Satellite lithium battery life evaluation method integrating multivariate orthogonal polynomial and response surface method

Abstract

The invention discloses a satellite lithium battery service life evaluation method integrating a multivariate orthogonal polynomial and a response surface method. The method mainly comprises the following steps: analyzing a stress factor of a satellite lithium battery and determining a stress level; designing a multi-factor orthogonal test matrix and acquiring test data; building a lithium battery cycle life evaluation model based on a multivariate orthogonal polynomial; and respectively carrying out significance test on the whole model and the model regression coefficient, and optimizing the model. According to the method, life modeling and evaluation are carried out by integrating a multivariate orthogonal polynomial and a response surface method, the nonlinear relation between multiple stress factors of the lithium battery and the response can be captured, the collaborative or antagonistic effect of different stress factors on the response can be revealed and quantified, and the precision of a life model is ensured; the method is suitable for multi-stress acceleration test design and rapid life evaluation of a long-life, high-reliability and small-sample lithium battery for a spacecraft, and has an important engineering application value.

Description

Technical Field

[0001] This invention relates to the field of satellite lithium battery life assessment technology, and in particular to a satellite lithium battery life assessment method that integrates multivariate orthogonal polynomial and response surface methodology. Background Technology

[0002] Lithium batteries, due to their high energy density, good rate performance, and long cycle life, have become a key energy storage component in satellite power systems. They are the only energy source for satellites to operate in orbit during the Earth's shadow period, and their cycle life directly affects whether satellites can operate normally in orbit and successfully complete their flight missions. Therefore, accurately verifying and evaluating the cycle life of lithium batteries used in satellites is of utmost importance.

[0003] The designed lifespan of lithium batteries for high-orbit satellites is often as long as 8 to 15 years. While conducting full-life tests under rated operating conditions can accurately assess the cycle life of lithium batteries, the testing cycle is long, costly, and inefficient, failing to meet the development schedule requirements of satellite models. Accelerated life testing has become an effective way to solve this problem. Currently, most commonly used accelerated testing methods employ single-stress acceleration models. However, the actual operating conditions of satellite lithium batteries in orbit are complex, simultaneously subjected to multiple stress coupling effects such as high and low temperature cycling, high-rate charging and discharging, and different depths of discharge. Single-stress accelerated testing cannot realistically simulate the failure physical process of multi-stress coupling, leading to significant deviations in life assessment results, underestimating or overestimating actual risks. Some experts and scholars have also established multi-stress acceleration models, but these typically assume that the stresses are independent of each other, using the product of various acceleration factors as the comprehensive acceleration factor, neglecting the impact of stress coupling on the cycle life of lithium batteries. Summary of the Invention

[0004] To address the aforementioned issues, this disclosure provides a satellite lithium battery life assessment method that integrates multivariate orthogonal polynomials and response surface methodology, thereby improving testing efficiency and the accuracy of life assessment.

[0005] This method mainly includes the following steps: S1, Stress Factor Analysis and Stress Level Determination for Satellite Lithium Batteries: Determine the main stress factors affecting the cycle life of satellite lithium batteries and the distribution range of each stress level; S2, Multi-factor orthogonal experimental matrix design and experimental data acquisition: The Box-Behnken method was used to design an orthogonal experimental matrix, implement accelerated life tests of lithium batteries, and complete life data acquisition. S3, Construction of a lithium battery cycle life assessment model based on multivariate orthogonal polynomials: Construct a lithium battery cycle life assessment model based on multivariate orthogonal polynomials; solve the model coefficients using the least squares method based on the encoded experimental data; S4, Model Validation and Lifetime Assessment: The significance of the overall model and the regression coefficients is tested separately, and insensitive stress factors are eliminated to obtain the optimized lithium battery cycle life assessment model.

[0006] Compared with the prior art, the beneficial effects of this disclosure are: ① The Box-Behnken method is used to design the cycle life test of lithium batteries, which covers the full factor space with fewer test cycles, which helps to shorten the test cycle, reduce costs, and improve quality and efficiency; ② Construct orthogonal polynomial basis functions to reduce multicollinearity among factors, simplify the solution process of the lifetime model, and ensure the stability of regression coefficient estimation; ③ By combining multivariate orthogonal polynomials and response surface methodology for lifetime modeling and evaluation, the nonlinear relationship between multiple stress factors and response of lithium batteries can be captured, revealing and quantifying the synergistic or antagonistic effects of different stress factors on the response, thus ensuring the accuracy of the lifetime model.

[0007] The method described in this disclosure is applicable to the accelerated test design and rapid life assessment of long-life, high-reliability, small-sample lithium batteries for spacecraft under multiple stresses, and has significant engineering application value. Attached Figure Description

[0008] The above and other objects, features and advantages of this disclosure will become more apparent from the more detailed description of exemplary embodiments of this disclosure taken in conjunction with the accompanying drawings, in which the same reference numerals generally represent the same components.

[0009] Figure 1 This is a flowchart of the satellite lithium battery life assessment method based on the integrated multivariate orthogonal polynomial and response surface method disclosed herein. Detailed Implementation

[0010] Preferred embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While preferred embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that the present disclosure will be thorough and complete, and will fully convey the scope of the present disclosure to those skilled in the art.

[0011] This disclosure provides a method for evaluating the lifespan of satellite lithium batteries that integrates multivariate orthogonal polynomial analysis and response surface methodology. The process is shown in the attached figure. Figure 1 As shown, the main steps include: S01, Stress Factor Analysis and Stress Level Determination of Lithium Batteries for Satellites (1) Stress factor analysis Lithium-ion batteries serve as a backup power source for satellites. During periods of sunshine, they are charged by solar cells, and during periods of shade or a combination of sunshine and shadow, they output power to the satellite platform and payload. During on-orbit operation, satellite lithium-ion batteries are subjected to various environmental conditions, including charged particle radiation, alternating high and low temperatures, and high vacuum. Factors affecting their cycle life primarily include temperature, depth of discharge, charging cut-off voltage, and discharge rate. These factors are used as stress factors in accelerated life testing. express.

[0012] (2) Stress level range analysis Without altering the failure mechanism, each stress factor is set according to the principle that the highest stress factor level should not exceed the lithium battery's stress tolerance limit and the lowest stress factor level should be appropriately close to the nominal operating condition. stress level ,in As a factor The number of levels is usually 3-4.

[0013] (3) Factor level coding Considering the different dimensions and level ranges of the various accelerating stress factors, and to facilitate experimental design and data processing, all factors are normalized. The factor levels are transformed into a "cube" centered at the origin, with the factor level encoding values ​​limited to the range [-1, 1]. The calculation steps are as follows: Assumption , , These are factors The lower level, upper level, and center, i.e., the zero level, can be represented as: Equation (1) The radius of change of the factor is: Equation (2) The factor level "coding formula" is: Equation (3) S02, Multi-factor orthogonal experimental matrix design and experimental data acquisition (1) Experimental matrix design Using the cycle life of satellite lithium batteries as the response variable and the acceleration stress factor determined by S01 as the independent variable, based on the number of stress factors and factor level coding values, the Box-Behnken experimental design method was adopted. Using Minitab software, n sets of orthogonal experimental matrices were constructed. Each set of factor level coding values ​​corresponds to a set of experimental conditions, so as to cover the first-order effect, second-order effect, and interactive coupling effect between different factors with fewer experiments.

[0014] (2) Experiment implementation and data collection First, the initial capacity of the lithium battery used in the satellite was determined to be Q0. Based on an orthogonal experimental matrix, charge-discharge cycle life tests were conducted. After a certain number of cycles, the remaining capacity was tested. The lifespan was terminated when the capacity fell below 80% of the initial capacity. The number of cycles for each test group was recorded as the cycle life data for each group of lithium batteries, resulting in n sets of test data. .

[0015] S03, Construction of a lithium battery cycle life assessment model based on multivariate orthogonal polynomials (1) Constructing a life assessment model Using the stress factor and factor level encoding values ​​determined in step S01 as independent variables, and the lithium battery cycle life measured in step S02 as the response variable, the stress factor is... The transformation is regularized to form three types of orthogonal polynomial basis functions, including linear terms, square terms, and interaction terms. These are then substituted into the second-order surface response model to form a lithium battery cycle life assessment model.

[0016] Equation (4) In the formula: —Influencing variable: lithium battery cycle life; —Independent variable: lithium battery acceleration stress factor; — First-order linear basis functions, characterizing the linear effect of the factor on the response; — Second-order squared basis functions, characterizing the nonlinear effect of the factor on the response; — Cross-term basis functions characterize the synergistic or antagonistic effects of two factors on the response; --factor The coefficients of the linear and quadratic terms; --factor The coefficients of the interaction terms; —Constant term; —The random error term is usually assumed to have a mean of 0 and a variance of 0. It follows a normal distribution.

[0017] (2) Determine the regularization rules Taking a three-level model as an example, the regularization rules for multivariate orthogonal polynomials are as follows: Equation (5) (3) Solve for the model coefficients ① Transform the model: Formula (4) can be written in matrix form as follows: Where: Y is an n×1 response vector, The design matrix is ​​an n×s matrix composed of orthogonal polynomial basis functions. Each row corresponds to a set of experimental schemes and experimental data, and each column corresponds to an orthogonal polynomial basis function. It is an s×1 model coefficient vector. It is an n×1 error vector.

[0018] ② Minimize the sum of squared residuals using the least squares estimation method:

[0019] ③ Taking the partial derivatives and setting them to zero, we obtain the expression for the model coefficients:

[0020] Assumption If it is reversible, then the solution is:

[0021] ④ Input the encoded n-cycle life test data into the lithium battery cycle life assessment model, solve the polynomial, and obtain the estimated values ​​of the regression coefficients corresponding to all orthogonal polynomial basis functions, i.e. , , ( ).

[0022] S04, Model Validation and Lifetime Assessment (1) Overall significance test of the model To test the significance of the life assessment model, let: Null hypothesis : This means the model is invalid and all factors contribute nothing. Alternative Hypothesis : If at least one of the values ​​is not zero, then the model is valid.

[0023] The F-statistic is constructed as follows: ( The number of significant orthogonal polynomials in the model. ) in, For the regression sum of squares, The formula for calculating the sum of squared residuals is as follows: Equation (6) Let the significance level =0.05, if If the model is significant overall, the life assessment model is meaningful; otherwise, the life assessment model is meaningless.

[0024] (2) Significance test of model coefficients Perform a significance test on the coefficients of each orthogonal polynomial in the life assessment model. Let: Null hypothesis coefficients of a certain orthogonal polynomial That is, the orthogonal polynomial is invalid; Alternative Hypothesis coefficients of a certain orthogonal polynomial That is, the orthogonal polynomial is valid.

[0025] The statistic is constructed as follows: Equation (7) in, This is an estimate of the coefficients of the j-th orthogonal polynomial; This is the standard deviation of the coefficient.

[0026] Let the significance level =0.05, if If the coefficients of the orthogonal polynomial are meaningful, then the coefficients of the orthogonal polynomial are considered meaningful; otherwise, the coefficients of the orthogonal polynomial are considered meaningless and can be removed from the model, thereby simplifying the model.

[0027] (3) Life assessment By substituting any operating condition of the satellite lithium battery into the verified life assessment model, the cycle life result is calculated, thereby realizing the life assessment of the satellite lithium battery.

[0028] Application Examples This embodiment is described in detail using a lithium battery for a satellite as an example. The data used in this case are for illustrative purposes only, and the predicted results are intended to illustrate the implementation process of this method and do not have practical engineering significance.

[0029] 1. Stress factor analysis and stress level determination for satellite lithium batteries (1) Stress factor analysis Temperature, depth of discharge, charge cut-off voltage, and discharge rate were selected as stress factors for accelerated life testing of lithium batteries for satellites, and are respectively expressed as follows: .

[0030] (2) Stress level range analysis Assuming the lithium battery has a maximum operating temperature of 50℃, a minimum operating temperature of 20℃, a maximum discharge depth of 80%, a minimum discharge depth of 30%, a maximum charging cut-off voltage of 4.2V, a minimum charging cut-off voltage of 4.0V, a maximum discharge rate of 2C, a minimum discharge rate of 1C, and three levels for each stress factor.

[0031] (3) Factor level coding Regarding the temperature stress factor, according to formulas (1) to (3), we can obtain: (°C) (°C). The "coding" result for the temperature stress level is:

[0032] The other three stress factor levels were coded sequentially, and the results are shown in the table below: Table 1 Stress factor level coding results

[0033] 2. Multi-factor orthogonal experimental matrix design and experimental data acquisition (1) Experimental matrix design Based on the number of stress factors and the coded stress level, the Box-Behnken experimental design method was used to design an experimental matrix with 4 factors, 3 levels, and 3 center points, resulting in 27 lithium battery accelerated life test schemes. The results are as follows.

[0034] Table 2. Experimental Scheme and Results

[0035] (2) Experiment implementation and data collection According to Table 3, the lithium battery accelerated life test was carried out until the remaining capacity of the lithium battery was lower than 80% of the initial capacity, and the corresponding number of cycles y was recorded, as shown in Table 2.

[0036] 3. Construction of a lithium battery cycle life assessment model based on multivariate orthogonal polynomials Using the stress factor and factor level coding value determined by S02 as independent variables and the lithium battery cycle life measured by S02 as the response variable, a surface response model based on a multivariate orthogonal polynomial is constructed as shown in the following equation, which serves as the lithium battery cycle life assessment model.

[0037]

[0038] (3) Solve for the model coefficients using the least squares estimation method. Substituting the data from 27 cycle life tests into the lithium battery cycle life assessment model, and using the least squares estimation method to estimate the model coefficients, the life assessment model expression is obtained as follows:

[0039] 4. Model Validation and Lifetime Assessment (1) Overall significance test of the model To test the significance of the life assessment model, let: Null hypothesis : This means the model is invalid; Alternative Hypothesis : If at least one of the values ​​is not zero, then the model is valid.

[0040] The F-statistic is constructed as follows:

[0041] in, For the regression sum of squares, The sum of squared residuals is calculated as follows:

[0042] but

[0043] Let the significance level =0.05, because =2.64, then the life assessment model is meaningful.

[0044] (2) Significance test of model coefficients Perform a significance test on the coefficients of each orthogonal polynomial in the life assessment model. Let: Null hypothesis coefficients of a certain orthogonal polynomial That is, the orthogonal polynomial is invalid; Alternative Hypothesis coefficients of a certain orthogonal polynomial That is, the orthogonal polynomial is valid.

[0045] The statistic is constructed as follows:

[0046] in, This is an estimate of the coefficients of the j-th orthogonal polynomial; This is the standard deviation of the coefficient.

[0047] The results obtained from solving the model coefficients are as follows: Table 3. Model coefficient estimates

[0048] Let the significance level =0.05, if If the coefficients of the orthogonal polynomial are within a certain range, then the orthogonal polynomial coefficients are considered meaningful; otherwise, they are considered meaningless. The results in the table above show that the coupling effect of temperature, depth of discharge, and charge cutoff voltage has the most significant impact on the cycle life of satellite lithium batteries.

[0049] (3) Life assessment By substituting the nominal operating conditions of the satellite lithium battery into the verified life assessment model, the cycle life results are calculated, thereby realizing the life assessment of the satellite lithium battery.

[0050] The above technical solutions are merely exemplary embodiments of the present invention. For those skilled in the art, based on the application methods and principles disclosed in the present invention, it is easy to make various types of improvements or modifications, and not limited to the methods described in the specific embodiments of the present invention. Therefore, the methods described above are merely preferred and not restrictive.

Claims

1. A lithium battery life assessment method for satellites that integrates multivariate orthogonal polynomials with response surface methodology, characterized by, The method comprises the following steps: S1, stress factor analysis and stress level determination of lithium battery for satellite: determining the main stress factors affecting the cycle life of lithium battery for satellite, and the distribution range of each stress level; S2, designing an orthogonal test matrix, implementing lithium battery accelerated life test and completing life data collection; S3, constructing a lithium battery cycle life evaluation model based on multivariate orthogonal polynomials; based on the coded test data, the model coefficients are solved by using the least square method; S4, performing significance test on the model as a whole and the model regression coefficients respectively, eliminating insensitive stress factors, and obtaining an optimized lithium battery cycle life evaluation model.

2. The method of claim 1, wherein, The step S1 specifically comprises: (1) Select the main stress factors affecting the cycle life of lithium batteries for satellites, including: temperature, discharge depth, charge cut-off voltage, discharge rate, as the stress factor of accelerated life test, denoted by ; (2) On the premise of not changing the failure mechanism, according to the principle that the highest stress factor level does not exceed the stress limit that the lithium battery can tolerate, and the lowest stress factor level is appropriately close to the nominal working condition, the stress levels of each stress factor are set The stress levels of each stress factor are set , wherein is the level number of the factor , and the value is 3 or 4; (3) Factor level coding: all factors are normalized, the factor level is converted into a "cube" centered at the origin, and the factor level coding value is limited in the range of [-1, 1], and the specific calculation steps comprise: Let , , be the lower, upper, and central levels of the factor , respectively. The factor change radius is: Then the factor level "coding formula" is: 。 3. The method of claim 2, wherein, The step S2 specifically comprises: (1) Test matrix design Taking the cycle life of lithium battery for satellite as the response variable, and the accelerated stress factors determined in the step S1 as the independent variable, based on the number of stress factors and the factor level coding value, the Box-Behnken test design method is adopted, and the Minitab software is used to construct n groups of orthogonal test matrixes, each group of factor level coding value corresponds to a group of test conditions, so that the first-order effect, the second-order effect of the same stress factor, and the interaction coupling effect between different factors are covered with fewer test times; (2) Test implementation and data collection First, the initial capacity of the lithium battery for satellite is determined as Q0, and the lithium battery charge-discharge cycle life test is carried out according to the orthogonal test matrix. After a certain number of cycles, the residual capacity is tested once, and the capacity less than 80% of the initial capacity is taken as the end criterion of life. The cycle number of each group of tests is recorded as the cycle life data of each group of lithium batteries, and n groups of test data are obtained .

4. The method of claim 2, wherein, The step S3 specifically comprises: (1) Constructing a life evaluation model Taking the stress factor and the factor level code value determined in step S1 as independent variables, and taking the cycle life of the lithium battery measured in step S2 as a response variable, the stress factor The transformation is normalized to form three types of orthogonal polynomial basis functions including linear terms, square terms and interaction terms, which are brought into the second-order curved surface response model to form the lithium battery cycle life evaluation model: In the formula: - impact variable, lithium battery cycle life; - independent variable, lithium battery acceleration stress factor; - a first order linear term basis function representing a linear effect of the factors on the response; - a second order squared term basis function representing a non-linear effect of the factors on the response; - cross-term basis functions, representing synergistic or antagonistic effects of two factors on the response; - factor linear, quadratic coefficients; - the interaction coefficient of the factor - the interaction coefficient of the factor - constant term; - a random error term, typically assumed to follow a normal distribution with mean 0 and variance . (2) Determining the regularization rule Taking three levels as an example, the regularization rule of multivariate orthogonal polynomials is as follows: (3) Solving the model coefficients ① Transforming the model: Equation (4) can be written in matrix form as: , wherein: Y is an n x 1 response vector, is an n x s design matrix composed of orthogonal polynomial basis functions, each row corresponds to a set of test schemes and test data, and each column corresponds to an orthogonal polynomial basis function, is an s x 1 model coefficient vector, is an n x 1 error vector; ② Minimizing the residual sum of squares by using the least square estimation method: iii. For Taking partial derivative and setting the derivative equal to 0, the model coefficient expression is obtained: Assume is reversible, then we have: ; IV. The coded n-cycle life test data is substituted into the lithium battery cycle life evaluation model, the polynomial is solved, and the regression coefficient estimates corresponding to all orthogonal polynomial base functions are obtained, i.e. 、 、 , .

5. The method of claim 4, wherein, The step S4 specifically comprises: (1) Model overall significance test The significance of the life evaluation model is tested, and the formula is as follows: Null hypothesis : that the model is invalid and that all factors contribute nothing. alternative hypothesis : at least one of the medians is not zero, i.e. the model is valid; (2) Model coefficient significance test , is the number of significant orthogonal polynomials in the model, , wherein is the regression sum of squares, is the residual sum of squares, calculated as follows: Let the significance level = 0.05, if then the model is overall significant, the lifetime assessment model is meaningful, otherwise the lifetime assessment model is not meaningful; The significance of each orthogonal polynomial coefficient in the life evaluation model is tested, and the formula is as follows: The method further comprises the following steps: Original hypothesis : a certain orthogonal polynomial coefficient , i.e. the orthogonal polynomial is invalid; alternative hypothesis : a certain orthogonal polynomial coefficient , i.e. that the orthogonal polynomial is valid; Any working condition of the lithium battery for satellite is substituted into the verified life evaluation model, the cycle life result is calculated, and the life evaluation of the lithium battery for satellite is realized. wherein is an estimate of the jth orthogonal polynomial coefficient; is the standard deviation of this coefficient; Let the significance level = 0.05, if then the orthogonal polynomial coefficient is considered to be significant, otherwise it is considered to be insignificant and is removed from the model, thereby simplifying the model.

6. The method according to any one of claims 1 to 5, characterized in that, ​ ​

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