A lithium battery residual life prediction method based on a multi-stage wiener process

Abstract

The application discloses a lithium battery residual life prediction method based on a multi-stage Wiener process, relates to the technical field of lithium batteries, and establishes a lithium battery degradation model based on a Wiener process; a degradation state and model parameters are adaptively estimated based on an expectation maximization EM algorithm and a Kalman smoothing method; in order to predict the residual life at the current moment, the degradation state at a change point is considered to be unknown, a probability density function of the residual life is solved, and an estimated value of the residual life is obtained. The application adopts the above lithium battery residual life prediction method based on the multi-stage Wiener process, establishes a multi-stage Wiener process degradation model based on measurement error, solves and simplifies the probability density function of the residual life, and improves the accuracy of lithium battery residual life prediction.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of lithium batteries, in particular to a lithium battery residual life prediction method based on a multi-stage Wiener process. BACKGROUND

[0002] In recent years, new energy has been increasingly valued by various industries with the concept of sustainable development and energy saving and environmental protection. Lithium batteries have been widely used in electronic, automotive, aerospace and other fields due to their recyclability, long service life, strong energy storage performance and other advantages. However, due to the gradual aging of lithium batteries during use, their reliability and safety are reduced, so it is important to accurately predict their remaining service life. Due to changes in internal mechanisms or external working conditions, the degradation trend usually presents a two-stage or even multi-stage degradation process. However, existing methods mostly focus on two-stage degradation processes, and two-stage degradation models still cannot solve degradation problems with multi-stage degradation characteristics, so it is necessary to consider the multi-stage degradation characteristics in the degradation process of lithium batteries. On the other hand, measurement errors cannot be avoided in actual measurement processes, and if they are not considered, the prediction accuracy of the remaining life will be reduced. Therefore, it is necessary to consider both the multi-stage degradation characteristics and the influence of measurement errors. SUMMARY

[0003] The purpose of the present application is to provide a lithium battery residual life prediction method based on a multi-stage Wiener process, which solves the problem of measurement error influence in the lithium battery residual life prediction process.

[0004] To achieve the above-mentioned purpose, the present application provides a lithium battery residual life prediction method based on a multi-stage Wiener process, comprising the following steps:

[0005] Step one, model establishment, based on a single-stage Wiener degradation model, a multi-stage degradation model of lithium batteries with measurement errors is established;

[0006] Step two, parameter estimation, the expectation maximization (EM) algorithm is combined with the Kalman smoothing method to estimate the degradation state and unknown parameters of each stage degradation model;

[0007] Step three, change point transition probability solving, the distribution form of the degradation amount at the change point under the concept of first arrival time is solved;

[0008] Step four, life expression solving, the probability density function of the life is solved;

[0009] Step five, residual life prediction, the residual life probability density function is further approximated and derived to solve the approximate analytical solution without multiple integrals, and the estimated value of the lithium battery residual life is obtained.

[0010] Preferably, the degradation model in step one is:

[0011]

[0012]

[0013] where X(t) and Y(t) represent the true degradation state value and the observation value at time t, respectively, t τi is the ith change point, the model segmentation point, is the degradation value corresponding to the change point , λ i and σ i are the drift coefficient and the diffusion coefficient of each stage, respectively, B(t) represents the standard Brownian motion, υ i represents the measurement error of the ith phase, R n is the variance.

[0014] Preferably, step two comprises the following steps:

[0015] S1, integrating each stage model to further convert into a state space model, the space model is:

[0016]

[0017] where let k represent the kth monitoring time point, x k and y k are the true degradation state value and the observation value,

[0018] S2, based on the EM algorithm, constructing a maximum likelihood function for parameter estimation;

[0019] S3, solving the degradation state by Kalman smoothing algorithm;

[0020] S4, iterating steps S2 and S3 until the convergence criterion is met.

[0021] Preferably, in S2, it is assumed that the degradation state at t τ satisfies normal distribution, the maximum likelihood Q function is:

[0022]

[0023] Preferably, in S3, the degradation state and the variance are represented as:

[0024]

[0025] where m = [τ, τ+1,..., k-1].

[0026] Preferably, in step three, the transition probability at the change point is:

[0027]

[0028] Preferably, the probability density function of the life in step four is as follows:

[0029]

[0030] Wherein, Φ(·) and φ(·) represent the cumulative distribution function and the probability density function of the standard normal distribution, respectively.

[0031] Preferably, when in step five, the probability density function expression is:

[0032]

[0033] Wherein, l k and x k represent the remaining life and the degradation state of the current time t k , y 0:k represents the degradation observation value sequence from 0 to t k , that is, y 0:k =[y0,y1,...y k ], and P kk represent the mean and variance of x k .

[0034] Preferably, when in step five, the density function expression is:

[0035]

[0036] Wherein,

[0037]

[0038] Therefore, the lithium battery remaining life prediction method based on the multi-stage Wiener process has the following beneficial effects:

[0039] (1) The parameter estimation method for simultaneously updating the hidden degradation state and unknown model parameters is proposed, which can describe the individual differences between different lithium batteries, has self-adaptive ability, and can improve the fitting accuracy of the lithium battery degradation trend.

[0040] (2) The multi-stage Wiener process degradation model based on measurement error is established, the probability density function of the remaining life is solved and simplified, and the accuracy of the lithium battery remaining life prediction is improved.

[0041] (3) At the same time, the multi-stage characteristics in the lithium battery degradation process and the influence of measurement error are considered, the shortcomings of inaccurate model description and low prediction accuracy of existing lithium battery residual life prediction technology are solved, and the safety and reliability of lithium battery use are improved.

[0042] The technical solutions of the present application will be further described in detail below with the help of the accompanying drawings and examples. BRIEF DESCRIPTION OF DRAWINGS

[0043] Figure 1 It is a flowchart of the present application scheme;

[0044] Figure 2 It is a lithium battery residual life probability density function diagram of the present application;

[0045] Figure 3 It is a residual life estimation value of the present application;

[0046] Figure 4 It is a residual life absolute error comparison diagram of the present application. DETAILED DESCRIPTION

[0047] The technical solutions of the present application will be further described in detail below with the help of the accompanying drawings and examples.

[0048] Unless otherwise defined, the technical terms or scientific terms used in the present application shall be understood as the usual meaning understood by those skilled in the art to which the present application belongs. The "first", "second" and similar words used in the present application do not represent any order, quantity or importance, but are only used to distinguish different components. "Include" or "contain" and similar words mean that the elements or objects before the word cover the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connected" or "connected" and similar words are not limited to physical or mechanical connection, but can include electrical connection, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to represent relative positional relationship, when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0049] EMBODIMENT

[0050] Please refer to Figures 1-4 The present application provides a lithium battery residual life prediction method based on a multi-stage Wiener process, comprising the following steps:

[0051] Step one, based on the classical single-stage Wiener degradation model, a more general lithium battery multi-stage degradation model with measurement error is established;

[0052] The change point in the degradation process is determined by historical degradation data of the same lithium battery sample, which is used as the segmentation point of different stages, and a multi-stage Wiener process degradation model with measurement error is established for lithium batteries.

[0053]

[0054]

[0055] where X(t) and Y(t) represent the true degradation state value and the observed value at time t respectively, is the i-th change point, i.e., the segmentation point of the model, is the change point corresponding to the degradation value at λ i and σ i are the drift coefficient and the diffusion coefficient of each stage respectively, B(t) represents the standard Brownian motion, and υ i represents the measurement error of the i-th stage. It is assumed that υ i obeys the zero-mean Gaussian distribution with variance R i .

[0056] Step two, based on the proposed degradation model, the expectation maximization (EM) algorithm is combined with the Kalman smoothing method to estimate the degradation state and unknown parameters of each stage degradation model, including the following steps:

[0057] S1, integrate the models of each stage and further convert them into a state space model;

[0058] The expectation maximization (EM) algorithm is combined with the Kalman smoothing method to adaptively update the degradation state and unknown parameters of each stage degradation model.

[0059] First, integrate the models of each stage proposed in step one and further convert them into a state space model as follows:

[0060]

[0061] where k represents the k-th monitoring time point, x k and y k are the true degradation state value and the observed value, the unknown parameters to be solved are represented as

[0062] S2, based on the EM algorithm, construct the maximum likelihood function for parameter estimation;

[0063] Based on the EM algorithm, the maximum likelihood function is constructed for parameter estimation. For simplicity, let θ = [λ, σ 2 , R] represent tτ denotes the initial time point of the current stage. In addition, it is assumed that the degradation state at t τ

[0064] The maximum likelihood Q function is constructed and simplified as follows:

[0065]

[0066] By solving the partial derivatives with respect to P m and a m and setting them to zero, the following equations are obtained:

[0067]

[0068] S3, solving the degradation state by Kalman smoothing algorithm;

[0069] The mean and variance of the degradation state in the above equation are obtained by the Kalman smoothing algorithm. First, introduce the Kalman filter algorithm to recursively estimate the degradation state as follows:

[0070]

[0071] where m and n represent the sampling points and iteration times of the current stage, respectively. The unknown parameters are obtained from the n-1th iteration result of the Q function. Then, introduce the Kalman smoothing algorithm to estimate the degradation state and variance as follows:

[0072]

[0073] where m = [τ, τ+1,..., k-1].

[0074] S4, iterate steps S2 and S3 until the convergence criterion is met;

[0075] By maximizing and iterating the Q function until the convergence criterion is met, the degradation state and model parameters can be adaptively updated.

[0076] Step three, considering the unknown degradation at the change point, solve the distribution form of the degradation at the change point under the concept of first arrival time, that is, the transition probability of the degradation state from the previous change point to the current change point under the condition that the degradation at the change point is less than the failure threshold, which includes the following steps:

[0077] 3.1, solve the transition probability from to under the absorbing boundary ω;

[0078] In the degradation process of lithium batteries, the degradation value at the change point is unknown, therefore, the distribution form of the change point under the concept of first arrival time is solved, that is, the transition probability of the degradation state from the previous change point to the current change point under the condition that the degradation at the change point is less than the failure threshold ω​ transition probability from to

[0079] First consider the transition probability from to , which has the analytical form:

[0080]

[0081] 3.2. Solving the transition probability from to given a degradation state

[0082] When , the transition probability from to is:

[0083]

[0084] 3.3. Solving the transition probability at the change point

[0085] The transition probability at the change point is:

[0086]

[0087] Step 4. According to the theorem that the remaining life of a Wiener process obeys inverse Gaussian distribution, the probability density function of life is obtained.

[0088] Since the life of a Wiener process obeys inverse Gaussian distribution, the probability density function of life under the concept of first passage time is:

[0089]

[0090] where x represents the true degradation value of time t, and Y is the sequence of degradation observations from 0 to t. In addition, for simplicity, it is assumed that X(0) is zero.

[0091] It can be seen that the above formula is a multiple integral, which is too complex to calculate. Therefore, when the failure probability at is small, can be approximated to satisfy Gaussian distribution, where the mean is the variance is and Then, when , the probability density function of life is as follows:

[0092]

[0093] where μ a1 = ω - λ ai , Φ(·) and φ(·) represent the cumulative distribution function and the probability density function of the standard normal distribution, respectively.

[0094] Step five, according to the relationship between the life and the remaining life, the remaining life probability density function is further approximated and derived, and the approximate analytical solution without multiple integrals is solved, and the estimation value of the remaining life of the lithium battery is obtained.

[0095] Based on the relationship between the life and the remaining life, the remaining life probability density function under the concept of first passage time is obtained. For convenience, it is assumed that l k and x k represent the remaining life and the degradation state of the current time t k , respectively. First, the case without change point is discussed, that is, 0 < t k ≤ t τ1 .

[0096] Case 1: 0 ≤ l k + t k ≤ t τ1 . It can be regarded as a single stage degradation, and the remaining life probability density function is only related to the first stage, and the expression has the following form:

[0097]

[0098] where y 0:k represents the degradation observation value sequence from 0 to t k , that is, y 0:k = [y0, y1,... y k ], and P kk represent the mean and variance of x k .

[0099] Case 2: , the probability density function is as follows:

[0100]

[0101] where,

[0102]

[0103] In summary, the remaining life probability density function is obtained when the change point does not appear. If the change point has appeared, it can be regarded as an n-i stage degradation process. That is, it is similar to the remaining life distribution when the change point does not appear. In this way, the remaining life estimation of the lithium battery can be completed.

[0104] Based on the MATLAB tool, the lithium battery dataset of CALCE center of University of Maryland is adopted, the lithium battery capacity degradation data of CS2-37 is selected to estimate the remaining life, and the other three groups of CS2-35, CS2-36 and CS2-38 data are used as training samples. The first change point of CS2-37 is 565 cycles, the second change point is 760 cycles, and the failure threshold is set to 45% of the rated capacity. Figures 2-4 The lithium battery remaining life probability density function, the prediction result and the prediction absolute error schematic diagram provided for the embodiment of the application are provided. Compared with the two-stage prediction method and the single-stage prediction method without considering the measurement error, the applicability and effectiveness of the method for predicting the lithium battery remaining life can be illustrated, and the method has higher prediction accuracy.

[0105] Therefore, the method for predicting the lithium battery remaining life based on the multi-stage Wiener process is adopted, a parameter estimation method for simultaneously updating the hidden degradation state and unknown model parameters is proposed, the individual difference between different lithium batteries can be described, the self-adaptive ability is provided, and the fitting accuracy of the lithium battery degradation trend can be improved. The degradation model based on the multi-stage Wiener process with measurement error is established, the probability density function of the remaining life is solved and simplified, and the accuracy of the lithium battery remaining life prediction is improved. The multi-stage characteristics and the influence of the measurement error in the lithium battery degradation process are considered, the defects of the existing lithium battery remaining life prediction technology, such as inaccurate model description and low prediction accuracy, are solved, and the safety and reliability of the lithium battery use are improved.

[0106] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the application but not to limit it, although the application has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the application can still be modified or replaced by the equivalent, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the application.

Claims

1. A method for predicting the remaining life of a lithium battery based on a multi-stage Wiener process, characterized in that, Comprising the following steps: Step one, model establishment, based on single stage wiener degradation model, establish multi-stage degradation model of lithium battery with measurement error; Step two, parameter estimation, combine expectation maximization (EM) algorithm with Kalman smoothing method to estimate the degradation state and unknown parameters of each stage degradation model; Step three, solving the transition probability of change point, solve the distribution form of degradation at change point under the concept of first passage time; Step four, solving the expression of life, solving the probability density function of life; Step five, residual life prediction, further approximation and derivation of the probability density function of residual life, solving the approximate analytical solution without multiple integrals, getting the estimated value of lithium battery residual life; The degradation model in step one is: ； ； wherein, and respectively represent the true degradation state value and the observed value at time is the change point, model segmentation point, is the degradation value corresponding to the change point , and are respectively the drift coefficient and the diffusion coefficient of each phase, represents the standard Brownian motion, represents the measurement error of the phase, is the variance; Step two includes the following steps: S1, integrate each stage model and further convert it into a state space model, the space model is: ； wherein let denote the monitoring time point, and the real degradation state value and the observation value, ; S2, based on EM algorithm, construct the maximum likelihood function for parameter estimation; S3, solve the degradation state by Kalman smoothing algorithm; S4, iterate steps S2 and S3 until the convergence criterion is met; Transition probabilities at the step three change point are: ； The probability density function of life in step four is as follows: ； wherein , , , , , and denote the cumulative distribution function and the probability density function of the standard normal distribution, respectively. In step five when the probability density function expression is: ； wherein, and represent the remaining lifetime and the degradation state of the current time , and stand for the mean and variance of ; In step five when , the density function expression is ； Where 。 2. The method of claim 1, wherein the method is based on a multi-stage Wiener process. S2 in the assumption degradation state at the time satisfies a normal distribution, The maximum likelihood Q function is: 。 3. The method of claim 2, wherein the method is based on a multi-stage Wiener process. The degradation state and variance in S3 are represented as: ； wherein .

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