A multi-parameter fast reverse correction analysis method for electrochemical calculation use

Abstract

The present application belongs to the technical field of electrochemistry, and particularly relates to a multi-parameter fast reverse correction analysis method for electrochemical calculation, comprising the following steps: obtaining initial values of electrochemical parameters and inputting the initial values into an electrochemical porous electrode model to calculate current-voltage values; updating the electrochemical parameters through an intelligent algorithm according to the obtained current-voltage values; repeating the above steps until global optimal electrochemical parameter solutions meeting the accuracy are obtained; and inputting the global optimal electrochemical parameters into the electrochemical porous electrode model to obtain updated current-voltage values. The method overcomes the shortcomings of the prior art, reversely corrects and calculates electrochemical parameters, and can quickly reversely correct various parameters in electrochemical reactions in view of limited measurable physical quantities, current and voltage, so as to help users improve the parameterization understanding of internal characteristics of electrochemical reactions.

Description

Technical Field

[0001] This invention belongs to the field of electrochemical technology, specifically relating to a rapid inverse correction analysis method for multiple parameters used in electrochemical calculations. Background Technology

[0002] In electrochemical research, the reaction processes are complex, and obtaining the various parameters describing the reactions is essential. However, there are problems with the inability to measure some parameters or the difficulty in measuring them accurately. This affects the understanding of electrochemical reaction processes.

[0003] Electrochemical reaction parameters are influenced by numerous and uncertain factors, making their modeling and calculation a multidisciplinary problem and a key and challenging research area. However, the physical quantities that can be obtained are limited, consisting only of the input current and output voltage.

[0004] Current calculation software Comsol can calculate current and voltage data using complex electrochemical parameters, but it lacks the function of reverse calculation to obtain various electrochemical parameters by inputting current and output voltage data.

[0005] Currently, there is no effective algorithm for rapid, multi-parameter reverse correction of electrochemical reaction parameters. The method developed in this invention, which uses a parallel fast optimization algorithm to calculate electrochemical parameters by reverse correction of current and voltage, fills this gap. Summary of the Invention

[0006] The purpose of this invention is to provide a rapid reverse calibration analysis method for multiple parameters used in electrochemical calculations, which overcomes the shortcomings of existing technologies. It performs reverse calibration calculations on various electrochemical parameters. For a limited number of measurable physical quantities, such as current and voltage, it can quickly reverse-calibrate various parameters in electrochemical reactions, thereby helping users improve their parameterized understanding of the internal characteristics of electrochemical reactions.

[0007] To solve the above problems, the technical solution adopted by the present invention is as follows:

[0008] A rapid inverse correction analysis method for multiple parameters used in electrochemical calculations includes the following steps:

[0009] Step 1: Obtain the initial values ​​of electrochemical parameters and input them into the electrochemical porous electrode model to calculate the current and voltage values;

[0010] Step 2: Update the electrochemical parameters using an intelligent algorithm based on the obtained current and voltage values;

[0011] Step 3: Repeat step 2 until a globally optimal electrochemical parameter solution with sufficient accuracy is obtained;

[0012] Step 4: Input the globally optimal electrochemical parameters into the electrochemical porous electrode model to obtain updated current and voltage values.

[0013] Furthermore, in step one, the current and voltage values ​​are calculated using an electrochemical porous electrode model. The specific steps include:

[0014] (1) The finite volume method is used to discretize the electrolyte diffusion equation, and the boundary conditions of the governing equation are solved. The expression is as follows:

[0015]

[0016]

[0017] Where, ∈ i It represents the electrolyte volume fraction, and t represents time. It is the electrolyte concentration, Δx i D is the mesh length in the finite volume method. eff Here, k is the electrolyte diffusion coefficient, k is the grid index, and a is the surface area-to-volume ratio of the electrode particles. It is ion flux;

[0018] (2) The finite difference discrete calculation of the solid-phase diffusion equation and the solution of the boundary conditions of the governing equation are expressed as follows:

[0019]

[0020]

[0021] in, It is the solid phase concentration, D s It is the solid-phase diffusion coefficient, Δr n It is the grid length in the direction of particle radius;

[0022] (3) The finite volume method is used to discretize the electrolyte potential equation, and the boundary conditions of the governing equation are solved. The expression is as follows:

[0023]

[0024]

[0025]

[0026] Where, k eff It is the electrolyte conductivity, Φ e Here, T is the electrolyte potential, T is the temperature, and F is the Faraday constant.

[0027] (4) For the current calculation of the BV equation, the boundary conditions are applied to the governing equation through the charge conservation equation, and its expression is:

[0028]

[0029] Where, η i This is an overpotential;

[0030] (5) The finite volume discretization calculation of the potential equation for the solid phase and the solution of the boundary conditions of the governing equation are expressed as follows:

[0031]

[0032]

[0033] Where, σ eff Φ is the solid-state conductivity. s For solid-state potential, I app The input current density;

[0034] (6) For the time ordinary differential equation system obtained above, the numerical solution is obtained by using the BDF backward difference method.

[0035] Furthermore, the time iteration formula used in the BDF backward difference method is as follows:

[0036]

[0037] Where y is the equation, s is the order of the BDF, and a k β is a constant coefficient, h is the time step, t0 is the initial time, and t n =t0+nh.

[0038] Furthermore, the specific steps for obtaining the globally optimal electrochemical parameter solution that satisfies the required accuracy, as described in step three, include:

[0039] (1) Generate new random parameters based on the current and voltage values, and evaluate the random parameters using the objective function;

[0040] (2) Accept random parameters with good objective function evaluation results, and at the same time randomly accept random parameters with poor objective function evaluation results;

[0041] (3) Lower the temperature and repeat steps (1) and (2) until the temperature or accuracy of the intelligent algorithm reaches the set value; and use the parallel memory container method to record the obtained random parameters;

[0042] (4) Compare the optimal solutions of each round to obtain the parameter solution that satisfies the global optimum.

[0043] Furthermore, the generation of new random parameters is optimized using an adaptive variable step size method, the expression of which is:

[0044] range=range*(1+2*(rate-a) / (1-a))

[0045] Where range is the step size range of the random new solution, and a is the variable step size optimization coefficient.

[0046] Furthermore, the objective function is the sum of squared residuals between the calculated data of random parameters and the original measurement data.

[0047] Furthermore, the temperature reduction process employs an optimized accelerated iteration strategy, resulting in the following temperature:

[0048]

[0049] Where T0 is the initial temperature, M is the number of iterations, and ck is the algorithm coefficient.

[0050] Furthermore, the method for updating electrochemical parameters using the intelligent algorithm described in step two includes using one or more of the following methods in combination: annealing algorithm, genetic algorithm, ant colony algorithm, and particle swarm optimization.

[0051] Compared with the prior art, the present invention has the following beneficial effects:

[0052] The present invention describes a rapid inverse correction analysis method for multiple parameters used in electrochemical calculations. By using a limited number of measurable physical quantities, such as current and voltage, it is possible to rapidly inversely correct various parameters in an electrochemical reaction. This can help users improve their parameterized understanding of the internal characteristics of electrochemical reactions. Attached Figure Description

[0053] Figure 1 This is a flowchart illustrating a rapid inverse correction analysis method for multiple parameters used in electrochemical calculations. Detailed Implementation

[0054] 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, and 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.

[0055] like Figure 1 As shown, the present invention provides a rapid inverse correction analysis method for multiple parameters used in electrochemical calculations, comprising the following steps:

[0056] Step 1: Obtain the initial values ​​of the electrochemical parameters and input them into the electrochemical porous electrode model to calculate the current and voltage values.

[0057] The current and voltage values ​​were calculated using an electrochemical porous electrode model. The specific steps included:

[0058] (1) The finite volume method is used to discretize the electrolyte diffusion equation, and the boundary conditions of the governing equation are solved. The expression is as follows:

[0059]

[0060]

[0061] Where, ∈ i It represents the electrolyte volume fraction, and t represents time. It is the electrolyte concentration, Δx i D is the mesh length in the finite volume method. eff Here, k is the electrolyte diffusion coefficient, k is the grid index, and a is the surface area-to-volume ratio of the electrode particles. It is ion flux;

[0062] (2) The finite difference discrete calculation of the solid-phase diffusion equation and the solution of the boundary conditions of the governing equation are expressed as follows:

[0063]

[0064]

[0065] in, It is the solid phase concentration, D s It is the solid-phase diffusion coefficient, Δr n It is the grid length in the direction of particle radius;

[0066] (3) The finite volume method is used to discretize the electrolyte potential equation, and the boundary conditions of the governing equation are solved. The expression is as follows:

[0067]

[0068]

[0069]

[0070] Where, k eff It is the electrolyte conductivity, Φ e Where F is the electrolyte potential, T is the temperature, and F is the Faraday constant.

[0071] (4) For the current calculation of the BV equation, the boundary conditions are applied to the governing equation through the charge conservation equation, and its expression is:

[0072]

[0073] Where, η iThis is an overpotential;

[0074] (5) The finite volume discretization calculation of the potential equation for the solid phase and the solution of the boundary conditions of the governing equation are expressed as follows:

[0075]

[0076]

[0077] Where, σ eff Φ is the solid-state conductivity. s For solid-state potential, I app The input current density;

[0078] (6) For the time ordinary differential equation system obtained above, the numerical solution is obtained by using the BDF backward difference method.

[0079] The time iteration formula used in the BDF backward difference method is as follows:

[0080]

[0081] Where y is the equation, s is the order of the BDF, and a k β is a constant coefficient, h is the time step, t0 is the initial time, and t n =t0+nh.

[0082] Step 2: Update the electrochemical parameters using an intelligent algorithm based on the obtained current and voltage values.

[0083] Step 3: Repeat step 2 until a globally optimal electrochemical parameter solution with sufficient accuracy is obtained.

[0084] The specific solution steps include:

[0085] (1) Generate new random parameters based on the current and voltage values, and evaluate the random parameters using an objective function. The objective function is the sum of squared residuals between the calculated random parameter data and the original measurement data.

[0086] (2) Accept random parameters with good objective function evaluation results, and at the same time randomly accept random parameters with poor objective function evaluation results;

[0087] (3) Lower the temperature and repeat steps (1) and (2) until the accuracy of the intelligent algorithm reaches the set value; and use the parallel memory container method to record the obtained random parameters;

[0088] (4) Compare the optimal solutions of each round to obtain the parameter solution that satisfies the global optimum.

[0089] The generation of new random parameters is optimized using an adaptive variable step size method, the expression of which is:

[0090] range=range*(1+2*(rate-a) / (1-a))

[0091] Where range is the step size range of the random new solution, and a is the variable step size optimization coefficient.

[0092] The temperature reduction process employs an optimized accelerated iteration strategy, resulting in the following temperature:

[0093]

[0094] Where T0 is the initial temperature, M is the number of iterations, and ck is the algorithm coefficient.

[0095] Step 4: Input the globally optimal electrochemical parameters into the electrochemical porous electrode model to obtain updated current and voltage values.

[0096] In step two, the methods for updating electrochemical parameters using intelligent algorithms include one or more of the following: annealing algorithm, genetic algorithm, ant colony algorithm, and particle swarm optimization.

[0097] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

Claims

1. A rapid inverse correction analysis method for multiple parameters used in electrochemical calculations, characterized in that: Includes the following steps: Step 1: Obtain the initial values ​​of electrochemical parameters and input them into the electrochemical porous electrode model to calculate the current and voltage values; Step 2: Update the electrochemical parameters using the annealing algorithm based on the obtained current and voltage values; Step 3: Repeat step 2 until a globally optimal electrochemical parameter solution with sufficient accuracy is obtained; Step 4: Input the globally optimal electrochemical parameters into the electrochemical porous electrode model to obtain updated current and voltage values; In step one, the current and voltage values ​​are calculated using an electrochemical porous electrode model. The specific steps include: (1) The finite volume method is used to discretize the electrolyte diffusion equation, and the boundary conditions of the governing equation are solved. The expression is as follows: ; ;in, It is the volume fraction of electrolytes. It is time. It is the electrolyte concentration. It is the mesh length of the finite volume method. It is the electrolyte diffusion coefficient. It is a grid index. It is the surface area to volume ratio of the electrode particles. It is ion flux; (2) The finite difference discrete calculation of the solid-phase diffusion equation and the solution of the boundary conditions of the governing equation are expressed as follows: ; ;in, It is the solid phase concentration. It is the solid-phase diffusion coefficient. It is the grid length in the direction of particle radius; (3) The finite volume method is used to discretize the electrolyte potential equation, and the boundary conditions of the governing equation are solved. The expression is as follows: ; ; ;in, It is the electrolyte conductivity. It is the electrolyte potential. It's temperature. It is Faraday's constant; (4) For the current calculation of the BV equation, the boundary conditions are applied to the governing equation through the charge conservation equation, and its expression is: in, This is an overpotential; (5) The finite volume discretization calculation of the potential equation of the solid phase and the solution of the boundary conditions of the governing equation are expressed as follows: ; ;in, For solid-state conductivity, For solid-state potential, The input current density is given. For the time-varying ordinary differential equations formed by the discrete calculation of the above equations, the numerical solution is obtained using the backward difference method of BDF.

2. The rapid inverse correction analysis method for multiple parameters used in electrochemical calculations according to claim 1, characterized in that: The time iteration formula used in the BDF backward difference method is as follows: ;in, It is an equation. It is the order of the BDF. and It is a constant coefficient. It is the time step. It is the initial time. .

3. The rapid inverse correction analysis method for multiple parameters used in electrochemical calculations according to claim 1, characterized in that: The solution to the globally optimal electrochemical parameters that meets the required accuracy, as described in step three, includes the following specific steps: (1) Generate new random parameters based on the current and voltage values, and evaluate the random parameters using the objective function; (2) Accept random parameters with good evaluation results of the objective function, and at the same time randomly accept random parameters with poor evaluation results of the objective function; (3) Lower the temperature and repeat steps (1) and (2) until the annealing algorithm temperature or accuracy reaches the set value; and use a parallel memory container method to record the obtained random parameters; compare the optimal solutions of each round to obtain the parameter solution that satisfies the global optimum; the generation of new random parameters is optimized using an adaptive variable step size method, the expression of which is: ;in, It is the range of step sizes for random new solutions. The coefficients are optimized for variable step size.

4. The rapid inverse correction analysis method for multiple parameters used in electrochemical calculations according to claim 3, characterized in that: The objective function is the sum of squared residuals between the calculated random parameter data and the original measurement data.

5. A rapid inverse correction analysis method for multiple parameters used in electrochemical calculations according to claim 3, characterized in that: The temperature reduction process employs an optimized accelerated iteration strategy, resulting in the following temperature: ;in, The initial temperature. For the number of iterations, These are the algorithm coefficients.

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