Electrochemical impedance spectroscopy automatic modeling and fitting method, system, device and medium

Abstract

The application provides an electrochemical impedance spectrum automatic modeling and fitting method, system, device and medium, and belongs to the technical field of electrochemical impedance spectrum data analysis. The method comprises the following steps: obtaining impedance spectrum data of an electrochemical system; performing relaxation time distribution analysis on the data to obtain a relaxation time distribution spectrum; identifying the number of effective peaks in the distribution spectrum; automatically constructing an equivalent circuit model based on the number of effective peaks; and determining the parameter values of each element in the equivalent circuit by using a complex nonlinear least square fitting method. The electrochemical impedance spectrum automatic modeling and fitting method, system, device and medium are used to automatically identify the number of internal physical and chemical processes of a system through a relaxation time distribution spectrum, and an equivalent circuit structure is constructed accordingly, so that the problems of the traditional modeling method, such as the dependence on artificial experience, the strong subjectivity of model selection, and the fragmentation of the DRT analysis and circuit modeling process, are solved, and the automatic impedance spectrum analysis of various electrochemical systems, such as fuel cells and electrolytic tanks, is applicable.

Description

Technical Field

[0001] This invention relates to the field of electrochemical impedance spectroscopy data analysis technology, and in particular to automatic modeling and fitting methods, systems, equipment and media for electrochemical impedance spectroscopy. Background Technology

[0002] Electrochemical impedance spectroscopy (EIS) is a core technique for characterizing the kinetic processes and interfacial properties of electrochemical devices, and its data analysis typically relies on the construction of equivalent circuit models (ECMs). For membrane electrode assemblies (MEAs) with reactive double-layer structures, their internal structure consists of multiple layers, including a catalyst layer, a proton (or anion) exchange membrane, and a gas diffusion layer. During operation, multiple physicochemical processes are involved, such as electron conduction, ion migration, gas diffusion, interfacial charge accumulation, and reaction product transport. Due to the different microporous structures and interfacial conductivity properties of each layer, MEA systems typically exhibit multiple time constants, resulting in impedance spectral curves displaying multiple relaxation processes and strong frequency coupling effects.

[0003] Traditional ECM modeling relies on pre-defined topologies based on experience (such as Randle circuits, transmission line models, etc.), which has the following drawbacks:

[0004] Highly subjective: The number and connection method of circuit components are preset manually, lacking objective basis;

[0005] Poor versatility: The model is difficult to adaptively match the dynamic reaction process under different devices (such as fuel cells, proton exchange membrane electrolyzers, electrochemical dehumidification membrane modules, etc.) or changing operating conditions;

[0006] Limited accuracy: In complex systems with multiple reaction interfaces or non-ideal double layers, the coupled reaction process is often simplified to a single RC module, resulting in large fitting errors and distortion of physical meaning.

[0007] Relaxation time distribution (DRT) analysis can convert electrochemical test data into a time-domain distribution function, reflecting independent electrochemical reaction processes through the number and position of relaxation peaks. However, existing DRT techniques have the following limitations:

[0008] Limited functionality and lack of mapping: Most studies only use DRT for visualization analysis, lacking a direct connection with equivalent circuit modeling; there is no strict correspondence between the number of relaxation peaks and the number of circuit modules, making it impossible to automatically generate circuit topology;

[0009] Insufficient practicality: It fails to effectively consider effects such as non-ideal capacitive behavior, interface charge leakage, and distributed resistance, which affects the accuracy of the model; at the same time, the overlap of peaks in different reaction stages also leads to a decrease in resolution.

[0010] The analysis process is fragmented: the number of relaxation peaks identified by DRT cannot directly drive the generation of the equivalent circuit structure; there is a lack of quantitative correlation between circuit element parameters (such as reactive resistance and double-layer capacitance) and DRT peak intensity; the coupling characteristics of multiple reaction processes cannot be identified and modeled by automated means.

[0011] In summary, the core problem with existing EIS analysis technology lies in the disconnect between DRT analysis and ECM modeling processes, which severely restricts its ability to perform objective, accurate, and automated diagnosis of complex electrochemical systems. Summary of the Invention

[0012] The purpose of this invention is to provide an automatic modeling and fitting method, system, device and medium for electrochemical impedance spectroscopy, in order to solve the problems of low accuracy and poor versatility caused by the strong subjectivity of model selection and the separation of DRT analysis and circuit modeling processes in the prior art.

[0013] To achieve the above objectives, this invention provides an automatic modeling and fitting method for electrochemical impedance spectroscopy, comprising the following steps:

[0014] Step S1: Acquire and process the impedance spectrum data of the electrochemical system. The impedance spectrum data includes frequency... Real part of impedance and the imaginary part of impedance The set of data points;

[0015] Step S2: Perform relaxation time distribution analysis on the impedance spectrum data to obtain the relaxation time distribution spectrum characterizing the internal electrochemical process of the electrochemical system;

[0016] Step S3: Identify the number of valid peaks in the relaxation time distribution spectrum;

[0017] Step S4: Based on the number of effective peaks, automatically construct an equivalent circuit model;

[0018] Step S5: Use the equivalent circuit model to perform complex nonlinear least squares fitting on the impedance spectrum data to determine the parameter values ​​of each component in the equivalent circuit.

[0019] Preferably, in step S1, the electrochemical system is a process involving the electrode-electrolyte interface double layer / capacitance effect, including: an electrochemical testing system based on catalyst slurry and a system with membrane electrode assembly, wherein the system with membrane electrode assembly includes proton exchange membrane fuel cell / electrolyte, anion exchange membrane fuel cell / electrolyte, steam electrolyzer, ambient humidity electrolyzer, alkaline water electrolyzer, CO2 electrolyzer, ammonia fuel cell / electrolyzer or metal-air battery with MEA structure.

[0020] Preferably, in step S2, the relaxation time distribution analysis is achieved by solving the following first-kind Fredholm integral equation:

[0021] ;

[0022] in, This represents the total impedance of the tested electrochemical system. Indicates ohmic resistance. Represents the relaxation time distribution function. Indicates the relaxation time. Represents angular frequency. Represents the imaginary unit;

[0023] Solving this equation is a typical ill-conditioned inverse problem. A Tikhonov regularization-based method is preferred to obtain a stable and physically plausible solution. The solution is found by minimizing the following objective function. Discretized representation:

[0024] ;

[0025] in, This represents the impedance data measured in the experiment. This represents the kernel function of the discretized integral operator. This represents a regularization matrix (usually an identity matrix or a derivative operator). Represents the regularization parameter. Denotes the relaxation time distribution function to be determined. .

[0026] Preferably, in step S3, identifying the number of effective peaks in the relaxation time distribution spectrum includes:

[0027] The local maxima in the relaxation time distribution spectrum are detected using a pre-defined peak identification criterion.

[0028] Traversal of relaxation time distribution function Given a discrete numerical array, for each element of the discrete numerical array... ,in This represents an array index, corresponding to a specific relaxation time. Check whether it satisfies the following mathematical conditions:

[0029] Condition one: That is, the distribution intensity at the current point is greater than the distribution intensity at the previous adjacent time point;

[0030] Condition two: That is, the distribution intensity at the current point is greater than the distribution intensity at the next adjacent time point;

[0031] Points that satisfy both of the above conditions These are identified as local maxima, and each such point corresponds to an independent relaxation process in the electrochemical system.

[0032] The number of local maxima is equal to the number of effective peaks, and the total number is counted. .

[0033] Preferably, each effective peak corresponds to an independent electrochemical process, including: oxygen evolution reaction, oxygen reduction reaction, or hydrogen evolution reaction; in the equivalent circuit model, each electrochemical process is transmitted through a... Parallel branch characterization, among which This indicates the reaction resistance of the process. This indicates a constant-phase element.

[0034] Preferably, the DRT analysis employs Toeplitz structure matrix construction based on kernel integral and conventional numerical linear algebra calculations; parameter fitting uses numerical difference to estimate the Jacobian and solves it using trust region reflection least squares optimization; parallel computing is used as an optional feature for some machine learning training modules to fully utilize multi-core processor resources, and the core DRT and impedance parameter fitting processes are executed in a single-threaded environment.

[0035] Preferably, multiple basic equivalent circuit models are preset, each containing a different number of electrochemical process units. Based on the determined number of peaks, the best-matching model is selected from the preset model library.

[0036] Preferably, in step S4, the equivalent circuit model consists of a series ohmic resistor. A series-connected inductor module as well as It consists of a series of parallel sub-circuits, and a series inductor module. Including inductors and starting resistor ;

[0037] Each parallel sub-circuit corresponds to one effective peak; each parallel sub-circuit consists of a reactive resistor. With Warburg diffusion impedance After being connected in series, it is then connected to a constant phase element. Composed of parallel connections. From constant values and exponential factors Parameterized definition.

[0038] Preferably, the total impedance of the equivalent circuit model Defined by the following expression:

[0039] ;

[0040] ;

[0041] in, Indicates the first Parallel sub-circuits ( The total resistance of the branch circuit. , , , They represent the first indivual The branch's reactive resistance, capacitance, dispersion coefficient, and Weber impedance. .

[0042] Preferably, in step S5, complex nonlinear least squares (CNLS) fitting is employed. An optimal set of parameters is found through iterative optimization algorithms (such as Levenberg-Marquardt or trust region reflection algorithms). This minimizes the sum of squared residuals between the impedance spectrum calculated by the model and the experimentally measured spectrum, where Indicates ohmic resistance. Indicates the inductance value, each The branch describes an independent electrochemical relaxation process, in which: Indicates the first The reaction resistance of the process Indicates the first The constant phase angle element value for each process, Indicates the first The dispersion coefficient of the process, Indicates the first Weber impedance of the process The value is 1- ,parameter The model contains The number of branches is determined based on the number of relaxation processes in the actual electrochemical system. To ensure the global optimality of the fitting results and the reasonableness of their physical meaning, the following strategy is further adopted:

[0043] Parameter boundary constraints: Set reasonable physical upper and lower limits for all parameters to be fitted (e.g., all resistors, inductors, etc.). The coefficient must be positive. The value is between 0 and 1.

[0044] Multi-round iteration and initial value optimization: Multiple rounds of fitting can be performed, with different initial values ​​used in each round (e.g., the initial values ​​can be estimated based on the position and height of the DRT peak) to effectively avoid getting trapped in local optima and improve the robustness and reliability of the fitting.

[0045] To ensure the convergence of parameter fitting, the following strategy is adopted:

[0046] ① Set the maximum number of iterations to 1000;

[0047] ② Convergence criterion: The parameter change between two consecutive iterations is less than 10. -6 ;

[0048] ③ Employ a multi-starting-point strategy: Randomly generate 5 to 10 different sets of initial parameters for parallel fitting;

[0049] ④ Select the result with the smallest objective function value as the final fitting result.

[0050] The output shows the optimal parameter values ​​for each element in the fitted ECM and their fit confidence intervals. It also generates a series of visualizations, including:

[0051] The original data and the fitted curve are compared on Nyquist and Bode plots, and the goodness of fit (such as chi-square) is calculated to visually demonstrate the fitting effect.

[0052] DRT analysis of the spectrum and the identified peaks.

[0053] The resistance corresponding to each (R / / CPE) branch obtained by fitting The value can be used to perform correlation analysis with the DRT peak area.

[0054] This invention also provides an automatic modeling and fitting system for electrochemical impedance spectroscopy, comprising:

[0055] The data input module is used to receive impedance spectrum data;

[0056] The DRT analysis module is used to perform relaxation time distribution analysis and identify the number of valid peaks.

[0057] The model building module is used to automatically generate an equivalent circuit model based on the number of effective peaks.

[0058] The parameter fitting module is used to fit impedance spectrum data to obtain component parameters;

[0059] The result output module is used to output component parameters.

[0060] The present invention also provides a computer device, including: a memory and a processor; the memory stores a computer program, and the processor executes the computer program to implement the steps of the above-described automatic modeling and fitting method for electrochemical impedance spectroscopy.

[0061] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-described automatic modeling and fitting method for electrochemical impedance spectroscopy.

[0062] Therefore, the present invention employs the above-mentioned automatic modeling and fitting method, system, equipment, and medium for electrochemical impedance spectroscopy, and the beneficial technical effects are as follows:

[0063] (1) This invention automatically identifies the number of physicochemical processes inside the system by means of relaxation time distribution spectrum, and objectively determines the structure of the equivalent circuit model accordingly, replacing the traditional method of relying on human experience to pre-set the model, thus ensuring the objectivity and repeatability of the analysis results.

[0064] (2) The present invention can automatically adjust the complexity of the equivalent circuit model according to different test objects or working conditions, thus making it widely applicable to various electrochemical systems such as fuel cells and electrolyzers, thereby improving the universality and analytical efficiency of the method.

[0065] (3) By establishing a strict correspondence between relaxation peaks and circuit units, this invention enables the model to more accurately describe the multiple and coupled interface reaction processes in the system, overcoming the defects of large fitting errors and distortion of physical meaning caused by traditional simplified models. Attached Figure Description

[0066] Figure 1 The DRT spectrum of Example 1;

[0067] Figure 2 This is the equivalent circuit of Example 1;

[0068] Figure 3 The Nyquist plot is shown in Example 1;

[0069] Figure 4 The DRT spectrum is shown in Example 2;

[0070] Figure 5 This is the equivalent circuit of Example 2;

[0071] Figure 6 The Nyquist plot is shown in Example 2;

[0072] Figure 7 The DRT spectrum is shown in Example 3;

[0073] Figure 8 The Nyquist plot is shown in Example 3;

[0074] Figure 9 This is the DRT diagram for Example 4;

[0075] Figure 10 The equivalent circuit diagram for Example 4 is shown below.

[0076] Figure 11 The Nyquist plot is shown in Example 4;

[0077] Figure 12This is the DRT diagram for Example 5;

[0078] Figure 13 This is the equivalent circuit diagram for Example 5;

[0079] Figure 14 The Nyquist plot is shown in Example 5;

[0080] Figure 15 This is a flowchart of the automatic modeling and fitting method for electrochemical impedance spectroscopy of the present invention. Detailed Implementation

[0081] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0082] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0083] Example 1

[0084] Currently, the processing of electrochemical impedance spectroscopy measurement data is typically accomplished using specialized AC impedance fitting software, with ZView developed by Derek Johnson being one of the most widely used tools. When using ZView for fitting, users need to manually import the impedance data to be processed and set the corresponding parameters according to specific requirements. A typical workflow includes: first, selecting a suitable frequency band to obtain initial parameter values; then, constructing a corresponding equivalent circuit model based on the understanding of the electrochemical system; and finally, conducting simulation and fitting analysis. This method equates the electrochemical system to a circuit network composed of basic components such as resistors, inductors, and phase-constant elements connected in series and parallel. After fitting, the absolute and relative errors of each component's parameters are evaluated, and the final fitting result is output. The advantage of ZView software lies in its high operational flexibility, allowing users to independently select a suitable model structure based on the specific system.

[0085] However, this method also has obvious limitations: the construction of the equivalent circuit model depends heavily on the user's electrochemical expertise and experience, which leads to significant subjective differences in the analytical results of different users for the same system.

[0086] Furthermore, the entire fitting process is cumbersome and requires a lot of manual intervention, making it difficult to achieve fast and efficient impedance analysis and result output.

[0087] Therefore, an automatic modeling and fitting method for electrochemical impedance spectroscopy is provided (its core process is as follows). Figure 15 As shown), the estimated values ​​of each element are obtained by rapidly fitting the electrochemical impedance spectroscopy, including:

[0088] Step 1: Data Acquisition.

[0089] EIS data for the electrolyte membrane dehumidification unit (i.e., the PEM electrolyzer fed with ambient humidity) was acquired under conditions of 21°C and 80%RH. The data file contains 44 data points, each represented by a frequency. Real part of impedance and the imaginary part of impedance Composition. The data has been processed and contains no obvious bad pixels.

[0090] Step 2, DRT analysis.

[0091] The method of this invention is used to perform DRT analysis on the above EIS data. Tikhonov regularization is employed in the analysis, and the regularization parameters are as follows: Automatically determined, the basis functions are Gaussian radial basis functions. The obtained DRT spectrum is analyzed as follows: Figure 1 As shown.

[0092] Step 3: Automatic identification of DRT spectral features.

[0093] right Figure 1 The DRT spectrum shown is used for automatic peak identification. Based on preset peak height and peak significance thresholds, the program automatically identifies two valid peaks. The specific parameters of the identified peak information are shown in Table 1.

[0094] The results show that the system mainly involves two independent electrochemical processes under the current operating conditions.

[0095] Table 1. DRT peak analysis results of Example 1

[0096]

[0097] Step 4: Adaptive construction of the equivalent circuit model.

[0098] like Figure 2 Based on the number of valid peaks identified in step 3 =2, this embodiment automatically constructs a system containing 1 ohm resistor ( ), 1 starting resistor ( A starting inductor ( ) and 2 ( The equivalent circuit model (ECM) of parallel branches, i.e. .

[0099] Total impedance The expression is:

[0100] ;

[0101] ;

[0102] in, Indicates ohmic resistance. Indicates inductance. Indicates the first Parallel sub-circuits ( The total resistance of the branch circuit. , , , They represent the first indivual The branch's reactive resistance, capacitance, dispersion coefficient, and Weber impedance. .

[0103] Step 5: Nonlinear fitting of model parameters.

[0104] The automatically constructed ECM was used to fit the original EIS data using complex nonlinear least squares. Physical boundaries for each parameter were set, and after multiple rounds of iterative optimization, the optimal parameter values ​​for each component were obtained. Some key parameters are shown in Table 2.

[0105] Step 6: Output the results.

[0106] The fitted impedance spectrum was compared with the original experimental data on a Nyquist plot, such as... Figure 3 As shown in the figure, the fitted curve highly overlaps with the experimental data points, proving that the model automatically constructed in this invention can accurately characterize the electrochemical system.

[0107] Table 2 ECM fitting parameters for Example 1

[0108]

[0109] Example 2

[0110] This embodiment demonstrates the process of analyzing EIS data collected from the dehumidified electrolyte membrane electrode (i.e., a PEM electrolyzer with ambient humidity feed) under the same operating conditions after the electrolyte membrane has degraded, in order to illustrate the adaptive capability of the present invention.

[0111] Repeat steps 1 to 6 of Example 1, with the following differences:

[0112] Step 3: DRT analysis and peak identification.

[0113] Perform DRT analysis on the data, such as Figure 4 As shown in Table 3, the method automatically identified three valid peaks, whose distribution differed significantly from that in Example 1, indicating that the internal process state of the system had changed.

[0114] The results show that the system mainly involves three independent electrochemical processes under the current operating conditions.

[0115] Table 3. DRT peak analysis results of Example 2

[0116]

[0117] Step 4: Adaptive construction of the equivalent circuit model.

[0118] like Figure 5 Based on the number of valid peaks identified in step 3 =3, the method of this invention automatically constructs a system containing a 1-ohm resistor ( ), 1 starting resistor ( A starting inductor ( ) and 3 ( The equivalent circuit model of parallel branches, i.e. .

[0119] The total impedance expression is:

[0120] ;

[0121] ;

[0122] Step 5: Nonlinear fitting of model parameters.

[0123] The automatically constructed ECM was used to fit the original EIS data using the complex nonlinear least squares method. Physical boundaries for each parameter were set, and after multiple rounds of iterative optimization, the optimal parameter values ​​for each component were obtained. Some key parameters are shown in Table 4.

[0124] Step 6: Output the results.

[0125] The fitted impedance spectrum was compared with the original experimental data on a Nyquist plot, such as... Figure 6 As shown in the figure, the fitted curve highly overlaps with the experimental data points, proving that the model automatically constructed in this invention can accurately characterize the electrochemical system.

[0126] Table 4. ECM fitting parameters for Example 2

[0127]

[0128] Example 3

[0129] This embodiment demonstrates the process of analyzing EIS data collected during performance testing of catalyst slurry to illustrate the adaptive capability of the present invention.

[0130] Repeat steps 1 to 6 of Example 1, with the following differences:

[0131] Step 3: DRT analysis and peak identification.

[0132] DRT analysis was performed on the data of the catalyst slurry, such as... Figure 7 As shown in Table 5, the method automatically identified three valid peaks, whose distribution differed significantly from that in Example 1, indicating that the internal process state had changed.

[0133] The results show that the system mainly involves three independent electrochemical processes under the current operating conditions.

[0134] Table 5. DRT peak analysis results of Example 3

[0135]

[0136] Step 4: Adaptive construction of the equivalent circuit model.

[0137] like Figure 7 Based on the number of valid peaks identified in step 3 =3 The method of this invention automatically constructs a structure containing a 1-ohm resistor ( ), 1 starting resistor ( A starting inductor ( ) and 3 ( Equivalent circuit model of parallel branches, .

[0138] The total impedance expression is:

[0139] ;

[0140] ;

[0141] Step 5: Nonlinear fitting of model parameters.

[0142] The automatically constructed ECM was used to fit the original EIS data using the complex nonlinear least squares method. Physical boundaries for each parameter were set, and after multiple rounds of iterative optimization, the optimal parameter values ​​for each component were obtained. Some key parameters are shown in Table 6.

[0143] Step 6: Output the results.

[0144] The fitted impedance spectrum was compared with the original experimental data on a Nyquist plot, such as... Figure 8 As shown in the figure, the fitted curve highly overlaps with the experimental data points, proving that the model automatically constructed in this invention can accurately characterize the electrochemical system.

[0145] Table 6. ECM fitting parameters for Example 3

[0146]

[0147] Example 4

[0148] This embodiment demonstrates the process of analyzing EIS data with Weber impedance to illustrate the adaptive capability of the present invention.

[0149] Repeat steps 1 to 6 of Example 1, with the following differences:

[0150] Step 3: DRT analysis and peak identification.

[0151] DRT analysis was performed on EIS data with Weber impedance, such as Figure 9 As shown in the figure. The method automatically identified four valid peaks. Peak information is shown in Table 7.

[0152] The results show that the system has four independent processes under the current operating conditions, including three electrochemical processes and one mass diffusion process.

[0153] Table 7. DRT Peak Analysis Results of Example 4

[0154]

[0155] Step 4: Adaptive construction of the equivalent circuit model.

[0156] like Figure 10 Based on the number of valid peaks identified in step 3 =4, the relaxation time of the fourth peak is in the range of 1-10s, and it is identified as the Weber impedance peak. The system can directly fit it, and there is no need to construct a separate one. Therefore, the method of this invention automatically constructs a parallel branch containing one ohm resistor ( ), 1 starting resistor ( A starting inductor ( ), 3 ( The equivalent circuit model of a parallel branch and a Weber impedance, i.e. .

[0157] The total impedance expression is:

[0158] ;

[0159] ;

[0160] Step 5: Nonlinear fitting of model parameters.

[0161] The automatically constructed ECM was used to fit the original EIS data using complex nonlinear least squares. Physical boundaries for each parameter were set, and after multiple rounds of iterative optimization, the optimal parameter values ​​for each component were obtained. Some key parameters are shown in Table 8.

[0162] Step 6: Output the results.

[0163] The fitted impedance spectrum was compared with the original experimental data on a Nyquist plot, such as... Figure 11 As shown in the figure, the fitted curve highly overlaps with the experimental data points, proving that the model automatically constructed in this invention can accurately characterize the electrochemical system.

[0164] Table 8. ECM fitting parameters for Example 4

[0165]

[0166] Example 5

[0167] This embodiment demonstrates the process of analyzing EIS data collected during performance testing of another electrolysis system: an electrolytic water vapor hydrogen production system, to illustrate the adaptive capability of the present invention.

[0168] Repeat steps 1 to 6 of Example 1, with the following differences:

[0169] Step 3: DRT analysis and peak identification.

[0170] DRT analysis was performed on the EIS data collected from the water electrolysis steam hydrogen production system, such as... Figure 12 As shown in Table 9, the method automatically identified three valid peaks.

[0171] The results show that the system mainly involves three independent electrochemical processes under the current operating conditions.

[0172] Table 9. DRT Peak Analysis Results of Example 5

[0173]

[0174] Step 4: Adaptive construction of the equivalent circuit model.

[0175] like Figure 13 Based on the number of valid peaks identified in step 3 =3, the method of this invention automatically constructs a system containing a 1-ohm resistor ( ), 1 starting resistor ( A starting inductor ( ) and 3 ( The equivalent circuit model of parallel branches, i.e. .

[0176] The total impedance expression is:

[0177] ;

[0178] ;

[0179] Step 5: Nonlinear fitting of model parameters.

[0180] The automatically constructed ECM was used to fit the original EIS data using the complex nonlinear least squares method. Physical boundaries for each parameter were set, and after multiple rounds of iterative optimization, the optimal parameter values ​​for each component were obtained. Some key parameters are shown in Table 10.

[0181] Step 6: Output the results.

[0182] The fitted impedance spectrum was compared with the original experimental data on a Nyquist plot, such as... Figure 14 As shown in the figure, the fitted curve highly overlaps with the experimental data points, proving that the model automatically constructed in this invention can accurately characterize the electrochemical system.

[0183] Table 10 ECM fitting parameters for Example 5

[0184]

[0185] Example 6

[0186] An automated modeling and fitting system for electrochemical impedance spectroscopy includes:

[0187] The data input module is used to receive impedance spectrum data;

[0188] The DRT analysis module is used to perform relaxation time distribution analysis and identify the number of valid peaks M.

[0189] The model building module is used to automatically generate an equivalent circuit model based on the number of effective peaks M.

[0190] The parameter fitting module is used to fit impedance spectrum data to obtain component parameters;

[0191] The result output module is used to output component parameters.

[0192] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0193] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-including system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device.

[0194] More specific examples of computer-readable media (a non-exhaustive list) include: electrical connections (electronic devices) having one or more wires, portable computer disk drives (magnetic devices), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Furthermore, computer-readable media can even be paper or other suitable media on which the program can be printed, because the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in computer memory.

[0195] It is worth noting that all contents not described in detail in this invention are existing technologies and are well known to those skilled in the art.

[0196] Therefore, the present invention employs the above-mentioned automatic modeling and fitting method, system, equipment and medium for electrochemical impedance spectroscopy, which can realize the objectivity, automation and high precision of electrochemical impedance spectroscopy analysis, improve the efficiency and reliability of impedance spectroscopy modeling of complex electrochemical systems, and has good versatility and application prospects.

[0197] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. An automatic modeling and fitting method for electrochemical impedance spectroscopy, characterized in that, Includes the following steps: Step S1: Obtain impedance spectroscopy data of the electrochemical system; Step S2: Perform relaxation time distribution analysis on the impedance spectrum data to obtain the relaxation time distribution spectrum characterizing the internal electrochemical process of the electrochemical system; Step S3: Identify the number of valid peaks in the relaxation time distribution spectrum; Step S4: Based on the number of effective peaks, automatically construct an equivalent circuit model; Step S5: Use the equivalent circuit model to perform complex nonlinear least squares fitting on the impedance spectrum data to determine the parameter values ​​of each component in the equivalent circuit. In step S3, the number of valid peaks in the relaxation time distribution spectrum is identified, including: The local maxima in the relaxation time distribution spectrum are detected using a pre-defined peak identification criterion. Traversal of relaxation time distribution function Given a discrete numerical array, for each element of the discrete numerical array... ,in This represents an array index, corresponding to a specific relaxation time. Check whether it satisfies the following mathematical conditions: Condition one: That is, the distribution intensity at the current point is greater than the distribution intensity at the previous adjacent time point; Condition two: That is, the distribution intensity at the current point is greater than the distribution intensity at the next adjacent time point; Points that satisfy both of the above conditions It was identified as a local maximum point; The number of local maxima is equal to the number of effective peaks, and the total number is counted. ; In step S4, the equivalent circuit model consists of a series ohmic resistor. A series-connected inductor module as well as It consists of a series of parallel sub-circuits, and a series inductor module. Including inductors and starting resistor ; Each parallel sub-circuit corresponds to one effective peak; each parallel sub-circuit consists of a reactive resistor. With Warburg diffusion impedance After being connected in series, it is then connected to a constant phase element. Composed of parallel connections; Total impedance of equivalent circuit model Defined by the following expression: ； ； in, Indicates the first The total resistance of the parallel sub-circuits , , , They represent the first The reactive resistance, capacitance, dispersion factor, and Weber impedance of each parallel sub-circuit. , Represents angular frequency. It represents the imaginary unit.

2. The automatic modeling and fitting method for electrochemical impedance spectroscopy according to claim 1, characterized in that, In step S1, the electrochemical system is a process involving the electrode-electrolyte interface double layer / capacitance effect, including: an electrochemical testing system based on catalyst slurry and a system with membrane electrode assembly.

3. The automatic modeling and fitting method for electrochemical impedance spectroscopy according to claim 1, characterized in that, In step S2, the relaxation time distribution analysis is achieved by solving the following first-kind Fredholm integral equation: ； in, This represents the total impedance of the tested electrochemical system. Indicates ohmic resistance. Represents the relaxation time distribution function. Indicates the relaxation time. Represents angular frequency. Represents the imaginary unit; The solution process employs the Tikhonov regularization method, combined with Gaussian radial basis functions to adjust the relaxation time distribution function. Discretize the solution.

4. The automatic modeling and fitting method for electrochemical impedance spectroscopy according to claim 1, characterized in that, In step S5, the complex nonlinear least squares fitting process sets physical boundary constraints for all parameters of the elements to be fitted and uses multiple sets of initial values ​​for parallel fitting.

5. An automatic modeling and fitting system for electrochemical impedance spectroscopy, characterized in that, An automatic modeling and fitting method for electrochemical impedance spectroscopy as described in any one of claims 1-4, comprising: The data input module is used to receive impedance spectrum data; The DRT analysis module is used to perform relaxation time distribution analysis and identify the number of valid peaks. The model building module is used to automatically generate an equivalent circuit model based on the number of effective peaks. The parameter fitting module is used to fit impedance spectrum data to obtain component parameters; The result output module is used to output component parameters.

6. A computer device, comprising: Memory and processor; The memory stores a computer program, characterized in that when the processor executes the computer program, it implements the steps of the automatic modeling and fitting method for electrochemical impedance spectroscopy as described in any one of claims 1-4.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the automatic modeling and fitting method for electrochemical impedance spectroscopy as described in any one of claims 1-4.

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