating on the negative electrode of the lithium battery. Calculation results exceeding this value are all unreasonable results caused by numerical noise.

[0102] The implementation of the logarithmic protection mechanism is as follows: Extract the absolute value of the imaginary part of the impedance spectrum of the denoising interface within the target frequency band, and compare it with the minimum constant 10^-6 ohms. If the absolute value of the imaginary part is greater than the constant, the imaginary part is directly selected; if the absolute value of the imaginary part is less than or equal to the constant, the minimum constant is selected as the calculated value, and then the selected value is transformed by natural logarithm to obtain the dependent variable. For example, if the absolute value of the imaginary part at a certain frequency is 5 x 10^-7 ohms, which is less than the minimum constant, then 10^-6 ohms is used for logarithmic calculation to avoid numerical anomalies of negative infinity.

[0103] The construction and application logic of the weighting coefficient is as follows: First, calculate the ratio of the absolute value of the real part to the absolute value of the imaginary part plus the minimum constant of the impedance spectrum of the denoising interface at each frequency point within the target frequency band. Then, calculate the sum of the square of this ratio and the constant 1. Finally, take the reciprocal of this sum as the weighting coefficient for that frequency point. This coefficient can automatically reduce the weight of frequency points where the absolute value of the real part is too large relative to the imaginary part. These frequency points have poor phase stability, and reducing the weight can effectively improve the accuracy of the evolution slope estimation. For example, for a frequency point where the absolute value of the real part is 5 milliohms, the absolute value of the imaginary part is 0.1 milliohms, the minimum constant is negligible, the ratio is 50, the square is 2500, and the sum with 1 is 2501, the weighting coefficient is approximately 0.0004, and this frequency point has almost no weight in the subsequent regression calculation.

[0104] The implementation logic of weighted least squares regression is as follows: First, the weighted average of the independent and dependent variables is calculated based on the weighting coefficients at each frequency point. Then, the linear fitting slope is obtained by dividing the sum of the weighted deviations from the mean by the sum of the squared weighted deviations from the mean of the independent variables. Finally, the negative of this fitted slope is taken as the evolution slope. Compared with ordinary least squares, weighted processing can specifically suppress the interference of noise frequencies and phase unstable frequencies on the slope, making the evolution slope more accurately reflect the changes in electrode interface structure caused by lithium plating.

[0105] The clamping process for the interface roughness parameter is as follows: The initial interface roughness is obtained by subtracting the evolution slope from a constant of 3. If the initial interface roughness is less than 2.0, it is forcibly set to 2.0 as the current interface roughness parameter; if the initial interface roughness is greater than 2.9, it is forcibly set to 2.9 as the current interface roughness parameter; if the initial interface roughness is within the range of 2.0 to 2.9, the initial value is directly used. For example, if the evolution slope is 0.8 and the initial interface roughness is 2.2, which is within the physical range, it can be directly used; if the evolution slope is 0.05 and the initial value is 2.95, which exceeds the physical upper limit, it is forcibly corrected to 2.9.

[0106] The mapping logic of the area magnification factor is as follows: the area magnification factor is obtained by taking the ratio of the upper and lower limits of the microscale interval as a power of the interface roughness parameter minus a constant of 2. This calculation transforms the dimensionless interface roughness parameter into an interface area magnification factor, directly mapping the change in the specific surface area of ​​the electrode interface after lithium plating on the negative electrode. The more severe the lithium plating on the battery negative electrode, the larger the value of the interface roughness parameter, and the higher the value of the area magnification factor, which can intuitively reflect the severity of the lithium plating failure.

[0107] The specific value of the minimum constant is 10 to the power of negative 6 ohms. This value is the logarithmic protection value adapted in the field of lithium battery impedance testing, matching the conventional value range of the imaginary part of the interface impedance. The absolute value of the imaginary part of all frequency points within the target frequency band is calculated using this constant as the protection threshold.

[0108] The specific value of the roughness lower limit is 2.0. This value is the fractal characteristic limit of the smooth interface of the lithium battery electrode. As the physical lower limit of the interface roughness parameter, all initial interface roughness calculation results that are less than this value are forcibly corrected to 2.0.

[0109] The specific value of the roughness upper limit is 2.9. This value is the limit of the fractal characteristics of the rough interface after lithium plating on the negative electrode of the lithium battery. As the physical upper limit of the interface roughness parameter, all cases where the initial interface roughness calculation result is greater than this value are forcibly corrected to 2.9.

[0110] The complete calculation rule for the weighting coefficient is: the sum of the squares of the quotients of 1 divided by 1, the absolute value of the real part divided by the absolute value of the imaginary part, and the minimum constant. This rule applies to all frequency points within the target frequency band, and each frequency point calculates its own weighting coefficient independently.

[0111] The timing for incorporating the temperature compensation frequency is as follows: after determining the target frequency band through the derivative value, immediately extract the temperature compensation frequency corresponding to each test frequency within the target frequency band, and directly use the natural logarithm of the temperature compensation frequency as the independent variable of the weighted least squares regression, rather than the original test frequency, to ensure that the influence of temperature on the test frequency is completely offset.

[0112] The steps for calculating the evolution slope are as follows: First, calculate the weighting coefficients for each frequency point within the target frequency band; second, calculate the weighted average of the independent and dependent variables based on the weighting coefficients; third, calculate the difference between the independent variable and the weighted average, and the difference between the dependent variable and the weighted average for each frequency point, multiply the two differences by the weighting coefficient for that frequency point respectively, and then sum the products of all frequency points; fourth, calculate the square of the difference between the independent variable and the weighted average for each frequency point, multiply it by the weighting coefficient for that frequency point, and then sum the products of all frequency points; fifth, divide the sum of products obtained in the third step by the sum of products obtained in the fourth step to obtain the linear fitting slope; sixth, take the negative of the linear fitting slope, which is the evolution slope.

[0113] The matching rule for calculating the area magnification factor is as follows: when calculating the area magnification factor, the upper and lower limits of the microscale interval used must be completely consistent with the upper and lower limits of the microscale interval of the reference area magnification factor to ensure that the deviation values ​​of the current area magnification factor and the reference area magnification factor are comparable.

[0114] Preferably, the deviation between the current area magnification factor and the reference area magnification factor is calculated, and the deviation value is compared with a preset judgment threshold to output a fault monitoring result, including: Calculate the current area magnification factor respectively. With the reference area magnification factor The natural logarithm of the current area magnification factor. The natural logarithm minus the reference area magnification factor The natural logarithm of the value is used to calculate the deviation value for the current testing period. : ; in, It is the natural logarithm function; Obtain the historical deviation value of the lithium battery under test in the previous test cycle. ; Obtain the mean sample deviation of the preset fault-free sample set. With sample bias standard deviation The standard deviation of the sample bias With the preset normal quantile constant Multiply to obtain the product, and then use the mean of the sample biases. The decision threshold is calculated by adding the product to the product. : ; Determine the deviation value for the current test cycle. The historical deviation value Are all not less than the determination threshold? If yes, output the fault monitoring result that is determined to be abnormal; otherwise, output the fault monitoring result that is determined to be normal. When the iterative minimization solution fails to converge within the set maximum number of iterations, or when the target frequency band is the test frequency corresponding to the forcibly extracted mid-frequency sequence interval, or when the calculated evolution slope shows an abnormal value, the fault monitoring result that is determined to be abnormal is forcibly output.

[0115] The number of samples in the fault-free sample set is the base number of healthy lithium battery samples used to calibrate the fault determination threshold. It is preferably no less than 30, because 30 samples is a large sample size in statistics, which can ensure the statistical reliability of the mean and standard deviation of the sample deviation and avoid the threshold calibration distortion caused by small samples.

[0116] The normal quantile constant is the standard normal distribution quantile coefficient used to calculate the fault judgment threshold. It is preferably 2.576, which corresponds to the 0.995th quantile of the standard normal distribution. This value is a safe and conservative design that can significantly reduce the probability of missing faults in lithium battery negative electrode lithium plating.

[0117] The number of confirmations for the de-jitter rule is the number of test cycles that need to exceed the threshold consecutively when determining a lithium battery fault. It is preferably 2 times, which can effectively suppress fault misjudgment caused by single measurement noise or accidental operating condition disturbances and ensure the robustness of fault monitoring results.

[0118] The logic for calculating logarithmic deviation is as follows: instead of directly calculating the difference between the area amplification factor and the reference area amplification factor, the deviation value is first calculated by taking the natural logarithm of the area amplification factor. This method eliminates the dimensional influence of the area amplification factor and the inherent manufacturing differences of the cells, ensuring that the deviation value only reflects the changes in the electrode interface structure caused by lithium plating on the negative electrode. For example, cell A has a reference area amplification factor of 5 and currently has a reference area amplification factor of 8, so the logarithmic deviation is approximately 0.47 (natural logarithm 8 minus natural logarithm 5). Cell B has a reference area amplification factor of 4 and currently has a reference area amplification factor of 6.4, so the logarithmic deviation is also approximately 0.47, indicating that the degree of lithium plating is similar for both cells. If the difference were directly calculated, the values ​​would be 3 and 2.4, making it impossible to directly compare the degree of lithium plating.

[0119] The statistical calibration method for determining the threshold is as follows: Based on a sample set of healthy lithium batteries of the same model and batch, the deviation value of each healthy cell is collected under uniform testing conditions. The mean and standard deviation of all deviation values ​​are calculated. The threshold is then obtained by multiplying the mean of the deviations by the normal quantile constant and the standard deviation of the deviations. For example, in a sample set of 30 healthy cells, the mean deviation is 0.05 and the standard deviation is 0.1. Substituting the normal quantile constant 2.576, the threshold is calculated to be 0.05 plus 2.576 multiplied by 0.1, which equals 0.3076. This threshold covers 99.5% of the deviation range of healthy cells.

[0120] The implementation logic of the two-confirmation de-jitter rule is as follows: a lithium battery is only deemed faulty when both the deviation value of the current test cycle and the historical deviation value of the previous test cycle are greater than or equal to the judgment threshold. A single deviation value exceeding the threshold does not trigger a fault judgment. For example, if the judgment threshold is 0.3076, and the first test deviation value is 0.32 and the second is 0.35, both exceeding the threshold, the cell is judged to be abnormal; if the first deviation value is 0.32 and the second is 0.28, only exceeding the threshold once, the cell is judged to be normal.

[0121] The strategy logic for forced fault output is as follows: when data distortion or solution anomalies occur in any process of lithium battery fault monitoring, the abnormal monitoring result is output directly without waiting for the deviation value to exceed the threshold. This follows the safety priority principle of lithium battery safety monitoring and avoids missed detection of negative electrode lithium plating faults due to test data distortion. For example, if the objective function of the equivalent circuit model fails to converge during iterative solution, it indicates that the impedance spectrum denoising and reconstruction has failed, and the data is of no reference value. The cell is directly judged to be abnormal, and potential risks are promptly warned.

[0122] The rules for storing and matching deviation values ​​are as follows: After the deviation value is calculated for each test cycle, it must be stored in real time and associated with the cell's unique number and test time. When obtaining the historical deviation value of the previous test cycle, the most recent stored data is matched according to the cell's unique number to ensure the time continuity of the deviation value and the cell's uniqueness.

[0123] The number of samples in the fault-free sample set shall be no less than 30, and the samples shall be lithium batteries of the same model and batch. At the same time, all samples shall be within the specified number of cycles in the fault-free state to ensure the consistency of the samples and avoid distortion of the threshold calibration due to differences in model, batch or number of cycles.

[0124] The specific value of the normal quantile constant is 2.576. This value is the quantile corresponding to the one-sided 99.5% confidence interval in the standard normal distribution. It is a commonly used safety conservative coefficient in the field of lithium battery health status monitoring and is suitable for the low omission detection requirement of lithium plating faults.

[0125] The specific number of confirmations for the de-jitter rule is 2. That is, only when the deviation value of two consecutive test cycles is not less than the judgment threshold will an abnormal fault monitoring result be output. If the deviation value exceeds the threshold once, only the data is recorded and no abnormal judgment is triggered.

[0126] The calculation conditions for the mean and standard deviation of the sample deviation are as follows: the deviation values ​​of the fault-free sample set must be collected under uniform test conditions, that is, the state of charge is discretized, the lithium battery reaches the thermal steady state of temperature, the resting time is within the preset time tolerance range, and the parameters such as the test frequency and AC excitation signal are completely consistent with the parameters of the actual fault monitoring.

[0127] The specific triggering scenarios for forced output anomalies are as follows: First, the iterative minimization of the objective function fails to converge within the set maximum number of iterations; Second, there is no constant phase frequency band that meets the conditions, so the test frequency corresponding to the intermediate frequency sequence interval is forcibly extracted as the target frequency band; Third, numerical anomalies such as infinity non-numerical values ​​appear when calculating the evolution slope; Fourth, the interface roughness parameter is repeatedly forcibly restricted to the lower or upper limit of roughness, indicating that the test data is distorted.

[0128] The rules for obtaining historical deviation values ​​are as follows: If the lithium battery under test is being monitored for fault for the first time and there is no corresponding historical deviation value from the previous test cycle, it is directly determined as a normal fault monitoring result and no abnormality judgment is triggered; if it is not the first test, the deviation value stored in the most recent test cycle is matched with the unique number of the lithium battery under test in the monitoring system as the historical deviation value.

[0129] The natural logarithmic values ​​of the current area magnification factor and the reference area magnification factor are calculated and retained to 4 decimal places. The deviation value is the difference between the two natural logarithmic values, which is also retained to 4 decimal places to ensure the accuracy of the deviation value calculation and avoid judgment errors caused by insufficient accuracy.

[0130] It should be noted that the interval and threshold sizes are set for ease of comparison. The size of the threshold depends on the amount of sample data and the base number set by those skilled in the art for each set of sample data, as long as it does not affect the proportional relationship between the parameter and the quantized value. Furthermore, the above formulas are all dimensionless calculations, and the formulas are derived from software simulations using a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0131] The embodiments of this example have been described above. However, this example is not limited to the specific implementation methods described above. The specific implementation methods described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms based on the guidance of this example, and all of them are within the protection scope of this example.

Claims

1. A fault monitoring method for SOH of lithium batteries based on electrochemical impedance spectroscopy, characterized in that, include: S1, under the set state of charge, test temperature and resting time, obtain the reference interface roughness parameter and reference area magnification factor of the lithium battery under test in a fault-free state. S2, apply an AC excitation signal to the lithium battery under test and collect raw impedance data at multiple test frequencies; S3, using the high-frequency values ​​in the original impedance data to strip away parasitic impedance and extract the effective interface impedance of the lithium battery under test. S4. Filter out the measurement noise in the effective interface impedance and reconstruct it to obtain the denoised interface impedance spectrum. S5, extract the derivative value based on the impedance phase angle of the denoised interface impedance spectrum as the test frequency changes, and determine the target frequency band with constant phase angle response based on the derivative value; S6, within the target frequency band, extract the evolution slope of the imaginary part of the impedance spectrum of the denoised interface as a function of the test frequency, calculate the current interface roughness parameter of the lithium battery under test based on the evolution slope, and convert the current interface roughness parameter into the current area magnification factor. S7, calculate the deviation between the current area magnification factor and the reference area magnification factor, and compare the deviation with a preset judgment threshold to output the fault monitoring result.

2. The fault monitoring method for SOH of lithium batteries based on electrochemical impedance spectroscopy according to claim 1, characterized in that, Under the set state of charge, test temperature, and resting time, obtain the reference interface roughness parameters and reference area magnification factor of the lithium battery under test in a fault-free state, including: The temperature change rate of the lithium battery under test is determined to meet the thermal steady-state requirements. The recorded actual temperature is used as the test temperature, and the remaining charge of the lithium battery under test is discretized according to a preset step size to obtain the set state of charge. Determine the time interval from the end of charging to the current time of the lithium battery under test. When the time interval is within the preset time tolerance range, the time interval is taken as the resting time. Within a specified number of cycles of the lithium battery under test in the fault-free state, reference impedance data is collected, and the temperature shift factor is calculated using the equivalent kinetic activation energy, the ideal gas constant, and the preset reference temperature. The temperature compensation frequency corresponding to each of the test frequencies is obtained by shifting and converting each of the test frequencies using the temperature shift factor. Based on the temperature compensation frequency and reference impedance data corresponding to each of the test frequencies, the reference interface roughness parameter is extracted and obtained. Then, according to the preset lower limit and upper limit of the microscale range, the reference interface roughness parameter is converted into the reference area magnification factor.

3. The fault monitoring method for SOH of lithium batteries based on electrochemical impedance spectroscopy according to claim 2, characterized in that, An AC excitation signal is applied to the lithium battery under test, and raw impedance data at multiple test frequencies are collected, including: Using a preset minimum test frequency, a preset maximum test frequency, and a preset total number of frequency points, each test frequency is generated through a logarithmic equidistant distribution. Based on the estimated internal resistance of the lithium battery under test, the preset upper limit of current disturbance, and the preset upper limit of voltage response, the amplitude of the AC excitation signal is determined so that the peak-to-peak value of the voltage response generated by the AC excitation signal is not greater than the upper limit of voltage response. At each of the aforementioned test frequencies, a constant current sinusoidal disturbance is constructed using the amplitude of the excitation signal to inject the AC excitation signal into the lithium battery under test, and the corresponding voltage sampling sequence and current sampling sequence are collected within the set integration window length. Perform Discrete Fourier Transform on the voltage sampling sequence and the current sampling sequence respectively to extract the corresponding fundamental voltage complex amplitude and fundamental current complex amplitude; Divide the fundamental voltage complex amplitude by the fundamental current complex amplitude to obtain the original impedance data at each of the test frequencies.

4. The fault monitoring method for SOH of lithium batteries based on electrochemical impedance spectroscopy according to claim 3, characterized in that, By using the high-frequency values ​​in the original impedance data to remove parasitic impedance, the effective interface impedance of the lithium battery under test is extracted, including: A predetermined number of consecutive test frequencies located at the highest frequency end are selected as a high-frequency test set; The imaginary part of the original impedance data corresponding to the high-frequency test set is extracted, and the linear proportional relationship between the imaginary part and the corresponding test frequency is fitted by the least squares method to calculate the equivalent parasitic inductance. When the equivalent parasitic inductance is less than zero, the value of the equivalent parasitic inductance is set to zero. Extract the real part of the original impedance data corresponding to the high-frequency test set, and calculate the average and variance of the real part. When the variance value is not greater than the preset variance threshold, the average value is used as the equivalent series ohmic resistance. When the variance value is greater than the preset variance threshold, the minimum real part value is extracted from the original impedance data corresponding to all the test frequencies and used as the equivalent series ohmic resistance. The effective interface impedance is obtained by subtracting the equivalent series ohmic resistance from the original impedance data and subtracting the pure imaginary impedance component corresponding to the product of the test frequency and the equivalent parasitic inductance.

5. The fault monitoring method for SOH of lithium batteries based on electrochemical impedance spectroscopy according to claim 4, characterized in that, The effective interface impedance is filtered to remove measurement noise and reconstructed to obtain a denoised interface impedance spectrum, including: The minimum relaxation time constant and the maximum relaxation time constant are determined by using the reciprocal of the preset maximum test frequency and the preset minimum test frequency, respectively. Based on the minimum relaxation time constant, the maximum relaxation time constant, and the preset total number of relaxation branches, each relaxation time constant is generated by a logarithmic equidistant distribution. Extract the imaginary part of the effective interface impedance corresponding to the high-frequency test set, calculate the standard deviation of the imaginary part, and use the product of the square of the standard deviation and the preset regularization factor as the smoothing regularization coefficient. An equivalent circuit representation model is constructed, consisting of a limiting high-frequency resistor connected in series with multiple relaxor branches with branch resistance weights. Set non-negative constraint conditions to ensure that the weights of the limiting high-frequency resistor and all the branch resistors are not less than zero. Construct an objective function, which includes an approximation error term between the effective interface impedance and the impedance calculation value of the equivalent circuit representation model, and a regularization penalty term consisting of the second-order difference term of the smoothing regularization coefficient and the branch resistance weight. Under the non-negative constraint, the objective function is iteratively minimized. If the iterative minimization fails to converge within the set maximum number of iterations, the smoothing regularization coefficient is amplified by a set factor and the solution is repeated. The impedance calculation value output by the equivalent circuit representation model after convergence is used as the impedance spectrum of the denoised interface.

6. The fault monitoring method for SOH of lithium batteries based on electrochemical impedance spectroscopy according to claim 5, characterized in that, Based on the impedance phase angle of the denoised interface impedance spectrum changing with the test frequency, the derivative value is extracted, and based on the derivative value, the target frequency band with a constant phase angle response is determined, including: Calculate the original impedance phase angle of the denoised interface impedance spectrum corresponding to each of the test frequencies; Compare the original impedance phase angles corresponding to adjacent test frequencies, and perform phase unwinding processing on the original impedance phase angles based on pi to obtain continuous impedance phase angles; The continuous impedance phase angle is averaged and smoothed using a preset sliding window to obtain a smoothed impedance phase angle; Extract the difference between adjacent smooth impedance phase angles, convert the test frequency into a natural logarithmic value, and calculate the logarithmic difference between adjacent natural logarithmic values. Divide the difference by the logarithmic difference to obtain the derivative value; Determine whether the absolute value of the derivative is not greater than a preset phase drift upper limit threshold, and filter out all the test frequencies that meet the condition to form a set of constant phase angle frequency points; In the set of constant phase angle frequency points, the continuous frequency band with the largest number of consecutive frequency points and a number of frequency points not less than a preset minimum consecutive point number threshold is extracted as the target frequency band; When there is no continuous frequency band in the set of constant phase angle frequency points where the number of frequency points is not less than the minimum continuous point threshold, the test frequency corresponding to the preset intermediate frequency sequence interval is extracted and forcibly used as the target frequency band.

7. The fault monitoring method for SOH of lithium batteries based on electrochemical impedance spectroscopy according to claim 6, characterized in that, Within the target frequency band, the evolution slope of the imaginary part of the impedance spectrum of the denoised interface as a function of the test frequency is extracted. Based on the evolution slope, the current interface roughness parameter of the lithium battery under test is calculated, and the current interface roughness parameter is converted into a current area magnification factor, including: Within the target frequency band, the temperature compensation frequency corresponding to each of the test frequencies is extracted, and the natural logarithm of the temperature compensation frequency is calculated as the independent variable. Extract the absolute value of the imaginary part of the impedance spectrum of the denoised interface within the target frequency band, compare the absolute value of the imaginary part with a preset minimum constant, and select the larger one to convert it into a natural logarithmic value as the dependent variable. Extract the absolute value of the real part of the impedance spectrum of the denoised interface within the target frequency band, divide the absolute value of the real part by the sum of the absolute value of the imaginary part and the minimum constant to obtain the ratio, and construct weighting coefficients based on the reciprocal of the sum of the squares of the constant and the ratio. Based on the weighting coefficients, a weighted least squares regression is performed on the independent variable and the dependent variable to obtain the inverse of the linear fit slope of the independent variable and the dependent variable as the evolution slope. The initial interface roughness is obtained by subtracting the evolution slope from the constant three, and the initial interface roughness is restricted between a preset lower roughness limit and a preset upper roughness limit to obtain the current interface roughness parameter. Calculate the scale ratio between the upper limit of the microscale interval and the lower limit of the microscale interval, and then use the scale ratio to the power of the current interface roughness parameter minus a constant of two to calculate the current area magnification factor.

8. The fault monitoring method for SOH of lithium batteries based on electrochemical impedance spectroscopy according to claim 7, characterized in that, Calculate the deviation between the current area magnification factor and the reference area magnification factor, compare the deviation with a preset judgment threshold to output a fault monitoring result, including: Calculate the natural logarithm of the current area magnification factor and the reference area magnification factor respectively; The deviation value for the current test cycle is calculated by subtracting the natural logarithm of the reference area magnification factor from the natural logarithm of the current area magnification factor. Obtain the historical deviation value of the lithium battery under test in the previous test cycle; Obtain the mean and standard deviation of the sample deviation of the preset fault-free sample set, multiply the standard deviation of the sample deviation by the preset normal quantile constant to obtain the product, add the mean of the sample deviation to the product, and calculate the judgment threshold. Determine whether both the deviation value and the historical deviation value are not less than the determination threshold. If yes, output the fault monitoring result that is determined to be abnormal; otherwise, output the fault monitoring result that is determined to be normal.

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