Lithium ion battery health state evaluation method based on individual characteristics

Abstract

The invention relates to the technical field of lithium battery health state estimation, in particular to a lithium ion battery health state estimation method based on individual characteristics, which comprises the following steps of: providing a lithium ion battery degradation modeling framework, mapping a relationship between an operation factor and a mixed effect by utilizing a B-spline primary function, and establishing a large covariance matrix model; estimating coefficients of the noise and the spline basis function respectively; according to the Bayesian theorem, different parameter updating strategies are provided for different conditions; performing SOH prediction of the battery; the lithium ion battery health state evaluation method based on the individual characteristics has the beneficial effects that the degradation process is modeled through operation factors; the method is different from a traditional degradation model, only overall behaviors among batteries are considered, and individual differences are ignored. By using the operation factors, the model can more accurately capture the unique degradation path of each battery, so that the prediction precision and stability are improved.

Description

Technical Field

[0001] The present invention relates to the field of lithium battery health state estimation, and in particular to a lithium ion battery health state assessment method based on individual characteristics. Background Art

[0002] As the world continues to transition to a more sustainable energy future, lithium-ion batteries have become an indispensable part of modern life and play an important role in many aspects. Lithium-ion batteries have high energy density and inherent characteristics of decay over time, so it is necessary to develop effective monitoring and control technologies to ensure their continued safety and reliability. The two most critical states of lithium batteries are the state of charge (SOC) and the state of health (SOH). Although the definition of SOH is not uniform, the most common definition is the ratio of the maximum remaining capacity to the initial rated capacity. The definition of SOC is the percentage of the current capacity to the maximum remaining capacity. From the above definitions, it can be concluded that the estimation of SOH is the basis for the estimation of SOC. However, it is difficult for battery management systems to accurately estimate SOH because lithium-ion batteries are complex electrochemical systems that operate in a dynamic environment and the internal reactions are elusive. On this basis, accurate estimation of the SOH of lithium-ion batteries has received widespread attention.

[0003] At present, the methods for predicting the degradation path of lithium-ion batteries are generally considered to be divided into model-based methods and data-driven methods. Electrochemical models (EM) and equivalent circuit models (ECM) are the two most common model-based methods. The SOH of lithium-ion batteries is regarded as a parameter in the model. By minimizing directly measurable parameters (such as voltage), the SOH of lithium-ion batteries can be obtained by statistical techniques, but the model generally involves some coupled characteristic parameters, so it is too complicated and has poor versatility. Recently, with the development of artificial intelligence, data-driven methods applied to SOH have made great progress, thus overcoming the shortcomings of model-based methods. Compared with model-based methods, data-driven methods do not require in-depth understanding of the intricate electrochemical processes inside lithium batteries. In the prior art, a time-series convolutional neural network without performing feature engineering steps is proposed for estimating the SOH of lithium batteries. In the prior art, a hybrid model is proposed, which combines empirical models and deep neural networks to estimate the SOH and remaining service life of lithium batteries using the characteristics of discharge curves.

[0004] Although the two prior arts disclosed above have achieved effective prediction of battery capacity degradation, they still have limitations, mainly manifested in: considering that it is not simple to obtain aging data from laboratories and actual environments, and the aging data may not only differ in operating conditions, but also in the batteries themselves. Both of these situations will cause most of the current SOH estimation algorithms to fail. In many applications, although similar lithium-ion batteries in the same group have certain similarities, each lithium-ion battery has its own unique individual characteristics due to different operating conditions. It is a challenging task to estimate SOH using existing degradation data under arbitrary operating conditions while fully reflecting the individual differences of each lithium-ion battery. Therefore, a lithium-ion battery health state estimation method that can take into account the unique operating state of individual batteries and make full use of existing battery aging data is imminent. Summary of the invention

[0005] The purpose of the present invention is to provide a method for evaluating the health status of lithium-ion batteries based on individual characteristics to solve the problems raised in the above background technology.

[0006] To achieve the above object, the present invention provides the following technical solution: a method for evaluating the health status of a lithium-ion battery based on individual characteristics, the method comprising the following steps:

[0007] A lithium-ion battery degradation modeling framework is proposed, which uses B-spline basis functions to map the relationship between operating factors and mixed effects, and establishes a large covariance matrix model;

[0008] Estimate the coefficients of noise and spline basis functions respectively;

[0009] According to Bayes' theorem, different parameter updating strategies are proposed for different situations;

[0010] Predict the battery's SOH.

[0011] Preferably, the specific operations of proposing a lithium-ion battery degradation modeling framework include:

[0012] Assume that there are N batteries with the same degradation pattern in the historical data set. For battery cell i∈{1,…,N}, at time t ij The degradation signal is y ij , where j = 1,…,n i is the observation time index, and the operating factor of battery cell i is In other words, s is the number of operating factors for each battery cell. Without considering generality, y ij The mixed effects model is written as:

[0013] y ij =z T(t ij )b i +ε ij (1)

[0014] z T (t ij ) is the regression coefficient, which is related to time, b i =[b i,1 ,…,b i,P ] T is the mixing effect of a specific battery cell, is Gaussian observation noise. To simplify the expression, the model is usually expressed in the following matrix form:

[0015]

[0016] in

[0017] The proposed framework attempts to present the relationship between the mixed effect coefficients and the operating factors through mapping; the B-spline basis function is used to approximate the mapping, and the natural cubic spline is selected as the basis function, that is, the basis function is a cubic spline.

[0018] Preferably, let K be a non-negative integer, Γ={γ0≤γ1≤…≤γ K-1} is an ordered set of K nodes. If k = 0, then Assume {ψ i,k,d (x), k=0,…,K+d} is a d-order basic function, then the 0-order B-spline linear basis function associated with the node Γ is defined as follows:

[0019]

[0020] Among them I (·) Represents the indicator function, and the inductive formula of the B-spline function of order 1≤d≤K is:

[0021]

[0022] The corresponding basis function is in the case of a B-spline curve of order 3, omitting the second subscript d representing the order and returning to the approximate b i , is the b of battery unit i i One of the dimensions, b i,p , where p∈{1,…,P}, in the framework of spline basis functions, for the p-dimensionality of unit i, it is expressed as:

[0023] b i,p =Ψ(x i ) T θ p , (5)

[0024] where θp =[θ p,0 ,θ p,1 ,…,θ p,K+3 ] T is the coefficient of the spline basis function, on this basis, using the operating factor x i Approximate calculation b for battery unit i i ,Right now:

[0025]

[0026] in is the Kronecker product, Use Φ(x i ) T It means that, therefore b i Written

[0027] b i =Φ(x i ) T θ (7)

[0028] Taking into account the mixed effect coefficient b i Assuming that θ also follows iid, it is defined as θ~N(μ θ ,∑ θ ),in:

[0029]

[0030] Mixed effect coefficient b i The prior distribution of follows the multivariate normal distribution, which is E(b i )=Φ(x i ) T μ θ The variance is Cov(b i ,b i )=K(x i ,x i )=Φ(x i ) T ∑ θ Φ(x i )), that is, b i ~MVN(Φ(x i ) T μ θ ,Φ(x i ) T Σ θ Φ(x i )), for any two units i,j∈{1,…,N}, the mixed effect coefficient b i and b j The covariance between them is given by Cov(b i ,b j)=K(x i ,x j ) is obtained, and the relationship between any two lithium-ion batteries is established. Two lithium-ion batteries with similar operating factors will be assigned a larger covariance, which will eventually lead to a similar degradation process.

[0031] Preferably, let b(x) = [b1(x),…,b P (x)] T , construct the b(x) covariance matrix of any x and x′ as follows:

[0032]

[0033] For each component of K(x,x′), Cov(b p (x),b q (x′)), we have:

[0034]

[0035] in, Yes θ The elements of the p-th row and q-th column of . Due to this framework, the degradation signal collected by the sensor from a single lithium-ion battery contains not only information reflecting the health status of the lithium-ion battery itself, but also information that can be shared with other lithium-ion batteries.

[0036] The complete model is represented as follows:

[0037]

[0038] Preferably, the specific operations of respectively estimating the coefficients of the noise and the spline basis function include:

[0039] Estimated noise and the coefficients θ of the spline basis function Ω θ ={μ θ ,∑ θ};

[0040] For the entire degradation signal of all battery cells, it is packaged as The design matrix is ​​therefore:

[0041]

[0042] is all errors;

[0043] set up are all mixed effect coefficients, The operating factor for all lithium-ion batteries is:

[0044]

[0045] and

[0046]

[0047] For formula (13), it contains the similarity information between any two lithium-ion batteries and makes it possible to jointly model the entire population to achieve information sharing. Now, formula (2) is further written as:

[0048] Y=Zb+ε (15)

[0049] Since b~MVN(Φ(X) T M,K(X,X)),Y also obey the multivariate normal distribution, that is,

[0050]

[0051] in is the identity matrix;

[0052] To estimate the unknown parameters in formula (15), the maximum likelihood estimation (MLE) method is used, that is,

[0053]

[0054] where logL p (Y|Ω ε ,Ω θ )=-(1 / 2)log|ZK(X,X)Z T +∑ ε |-(1 / 2)(Y-ZΨ(X) T M) T (ZK(X,X)Z T +∑ ε ) -1 (Y-ZΨ(X) T M).

[0055] Preferably, the specific operations of updating the parameters include:

[0056] Using all existing data from all batteries for updating without using any new sensor measurement data, after parameter estimation, we get the prior distribution b~MVN(Φ(X)TM,K(X,X)), and then we need to get the posterior distribution b|Y, considering Y|b~MVN(Zb,∑ ε ), according to Bayes' theorem, we get:

[0057]

[0058]

[0059] use and represents the posterior mean and covariance, that is, Its expression is:

[0060]

[0061] It should be noted that it is also possible to obtain the posterior distribution of any lithium-ion battery, rather than the posterior distribution of the entire population, and obtain the b of battery cell r r The posterior distribution is:

[0062]

[0063] in, yes The rth subvector of yes The r-th diagonal submatrix of .

[0064] Preferably, the specific operations of updating the parameters include:

[0065] Updated with newly collected measurement data,Online monitoring and evaluation are very important for battery applications. During the use of the battery, the sensor will provide direct degradation information. Assuming that there are some newly collected measurements to further update the posterior distribution of b, represents the new measurement from unit p, where is the collected time point. Similarly, the update formula of the posterior distribution is:

[0066]

[0067] and The posterior mean and covariance of are expressed as Its expression can be derived according to formula (19):

[0068]

[0069] in is the error matrix of unit p,

[0070] There are elements All other elements are equal to 0, that is Given the similarity with the previous content, the proof is omitted. This part applies to online updates, which are different from holistic updates using existing data; when new measurements are obtained from units, this information acts on the entire population, thereby updating the posterior distribution of p for the unit, rather than just updating the posterior distribution of p for the unit in existing methods.

[0071] Preferably, the specific operations of updating the parameters include:

[0072] Introducing the "zero sample" evaluation, the so-called "zero sample" refers to the target battery In the absence of any collected measurement data, i.e. It is newly operated under specific operating conditions, that is, its operating factor is x j , which is a long-term challenge faced by existing research. This means that it can not only achieve the purpose of early prediction, but also adapt to the situation where the operating factors are different from any battery in history. In the proposed transfer learning framework, how to use the information of other batteries to make up for the deficiency of target battery data j and update b j This is the key point. For the "zero sample" battery j, the mixed effect coefficient b j , given the Gaussian distribution of all historical batteries {1,…,N}:

[0073]

[0074] Where K(x j ,X)=(K(x j ,x1),…,K(x j ,x N )), according to Bayes’ theorem, the conditional distribution is p(b j |b)=p(b j ,b) / p(b), so we have in:

[0075]

[0076] Considering the marginal distribution b j |Y is:

[0077] p(b j |Y)=∫p(b j ,b|Y)db

[0078] =∫p(b j |b,Y)p(b|y)db,

[0079] =∫p(b j |b)p(b|Y)db (25)

[0080] And formula (19) and (24), we can further conclude that in:

[0081]

[0082] On the other hand, if we do not transfer the information of other lithium-ion batteries, b j Its variance will be K(xj ,x j ). Considering:

[0083]

[0084] This means that the matrix It is a positive semi-finite matrix. After information transmission, the matrix variance will decrease, that is, it will become more accurate.

[0085] Preferably, the specific operation of battery SOH prediction includes:

[0086] The estimated time distribution of the future degradation state of a battery r∈{1,…,N} can be written as:

[0087] c r (t) = z T (t)b r (28)

[0088] On the other hand, according to formula (20), we get b r The posterior distribution of b r |Y, so we further deduce:

[0089]

[0090] Compared with the prior art, the present invention has the following beneficial effects:

[0091] The lithium-ion battery health status assessment method based on individual characteristics proposed in this invention models the degradation process through operating factors. This approach is different from the traditional degradation model, which only considers the overall behavior between batteries and ignores individual differences. By utilizing operating factors, the model can more accurately capture the unique degradation path of each battery, thereby improving the accuracy and stability of the prediction.

[0092] Using B-splines and constructing a covariance matrix to model the similarities between units allows information to be effectively transferred between different battery units. This means that even if the degradation signal of some battery units is incomplete, the model can still use the signals of other similar battery units to reduce prediction uncertainty.

[0093] In the face of zero-sample problems (new battery units with no degradation data), reasonable predictions can be made by relying only on operational factor information. In addition, the method can update degradation predictions in real time to adapt to scenarios where signals are collected gradually. This flexibility makes the model not only suitable for situations with abundant existing data, but also provides effective predictions when data is insufficient. BRIEF DESCRIPTION OF THE DRAWINGS

[0094] Figure 1 This is a schematic diagram of the lithium battery SOH prediction framework of the present invention;

[0095] Figure 2 Schematic diagram of SOH degradation paths of some lithium-ion batteries at different temperatures in data set A of the present invention;

[0096] Figure 3 The present invention uses different available data to estimate the SOH of related lithium-ion batteries and a schematic diagram of the error;

[0097] Figure 4 It is a schematic diagram of the results of different usable ratios of A121 and A58 of the present invention;

[0098] Figure 5 Schematic diagram of estimation errors (RMSE and MAE) of the long short-term memory (LSTM), gated recurrent unit (GRU), traditional MEM and the proposed method at different “available scales”;

[0099] Figure 6 It is a schematic diagram of the estimation result after the increase of available data for each test unit of the present invention;

[0100] Figure 7 It is a schematic diagram of the results of A41 and A82 under the zero sample condition of the present invention. DETAILED DESCRIPTION

[0101] In order to make the purpose and technical solution of the present invention clearly and completely described, and the advantages more clearly understood, the embodiments of the present invention are further described in detail with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are part of the embodiments of the present invention, rather than all of the embodiments, and are only used to explain the embodiments of the present invention, and are not used to limit the embodiments of the present invention. All other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0102] Embodiment 1, refer to the attached Figure 1 , the present invention provides a technical solution: Figure 1The proposed SOH prediction framework for lithium batteries is presented. The framework is divided into four key parts: degradation modeling, parameter estimation, parameter updating, and SOH prediction. Specifically, in the degradation modeling stage, after inputting historical data, two main tasks are performed: similarity modeling and mapping construction. Considering that operating factors affect the degradation trajectory of batteries and reflect the uniqueness of each battery, we use operating factors to quantify the similarity between any two batteries and construct a large covariance matrix containing the similarity information of any two batteries. Based on this matrix, the degradation signal collected from one battery can be shared in a heterogeneous group. In the process of mapping, B-spline basis functions are used to approximate the relationship between operating factors and mixed effects. Then they are integrated into MEM to form an extended mixed effect model. In terms of parameter estimation, the maximum likelihood estimation method (MLE) is used to estimate unknown parameters. In the parameter updating stage, the application scenario is first determined based on the existing information to select a suitable strategy. The estimation results are then treated as prior information and updated using the Bayesian inference method under the transfer learning framework to obtain the posterior distribution. Finally, the posterior distribution is used to predict the SOH of one or more batteries.

[0103] The data comes from the dataset publicly available by Diao et al. of the Center for Advanced Life Cycle Engineering (CALCE). It is named Dataset A here. Dataset A contains data from 192 batteries with four different ambient temperatures (10°C, 25°C, 45°C, and 60°C), two different charge cutoff rates (C / 5 and C / 40), and three different discharge rates (0.7, 1, and 2C), so there are 24 batches corresponding to these design factors, each with 8 batteries. The batteries used are pouch batteries with a nominal capacity of 3.36Ah. The maximum number of cycles is 800, with every 50 cycles being a controlled cycle. It is worth noting that for some unknown reasons, only the first 3 batteries are available under the two conditions of an ambient temperature of 60°C and a discharge C rate of 2C, so a total of 182 batteries are available. The cycle test matrix is ​​shown in Table 1.

[0104] Table 1. Cyclic test table of dataset A.

[0105]

[0106] Figure 2 The SOH degradation paths of some lithium-ion batteries in dataset A at different temperatures are shown, where C cut is the charge cut-off rate, C dischDischarge rate. Generally speaking, in the battery manufacturing industry, when the battery capacity decays to the initial capacity, it is considered to have reached the end of life (EOL). Therefore, the figure only uses data from the initial state to when the battery capacity drops to 80% of the initial value.

[0107] We calculate the mean absolute error (MAE) and root mean square error (RMSE) to evaluate the overall estimation error, which are defined as

[0108]

[0109] in, is the observed value, x j is the corresponding estimation result, and n is the number of samples.

[0110] Embodiment 2, based on embodiment 1, proposes scenario 1: batch update.

[0111] In scenario one, we randomly select 4 batteries from each batch of batteries in Table 1, except for groups and groups with only 3 batteries and fewer observation points. Therefore, there are 22 small groups and 88 lithium-ion batteries in total. Then, two individuals are randomly selected from each group as training units, and the remaining individuals are test units. In scenario one, the training unit is a historical battery group with fully available data, while the test unit is an in-service battery group with data available before some random points.

[0112] The term "usable fraction" is used to denote these points, representing the amount of time that a product will take to reach its end of life (EOL).

[0113] The amount of observations accumulated previously, so the increase in proportion reflects the fact that more observations are collected over time. For example, "30% available" means that only the first 30% of the degradation signals were observed for each test unit. Each test selected from each batch of tests is repeated 100 times. Figure 3 The SOH estimation results and errors for relevant lithium-ion batteries using different available data are shown. Figure 3 (ac) compare the estimated results with the ground truth, Figure 3 (d) shows the distribution of the corresponding errors intuitively. It should be noted that the numbers shown here only represent the root mean square error of the error; the corresponding results of MAE can be found in the following Figure 7 It can be seen that as the available battery data increases, the average error gradually decreases (from 0.02709 to 0.0128). Figure 3 As shown in (ac), as the “available ratio” increases, the corresponding blue ball shows a trend of moving closer to the zero error black line. In the early stage, that is, when the “available ratio is 30%”, the proposed method shows high accuracy in SOH estimation, with an error rate of less than 3% on the used dataset. Figure 4 Results for A121 and A58 are shown for different available ratios. Figure 3 (ac) is similar, Figure 4 In the above figure, as the available proportion increases, the predicted value approaches the true value, the error gradually decreases, and the confidence interval narrows.

[0114] Figure 5 (ab) show the estimation errors (RMSE and MAE) of Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), traditional MEM and the proposed method at different “available scales”. It can be seen that the proposed method can provide more accurate and stable SOH estimation results compared with other methods. Figure 6 It is also shown that in all methods, the estimation results improve with the increase in the available proportion, i.e., the increase in the data available per test unit. Figure 5 It shows the superiority of the proposed method.

[0115] Table 2 lists the computational costs of using the proposed method and the baseline method. The number of training units and test units is fixed to 44 and 44 respectively, and the available ratio is set to 30%. All models are tested using an Intel Core i5-13600KF CPU 3.50 GHz and 32 GB memory.

[0116] The test was repeated 20 times. The results are shown in Table 5. The proposed method takes the least time to estimate the 44 tested Li-ion batteries, which is about 0.005 seconds. This result shows that the batch update feature of the proposed method can estimate SOH more effectively and quickly. It is worth noting that compared with the traditional MEM, the proposed method is not only faster, but also able to update the entire tested Li-ion battery at the same time, which is completely different from the one-by-one update method adopted by the traditional MEM.

[0117] Table 2. Average computational cost of different methods

[0118]

[0119] Embodiment 3, based on embodiment 2, proposes partial battery update and its impact on the group.

[0120] In this section, unlike scenario 1, we will simulate the situation where only some of the Li-ion batteries get new measurements. This will allow us to explore the SOH estimation behavior of different methods. It highlights the benefits of establishing similarities between Li-ion batteries, especially when comparing Li-ion batteries that get new information and Li-ion batteries that don't. We randomly select two individuals from each group in dataset A as training units, the rest as test units, and set the available proportion of all test units to 30%. Next, we assume that one of the test units collects new signals, that is, its available proportion increases, and we call this Li-ion battery the Li-ion battery of interest. Then, we update the SOH prediction value based on the new measurement results. This case study is also repeated 100 times. Figure 7 The results are shown. First, in the horizontal view, Figure 6 (ac) show the results for the relevant lithium-ion battery, while Figure 6 (de) shows the results for the Li-ion batteries without new information. It can be seen that both the proposed method and the conventional MEM are able to update the SOH estimates for the Li-ion batteries with new information. Moreover, the estimation error decreases as the proportion of available data increases. However, for the Li-ion batteries without new information, only the proposed method is able to reduce the prediction errors for these Li-ion batteries. Figure 6 (a) and (d) illustrate the results of the relevant lithium-ion battery and the lithium-ion battery without new information after using 30% of the available ratio, respectively. It is worth noting that Figure 6 (a) and (b) only depict the results of a single Li-ion cell for both the proposed method and the conventional MEM method. Figure 6 (b) and (e) show the results of the relevant lithium-ion battery and the lithium-ion battery without new information, respectively, as the available ratio increases. Figure 6 (ab) and (de) reflect a dynamic process, indicating that for the proposed method, some Li-ion batteries (Li-ion battery s) with new information can not only update their or their posterior SOH estimates, but also affect the estimates of other Li-ion battery s.

[0121] Embodiment 4, based on embodiment 3, proposes scenario 3: zero sample situation.

[0122] We can assume that there is no degradation information for the test lithium-ion batteries, i.e., the usable ratio is 0%, and we only know their operating factors. We randomly select the test lithium-ion batteries. Table 6 lists the MAE results of the proposed method and the traditional MEM.

[0123] For MEM, since there is no signal of the test Li-ion battery, only the prior distribution obtained from the training Li-ion battery is used to estimate the mixed effect. As shown in Table 3, the error of the proposed method is lower than that of the traditional MEM method. In addition, Table 3 also shows that the estimation results of both methods improve as the number of training Li-ion batteries increases. Although the number of training Li-ion batteries increases, the accuracy of the traditional MEM is still lower than that of the proposed method. This is because the accuracy of the traditional MEM depends on the similarity between the test Li-ion battery and the training Li-ion battery.

[0124] Table 3. Average MAE error in zero-shot case

[0125]

[0126] Figure 7 The results of A41 and A82 in the zero-sample case are shown. It can be seen that the result of A41 is of a high level: the degradation trend is accurate and the 95% CI covers the true line. However, the situation of A82 is different: there is a distance between the predicted value and the true value, and the 95% CI cannot cover the true line. This is normal because the working state of the battery itself is affected by many factors, which are difficult to fully take into account, and this prediction is still made in the zero-sample case. We believe that despite the existence of A82, the proposed method is still of reference value when predicting the zero-sample case and has a relatively high estimation level.

[0127] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for assessing the health status of lithium-ion batteries based on individual characteristics, characterized in that: The method comprises the following steps: A lithium-ion battery degradation modeling framework is proposed, which uses B-spline basis functions to map the relationship between operating factors and mixed effects, and establishes a large covariance matrix model; Estimate the coefficients of noise and spline basis functions respectively; According to Bayes' theorem, different parameter updating strategies are proposed for different situations; Predict the battery's SOH.

2. The method for evaluating the health status of a lithium-ion battery based on individual characteristics according to claim 1, characterized in that: The specific operations of the proposed lithium-ion battery degradation modeling framework include: Assume that there are N batteries with the same degradation pattern in the historical data set. For battery cell i∈{1,…,N}, at time t ij The degradation signal is y ij , where j = 1,…,n i is the observation time index, and the operating factor of battery cell i is In other words, s is the number of operating factors for each battery cell. Without considering generality, y ij The mixed effects model is written as: y ij =z T (t ij )b i +ε ij (1) z T (t ij ) is the regression coefficient, which is related to time, b i =[b i,1 ,…,b i,P ] T is the mixing effect of a specific battery cell, is Gaussian observation noise. To simplify the expression, the model is usually expressed in the following matrix form: in The proposed framework attempts to present the relationship between the mixed effect coefficients and the operating factors through mapping; the B-spline basis function is used to approximate the mapping, and the natural cubic spline is selected as the basis function, that is, the basis function is a cubic spline.

3. The method for evaluating the health status of a lithium-ion battery based on individual characteristics according to claim 2, characterized in that: Let K be a non-negative integer, Γ={γ0≤γ1≤…≤γ K-1 } is an ordered set of K nodes. If k = 0, then Assume {ψ i,k,d (x), k=0,…,K+d} is a d-order basic function, then the 0-order B-spline linear basis function associated with the node Γ is defined as follows: Among them I (·) Represents the indicator function, and the inductive formula of the B-spline function of order 1≤d≤K is: The corresponding basis function is in the case of a B-spline curve of order 3, omitting the second subscript d representing the order and returning to the approximate b i , is the b of battery unit i i One of the dimensions, b i,p , where p∈{1,…,P}, in the framework of spline basis functions, for the p-dimensionality of unit i, it is expressed as: b i,p =Ψ(x i ) T θ p , (5) where θ p =[θ p,0 ,θ p,1 ,…,θ p,K+3 ] T is the coefficient of the spline basis function, on this basis, using the operating factor x i Approximate calculation b for battery unit i i ,Right now: in is the Kronecker product, Use Φ(x i ) T It means that, therefore b i Written b i =Φ(x i ) T θ (7) Taking into account the mixed effect coefficient b i Assumption, θ also follows iid, which is defined as θ~N(μ θ ,∑ θ ),in: Mixed effect coefficient b i The prior distribution of follows the multivariate normal distribution, which is E(b i )=Φ(x i ) T μ θ The variance is Cov(b i ,b i )=K(x i ,x i )=Φ(x i ) T ∑ θ Φ(x i )), that is, b i ~ MVN(Φ(x i ) T μ θ ,Φ(x i ) T ∑ θ Φ(x i )), for any two units i,j∈{1,…,N}, the mixed effect coefficient b i and b j The covariance between them is given by Cov(b i ,b j )=K(x i ,x j ) is obtained, and the relationship between any two lithium-ion batteries is established. Two lithium-ion batteries with similar operating factors will be assigned a larger covariance, which will eventually lead to a similar degradation process.

4. The method for assessing the health status of a lithium-ion battery based on individual characteristics according to claim 3, characterized in that: Let b(x)=[b1(x),…,b P (x)] T , construct the b(x) covariance matrix of any x and x′ as follows: For each component of K(x,x′), Cov(b p (x),b q (x′)), we have: in, Yes θ The elements of the p-th row and q-th column of . Due to this framework, the degradation signal collected by the sensor from a single lithium-ion battery contains not only information reflecting the health status of the lithium-ion battery itself, but also information that can be shared with other lithium-ion batteries. The complete model is represented as follows:

5. The method for assessing the health status of a lithium-ion battery based on individual characteristics according to claim 4, characterized in that: The specific operations for estimating the coefficients of the noise and spline basis functions include: Estimated noise and the coefficients θ of the spline basis function Ω θ ={μθ,∑ θ }; For the entire degradation signal of all battery cells, it is packaged as The design matrix is ​​therefore: is all errors; set up are all mixed effect coefficients, is the operating factor of all lithium-ion batteries, denoted as: and For formula (13), it contains the similarity information between any two lithium-ion batteries and makes it possible to jointly model the entire population to achieve information sharing. Now, formula (2) is further written as: Y=Zb+ε (15) Since b~MVN(Φ(X) T M,K(X,X)),Y also obey the multivariate normal distribution, that is, in is the identity matrix; To estimate the unknown parameters in formula (15), the maximum likelihood estimation (MLE) method is used, that is, in logL p (Y|Ω ε ,Ω θ )=-(1 / 2)log|ZK(X,X)Z T +∑ ε |-(1 / 2)(Y-ZΨ(X) T M) T (ZK(X,X)Z T +∑ ε ) -1 (Y-ZΨ(X) T M)。 6. The method for assessing the health status of a lithium-ion battery based on individual characteristics according to claim 5, characterized in that: The specific operations of parameter update include: Using all existing data from all batteries for updating without using any new sensor measurement data, after parameter estimation, we get the prior distribution b~MVN(Φ(X) T M, K(X, X)), and then we need to get the posterior distribution b|Y, considering Y|b~MVN(Zb,∑ ε ), according to Bayes' theorem, we get: p(b|Y)∝p(Y|b)p(b) use and represents the posterior mean and covariance, that is, Its expression is: It should be noted that it is also possible to obtain the posterior distribution of any lithium-ion battery, rather than the posterior distribution of the entire population, and obtain the b of battery cell r r The posterior distribution is: in, yes The rth subvector of yes The r-th diagonal submatrix of .

7. The method for evaluating the health status of a lithium-ion battery based on individual characteristics according to claim 5, characterized in that: The specific operations of parameter update include: Updated with newly collected measurement data,Online monitoring and evaluation are very important for battery applications. During the use of the battery, the sensor will provide direct degradation information. Assuming that there are some newly collected measurements to further update the posterior distribution of b, represents the new measurement from unit p, where is the collected time point. Similarly, the update formula of the posterior distribution is: and The posterior mean and covariance of are expressed as Its expression can be derived according to formula (19): in is the error matrix of unit p, It has elements All other elements are equal to 0, that is Given the similarity with the previous content, the proof is omitted. This part applies to online updates, which are different from the overall update using existing data; when new measurements are obtained from units, this information acts on the entire population, thereby updating the posterior distribution of p for the unit, rather than just updating the unit in existing methods. p The posterior distribution of .

8. The method for evaluating the health status of a lithium-ion battery based on individual characteristics according to claim 5, characterized in that: The specific operations of parameter update include: Introducing the "zero sample" evaluation, the so-called "zero sample" refers to the target battery In the absence of any collected measurement data, i.e. It is newly operated under specific operating conditions, that is, its operating factor is x j , which is a long-term challenge faced by existing research. This means that it can not only achieve the purpose of early prediction, but also adapt to the situation where the operating factors are different from any battery in history. In the proposed transfer learning framework, how to use the information of other batteries to make up for the deficiency of target battery data j and update b j This is the key point, for the "zero sample" battery j the mixed effect coefficient b j , given the Gaussian distribution of all historical batteries {1,…,N}: Where K(x j ,X)=(K(x j ,x1),…,K(x j ,x N )), according to Bayes’ theorem, the conditional distribution is p(b j |b)=p(b j ,b) / p(b), so we have in: Considering the marginal distribution b j |Y is: And formula (19) and (24), we can further conclude that in: On the other hand, if we do not transfer the information of other lithium-ion batteries, b j Its variance will be K(x j ,x j ), taking into account: This means that the matrix It is a positive semi-finite matrix. After information transmission, the matrix variance will decrease, that is, it will become more accurate.

9. The method for evaluating the health status of a lithium-ion battery based on individual characteristics according to claim 6, characterized in that: The specific operations of battery SOH prediction include: The estimated time distribution of the future degradation state of a battery r∈{1,…,N} can be written as: c r (t) = z T (t)b r (28) On the other hand, according to formula (20), we get b r The posterior distribution of b r |Y, so we further deduce:

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