Method for predicting DC internal resistance of battery based on pore network model

Abstract

The invention discloses a method for predicting the DC internal resistance of a battery based on a pore network model. The method comprises the following steps: S1, constructing a lithium manganate battery pore network model; s2, selecting a JEVS method to test the internal resistance on the basis of the pore network model; s3, predicting from the structure to the direct-current internal resistance through Gaussian process regression machine learning; s4, explaining a machine learning result by adopting a Shapley value, and obtaining electrode structure parameters, including electrode thickness, porosity and average particle size; and S5, deriving a formula for predicting the direct-current internal resistance from the electrode structure parameters by adopting symbolic regression machine learning based on a genetic algorithm. According to the method for predicting the direct current internal resistance of the battery based on the pore network model and machine learning, powerful support is provided for calculation of the quantitative relation between the electrode structure and the DCR, and therefore the positive electrode structure of the lithium manganate battery is designed.

Description

Technical Field

[0001] The present invention relates to the field of batteries, and in particular to a method for predicting the direct current internal resistance of a battery based on a pore network model. Background Art

[0002] Lithium-ion batteries, as the energy storage device of choice for portable electronic devices and electric vehicles, have attracted widespread attention for their fast-charging performance, thermal safety, and battery state. These performance characteristics are closely related to the battery's internal resistance. Techniques for estimating battery resistance primarily include direct current (DC) and alternating current (AC) methods. The DC method is widely used due to its simplicity and accuracy to actual values. Battery internal resistance includes ohmic resistance, concentration polarization resistance, and electrochemical polarization resistance. Complex porous electrodes affect the movement of ions and electrons, as well as the electrochemical reactions within the battery, so electrode structure affects DCR (Direct Current Resistance). Therefore, exploring the relationship between electrode structure and DCR can help design high-performance batteries.

[0003] Existing research on the effect of electrode structure on DCR suffers from significant limitations: simplified two-dimensional or quasi-two-dimensional geometric models with limited structural parameters are commonly used, failing to fully characterize the coupled effects of the numerous parameters of electrode materials. This results in significant deviations from the complex three-dimensional structure of actual battery systems, failing to reflect the true reality and lacking a quantitative relationship between electrode structure and DCR. The classic pseudo-two-dimensional model (P2D), based on the idealized assumption of uniform electrode particle size, cannot accurately describe the actual structure, and the numerous partial differential equations involved complicate the calculations. In recent years, the emerging pore network model (PNM) accurately captures the heterogeneous structure of electrodes with high computational efficiency. PNM has been used to investigate the effects of tortuosity, particle size distribution, connectivity, and porosity on battery performance. Common DC internal resistance testing methods include HPPC (Hybird Pulse Power Characterization) and JEVS (Japan Electric Vehicle Standard). Compared to the HPPC method, the JEVS method uses a current range of 0–10C, avoiding the bias associated with using a single current and resulting in more accurate results. In recent years, machine learning has been widely applied to electrode design, but it suffers from a widespread black-box problem. Research has used symbolic regression to discover new formulas for predicting the lifespan of lithium-ion batteries. Symbolic regression has also been used to obtain power-type expressions for parameters related to the battery thermal model, enabling optimization of the battery thermal model. Therefore, symbolic regression can be used to develop a predictive formula for calculating DCR from electrode structural parameters. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for predicting the DC internal resistance of a battery based on a pore network model to solve the problems raised in the above background technology.

[0005] To achieve the above-mentioned object of the invention, the present invention provides a method for predicting the DC internal resistance of a battery based on a pore network model, comprising the following steps:

[0006] Step S1, constructing a pore network model of a lithium manganese oxide battery;

[0007] Step S2, selecting the JEVS method to test the internal resistance based on the pore network model;

[0008] Step S3, predicting the structure to the DC internal resistance through Gaussian process regression machine learning;

[0009] Step S4, using Shapley value to interpret the results of machine learning to obtain electrode structural parameters, including electrode thickness, porosity, and average particle size;

[0010] Step S5: Using symbolic regression machine learning based on a genetic algorithm to derive a formula for predicting the DC internal resistance from the electrode structure parameters.

[0011] Furthermore, in step S1, the method for constructing a pore network model of a lithium manganese oxide battery is as follows: lithium manganese oxide is used as the positive electrode material and graphite is used as the negative electrode material, Porespy is used to randomly generate a disordered structure and OpenPNM is used to extract the pore throat structure, and the diaphragm and the negative electrode are randomly generated into regular structures by OpenPNM to construct a three-dimensional pore network model of a lithium manganese oxide battery divided into an electrolyte phase, an active material phase and a carbon binder phase.

[0012] Furthermore, in step S2, the conductance is calculated by assuming that the cell volume does not change during the intercalation reaction and the concentration in each pore is uniform. The PNM is composed of a pore-throat structure. A pore-throat-pore structure in the model is regarded as a combined conductance, and the resistance series principle is used for calculation. The conductance calculation formula is as follows:

[0013] ;

[0014] in, is the diffuse liquid phase conductivity: is the diffuse solid phase conductivity, is the ionic liquid phase conductivity, is the ohmic solid-phase conductance, Indicates the length of the throat connecting these two holes. , represents the cross-sectional area of ​​the throat, They refer to the diffusion coefficient and conductivity of lithium ions in the electrolyte, They refer to the diffusion coefficient and electrical conductivity of lithium in the solid phase, respectively, where the diffusion of lithium mainly occurs between the active material particles.

[0015] Furthermore, in step S2, in the electrolyte phase, the diffusion and migration of lithium ions and the intercalation reaction occurring at the solid-liquid interface together constitute the concentration change of lithium ions, which is described by the NP equation and the BV equation, and the flux of lithium ions at the interface between the electrolyte and the current collector is stipulated to be zero. The calculation formula is:

[0016] ;

[0017] in, , is the lithium ion liquid phase transfer coefficient, is the interfacial area between the active material and the electrolyte, Refers to the lithium ion flow density at the solid-liquid interface, is the concentration of lithium ions in pore i, is the liquid phase diffusive conductivity, , unit is C / mol;

[0018] The potential of lithium ions in the electrolyte phase is calculated using the modified Ohm's law and the BV equation, and it is stipulated that there is no current flux at the interface between the electrolyte phase and the current collector. The calculation formula is:

[0019] ;

[0020] in, is the lithium ion liquid phase transfer coefficient, is the interfacial area between the active material and the electrolyte, is the lithium ion flux density at the solid-liquid interface, is the potential of hole i, is the concentration of lithium ions in pore i, is the liquid phase ionic conductivity, k is the reaction rate, F is the Faraday constant in C / mol, R is the gas constant in J / (mol·K), is the temperature in K;

[0021] The solid-phase lithium concentration is mainly composed of lithium diffusion in the active material phase and the intercalation reaction between the electrolyte phase and the active material phase. When constructing the PNM structure of the separator, it is assumed that all the pores are electrolyte phases. At the same time, it is stipulated that lithium cannot be transferred from the active material phase to the separator, and the flux of lithium metal at the interface between the current collector and the active material phase is also zero. It is calculated using Fick's law and the BV equation. The calculation formula is:

[0022] ;

[0023] in, The active material mesopores The volume, is the lithium ion liquid phase transfer coefficient, is the interfacial area between the active material and the electrolyte, is the lithium ion flux density at the solid-liquid interface, is the concentration of lithium ions in pore i, is the solid phase diffusion conductivity, k is the reaction rate, and F is the Faraday constant in C / mol;

[0024] The solid phase potential is expressed using Ohm's law and the BV equation, and assuming that the carbon binder phase does not react, the calculation formula is:

[0025] ;

[0026] in, is the interfacial area between the active material and the electrolyte, is the lithium ion flux density at the solid-liquid interface, is the solid-phase conductivity of the active material, is the solid phase conductivity of chemical water bath deposition, is the potential of hole i, is the concentration of lithium ions in pore i, F is the Faraday constant in C / mol;

[0027] The electrochemical reaction at the solid-liquid interface is described by the BV kinetic equation, and the calculation formula is:

[0028] ;

[0029] ;

[0030] ;

[0031] ;

[0032] in, are the anodic and cathodic transfer coefficients, respectively, are the exchange current density and overpotential, respectively, Refers to the equilibrium potential, is the lithium ion flux density at the solid-liquid interface, is the concentration of lithium ions in pore i, k is the reaction rate, F is the Faraday constant in C / mol, R is the gas constant in J / (mol·K), is the temperature in K.

[0033] Furthermore, in step S2, the internal resistance is calculated using the JEVS method as follows: applying an increasing pulse current at the same SOC, selecting 1C, 2C, 5C and 10C current charging and discharging, the pulse time is 10s, the shelf time is 60s, the last second of each pulse charging and discharging is selected, the voltage and current values ​​at this time are recorded, and then a linear fit is performed, and the slope obtained is used as the charging and discharging DC internal resistance.

[0034] Furthermore, in step S4, the SHAP model is used to interpret the results of machine learning, and the degree of influence of each feature on the final prediction result is obtained. The contribution of each feature in the machine learning model is quantified by the Shapley value. The Shapley value calculation formula is:

[0035] ;

[0036] in, is the total number of features, The set of all possible features of The feature set in Respectively represent the addition of prediction results.

[0037] Furthermore, in step S5, the electrode thickness, porosity and average particle size are selected as the input parameters of the symbolic regression, the data set is normalized and divided into a training set and a test set in a ratio of 7:3, and symbolic regression learning is performed to predict the charging DC internal resistance through symbolic regression based on the genetic algorithm. and discharge DC internal resistance The formulas are:

[0038] ;

[0039] ;

[0040] Where: L is the electrode thickness, ε is the porosity, and d is the average particle size.

[0041] Compared with the prior art, the present system and method have the following advantages:

[0042] (1) The present invention constructs a pore network model that can accurately extract the heterogeneous structure of the electrode and discretize the complex partial differential equations in the P2D model, greatly improving the computational efficiency.

[0043] (2) The present invention uses Gaussian regression machine learning to predict the DC internal resistance of the battery, solves the black box problem in machine learning through the SHAP interpretation model, and ultimately provides a quantitative relationship between electrode structure and DCR.

[0044] (3) The same method can also be used in lead-acid batteries, fuel cells and other types of batteries. At the same time, this method is not limited to the positive and negative electrodes of the battery, and can be used with porous electrode materials. It provides strong support for the design of the positive electrode structure of lithium manganese oxide batteries. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 Flowchart of a method for predicting battery DC internal resistance based on a pore network model.

[0046] Figure 2 Diagram of the pore network model construction process.

[0047] Figure 3 (a) is a diagram of pulse charge and discharge tests on the battery using currents of 1C, 2C, 5C and 10C, and (b) is a diagram of the calculation principle of the JEVS internal resistance test method.

[0048] Figure 4 (a) is the lithium ion concentration and voltage distribution diagram of lithium manganese oxide battery, and (b) is the comparison diagram of PNM simulation and experimental results.

[0049] Figure 5 (a) is the Gaussian regression prediction result of the discharge DC internal resistance of the lithium manganese oxide battery in the training set, (b) is the Gaussian regression prediction result of the discharge DC internal resistance of the lithium manganese oxide battery in the test set, and (c) is the SHAP value diagram of each structural parameter of the discharge DC internal resistance; (d) is the Gaussian regression prediction result of the charging DC internal resistance of the lithium manganese oxide battery in the training set, (e) is the Gaussian regression prediction result of the charging DC resistance of the lithium manganese oxide battery in the test set, and (f) is the SHAP value diagram of each structural parameter of the charging DC internal resistance.

[0050] Figure 6 (a) Output formula for symbolic regression The tree structure diagram is as follows: (b) is the symbolic regression prediction result diagram of the DC internal resistance of the lithium manganese oxide battery in the training set, (c) is the symbolic regression prediction result diagram of the DC internal resistance of the lithium manganese oxide battery in the test set; (d) is the symbolic regression prediction result diagram of the DC internal resistance of the lithium manganese oxide battery in the training set, (e) is the symbolic regression prediction result diagram of the DC internal resistance of the lithium manganese oxide battery in the test set. DETAILED DESCRIPTION

[0051] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0052] like Figure 1The figure shows a flow chart of a method for predicting the DC internal resistance of a battery based on a pore network model provided by the present invention. The main steps are as follows:

[0053] Step S1, constructing a pore network model of a lithium manganese oxide battery;

[0054] Step S2, selecting the JEVS method based on PNM to test the internal resistance;

[0055] Step S3, predicting the structure to the DC internal resistance through Gaussian process regression machine learning;

[0056] Step S4, using Shapley value to interpret the results of machine learning and obtain several main structural parameters;

[0057] Step S5: Using symbolic regression machine learning based on a genetic algorithm to derive a formula for predicting the DC internal resistance from the electrode structure parameters.

[0058] like Figure 2 The figure shows the process of constructing the pore network model. Lithium manganese oxide is used as the positive electrode material and graphite is used as the negative electrode material. For the positive electrode, we use Porespy to randomly generate a disordered structure and use OpenPNM to extract the pore throat structure, as shown in the figure. Figure 2 (a) As shown. The separator and negative electrode are randomly generated into regular structures through OpenPNM, and a three-dimensional pore network model of lithium manganese oxide battery is constructed, which can be divided into electrolyte phase, active material phase and carbon binder phase, as shown in Figure 2 (b) As the calculation efficiency of complex disordered structures is low, the positive electrode structure used in the quantitative relationship between the positive electrode structure and the DC internal resistance is as follows: Figure 2 The negative electrode in (b) also has a regular structure.

[0059] When lithium manganese oxide batteries are working, lithium ions diffuse and migrate in the electrolyte, undergo electrochemical reactions, transfer electrons, and transport lithium ions in the solid phase particles of the electrode. The pore network model can discretize the complex partial differential equations in the P2D model. First, it is assumed that the battery volume does not change during the intercalation reaction and the concentration in each pore is uniform. PNM is composed of pore throat structures. A pore-throat-pore structure in the model can be regarded as a combined conductivity, which is calculated using the resistance series principle. In the battery charging and discharging process, the diffusion conductivity (liquid phase: , solid phase: )Ionic conductivity (liquid phase: ) and ohmic conductance (solid phase: ), as shown in formula (1):

[0060] (1)

[0061] in, is the diffuse liquid phase conductivity: is the diffuse solid phase conductivity, is the ionic liquid phase conductivity, is the ohmic solid-phase conductance, Indicates the length of the throat connecting these two holes. , represents the cross-sectional area of ​​the throat, They refer to the diffusion coefficient and conductivity of lithium ions in the electrolyte, Refers to the diffusion coefficient and conductivity of lithium in the solid phase, respectively, where the diffusion of lithium mainly occurs between the active material particles

[0062] In the electrolyte phase, the diffusion and migration of lithium ions and the intercalation reaction occurring at the solid-liquid interface together constitute the concentration change of lithium ions, which is described by the NP (Nernst-Planck) equation and the BV (Butler-Volmer) equation, as shown in Equation (2), and stipulates that the flux of lithium ions at the interface between the electrolyte and the current collector is zero.

[0063] (2)

[0064] in, , is the lithium ion liquid phase transfer coefficient, is the interfacial area between the active material and the electrolyte, Refers to the lithium ion flow density at the solid-liquid interface, is the concentration of lithium ions in pore i, is the liquid phase diffusive conductivity, , unit is C / mol.

[0065] The current generated by the concentration difference and potential difference of lithium ions in the electrolyte phase causes the flow of charge. The potential is calculated using the modified Ohm's law and the BV equation, as shown below, and it is stipulated that there is no current flux at the junction of the electrolyte phase and the current collector.

[0066] (3)

[0067] in, is the lithium ion liquid phase transfer coefficient, is the interfacial area between the active material and the electrolyte, is the lithium ion flux density at the solid-liquid interface, is the potential of hole i, is the concentration of lithium ions in pore i, is the liquid phase ionic conductivity, k is the reaction rate, F is the Faraday constant in C / mol, R is the gas constant in J / (mol·K), is the temperature in K.

[0068] The solid-phase lithium concentration is mainly composed of lithium diffusion in the active material phase and intercalation reactions between the electrolyte phase and the active material phase. It is calculated using Fick's law and the BV equation and can be expressed as Equation (4). When constructing the PNM structure of the separator, it is assumed that all its pores are electrolyte phases. At the same time, it is stipulated that lithium cannot be transferred from the active material phase to the separator, and the flux of lithium metal at the interface between the current collector and the active material phase is also zero.

[0069] (4)

[0070]

[0071] The solid phase potential is expressed using Ohm's law and the BV equation, and assuming that the carbon binder phase does not react, it can be calculated using equation (5):

[0072] (5)

[0073]

[0074]

[0075] (6)

[0076] (7)

[0077] (8)

[0078] (9)

[0079]

[0080] At the same time, the current is conserved in the active material phase and the electrolyte phase.

[0081] (10)

[0082] This method uses the JEVS method to calculate the internal resistance. The basic idea is to apply increasing pulse current at the same SOC. Select 1C, 2C, 5C and 10C current charging and discharging, the pulse time is 10s, and the shelf time is 60s. Figure 3 (a) Select the last second of each pulse charge and discharge, record the voltage and current values ​​at this time, and perform linear fitting, as shown in Figure 3 As shown in (b), the slope obtained is the required charging and discharging DC internal resistance. and is the slope angle of the charge and discharge voltage-current curve, as shown in formula (11).

[0083] (11)

[0084] This method uses Gaussian regression machine learning, a simple and robust method for prediction. A Gaussian process is a random process defined on a continuous domain over an infinite number of random variables that obey a Gaussian distribution, and can be expressed using Equation (12). The Gaussian regression model, based on Bayesian probability theory, is a nonlinear, nonparametric regression tool.

[0085] (12)

[0086] in, is the average function, is the covariance function.

[0087] The SHAP model is used to interpret the results of machine learning and obtain the degree of influence of each feature on the final prediction result. The SHAP interpretation method is extended from the concept of Shapley value in game theory, which quantifies the contribution of each feature in the machine learning model through the Shapley value. The Shapley value of can be expressed by formula (13).

[0088] (13)

[0089]

[0090] All the structures used in the aforementioned exploration of the relationship between structural parameters and DC internal resistance were integrated together. The data set was normalized and divided into training and test sets in a ratio of 7:3. Gaussian regression machine learning training was performed in Matlab R2023b.

[0091] In order to solve the black box problem of machine learning, this method uses the SHAP model to give the possible relationship between the predicted value and certain features. Figure 5 As shown in the figure, using the porosity characteristic as an example, it can be seen that as the porosity increases, the SHAP value becomes less than zero, and this is the case for most samples, indicating that porosity is inversely proportional to the DC internal resistance. Here, the characteristics are arranged from top to bottom according to their average absolute value, which represents the order of influence of each structural parameter on the DC internal resistance from greatest to least. Figure 5 (c) It can be seen that porosity, average particle size and specific surface area have the greatest impact on discharge DCR, while electrode thickness, porosity and average particle size have the greatest impact on charge DCR. This can be seen from Figure 5 (f) and the one with the least impact is the pore connectivity.

[0092] Symbolic regression is implemented using a genetic algorithm. Descriptors, operators, and mathematical functions are combined into chromosomes to form individuals. Based on a finite set of solutions, appropriate scoring criteria are used to determine the survival of the fittest. Individuals with good fitness are replicated, mated, and mutated, ensuring that solutions that best match the objective function are effectively propagated to the next generation, thereby continuously approximating the data distribution. Symbolic regression based on genetic algorithms can effectively and automatically design hybrid descriptors that outperform individual descriptors.

[0093] Usually, the formula for calculating DC internal resistance requires the battery to be charged and discharged and to be left standing for a certain period of time, and it cannot be obtained directly from the battery leaving the factory. Since the DC internal resistance of the battery has a certain correlation with the battery structural parameters, this method predicts the DC internal resistance formula through several important structural parameters through a symbolic regression model based on a genetic algorithm. When interpreting the SHAP model, the order of influence of different structural parameters on the DC internal resistance is analyzed. Since there is a large correlation between connectivity and porosity, and average particle size and specific surface area, this method selects electrode thickness, porosity and average particle size as input parameters for symbolic regression after comprehensive consideration. According to Figure 6 The tree structure shown in (a) outputs the DC internal resistance in the form of Formula 14.

[0094] (14)

[0095] The data set was normalized and divided into a training set and a test set in a ratio of 7:3. Symbolic regression learning was performed in Matlab R2023b. The charging and discharging DC internal resistance formula (15, 16) was predicted by symbolic regression based on genetic algorithm. The coefficients in the formula of charging DC internal resistance are The physical meaning is that the resistance per unit volume is 0.168, and the coefficient in the formula of discharge DC internal resistance is The physical meaning is that the resistance per unit area is 0.072. Figure 6 (b) shows the results of the actual value and the predicted value in the training set and the test set according to the prediction formula. It can be seen that the RMSE (root mean square error) is less than 20% and the MAE is less than 10%. The largest RMSE is 11% for the test set of the charging DC internal resistance formula. This shows the accuracy of formulas (15) and (16). The structures corresponding to the scattered points may have large changes in pore connectivity or specific surface area of ​​the electrodes, which makes these two structural parameters have a greater impact on the DC internal resistance.

[0096] (15)

[0097] (16)

[0098] in: .

[0099] The present invention constructs a pore network model of lithium manganese oxide batteries and analyzes the relationship between different positive electrode structural parameters and charge and discharge DC internal resistance. In order to compare the influence of each structural parameter, Gaussian regression machine learning is combined and the results of machine learning are explained using the SHAP model. The study found that porosity, average particle size and specific surface area have the greatest influence on discharge DCR, while electrode thickness, porosity and average particle size have the greatest influence on charge DCR. Since porosity and connectivity, average particle size and specific surface area are closely related, symbolic regression based on genetic algorithm is used to explore the relationship between positive electrode thickness, porosity and average particle size and charge and discharge DC internal resistance, and finally obtain 、 This relationship can help improve battery health state estimation based on the internal resistance method.

[0100] In summary, the present invention proposes a method for predicting the DC internal resistance of a battery based on a pore network model combined with machine learning, which can study the quantitative relationship between electrode structure and DCR. This method constructs a pore network model for lithium manganese oxide batteries, selects the JEVS method to test the internal resistance based on PNM; predicts the DC internal resistance from structure through Gaussian process regression machine learning; uses Shapley value to interpret the results of machine learning, obtains several main structural parameters, and finally uses symbolic regression machine learning based on genetic algorithm to derive a formula for predicting the DC internal resistance from the electrode structure parameters. The same method can also be used for lead-acid batteries, fuel cells and other types of batteries. At the same time, this method is not limited to the positive and negative electrodes of the battery, and porous electrode materials can be used. It helps in the design of the positive electrode structure of lithium manganese oxide batteries.

[0101] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A method for predicting battery DC internal resistance based on a pore network model, characterized in that: The following steps are involved: Step S1, constructing a pore network model of a lithium manganese oxide battery; Step S2, selecting the JEVS method to test the internal resistance based on the pore network model; Step S3, predicting the structure to the DC internal resistance through Gaussian process regression machine learning; Step S4, using Shapley value to interpret the results of machine learning to obtain electrode structural parameters, including electrode thickness, porosity, and average particle size; Step S5: Using symbolic regression machine learning based on a genetic algorithm to derive a formula for predicting the DC internal resistance from the electrode structure parameters.

2. The method for predicting battery DC internal resistance based on a pore network model according to claim 1, characterized in that: In step S1, the method for constructing a pore network model of a lithium manganese oxide battery is as follows: lithium manganese oxide is used as the positive electrode material and graphite is used as the negative electrode material, Porespy is used to randomly generate a disordered structure and OpenPNM is used to extract the pore throat structure, and the diaphragm and the negative electrode are randomly generated into regular structures by OpenPNM to construct a three-dimensional pore network model of a lithium manganese oxide battery divided into an electrolyte phase, an active material phase and a carbon binder phase.

3. The method for predicting battery DC internal resistance based on a pore network model according to claim 1, characterized in that: In step S2, the conductance is calculated by assuming that the cell volume does not change during the intercalation reaction and the concentration in each pore is uniform. The PNM is composed of a pore-throat structure. A pore-throat-pore structure in the model is regarded as a combined conductance and calculated using the resistance series principle. The conductance calculation formula is as follows: ； in, is the diffusion liquid phase conductivity: is the diffuse solid phase conductivity, is the ionic liquid phase conductivity, is the ohmic solid-phase conductance, Indicates the length of the throat connecting these two holes. , represents the cross-sectional area of ​​the throat, They refer to the diffusion coefficient and conductivity of lithium ions in the electrolyte, They refer to the diffusion coefficient and electrical conductivity of lithium in the solid phase, respectively, where the diffusion of lithium mainly occurs between the active material particles.

4. The method for predicting battery DC internal resistance based on a pore network model according to claim 3, characterized in that: In step S2, in the electrolyte phase, the diffusion and migration of lithium ions and the intercalation reaction occurring at the solid-liquid interface together constitute the concentration change of lithium ions, which is described by the NP equation and the BV equation, and the flux of lithium ions at the interface between the electrolyte and the current collector is stipulated to be zero. The calculation formula is: ； in, , is the lithium ion liquid phase transfer coefficient, is the interfacial area between the active material and the electrolyte, Refers to the lithium ion flow density at the solid-liquid interface, is the concentration of lithium ions in pore i, is the liquid phase diffusive conductivity, , unit is C / mol; The potential of lithium ions in the electrolyte phase is calculated using the modified Ohm's law and the BV equation, and it is stipulated that there is no current flux at the interface between the electrolyte phase and the current collector. The calculation formula is: ； in, is the lithium ion liquid phase transfer coefficient, is the interfacial area between the active material and the electrolyte, is the lithium ion flux density at the solid-liquid interface, is the potential of hole i, is the concentration of lithium ions in pore i, is the liquid phase ionic conductivity, k is the reaction rate, F is the Faraday constant in C / mol, R is the gas constant in J / (mol·K), is the temperature in K; The solid-phase lithium concentration is mainly composed of lithium diffusion in the active material phase and the intercalation reaction between the electrolyte phase and the active material phase. When constructing the PNM structure of the separator, it is assumed that all the pores are electrolyte phases. At the same time, it is stipulated that lithium cannot be transferred from the active material phase to the separator, and the flux of lithium metal at the interface between the current collector and the active material phase is also zero. It is calculated using Fick's law and the BV equation. The calculation formula is: ； in, The active material mesopores The volume, is the lithium ion liquid phase transfer coefficient, is the interfacial area between the active material and the electrolyte, is the lithium ion flux density at the solid-liquid interface, is the concentration of lithium ions in pore i, is the solid phase diffusion conductivity, k is the reaction rate, and F is the Faraday constant in C / mol; The solid phase potential is expressed using Ohm's law and the BV equation, and assuming that the carbon binder phase does not react, the calculation formula is: ； in, is the interfacial area between the active material and the electrolyte, is the lithium ion flux density at the solid-liquid interface, is the solid-phase conductivity of the active material, is the solid phase conductivity of chemical water bath deposition, is the potential of hole i, is the concentration of lithium ions in pore i, F is the Faraday constant in C / mol; The electrochemical reaction at the solid-liquid interface is described by the BV kinetic equation, and the calculation formula is: ； ； ； ； in, are the anodic and cathodic transfer coefficients, respectively, are the exchange current density and overpotential, respectively, Refers to the equilibrium potential, is the lithium ion flux density at the solid-liquid interface, is the concentration of lithium ions in pore i, k is the reaction rate, F is the Faraday constant in C / mol, R is the gas constant in J / (mol·K), is the temperature in K.

5. The method for predicting battery DC internal resistance based on a pore network model according to claim 1, characterized in that: In step S2, the internal resistance is calculated using the JEVS method as follows: applying an increasing pulse current at the same SOC, selecting 1C, 2C, 5C and 10C current charging and discharging, with a pulse time of 10s and a rest time of 60s. The last second of each pulse charging and discharging is selected, the voltage and current values ​​at this time are recorded, and then a linear fit is performed. The slope obtained is used as the DC internal resistance of charging and discharging.

6. The method for predicting battery DC internal resistance based on a pore network model according to claim 1, characterized in that: In step S4, the SHAP model is used to interpret the results of machine learning, and the influence of each feature on the final prediction result is obtained. The contribution of each feature in the machine learning model is quantified by the Shapley value. The Shapley value calculation formula is: ； in, is the total number of features, The set of all possible features of The feature set in Respectively represent the addition of prediction results.

7. The method for predicting battery DC internal resistance based on a pore network model according to claim 1, characterized in that: In step S5, electrode thickness, porosity, and average particle size are selected as input parameters for symbolic regression. The data set is normalized and divided into a training set and a test set in a ratio of 7:

3. Symbolic regression learning is performed to predict the charging DC internal resistance through symbolic regression based on genetic algorithm. and discharge DC internal resistance The formulas are: ； ； Where: L is the electrode thickness, ε is the porosity, and d is the average particle size.

Images