Test method for rapidly optimizing lithium battery formula system

Abstract

The invention belongs to the technical field of lithium ion batteries, and particularly discloses a test method for quickly optimizing a lithium battery formula system, which comprises the following steps: S1, confirming the performance of a lithium battery, determining the population size by adopting a Schefe polynomial, establishing a design model, and determining that an experimental scheme is at an extreme vertex; s2, according to the order number of the Schefe polynomial mathematical model and the number of the test components, determining the proportion of the test times and the test components; s3, testing according to the test times and the test component proportion given by the model in S2 to obtain each electrical performance parameter of the battery, performing linear regression analysis, and establishing a mathematical relationship between response variables and the component proportion; s4, analyzing a response trace graph between test scheme result data and the materials, and judging the optimal proportion of each material; s5, performing data optimization on the experimental result and the experimental material ratio to obtain an optimal formula of the system; s6, carrying out a singleness test, and further determining the effectiveness of the optimal proportion value; and S7, repeatedly verifying and determining the reliability of the optimal ratio.

Description

Technical Field

[0001] The invention relates to the technical field of lithium ion batteries, and in particular to a test method for rapidly optimizing a lithium battery formula system. Background Art

[0002] As countries and environmental protection organizations around the world put forward requirements such as "carbon neutrality" and "low-carbon travel", the application fields of rechargeable, dischargeable and long-cycle lithium-ion batteries are becoming more and more extensive. The application performance requirements of lithium batteries are becoming more and more diverse due to their use in different environments and conditions; such as application requirements under long-term low temperature conditions, long-term high temperature conditions, long-term high-power frequent use requirements, etc. This requires the R&D departments of lithium battery manufacturers to frequently develop various battery performances required by the market. The positive and negative electrode formula system of lithium batteries is directly related to whether the electrical performance of lithium batteries can meet the market requirements. Therefore, the R&D departments of lithium battery manufacturers need to continuously optimize the positive and negative electrode formula systems of lithium batteries to meet market needs.

[0003] At present, the R&D departments of lithium battery manufacturers at home and abroad are still optimizing the positive and negative electrode formula systems of lithium batteries by using the trial and error elimination method. That is, first determine the various properties required of the lithium battery, and based on past experience, add one or more material proportions for each test. Then, test the performance results through test samples, and continuously improve the system formula through trial and error. This trial and error elimination method consumes immeasurable manpower and material resources, and consumes an indeterminate amount of time.

[0004] The positive and negative electrode formula system of lithium batteries involves the usage ratio of positive and negative electrode main materials, binders, and conductive agents. The use of positive and negative electrode materials is mainly reflected in the processing and manufacturing process and capacity performance of lithium batteries. The polarization resistance, first effect, energy efficiency, constant current and constant voltage ratio of lithium batteries are generally determined by the proportion of conductive agents used. There are three main types of conductive agents for lithium batteries: point conductive agents: such as conductive carbon black (SP), artificial graphite (Ks-6), etc.; sheet conductive agents: such as graphene (Gr), etc.; linear conductive agents: such as carbon nanotubes (CNTs), carbon fibers (CF), etc. The application of these three conductive agents is closely related to the particle size of the positive and negative electrode materials, and is directly related to the polarization internal resistance, first effect, energy efficiency, and constant current and constant voltage ratio of lithium batteries. In the process of optimizing the positive and negative electrode systems, the optimization of the proportion of conductive agents is the most critical and time-consuming. Often, the R&D department of battery manufacturers uses trial and error elimination to find the correct positive and negative electrode formula system and produce lithium batteries that meet the performance requirements of use. However, due to the long time, the market has long been occupied by other lucky lithium batteries. The R&D expenses incurred during this period have no economic value. Summary of the invention

[0005] The purpose of the present invention is to solve the shortcomings of the existing formula optimization method and provide a test method for quickly optimizing the lithium battery formula system. Under the condition of determining the performance requirements of the lithium battery, the optimal ratio of each component in the lithium battery formula can be quickly determined to reduce the trial and error time.

[0006] The objective of the present invention is achieved through the following technical solutions:

[0007] A test method for rapidly optimizing a lithium battery formulation system comprises the following steps:

[0008] S1. Confirm the performance of lithium batteries. According to the material properties, use Scheffé polynomials to determine the population size, determine the upper and lower limits of each material in the lithium battery formula system, establish an extreme vertex design model, and determine that the experimental plan is at the extreme vertex;

[0009] S2. Determine the number of experiments N and the ratio of the experimental components according to the design model established in S1 and the order of the Scheffé polynomial mathematical model and the number of experimental components q;

[0010] S3. According to the number of tests N and the proportion of test components given in the model in S2, the electrical performance parameters of the battery are obtained, and after entering the corresponding experimental plan, a linear regression analysis is performed to establish a mathematical relationship between the response variable and the component ratio;

[0011] S4. Analyze the response trace diagram between the test plan result data and the materials, and determine the optimal ratio of each material based on the linear trend of the response trace diagram;

[0012] S5. Optimize all experimental results and test material ratios, and optimize the best formula for the system by inputting the expected values ​​of various performances of the lithium battery;

[0013] S6. Give the optimal ratio of each material through optimization analysis, conduct a single test, and further determine the effectiveness of the optimal ratio through test data;

[0014] S7. After the optimal ratio value is determined, the optimal ratio of each material in the system is repeatedly verified to determine the reliability of the optimal ratio.

[0015] The material is a lithium battery system including a main material, a binder, a main conductive agent, CNTs, Ks-6, and functional graphene; the main material and binder are lithium iron phosphate and polyvinylidene fluoride respectively, the main conductive agent is SP, and the CNTs, Ks-6 and functional graphene each account for a proportion of ≤1.0%, and the extreme vertex design model is established using the mathematical principle of Scheffe polynomials, and only the proportion of the main material is changed.

[0016] In a mixture test, each component is often restricted by upper and lower bounds and needs to meet certain constraints. The intersection of these restricted planes is called an extreme vertex, and the mixture test plan composed of these extreme vertex sets is an extreme vertex design. This design method is particularly suitable for the optimization of complex system material formulas that need to consider multiple component ratios and interactions at the same time.

[0017] The Scheffé polynomial model is a simplified polynomial model used to describe the relationship between the response variable and the factors in a mixture experiment. In this model, the parameters are simplified, making the model easier to understand and apply. For example, for a three-component mixture system, a first-order or second-order Scheffé model can be used to describe its response surface.

[0018] The multi-response Scheffé second-order mixture model is a special design that combines the Scheffé second-order model of multiple response variables and determines the optimal configuration of the test points based on the D-optimal design criterion. This method ensures that the most comprehensive information about the response variables can be obtained under given experimental conditions, thereby improving the efficiency and accuracy of the experiment.

[0019] When using Scheffé polynomials to build response surface models in mixture experiments, the formula for determining the number of experiments depends on the order of the polynomial and the number of components. For second-order Scheffé polynomials (also called quadratic models), the number of extreme vertices is q in the case of q components. This is because each extreme vertex corresponds to a case where the proportion of one component is 1 and the proportions of the other components are 0.

[0020] In addition to the extreme vertices, other design points need to be considered to estimate the interaction terms in the polynomial. For a second-order Scheffé polynomial, it is usually necessary to include linear terms for all component proportions, square terms, and pairwise interaction terms. Therefore, the total number of experiments should be at least the sum of the number of these terms.

[0021] In the present invention, the Scheffé polynomial mathematical model is expressed as:

[0022]

[0023] in;

[0024] represents the sum of all linear terms;

[0025] represents the sum of all quadratic terms;

[0026] represents the sum of all cross terms.

[0027] q is the number of experimental components in the mixture experiment, y is the response variable, and x i is the proportion of the i-th component, β0 is a constant term, β i , β ii , β ij are model parameters.

[0028] In this model, we have:

[0029] q linear terms β i x i

[0030] q square terms

[0031] The interaction term β ij x i x j

[0032] The total number of parameters is

[0033] The number of test scenarios N≥the total number of parameters.

[0034] Since each experiment can only provide one observation, the number of experimental schemes N is at least equal to the total number of parameters.

[0035] For example, for a mixture experiment with 3 ingredients (q=3), the number of parameters of the second-order Scheffé polynomial model is: 1+2×3+3(3-1) / 2=1+6+3=10; this means that at least 10 experiments are required to estimate all model parameters. This does not include possible repeated experiments to improve the accuracy of the estimates or to take into account experimental errors.

[0036] In a mixture experiment, when using a second-order Scheffé polynomial model, the material grouping ratio in each experiment usually follows specific experimental design rules. These rules ensure the comprehensiveness of the experiment and the validity of the data. Usually, the simplex lattice design rules and / or the simplex central composite design rules are followed.

[0037] (1) Simplex lattice design

[0038] Simplex lattice design is a method to systematically explore the space of ingredients by assigning the proportion of each ingredient to different levels, which includes all possible combinations of ingredient proportions. For q ingredients, the simplex lattice design considers combinations where the sum of all ingredient proportions is 1 at the dth order (d is the order of the simplex), where the proportion of each ingredient can take d+1 levels from 0 to 1. When considering combinations where the sum of all ingredients is 1, the proportion of each ingredient can be viewed as a weight to be distributed among the q ingredients.

[0039] The simplex lattice design rule is:

[0040]

[0041] Where: i is an integer from 1 to q+1, indicating the i-th level.

[0042] In a simplex lattice design, the "i-th level" refers to the i-th possible value of a component ratio. Since each component ratio can take d+1 levels, the "i-th level" is the i-th of these levels, usually expressed as

[0043] For example, for a second-order model (d = 2), if there are three components x1, x2, x3, the possible design points include:

[0044] (0,0,1)

[0045] (0,1,0)

[0046] (1,0,0)

[0047] (2 / 3,1 / 3,0)

[0048] (1 / 3,2 / 3,0)

[0049] (0,2 / 3,1 / 3)

[0050] (0,1 / 3,2 / 3)

[0051] (1 / 3,0,2 / 3)

[0052] (2 / 3,0,1 / 3)

[0053] (0,0,0)

[0054] Other design points obtained through symmetry or repetition.

[0055] (2) Simplex Central Composite Design

[0056] The simplex central composite design adds central points and axial points to the simplex lattice design.

[0057] The simplex central composite design rule is:

[0058] Center Point:

[0059] for all i=1,2,…,q

[0060] Axial point:

[0061] x i =0 for all j

[0062] x i =1 when i=k.

[0063] k represents the simplex central composite design rule, when k = 1 is the number of constraints; "axis points" in simplex lattice design usually refer to specific points obtained by equally dividing the multidimensional space along the edge or axis of the simplex. These points play an important role in mixture design (as shown in question 1), they help define the distribution of test points and the changing trend of the response variable.

[0064] In simplex lattice design, the choice of pivot points is based on the order of the simplex (d) and the number of components (q). For each component, its scale can vary from 0 to 1, and the sum of all component scales must equal 1. When considering pivot points, we are usually interested in specific points on or inside the edge of the simplex, which are obtained by bisecting the edge and taking its midpoint or other specific location.

[0065] The center point is the point where all components are equal in proportion, such as (1 / 3,1 / 3,1 / 3)(1 / 3,1 / 3,1 / 3), while the axial point is the point where one component has the maximum value and the other components have zero, such as (1,0,0)(1,0,0).

[0066] This design ensures that the experiments fully explore the compositional space, allowing for efficient estimation of the parameters of the second-order Scheffé polynomial mathematical model.

[0067] Scheffé polynomial mathematical model In the design of mixture experiments, by giving the experimental plan and inputting the corresponding experimental results, the mathematical relationship between the response value (experimental result) and the experimental plan can be established. The Scheffé polynomial mathematical model is used to perform linear regression analysis on the experimental data to establish the mathematical relationship between the response variable and the component ratio.

[0068] In the present invention, the effects of the regression analysis are as follows:

[0069] (1) Model fitting: Through regression analysis, the coefficients of the Scheffé polynomial are determined to obtain the specific regression equation.

[0070] (2) Optimizing the formula: Based on the regression equation, the optimal mixing formula can be found to optimize a certain indicator of the product.

[0071] (3) Predicting new formulas: The obtained regression equation can be used to predict the response values ​​under other untested ingredient ratios, providing a reference for new mixture formulas.

[0072] (4) Solution of model parameters:

[0073] Coefficient estimation: Based on the experimental data, the coefficients in the response surface equation can be estimated by the least squares method. These coefficients reflect the degree of influence of different component proportions on the response value.

[0074] Model validation: Once the model parameters are determined, additional experimental data is needed to verify the accuracy and predictive power of the model. This helps ensure the reliability of the model in practical applications.

[0075] (5) The relationship between the experimental plan and the results is obtained:

[0076] Direct correlation: Each experimental scheme corresponds to one or more response values, which directly reflect the product performance or effect under the scheme.

[0077] Optimization strategy: By analyzing the response values ​​under different schemes, the best combination of ingredient ratios can be identified to optimize product performance.

[0078] The method for drawing the response trace diagram between materials in step S4 of the present invention is as follows:

[0079] (1) Determine that the material composition is q, and the proportion of each component is x1, x2, …, x i ,…,x q , and satisfy the constraints: x1+x2+…x i +…+x q =1;

[0080] (2) The response value y is expressed as a polynomial function of the proportions of these components:

[0081] The response function can be expressed as:

[0082] y=β0+β1x1+β2x2+…β i x i +…+β p x p +∈ (1)

[0083] where β i is the coefficient of the i-th component, p is the number of factors, which refers to the independent variable of each material, and ∈ is the tolerance;

[0084] In the present invention, the response function y is also usually represented by x1, x2…, x i ,…,x p A d-degree polynomial representation of , where p is the number of factors, referring to the independent variables for each material, and d is the degree of the response polynomial.

[0085] The response function can also be expressed as:

[0086]

[0087] in:

[0088] β0 is the constant term (intercept).

[0089] β i is related to a single variable x i The coefficient of the linear term of the correlation.

[0090] β ij is related to two variables x i and x j The coefficients of the relevant interaction terms.

[0091] β ii is related to a single variable x i The coefficient of the associated quadratic term.

[0092] β α are the coefficients of the higher-order terms associated with the multiple exponent α.

[0093] x α express where α=(a1,a2,…,a p ) is a multiple index, and |α|=a1+a2+…+a p ≤d.

[0094] This formula is applicable to more complex relationships and can capture nonlinearities and interactions. In the process of seeking the best optimization for all response values ​​and all experimental factors, it is necessary to consider the interactions and sublinear relationships between the response values ​​and each experimental factor;

[0095] In the present invention, q is used as the number of experimental components: In a mixture experiment, q usually represents the number of different components or factors. Each component can have different proportions or levels. p is used as the number of independent variables (number of factors). The relationship between p and q usually depends on the design of the experiment:

[0096] If the proportion of each component varies independently and there are no additional constraints, then p = q.

[0097] If there are constraints (such as the sum of component proportions must be 1), then p may be less than q because not all component proportions vary independently; this relationship is crucial to understanding the complexity of the model and the number of parameters.

[0098] The above two formulas (1) and (2) both involve regression models, but they differ in form and application. You can choose the appropriate one according to the needs of the specific problem. If the data relationship is simple, you can use formula (1) (such as: experimental response trace plotting); if the data relationship is complex, you should use formula (2) when analyzing (such as: experimental recipe response optimization).

[0099] (3) Select one component as the independent variable, and the proportions of other components are automatically determined by constraints, and then calculate the different components x i The response value y under the value and plot the image of y with respect to x;

[0100] (4) Repeat the above process to obtain the trace graphs of other components.

[0101] The response trace diagram in the present invention has the following functions:

[0102] (1) Visual analysis: By plotting the response trace diagram between the proportions of different material components and the response values, the influence trend of each component on the response value can be intuitively displayed; this kind of diagram helps to understand the interaction between different components and their combined impact on product performance.

[0103] (2) Optimization guidance: Based on the analysis results of the trace graph, researchers can adjust the formulation more specifically to achieve the desired performance goals.

[0104] For example, if a certain ingredient has a significant positive effect on the response value, then you can consider increasing the proportion of this ingredient; otherwise, you should reduce or avoid its use.

[0105] Responsive optimization:

[0106] When the unknown parameters in the response function are replaced by estimated values, the regression equation, also known as the response surface equation, is obtained. This equation describes the relationship between the response value and the experimental plan.

[0107] In order to optimize the response, we need to find a combination of component ratios that maximizes (or minimizes, depending on the target) the response value Y. This can be achieved by solving the maximum (or minimum) value of the above polynomial function.

[0108] Specifically, the Lagrange multiplier method can be used to solve the above problem. The algorithm will give a set of x1, x2…, x i ,…,x pSolving this system of equations can yield the optimal combination of component ratios.

[0109] It should be noted that due to the constraint that the sum of the component proportions in the mixture experiment is 1, we need to introduce Lagrange multipliers in the solution process to deal with this constraint.

[0110] To build the response surface equation, we need to use the Lagrange multiplier method to deal with constrained optimization problems. In this problem, we have multiple variables (mixture proportions) and a performance value, and the goal is to find a response surface that describes the relationship between these mixture proportions and the performance value.

[0111] In the present invention, the specific steps of response optimization in step S5 are as follows:

[0112] (1) Define the objective function and constraints:

[0113] Objective function: The goal is to minimize the prediction error, that is, to find a response surface model f(x1,x2…,x i ,…,x q ), so that the difference between the predicted performance value and the actual observed value is minimized. The response surface model f(x) is a polynomial model, and x i is the i-th mixture ratio;

[0114] Constraints: g(x) = x1 + x2 + ... x i +…+x q -1=0;

[0115] (2) Construct the Lagrangian function:

[0116] The form of the Lagrangian function is L(x,λ)=f(x)+λg(x), where λ is the Lagrangian multiplier;

[0117]

[0118] Among them, β0 is a constant term, β i is the linear coefficient, β ii is the coefficient of the quadratic term, β ij is the cross-term coefficient, x i is the i-th mixture ratio, ∈ is the tolerance;

[0119] In the Lagrange multiplier method, we solve constrained optimization problems by constructing the Lagrangian function L(x,λ). Assuming we have n variables and k constraints, the Lagrangian function is usually expressed as:

[0120]

[0121] Where: f(x1,x2…,x i ,…,x n ) is the objective function; g i (x1,x2…,x i ,…,x n )=0 is the i-th constraint; λ i is the i-th Lagrange multiplier.

[0122] (3) Solve the extreme value of the Lagrangian function:

[0123] For the Lagrangian function L(x,λ) with respect to x1,x2…,x i ,…,x6,λ, and set them to zero to obtain a system of equations containing n+k variables, where n is the number of variables and k is the number of constraints. Solving the system of equations can obtain points that make L(x,k) reach extreme values, and these points are potential optimal solutions.

[0124] In order to find the point where L(x,λ) reaches its extreme value, we need to calculate L with respect to each variable x. i and each Lagrange multiplier λ i Find the partial derivatives and set them to zero. This will form a system of n+k equations.

[0125] The specific steps are as follows:

[0126] ①Construct Lagrangian function:

[0127]

[0128] ②Find the partial derivative and set it to zero:

[0129] For each x i Find partial derivatives:

[0130]

[0131] For each λ i Find partial derivatives:

[0132]

[0133] ③Form a system of equations:

[0134] There are n total about x i There are k equations about λ i equations (i.e. the original constraints).

[0135] ④Solve the system of equations:

[0136] Solve this system of n+k equations to obtain x1,x2,…,x i,…,x n and λ1,λ2,…,λ i ,…,λ k These points are potential optimal solutions.

[0137] (4) Verify extreme points:

[0138] Substitute the obtained extreme value points into the original objective function f(x) and the constraint condition g(x), check whether the constraint conditions are met and whether they are maximum or minimum values. If all conditions are met, these points can be used as key points on the response surface;

[0139] (5) Construct response surface:

[0140] Using the data points obtained in the above steps, a response surface equation is constructed through fitting technology. This equation can be used to describe the relationship between the mixture ratio and the performance value, and can be used to predict the performance values ​​under other mixture ratio combinations.

[0141] The response function is usually represented by x1, x2, …, x p is a d-degree polynomial representation of , where p is the number of factors and d is the degree of the response polynomial.

[0142] An experiment can obtain specific values ​​of various product performances. After any product is realized, it is impossible to only look at all the advantageous performances. The defective performance is also within the focus of the experiment. Through the response optimization calculation method, the advantageous performance is maximized and the defective performance is minimized. For example, the lithium battery product of the present invention has several important performance indicators: internal resistance, first efficiency, energy efficiency, constant current and constant voltage ratio, capacity, etc. The internal resistance of the lithium battery is the defective performance of this product. When calculating the response optimization value, a minimum value (hopefully small) is set.

[0143] In the present invention, the specific method for determining the validity of the optimal ratio value in step S6 is as follows:

[0144] 1) By using the response optimizer, an optimal combination of component ratios is found while meeting all response index requirements;

[0145] 2) Find the best material combination by building a composite desirability model to consider both internal resistance and other performance indicators;

[0146] 3) According to the response optimization calculation, find the best material combination, make the product and test the results of multiple product performance indicators, and compare the results with the indicators given by the composite desirability model in 2); if the results are close to the indicators given by the composite desirability model, the optimization effectiveness is confirmed. In the development of new products, it is crucial to ensure the reliability of experimental results.

[0147] At the same time, the results of the first experiment may be affected by many factors, including accidental errors, operational errors or changes in the external environment, so its effectiveness often needs to be further verified by repeated experiments. Repeatability is a basic element in scientific experimental design, which helps to confirm the stability and consistency of experimental results.

[0148] Repeating experiments can reveal problems that may not have been noticed in the first experiment, such as abnormal fluctuations or deviations in the data, thus providing a basis for improving the experimental design and methods. At the same time, the data obtained through multiple experiments can be statistically analyzed to evaluate the significance and credibility of the results. This process not only enhances the persuasiveness of the experimental results, but also provides a solid foundation for subsequent batch manufacturing.

[0149] In the present invention, the significance of determining the reliability of the optimal ratio is:

[0150] After the optimization of composite desirability verification is effective, the experimental results will be expanded for verification (promote experimental pilot), and batch pilot will be carried out according to the best proportion results of response optimization composite desirability to verify whether factors such as batch product manufacturing equipment, personnel, processes, materials, and environment will lead to product performance variables, whether the variable range is controllable, and whether the product performance meets the initial design expectations under the experimental optimal ratio of batch scale manufacturing; the larger the number of pilot product samples, the better it can reflect the reliability of product performance, and evaluate whether the experimental results can be used for batch scale production.

[0151] Compared with the prior art, the present invention has the following advantages:

[0152] The present invention is used for optimizing the positive and negative electrode formula system of lithium batteries. Under the condition of determining the performance requirements of lithium batteries, the optimal ratio of the positive and negative electrode formula system can be determined quickly and easily through experiments and software application analysis, so that the lithium battery can meet the various performance requirements of development. This method is time-saving, reduces a lot of manpower and material resources in the test process, and shortens the traditional trial and error time.

[0153] This process method is also applicable to the selection experiments of various auxiliary materials such as positive and negative electrode conductive agents, binders, etc. of lithium batteries; in addition, it is also applicable to the fields of pharmaceutical synthesis, chemical product synthesis, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0154] Figure 1 It is a simplex grid design diagram of a lithium battery in an embodiment of the present invention;

[0155] Figure 2 is a corresponding trace diagram of a lithium battery in an embodiment of the present invention;

[0156] Figure 3 By inputting the expected values ​​of various performances of lithium batteries, the optimal formula result diagram of the system is optimized;

[0157] Figure 4 The statistical result of the optimal ratio internal resistance of the lithium battery system formula of the embodiment of the present invention;

[0158] Figure 5 The statistical results of the optimal ratio of the lithium battery system formula of the embodiment of the present invention;

[0159] Figure 6 The statistical results of energy efficiency of the optimal proportion of the lithium battery system formula of the embodiment of the present invention;

[0160] Figure 7 The statistical results of the constant current and constant voltage ratios of the lithium battery system formula of the embodiment of the present invention;

[0161] Figure 8 The figure is the statistical result of the optimal capacity ratio of the lithium battery system formula of the embodiment of the present invention. DETAILED DESCRIPTION

[0162] The present invention is further described in detail below with reference to specific embodiments.

[0163] In the specific embodiment of the present invention, a total of 131 lithium batteries were produced in the experiment, meeting the number requirement of experimental samples.

[0164] In this specific embodiment, a test method for rapidly optimizing a lithium battery formulation system includes the following processing steps:

[0165] Step 1: After determining the performance of the lithium battery, according to the material properties, the Scheffé polynomial mathematical model (the polynomial model has quadratic, perfect cubic and other forms) is used to determine the population size, and a single population synthesis ratio is set at 1 (100%) to determine the upper and lower limits of each material in the lithium battery formula system, establish an extreme vertex design model, and determine that the experimental plan is at the extreme vertex;

[0166] This embodiment optimizes the positive electrode system. The main material and binder are lithium iron phosphate and polyvinylidene fluoride (PVDF) respectively, the main conductive agent is SP, and the proportion of CNTs, Ks-6 and functional graphene (G120) should be ≤1.0%. When the extreme vertex design model is established using the mathematical principle of Scheffe polynomials, only the proportion of the main materials is changed.

[0167] like Figure 1 As shown, in this embodiment, when the proportions of CNTs, Ks-6 and functional graphene (G120) are always maintained at 0.5%, 0.5% and 0.3%. Figure 1 It can be seen that the maximum value of lithium iron phosphate is 96.1% and the minimum value is 94.2%; the maximum value of PVDF is 3.5% and the minimum value is 1.6%; the maximum value of SP is 2.9% and the minimum value is 1.0%; and the sum of the proportions of the above 6 substances is equal to 1 (100%).

[0168] Step 2: Through the design model established in the first step, determine the number of experiments N and the proportion of the experimental components according to the order of the Scheffé polynomial and the number of experimental components q;

[0169] The Scheffé polynomial mathematical model is expressed as:

[0170]

[0171] Where q is the number of experimental components in the mixture experiment, y is the response variable, and x i is the proportion of the i-th component, β0 is a constant term, β i and β ij are model parameters.

[0172] The order of the lithium Scheffé polynomial in this embodiment is 2, and q=6 in the battery formula system, including 6 linear terms and 6 square terms. interaction terms, the number of trials Therefore, at least 28 experiments are required to estimate all model parameters.

[0173] In this embodiment, the number of experimental schemes and the proportion of experimental components determined by the established model are shown in Table 1 below.

[0174] Figure 2 The number of tests and the proportion of test components determined by the established model in the lithium battery formulation system

[0175]

[0176]

[0177] Step 3: According to the test number N=28 and test component ratio test given by the model in step 2, the battery electrical performance parameters are obtained and the corresponding experimental plan is input, as shown in Table 2 below;

[0178]

[0179]

[0180] Table 2 The number of tests, the proportion of test components, and the electrical performance parameters of the battery determined by the established model in the lithium battery formulation system

[0181] Linear regression analysis was then performed to establish the mathematical relationship between the response variable and the component ratio, as shown below: Internal resistance and lithium iron phosphate, PVDF, SP, CNTs, KS-6, G120 and internal resistance estimated regression coefficients.

[0182] Mixed material regression: internal resistance mΩ and lithium iron phosphate, PVDF, SP, CNTs, KS-6, G120

[0183] Estimated regression coefficients of internal resistance mΩ (component ratios)

[0184]

[0185] ANOVA for internal resistance mΩ (component ratio)

[0186]

[0187]

[0188] Estimated regression coefficient of internal resistance mΩ (number of components)

[0189]

[0190] Step 4: Analyze the response trace diagram between the test results and the materials, and determine the optimal ratio of each material according to the linear trend of the response trace diagram; the internal resistance response trace diagram of the lithium battery system (such as Figure 2 shown), according to Figure 2 The response trace diagram between the test results and the materials shows that the proportions of each material are: 95.15% lithium iron phosphate, 0.18% PVDF, 1.25% SP, 0.0065 CNTs, 0.0075 KS-6, 0.0040 G120. Based on each performance result obtained in each experiment, determine the role of each material in the performance and the interaction of the five materials in the performance;

[0191] The formation formula of the corresponding trace diagram between materials in the lithium battery system of this embodiment is:

[0192] There are 6 material components in the lithium battery system. The proportion of each component is x1, x2, x3, x4, x5, and x6, and x1+x2+x3+x4+x5+x6=1.

[0193] The response y can be expressed as a polynomial function of the proportions of these components:

[0194] y=β0+β1x1+β2x2+β3x3+β4x4+β5x5+β6x6+∈ (1)

[0195] Where β1 is the coefficient of the first component, β2 is the coefficient of the second component, and ∈ is the error term.

[0196] When drawing a trace graph, you can select one component, PVDF, as the independent variable, and the proportions of the other components are automatically determined by the constraints. Then calculate the response value Y of PVDF at different proportions, and draw an image of Y with respect to PVDF. This is the basic formula for forming the corresponding trace graph between materials. Repeat the above process for other components to obtain their respective trace graphs, such as Figure 2 shown.

[0197] Figure 2 When 1.8% PVDF material is added, the internal resistance of the lithium battery (experimental result = response value) is between 0.7-0.92mΩ, and the G120 material has little effect on the upper and lower limits of the response value; this means that to optimize this formula, it is necessary to reduce the amount of PVDF and increase the amount of G120 material; according to this rule, the optimal ratio of each material in the lithium battery system is optimized.

[0198] Step 5: Optimize all experimental results and test material ratios, input the expected values ​​of various performances of lithium batteries, and optimize the best formula for the system;

[0199] In the present invention, the response function y is usually optimized using x1, x2…, x i ,…,x p is a d-degree polynomial representation of , where p is the number of factors and d is the degree of the response polynomial.

[0200] The response function can be expressed as:

[0201]

[0202] in:

[0203] β0 is the constant term (intercept);

[0204] β i is related to a single variable x i The coefficient of the relevant linear term;

[0205] β ij is related to two variables x i and x j The coefficients of the relevant interaction terms;

[0206] β ii is related to a single variable x i The coefficient of the relevant quadratic term;

[0207] β α is the coefficient of the higher-order term associated with the multiple exponent α;

[0208] x α express where α=(a1,a2,…,a p) is a multiple exponent, and |α| = a1 + a2 + … + e p ≤ d.

[0209] The above response function (2) includes linear terms, interaction terms, quadratic terms, and higher-order terms. Therefore, it can capture the complex relationships between variables.

[0210] When the unknown parameters in the response function are replaced with estimated values (the determination of the estimated values is an iterative and fine-tuning process involving data collection, model selection, parameter estimation, and model validation. This process ensures that the model can accurately reflect the relationship between the response variable and the experimental factors, providing a reliable basis for further analysis and application. After replacement, the regression equation, also known as the response surface equation, is obtained. This equation describes the relationship between the response value and the experimental scheme.

[0211] The determination of the estimated values can be completed through various statistical tests and diagnostic plots, such as residual analysis, R 2 value, etc.

[0212] To perform response optimization, a combination of component ratios needs to be found such that the response value y reaches the maximum (or minimum, depending on the objective). This can be achieved by solving the maximum (or minimum) of the above polynomial function.

[0213] As Figure 3 shown, in the lithium battery system of this embodiment, the composite desirability D of the performance expectations for each item is 0.8900; when d = 0.80802, the minimum value of the internal resistance y = 0.7254 mΩ (desired small); when d = 0.97321, the maximum value of the first efficiency is 88.6725% (desired large); when d = 0.90644, the maximum value of the energy efficiency y = 95.6119% (desired large); when d = 0.88157, the maximum value of the constant current-constant voltage ratio is 975325% (desired large); when d = 0.92774, the maximum value of the capacity is 40.4723 Ah (desired large).

[0214] Where: desired small = the optimal ratio for a single experiment. If this performance value is less than or equal to the calculated value given by the composite desirability, it is considered that the ratio given by the composite desirability is accurate;

[0215] desired large = the optimal ratio for a single experiment. If this performance value is greater than or equal to the calculated value given by the composite desirability, it is considered that the ratio given by the composite desirability is accurate;

[0216] The specific steps for the response optimization of the lithium battery system in this embodiment are as follows:

[0217] (1) Define the objective function and constraints:

[0218] Objective function: The goal is to minimize the prediction error, that is, to find a response surface model f(x1,x2…,x i ,…,x q ), so that the difference between the predicted performance value and the actual observed value is minimized, f(x) is the response surface model, and i is the i-th mixture ratio.

[0219] Constraints: g(x) = x1 + x2 + ... x i +…+x q -1=0;

[0220] (2) Construct the Lagrangian function:

[0221] The form of the Lagrangian function is L(x,λ)=f(x)+λg(x), where λ is the Lagrangian multiplier;

[0222] The response surface model is a polynomial model.

[0223] f(x)=β0+β1x1+β2x2+…β i x i +…β6x6+β ii x i 2 +∈

[0224] Among them, β0 is a constant term, β i is a linear coefficient model, β ii is the coefficient of the quadratic term, x i is the i-th mixture ratio, ∈ is the tolerance;

[0225] (3) Solve the extreme value of the Lagrangian function:

[0226] For the Lagrangian function L(x,λ) with respect to x1,x2…,x i ,…,x6,λ, and set them to zero, resulting in a system of equations containing n+k variables, where n is the number of variables and k is the number of constraints. Solving the system of equations yields points that make L(x,λ) reach extreme values, and these points are potential optimal solutions.

[0227] In the Lagrange multiplier method, we solve constrained optimization problems by constructing the Lagrangian function L(x,λ). Assuming we have n variables and k constraints, the Lagrangian function is usually expressed as:

[0228]

[0229] Where: f(x1,x2…,x i ,…,x n ) is the objective function; g i (x1,x2…,xi ,…,x n )=0 is the i-th constraint; λ i is the i-th Lagrange multiplier.

[0230] In order to find the point where L(x,λ) reaches its extreme value, we need to calculate L with respect to each variable x. i and each Lagrange multiplier λ i Find the partial derivatives and set them to zero. This will form a system of n+k equations.

[0231] The specific steps are as follows:

[0232] ①Construct Lagrangian function:

[0233]

[0234] ②Find the partial derivative and set it to zero:

[0235] For each x i Find the partial derivative:

[0236]

[0237] For each λ i Find partial derivatives:

[0238]

[0239] ③Form a system of equations:

[0240] There are n total about x i There are k equations about λ i equations (i.e. the original constraints).

[0241] ④Solve the system of equations:

[0242] Solve this system of n+k equations to obtain x1,x2,…,x i ,…,x n and λ1,λ2,…,λ i ,…,λ k The value of .

[0243] In this embodiment, n=6, k=6, that is, there are 6 variables x1, x2, ..., x6 and 6 constraints λ1, λ2, ...λ6. Therefore, in this embodiment:

[0244] The Lagrangian function L(x,λ) can be expressed as:

[0245]

[0246] In order to find the point where L(x,λ) reaches its extreme value, it is necessary to calculate L with respect to each variable x i and each Lagrange multiplier λ i Find the partial derivatives and set them to zero. This will form a system of n+k=6+6=12 equations.

[0247] For each x i Finding partial derivatives

[0248]

[0249] For each λ i Find partial derivatives:

[0250]

[0251] According to the calculation Figure 3 The “highs and lows” above and below the “curve” shown are the extreme points.

[0252] (4) Verify extreme points:

[0253] Substitute the obtained extreme value points into the original objective function and constraints to check whether the constraints are met and whether they are maximum or minimum values. If all conditions are met, these points can be used as key points on the response surface.

[0254] (5) Construct response surface:

[0255] Using the data points obtained in the above steps, a response surface equation is constructed through fitting technology. This equation can be used to describe the relationship between the mixture ratio and the performance value, and can be used to predict the performance values ​​under other mixture ratio combinations.

[0256] like Figure 3 As shown, the optimal formula of the lithium battery system in this embodiment is: 95.4463% lithium iron phosphate, 1.6117% PVDF, 1.2778% SP, 0.5514% CNTs, 0.8127% KS-6, and 0.30% G120.

[0257] Step 6: After optimization analysis, the optimal ratio of each material is given, and a single test is conducted. Through the test data, the effectiveness of the optimal ratio is further determined;

[0258] In this embodiment, the specific method for determining the validity of the optimal ratio value is as follows:

[0259] 1) By using the response optimizer, an optimal combination of component ratios is found while meeting all response index requirements;

[0260] 2) Find the best material combination by building a composite desirability model to consider both internal resistance and other performance indicators;

[0261] 3) According to the response optimization calculation, find the best material combination, make the product and test the results of multiple product performance indicators, and compare the results with the indicators given by the composite desirability model in 2); if the results are close to the indicators given by the composite desirability model, the optimization effectiveness is confirmed. In the development of new products, it is crucial to ensure the reliability of experimental results.

[0262] At the same time, the results of the first experiment may be affected by many factors, including accidental errors, operational errors or changes in the external environment, so its effectiveness often needs to be further verified by repeated experiments. Repeatability is a basic element in scientific experimental design, which helps to confirm the stability and consistency of experimental results. Repeating the single experiment to determine the best data statistics for various performance of lithium batteries Figure 4-8 shown.

[0263] According to the optimal ratio of each material given after optimization analysis, a single test was carried out to determine the performance data of the lithium battery as shown in Table 3.

[0264] Table 3 Lithium battery performance determined by response optimization calculation

[0265] Experimental conclusion:

[0266] 1. The electrical performance results of the experimental finished product are better than the composite desirability calculation results

[0267] 2. The test results of the number of lithium battery electrical performance monomers are close to the mean

[0268] 3. It can be determined that the best composite consensus obtained from the 28-group experiment is effective.

[0269] Step 7: After the optimal ratio value is determined, the optimal ratio of each material in the system is repeatedly verified to determine the reliability of the optimal ratio.

[0270] Repeating experiments can reveal problems that may not have been noticed in the first experiment, such as abnormal fluctuations or deviations in the data, thus providing a basis for improving the experimental design and methods. At the same time, the data obtained through multiple experiments can be statistically analyzed to evaluate the significance and credibility of the results. This process not only enhances the persuasiveness of the experimental results, but also provides a solid foundation for subsequent batch manufacturing.

[0271] This embodiment has been verified through repeated experiments, and it is determined that the optimal ratio obtained in the sixth step is reliable.

Claims

1. A test method for rapidly optimizing a lithium battery formulation system, characterized in that The following steps are involved: S1. Confirm the performance of lithium batteries. According to the material properties, use Scheffé polynomials to determine the population size, determine the upper and lower limits of each material in the lithium battery formula system, establish an extreme vertex design model, and determine that the experimental plan is at the extreme vertex; S2. Determine the number of experiments N and the ratio of the experimental components according to the design model established in S1 and the order of the Scheffé polynomial mathematical model and the number of experimental components q; S3. According to the number of tests N and the proportion of test components given in the model in S2, the electrical performance parameters of the battery are obtained, and after entering the corresponding experimental plan, a linear regression analysis is performed to establish a mathematical relationship between the response variable and the component ratio; S4. Analyze the response trace diagram between the test plan result data and the materials, and determine the optimal ratio of each material based on the linear trend of the response trace diagram; S5. Optimize all experimental results and test material ratios, and optimize the best formula for the system by inputting the expected values ​​of various performances of the lithium battery; S6. Give the optimal ratio of each material through optimization analysis, conduct a single test, and further determine the effectiveness of the optimal ratio through test data; S7. After the optimal ratio value is determined, the optimal ratio of each material in the system is repeatedly verified to determine the reliability of the optimal ratio.

2. The test method for rapidly optimizing the lithium battery formulation system according to claim 1, characterized in that The material is a lithium battery system including a main material, a binder, a main conductive agent, CNTs, Ks-6, and functional graphene; the main material and binder are lithium iron phosphate and polyvinylidene fluoride respectively, the main conductive agent is SP, and the CNTs, Ks-6 and functional graphene each account for a proportion of ≤1.0%, and the extreme vertex design model is established using the mathematical principle of Scheffe polynomials, and only the proportion of the main material is changed.

3. The test method for rapidly optimizing the lithium battery formulation system according to claim 2, characterized in that The Scheffé polynomial mathematical model is expressed as: Where q is the number of experimental components in the mixture experiment, y is the response variable, and x i is the proportion of the i-th component, β0 is a constant term, β i , β ii , β ij are model parameters.

4. The test method for rapidly optimizing the lithium battery formulation system according to claim 3, characterized in that In the Scheffé polynomial mathematical model, we have: q linear terms β i x i q square terms The interaction term β ij x i x j The total number of parameters is The number of test scenarios N≥the total number of parameters.

5. The test method for rapidly optimizing the lithium battery formulation system according to claim 4, characterized in that When using the Scheffé polynomial model, the material composition ratio in each experiment needs to follow the simplex lattice design rule and / or the simplex central composite design rule.

6. According to the test method for rapid optimization of lithium battery formulation system according to claim 5, the simplex lattice design rule is: Where: i is an integer from 1 to q+1, indicating the i-th level.

7. The test method for rapidly optimizing a lithium battery formulation system according to claim 5, wherein the simplex central composite design rule is: Center Point: Axial point: x i =0 for all j x i =1 when i=k; where k represents the simplex central composite design rule.

8. According to the test method for rapid optimization of lithium battery formulation system in claim 3, the method for drawing the response trace diagram between materials in step S4 is as follows: (1) Determine that the material composition is q, and the proportion of each component is x1, x2, …, x i ,…,x q , and satisfy the constraints: x1+x2+…x i +…+x q =1; (2) The response value y is expressed as a polynomial function of the proportions of these components: y=β0+β1x1+β2x2+…β i x i +…+b p x p +∈ where β i is the coefficient of the i-th component, p is the number of factors, and ∈ is the tolerance; (3) One component is selected as the independent variable, and the proportions of other components are automatically determined by constraints. Then the response value y under different component x values ​​is calculated and a graph of y with respect to x is plotted. (4) Repeat the above process to obtain the trace graphs of other components.

9. The test method for rapidly optimizing a lithium battery formulation system according to claim 3, wherein the specific steps of response optimization in step S5 are as follows: (1) Define the objective function and constraints: Objective function: Find a response surface model f(x1,x2…,x i ,…,x q ), so that the difference between the predicted performance value and the actual observed value is minimized, f(x) is the response surface model, x i is the i-th mixture ratio; constraints: g(x)=x1+x2+…x i +…+x q -1=0: (2) Construct the Lagrangian function: The form of the Lagrangian function is L(x,λ)=f(x)+λg(x), where λ is the Lagrangian multiplier; Among them, β0 is a constant term, β i is the linear coefficient, β ii is the coefficient of the quadratic term, β ij is the cross-term coefficient, x i is the i-th mixture ratio, ∈ is the tolerance; The Lagrangian function is usually expressed as: in: f(x1,x2…,x i ,…,x n ) is the objective function; g i (x1,x2…,x i ,…,x n )=0 is the i-th constraint; λ i is the i-th Lagrange multiplier, n is the number of variables, and k is the number of constraints; (3) Solve the extreme value of the Lagrangian function: For the Lagrangian function L(x,λ) with respect to x1,x2…,x i ,…,x n ,λFind partial derivatives and set them to zero, and get a system of equations containing n+u variables. Solving the system of equations can get the point where L(x,λ) reaches the extreme value; (4) Verify extreme points: Substitute the obtained extreme value points into the original objective function f(x) and the constraint condition g(x), check whether the constraint conditions are met and whether they are maximum or minimum values. If all conditions are met, these points can be used as key points on the response surface; (5) Construct response surface: Using the data points obtained in the above steps, the response surface equation is constructed through fitting techniques.

10. The test method for rapidly optimizing a lithium battery formulation system according to claim 3, wherein the specific method for determining the effectiveness of the optimal ratio value in step S6 is as follows: 1) By using the response optimizer, an optimal combination of component ratios is found while meeting all response index requirements; 2) Find the best material combination by building a composite desirability model to consider both internal resistance and other performance indicators; 3) According to the response optimization calculation, find the best material combination, make the product and conduct multiple product performance index test results, and compare the results with the indicators given by the composite desirability model in 2); if the results are close to the indicators given by the composite desirability model, the optimization effectiveness is confirmed.

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