Lithium battery residual life prediction method based on multi-stage Wiener process

Abstract

The invention discloses a lithium battery residual life prediction method based on a multi-stage Wiener process, and relates to the technical field of lithium batteries, and the method comprises the steps: building a lithium battery degradation model based on the Wiener process; self-adaptively estimating a degradation state and model parameters based on an expectation maximization (EM) algorithm and a Kalman smoothing method; and in order to predict the residual life at the current moment, considering the condition that the degradation state at the change point is unknown, solving a probability density function of the residual life, and obtaining an estimated value of the residual life. According to the lithium battery residual life prediction method based on the multi-stage Wiener process, the degradation model based on the multi-stage Wiener process with the measurement error is established, the probability density function of the residual life is solved and simplified, and the accuracy of lithium battery residual life prediction is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of lithium batteries, and in particular to a method for predicting the remaining life of a lithium battery based on a multi-stage Wiener process. Background Art

[0002] In recent years, new energy has been increasingly valued by various industries with the proposal of sustainable development and energy conservation and environmental protection concepts. Lithium batteries have been widely used in electronics, automobiles, aerospace and other fields due to their advantages such as recyclability, long life and strong energy storage performance. However, since lithium batteries will gradually age during use, resulting in reduced reliability and safety, it is of great significance to accurately predict their remaining service life. Due to changes in internal mechanisms or external working conditions, their degradation trend usually presents a two-stage or even multi-stage degradation process. However, most of the existing methods focus on the two-stage degradation process, and the two-stage degradation model still cannot solve the degradation problem with multi-stage degradation characteristics. Therefore, it is necessary to consider the multi-stage degradation characteristics of lithium battery degradation process. On the other hand, in the actual measurement process, measurement errors are unavoidable. If they are not taken into account, the prediction accuracy of the remaining life will be reduced. In summary, it is necessary to consider the multi-stage degradation characteristics and the influence of measurement errors at the same time. Summary of the invention

[0003] The purpose of the present invention is to provide a method for predicting the remaining life of a lithium battery based on a multi-stage Wiener process, so as to solve the problem of the influence of measurement errors in the process of predicting the remaining life of a lithium battery.

[0004] To achieve the above object, the present invention provides a method for predicting the remaining life of a lithium battery based on a multi-stage Wiener process, comprising the following steps:

[0005] Step 1: Model establishment: Based on the single-stage Wiener degradation model, a multi-stage degradation model of lithium batteries with measurement errors is established;

[0006] Step 2: Parameter estimation: combining the expectation maximization EM algorithm with the Kalman smoothing method to estimate the degradation state and unknown parameters of the degradation model at each stage;

[0007] Step 3: Solve the probability of change point transfer and solve the distribution form of the degradation amount at the change point under the concept of first arrival time;

[0008] Step 4: Solve the lifespan expression and solve the probability density function of lifespan;

[0009] Step 5: Remaining life prediction: further approximate and derive the remaining life probability density function, solve the approximate analytical solution without multiple integrals, and obtain the estimated value of the remaining life of the lithium battery.

[0010] Preferably, the degradation model in step 1 is:

[0011]

[0012]

[0013] Among them, X(t) and Y(t) represent the actual degradation state value and observed value at time t, respectively. τi is the i-th change point, the model segmentation point, For the change point The corresponding degenerate value at i and σ i are the drift coefficient and diffusion coefficient of each stage, B(t) represents the standard Brownian motion, υ i represents the measurement error of the i-th phase, R n is the variance.

[0014] Preferably, step 2 comprises the following steps:

[0015] S1. Integrate the models of each stage and further transform them into a state space model. The space model is:

[0016]

[0017] In which, let k represent the kth monitoring time point, x k and k are the true degradation state value and the observed value,

[0018] S2. Based on the EM algorithm, the maximum likelihood function is constructed for parameter estimation;

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

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

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

[0022]

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

[0024]

[0025] Among them, m=[τ,τ+1,...,k-1].

[0026] Preferably, the change point in step 3 The transition probability at is:

[0027]

[0028] Preferably, the probability density function of the life span in step 4 is as follows:

[0029]

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

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

[0032]

[0033] Among them, l k and x k Respectively represent the current time t k The remaining life and degradation state of 0:k Represents from 0 to t k The degenerate observation sequence of y 0:k =[y0,y1,...y k ], and P kk Represents x k The mean and variance of .

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

[0035]

[0036] in,

[0037]

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

[0039] (1) The present invention proposes a parameter estimation method for simultaneously updating hidden degradation states and unknown model parameters, which can describe the individual differences between different lithium batteries, has adaptive capabilities, and can improve the fitting accuracy of lithium battery degradation trends.

[0040] (2) The present invention establishes a multi-stage Wiener process degradation model with measurement errors, solves and simplifies the probability density function of the remaining life, and improves the accuracy of the remaining life prediction of the lithium battery.

[0041] (3) The multi-stage characteristics of the lithium battery degradation process and the influence of measurement errors are taken into account at the same time, which solves the shortcomings of the existing lithium battery remaining life prediction technology model, such as inaccurate description and low prediction accuracy, and is conducive to improving the safety and reliability of lithium battery use.

[0042] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 It is a schematic diagram of the process flow of the present invention;

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

[0045] Figure 3 is the estimated value of the remaining life of the present invention;

[0046] Figure 4 This is a comparison chart of the absolute error of the remaining life of the present invention. DETAILED DESCRIPTION

[0047] The technical solution of the present invention is further described below through the accompanying drawings and embodiments.

[0048] Unless otherwise defined, the technical terms or scientific terms used in the present invention should be understood by people with ordinary skills in the field to which the present invention belongs. The words "first", "second" and similar words used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. "Include" or "comprise" and similar words mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connect" or "connected" and similar words are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0049] Example

[0050] See also Figure 1-4 The present invention provides a method for predicting the remaining life of a lithium battery based on a multi-stage Wiener process, comprising the following steps:

[0051] Step 1: Based on the classic single-stage Wiener degradation model, a more general multi-stage degradation model of lithium batteries with measurement errors is established;

[0052] The change points in the degradation process are determined through the historical degradation data of similar lithium battery samples, which are used as the segmentation points of different stages to establish a multi-stage Wiener process degradation model of lithium batteries with measurement errors. The constructed model is:

[0053]

[0054]

[0055] Among them, X(t) and Y(t) represent the true degradation state value and observed value at time t, respectively. is the i-th change point, i.e., the model segmentation point, For the change point The corresponding degenerate value at i and σ i are the drift coefficient and diffusion coefficient of each stage, B(t) represents the standard Brownian motion, υ i represents the measurement error of the i-th phase. Assuming υ i Subject to variance R i A zero-mean Gaussian distribution.

[0056] Step 2: 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 the degradation model at each stage, which includes the following steps:

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

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

[0059] First, the models of each stage proposed in step 1 are integrated and further converted into a state space model as shown below:

[0060]

[0061] In which, let k represent the kth monitoring time point, x k and k are the true degradation state value and the observed value, The unknown parameters to be solved are expressed as

[0062] S2. Based on the EM algorithm, the maximum likelihood function is constructed for parameter estimation;

[0063] Based on the EM algorithm, the maximum likelihood function is constructed for parameter estimation. For the sake of simplicity, θ=[λ,σ 2 ,R] represents tτ represents the initial time point of the current stage. In addition, assuming that t τ The degenerate state at satisfies the normal distribution, that is,

[0064] Construct and simplify the maximum likelihood Q function as follows:

[0065]

[0066] By asking about P m and α m The partial derivative of and set to 0, we get the following formula:

[0067]

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

[0069] The mean and variance of the degradation state in the above formula are obtained by the Kalman smoothing algorithm. First, the Kalman filter algorithm is introduced to recursively estimate the degradation state, as shown below:

[0070]

[0071] Where m and n represent the sampling point and iteration number of the current stage respectively. The unknown parameters are obtained from the n-1th iteration result of the Q function. Then, the Kalman smoothing algorithm is introduced to estimate the degradation state and variance, as shown below:

[0072]

[0073] Among them, m=[τ,τ+1,...,k-1].

[0074] S4, iterating 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 can be completed and the model parameters can be adaptively updated.

[0076] Step 3: Considering the unknown degradation amount at the change point, solve the distribution form of the degradation amount 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 amount at the change point is less than the failure threshold, which includes the following steps:

[0077] 3.1. Solve the absorbing boundary ω from Transfer to The transition probability of

[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 degradation state changes from Transfer to The transition probability.

[0079] First, consider the absorbing boundary ω from Transfer to The transition probability of is expressed in analytical form as:

[0080]

[0081] 3.2. Solving for a given degenerate state Down The transition probability of

[0082] When When the degenerate state is given The transition probability is:

[0083]

[0084] 3.3 Solving the change point The transition probability at ;

[0085] Change Point The transition probability at is:

[0086]

[0087] Step 4: According to the inverse Gaussian distribution theorem of the remaining life of the Wiener process, the probability density function of the life is obtained;

[0088] Since the life of the Wiener process follows an inverse Gaussian distribution, the probability density function of the life under the concept of first arrival time is obtained as follows:

[0089]

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

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

[0092]

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

[0094] Step 5. Based on the relationship between life span and remaining life span, the remaining life span probability density function is further approximated and derived to obtain an approximate analytical solution without multiple integrals, thereby obtaining an estimated value of the remaining life span of the lithium battery.

[0095] Based on the relationship between life span and remaining life span, the probability density function of remaining life span under the concept of first arrival time is obtained. For convenience, it is assumed that l k and x k Respectively represent the current time t k First, we discuss the case where there is no change point, 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 from 0 to t k The degenerate observation sequence of y 0:k =[y0,y1,...y k ], and P kk Represents x k The mean and variance of .

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

[0100]

[0101] in,

[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 a ni-stage degradation process. In other words, 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 MATLAB tools, the lithium battery data set of the CALCE Center of the University of Maryland was used to select the lithium battery capacity degradation data of CS2-37 to estimate the remaining life, and the other three groups of CS2-35, CS2-36 and CS2-38 data were used as training samples. The first change point of CS2-37 was 565 cycles, the second change point was 760 cycles, and the failure threshold was set to 45% of the rated capacity. Figure 2-4 The remaining life probability density function, prediction results, and prediction absolute error diagram of lithium batteries provided in the embodiments of the present invention. Comparing this method with the two-stage prediction method and the single-stage prediction method that do not consider the measurement error, it can be shown that the proposed method is applicable and effective for predicting the remaining life of lithium batteries, and this method has a high prediction accuracy.

[0105] Therefore, the present invention adopts the above-mentioned method for predicting the remaining life of lithium batteries based on the multi-stage Wiener process, and proposes a parameter estimation method that simultaneously updates the hidden degradation state and unknown model parameters, which can describe the individual differences between different lithium batteries, has adaptive capabilities, and can improve the fitting accuracy of the degradation trend of lithium batteries. A multi-stage Wiener process degradation model with measurement errors is established, and the probability density function of the remaining life is solved and simplified, thereby improving the accuracy of the prediction of the remaining life of lithium batteries. At the same time, the multi-stage characteristics and measurement errors in the degradation process of lithium batteries are taken into account, which solves the shortcomings of inaccurate model description and low prediction accuracy of the existing lithium battery remaining life prediction technology, and is conducive to improving the safety and reliability of lithium battery use.

[0106] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A method for predicting the remaining life of a lithium battery based on a multi-stage Wiener process, characterized in that: The following steps are involved: Step 1: Model establishment: Based on the single-stage Wiener degradation model, a multi-stage degradation model of lithium batteries with measurement errors is established; Step 2: Parameter estimation: combining the expectation maximization EM algorithm with the Kalman smoothing method to estimate the degradation state and unknown parameters of the degradation model at each stage; Step 3: Solve the probability of change point transfer and solve the distribution form of the degradation amount at the change point under the concept of first arrival time; Step 4: Solve the lifespan expression and solve the probability density function of lifespan; Step 5: Remaining life prediction: further approximate and derive the remaining life probability density function, solve the approximate analytical solution without multiple integrals, and obtain the estimated value of the remaining life of the lithium battery.

2. The method for predicting the remaining life of a lithium battery based on a multi-stage Wiener process according to claim 1, characterized in that: The degradation model in step 1 is: Among them, X(t) and Y(t) represent the true degradation state value and observed value at time t, respectively. is the i-th change point, the model segmentation point, For the change point The corresponding degenerate value at i and σ i are the drift coefficient and diffusion coefficient of each stage, B(t) represents the standard Brownian motion, υ i represents the measurement error of the i-th phase, R n is the variance.

3. The method for predicting the remaining life of a lithium battery based on a multi-stage Wiener process according to claim 2, characterized in that: Step 2 includes the following steps: S1. Integrate the models of each stage and further transform them into a state space model. The space model is: In which, let k represent the kth monitoring time point, x k and k are the true degradation state value and the observed value, S2. Based on the EM algorithm, the maximum likelihood function is constructed for parameter estimation; S3, solving the degradation state by Kalman smoothing algorithm; S4. Iterate steps S2 and S3 until the convergence criterion is met.

4. The method for predicting the remaining life of a lithium battery based on a multi-stage Wiener process according to claim 3, characterized in that: In S2, it is assumed that t τ The degenerate state at satisfies the normal distribution. The maximum likelihood Q function is:

5. The method for predicting the remaining life of a lithium battery based on a multi-stage Wiener process according to claim 4, characterized in that: The state and variance of S3 are expressed as: Among them, m=[τ,τ+1,...,k-1].

6. The method for predicting the remaining life of a lithium battery based on a multi-stage Wiener process according to claim 5, characterized in that: Step 3: Change point The transition probability at is:

7. The method for predicting the remaining life of a lithium battery based on a multi-stage Wiener process according to claim 6, characterized in that: The probability density function of life span in step 4 is as follows: in, μ a1 =ω-λ ai , Φ(·) and φ(·) represent the cumulative distribution function and probability density function of the standard normal distribution, respectively.

8. The method for predicting the remaining life of a lithium battery based on a multi-stage Wiener process according to claim 7, characterized in that: In step five, When , the probability density function expression is: Among them, l k and x k Respectively represent the current time t k The remaining life and degradation state of 0:k Represents from 0 to t k The degenerate observation sequence of y 0:k =[y0,y1,...y k ], and P kk Represents x k The mean and variance of .

9. The method for predicting the remaining life of a lithium battery based on a multi-stage Wiener process according to claim 8, characterized in that: In step five, 1≤i≤n-1), the density function expression is: in

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