Continuous DRT analysis method based on priority peak division processing

Abstract

The invention provides a continuous DRT analysis method based on priority peak division processing, which comprises the following steps: peak division processing is carried out based on electrochemical characteristics of a target battery, core kernel functions of a plurality of peak shapes are determined, each core kernel function corresponds to a single dynamic process of the target battery, and position parameters and shape parameters are adjustable; determining an overall DRT curve and a DRT equation set of the target battery based on the core kernel function; performing iterative search to obtain optimal values and corresponding amplitudes of position parameters and shape parameters of each core kernel function; and determining an overall DRT curve of the target battery and / or a DRT curve corresponding to the single dynamic process based on the search result. According to the method, the core kernel function clearly corresponding to the dynamic process is established, and the optimal values and the corresponding amplitude values of the position and the shape of the core kernel function are searched, so that the analysis result does not depend on the actually measured data frequency resolution, and the physical meaning is clear.

Description

Technical Field

[0001] This application belongs to the field of battery testing technology, and further relates to DRT analysis technology of electrochemical impedance spectroscopy, specifically providing a continuous DRT analysis method based on preferential peak segmentation. Background Technology

[0002] Electrochemical Impedance Spectroscopy (EIS) is an in-situ battery performance analysis and testing technique. It analyzes the battery's impedance characteristics at corresponding frequencies by testing the excitation and response of the battery under an alternating current signal. Since EIS is a concentrated representation of the kinetic processes at different rates within the battery, it has a strong correlation with the battery's electrochemical behavior, thus providing effective information for in-depth analysis of the battery's electrochemical principles, aging mechanisms, and failure characteristics. However, EIS itself is highly complex, and explaining the intricate kinetic processes from it remains very difficult. To address this issue, researchers typically use Distribution of Relaxation Times (DRT) analysis to extract the core features of EIS, simplifying the analysis.

[0003] DRT is a model-free EIS analysis method that explains the contribution of internal dynamic processes to the overall impedance by constructing the distribution of impedance versus relaxation time from measured discrete impedance data. The basic assumption of this method is that any polarization process in an electrochemical system can be described by one or more standard relaxation processes with characteristic time constants. This process usually involves discretizing the impedance expression and converting it into solving a system of linear equations.

[0004] Currently, common methods for constructing linear equation systems using Direct Reduction Theorem (DRT) can be divided into direct discretization methods and kernel function-based methods. Direct discretization methods directly discretize the DRT formulas to construct the equation system. This method is relatively simple, but the resistance definition only exists at a specified relaxation time constant point, lacking clear physical meaning elsewhere. Kernel function-based methods utilize radial basis functions to construct continuous DRT curves with clear physical meaning, allowing for continuous DRT solutions in the time domain. They offer significant advantages in convergence, boundary handling, and physical interpretability. However, existing kernel function-based continuous DRT methods are generally heavily influenced by preset parameters such as the frequency density of the EIS test and the peak width coefficient of the regularization process. When the frequency density is low or the parameters cannot be accurately estimated, the accuracy of the DRT solution is poor. Summary of the Invention

[0005] The purpose of this application is to provide a continuous DRT analysis method based on priority peak splitting, the method comprising the following steps: Step 1: Based on the electrochemical characteristics of the target battery, peak segmentation is performed to determine several core kernel functions used to characterize the overall DRT curve of the target battery. The core kernel functions are peak shape functions with adjustable position and shape parameters, and each core kernel function corresponds to a single kinetic process of the target battery. Step 2: Determine the overall DRT curve and the expression of the DRT equation system of the target battery based on the core kernel function; Step 3: With the goal of minimizing the fitness function, iteratively search to obtain the optimal values ​​of the position and shape parameters of each core kernel function and their corresponding amplitudes. In each iteration, when solving the DRT equations to obtain the amplitudes of each core kernel function, no regularization is performed. Step 4: Determine the overall DRT curve of the target battery and / or the DRT curve corresponding to a single kinetic process of the target battery based on the search results.

[0006] The continuous DRT analysis method based on priority peak splitting provided in this application has at least the following advantages: (1) By constructing the overall DRT curve through a small number of core kernel functions corresponding to a single dynamic process, the computational uncertainty caused by the selection of the number of kernel functions, regularization parameters and half-peak width coefficient in the traditional DRT method is avoided. Therefore, the position and shape of the calculated overall DRT curve are highly controllable and the computational stability is stronger.

[0007] (2) The process of obtaining the DRT curve takes into account the inherent characteristics of the battery, effectively constrains the randomness of the DRT calculation, and makes the overall DRT curve more interpretable.

[0008] (3) In addition to obtaining the overall DRT curve, since the adjustable parameters of the core kernel function are based on the relaxation time constant, range and intensity of each individual kinetic process, these parameters naturally distinguish the DRT curve based on the kinetic process. This makes it possible to analyze a certain peak separately based on the search optimization results with clear physical meaning, which greatly simplifies the post-analysis and parameterization of the DRT curve and provides more intuitive and accurate numerical parameter information for battery state estimation, fault analysis and other tasks. Attached Figure Description

[0009] Figure 1 This is a schematic diagram of the individual kernel function curves and the overall DRT curve obtained using existing kernel function-based DRT analysis methods. Figure 2This is a schematic diagram of the DRT curves of an existing kernel function-based DRT analysis method under different ppd values. Figure 3 This is a flowchart of a continuous DRT analysis method based on priority peak splitting processing provided in an embodiment of this application; Figure 4 This is a flowchart illustrating the specific implementation of steps three and four of the continuous DRT analysis method based on priority peak splitting provided in the embodiments of this application; Figure 5 This is a schematic diagram of the overall DRT curves obtained using the analytical method of this application and conventional methods in Specific Embodiment 1; Figure 6 This is a schematic diagram showing the EIS results of the overall DRT curve fitting obtained using the analysis method of this application and conventional methods in Specific Embodiment 1; Figure 7 This is a schematic diagram showing the DRT analysis results of the analysis method of this application and conventional methods used in specific embodiment 2; Figure 8 This is a schematic diagram of the seven individual peaks obtained using the analytical method of this application in Specific Embodiment 2; Figure 9 This is a schematic diagram showing the DRT analysis results of the analysis method of this application and conventional methods used in specific embodiment 3; Figure 10 This is a schematic diagram of the seven individual peaks obtained using the analytical method of this application in Specific Embodiment 3; Figure 11 This is a schematic diagram showing the results of DRT analysis using this method under different ppd values ​​in specific embodiment 4; Figure 12 This is a schematic diagram showing the results of DRT analysis using conventional methods under different ppd values ​​in specific embodiment 4. Detailed Implementation

[0010] The DRT method is a model-free EIS analysis method that can construct the impedance-relaxation-time distribution from the battery's impedance data to explain the contribution of internal kinetic processes to the overall impedance. The basic assumption of this method is that any polarization process in an electrochemical system can be described by one or more standard relaxation processes with characteristic time constants. Since, in circuit theory, a standard relaxation process can be simply expressed in the time domain by a parallel resistor (R) and capacitor (C) element, the frequency domain impedance characteristics of the battery can be converted into time domain time constant distribution characteristics using an infinite series connection of RC elements and a resistor. Under this method, the complex impedance of the battery... It is expressed as: (1), in, The DRT distribution function is... For ohmic internal resistance, To test the inductance, The independent variable is the relaxation time constant. Angular frequency, It is the imaginary unit.

[0011] The core problem of Discrete Impedance Theory (DRT) is to calculate a reliable DRT distribution function from the measured discrete impedance data. This is an ill-posed problem, and the existence, uniqueness, and stability of the calculated results are difficult to guarantee. Therefore, additional constraints or regularization methods are needed to obtain relatively stable approximate solutions. This process usually involves discretizing the equations, transforming the above expression into a system of linear equations. Generally speaking, methods for constructing linear equation systems can be divided into two types: direct discretization methods and continuous methods based on kernel functions.

[0012] Among them, the discretization method directly discretizes the impedance expression of DRT to construct a system of equations. This method is relatively simple in principle. However, the standard discretization method only has a physically clear resistance definition at a specified time constant point (rather than on a continuous DRT curve). In order to overcome the above defects, the applicant proposed a mid-to-high frequency fractional-order model (RQ model) for battery electrochemical processes in Chinese invention patent CN121142325A. This model uses parallel R-CPE elements to replace multiple series RC elements and establishes corresponding discrete RQ-DRT equations. By solving the discrete RQ-DRT equations, the EIS spectrum of each electrochemical process can be extracted separately. However, this method requires pre-dividing multiple relaxation time distribution intervals. When solving the discrete RQ-DRT equations in each preset relaxation time distribution interval, a large number of discrete solutions will still be obtained. It is necessary to further limit the form of the solution with specific constraints in order to obtain a non-zero solution in each relaxation time distribution interval.

[0013] Unlike discrete methods, kernel function methods construct DRT curves using radial basis functions. This method allows for continuous DRT solutions in the time domain, offering significant advantages in solution convergence, boundary handling, and the physical interpretability of the results. Currently, the standard workflow for continuous DRT analysis based on kernel functions is preprocessing-computation-peak analysis. For example, Wan et al. (Wan TH, Saccoccio M, Chen C, et al. Influence of the discrete methods on the distribution of relaxation times deconvolution:implementing radial basis functions with DRTtools[J]. Electrochimica Acta,2015, 184: 483-499.) proposed a kernel function-based DRT calculation method. The core idea is that the DRT distribution function can be considered as a combination of multiple kernel functions with the same shape but different positions. The DRT solution is transformed from directly calculating the DRT distribution function to calculating the amplitude of the kernel function. Specifically, based on various measurement frequencies measured by EIS, kernel functions are selected and DRT functions of the following form are constructed: (2), in, This refers to the total number of measurement frequency points included in the EIS measured data. For the first One kernel function, For the first The center of the kernel function, i.e. the th kernel function The center position of each kernel function on the relaxation time axis is determined by the sampling frequency points of the test data. For the first Kernel functions The range.

[0014] Kernel function Radial basis functions such as Gaussian, C2 Matern, C4 Matern, and C6 Matern can usually be selected. Obviously, the shapes of each kernel function in equation (2) are the same. The only difference is that the center position of each kernel function is determined according to the frequency points of the EIS measured data as needed. its magnitude It is then determined by solving the DRT equation system.

[0015] Figure 1The diagram shows the curves of each kernel function obtained according to existing kernel function-based methods, as well as the overall DRT curve obtained by superimposing the kernel functions, as shown below. Figure 1 As shown, in the EIS measurement process, in order to improve the analysis accuracy, the number of measurement frequency points may be dozens or even hundreds. On the one hand, this inevitably leads to the DRT analysis accuracy being directly affected by the number of EIS measurement frequency points; on the other hand, the center position of each kernel function... The relaxation time constant represented There is no clear correspondence between the DRT calculation impedance and the actual time constant, which will cause the calculated impedance to leak to both sides of the actual time constant, thus producing an "impedance leakage" problem similar to the spectral leakage in Fourier transform. In addition, in order to make the calculation results more stable, regularization processing is required to ensure the smoothness of the final calculation results during the solution of the DRT equation system.

[0016] To improve the accuracy of various continuous DRT analysis methods, Niu et al. (Niu P, Yang K, Song Z, et al. An efficient electrochemical optimizer for the distribution of relaxation times of lithium-ion batteries[J]. Journal of Power Sources, 2024, 605:234489.) proposed an improved scheme that treats the shape of each kernel function as an adjustable term, characterizes it using a peak width coefficient, and then proposes to optimize the optimal regularization coefficient and peak width coefficient through an optimization algorithm. Multiple objective functions are used to ensure the peak separation of the final calculated DRT curve. However, in their method, the number and center position of the kernel functions are still determined by the EIS measurement frequency. Therefore, it does not solve the dependence of the DRT solution on the frequency sampling of the measured data, and even after optimizing the peak width, the kernel functions still cannot clearly correspond to each electrochemical process, resulting in a lack of clear physical interpretation for the optimization of each kernel function. Figure 2 As shown, although the method proposed by Niu et al. performed regularization and peak width coefficient optimization, the shape of the overall DRT curve obtained by it changed significantly with the change of ppd (points per decade, the number of test frequency points within each 10 octave, used to characterize the density of measurement frequency points).

[0017] Furthermore, when constructing the overall DRT curve using kernel functions corresponding to the measured frequency points of the actual EIS, even if the shape of each kernel function is treated as an adjustable term and the peak width coefficient is optimized using an optimization algorithm, since each kernel function itself has no clear correspondence with a single dynamic process, the optimization of the kernel function shape is merely a mathematical processing method used to improve the curve approximation. When the same objective function can be achieved by optimizing different kernel function shapes, it is impossible to give a clear physical explanation for the different optimization results.

[0018] Similarly, existing kernel function methods generally require regularization to control the smoothness of the final overall DRT curve. The regularization parameter... The larger the setting, the smoother the overall DRT curve, but the individual peaks become blurred. Setting the value smaller improves peak separation but introduces small spurious peaks between large peaks. Clearly, similar to the problems with kernel function shape optimization, utilizing regularization parameters... Controlling the smoothness of the overall DRT curve only yields a purely mathematical curve approximation result, and it is impossible to definitively determine whether this optimization result matches the actual dynamic process inside the battery.

[0019] To address the problems of existing continuous DRT analysis methods based on kernel functions, this application provides a continuous DRT analysis method based on priority peak splitting. By changing the preprocessing-computation-peak analysis process of existing methods, this method prioritizes peak splitting to obtain kernel function curves that have a clear correspondence with a finite number of dynamic processes. This effectively eliminates the dependence of the solution results on measured frequencies and kernel function settings, enhances the physical interpretability and reliability of the optimization results, and significantly reduces the computational scale of linear equations.

[0020] Figure 3 The following is an overall flowchart of the continuous DRT analysis method based on priority peak splitting provided according to the embodiments of this application. The technical solution of this application will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0021] like Figure 3 As shown, the continuous DRT analysis method based on priority peak splitting provided in this application includes the following steps: Step 1: Based on the electrochemical characteristics of the target battery, peak segmentation is performed to determine several core kernel functions used to characterize the overall DRT curve of the target battery. The core kernel functions are peak shape functions with adjustable position and shape parameters, and each core kernel function corresponds to a single kinetic process of the target battery. Step 2: Determine the overall DRT curve and the expression of the DRT equation system of the target battery based on the core kernel function; Step 3: With the goal of minimizing the fitness function, iteratively search to obtain the optimal values ​​of the position and shape parameters of each core kernel function, as well as the corresponding magnitudes. Step 4: Determine the overall DRT curve of the target battery and / or the DRT curve corresponding to a single kinetic process of the target battery based on the search results.

[0022] The specific implementation process of steps one to four will be described in detail below with reference to specific embodiments.

[0023] <Step 1> Step one is used to perform peak segmentation processing on the target battery to be analyzed in advance. In the embodiments of this application, peak segmentation processing is to determine how many core kernel functions corresponding to each kinetic process need to be used to characterize the overall DRT curve based on the electrochemical characteristics of the target battery. After the position, width and amplitude of each core and function are determined through the iterative search process described later, each core kernel function will naturally match each kinetic process. Accordingly, the overall DRT curve can be obtained directly by superimposing each core kernel function. At this time, the overall DRT curve can be determined as the sum of each kinetic process inside the battery. Therefore, there is no need to artificially "modify" its curve shape through regularization processing.

[0024] The number and shape of the core kernel functions determined by peak segmentation need to be determined based on the electrochemical characteristics of the target battery. These electrochemical characteristics can be obtained by analyzing historical data acquired through measurements of the target battery. Taking lithium-ion batteries as an example, based on current research on the electrochemical characteristics of lithium-ion batteries, there are seven specific kinetic processes within them. Each kinetic process can be equivalent to a resistance effect with a specific relaxation time constant. These seven equivalent resistance effects are: contact resistance effect, anode passivation layer resistance effect, cathode passivation layer resistance effect, anode charge transfer resistance effect, cathode charge transfer resistance effect, liquid phase diffusion resistance effect, and solid phase diffusion resistance effect. Therefore, for lithium-ion batteries, the total number of core kernel functions can be set to 7. Obviously, for other types of batteries, such as lithium iron phosphate batteries, the number of core kernel functions and the corresponding kinetic processes may be the same as or different from those of lithium-ion batteries, and need to be set by those skilled in the art based on their existing research on battery electrochemical characteristics.

[0025] The core kernel function should be a peak shape function whose position and shape are adjustable. The peak shape function should open downwards, have a maximum value at the center, and approach zero as the distance from the center increases. For example, a kernel function similar to the Gaussian function can be used. In the form of, As the independent variable, For position parameters, For shape parameters, Value at In the center The maximum peak value is 1, and so on. keep away And gradually decrease and approach 0, Used to adjust the width of the entire curve. The smaller the value, the narrower the function curve, and vice versa. Considering that the relaxation time coordinate is generally in logarithmic form, the core kernel function of the form (3) can be obtained: (3), in, Let the relaxation time constant be the independent variable of the logarithmic coordinate. The position parameter is in logarithmic coordinates, representing the relaxation time constant of the dynamic process corresponding to the core kernel function. The shape parameter controls the width of the core kernel function curve. After determining the number of core kernel functions, a linear weighted superposition of the individual core kernel functions yields the overall DRT curve characterized by these core kernel functions.

[0026] It is understandable that the form of the core kernel function given in equation (3) is only one option. Those skilled in the art can also choose other core kernel function forms that conform to each kinetic process based on their prior knowledge of the electrochemical characteristics of the target battery. They only need to ensure that the selected core kernel function has adjustable position and shape parameters.

[0027] Step Two Step 2 determines the expression for the overall DRT curve of the target battery, as well as the expression for the DRT equation system, based on the selected core kernel function.

[0028] Specifically, based on prior knowledge of the electrochemical characteristics of the target battery, multiple core kernel functions are selected to characterize the overall DRT curve of the target battery. hour, It can be expressed in the form shown in equation (4): (4), in, This represents the total number of core kernel functions used to characterize the overall DRT curve of the target battery. For the first One core kernel function, Let the relaxation time constant be the independent variable of the logarithmic coordinate. For the first Adjustable position parameters of the logarithmic coordinates of each core kernel function. For the first Adjustable shape parameters of each core kernel function For the first The magnitude of each core kernel function.

[0029] It should be noted that although equation (4) and equation (2) have similar forms of linear superposition of functions, they reflect completely different ways of representing the overall DRT curve of the target battery: (2) The number of kernel functions is determined by the number of measured frequency points in the measured EIS data. At the same time, the center position of each kernel function is determined by its corresponding frequency point. As the number of measured frequency points in the measured data changes, the shape of the overall DRT curve obtained by superposition will inevitably change. Meanwhile, since there is no clear correspondence between any single kernel function and any single dynamic process, and the number of kernel functions that fit the same dynamic process will also change as the number of measured frequency points changes, the shape of the DRT curve representing a single dynamic process will also inevitably change with the number of measured frequency points. Therefore, it is extremely difficult to separate the DRT curves of each single dynamic process from the overall DRT.

[0030] (4) The core kernel function and its linear superposition represent a completely different way of characterizing the overall DRT curve: the overall electrochemical characteristics of the target battery can be represented by "sub-curves" that have a clear correspondence with a fixed number of single kinetic processes, wherein the position parameters of each "sub-curve" are... This represents the central location of the relaxation time constant and the shape parameter of the corresponding single dynamic process. This represents the extent and magnitude of the diffusion of the corresponding single dynamic process from the center outwards along the relaxation time constant dimension. This represents the intensity of the corresponding single dynamic process. Clearly, when the number of core kernel functions is fixed, and the intensity, center position, and diffusion degree of each single dynamic process are determined, the shape of the overall DRT curve is uniquely determined. The shape of this overall curve is independent of the number and position of frequency points in the EIS measured data. Therefore, regardless of the frequency of the EIS data used, the resulting overall DRT curve remains consistent. Furthermore, since the overall DRT curve is obtained by superimposing physically meaningful "sub-curves," its actual shape also has a clear physical meaning, thus eliminating the need for artificial modification through regularization.

[0031] Furthermore, after obtaining the overall DRT curve expression obtained by the weighted linear superposition of the core kernel functions through the above steps, the accurate DRT analysis of the target battery is transformed into how to search for the position parameters of each core kernel function. and shape parameters The optimal value is determined, and the magnitude of each core kernel function is determined. In the embodiments of this application, for , The search for the optimal value can be carried out by minimizing the search objective function in the search parameter space. For any given unknown parameters and shape parameters, the magnitude of each core kernel function is determined by solving the DRT equation system. Therefore, after obtaining the overall DRT curve expression represented by the core kernel function in step two, the DRT equation system of the target battery based on the core kernel function can be established in the same way as the standard DRT equation system.

[0032] Specifically, based on equations (1) and (4), and substituting the measured EIS data of the target battery, the complete complex impedance of the target battery can be obtained. and the complex impedance corresponding to the DRT curve. The expression: (5), In some alternative embodiments, it can be based on The expression constructs the DRT equation system for solving the amplitudes of each core kernel function, due to the ohmic internal resistance. and linear inductance terms Since the impedance is separated from the known parameters, the resulting core kernel function curves and overall DRT curve only reflect the various kinetic processes inside the target battery.

[0033] Considering the ohmic internal resistance It does not involve the kinetic relaxation of the battery. In some alternative embodiments, the effects of the linear terms introduced solely for measuring inductance can be pre-separated. This pre-processing allows for direct measurement based on... The expression is used to construct the DRT equations for solving the amplitudes of each core kernel function.

[0034] For ease of expression, the following text will use " To explain the specific form and solution method of the DRT equations, it should be understood that, based on and based on The constructed DRT equations are essentially equivalent. By adding ohmic resistance and inductance terms to the DRT equations constructed based on the former, the DRT equations constructed based on the latter can be easily obtained.

[0035] Equation (5) holds true at all discrete measurement frequencies, separating the real and imaginary parts and using... As an intermediate variable, let The discrete form of the impedance expression for the target battery can be obtained: (6), in, The total number of EIS measurement frequency points for the target battery. The total number of core kernel functions, based on the analysis above, , For the first angular frequency at each measurement point For the target battery in the first The complex impedance corresponding to the portion of the DRT curve at each measurement frequency point. and They are respectively The real and imaginary parts, , The first The core kernel function in the first The real and imaginary coefficients at each measurement frequency point, considering that the relaxation time constant and the corresponding angular frequency are reciprocals, are... Its corresponding angular frequency satisfy , , The specific expression is: (7).

[0036] Obviously, , This represents the target battery's first... The dynamic process in the first... The impact of each measurement frequency point on the overall DRT curve.

[0037] Equation (6) is used to solve for the amplitude of each core kernel function. The DRT equations, in combination of position and shape parameters Given the conditions, after removing the influence of ohmic internal resistance and measured inductance from the measured impedance data of the target battery, we can obtain... measured value ,in , They are respectively Substituting the real and imaginary parts of the equation into equation (6) and solving for them, we can determine the value of the real and imaginary parts in this group. Under what conditions .

[0038] Alternatively, equation (6) can be rewritten in an equivalent matrix multiplication form: (8), in, , They are respectively The real and imaginary coefficient matrices of dimension , their ... Line 1 The element values ​​of the column are given by equation (7). for The core kernel function magnitude column vector of the dimension and They are respectively The column vectors of the real and imaginary parts of the DRT impedance in dimension: (9).

[0039] Since the total number of individual kinetic processes within a target battery is generally no more than 10, and to ensure EIS spectral resolution, the minimum measurement frequency density must be no less than 5 ppd, typically measured at 10–20 ppd, with some high-precision measurements even reaching 30 ppd, the total number of EIS measurement frequencies for the target battery is... to The magnitude is obviously different from conventional kernel function-based methods. In the embodiments of this application, much smaller At this point, the number of unknowns in the DRT equation system of equations (6) or (8) is less than the number of equations. Therefore, the overdetermined system can be converted into a solution system using the least squares method. The optimization problem of finding the optimal fitting solution can be solved using various quadratic optimization methods known to those skilled in the art, such as gradient descent, conjugate gradient, interior point method, etc. Solve for it.

[0040] Since the overall DRT curve consists of only a finite number of peak-shaped kernel functions, the shape of the DRT curve has already changed from... and The smoothness and stability of the solution are fully controlled, so no regularization is required during the solution process.

[0041] Step 3 After obtaining the DRT equation system based on a finite number of core kernel functions, each core kernel function can be optimized based on EIS measured data so that the overall DRT curve constructed based on the finite number of core kernel functions can fit the EIS measured spectrum.

[0042] Figure 4 The following is a flowchart illustrating the implementation of steps three and four in a specific embodiment, as shown below. Figure 4 As shown, step three consists of an initialization operation and multiple iterative search processes. Each iterative search process includes the following steps: S31, based on the current position and shape parameters, the amplitude of each core kernel function is determined by solving the DRT equation system; S32, based on the solution results of step S31, update the position parameters and shape parameters with the goal of minimizing the fitness function, and enter the next iteration until the iteration search termination condition is met.

[0043] Specifically, the initialization operation is used to set the position parameters of each core kernel function. and shape parameters The initial value, search range (upper and lower limits), search size, and search termination conditions, etc.

[0044] Position parameters The initial value can be determined based on prior knowledge of the target battery. Taking lithium-ion batteries as an example, the contact resistance process is the kinetic process with the minimum relaxation time constant inside the battery, and the relaxation time constant range is... arrive The relaxation time constant of lithium ions passing through the interface film between the cathode and anode varies due to differences in the composition and structure of the interface film. The relaxation time constant due to the resistance effect of the anode passivation layer is smaller, approximately [value missing]. s, the relaxation time constant of the cathode passivation layer resistance effect is in arrive Between s; the charge transfer processes of the cathode and anode also exhibit differences in relaxation time constants, mainly due to differences in electrode materials. Specifically, the relaxation time constant of the anode charge transfer resistance effect corresponding to the graphite electrode is approximately s, while the relaxation time constant of the cathode charge transfer resistance effect is approximately arrive Regarding the diffusion process, there are two diffusion-related kinetic processes within the battery: diffusion in the liquid electrolyte and diffusion in the solid electrolyte. Due to the differences in the media, the diffusion coefficient of lithium ions varies considerably, which leads to corresponding deviations in its time constant. Generally speaking, we consider the relaxation time constant of the liquid-phase diffusion resistance effect to be approximately... s, while the time constant of the solid-state diffusion resistance effect can reach s or higher.

[0045] Based on the above analysis, in an optional embodiment, for lithium-ion batteries, the position parameters of each core kernel function can be... The initial value is set to: (10).

[0046] Position parameters The lower and upper limits of the search can be obtained by expanding downwards and upwards from their initial values, respectively. Since different position parameters characterize the relaxation time constants corresponding to different kinetic processes, the search range needs to be set based on the specific mechanism of the kinetic process. Considering that the range of expansion from the initial value for diffusion processes is greater than that for other non-diffusion processes, in some preferred embodiments, the search range for the position parameters corresponding to a single diffusion-related kinetic process or an equivalent diffusion resistance effect (such as liquid-phase diffusion resistance effect and solid-phase diffusion resistance effect) is greater than the search range for the position parameters corresponding to other single kinetic processes or equivalent resistance effects. For example, the lower and upper limits of the search for liquid-phase diffusion resistance effect and solid-phase diffusion resistance effect can be expanded downwards or upwards from their initial values, respectively. to s is obtained, while the search lower and upper limits for the position parameters corresponding to other resistive effects are expanded downward or upward from their initial value positions, respectively. arrive s is obtained.

[0047] In some alternative embodiments, the various shape parameters The initial value can be set to to Similarly, the upper and lower limits of the search range can be obtained by expanding upwards or downwards from their initial values, for example, in some optional embodiments, the various shape parameters The lower and upper search limits are expanded downwards and upwards respectively from their initial values. It is obtained at 0.1 to 0.2 times.

[0048] The search scale can be determined based on the specific search algorithm used. It is understood that in the embodiments of this application, there is no limitation on the specific search algorithm used. Those skilled in the art can select various algorithms that optimize parameters with the goal of minimizing the fitness function (loss function, cost function, etc.) based on their knowledge, such as particle swarm optimization, genetic algorithm, simulated annealing algorithm, etc. Accordingly, the size of the search scale can be determined by setting the number of particles, the number of genetic populations, etc.

[0049] The search termination condition can use various judgment conditions known to those skilled in the art, such as the number of iterations reaching a preset upper limit, or the difference between the search results of adjacent iterations being less than a preset threshold. In some optional embodiments, the above search termination conditions can be used in combination or nested. For example, the search can be completed when either the number of iterations reaches the upper limit or the iteration results converge; or the search can end only when the iteration results converge, and the upper and lower limits of the search can be updated when the iteration results have not converged but the number of iterations has reached the upper limit, so as to avoid failing to find the optimal value within an excessively small parameter search range.

[0050] After initializing the parameters, the search process can proceed in multiple iterations. For example, when using a genetic algorithm or particle swarm optimization algorithm, each iteration involves evaluating and updating the search results represented by multiple particles, where each particle corresponds to a set of position parameters. and shape parameters The alternative values ​​are obtained by substituting each set of alternative parameters into equation (6) or (8) in step S31 to solve the DRT equation system and obtain the corresponding values. (Based on the preceding analysis, preferably, no regularization is performed when solving the DRT equations to obtain the amplitude of each core kernel function during each iterative search process.) Then, in step S32, the amplitudes of each particle (i.e., each group) are calculated separately. , , The fitness function corresponding to the current iteration is used to determine the optimal parameter from each set of candidate parameters based on the fitness function calculation result. This parameter is then compared with the fitness function of the global optimal parameter obtained in the previous iteration. Based on the comparison result, it is determined whether to update the global optimal parameter. Finally, based on the position corresponding to the global optimal parameter value and the position of each particle itself, the position of each particle is updated and a new round of iterative search process begins.

[0051] The fitness function is used to characterize the location parameters of each group. Shape parameters and the corresponding core kernel function amplitude value The degree of deviation between the constructed overall DRT curve and the measured data is determined by the fitness function in some specific embodiments: (11), in, It is the L2 norm. , , That is, the real coefficient matrix, imaginary coefficient matrix, and core kernel function magnitude column vector in the DRT equation system shown in equation (8). This is the measured column vector of the real part of the DRT impedance. This is the measured column vector of the imaginary part of the DRT impedance. It can be obtained by substituting the measured DRT impedance results at each measurement frequency point into the vector. and get.

[0052] Therefore, the above iterative process aims to minimize the fitness function: The process of updating and searching for the optimal position, shape, and amplitude of each core kernel function.

[0053] The system can decide whether to stop iterating based on preset convergence conditions (e.g., the difference in fitness functions of the best particles obtained in two adjacent iterations is less than a preset threshold) or an upper limit on the number of iterations (e.g., 100 times), and use the global optimal position parameters, shape parameters, and corresponding amplitude at the end of the iteration as the search result.

[0054] Step Four like Figure 4 As shown, in step four, the optimal result obtained from the search is corresponding to... Substituting into equation (4), we obtain the overall DRT curve based on the core kernel function representation.

[0055] Furthermore, since in the embodiments of this application, each core kernel function has a clear correspondence with each individual dynamic process of the target battery, therefore, in step four, as... Figure 4 As shown, it can also be based on any set of optimal... Establish the DRT curves corresponding to each individual kinetic process, for example, when numbered as When the core kernel function is used to characterize the contact resistance effect, the searched kernel function will be used to obtain the following kernel function. Substitute the optimal value This allows us to obtain the DRT curve corresponding to the contact resistance effect.

[0056] Compared to existing continuous DRT analysis methods based on kernel functions, the core advantage of the continuous DRT analysis method based on priority peak splitting provided in this application is: (1) By constructing the overall DRT curve through a small number of core kernel functions corresponding to a single dynamic process, the computational uncertainty caused by the selection of the number of kernel functions, regularization parameters and half-peak width coefficient in the traditional DRT method is avoided. Therefore, the position and shape of the calculated overall DRT curve are highly controllable and the computational stability is stronger.

[0057] (2) The process of obtaining the DRT curve takes into account the inherent characteristics of the battery, effectively constrains the randomness of the DRT calculation, and makes the overall DRT curve more interpretable.

[0058] (3) In addition to obtaining the overall DRT curve, since the adjustable parameters of the core kernel function are based on the relaxation time constant, range and intensity of each individual kinetic process, these parameters naturally distinguish the DRT curve based on the kinetic process. This makes it possible to analyze a certain peak separately based on the search optimization results with clear physical meaning, which greatly simplifies the post-analysis and parameterization of the DRT curve and provides more intuitive and accurate numerical parameter information for battery state estimation, fault analysis and other tasks. Specific Implementation Example 1 In this embodiment, a third-order RC model of the battery is used to verify the analysis method provided in this application. The impedance of this battery model is expressed as: (12) in, For the first The resistance value of a parallel RC element.

[0060] Since RC itself is a standard impedance semicircle, its theoretical shape in the DRT spectrum is an isolated pulse at a time constant point. Continuous DRT simulation will introduce certain errors. If the position parameter identification effect is poor, this error will be significantly amplified. Therefore, the analysis of this battery model can well verify the ability of the method in this application to identify the relaxation time constant of the EIS internal impedance. Comparing the DRT formula and the impedance formula of RC, it can be seen that the integral of the core kernel function in the domain is R in RC, as shown in equation (13): (13).

[0061] In this third-order RC model, the values ​​of R0 and R1 are preset to 5Ω, and the relaxation time constant is... s, R2 is 10Ω, and the relaxation time constant is s, R3 has a value of 5Ω, and the relaxation time constant is The simulated EIS frequency range is 0.01Hz to 10000Hz. During the parameter search for the core kernel function, the position parameters... , , The initial value is s, s and s, the search upper and lower limits are set to expand the initial value upwards and downwards. s.

[0062] Figure 5 The overall DRT curves of the battery's third-order RC model are shown, calculated using the analysis method of this application (hereinafter referred to as the method) and the conventional kernel function-based DRT analysis method (hereinafter referred to as the conventional method).

[0063] As can be seen, when the shape parameter is taken as At time s, the overall DRT curve obtained by this method shows three narrow peaks, with values ​​concentrated at the three positional parameters of the core kernel function (i.e., the relaxation time constants corresponding to R1, R2, and R3). The identified relaxation time constants are... , and The areas of the three peaks were 4.997, 5.06 and 10.005, respectively, which showed good agreement with the preset parameters.

[0064] When calculating the DRT curve using the conventional method, the regularization parameter λ=1 and the full width at half maximum (FWHM) coefficient is set to 2. The peak width of the calculated DRT curve is close to that obtained by this method, but spurious peaks are also generated near the main relaxation time constant. This also shows the limitations of the conventional method in handling spurious peaks when calculating DRT.

[0065] Figure 6 The results of fitting the overall DRT curve to EIS based on these two methods are presented, along with a comparison with the simulated EIS. It can be seen that both methods can accurately fit the EIS; however, combining... Figure 5 It is evident that the ability to accurately identify peaks is a significant advantage of this method over conventional methods. Specific Implementation Example 2 This embodiment uses sample EIS data from the DRT Tools toolbox to perform DRT analysis and EIS fitting using both this method and conventional methods.

[0067] Figure 7 The comparison of DRT analysis results using this method and conventional methods is shown, with part (a) showing the comparison of the overall DRT curves. It can be seen that... ~ Within the range of s, the overall DRT curves obtained by the two methods show good consistency; at high frequencies ( ~ Within the s interval, significant differences appear, which is due to the fitting error of the conventional method for high-frequency EIS. Part (b) shows the comparison of EIS fitted using the DRT curve. It can be seen that this method fits the EIS with high accuracy across the entire frequency range, while the conventional method shows a large deviation in fitting the EIS in the high-frequency range.

[0068] Figure 8The results show the results obtained using this method for seven individual peaks, which cannot be clearly obtained using conventional methods. This also demonstrates the key advantage of this method over conventional methods, namely, the obvious analyzability for each individual kinetic process. Specific Implementation Example 3 This embodiment uses the measured EIS of Panasonic batteries to perform DRT analysis and EIS fitting using both this method and conventional methods.

[0070] Figure 9 The comparison of DRT analysis results using this method and the conventional method is shown, with (a) showing the comparison of the overall DRT curves and (b) showing the comparison of EIS fitted using the DRT curves. It can be seen that the overall DRT curves of the two methods exhibit significant differences. Each peak of this method shows clear separation. Conversely, the results of the conventional method are close to a smooth fit of the overall DRT curve obtained by this method, resulting in a lack of accurate separation between different kinetic processes. This demonstrates that, without explicit kinetic constraints, artificially "modifying" the DRT curve through regularization and other means actually leads to deviations from reality.

[0071] Figure 10 The results for seven individual peaks obtained using this method are also shown. Specific Implementation Example 4 This embodiment uses 18650 batteries to perform EIS tests at different measurement frequency densities. Figure 11 The results of DRT analysis using this method under different ppd are shown, where (a) is the EIS obtained by fitting the DRT curve, and (b) is the DRT curve. It can be seen that under different ppd, this method can accurately fit the EIS, and the final DRT shape does not change significantly due to changes in frequency point density.

[0073] Figure 12 The results of DRT analysis using the conventional method are shown at different ppd values. Part (a) shows the EIS obtained by fitting the DRT curve, and part (b) shows the DRT curve. It can be seen that as ppd increases, the fitting accuracy of the conventional method for EIS decreases, mainly in the high-frequency part. The enlarged plot on the right side of part (a) shows the fitting error of the conventional method at high frequencies.

[0074] from Figure 12As can be seen in part (b), when ppd=30, the calculated DRT curves are relatively separated. As ppd decreases, the DRT curves show a clear trend of increasing width and decreasing height, that is, the "impedance leakage" problem gradually becomes more serious. This further highlights the advantage of this method, that is, for a small number of frequency points, this method can also clearly and accurately calculate the separated impedance peaks without the problem of "impedance leakage".

[0075] The specific embodiments of this application have been described in detail above. For those skilled in the art, several improvements and modifications can be made to this application without departing from the principle of this application, and these improvements and modifications also fall within the protection scope of the claims of this application.

Claims

1. A continuous DRT analysis method based on priority peak splitting, characterized in that, Includes the following steps: Step 1: Based on the electrochemical characteristics of the target battery, peak segmentation is performed to determine several core kernel functions used to characterize the overall DRT curve of the target battery. The core kernel functions are peak shape functions with adjustable position and shape parameters, and each core kernel function corresponds to a single kinetic process of the target battery. Step 2: Determine the overall DRT curve and the expression of the DRT equation system of the target battery based on the core kernel function; Step 3: With the goal of minimizing the fitness function, iteratively search to obtain the optimal values ​​of the position and shape parameters of each core kernel function, as well as the corresponding magnitudes. Step 4: Determine the overall DRT curve of the target battery and / or the DRT curve corresponding to a single kinetic process of the target battery based on the search results.

2. A continuous DRT analysis method based on priority peak splitting, characterized in that, The total number of single kinetic processes of the target battery Furthermore, the total number of single dynamic processes of the target battery is much smaller than the total number of EIS measurement frequencies.

3. The continuous DRT analysis method based on priority peak splitting processing according to claim 2, characterized in that, Step 3 consists of initialization operations and multiple iterative search processes, each of which includes the following steps: S31, based on the current position and shape parameters, the amplitude of each core kernel function is determined by solving the DRT equation system; S32, based on the solution results of step S31, update the position parameters and shape parameters with the goal of minimizing the fitness function, and enter the next iteration until the iteration search termination condition is met.

4. The continuous DRT analysis method based on priority peak splitting processing according to claim 3, characterized in that, No regularization is performed when solving the DRT equations to obtain the magnitude of each core kernel function during each iterative search process.

5. The continuous DRT analysis method based on priority peak splitting processing according to claim 4, characterized in that, The DRT equation set is as follows: ， in, The total number of EIS measurement frequency points for the target battery. The total number of core kernel functions and , For the first angular frequency at each measurement point For the target battery in the first The complex impedance corresponding to the portion of the DRT curve at each measurement frequency point. The imaginary unit, and They are respectively The real and imaginary parts, , The first The core kernel function in the first Real and imaginary coefficients at each measurement frequency point For the first The magnitude of each core kernel function.

6. The continuous DRT analysis method based on priority peak splitting processing according to claim 5, characterized in that, , The specific expression is: ， in, Let the relaxation time constant be the independent variable of the logarithmic coordinate. For the first Adjustable position parameters of the logarithmic coordinates of each core kernel function. As an intermediate variable, For the first Adjustable shape parameters for each core kernel function; For the first There are 1 core kernel function, and each core kernel function opens downwards, with the maximum value at the center position. As the distance from the center position increases, the function value approaches 0.

7. The continuous DRT analysis method based on priority peak splitting processing according to claim 5, characterized in that, The fitness function is: ， in, It is the L2 norm. , , This represents the real part coefficient matrix, the imaginary part coefficient matrix, and the column vector of the magnitude of the core kernel function in the DRT equation system. This is the measured column vector of the real part of the DRT impedance. This is the measured column vector of the imaginary part of the DRT impedance.

8. The continuous DRT analysis method based on priority peak splitting processing according to claim 3, characterized in that, In step three, the initialization operation is used to set the initial values ​​of the position and shape parameters of each core kernel function, the search range, the search size, and the search termination condition. Among them, the search range of the position parameters corresponding to a single diffusion-related kinetic process or an equivalent resistance effect is larger than the search range of the position parameters corresponding to other single kinetic processes or equivalent resistance effects.

9. The continuous DRT analysis method based on priority peak splitting processing according to claim 8, characterized in that, The target battery is a lithium-ion battery, and the total number of core kernel functions is... The initial values ​​of the position parameters of each core kernel function are: .

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