Method for estimating cyclic stress and stress reliability of silicon-carbon lithium battery

Abstract

The invention relates to the technical field of lithium battery state analysis, and discloses a method for estimating cyclic stress and stress reliability of a silicon-carbon lithium battery. The method comprises the following steps: firstly, constructing a thermal model, an electrochemical model and a mechanical model of the silicon-carbon lithium battery, and calculating a cell stress peak value by comprehensively considering cell structure parameters, circulating working conditions and a temperature rise effect; secondly, through global sensitivity analysis, parameter uncertainty modeling and probability density function estimation, the influence of high-sensitivity parameters on stress response is evaluated, and the stress reliability of the battery under the uncertain condition is quantified; compared with the prior art, the method integrates multi-physical field analysis modeling and cyclic stress uncertainty analysis, has the advantages of convenience in parameter sample acquisition, low calculation cost, high robustness and the like, and is suitable for various application scenes such as battery design optimization, online state evaluation, health management and the like.

Description

Technical Field

[0001] The present invention relates to the technical field of lithium battery state analysis, and in particular, to a method for estimating the cyclic stress and stress reliability of a silicon-carbon lithium battery. Background Art

[0002] Lithium-ion batteries have been widely used in fields such as consumer electronics, new energy vehicles, and energy storage systems due to their high energy density, no memory effect, fast charging characteristics, and low self-discharge advantages. To further improve the energy density, the development of advanced electrode materials has become a research hotspot. Among them, the silicon-carbon anode is regarded as a highly potential high specific energy anode solution because it combines high-capacity silicon particles with a carbon skeleton structure with a buffering effect. The theoretical specific capacity of silicon is as high as about 4200 Ah / kg, far exceeding 372 Ah / kg of traditional graphite. In theory, a fully silicon anode can achieve nearly a ten-fold increase in capacity. Currently, Tesla and CATL have achieved the commercialization of silicon-carbon anode lithium batteries, with energy densities reaching 244 Wh / kg and 255 Wh / kg respectively. However, due to the volume change of silicon during lithium insertion and extraction reaching up to 300%, the silicon content in practical applications is still limited to 5%-15% to control the structural damage caused by stress fluctuations. Especially under high-rate charge and discharge conditions, the intense lithium insertion and extraction reactions release a large amount of heat, which easily induces side reactions and significantly increases the stress peak. Repeated stress exceeding the material limit will lead to rapid capacity decay and potential safety hazards. Therefore, compared with the graphite anode system, silicon-carbon lithium batteries face more complex service stress problems, and it is urgent to conduct in-depth research on their stress evolution mechanism and reliability assessment to ensure the safety of batteries in practical applications.

[0003] Reducing the risk of electrode stress damage is a crucial part of ensuring the safety of silicon-carbon anode lithium batteries. Mechanical stress is affected by factors such as temperature, deformation, and charge state. These factors are closely coupled with the electrochemical reactions, heat conduction, and mechanical deformation during charge and discharge, determining the internal stress distribution and evolution of the battery. In recent years, pioneering progress has been made in the research on the expansion deformation and stress reliability of silicon-carbon lithium batteries. For example, CN218333919U discloses a silicon-based high-energy cylindrical lithium-ion battery. CN115275209A discloses a high first-efficiency silicon anode with a stable structure, a preparation method, and a lithium-ion battery. CN116014141A discloses a porous silicon anode material, a silicon anode sheet, and a lithium-ion battery. CN115036511A discloses a low-expansion silicon-based anode material, its preparation method, and applications. CN116259738A discloses a nano-silicon-carbon composite anode material, a preparation method, and a lithium-ion battery. CN118275896A discloses a method for identifying the viscoelastic constitutive parameters and analyzing the thermodynamic state of a silicon-carbon anode lithium battery.

[0004] Establishing a lithium - battery state - evaluation model under cyclic conditions to obtain the stress peak is the key to reducing stress damage to the silicon - carbon anode. However, cyclic stress is affected by multiple factors such as material properties, manufacturing processes, and operating conditions. There is significant uncertainty in the stress peak, showing random fluctuations. The core of stress reliability estimation lies in calculating the probability of stress - peak exceeding under uncertain conditions. Currently, there are mainly two major challenges: First, there is a lack of a stress - uncertainty quantification framework. The stress - evaluation model involves numerous input parameters. It is costly and difficult to comprehensively collect their statistical characteristics to evaluate the combined effects. Second, online reliability estimation has extremely high requirements for efficiency and convergence. It is necessary to call the stress - evaluation model tens of thousands of times to statistically calculate the probability of stress exceeding. Therefore, there is an urgent need to construct an efficient and robust cyclic - stress evaluation and uncertainty - analysis method. Summary of the Invention

[0005] The present invention overcomes the deficiencies of the prior art and provides a method for estimating cyclic stress and stress reliability of a silicon - carbon lithium battery. First, a thermal model, an electrochemical model, and a mechanical model of the silicon - carbon lithium battery are constructed. Considering the cell - structure parameters, cyclic conditions, and temperature - rise effect, the stress peak of the cell is calculated. Second, through global sensitivity analysis, parameter - uncertainty modeling, and probability - density - function estimation, the influence of high - sensitivity parameters on the stress response is evaluated, and the stress reliability of the battery under uncertain conditions is quantified.

[0006] To achieve the above - mentioned purpose, a method for estimating cyclic stress of a silicon - carbon lithium battery proposed by the present invention adopts the following technical solutions.

[0007] Step A1: Determine the characteristic parameters of the silicon - carbon lithium battery.

[0008] Step A2: Establish the cyclic conditions of the silicon - carbon lithium battery.

[0009] Step A3: Establish the thermal model of the silicon - carbon lithium battery.

[0010] Step A4: Establish the electrochemical model of the negative electrode.

[0011] Step A5: Establish the mechanical model of the silicon - carbon lithium battery.

[0012] Further, in the step A1, the silicon - carbon lithium battery includes a cell, a housing, and an electrolyte; the cell is composed of alternately stacked positive and negative electrodes, and each positive electrode and negative electrode are insulated by a separator; the housing refers to a closed housing that encapsulates the cell and the electrolyte; the characteristic parameters include H0, H0 an 、A、C、c T 、R in 、c E 、c n 、C V Si 、c P an, c P ca , E0 an , E0 ca , α, β; H0 represents the initial value of the cell height, H0 an represents the initial value of the negative electrode height, A represents the cell area perpendicular to the height direction, C represents the cell charge capacity, R in represents the internal resistance of the cell, c E represents the entropy heat coefficient of the cell, c T represents the thermal expansion coefficient of the cell, c n represents the cyclic deformation coefficient, C V Si represents the volume fraction of silicon particles, c P an represents the negative electrode porosity, c P ca represents the positive electrode porosity, E0 an represents the negative electrode elastic coefficient, E0 ca represents the positive electrode elastic coefficient, α represents the negative electrode strain index, and β represents the positive electrode strain index.

[0013] Further, in the step A2, the cyclic working condition refers to setting a spatial constraint on the silicon-carbon lithium battery in the height direction and implementing charge and discharge cycles to simulate the charge and discharge process of the silicon-carbon lithium battery under the assembly condition; the spatial constraint refers to limiting the dimension of the silicon-carbon lithium battery in the height direction to a fixed value; the charge and discharge cycles are composed of several cycles, and each cycle includes a charging link in which the state of charge (SOC) of the cell experiences from 0% to 100% and a discharging stage from 100% to 0%; the working condition parameters included in the cyclic working condition are: δ, T0, T A , h A , c I , n; δ represents the assembly gap, T0 represents the initial value of the cell temperature, T A represents the ambient temperature, h A represents the convective heat transfer coefficient, c I represents the operating current multiple, and n represents the current cycle number.

[0014] Further, in the step A3, the thermal model describes the heat transfer behavior of the silicon-carbon lithium battery to the environment under the cyclic working condition, calculates the temperature difference between the peak cell temperature at the moment of the maximum SOC and the initial cell temperature, and the peak thermal deformation of the cell caused by the temperature difference.

[0015] The construction process of the thermal model of the silicon-carbon lithium battery is as follows.

[0016] Step A3.1: Establish a heat balance equation. According to Kirchhoff's law, it is written as Equation (1):

[0017] P = (T - T A ) / R A ;

[0018] Where P represents the heat generation rate of the battery cell, T represents the peak temperature of the battery cell, and R A represents the thermal resistance from the lithium battery to the environment, written as the formula: R A = 1 / (2·h A ·A).

[0019] Step A3.2: Establish the battery cell heat generation equation. According to the Bernardi equation based on the first law of thermodynamics, it is written as formula (2):

[0020] P = (c I ·C) 2 ·R in + c I ·C·c E ·T;

[0021] Note: The internal resistance of the battery cell and the entropy heat coefficient of the battery cell are the inherent properties of the silicon-carbon lithium battery, and the product of the current rate and the charge capacity is the operating current.

[0022] Step A3.3: Solve for the peak temperature of the battery cell, which means solving the system of equations composed of formula (1) and formula (2) to obtain the peak temperature of the battery cell.

[0023] Step A3.4: Calculate the peak thermal deformation of the battery cell, written as formula (3):

[0024] D T = c T ·(T - T0)·H0.

[0025] Furthermore, in step A4, the negative electrode electrochemical model describes the volume change caused by the lithium insertion phase change of silicon particles and carbon particles in the negative electrode of the silicon-carbon lithium battery at the moment when the SOC is maximum in the cycle condition, and calculates the peak cycle deformation of the battery cell.

[0026] The construction process of the negative electrode electrochemical model is as follows.

[0027] Step A4.1: Calculate the lithium insertion deformation of silicon particles, written as formula (4):

[0028] d V Si = V m LiSi / V m Si ·x Si ;

[0029] Where, d V Sirepresents the deformation rate of silicon particles, x Si represents the number of silicon atoms in lithiated silicon. V m LiSi represents the molar volume of lithiated silicon, V m Si represents the molar volume of silicon.

[0030] Step A4.2: Calculate the lithium intercalation deformation of carbon particles, written as Equation (5):

[0031] d V C =V m LiC / V m C ·x C ;

[0032] where d V C represents the deformation rate of carbon particles, x C represents the number of carbon atoms in lithiated carbon. V m LiC represents the molar volume of lithiated carbon, V m C represents the molar volume of carbon.

[0033] Note: The molar volumes of Li 15 Si4, LiC6, Si, and C are constants determined by their crystal phases, which are 183.59 cm 3 / mol, 37.62 cm 3 / mol, 12.06 cm 3 / mol, 5.40 cm 3 / mol. The number of silicon atoms in lithiated silicon Li 15 Si4 is 4, and the number of carbon atoms in lithiated carbon LiC6 is 6.

[0034] Step A4.3: Calculate the material utilization rate of the silicon-carbon particle material, which refers to the material utilization rates of the silicon particles and carbon particles under the charge capacity limit of the silicon-carbon lithium battery, written as Equation (6):

[0035] c M =C / (q Si ·ρ Si ·V0 Si +q C ·ρ C ·V0 C );

[0036] where c M represents the material utilization rate of the silicon-carbon particle material, q Si represents the theoretical specific capacity of silicon particles, q C represents the theoretical specific capacity of carbon particles, ρ SiDenotes the density of silicon particles, ρ C Denotes the density of carbon particles.

[0037] V0 Si Denotes the volume of silicon particles before lithium intercalation, written as Equation (7):

[0038] V0 Si = H0 an ·A·(1 - c P an )·C V Si ;

[0039] V0 C Denotes the volume of carbon particles before lithium intercalation, written as Equation (8):

[0040] V0 C = H0 an ·(1 - c P an )·(1 - C V Si );

[0041] The theoretical specific capacities of silicon and carbon particles are constants, 3.578 Ah / g and 0.372 Ah / g respectively. The densities of silicon and carbon particles are constants, 2.33 g / cm 3 、2.25 g / cm 3 .

[0042] Step A4.4: Calculate the volume of the negative electrode at the moment of maximum SOC, written as Equation (9):

[0043] V E an = c M ·(V0 Si ·d V Si + V0 C ·d V C )+(1 - c M )·(V0 Si + V0 C )+ H0 an ·A·c P an ;

[0044] where V E an denotes the volume of the negative electrode at the moment of maximum SOC.

[0045] Step A4.5: Calculate the peak value of the cell cycle deformation, written as Equation (10):

[0046] D C =(c n·n + 1)·(H E an - H0 an );

[0047] Where D C represents the peak value of cyclic deformation in the height direction, c n represents the cyclic deformation coefficient, and n represents the number of cycles. H E an represents the peak value of the cell height, written as Equation (18): H E an = V E an / A.

[0048] Furthermore, in the step A5, the mechanical model describes the mechanical behavior of the cell under cyclic conditions, and calculates the peak value of the cell stress of the silicon-carbon lithium battery at the moment when the SOC is maximum in the cyclic conditions.

[0049] The construction process of the mechanical model is as follows.

[0050] Step A5.1: Calculate the peak value of cell deformation, written as Equation (11):

[0051] D = D C + D T - δ;

[0052] Where D represents the peak value of cell deformation.

[0053] Step A5.2: Establish a deformation stress equation to describe the relationship between the deformation and stress of the positive electrode and the negative electrode, written as Equation (12):

[0054] σ = E an ·(D an / H0 an ) α = E ca ·(D ca / (H0 - H0 an )) β ;

[0055] Where σ represents the peak value of cell stress; D an represents the peak value of the negative electrode deformation, D ca represents the peak value of the positive electrode deformation; E an represents the negative electrode elastic modulus, written as: E an = E0 an ·(1 - c P an ); E ca represents the positive electrode elastic modulus, written as: E ca = E0 ca ·(1 - cP ca ).

[0056] Step A5.3: Establish a geometric equilibrium equation to describe the equilibrium state between the cell deformation peak value and the negative electrode deformation peak value and the positive electrode deformation peak value under space constraints, and write it as formula (13):

[0057] D=D an +D ca ;

[0058] Step A5.4: solving the peak value of the cell stress refers to solving the equation group consisting of equation (11), equation (12), and equation (13) to obtain the peak value of the cell stress.

[0059] The present invention further proposes a silicon-carbon-lithium battery stress reliability estimation method, which is used to perform reliability estimation on the cell stress peak value of the silicon-carbon-lithium battery obtained by the above method. The reliability estimation method adopts the following technical scheme.

[0060] Step B1: Establish the stress function of silicon-carbon-lithium battery.

[0061] Step B2: Determine the uncertainty domain of the input vector elements.

[0062] Step B3: Perform global sensitivity analysis.

[0063] Step B4: Establish the probability density distribution of the highly sensitive input parameters.

[0064] Step B5: Construct a high-sensitivity vector sample.

[0065] Step B6: Calculate the stress reliability of the silicon-carbon lithium battery.

[0066] Further, in the step B1, the stress function is written as: f(X), where f(X) represents the cell stress peak value of the silicon-carbon lithium battery calculated through the steps A1 to A5 based on X; wherein X represents an input vector, which is obtained by aggregating the characteristic parameters in the step A1 and the operating condition parameters in the step A2, and is written as: X=(X1, X2, ..., X N ); the vector contains N elements in total, N represents the number of elements; X1 represents the first element of X, corresponding to H0 in the characteristic parameter; the corresponding relationship between the remaining elements in X and the characteristic parameters and the operating parameters is deduced in the same way.

[0067] Furthermore, in step B2, determining the uncertainty domain of the input vector element refers to determining the X of each element according to the engineering data. j L , X j R , written as: Xj ∈ [X j L , X j R , j = 1, 2, ..., N; where X j represents the j-th element of the vector, and X j L represents the upper boundary of the j-th element, and X j R represents the lower boundary of the j-th element.

[0068] Furthermore, in step B3, the global sensitivity analysis refers to describing the influence of the uncertainty of the vector elements on the fluctuation range of the output value of the stress function, and obtaining high-sensitivity input parameters. The process of the global sensitivity analysis is as follows.

[0069] Step B3.1: Establish the main sample matrix of vector elements, including the first main sample matrix and the second main sample matrix. Use the Latin hypercube sampling (lhsdesign) provided by MATLAB to simulate and generate M samples of the vector elements in the uncertainty domain of the elements. M represents the number of samples, and its value range is [10 4 , 10 5 ; the first main sample matrix is written as A, and the second main sample matrix is written as B, both of which are two-dimensional matrices with M rows and N columns; the vector composed of the elements in the i-th row of A is written as A i , i = 1, 2, ..., M; the vector composed of the elements in the i-th row of B is written as B i , i = 1, 2, ..., M.

[0070] Step B3.2: Establish the cross matrix, including the first cross sample matrix, the second cross sample matrix, ...., the N-th cross sample matrix. The first cross sample matrix is obtained by replacing the first column of A with the first column of B, and is written as C (1) ; the vector composed of the elements in the i-th row of C (1) is written as C i (1) ; and so on, establish the other cross sample matrices. The cross sample matrices are written as: C (j) , j = 1, 2, ..., N, all of which are two-dimensional matrices with M rows and N columns. C (j) represents the j-th cross sample matrix of the cross sample matrix, and the vector composed of the elements in the i-th row of C (j) is written as C i (j) , i = 1, 2, ..., M.

[0071] Step B3.2: Calculate the main response vector of stress, written as: f B = (f1B , f2 B ,... f M B ), f1 B represents the first element of f B , which is the stress function value calculated by taking B1 in B, i = 1, 2,..., M as the input vector of f(X), and so on for the other elements of f i , i = 1, 2,..., M as the input vector of f(X), and so on for the other elements of f B And so on for the other elements of f

[0072] Step B3.3: Calculate the stress response vectors, including the first response vector, the second response vector,..., the Nth response vector. The first response vector is written as: f C(1) = (f1 C(1) , f2 C(1) ,... f M C(1) ), f1 C(1) represents the first element of f C(1) , which is the stress function value calculated by taking C1 in C, i = 1, 2,..., M as the input vector of f(X), and the other elements of C are obtained in a similar way. And so on for the other response vectors i (j) , i = 1, 2,..., M as the input vector of f(X), and the other elements of C are obtained in a similar way. And so on for the other response vectors (j) as the input vector of f(X), and the other elements of C are obtained in a similar way. And so on for the other response vectors i (j) And so on for the other response vectors

[0073] Step B3.4: Calculate the principal response sample variance, written as Equation (14):

[0074] V f = mean(f i B - mean(f B ), i = 1, 2,..., M);

[0075] where V f represents the principal response sample variance, f i B represents f B 's ith element; mean represents the mean operator

[0076] Step B3.5: Calculate the global sensitivity index, written as

[0077] S j = mean(square(f B - f C(j) ), j = 1, 2,..., N

[0078] where S j represents the global sensitivity index corresponding to the jth element in the input vector, fC(j) Denote the j-th response vector of the said response vector. Square represents the operation of forming a new vector by squaring each element in the vector.

[0079] Step B3.6: Select highly sensitive input parameters. Set a sensitivity threshold, and determine the elements in the input vector whose global sensitivity index is higher than the sensitivity threshold as highly sensitive input parameters, that is, the highly sensitive input parameters selected from X = (X1, X2,..., X N ) form a highly sensitive input vector Y = (Y1, Y2,..., Y L ), where L is the number of the highly sensitive input parameters. Process the elements in the other said input vectors into deterministic input parameters, and their values are given as the median of the uncertainty domain of the elements.

[0080] Furthermore, in the said step B4, the establishment of the probability density distribution of the highly sensitive input parameters means collecting engineering sample data for the first element in the highly sensitive input vector, and obtaining the probability density distribution of the first element through the kernel density estimation solver (ksdensity) provided by MATLAB. The probability density distributions of the other elements in the highly sensitive input vector are obtained by analogy.

[0081] Furthermore, in the said step B5, the construction of the highly sensitive vector samples means obtaining M highly sensitive vector samples based on the probability density distribution through the one-dimensional interpolation solver (interp1) provided by MATLAB.

[0082] Furthermore, in step B6, the stress reliability of the silicon-carbon lithium battery means the probability that the random response of the stress peak of the battery cell is lower than a given stress threshold under uncertain conditions; the given stress threshold, and M stress peak response sample values calculated by taking each of the highly sensitive vector samples as the input vector of f(X) one by one; count the probability that the response sample values are less than the given stress threshold, that is, the reliability of the stress peak of the battery cell of the silicon-carbon lithium battery.

[0083] The present invention further provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, it realizes the steps of the above-mentioned silicon-carbon lithium battery cycle stress estimation method, or realizes the steps of the above-mentioned silicon-carbon lithium battery stress reliability estimation method.

[0084] Compared with the prior art, the cyclic stress estimation method for silicon-carbon lithium batteries of the present invention has the following advantages: In terms of accuracy, this method integrates multi-field coupling modeling of heat transfer / electrochemistry / mechanics to achieve accurate estimation of the cyclic stress of silicon-carbon lithium batteries; in terms of efficiency, through the construction of analytical expressions and the solution of equations, the computational complexity is significantly reduced, and the efficiency of stress peak estimation at the millisecond level is achieved, meeting the requirements of online state estimation; in terms of applicability, the input parameters required by the method can be obtained through conventional battery tests or design parameters, and the cyclic stress estimation model has good robustness and scalability.

[0085] The stress reliability estimation method for silicon-carbon lithium batteries of the present invention has the following advantages: In terms of effectiveness, the method combines multi-physical-field stress functions with global sensitivity analysis to identify highly sensitive input parameters and establish a probability density distribution to achieve accurate estimation of stress reliability. In terms of efficiency, the global sensitivity analysis is based on the parameter fluctuation range, avoiding the high cost of sample collection; only relying on the engineering samples of a small number of key parameters to calculate the stress random response, significantly reducing the sample collection cost and computational volume, meeting the requirements of online reliability estimation of silicon-carbon lithium batteries. In terms of applicability, the method does not rely on time-consuming finite element simulations and high-dimensional parameter sample data, has good scalability and engineering adaptability, and is applicable to multi-scenario requirements such as battery design optimization, online state monitoring, and battery health management. Brief Description of the Drawings

[0086] Figure 1 Shows the cyclic stress estimation process of a specific application example of the present invention;

[0087] Figure 2 Shows the structure of a silicon-carbon lithium battery of a specific application example of the present invention;

[0088] Figure 3 Shows the mechanical model of a silicon-carbon lithium battery of a specific application example of the present invention;

[0089] Figure 4 Shows the cyclic stress peak curve of a specific application example of the present invention;

[0090] Figure 5 Shows the stress reliability estimation process of a specific application example of the present invention;

[0091] Figure 6 Shows the probability density distribution of the initial value of the cell height of a specific application example of the present invention;

[0092] Figure 7 Shows the probability density distribution of the cell charge capacity of a specific application example of the present invention;

[0093] Figure 8 Shows the probability density distribution of the cyclic deformation coefficient of a specific application example of the present invention.

[0094] Reference numerals: 21, battery cell; 22, housing; 23, electrolyte; 24, positive electrode; 25, negative electrode; 31, negative electrode elastic element; 32, positive electrode elastic element; 33, battery cell thermal deformation element; 34, battery cell cyclic deformation element. Detailed implementation mode

[0095] The following is a description of the present invention in combination with embodiments, but it does not constitute any limitation to the present invention. Any limited number of modifications made within the scope of the claims of the present invention are still within the scope of the claims of the present invention.

[0096] The present invention provides a method for estimating the cyclic stress of a silicon-carbon lithium battery. In this embodiment, the method of the present invention is applied to two square silicon-carbon lithium batteries to illustrate the steps and method performance. The negative electrode material of the silicon-carbon lithium battery is a silicon-carbon composite material, and the positive electrode material is lithium cobaltate. The main components of the electrolyte are lithium hexafluorophosphate and carbonate / propionate solvents. As Figure 1 shown, the method includes the following processing steps.

[0097] Step A1: Determine the characteristic parameters of the silicon-carbon lithium battery. As Figure 2 shown, the silicon-carbon lithium battery includes a battery cell 21, a housing 22, and an electrolyte 23; the battery cell 21 is composed of an alternating stack of a positive electrode 24 and a negative electrode 25, and each positive electrode and negative electrode are insulated from each other by a separator; the housing 22 refers to a closed housing that encapsulates the battery cell 21 and the electrolyte 23; the characteristic parameters include H0, H0 an , A, C, c T , R in , c E , c n , C V Si , c P an , c P ca , E0 an , E0 ca , α, β; H0 represents the initial value of the battery cell height, H0 an represents the initial value of the negative electrode height, A represents the area of the battery cell perpendicular to the height direction, C represents the charge capacity of the battery cell, R in represents the internal resistance of the battery cell, c E represents the entropy heat coefficient of the battery cell, c T represents the thermal expansion coefficient of the battery cell, c n represents the cyclic deformation coefficient, C V Si represents the volume ratio of silicon particles, c P an represents the negative electrode porosity, c P ca represents the positive electrode porosity, E0 an represents the negative electrode elastic coefficient, E0ca represents the positive electrode elastic coefficient, α represents the negative electrode strain index, and β represents the positive electrode strain index.

[0098] Note: In this embodiment, the characteristic parameters of the two square silicon-carbon lithium batteries are shown in Table 1.

[0099] Table 1:

[0100]

[0101]

[0102] Step A2: Establish a cycling condition for the silicon-carbon lithium battery. The cycling condition refers to setting a spatial constraint on the silicon-carbon lithium battery in the height direction and implementing charge and discharge cycles to simulate the charge and discharge process of the silicon-carbon lithium battery under assembly conditions; the spatial constraint means limiting the size of the silicon-carbon lithium battery in the height direction to a fixed value; the charge and discharge cycles consist of several cycles, and each cycle includes a charging link where the state of charge (SOC) of the battery cell 21 goes through from 0% to 100% and a discharging stage from 100% to 0%; the working condition parameters included in the cycling condition are: δ, T0, T A , h A , c I , n; δ represents the assembly gap, T0 represents the initial value of the battery cell temperature, T A represents the ambient temperature, h A represents the convective heat transfer coefficient, c I represents the operating current multiple, and n represents the current cycle number.

[0103] Note: In this embodiment, the working condition parameters of the two square silicon-carbon lithium batteries are the same, as shown in Table 2.

[0104] Table 2:

[0105] Characteristic parameter δ <![CDATA[T0]]> <![CDATA[T A > <![CDATA[h A > <![CDATA[c I > n Unit mm K K <![CDATA[W·mm 2 / K]]> / / Parameter value 0.05 293 293 35E-6 1.0 1,2,...,100

[0106] Note: The cyclic stress is mainly caused by the volume expansion of the silicon-carbon negative electrode during lithium insertion in the charging stage, resulting in an increase in stress response, and the volume contraction during lithium extraction in the discharging stage, resulting in a decrease in stress response, thus forming an evolution process of the cyclic stress state. Near the moment of the maximum SOC in each cycle, the silicon-carbon lithium battery presents a stress peak. The method of the present invention is used to estimate the stress peak of the silicon-carbon lithium battery in each cycle, and the mechanical behavior of the battery cell of the silicon-carbon lithium battery at the moment of the maximum SOC is processed into two stages: expansion and compression. In the expansion stage, the battery cell freely expands in the height direction under the action of the lithium insertion reaction and temperature change; in the compression stage, the battery cell is compressed into the constrained space. The cycling condition in this embodiment includes a total of 100 cycles.

[0107] Step A3: Establish a thermal model for the silicon-carbon lithium battery. The thermal model describes the heat transfer behavior from the silicon-carbon lithium battery to the environment under the cyclic working conditions, calculates the temperature difference between the peak cell temperature at the moment of maximum SOC and the initial cell temperature, and the peak thermal deformation of the cell caused by the temperature difference.

[0108] Note: Since the temperature from the center to the surface of the lithium battery cell is usually less than 2 °C, the thermal model treats the cell temperature and heat generation rate as uniformly distributed; since only the peak temperature is calculated, the heat capacity effect of the lithium battery is ignored.

[0109] The construction process of the thermal model of the silicon-carbon lithium battery is as follows.

[0110] Step A3.1: Establish a heat balance equation. According to Kirchhoff's law, it is written as Equation (1):

[0111] P = (T - T A ) / R A ;

[0112] where P represents the heat generation rate of the cell, T represents the peak cell temperature, and R A represents the thermal resistance from the lithium battery to the environment, written as: R A = 1 / (2·h A ·A).

[0113] Step A3.2: Establish a cell heat generation equation. According to Bernardi's equation based on the first law of thermodynamics, it is written as Equation (2):

[0114] P = (c I ·C) 2 ·R in + c I ·C·c E ·T;

[0115] Note: The internal resistance of the cell and the entropy heat coefficient of the cell are the inherent properties of the silicon-carbon lithium battery, and the product of the current rate and the charge capacity is the operating current.

[0116] Step A3.3: Solve for the peak cell temperature, which means solving the system of equations composed of Equation (1) and Equation (2) to obtain the peak cell temperature.

[0117] Step A3.4: Calculate the peak thermal deformation of the cell, written as Equation (3):

[0118] D T = c T ·(T - T0)·H0.

[0119] Step A4: Establish a negative electrode electrochemical model. The negative electrode electrochemical model describes the volume changes caused by the lithium insertion phase transformation of silicon particles and carbon particles in the negative electrode of the silicon-carbon lithium battery at the moment of the maximum SOC in the cycle condition, and calculates the peak value of the cell cycle deformation.

[0120] Note: The insertion of lithium ions into silicon and carbon particles in the negative electrode causes their crystal phase changes and volume expansion. Due to different lithium insertion depths, the lithium silicide crystal phases formed by lithium insertion into silicon particles include Li2Si, Li 15 Si4, Li 22 Si5, and the lithium insertion into carbon particles may form LiC 18 , LiC 12 , LiC6. At the moment of the maximum SOC, the silicon and carbon particles are close to complete lithiumation and form stable high-lithiated crystal phases, namely Li 15 Si4, LiC6.

[0121] The construction process of the negative electrode electrochemical model is as follows.

[0122] Step A4.1: Calculate the lithium insertion deformation of silicon particles and write it as Equation (4):

[0123] d V Si =V m LiSi / V m Si ·x Si ;

[0124] Among them, d V Si represents the silicon particle deformation rate, and x Si represents the number of silicon atoms in lithiated silicon. V m LiSi represents the molar volume of lithiated silicon, and V m Si represents the molar volume of silicon.

[0125] Step A4.2: Calculate the lithium insertion deformation of carbon particles and write it as Equation (5):

[0126] d V C =V m LiC / V m C ·x C ;

[0127] Among them, d V C represents the carbon particle deformation rate, and x C represents the number of carbon atoms in lithiated carbon. V m LiC represents the molar volume of lithiated carbon, and Vm C represents the molar volume of carbon.

[0128] Note: Li 15 The molar volumes of Li 3 Si4, LiC6, Si, and C are constants determined by their crystal phases, which are 183.59 cm 3 / mol, 37.62 cm 3 / mol, 12.06 cm 3 / mol, and 5.40 cm 15 / mol, respectively. The number of silicon atoms in lithium silicide Li

[0129] Step A4.3: Calculate the material utilization rate of the silicon-carbon particle material, which refers to the material utilization rate of the silicon particles and carbon particles under the charge capacity limit of the silicon-carbon lithium battery, written as Equation (6):

[0130] c M = C / (q Si · ρ Si · V0 Si + q C · ρ C · V0 C );

[0131] where c M represents the material utilization rate of the silicon-carbon particle material, q Si represents the theoretical specific capacity of the silicon particles, q C represents the theoretical specific capacity of the carbon particles, ρ Si represents the density of the silicon particles, ρ C represents the density of the carbon particles.

[0132] V0 Si represents the volume of the silicon particles before lithium intercalation, written as Equation (7):

[0133] V0 Si = H0 an · A · (1 - c P an ) · C V Si ;

[0134] V0 C represents the volume of the carbon particles before lithium intercalation, written as Equation (8):

[0135] V0 C = H0 an · (1 - c P an ) · (1 - C V Si );

[0136] Note: In the negative electrode of a silicon-carbon lithium battery, the silicon particles, carbon particles, and lithium ion concentration are evenly distributed, and the silicon and carbon particles have the same material utilization rate. The theoretical specific capacities of the silicon and carbon particles are constants, which are 3.578 Ah / g and 0.372 Ah / g respectively. The densities of the silicon and carbon particles are constants, which are 2.33 g / cm 3 、2.25 g / cm 3 .

[0137] Step A4.4: Calculate the negative electrode volume at the moment of maximum SOC, and write it as Equation (9):

[0138] V E an = c M ·(V0 Si ·d V Si + V0 C ·d V C ) + (1 - c M )·(V0 Si + V0 C ) + H0 an ·A·c P an ;

[0139] Where V E an represents the negative electrode volume at the moment of maximum SOC.

[0140] Note: The first term on the right side of Equation (9) reflects the volume expansion of the silicon and carbon particles after the lithium insertion reaction, and the second and third terms reflect that the volume of the unutilized active material and the negative electrode pores in the anode remains unchanged.

[0141] Step A4.5: Calculate the peak value of the cell cycle deformation, and write it as Equation (10):

[0142] D C = (c n ·n + 1)·(H E an - H0 an );

[0143] Where D C represents the peak value of the cycle deformation in the height direction, c n represents the cycle deformation coefficient, and n represents the number of cycles. H E an represents the peak value of the cell height, and is written as Equation (18): H E an = V E an / A.

[0144] Note: The cyclic deformation coefficient describes the phenomenon that the lithium insertion deformation of the silicon-carbon lithium battery is amplified as the number of cycles increases. For a square lithium battery, the deformation is concentrated in the height direction, so the cyclic deformation is established based on the height direction.

[0145] Step A5: Establish a mechanical model of the silicon-carbon lithium battery. The mechanical model describes the mechanical behavior of the battery cell under cyclic conditions and calculates the peak stress of the battery cell of the silicon-carbon lithium battery at the moment when the SOC is the maximum in the cyclic conditions. As Figure 3 shown, the mechanical model includes a negative electrode elastic element 31, a positive electrode elastic element 32, a battery cell thermal deformation element 33, and a battery cell cyclic deformation element 34; the negative electrode elastic element 31 corresponds to the peak negative electrode deformation, the positive electrode elastic element 32 corresponds to the peak positive electrode deformation, the battery cell thermal deformation element 33 corresponds to the peak thermal deformation of the battery cell, and the battery cell cyclic deformation element 34 corresponds to the peak cyclic deformation of the battery cell.

[0146] The construction process of the mechanical model is as follows.

[0147] Step A5.1: Calculate the peak battery cell deformation and write it as Equation (11):

[0148] D = D C + D T - δ;

[0149] where D represents the peak battery cell deformation.

[0150] Note: The assembly gap refers to the initial value of the gap between the battery cell and the housing, and its being greater than, equal to, or less than zero respectively reflects the initial assembly states of clearance, transition, and interference.

[0151] Step A5.2: Establish a deformation stress equation to describe the relationship between the deformation and stress of the positive electrode and the negative electrode, and write it as Equation (12):

[0152] σ = E an · (D an / H0 an ) α = E ca · (D ca / (H0 - H0 an )) β ;

[0153] where σ represents the peak battery cell stress; D an represents the peak negative electrode deformation, D ca represents the peak positive electrode deformation; E an represents the negative electrode elastic modulus and is written as: E an = E0 an · (1 - c P an ); E caDenote the elastic modulus of the positive electrode as: E ca = E0 ca ·(1 - c P ca ).

[0154] Note: The ratio of the peak deformation of the negative electrode to the initial value of the height of the negative electrode is the peak strain of the negative electrode; the ratio of the peak deformation of the positive electrode to the initial value of the height of the positive electrode is the peak strain of the positive electrode; the initial value of the height of the cell minus the initial value of the height of the negative electrode is the initial value of the height of the positive electrode. The elastic coefficient and strain index of the negative and positive electrodes are constitutive characteristic parameters of the electrode material. The strain index indicates that the stiffness of the electrode material increases exponentially with the increase of strain. The constitutive characteristic parameters can be calibrated through experiments. The insertion or extraction of lithium ions will not cause significant volume change of the separator, so the contribution of the separator deformation is ignored in the mechanical model. The electrode material has a porous composite micro-nano structure and exhibits mechanical characteristics such as non-linear elasticity and viscoplasticity. In the stage where the effective capacity of the lithium battery has not significantly decayed, the deformation of the electrode is recoverable elastic deformation. Therefore, when calculating the peak stress, the viscoplastic characteristics of the electrode material are ignored. Although the anode and cathode are alternately arranged in the lithium battery layer structure, all cathodes or anodes have the same material, and the anode and cathode are grouped into two layers. The deformation stress is conducted along the height direction to each electrode. The elastic modulus of the electrode is related to the designed porosity. In actual engineering, the design domain of the porosity is usually a narrow interval. For example, the design domain of the negative electrode porosity is [25%, 35%], and the design domain of the positive electrode porosity is [15%, 25%]. The elastic modulus of the electrode is approximately treated as linearly related to the designed porosity.

[0155] Step A5.3: Establish a geometric equilibrium equation to describe the equilibrium state between the peak deformation of the cell, the peak deformation of the negative electrode, and the peak deformation of the positive electrode under spatial constraints, written as Equation (13):

[0156] D = D an + D ca ;

[0157] Step A5.4: Solve for the peak stress of the cell, which means solving the system of equations composed of Equation (11), Equation (12), and Equation (13) to obtain the peak stress of the cell.

[0158] In this embodiment, applying the method of the present invention to obtain the numerical results of the peak stress of two samples and comparing them with the experimental results, as Figure 4 shown. The peak stress increases with the number of cycles within each cycle, which is caused by the amplification of the lithium battery volume expansion rate with the number of cycles. The root mean square errors of the predicted values of the peak stress of the two samples by the method of the present invention are 4.85% and 3.77%. The root mean square errors of the peak stress estimation are both lower than 5%, verifying the accuracy of the method of the present invention; the calculation time consumption of the two solving processes is at the millisecond level.

[0159] This embodiment shows that the method for estimating the cyclic stress of silicon-carbon lithium batteries provided by the present invention has the following advantages. In terms of accuracy, the method integrates heat transfer / electrochemistry / mechanics multi-field coupling modeling to achieve accurate estimation of the cyclic stress of silicon-carbon lithium batteries; in terms of efficiency, through analytical formula construction and equation group solution, the computational complexity is significantly reduced, and the millisecond-level efficiency of stress peak estimation is achieved to meet the requirements of online state estimation; in terms of applicability, the input parameters required by the method can be obtained through conventional battery testing or design parameters, and the model structure has good versatility and extensibility.

[0160] The present invention also provides a method for estimating stress reliability of silicon-carbon-lithium batteries. In this embodiment, the method of the present invention is applied to the two square silicon-carbon-lithium batteries to illustrate the steps and method performance. Figure 5 As shown, the method includes the following processing steps.

[0161] Step B1: Establish a stress function for a silicon-carbon lithium battery. The stress function is written as: f(X), where f(X) represents the cell stress peak value of the silicon-carbon lithium battery calculated based on X through steps A1 to A5; where X represents an input vector, which is obtained by aggregating the characteristic parameters in step A1 and the operating parameters in step A2, and is written as: X=(X1, X2, ..., X N ); the vector contains N elements in total, N represents the number of elements; X1 represents the first element of X, corresponding to H0 in the characteristic parameter; the corresponding relationship between the remaining elements in X and the characteristic parameters and the operating parameters is deduced in the same way.

[0162] Step B2: Determine the uncertainty domain of the input vector element, which means to determine the X of each element according to the engineering data. j L , X j R , written as: X j ∈[X j L ,X j R ], j = 1, 2, ..., N; where X j represents the jth element of the vector, X j L represents the upper boundary of the j-th element, X j R Represents the lower bound of the j-th element.

[0163] Note: The uncertainty domain of the input vector elements of the two samples is listed in Table 3.

[0164] Table 3:

[0165]

[0166]

[0167] Step B3: Conduct global sensitivity analysis to describe the impact of the uncertainty of the vector elements on the fluctuation range of the output value of the stress function, and obtain high-sensitivity input parameters. The process of the global sensitivity analysis is as follows.

[0168] Step B3.1: Establish the main sample matrices of the vector elements, including the first main sample matrix and the second main sample matrix. Use the Latin hypercube sampling solution (lhsdesign) provided by MATLAB to simulate and generate M samples of the vector elements in the uncertainty domain of the elements. M represents the number of samples, and its value range is [10 4 , 10 5 ; The first main sample matrix is written as A, and the second main sample matrix is written as B, both of which are two-dimensional matrices with M rows and N columns; The vector composed of the elements in the i-th row of A is written as A i , i = 1, 2,..., M; The vector composed of the elements in the i-th row of B is written as B i , i = 1, 2,..., M.

[0169] Note: In this embodiment, the number of samples M = 10 5 .

[0170] Step B3.2: Establish the cross matrices, including the first cross sample matrix, the second cross sample matrix,..., the Nth cross sample matrix. The first cross sample matrix is obtained by replacing the first column of A with the first column of B, and is written as C (1) ; The vector composed of the elements in the i-th row of C (1) is written as C i (1) ; And so on, establish the other cross sample matrices. The cross sample matrices are written as: C (j) , j = 1, 2,..., N, all of which are two-dimensional matrices with M rows and N columns. C (j) represents the j-th cross sample matrix of the cross sample matrices, and the vector composed of the elements in the i-th row of C (j) is written as C i (j) , i = 1, 2,..., M.

[0171] Step B3.2: Calculate the main response vector of stress, written as: f B = (f1 B , f2 B ,... f M B ), where f1 B represents the first element of f B , and is obtained by replacing B i, i=1,2,...,M, where B1 is the stress function value calculated as the input vector of f(X), f B And so on for other elements.

[0172] Step B3.3: Calculate the stress response vector, including the first response vector, the second response vector, ..., the Nth response vector. The first response vector is written as: C(1) =(f1 C(1) ,f2 C(1) ,...f M C(1) ), f1 C(1) represents f C(1) The first element is C i (j) ,i=1,2,...,C1 in M (j) The stress function value calculated as the input vector of f(X), C i (j) The other elements of are obtained in a similar way. The other response vectors are deduced in the same way.

[0173] Step B3.4: Calculate the sample variance of the main response, written as formula (14):

[0174] V f =mean(f i B -mean(f B ),i=1,2,...,M);

[0175] Where V f represents the sample variance of the main response, f i B represents f B The i-th element of ; mean represents the average operator.

[0176] Step B3.5: Calculate the global sensitivity index, written as

[0177] S j =mean(square(f B -f C(j) )),j=1,2,...,N

[0178] Where S j represents the global sensitivity index corresponding to the jth element in the input vector, f C(j) represents the jth response vector of the response vector. square represents the operation of squaring each element in the vector to form a new vector.

[0179] Step B3.6: Select high-sensitivity input parameters. Set a sensitivity threshold, and determine the elements in the input vector whose global sensitivity index is higher than the sensitivity threshold as high-sensitivity input parameters, that is, the high-sensitivity input parameters selected from X = (X1, X2,..., X N ) form a high-sensitivity input vector Y = (Y1, Y2,..., Y L ), where L is the number of high-sensitivity input parameters. Process the elements in other input vectors into deterministic input parameters, and their values are given as the median of the uncertainty domain of the elements.

[0180] In this embodiment, a sensitivity threshold of 0.01 is given, and the high-sensitivity input parameters and their global sensitivity indices are listed in Table 4.

[0181] Table 4:

[0182]

[0183] Step B4: Establish the probability density distribution of high-sensitivity input parameters. Collect engineering sample data for the first element in the high-sensitivity input vector, and obtain the probability density distribution of the first element through the kernel density estimation solver (ksdensity) provided by MATLAB. The probability density distributions of other elements in the high-sensitivity input vector are obtained in the same way.

[0184] In this embodiment, the operating temperature and assembly gap belong to working condition parameters, and their probability densities are given as uniformly distributed within the uncertainty domain. According to the sample data of the initial value of the cell height, charge capacity, and cyclic deformation coefficient source, the calculated probability density distributions are as shown in Figure 6 、 Figure 7 、 Figure 8 .

[0185] Step B5: Construct high-sensitivity vector samples. Based on the probability density distribution, obtain M high-sensitivity vector samples through the one-dimensional interpolation solver (interp1) provided by MATLAB.

[0186] Step B6: Calculate the stress reliability of the silicon-carbon lithium battery. The stress reliability of the silicon-carbon lithium battery refers to the probability that the random response of the peak stress of the cell is lower than the given stress threshold under uncertain conditions; for the given stress threshold, M stress peak response sample values are calculated by taking each high-sensitivity vector sample as the input vector of f(X); count the probability that the response sample values are less than the given stress threshold, that is, the reliability of the peak stress of the cell of the silicon-carbon lithium battery.

[0187] In this embodiment, the given stress threshold is 0.18 MPa, and the calculated stress reliability results of the two samples are 99.54% and 86.80% respectively. The time consumption of the two solution processes on a general computer (Core i5@3.1GHz / RAM@16GB) is less than 3 minutes.

[0188] This embodiment shows that the stress reliability estimation method for silicon-carbon lithium batteries provided by the present invention has the following advantages. In terms of effectiveness, the method combines a multi-physical field stress function with global sensitivity analysis to identify highly sensitive input parameters and establish a probability density distribution, realizing accurate estimation of stress reliability. In terms of efficiency, the global sensitivity analysis is based on the parameter fluctuation range, avoiding the high cost of sample collection; only relying on the engineering samples of a small number of key parameters to calculate the stress random response, greatly reducing the sample collection cost and the amount of calculation, and meeting the on-line estimation requirements of the reliability of silicon-carbon lithium batteries. In terms of applicability, the method does not rely on time-consuming finite element simulations and high-dimensional parameter sample data, has good scalability and engineering adaptability, and is applicable to multi-scenario requirements such as battery design optimization, on-line status monitoring, and battery health management.

[0189] The present invention also provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, it realizes each process of the embodiment of the silicon-carbon lithium battery cycle stress estimation method, or realizes each process of the embodiment of the silicon-carbon lithium battery stress reliability estimation method, and can achieve the same technical effects. To avoid repetition, it will not be elaborated here. Among them, the computer-readable storage medium is, for example, ROM, RAM, magnetic disk or optical disc, etc.

[0190] Through the description of the above embodiments, those skilled in the art can clearly understand that the above embodiment methods can be implemented by means of software plus a necessary general hardware platform. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on such an understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disc), and includes several instructions for causing a terminal (which can be a mobile phone, computer, server, air conditioner, or network device, etc.) to execute the methods described in each embodiment of the present invention.

[0191] The above describes the embodiments of the present invention in conjunction with the drawings, but the present invention is not limited to the above specific embodiments. The above specific embodiments are only illustrative and not restrictive. Under the inspiration of the present invention, those of ordinary skill in the art can also make many forms without departing from the purpose and scope protected by the claims of the present invention, and all belong to the protection scope of the present invention.

Claims

1. A method for estimating the cyclic stress of a silicon-carbon lithium battery, characterized in that, The method includes the following processing steps: Step A1: Determine the characteristic parameters of the silicon-carbon lithium battery; Step A2: Establish the cycling working conditions of the silicon-carbon lithium battery; Step A3: Establish a thermal model of the silicon-carbon lithium battery; Step A4: Establish a negative electrode electrochemical model; Step A5: Establish a mechanical model of the silicon-carbon lithium battery; In the step A1, the silicon-carbon lithium battery includes a battery cell, a housing, and an electrolyte; the battery cell is composed of an alternating stack of a positive electrode and a negative electrode, and each positive electrode and negative electrode are insulated from each other by a separator; the housing refers to a closed housing that encapsulates the battery cell and the electrolyte; the characteristic parameters include H0, H0 an , A, C, c T , R in , c E , c n , C V Si , c P an , c P ca , E0 an , E0 ca , α, β; H0 represents the initial value of the height of the battery cell, H0 an represents the initial value of the height of the negative electrode, A represents the area of the battery cell perpendicular to the height direction, C represents the charge capacity of the battery cell, R in represents the internal resistance of the battery cell, c E represents the entropy heat coefficient of the battery cell, c T represents the thermal expansion coefficient of the battery cell, c n represents the cyclic deformation coefficient, C V Si represents the volume fraction of silicon particles, c P an represents the porosity of the negative electrode, c P ca represents the porosity of the positive electrode, E0 an represents the elastic coefficient of the negative electrode, E0 ca represents the elastic coefficient of the positive electrode, α represents the strain index of the negative electrode, and β represents the strain index of the positive electrode; In the step A2, the cycling condition refers to setting a spatial constraint in the height direction of the silicon-carbon lithium battery and implementing charge-discharge cycles to simulate the charge-discharge process of the silicon-carbon lithium battery under assembly conditions; the spatial constraint refers to limiting the size of the silicon-carbon lithium battery in the height direction to a fixed value; the charge-discharge cycle consists of several cycles, and each cycle includes a charging process in which the state of charge (SOC) of the battery cell experiences from 0% to 100% and a discharging process from 100% to 0%; the working parameters included in the cycling condition are: δ, T0, T A , h A , c I , n; δ represents the assembly gap, T0 represents the initial value of the battery cell temperature, T A represents the ambient temperature, h A represents the convective heat transfer coefficient, c I represents the operating current rate, and n represents the current cycle number; In the said Step A3, the thermal model of the silicon-carbon lithium battery describes the heat transfer behavior from the silicon-carbon lithium battery to the environment under the said cycling working conditions, calculates the temperature difference between the peak temperature of the battery cell at the moment of maximum SOC and the initial temperature of the battery cell, and the peak thermal deformation of the battery cell caused by the said temperature difference; In the said Step A4, the negative electrode electrochemical model describes the volume change caused by the lithium insertion phase change of silicon particles and carbon particles in the negative electrode of the silicon-carbon lithium battery at the moment of maximum SOC under the said cycling working conditions, and calculates the peak cyclic deformation of the battery cell; In the said Step A5, the mechanical model describes the mechanical behavior of the battery cell under the cycling working conditions, and calculates the peak stress of the battery cell of the silicon-carbon lithium battery at the moment of maximum SOC under the said cycling working conditions.

2. The method according to claim 1, characterized in that, The construction process of the thermal model of the silicon-carbon lithium battery is as follows; Step A3.1: Establish a heat balance equation, which is written as Equation (1) according to Kirchhoff's law: P = (T - T A ) / R A ; Where P represents the heat generation rate of the battery cell, T represents the peak temperature of the battery cell, and R A represents the thermal resistance from the lithium battery to the environment, written as the formula: R A = 1 / (2·h A ·A); Step A3.2: Establish a heat generation equation of the battery cell, which is written as Equation (2) according to the Bernardi equation based on the first law of thermodynamics: P = (c I · C) 2 · R in + c I · C · c E · T; Step A3.3: Solve for the peak temperature of the battery cell, which means solving the system of equations composed of Equation (1) and Equation (2) to obtain the peak temperature of the battery cell; Step A3.4: Calculate the peak thermal deformation of the battery cell, which is written as Equation (3): D T = c T ·(T - T0)·H0; D T represents the peak value of the thermal deformation of the battery cell.

3. The method according to claim 1, characterized in that, The construction process of the negative electrode electrochemical model is as follows; Step A4.1: Calculate the lithium insertion deformation of silicon particles, which is written as Equation (4): d V Si = V m LiSi / V m Si ·x Si ; where d V Si represents the deformation rate of silicon particles, and x Si represents the number of silicon atoms in lithiated silicon; V m LiSi represents the molar volume of lithiated silicon, and V m Si represents the molar volume of silicon; Step A4.2: Calculate the lithium insertion deformation of carbon particles, which is written as Equation (5): d V C = V m LiC / V m C · x C ; Among them, d V C represents the carbon particle deformation rate, and x C represents the number of carbon atoms in lithiated carbon; V m LiC represents the molar volume of lithiated carbon, and V m C represents the molar volume of carbon; Step A4.3: Calculate the material utilization rate of silicon-carbon particles, which means the material utilization rate of silicon particles and carbon particles under the charge capacity limit of the silicon-carbon lithium battery, and is written as Equation (6): c M = C / (q Si · ρ Si · V0 Si + q C · ρ C · V0 C ); Among them, c M represents the utilization rate of the silicon-carbon particle material, q Si represents the theoretical specific capacity of silicon particles, q C represents the theoretical specific capacity of carbon particles, ρ Si represents the density of silicon particles, ρ C represents the density of carbon particles; V0 Si It represents the volume of silicon particles before lithium intercalation, and is written as formula (7): V0 Si = H0 an ·A·(1 - c P an )·C V Si ; V0 C Denote the volume of carbon particles before lithium intercalation, written as Equation (8): V0 C = H0 an ·(1 - c P an )·(1 - C V Si ); Step A4.4: Calculate the volume of the negative electrode at the moment of maximum SOC, which is written as Equation (9): V E an = c M · (V0 Si · d V Si + V0 C · d V C ) + (1 - c M ) · (V0 Si + V0 C ) + H0 an · A · c P an ; Among them, V E an represents the negative electrode volume at the maximum moment of SOC; Step A4.5: Calculate the peak cyclic deformation of the battery cell, which is written as Equation (10): D C = (c n ·n + 1)·(H E an - H0 an ); Among which D C represents the peak value of cyclic deformation in the height direction, c n represents the cyclic deformation coefficient, and n represents the number of cycles; H E an represents the peak value of the cell height, written as formula (18): H E an =V E an / A.

4. The method according to claim 1, wherein The construction process of the mechanical model is as follows; Step A5.1: Calculate the peak deformation of the battery cell, which is written as Equation (11): D = D C + D T - δ; where D represents the peak deformation of the battery cell; Step A5.2: Establish a deformation stress equation to describe the relationship between the deformation and stress of the positive electrode and the negative electrode, which is written as Equation (12): σ = E an ·(D an / H0 an ) α = E ca ·(D ca / (H0 - H0 an )) β ; Among them, σ represents the peak value of the stress of the battery cell; D an represents the peak value of the deformation of the negative electrode, D ca represents the peak value of the deformation of the positive electrode; E an represents the elastic modulus of the negative electrode, written as: E an = E0 an ·(1 - c P an ); E ca represents the elastic modulus of the positive electrode, written as: E ca = E0 ca ·(1 - c P ca ); Step A5.3: Establish a geometric balance equation to describe the equilibrium state between the peak deformation of the battery cell and the peak deformations of the negative electrode and the positive electrode under spatial constraints, which is written as Equation (13): D = D an + D ca ; Step A5.4: Solve for the peak stress of the battery cell, which means solving the system of equations composed of Equation (11), Equation (12), and Equation (13) to obtain the peak stress of the battery cell.

5. A method for estimating the stress reliability of a silicon-carbon lithium battery, characterized in that, For reliability estimation of the peak stress of the battery cell of the silicon-carbon lithium battery obtained by the method according to any one of claims 1 to 4, the reliability estimation method includes the following processing steps: Step B1: Establish a stress function of the silicon-carbon lithium battery; Step B2: Determine the uncertainty domain of the input vector elements; Step B3: Perform global sensitivity analysis; Step B4: Establish the probability density distribution of high-sensitivity input parameters; Step B5: Construct high-sensitivity vector samples; Step B6: Calculate the stress reliability of the silicon-carbon lithium battery; In the step B1, the stress function is written as: f(X), where f(X) represents the peak stress of the battery cell of the silicon-carbon lithium battery based on X; wherein, X represents an input vector, which is obtained by aggregating the characteristic parameters in the step A1 and the working condition parameters in the step A2, and is written as: X = (X1, X2,..., X N ); the vector contains N elements in total, and N represents the number of elements; X1 represents the first element of X, corresponding to H0 in the characteristic parameters; the corresponding relationships between the remaining elements in X and the characteristic parameters and the working condition parameters are deduced by analogy; In the step B2, the determination of the uncertainty domain of the input vector elements refers to determining the X of each element according to the engineering data j L , X j R , written as: X j ∈[X j L , X j R , j = 1, 2,..., N; where X j represents the j-th element of the vector, X j L represents the upper boundary of the j-th element, X j R represents the lower boundary of the j-th element; In Step B6, the stress reliability of the silicon-carbon lithium battery refers to the probability that the random response of the stress peak value of the battery cell is lower than the given stress threshold under uncertain conditions; the given stress threshold is the M stress peak response sample values obtained by taking each of the high-sensitivity vector samples as the input vector of f(X); count the probability that the response sample values are less than the given stress threshold, which is the reliability of the stress peak value of the battery cell of the silicon-carbon lithium battery.

6. The method according to claim 5, wherein In Step B3, the global sensitivity analysis refers to describing the influence of the uncertainty of the vector elements on the fluctuation range of the output value of the stress function to obtain high-sensitivity input parameters.

7. The method according to claim 6, characterized in that, The process of the global sensitivity analysis is as follows; Step B3.1: Establish the vector element main sample matrices, including the first main sample matrix and the second main sample matrix. Use Latin hypercube sampling (lhsdesign) provided by MATLAB to simulate and generate M samples of the vector elements in the element uncertainty domain, where M represents the number of samples and its value range is [10 4 , 10 5 ; The first main sample matrix is written as A, and the second main sample matrix is written as B, both of which are two-dimensional matrices with M rows and N columns; The vector composed of the elements in the i-th row of A is written as A i , i = 1, 2,..., M; The vector composed of the elements in the i-th row of B is written as B i , i = 1, 2,..., M; Step B3.2: Establish a cross matrix, including a first cross-sample matrix, a second cross-sample matrix,...., an Nth cross-sample matrix; the first cross-sample matrix is obtained by replacing the first column of A with the first column of B and writing it as C (1) ; C (1) The vector composed of the elements in the ith row of is written as C i (1) ; and so on, establish the other cross-sample matrices, and the cross-sample matrix is written as: C (j) , j = 1, 2,..., N, are all two-dimensional matrices with M rows and N columns; C (j) Represents the jth cross-sample matrix of the cross-sample matrix, C (j) The vector composed of the elements in the ith row of is written as C i (j) , i = 1, 2,..., M; Step B3.2: Calculate the principal stress response vector, written as: f B =(f1 B ,f2 B ,...f M B ), f1 B represents f B The first element is to convert B i , i=1,2,...,M, where B1 is the stress function value calculated as the input vector of f(X), f B And so on for the other elements; Step B3.3: Calculate the stress response vector, including the first response vector, the second response vector, ..., the Nth response vector; the first response vector is written as: f C(1) =(f1 C(1) ,f2 C(1) ,...f M C(1) ), f1 C(1) represents f C(1) The first element is C i (j) ,i=1,2,...,C1 in M (j) The stress function value calculated as the input vector of f(X), C i (j) The other elements of are obtained in a similar way; and the other response vectors are obtained by analogy. Step B3.4: Calculate the main response sample variance and write it as Equation (14): V f = mean(f i B - mean(f B ), i = 1, 2, ..., M); Where V f represents the main response sample variance, f i B represents the i-th element of f B ; mean represents the mean operator; Step B3.5: Calculate the global sensitivity index and write it as: S j = mean(square(f B - f C(j) ))), j = 1, 2, ..., N; where S j represents the global sensitivity index corresponding to the j-th element in the input vector, and f C(j) represents the j-th response vector of the response vector; square represents an operation of forming a new vector by squaring each element in the vector; Step B3.6: Select highly sensitive input parameters; set a sensitivity threshold, and determine the elements in the input vector whose global sensitivity index is higher than the sensitivity threshold as highly sensitive input parameters, that is, the highly sensitive input parameters selected from X = (X1, X2,..., X N ) form a highly sensitive input vector Y = (Y1, Y2,..., Y L ), where L is the number of highly sensitive input parameters; process the elements in other input vectors into deterministic input parameters, and their values are given as the median of the uncertainty domain of the elements.

8. The method according to claim 7, wherein In Step B4, establishing the probability density distribution of high-sensitivity input parameters means collecting engineering sample data for the first element in the high-sensitivity input vector and obtaining the probability density distribution of the first element through the kernel density estimation solver (ksdensity) provided by MATLAB; the probability density distributions of the other elements of the high-sensitivity input vector are obtained in the same way in turn.

9. The method according to claim 8, wherein In Step B5, constructing high-sensitivity vector samples means obtaining M high-sensitivity vector samples based on the probability density distributions of the elements in the high-sensitivity input vector through the one-dimensional interpolation solver (interp1) provided by MATLAB.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, it implements the steps of the silicon-carbon lithium battery cyclic stress estimation method according to any one of claims 1 to 4, or implements the steps of the silicon-carbon lithium battery stress reliability estimation method according to any one of claims 5 to 9.

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