Automatic equivalent circuit fitting method for batch electrochemical impedance spectroscopy data

Abstract

The embodiment of the invention discloses an equivalent circuit automatic fitting method for batch electrochemical impedance spectroscopy data, and the method comprises the steps: carrying out the electrochemical impedance spectroscopy test of a cement-based test piece, and obtaining the actual measurement value of each item of AC impedance spectroscopy data in test data; in combination with the composite optimization objective function, obtaining element parameter vectors in the candidate equivalent circuit after local refinement; after all the candidate equivalent circuits are traversed, an optimal candidate equivalent circuit is found, and then a final expression of the optimal candidate equivalent circuit based on test data is obtained; and completing fitting of the equivalent circuit for batch electrochemical impedance spectroscopy data. According to the method, the global reliability and batch processing capability of equivalent circuit parameter inversion can be improved while the fitting precision is ensured, and the engineering application of the electrochemical impedance spectroscopy technology in cement-based material performance evaluation and durability analysis can be better supported.

Description

Technical Field

[0001] This invention relates to the field of impedance spectroscopy analysis technology, and in particular to an automatic equivalent circuit fitting method for batch electrochemical impedance spectroscopy data. Background Technology

[0002] Cement-based materials, as the most commonly used structural materials in civil engineering, depend to a large extent on their service performance and durability, including their internal pore structure, ion transport characteristics, and the evolution of hydration reactions and degradation processes. To effectively characterize the microstructure and service condition of cement-based materials, researchers have developed various non-destructive or micro-destructive testing methods. Among these, electrical testing methods have attracted widespread attention due to their high sensitivity to pore solutions, electrolyte transport, and interfacial reactions.

[0003] Electrochemical impedance spectroscopy (EIS) is an electrochemical testing technique based on frequency domain analysis. It obtains the complex impedance response of a material system by applying a small-amplitude AC perturbation signal over a wide frequency range. Existing research has shown that the impedance response of cement-based materials is closely related to porosity, pore size distribution, pore connectivity, and the conductivity of the pore solution. Therefore, EIS has been widely used in research fields such as monitoring cement hydration processes, identifying setting and hardening characteristics, evaluating chloride ion transport capacity, and analyzing the corrosion behavior of reinforced concrete.

[0004] In the early stages, the evolution of pore structure caused by hydration reaction can be reflected by the change of resistivity or impedance over time, and a quantitative correlation can be established with the degree of hydration, setting time and strength development. In the service stage, characteristic parameters related to pore connectivity, electrolyte migration resistance and interface polarization process can be extracted by impedance spectroscopy analysis, which can be used to characterize the material's impermeability, resistance to chloride ion erosion and the corrosion kinetics of steel bars.

[0005] Because cement-based materials are highly heterogeneous, multi-scale coupled systems, their EIS response typically exhibits Nyquist curves with multiple overlapping time constants and complex Bode characteristics. To separate and quantify different physical processes, equivalent circuit models are widely used to establish a correspondence between impedance spectra and parameters such as resistance, capacitance, constant-phase elements, and diffusion elements. Through the inversion of equivalent circuit parameters, the electrical response can be further linked to the microstructural characteristics of the material, thereby improving the engineering applicability of EIS in the characterization of cement-based materials.

[0006] However, in existing technologies, obtaining the equivalent circuit parameters of EIS for cement-based materials highly depends on human experience and local optimization algorithms. On the one hand, the selection of initial parameters for the equivalent circuit is highly subjective, and different initial values ​​may lead to significant differences in the fitting results. On the other hand, traditional least squares or gradient-based algorithms are prone to getting trapped in local optima, making it difficult to guarantee obtaining the global optimal solution in a multi-peak, highly nonlinear parameter space. Furthermore, in practical engineering applications, it is often necessary to process multiple sets of impedance spectrum data in batches, and existing methods have significant shortcomings in terms of stability, automation, and computational efficiency. Summary of the Invention

[0007] This invention discloses an automatic equivalent circuit fitting method for batch electrochemical impedance spectroscopy data to overcome the above-mentioned technical problems.

[0008] To achieve the above objectives, the technical solution of the present invention is as follows: An automatic equivalent circuit fitting method for batch electrochemical impedance spectroscopy data includes the following steps: S1: Obtain the equivalent circuit text collected by the user to describe the conductivity mechanism of cement-based materials, and convert it into an equivalent circuit expression to establish a candidate equivalent circuit set, and set the initial values ​​of the component parameters in the candidate equivalent circuit. S2: Perform electrochemical impedance spectroscopy on cement-based specimens to obtain experimental data; the experimental data includes multiple AC impedance spectral data, which include imaginary components, real components, frequency, impedance mode, and phase angle; S3: Establish a composite optimization objective function, namely a three-domain composite chi-square; S4: Based on the imaginary components, real components, frequency, impedance magnitude and phase angle of the experimental data, the initial values ​​of the component parameters of the candidate equivalent circuits in the candidate equivalent circuit set, and the composite optimization objective function, obtain the component parameter vector in the candidate equivalent circuits after local refinement. S5: Traverse all candidate equivalent circuits in the candidate equivalent circuit set, and according to the composite optimization objective function, obtain the component parameter vector in the optimal candidate equivalent circuit after local refinement, so as to obtain the optimal candidate equivalent circuit, and then obtain the final expression of the optimal candidate equivalent circuit based on experimental data; complete the fitting of the equivalent circuit for batch electrochemical impedance spectroscopy data.

[0009] Furthermore, the method used to obtain the component parameter vectors in the equivalent circuit after local refinement is as follows: S41: In D Within the dimensional search domain, an initial population is randomly generated based on the initial values ​​of the candidate circuit elements; S42: Constructing the first The mutated vector of the individual vectors in the population at the next iteration; S43: According to the... The mutation vectors of individuals in the population at the nth iteration and the 1st iteration The individual vectors in the population at the nth iteration are obtained. The trial vector of an individual in the population at the next iteration; S44: According to the... The vector of each individual in the population at the nth iteration, the... The trial vectors of individuals in the population and the composite optimization objective function at the nth iteration determine the nth iteration. The final individual vector in the population at the next iteration; S45: Based on the first The final individual vector in the population at the next iteration is used to re-execute S33-S35 until the iteration termination condition is met, and the optimal individual vector is obtained. S46: Based on the optimal individual vector, obtain the component parameter vector in the equivalent circuit after local refinement.

[0010] Furthermore, the composite optimization objective function is expressed as follows: (1) In the formula: OBJ To optimize the value of the objective function; , , These are the weights of the chi-square corresponding to the Nyquist curve, the weight of the chi-square corresponding to the Bode-phase curve, and the weight of the chi-square corresponding to the Bode-impedance mode curve, respectively, obtained based on the fitted equivalent circuit. Chi-square of the Nyquist curve fitting result; Chi-square of the Bode-phase curve fitting result; Chi-square of the Bode-impedance mode curve fitting result; in, (2) (3) (4) In the formula: i For the index of the measurement point; N This represents the total number of measuring points. and The first Calculated and measured values ​​of the real components of AC impedance from the test group; For the first The first set of experimental data i The frequency of each measuring point; and The first Calculated and measured values ​​of the imaginary component of AC impedance in the test data; This is the variance calculation function; Z EXP For the first The measured values ​​of the impedance vector sum in the set of test data; and The first Group 1 test data i Calculated and measured values ​​of impedance modulus at each measuring point; and The first Group 1 test data i Calculated and measured values ​​of phase angle at each measuring point; For the first Measured values ​​of impedance modulus in the test data set; For the first The measured values ​​of the phase angle in the set of experimental data.

[0011] Furthermore, the individual representation diagram in the initial population is as follows: (5) In the formula: The first in the population p The initial values ​​of the equivalent circuit element parameters for each individual; Rand(·) is a random function; [ x ] min and[ x ] max These are the lower and upper bounds of the equivalent circuit element parameters, respectively. This is an index of individuals within the population.

[0012] Furthermore, construct the first The mutation vector of the individual vectors in the population during the next iteration is calculated using the following formula: (6) In the formula: For the first During the nth iteration, the population is at the... The variation vector of each individual vector; x ] r1 、[ x ] r2 and[ x ] r3 These are all individual vectors within the population. r 1. r 2. r 3 are all indices of individuals within the population. r 1≠ r 2≠r 3≠ ; , , The first During the nth iteration, the population is at the... r 1. r 2. r 3 individuals; F This is the scaling factor; This is the index of the iteration count.

[0013] Furthermore, the first In the nth iteration, the trial vector of an individual in the population is the first... m Each element is represented as follows: (7) In the formula: , and The first In the nth iteration The first individual m New, variable, and original values ​​of each component parameter; R dm For the first m The random number corresponding to each component parameter; CR This represents the probability of cross-fusion. m This is the index of the component parameters.

[0014] Furthermore, determine the first The final individual vector in the population at the next iteration is given by the following formula: (8) in: For the first During the nth iteration, the population is at the th... Individual vectors; For the first In the next iteration, the value of the objective function is optimized; For the first Optimize the value of the objective function in -1 iterations; For the first The trial vector of an individual in the population at the next iteration; For the first The final individual vector in the population at the next iteration.

[0015] Furthermore, the equivalent circuit element parameter vector after local refinement is obtained; the formula used is as follows: (9) In the formula: This is the equivalent circuit element parameter vector after local refinement; It is a 2-norm; x [ ] represents the optimal individual vector; d 1 represents the real part residual of the impedance in the Nyquist curve; d 2 represents the residual of the imaginary part of the impedance in the Nyquist curve; d 3 represents the impedance mode in the Bode-impedance mode curve. Z | residual; d 4 represents the residual of the phase angle in the Bode-phase angle curve.

[0016] Furthermore, the component parameters of the candidate equivalent circuit include: the diffusion coefficient of the resistor, capacitor, and impedance components, the amplitude parameter of the constant phase component, and the exponent of the constant phase component.

[0017] Beneficial Effects: This invention provides an automatic equivalent circuit fitting method for batch electrochemical impedance spectroscopy (EIS) data. It obtains measured values ​​of various AC impedance spectroscopy parameters from cement-based specimens through EIS testing. Combining this with a composite optimization objective function, it acquires the component parameter vectors in candidate equivalent circuits after local refinement. After traversing all candidate equivalent circuits, it finds the optimal candidate equivalent circuit and obtains the final expression for this optimal candidate equivalent circuit based on the experimental data. This completes the fitting of equivalent circuits for batch EIS data. This invention can objectively determine the optimal equivalent circuit from multiple candidate equivalent circuits, improving the global reliability and batch processing capability of equivalent circuit parameter inversion while ensuring fitting accuracy. This better supports the engineering application of EIS technology in the performance evaluation and durability analysis of cement-based materials. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This is a flowchart of the automatic equivalent circuit fitting method for batch electrochemical impedance spectroscopy data according to the present invention; Figure 2 This is a schematic diagram of the system main interface and running results in an embodiment of the present invention; Figure 3 This is a schematic diagram of the unified refit interface in an embodiment of the present invention; Figure 4 This is a schematic diagram of the raw data from uninterrupted detection of electrochemical impedance spectroscopy in an embodiment of the present invention; Figure 5 This is a schematic diagram of the chi-square of the equivalent circuit after refitting the specified equivalent circuit in the free selection stage of the embodiment of the present invention. Figure 6 This is a schematic diagram of the evolution process of component parameters obtained after unified fitting in an embodiment of the present invention. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] This embodiment introduces an automatic equivalent circuit fitting method for batch electrochemical impedance spectroscopy data, including the following steps: Figure 1 As shown: S1: Obtain the equivalent circuit text collected by the user, which describes the conductivity mechanism of cement-based materials and is represented in character form, and convert it into an equivalent circuit expression to establish a set of candidate equivalent circuits; and set the initial values ​​of the component parameters in the candidate equivalent circuits. The component parameters of the candidate equivalent circuit include: the diffusion coefficient of resistors, capacitors, and impedance components, the amplitude parameter of constant-phase components, and the exponent of constant-phase components.

[0022] In this embodiment, the equivalent circuit text " R 0( R 1 W 1( CPE 1))” is converted into an equivalent circuit expression usable by the impedance module, i.e., “ R 0-p( R 1 W 1, CPE 1) After completion, all equivalent circuits are compiled into a set of candidate equivalent circuits. The process of converting the equivalent circuit text into equivalent circuit expressions can be accomplished by conventional techniques within the field, and therefore will not be described in detail here.

[0023] In the AC impedance spectroscopy test of cement-based materials, resistance is commonly used ( R ),capacitance( C ), Warburg impedance element ( W ) and constant phase element ( CEPThe equivalent circuit formed by the components is used to characterize the microstructure evolution and electrical behavior. The impedance expressions, key parameters, and electrical behaviors of each component are detailed in Table 1. After a single AC impedance spectrum test, the test equipment returns the real impedance (Re), imaginary impedance (Im), and phase angle (Im) of the specimen at a given test frequency and voltage amplitude. φ By using the complex plane formed by the combination of Re and Im (i.e., the Nyquist plot), researchers can analyze the complex response of cement-based materials at different AC frequencies, directly analyze the data (e.g., volume resistance) or indirectly analyze the component parameters by fitting equivalent circuits (e.g., pore liquid resistance, dielectric constant, Warburg coefficient, etc.).

[0024] Table 1 Commonly used components for AC impedance spectroscopy testing of cement-based materials

[0025] in: ω The angular frequency is the frequency of the voltage input to the impedance spectrum. f Conversion relationship is f = 2π ω ; σ Warburg coefficient; Q and n They are respectively CPE The amplitude parameter and exponent term; j 2 = -1.

[0026] Specifically, the candidate equivalent circuits in the candidate equivalent circuit set of this embodiment are assumed to have initial component values ​​according to the component parameters shown in Table 2. Wherein, R Indicates resistance; C Indicates capacitance; σ This represents the Warburg (impedance element) diffusion coefficient; Q express CPE The amplitude parameter is the double-layer capacitance; n express CPE The index.

[0027] Table 2 Default Component Parameters

[0028] Specifically, this embodiment limits all component parameters to a reasonable range that conforms to the electrical properties of cement-based materials. For example, constant phase components... CPE index n The denominator is limited to [0, 1]. If numerical overflow occurs during the calculation, such as infinity, the kinetic energy overflow prevention function of ABAQUS / Explicit is referenced, and the denominator is limited to 10. -16 The corresponding order of magnitude.

[0029] S2: Perform electrochemical impedance spectroscopy on cement-based specimens to obtain experimental data; the experimental data includes multiple AC impedance spectral data, which include imaginary components, real components, frequency, impedance mode, and phase angle; This embodiment obtains multiple AC impedance spectroscopy data, including imaginary and real components, frequency, impedance mode, and phase angle, by performing electrochemical impedance spectroscopy (EIS) tests on cement-based specimens. Specifically, after completing the EIS tests on the cement-based specimens, the XLSX table storing the experimental data is divided into multiple independent datasets composed of impedance spectroscopy data. The imaginary and real components, frequency, impedance mode, and phase angle of the AC impedance spectrum of each independent dataset are read individually.

[0030] S3: Establish a composite optimization objective function, namely a three-domain composite chi-square; After setting the initial values ​​of default component parameters in the candidate equivalent circuit, this embodiment uses a differential evolution algorithm to search for component parameters in the real number domain that conforms to the properties of each component, and to optimize the composite objective ( OBJ Minimize. The composite optimization objective function is established as follows: (1) In the formula: OBJ To optimize the value of the objective function; , , These are the weights of the chi-square corresponding to the Nyquist curve, the weight of the chi-square corresponding to the Bode-phase curve, and the weight of the chi-square corresponding to the Bode-impedance mode curve, respectively, obtained based on the fitted equivalent circuit. Chi-square of the Nyquist curve fitting result; Chi-square of the Bode-phase curve fitting result; This is the chi-square of the Bode-impedance mode curve fitting result.

[0031] Specifically, in a single test, each selected frequency corresponds to a set of imaginary and real impedance components, impedance magnitude, and phase angle; this set of data is called a single measurement point. Among these, for those with… N The chi-square is calculated for a single test at each measuring point as follows: (2) (3) (4) In the formula: i For the index of the measurement point; N This represents the total number of measuring points. and The first Calculated and measured values ​​of the real components of AC impedance from the test group; For the first The first set of experimental data i The frequency of each measuring point; and The first Calculated and measured values ​​of the imaginary component of AC impedance in the test data; This is the variance calculation function; Z EXP For the first The measured values ​​of the impedance vector sum in the set of test data; and The first Group 1 test data i Calculated and measured values ​​of impedance modulus at each measuring point; and The first Group 1 test data i Calculated and measured values ​​of phase angle at each measuring point; For the first Measured values ​​of impedance modulus in the test data set; For the first The measured values ​​of the phase angle in the set of experimental data.

[0032] S4: Based on the imaginary components, real components, frequency, impedance magnitude and phase angle of the experimental data, the initial values ​​of the component parameters of the candidate equivalent circuits in the candidate equivalent circuit set, and the composite optimization objective function, obtain the component parameter vector in the candidate equivalent circuits after local refinement. Specifically, the Differential Evolutionary Algorithm (DEA) was proposed by Storm in 1996. DEA is a population-based stochastic optimization algorithm whose search process relies entirely on numerical evaluation of the optimization, without requiring assumptions about gradients or function continuity. DEA determines the search direction by driving the differential information of the entire population. Therefore, DEA can escape the limitations of local optima and possesses strong exploration capabilities across the entire search domain.

[0033] Specifically, the computational process of the differential evolution algorithm consists of four steps: initialization, mutation, crossover fusion, and selection. S41: In D Within the dimensional search domain, based on the initial values ​​of candidate circuit elements, a random number of elements of size are generated. N P The initial population was determined using the following formula: (5) In the formula: The first in the population pThe initial values ​​of the equivalent circuit element parameters for each individual (i.e., the values ​​at the 0th iteration); Rand(·) is a random function used to randomly generate floating-point numbers in the range [0, 1]; x ] min and[ x ] max These are the lower and upper bounds of the equivalent circuit element parameters, respectively. An index for an individual in the population; S42: Randomly select three distinct individuals. x ] r1 、[ x ] r2 and[ x ] r3 (in, r 1, r 2, r 3≠ p Construct the first The mutation vector of individual vectors in the population at the next iteration : (6) In the formula: For the first During the nth iteration, the population is at the... The variation vector of each individual vector; x ] r1 、[ x ] r2 and[ x ] r3 These are all individual vectors within the population. r 1. r 2. r 3 are all indices of individuals within the population. r 1≠ r 2≠ r 3≠ ; , , The first During the nth iteration, the population is at the... r 1. r 2. r 3 individuals; F is the scaling factor, with a value between [0, 1]; where,

[0034] S43: According to the... The mutation vector of individuals in the population at the next iteration and the The individual vectors in the population at the nth iteration are obtained. The trial vector of an individual in the population at the next iteration; where, for D dimensional test vector, the first In the nth iteration, the trial vector of an individual in the population is the first... m ( m ≤ D The number of elements is represented as follows: (7) In the formula: , and The first In the nth iteration The first individual m The new values, variant values, and original values ​​(i.e., the initial values ​​for the next optimization) of each component parameter. R dm For the first m The random number corresponding to each component parameter; CR This represents the probability of cross-fusion. m Index to component parameters; D This represents the dimension of the test vector, and also the total number of component parameters; in, and It also represents the mutation vector. and individual vectors The first in m The value corresponding to the parameter of the first component; The trial vector of an individual in the population at the next iteration ;No. The vector of each individual in the population at the next iteration .

[0035] Specifically, the mutation vector With the individual vectors in the corresponding population Perform cross-fusion to generate test vectors For the first m The standard binomial cross-fusion expression for the component parameters is Equation (7). In the first... The next iteration, the... For each individual, first generate a set of random numbers that conform to a uniform distribution. R d ~U (0,1). If the first... m The random number corresponding to each component parameter R dm Less than the cross-fusion probability CR Then the individual's first m If a component parameter changes, it does not change; otherwise, it retains its original value. CRThis is used to control the proportion of inherited mutation vector components in the experimental vector, and its value range is [0,1]. In this embodiment, considering the strong nonlinearity and multi-peak characteristics of the equivalent circuit parameter identification problem, the following is selected: CR = 0.8, to enhance global exploration capabilities while ensuring search stability.

[0036] S44: According to the... The individual vectors in the population at the nth iteration and the nth iteration The trial vectors of individuals in the population at the nth iteration determine the th... The final individual vector in the population at the next iteration; Finally, the adoption of new component parameters is determined based on whether it minimizes the numerical value of the objective function after this iteration. x ] (g) k No or no: (8) in: For the first During the nth iteration, the population is at the th... Individual vectors; For the first In the next iteration, the value of the objective function is optimized; For the first Optimize the value of the objective function in -1 iterations; For the first The trial vector of an individual in the population at the next iteration; For the first The final individual vector in the population at the next iteration; S45: Based on the first The final individual vector in the population at the next iteration is used to re-execute S33-S35 until the iteration termination condition is met, thereby obtaining the optimal individual vector, which is the optimal combination of component parameters for the candidate equivalent circuit. x ]; S46: Based on the optimal individual vector, refine the optimal individual vector to obtain the equivalent circuit element parameter vector after local refinement; Specifically, the iteration termination condition in this embodiment is that when the number of iterations reaches 1000 or the reduction rate of OBJ compared to the previous iteration is less than 5%, the optimal combination of component parameters of the candidate equivalent circuit obtained by the differential evolution algorithm is determined. x The parameter combination was then fine-tuned locally to obtain... The process involves several steps, including the following sub-steps: (The process is repeated in the original text.) Specifically, first, determine the initial parameter vector for local refinement. The optimal component parameter vector, i.e., the optimal individual vector, is denoted as [ x[] This serves as the initial parameter vector for the least squares method, ensuring that local optimization occurs within the neighborhood of the global optimum.

[0037] Secondly, construct the least squares residual vector; Based on the equivalent circuit model, the experimental impedance and model impedance are calculated at a given frequency point, and a residual vector containing the following components is constructed: (1) the real part residual of the impedance in the Nyquist curve. d 1; (2) The residual of the imaginary part of the impedance in the Nyquist curve d 2; (3) Impedance mode in Bode-impedance mode curve | Z | residual d 3; (4) The residual of the phase angle in the Bode-phase angle curve d 4. By concatenating the above residual terms in sequence, a comprehensive residual vector for least squares optimization is formed. d The overall optimization problem can be written as: (9) In the formula: This is the equivalent circuit element parameter vector after local refinement; It is a 2-norm; x [ ] represents the optimal individual vector; d 1 represents the real part residual of the impedance in the Nyquist curve; d 2 represents the residual of the imaginary part of the impedance in the Nyquist curve; d 3 represents the impedance mode in the Bode-impedance mode curve. Z | residual; d 4 represents the residual of the phase angle in the Bode-phase angle curve.

[0038] Specifically, when the least squares method has been iterated more than 1000 times or when each component parameter has changed by less than 5% compared to the previous iteration, the iteration is stopped and the final refined combination of component parameters is obtained. .

[0039] Specifically, will Substitute back to candidate equivalent circuit model Z Recalculate the impedance response over the full frequency range. Z ( ω , ), and based on this, generate: (1) Nyquist curve; (2) Bode-phase angle curve; (3) Bode-impedance mode curve. Finally, based on the refined component parameters [ x *Chi-square of the obtained equivalent circuit element parameters and Nyquist fitting results χ 2 1. Combine and output the component parameters to the result file and GUI, and draw the relevant images.

[0040] Specifically, the evolutionary information of the internal structure of cement-based materials is contained in the changes in the component parameters of the equivalent circuit. However, with the deepening of research in this field, the form of the equivalent circuit has not been unified. Therefore, for a set of experimental data, the equivalent circuit suitable for the working condition can be determined by comparing multiple equivalent circuits, thereby quantitatively characterizing the evolution of the internal structure of cement-based materials. Meanwhile, to obtain a more detailed evolutionary process of the component parameters of the equivalent circuit, continuous detection is often used to acquire a large amount of data. The equivalent circuit obtained from each detection may be different. Therefore, this embodiment uses a combination of differential evolution method and least squares method to select the equivalent circuit that minimizes the composite objective function value from many candidate equivalent circuits, which is used to describe the evolutionary information of the internal structure of cement-based materials.

[0041] S5: Traverse all candidate equivalent circuits in the candidate equivalent circuit set, and according to the composite optimization objective function, obtain the component parameter vector in the optimal candidate equivalent circuit after local refinement, so as to obtain the optimal candidate equivalent circuit, and then obtain the final expression of the optimal candidate equivalent circuit based on experimental data; complete the fitting of the equivalent circuit for batch electrochemical impedance spectroscopy data.

[0042] Specifically, all candidate equivalent circuits are traversed. Finally, for a single experimental data point, the optimal candidate equivalent circuit with the smallest three-domain composite chi-square value is selected after local refinement, based on the parameter tuning of two optimization algorithms. This yields the optimal candidate equivalent circuit, from which those skilled in the art can obtain the expression for the equivalent circuit using conventional techniques.

[0043] Specifically, after selecting the optimal equivalent circuit, this system decides whether to use it based on the user's wishes, and can specify the equivalent circuit to refit the selected dataset.

[0044] In this embodiment, the user can specify an equivalent circuit to refit one or more selected experimental data according to their needs, and at the same time update the GUI diagram and the xlsx result file.

[0045] Specifically, after all experimental data has been traversed, the fitting results are stored in an XLSX table. Then, the system reads the parameters from the XLSX table and plots the Nyquist curve, Bode-phase curve, Bode-impedance mode curve, textual information about the fitting results, equivalent circuit diagram, and component parameters and their units for each set of experimental data on the GUI atlas. Furthermore, because no external data is called or recalculated, users can quickly browse the GUI atlas.

[0046] Users can also export the visualization of the fitting results as a single PNG image or as a PDF in the form of an album, depending on their needs.

[0047] The system in this embodiment requires the support of the third-party Python modules shown in Table 3 to operate.

[0048] Table 3. Third-party Python modules required for system operation

[0049] After selecting equivalent circuits in batches, the system displays the main interface, such as... Figure 2 As shown in the diagram. The left side of the plotting area displays the Nyquist curve of the experimental data versus the fitting results, while the top and bottom right sides display the Bode-phase curve and the Bode-impedance mode curve, respectively. The three vertically arranged information columns on the right side display the chi-square of the fitted equivalent circuit and related documentation, the equivalent circuit diagram and its textual expression, and component parameters. Users can use the up and down arrow keys or click the corresponding buttons to switch between GUI atlas pages.

[0050] The layered architecture of the system in this embodiment is as follows: Equivalent Circuit Text Conversion: As shown in Table 4, there are many ways to express equivalent circuits in text. However, the impedance module used in this embodiment can only read the equivalent circuit (type #2) used by Zview. Considering the user's writing and usage habits, the system converts the text expression of the equivalent circuit into the equivalent circuit form (type #2) available to the impedance module before calling the equivalent circuit, but it is still represented in the user-defined form in the subsequent preview and report stages.

[0051] Data reading and parameter tuning: The original experimental dataset is split according to the experimental steps and the number of cycles, and the component parameters of the selected equivalent circuit are tuned using a combination of differential evolution algorithm (DEA) and least squares method, as well as the equivalent circuit type is selected.

[0052] Quick Preview Interface: After the free selection phase, the result file is read and the visualization data is stored in the computer memory. At this point, the .xlsx file corresponding to the fitting result is operable. Based on the visualization data, the GUI displays the Nyquist plot, Bode plot, equivalent circuit diagram, and component parameters and units of the fitting result and equivalent circuit in a gallery format, showing the original data and the fitting result.

[0053] Refitting module: Based on user needs, specify an equivalent circuit to refit all data and refresh the result file and visualization.

[0054] Data and Image Export Module: Allows the program to: (1) store all freely selected or specified equivalent circuit fitting results in an xlsx spreadsheet, as shown in Table 6, so that users can quickly preview the equivalent circuit fitting results corresponding to the experimental data of each cycle; (2) export the fitting results of individual data in the form of png images; (3) export all datasets in the form of a PDF album, with attached reports and equivalent circuit diagrams.

[0055] Table 4 Equivalent Circuit Representation

[0056] Specifically, this embodiment, based on Python programming, relates to batch fitting of equivalent circuits in the electrochemical detection process of cement-based materials. First, user-collected or user-defined equivalent circuits are compiled into a document. Then, equivalent circuits are selected from the document, and the component parameters of the corresponding equivalent circuits are fitted according to an optimization algorithm, selecting the optimal equivalent circuit. Finally, this method is used to fit each experimental step and cycle of the original electrochemical detection data file, and the fitting results are presented in a GUI-based preview page with Nyquist and Bode plots. During the preview, the user can refit the selected experimental data with specified equivalent circuits as needed. The refit interface is shown in Figure 3.

[0057] Application example: Continuous monitoring during the ultra-early curing process of cement mortar.

[0058] Scenario and Objective: The mortar curing process involves phase changes caused by cement hydration, which alters the internal current transport path and thus affects the electrochemical impedance spectroscopy (EIS) of the specimen. Therefore, EIS information can be obtained by continuously performing electrochemical monitoring on the curing mortar. Then, the reconstruction of ion transport channels within the mortar can be inferred by analyzing the evolution of equivalent circuit parameters, thereby analyzing the evolution of the mortar's internal structure.

[0059] Original data acquisition: The test materials are as follows: (1) Dalian Onoda PO 42.5R ordinary Portland cement, (2) river sand with a fineness modulus of 2.7 and a particle size not exceeding 2.5 mm, and (3) tap water from Dalian. Cement mortar was prepared according to the ratio of water:cement:sand = 1:2:6. It was then poured into a 40 mm × 40 mm × 160 mm plastic mold with 1.0 mm thick stainless steel electrode plates placed at both ends. After completing the relevant operations, the electrochemical impedance spectrum of the mortar was detected using a BioLogic SP-300 electrochemical workstation from 20 min after contact with cement to 12 h as displayed in EC-Lab. The instrument input for this experiment was a sinusoidal AC voltage. E we= 10 mV, detection frequency band from 7 MHz to 50 MHz, 10 test points per frequency order of magnitude. Finally, the raw EC-Lab data output from the electrochemical workstation was converted into a format usable by the system. The raw data obtained from the experiment are as follows: Figure 3 A total of 102 sets of test data were collected. Re and Im represent the real and imaginary components of the impedance spectrum, respectively, and Phase represents the phase angle. Z | represents the impedance mode, Freq. represents the detection frequency, and the color scale reflects the increase in detection time from 20 min to 12 h. Figure 4 This diagram illustrates the raw data from continuous electrochemical impedance spectroscopy detection in this embodiment.

[0060] Operation Process and Results: After collecting the equivalent circuit expressions shown in Table 5, the raw experimental data were imported into the system. The system read the electrochemical impedance spectroscopy data from the table one by one according to the experimental steps and the number of repeated tests. Then, based on the impedance spectroscopy data, the equivalent circuit and component parameters were selected one by one according to the minimum chi-square value. Finally, the results were previewed and output in GUI and XLSX table format. Figure 5 Part (a) represents the free selection phase, showing the equivalent circuit fitting results for all datasets. The top 10 chi-square-optimal equivalent circuits are given in Table 6. The selected equivalent circuits were chosen based on the chi-square of the equivalent circuit across all datasets and the resulting conduction mechanism. Therefore, the specified equivalent circuits are... R 0( C 1( R 1 CPE 2( R 2 W 2))) The equivalent circuit is refitted for all data, and the chi-square of the equivalent circuit for all datasets is as follows: Figure 5 Part (b). Based on the selected equivalent circuit, the user can analyze the evolution of component parameters over time as the cement-based material cures, and thus analyze the process of internal structure formation. Figure 6 Equivalent circuit R 0( C 1( R 1 CPE 2( R 2 W 2))) Over time, the Warburg impedance, solution resistance, and double layer of the mortar specimens... CPE The evolution of the index.

[0061] Figure 6Part (a) shows the evolution of the Warburg diffusion impedance parameters of the specimen, but the values ​​exhibit significant dispersion. In the mortar, low-frequency alternating current is transmitted through diffusion, a process limited by the Warburg impedance. Ion transport in the pore liquid within the hydrated calcium silicate (CSH) / hydrated calcium aluminosilicate (CASH) gel network is achieved through diffusion. In the early curing stage, the pores inside the specimen are not yet sealed by hydration products, and the diffusion paths remain unobstructed. However, within the 7–11 h range, due to local nucleation of hydration products and redistribution of conductive paths, the diffusion impedance values ​​exhibit local fluctuations during this period.

[0062] exist Figure 6 In part (b) of the specimens, the pore fluid resistivity first decreased and then increased with the progress of curing time. During the initial stage of cement hydration, cement clinker such as dicalcium silicate gradually dissolved, increasing the Ca content in the pore fluid. 2+ OH - The concentration of ions participating in the hydration reaction increases, which is consistent with the phenomena that occur during the hydration induction period. Subsequently, due to the advancement of the hydration reaction and the generation of solid phases such as ettringite and calcium hydroxide, a network of hydration products gradually forms inside the specimen, the internal structure gradually becomes denser, and the ion transport channels become more tortuous or are blocked. Therefore, the pore liquid resistivity continues to increase in the later stage.

[0063] Figure 6 The middle (c) section is a constant phase element. CPE The time history curve of the exponential term. Cement-based materials have a highly heterogeneous and multi-scale porous structure, and their electrical response exhibits significant phase dispersion characteristics, making it difficult to accurately describe using an ideal capacitor element. Therefore, this embodiment uses... CPE To characterize the electrical behavior of the solid-liquid interface and pore structure. CPE Through power index n This effectively reflects the distribution characteristics of interface roughness and time constant. In the initial stage, due to the non-uniform nucleation of hydration products, the local pore structure inside the mortar varies significantly, and the conductive path exhibits a multi-scale distribution. After 10 hours, with the gradual formation of hydration products, the pore structure inside the mortar gradually becomes denser, and the electrical behavior of the specimen gradually stabilizes and tends towards ideal capacitance.

[0064] Table 5 Excerpt from the Alternative Equivalent Circuit Library

[0065] Table 6. Excerpt of equivalent circuit fitting results (sorted by chi-square)

[0066] In this embodiment, the user can fit each set of experimental data using the collected and entered equivalent circuit, and then select the optimal equivalent circuit to refit the specified data according to requirements. This allows the user to obtain the evolution process of component parameters based on the specified equivalent circuit. This system enables the user to try different equivalent circuits on a large amount of data, thereby determining the optimal equivalent circuit from the candidate list.

[0067] In this embodiment, the equivalent circuit text expression, represented in character form, is first obtained, and the circuit component identifiers are uniformly processed. Then, the circuit text is symbolically decomposed, and based on pre-defined series and parallel semantic rules and bracket priority, the circuit text is parsed layer by layer to construct a structured circuit topology model that clearly reflects the series and parallel relationships of each circuit component. This achieves automatic conversion from circuit text description to a circuit structure model that can be used for impedance calculation. The circuit expression text conversion function in this embodiment allows the circuit expression format to be used in the impedance module. The process of entering circuit expressions is more in line with the user's writing habits.

[0068] In this embodiment, a global optimization algorithm is used to select component parameters, avoiding getting trapped in local optima. Users can obtain the optimal equivalent circuit for this batch of data in the preview interface and the generated XLSX table, and then select a specified equivalent circuit to refit the selected data, thereby obtaining the component parameter evolution process under that equivalent circuit. In summary, this embodiment achieves large-scale, automated fitting of electrochemical impedance spectroscopy equivalent circuits to accelerate the processing of large amounts of data.

[0069] 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 the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. An automatic equivalent circuit fitting method for batch electrochemical impedance spectroscopy data, characterized in that, Includes the following steps: S1: Obtain the equivalent circuit text collected by the user to describe the conductivity mechanism of cement-based materials, and convert it into an equivalent circuit expression to establish a candidate equivalent circuit set, and set the initial values ​​of the component parameters in the candidate equivalent circuit. S2: Perform electrochemical impedance spectroscopy on cement-based specimens to obtain experimental data; the experimental data includes multiple AC impedance spectral data, which include imaginary components, real components, frequency, impedance mode, and phase angle; S3: Establish a composite optimization objective function, namely a three-domain composite chi-square; S4: Based on the imaginary components, real components, frequency, impedance magnitude and phase angle of the experimental data, the initial values ​​of the component parameters of the candidate equivalent circuits in the candidate equivalent circuit set, and the composite optimization objective function, obtain the component parameter vector in the candidate equivalent circuits after local refinement. S5: Traverse all candidate equivalent circuits in the candidate equivalent circuit set, and according to the composite optimization objective function, obtain the component parameter vector in the optimal candidate equivalent circuit after local refinement, so as to obtain the optimal candidate equivalent circuit, and then obtain the final expression of the optimal candidate equivalent circuit based on the experimental data. Complete the fitting of the equivalent circuit for batch electrochemical impedance spectroscopy data.

2. The automatic equivalent circuit fitting method for batch electrochemical impedance spectroscopy data according to claim 1, characterized in that, The method used to obtain the component parameter vectors in the equivalent circuit after local refinement is as follows: S41: In D Within the dimensional search domain, an initial population is randomly generated based on the initial values ​​of the candidate circuit elements; S42: Constructing the first The mutated vector of the individual vectors in the population at the next iteration; S43: According to the... The mutation vectors of individuals in the population at the nth iteration and the 1st iteration The individual vectors in the population at the nth iteration are obtained. The trial vector of an individual in the population at the next iteration; S44: According to the... The vector of each individual in the population at the nth iteration, the... The trial vectors of individuals in the population and the composite optimization objective function at the nth iteration determine the nth iteration. The final individual vector in the population at the next iteration; S45: Based on the first The final individual vector in the population at the next iteration is used to re-execute S33-S35 until the iteration termination condition is met, and the optimal individual vector is obtained. S46: Based on the optimal individual vector, obtain the component parameter vector in the equivalent circuit after local refinement.

3. The automatic equivalent circuit fitting method for batch electrochemical impedance spectroscopy data according to claim 2, characterized in that, The composite optimization objective function is expressed as follows: (1) In the formula: OBJ To optimize the value of the objective function; , , These are the weights of the chi-square corresponding to the Nyquist curve, the weight of the chi-square corresponding to the Bode-phase curve, and the weight of the chi-square corresponding to the Bode-impedance mode curve, respectively, obtained based on the fitted equivalent circuit. Chi-square of the Nyquist curve fitting result; Chi-square of the Bode-phase curve fitting result; Chi-square of the Bode-impedance mode curve fitting result; in, (2) (3) (4) In the formula: i For the index of the measurement point; N This represents the total number of measuring points. and The first Calculated and measured values ​​of the real components of AC impedance from the test group; For the first The first set of experimental data i The frequency of each measuring point; and The first Calculated and measured values ​​of the imaginary component of AC impedance in the test data; This is the variance calculation function; Z EXP For the first The measured values ​​of the impedance vector sum in the set of test data; and The first Group 1 test data i Calculated and measured values ​​of impedance modulus at each measuring point; and The first Group 1 test data i Calculated and measured values ​​of phase angle at each measuring point; For the first Measured values ​​of impedance modulus in the test data set; For the first The measured values ​​of the phase angle in the set of experimental data.

4. The automatic equivalent circuit fitting method for batch electrochemical impedance spectroscopy data according to claim 2, characterized in that, The individual representation diagram of the initial population is as follows: (5) In the formula: The first in the population p The initial values ​​of the equivalent circuit element parameters for each individual; Rand(·) is a random function; [ x ] min and[ x ] max These are the lower and upper bounds of the equivalent circuit element parameters, respectively. This is an index of individuals within the population.

5. The automatic equivalent circuit fitting method for batch electrochemical impedance spectroscopy data according to claim 2, characterized in that, Construct the first The mutation vector of the individual vectors in the population during the next iteration is calculated using the following formula: (6) In the formula: For the first During the nth iteration, the population is at the... The variation vector of each individual vector; x ] r1 、[ x ] r2 and[ x ] r3 These are all individual vectors within the population. r 1. r 2. r 3 are all indices of individuals within the population. r 1≠ r 2≠ r 3≠ ; , , The first During the nth iteration, the population is at the... r 1. r 2. r 3 individuals; F This is the scaling factor; This is the index of the iteration count.

6. The automatic equivalent circuit fitting method for batch electrochemical impedance spectroscopy data according to claim 2, characterized in that, No. In the nth iteration, the trial vector of an individual in the population is the first... m Each element is represented as follows: (7) In the formula: , and The first In the nth iteration The first individual m New, variable, and original values ​​of each component parameter; R dm For the first m The random number corresponding to each component parameter; CR This represents the probability of cross-fusion. m This is the index of the component parameters.

7. The automatic equivalent circuit fitting method for batch electrochemical impedance spectroscopy data according to claim 2, characterized in that, Determine the first The final individual vector in the population at the next iteration is given by the following formula: (8) in: For the first During the nth iteration, the population is at the th... Individual vectors; For the first In the next iteration, the value of the objective function is optimized; For the first Optimize the value of the objective function in -1 iterations; For the first The trial vector of an individual in the population at the next iteration; For the first The final individual vector in the population at the next iteration.

8. The automatic equivalent circuit fitting method for batch electrochemical impedance spectroscopy data according to claim 2, characterized in that, The equivalent circuit element parameter vector after local refinement is obtained; the formula used is as follows: (9) In the formula: This is the equivalent circuit element parameter vector after local refinement; It is a 2-norm; x [ ] represents the optimal individual vector; d 1 represents the real part residual of the impedance in the Nyquist curve; d 2 represents the residual of the imaginary part of the impedance in the Nyquist curve; d 3 represents the impedance mode in the Bode-impedance mode curve. Z | residual; d 4 represents the residual of the phase angle in the Bode-phase angle curve.

9. The automatic equivalent circuit fitting method for batch electrochemical impedance spectroscopy data according to claim 1, characterized in that, The component parameters of the candidate equivalent circuit include: the diffusion coefficient of resistors, capacitors, and impedance components, the amplitude parameter of constant-phase components, and the exponent of constant-phase components.

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