Lithium-ion battery state of health prediction method based on mixed effect model

Abstract

The present application relates to lithium ion battery health state prediction technical field, specifically for lithium ion battery health state prediction method based on mixed effect model, the prediction method includes the following steps: utilize multinomial distribution to describe the degradation path of different group lithium ion battery;Obtain the offline estimation of corresponding parameters by using the restricted maximum likelihood estimation, obtain the mixed prior information of SOH degradation signal of different lithium ion battery group on the overall level;Beneficial effect is: the lithium ion battery health state prediction method based on mixed effect model proposed in the application aims at the problem that can only be predicted in the average sense of the group, introduces the structure of mixed prior distribution, considers the clustering behavior of lithium ion battery, so that the mixed historical data information can be more fully utilized, the purpose of improving the SOH prediction precision is achieved, the problem that can only be predicted in the average sense of the group is solved.

Description

Technical Field

[0001] This invention relates to the field of lithium-ion battery health status prediction technology, specifically a lithium-ion battery health status prediction method based on a mixed-effects model. Background Technology

[0002] The State of Health (SOH) of a battery represents its state from the beginning to the end of its lifespan, quantitatively describing its current performance. Considering practical production, on the one hand, battery charging and discharging are controlled by the battery management system, and battery capacity is one of the parameters affecting this control. Inaccurate SOH prediction will severely impact the battery's charging and discharging state, leading to overcharging and over-discharging, thus reducing battery lifespan. On the other hand, accurate SOH prediction can directly reflect the battery's aging level, allowing for timely replacement of aging batteries and protecting the safety of users and their property. Through extensive literature review, scholars have proposed various methods for estimating the SOH of electric vehicle power batteries, broadly categorized as: electrochemical modeling, equivalent circuit modeling, and data-driven methods. Among these, data-driven methods have the widest applicability and are currently a hot research topic.

[0003] In the existing technology, driven by the wave of artificial intelligence, data-driven methods have been widely used in the prediction of battery SOH in recent years. Reference [1] Wu J, Zhang CB, Chen Z H. An online method for lithium-ion battery remaining useful life estimation using importancesampling and neural networks[J]. Applied Energy, 2016, 173: 134-140, uses feedforward neural network (FFNN) to simulate the relationship between the battery's remaining capacity and the charging voltage curve under different cycle numbers. This paper selects importance sampling as the input of FFNN. From the simulation results, the actual running accuracy of this method is relatively high. Reference [2] Weng CH, Cui YJ, Sun J, et al. On-board state of health monitoring of lithium-ion batteries using incremental capacity analysis with support vector regression[J]. Journal of Power Sources, 2013, 235: 36-44, firstly, the incremental capacity method was used to analyze the battery aging data, and the features with high correlation to battery SOH were selected. Then, by comparing several algorithms, the optimal conclusion of the support vector regression method was drawn. Finally, the test data was used to prove that the support vector regression method can predict battery SOH within 1% error range. Reference [3] Chen T, Morris J, Martin E. Gaussian process regression for multivariate spectroscopic calibration[J]. Chemometrics and Intelligent Laboratory Systems, 2007, 87(1): 59-67, used probability to describe the prediction results of battery SOH, and used the data after principal component analysis as the input of Gaussian process regression to achieve a more accurate SOH estimation.Reference [4] Sun PK, Wang Z P. Research of the Relationship between Li-ion Battery Charge Performance and SOH based on MIGA-GPR Method [C]. Applied Energy Symposium and Summit-Low Carbon Cities and Urban Energy Systems (CUE), 2015: 608-613. Based on the joint algorithm of multi-island genetic algorithm (MIGA) and Gaussian process regression, the charging performance parameters after grey relational analysis (GIA) are used as input to predict SOH and calculate the estimated variance. The results show that the method can evaluate SOH well.

[0004] However, based on the literature review above, there has been a large body of research on SOH prediction for lithium-ion batteries. As for data-driven methods, although existing methods have achieved good estimation results, they are limited to the degradation path research in the sense of the group average of lithium-ion batteries, and have not yet discussed and studied the clustering behavior that occurs in different lithium-ion battery degradation paths. Summary of the Invention

[0005] The purpose of this invention is to provide a method for predicting the health status of lithium-ion batteries based on a hybrid effect model, so as to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a method for predicting the health status of lithium-ion batteries based on a hybrid effect model, the prediction method comprising the following steps:

[0007] The degradation paths of different groups of lithium-ion batteries are described using multinomial distributions;

[0008] By using constrained maximum likelihood estimation, offline estimates of the corresponding parameters are obtained, and mixed prior information of SOH degradation signals of different lithium-ion battery packs is obtained at the overall level.

[0009] New data is collected from specific units of interest. Bayesian theory is used to integrate this data with parameters obtained from offline prior estimation, and the posterior distribution of the specific unit is updated to achieve SOH prediction for the specific unit.

[0010] Preferably, when using a multinomial distribution to describe the degradation paths of different groups of lithium-ion batteries, it is assumed that there are n subgroups of lithium-ion batteries in different experimental states in the historical data, denoted as S1, S2, ..., S... n Simultaneously define: S1={i:η i=1}, S2={i:η i =2},…,S n ={i:η i =n}, where η i =1,2,…,n are grouping indicators, corresponding to the subgroup type.

[0011] Preferably, without loss of generality, we assume S1, S2, ..., S n The proportions in the overall data are λ1, λ2, ..., λ. n , where 0≤λ k ≤1, and λ1+λ2+...+λ n =1; then the model of the degenerate signal path can be defined as:

[0012]

[0013] When i∈S1, r i (t) by b i,1 and ε i,1 (t) is defined, and others are similar; here, the PDF of η is represented by the Dirac delta function, that is:

[0014]

[0015] Preferably, P(η=η) k )=λ k The degradation signal r is derived. i The edge PDF of (t) is:

[0016]

[0017] The above formula can be expressed in the form of a mixed normal distribution as follows:

[0018]

[0019] Preferably, the characteristics of the degradation signal at the overall level are obtained based on historical data.

[0020] The unknown parameters in the text are collectively referred to as

[0021]

[0022] Suppose we collect historical data from N units. For the i-th unit, its historical data is represented as r. i h Let i = 1, 2, ..., N. Then the historical data can be divided into n groups, B k ={B i |η i =k}, k = 1, 2, ..., n;

[0023] Based on historical data, the weight estimates can be obtained as follows:

[0024]

[0025] Preferably, the estimate is obtained using the restricted maximum likelihood estimation method.

[0026] Preferably, data is collected from a specific unit p at time t. * Observational data up to date: i.e. Where t pm ≤t * By integrating the data with offline prior estimates using Bayesian theory, the posterior distribution of a specific unit p can be updated.

[0027] Preferably, according to the law of total probability:

[0028]

[0029] For S1, according to the conditional probability, we have:

[0030]

[0031] in This is for η p =1 in the posterior probability, and the prior probability is According to Bayes' theorem It can be represented as:

[0032]

[0033] Preferably, for Firstly:

[0034]

[0035] Therefore, the posterior can be calculated as

[0036]

[0037] Where the prior p(b) p,1 |η p =1) is equivalent to The posterior distribution is then:

[0038]

[0039] Where C1 and C2 are constants, and b is not involved. p,1 ν is a vector defined as

[0040]

[0041] definition

[0042]

[0043] They are respectively denoted as

[0044] Therefore, for the overall posterior distribution, according to the law of total probability, we have:

[0045]

[0046] Preferably, according to the law of total probability and get:

[0047]

[0048] Substitution have

[0049] At this point, the complete posterior distribution has been obtained, and based on this, the SOH prediction of in-service batteries can be achieved.

[0050] Compared with the prior art, the beneficial effects of the present invention are:

[0051] The proposed lithium-ion battery health state prediction method based on a mixed-effects model addresses the problem that predictions can only be made on an average basis for the population. By introducing a mixed prior distribution structure and considering the clustering behavior of lithium-ion batteries, the method can make fuller use of mixed historical data information, thereby improving the accuracy of SOH prediction and solving the problem that predictions can only be made on an average basis for the population.

[0052] Mixed-effects models based on mixed prior distributions can fully utilize valuable information from groups with similar degradation paths while avoiding negative impacts from other groups with different degradation paths. Attached Figure Description

[0053] Figure 1 This is a schematic diagram of the lithium-ion battery health status prediction method of the present invention;

[0054] Figure 2 This is a graph showing the capacity change trend of the battery in Example 3;

[0055] Figure 3 This is a graph showing the prediction error of the model in Example 3;

[0056] Figure 4 This is a diagram showing the predicted battery degradation path for the second group in Example 3. Detailed Implementation

[0057] To make the objectives, technical solutions, and advantages of the present invention clear and complete, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are only some, not all, embodiments of the present invention, and are merely illustrative of the embodiments of the present invention. They are not intended to limit the embodiments of the present invention. All other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0058] Example 1

[0059] See attached document Figure 1 As shown, a method for predicting the health status of lithium-ion batteries based on a mixed-effects model is presented. This prediction method includes the following steps:

[0060] 1. Model Building

[0061] Suppose there are n subgroups of lithium-ion batteries in different experimental states in the historical data, denoted as S1, S2, ..., S... n Simultaneously define: S1={i:η i =1}, S2={i:η i =2},…,S n ={i:η i =n}, where η i =1,2,…,n are grouping indicators, corresponding to the subgroup types. These n subgroups are identical in all conditions except for the set experimental states (such as charging and discharging methods, see specific examples later).

[0062] Without loss of generality, assume S1, S2, ..., S n The proportions in the overall data are λ1, λ2, ..., λ. n , where 0≤λ k ≤1, and λ1+λ2+...+λ n =1. Therefore, the model of the degraded signal path can be defined as:

[0063]

[0064] Where b i,1 ~N(μ1,∑1), b i,2 ~N(μ2,∑2),…,b i,n ~N(μ) n ,∑ n ), I(·) is an indicator function, which can take the values ​​1 and 0. It takes the value 1 if the condition in parentheses is satisfied, and 0 otherwise. According to equation (1), it can be seen that when i∈S1, r i (t) by b i,1 and εi,1 (t) is defined, and others are similar. Here, the Dirac delta function is used to represent the PDF of η. That is:

[0065]

[0066] Where, P(η=η) k )=λ k Therefore, the degradation signal r can be derived. i The edge PDF of (t) is:

[0067]

[0068] (3) can be expressed in the form of a mixed normal distribution as follows:

[0069]

[0070] Where f N (x;μ,∑) denotes the PDF of a multivariate Gaussian distribution with mean μ and variance-covariance matrix ∑. Therefore, p{r i λ(t)} is a mixture distribution consisting of n normal distributions, λ1, λ2, ..., λn. n It can be viewed as the weight of each part.

[0071] 2. Offline parameter estimation

[0072] To achieve offline estimation of battery SOH, the first step is to acquire characteristics of the degradation signal at the overall level based on historical data. The unknown parameters in equation (4) are collectively referred to as

[0073]

[0074] Meanwhile, the above parameter set can be decomposed into {λ,Ψ1,Ψ2,…,Ψ} n}, where λ={λ1, λ2,…,λ k}, k = 1, 2, ..., n. Assume historical data is collected from N units. For the i-th unit, its historical data is represented as r. i h Let i = 1, 2, ..., N. Then the historical data can be divided into n groups, B k ={B i |η i =k}, k = 1, 2, ..., n.

[0075] Based on historical data, the weight estimates can be obtained as follows:

[0076]

[0077] The second step is to estimate Ψ. According to equations (1) and (4), we can see that Ψ1, Ψ2, ..., Ψ n It can be composed of B1, B2, ..., B n Estimate. In other words, an estimate can be obtained using the restricted maximum likelihood estimation method. At this point, all the prior information required for the online update has been obtained.

[0078] 3. Online parameter updates

[0079] First, time t is collected from a specific unit p. * Observational data up to date: i.e. Where t pm ≤t * Next, Bayesian theory is used to integrate this data with offline prior estimates to update the posterior distribution of a specific unit p. Under this assumption, S1, S2, ..., S... n The distribution characteristics of the models differ, making online Bayesian updates less direct. However, despite the increased complexity, the proposed improved model can still be effectively updated using the method described below.

[0080] According to the law of total probability:

[0081]

[0082] For S1, according to the conditional probability, we have:

[0083]

[0084] in This is for η p =1 in the posterior probability, and the prior probability is According to Bayes' theorem It can be represented as:

[0085]

[0086] for Firstly:

[0087]

[0088] Therefore, the posterior can be calculated as

[0089]

[0090] Where the prior p(b) p,1 |η p =1) is equivalent to The posterior distribution is then:

[0091]

[0092] Where C1 and C2 are constants, and b is not involved. p,1 ν is a vector defined as

[0093]

[0094] definition

[0095]

[0096] Then, equation (10) can be rewritten as

[0097]

[0098] Equation (12) defines the multivariate normal distribution. Similarly, we can obtain S2, S3, ..., S n The posterior distribution, i.e. They are respectively denoted as

[0099] Therefore, for the overall posterior distribution, according to the law of total probability, we have:

[0100]

[0101] Among them, according to the law of total probability and equation (13)

[0102]

[0103] Substituting into equation (14), we have

[0104]

[0105] At this point, the complete posterior distribution has been obtained, which can be used to predict the SOH of in-service batteries.

[0106] Example 2

[0107] A method for predicting the health status of lithium-ion batteries based on a mixed-effects model, comprising the following steps:

[0108] In the offline estimation stage, the degradation path of different groups of lithium-ion batteries is described by multinomial distribution. Then, the corresponding parameters are estimated offline by constrained maximum likelihood estimation. That is, the mixed prior information of SOH degradation signals of different lithium-ion battery packs is obtained at the overall level.

[0109] In the online parameter update phase, new data is first collected from the specific unit of interest. Then, Bayesian theory is used to integrate this data with the parameters obtained from offline prior estimation, thereby updating the posterior distribution of the specific unit and finally achieving SOH prediction for the specific unit.

[0110] Example 3

[0111] We used degradation data from lithium-ion batteries to verify the superiority of the proposed mixed-effects model based on mixed prior distributions compared to traditional mixed-effects models. The experimental data came from the NASA lithium-ion battery aging dataset.

[0112] In this specific implementation method, six groups of lithium-ion batteries (four in each group) were selected and cycled under different random charge-discharge curves. The cycling conditions are as follows:

[0113] Group 1: Continuous operation using a series of charge and discharge currents between -4.5A and 4.5A. Each load cycle lasts 5 minutes, and after 1500 cycles (approximately 5 days), a series of reference charge and discharge cycles are performed.

[0114] Group 2: Continuous operation at room temperature using a random discharge current sequence between 0.5A and 4A. A series of reference charge and discharge cycles are performed after every 50 cycles.

[0115] Group 3: Cycled under the same random discharge conditions as Group 2, except that each discharge cycle is one foot, and the battery charging time is randomly selected between 0.5 hours and 3 hours.

[0116] Group 4: Operation at room temperature under a custom right-skewed distribution a. The probability distribution is used to select a new load setpoint between 0.5A and 5A every minute during discharge;

[0117] Group 5: Operation under a custom left-skew distribution at 40℃. The probability distribution is used to select a new load setpoint between 0.5A and 5A every minute during the discharge operation;

[0118] Group 6: Cycled under the same random discharge conditions as Group 5, except that the experiment was conducted at room temperature.

[0119] Note: For details on distribution a, please refer to the explanation in the dataset.

[0120] like Figure 2 The figure shows the capacity variation trend of these batteries.

[0121] The prediction results will be repeated 24 times, each time selecting one lithium-ion battery as the in-service unit for online updates, with the rest as offline data. For the mixed-effects model with mixed prior distributions, the prior weight of each group is calculated by dividing the number of batteries in that group by the total number of batteries in the offline data. Then, three time points in the battery cycle life, namely 30%, 50%, and 70%, are selected as prediction times. Finally, the root mean square error (RMSE) is selected as the evaluation criterion for performance comparison. The prediction errors of the two models are as follows: Figure 3 As shown.

[0122] from Figure 3 It can be seen that the proposed mixed-effects model based on mixed prior distributions is consistently superior to the traditional mixed-effects model. In particular, when the prediction time is only 30%, the proposed model already has high prediction accuracy, indicating that the model can effectively estimate the degradation path of the battery's early lifespan.

[0123] To further demonstrate the ability of the mixed-effects model based on mixed prior distributions to capture degradation paths, the prediction results for the second group of batteries at 30% of their cycle life are presented here, such as... Figure 4 As shown in the figure, the predictions of the traditional mixed-effects model are all greater than the actual results of the predicted objects. This is due to the negative impact of the information in the first, fourth, and fifth groups. However, the predictions of the proposed model are able to follow the actual degradation path without being affected.

[0124] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for predicting the health status of lithium-ion batteries based on a mixed-effects model, characterized in that, The prediction method includes the following steps: The degradation paths of different groups of lithium-ion batteries are described using multinomial distributions; By using constrained maximum likelihood estimation, offline estimates of the corresponding parameters are obtained, and mixed prior information of SOH degradation signals of different lithium-ion battery packs is obtained at the overall level. New data is collected from specific units of interest, and Bayesian theory is used to integrate this data with parameters obtained from offline prior estimation. The posterior distribution of the specific unit is then updated, and the SOH prediction of the specific unit is finally achieved. When using multinomial distributions to describe the degradation paths of different groups of lithium-ion batteries, it is assumed that historical data contains... The lithium-ion battery subgroups in different experimental states are denoted as follows: Simultaneously define: , ,…, ,in It is a grouping indicator, corresponding to the subgroup type; Without loss of generality, assume The proportions in the overall data are respectively ,in ,and The model for the degraded signal path can then be defined as: ； when hour, Depend on and The definition is the same for others; here, we use Dirac. To represent by function The PDF, i.e.: 。 2. The method for predicting the health status of lithium-ion batteries based on a mixed-effects model according to claim 1, characterized in that: The degradation signal was derived. The edge of the PDF is: ； The above formula can be expressed in the form of a mixed normal distribution as follows: ; in Indicates having a mean Sum of variance-covariance matrix The PDF of the multivariate Gaussian distribution; therefore, It is by A mixed distribution composed of normal distributions , , ..., It can be considered as the weight of each part.

3. The method for predicting the health status of lithium-ion batteries based on a mixed-effects model according to claim 2, characterized in that: Based on historical data, the characteristics of the degradation signal at the overall level were obtained. The unknown parameters in the text are collectively referred to as ； Assuming from Historical data is collected in each unit, for the first unit... Each unit, whose historical data is represented as: ,in Historical data can then be divided into... Group, , ; Based on historical data, the weight estimates can be obtained as follows: 。 4. The method for predicting the health status of lithium-ion batteries based on a mixed-effects model according to claim 3, characterized in that: The estimate is obtained using the restricted maximum likelihood estimation method. , ,…, ; The above parameter set is decomposed into ,in , , Assuming from Historical data is collected in each unit, for the first unit... Each unit, whose historical data is represented as: ,in The historical data will then be divided into... Group, , .

5. The method for predicting the health status of lithium-ion batteries based on a mixed-effects model according to claim 1, characterized in that: From a specific unit Collected moments Observational data up to date: i.e. ,in By integrating the data with offline prior estimates using Bayesian theory, the specific unit can be updated. The posterior distribution.

6. The method for predicting the health status of lithium-ion batteries based on a mixed-effects model according to claim 5, characterized in that: According to the law of total probability: ； for According to conditional probability, we have: ； in This is for The posterior probability, and the prior probability. According to Bayes' theorem, It can be represented as: 。 7. The method for predicting the health status of lithium-ion batteries based on a mixed-effects model according to claim 6, characterized in that: for Firstly: Therefore, the posterior can be calculated as Prior Equivalent to Then the posterior distribution is: in and It is a constant and does not involve , A vector is defined as definition after, Rewritten as ； The multivariate normal distribution is defined. Similarly, we get , , ..., The posterior distribution, i.e. ,…, They are respectively denoted as ; Therefore, for the overall posterior distribution, according to the law of total probability, we have: 。 8. The method for predicting the health status of lithium-ion batteries based on a mixed-effects model according to claim 7, characterized in that: According to the law of total probability and get: Substitution ,have At this point, a complete posterior distribution has been obtained, which is used to predict the SOH of in-service batteries.

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