Battery life prediction method based on accelerated degradation test data

Abstract

The invention relates to a battery life prediction method based on accelerated degradation test data, and belongs to the field of electric energy storage health management. The method comprises the following steps: based on a Wiener random process, performing performance degradation modeling by using battery performance degradation parameters to determine an accumulative distribution function and a probability density function of battery life; determining the change conditions of diffusion parameters and drift parameters in the model parameters along with the change of the acceleration stress based on an acceleration factor invariant principle; and measuring the total life prediction result of the battery by using the reliability curve and the probability density curve. According to the method, battery performance degradation modeling is carried out on battery performance degradation data under different accelerated stresses through a Wiener random process, and finally, the total life prediction result of the battery under different accelerated stress degradation is obtained.

Description

Technical Field

[0001] The present invention belongs to the field of electric energy storage health management and relates to a battery life prediction method based on accelerated degradation test data. Background Art

[0002] At present, with the increasing global attention to energy conservation, emission reduction and sustainable development, lithium batteries, as important energy storage devices, are increasingly being used. However, the service life of lithium batteries has always been a key factor restricting their development. Accurately predicting the life of lithium batteries is of great significance for reducing operating costs, improving resource utilization, and effectively controlling the recycling of waste batteries.

[0003] Deficiencies of existing technology:

[0004] Most of the existing lithium battery life prediction methods are based on empirical formulas or simple mathematical models, with low prediction accuracy and difficulty in meeting actual application needs.

[0005] Some life prediction methods mainly rely on the actual usage data of the battery, while accelerated degradation test data can provide richer battery degradation information and help improve prediction accuracy.

[0006] Different operating conditions and stress levels can have a significant impact on the battery life, and existing life prediction methods fail to fully consider this factor.

[0007] The purpose of the present invention is to provide a battery life prediction method based on accelerated degradation test data, which can predict the overall life of batteries under different accelerated stresses, improve the prediction accuracy, and provide more reliable data support for battery manufacturers and end users. Summary of the invention

[0008] In view of this, an object of the present invention is to provide a battery life prediction method based on accelerated degradation test data to predict the overall life of batteries under different accelerated stresses.

[0009] In order to achieve the above object, the present invention provides the following technical solutions:

[0010] A battery life prediction method based on accelerated degradation test data, the method comprising the following steps:

[0011] S1: Modeling the battery performance degradation process based on the Wiener stochastic process model;

[0012] S2: Determine the changes of diffusion parameters and drift parameters in the model with different stress changes based on the principle of constant acceleration factor;

[0013] S3: The overall life results of the battery are measured by the battery reliability curve and life probability density curve.

[0014] Furthermore, the said S1 includes:

[0015] S11: Characterization of the Wiener process. The Wiener process has three major characteristics, including:

[0016] The function representing the Wiener process is

[0017] Y(t) = μ·Λ(t) + σ·B(Λ(t))

[0018] In this function, μ represents the drift parameter and is greater than 0, σ represents the diffusion parameter and is also greater than 0, B(·) represents the standard Brownian motion, and the introduced time function Λ(t) satisfies the initial condition Λ(0) = 0;

[0019] (1) Y(t) is continuous at the starting point t = 0 and satisfies the condition Y(0) = 0 with probability 1;

[0020] (2) For any non - negative and successively increasing time points 0 ≤ t1 < t2 ≤ t3 < t4, the increments Y(t2) - Y(t1) and Y(t4) - Y(t3) in the two time periods are statistically independent of each other;

[0021] (3) The independent time - interval increment of the Wiener process ΔY(t) = Y(t + Δt) - Y(t) follows a normal distribution, that is, ΔY(t) ~ N(μΔΛ(t), σ 2 ΔΛ(t)), where ΔΛ(t) = Λ(t + Δt) - Λ(t);

[0022] S12: By continuously accumulating these independent increments, it is deduced that Y(t) ~ N(μΛ(t), σ 2 Λ(t)), and the specific form of the probability density function (PDF) of Y(t) is deduced as:

[0023]

[0024] S13: Set a performance failure threshold D; the service life ξ of the battery is the time point when the performance parameter first touches or exceeds the threshold D, that is, ξ is expressed as the first moment when Y(t) reaches or exceeds D: ξ = inf{t∣Y(t) ≥ D}; the calculation formula for the cumulative distribution function (CDF) of the battery life ξ is:

[0025]

[0026] In the above formula, Φ(·) is the standard normal CDF; the PDF calculation formula of the battery is:

[0027]

[0028] Furthermore, in S2, the accelerated degradation modeling process is divided into:

[0029] S21: Define the acceleration factor, with two different battery stress levels S k and S h , and for each stress level, the performance parameter degradation of the battery follows the above Wiener process degradation model; the battery at stress level S k The cumulative distribution function of the life span is expressed as F k (t k ), F k (t k ) gives the time t when the battery reaches or exceeds the life span at this stress level k probability; at higher stress levels S h Under this condition, the cumulative distribution function of battery life is expressed as F h (t h ), represents the battery under stress level S h The lower lifespan reaches at least time t h probability;

[0030] When F k (t k )=F h (t h ), then the stress S k Equivalent to S h The acceleration factor A k,h Defined as:

[0031] A k,h =t h / t k

[0032] S22: Derivation after the acceleration factor unchanged principle is established. Let the acceleration factor unchanged principle be established, then A k,h Is a non-conformist h , t k Changes, only two stresses S k , S h The determined constants give the following relationship:

[0033] f k (t k )=A k,h f h (t h )

[0034] Let Λ(t) = t, we get

[0035]

[0036] To ensure A k,h Is a non-conformist k The constant of change requires that t k The coefficient term is 0, that is

[0037]

[0038] From the above formula, we can deduce:

[0039]

[0040] By A k,h ≠1, k≠h, we know μ and σ 2 All of them change with the change of stress, that is, it is assumed that the drift parameters and diffusion parameters in the Wiener process model are related to the accelerated stress level of the battery.

[0041] Furthermore, in S3, the overall lifespan prediction is:

[0042] According to the ohmic resistance data of the EIS test of the battery under various stresses, the reliability function is established as follows:

[0043]

[0044] The predicted life probability density curve function is:

[0045]

[0046] The likelihood function used for model parameter estimation is:

[0047]

[0048] The beneficial effects of the present invention are as follows: the present invention provides a battery life prediction method based on accelerated degradation test data, the method includes a detailed description of a life prediction method based on a Wiener process model from the aspect of performance degradation modeling, and the drift parameter and diffusion parameter are proposed to change with the change of stress from the accelerated degradation modeling process. The ohmic resistance obtained by fitting the EIS test data in the characteristic test is used as the performance degradation parameter, a Wiener random process model is established, and the maximum likelihood function estimation is performed through the fmincon function to solve the corresponding model parameter values ​​under different SOC levels under different working conditions. The Wiener random process model is used to determine the reliability evaluation function and the predicted life probability density function as indicators for reliable life prediction, and the reliability curve and probability density curve are drawn for the battery under different working conditions. From the reliability curve, the battery reliability under T35C2 condition is the best, and the battery reliability under T35C4 condition and T25C4 condition is the worst. The reliability curves under each condition are consistent with the actual test results. From the probability density curve of the battery predicted life under each condition, it can be seen that the probability density curves under T35C4, T25C4, and T45C4 conditions reach the maximum probability in the early stage and drop rapidly, indicating that the life of these three conditions is short. The probability density curves of T35C2, T35C1, T35C3, and T45C4 reach the maximum probability in the later stage of the cycle and drop slowly, indicating that the life of these four conditions is longer. All of them are consistent with the test measurement.

[0049] Other advantages, objectives and features of the present invention will be described in the following description to some extent, and to some extent, will be obvious to those skilled in the art based on the following examination and study, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below in conjunction with the accompanying drawings, wherein:

[0051] Figure 1 A framework diagram of the battery life prediction technology based on accelerated degradation test data;

[0052] Figure 2 Reliability curve and life probability density curve at SOC10% level; Figure 2 (a) is the reliability curve; Figure 2 (b) is the life probability density curve;

[0053] Figure 3 Reliability curve and life probability density curve at SOC20% level; Figure 3 (a) is the reliability curve; Figure 3 (b) is the life probability density curve;

[0054] Figure 4 Reliability curve and life probability density curve at SOC40% level; Figure 4 (a) is the reliability curve; Figure 4 (b) is the life probability density curve;

[0055] Figure 5 Reliability curve and life probability density curve at SOC60% level; Figure 5 (a) is the reliability curve; Figure 5 (b) is the life probability density curve;

[0056] Figure 6 Reliability curve and life probability density curve at SOC80% level; Figure 6 (a) is the reliability curve; Figure 6 (b) is the life probability density curve;

[0057] Figure 7 Reliability curve and life probability density curve at SOC100% level; Figure 7 (a) is the reliability curve; Figure 7 (b) is the life probability density curve. DETAILED DESCRIPTION

[0058] The following describes the embodiments of the present invention by specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments only illustrate the basic concept of the present invention in a schematic manner, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0059] Among them, the drawings are only used for illustrative explanations, and they only represent schematic diagrams rather than actual pictures, and should not be understood as limitations on the present invention. In order to better illustrate the embodiments of the present invention, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the size of actual products. For those skilled in the art, it is understandable that some well-known structures and their descriptions in the drawings may be omitted.

[0060] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components; in the description of the present invention, it should be understood that if there are terms such as "upper", "lower", "left", "right", "front", "rear", etc. indicating the orientation or positional relationship, they are based on the orientation or positional relationship shown in the accompanying drawings. This is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, the terms describing the positional relationship in the accompanying drawings are only for illustrative purposes and should not be construed as a limitation of the present invention. For those of ordinary skill in the art, the specific meanings of the above terms can be understood according to specific circumstances.

[0061] As Figure 1 shown, the battery life prediction method based on accelerated degradation test data provided in the embodiments of the present application includes:

[0062] S1: Perform battery performance degradation modeling on the degradation process of battery performance parameters based on the Wiener random process model.

[0063] S2: Determine the variation of the diffusion parameter and the drift parameter in the model with different stresses based on the principle of constant acceleration factor.

[0064] S3: Measure the overall life result of the battery with the reliability curve and the life probability density curve of the battery.

[0065] Further, the S1 includes:

[0066] S11: Characteristic description of the Wiener process. The Wiener process has three major characteristics, including:

[0067] The function representing the Wiener process is

[0068] Y(t) = μ·Λ(t) + σ·B(Λ(t))

[0069] In this function, μ represents the drift parameter and is greater than 0, σ represents the diffusion parameter and is also greater than 0, and B(·) represents the standard Brownian motion. At the same time, the introduced time function Λ(t) satisfies the initial condition Λ(0) = 0.

[0070] (1) Y(t) is continuous at the starting point t = 0 and satisfies the condition Y(0) = 0 with probability 1;

[0071] (2) For any non - negative and successively increasing time points 0 ≤ t1 < t2 ≤ t3 < t4, the increments Y(t2) - Y(t1) and Y(t4) - Y(t3) in the two time periods are statistically independent of each other;

[0072] (3) The independent time interval increment of the Wiener process ΔY(t) = Y(t+Δt)-Y(t) obeys the normal distribution, that is, ΔY(t)~N(μΔΛ(t),σ 2 ΔΛ(t)), where ΔΛ(t)=Λ(t+Δt)-Λ(t).

[0073] S12: By continuously accumulating these independent increments, we can deduce Y(t)~N(μΛ(t),σ 2 Λ(t)), from which the specific form of the probability density function (Probability Density Function, PDF) of Y(t) is further deduced as:

[0074]

[0075] S13: Set a performance failure threshold D. The battery life ξ can be understood as the time point required for the performance parameter to reach or exceed the threshold D for the first time, that is, ξ is expressed as the first moment that makes Y(t) reach or exceed D: ξ=inf{t|Y(t)≥D}. The cumulative distribution function (CDF) of battery life ξ is calculated as:

[0076]

[0077] In the above formula, Φ(·) is the standard normal CDF. The PDF calculation formula for the battery is:

[0078]

[0079] Furthermore, S2 divides the accelerated degradation modeling process into:

[0080] S21: Define the acceleration factor, assuming there are two different battery stress levels S k and S h , and for each stress level, the performance parameter degradation of the battery follows the above Wiener process degradation model. Correspondingly, the battery at stress level S k The cumulative distribution function of the life span is expressed as F k (t k ), that is, F k (t k ) gives the time t when the battery reaches or exceeds the life span at this stress level k Similarly, at higher stress levels S h Under this condition, the cumulative distribution function of battery life is expressed as F h (t h ), which represents the battery under stress level S hThe lower lifespan reaches at least time t h probability.

[0081] when

[0082] F k (t k )=F h (t h )

[0083] When k Equivalent to S h The acceleration factor A k,h Defined as

[0084] A k,h =t h / t k

[0085] S22: Derivation after the acceleration factor unchanged principle is established. Let the acceleration factor unchanged principle be established, then A k,h It should be a non-conventional h , t k Changes, only two stresses S k , S h The constant determined by . The relationship is:

[0086] f k (t k )=A k,h f h (t h )

[0087] Let Λ(t) = t, we get

[0088]

[0089] To ensure A k,h Is a non-conformist k The constant of change requires that t k The coefficient term is 0, that is

[0090]

[0091] From the above formula, we can deduce

[0092]

[0093] By A k,h ≠1(k≠h) we know μ and σ 2 All of them change with the change of stress, that is, it is assumed that the drift parameters and diffusion parameters in the Wiener process model are related to the accelerated stress level of the battery.

[0094] Furthermore, the overall life prediction result of S3 is:

[0095] According to the ohmic resistance data of the EIS test of the battery under various stresses, the reliability function is established as follows:

[0096]

[0097] The predicted life probability density curve function is:

[0098]

[0099] The likelihood function used for model parameter estimation is:

[0100]

[0101] The reliability curve shows the corresponding relationship between the battery's service life and reliability under different working conditions; the life probability density curve shows the probability of battery failure per unit time near a specific life moment under different working conditions. At the same time, the overall shape of each curve can reflect the distribution characteristics of the battery life of the same batch under the working condition. Figure 2 to Figure 7 The figure shows the overall battery life prediction results. Figure 2 Reliability curve and life probability density curve at SOC10% level; Figure 2 (a) is the reliability curve; Figure 2 (b) is the life probability density curve; Figure 3 Reliability curve and life probability density curve at SOC20% level; Figure 3 (a) is the reliability curve; Figure 3 (b) is the life probability density curve; Figure 4 Reliability curve and life probability density curve at SOC40% level; Figure 4 (a) is the reliability curve; Figure 4 (b) is the life probability density curve; Figure 5 Reliability curve and life probability density curve at SOC60% level; Figure 5 (a) is the reliability curve; Figure 5 (b) is the life probability density curve; Figure 6 Reliability curve and life probability density curve at SOC80% level; Figure 6 (a) is the reliability curve; Figure 6 (b) is the life probability density curve; Figure 7 Reliability curve and life probability density curve at SOC100% level; Figure 7 (a) is the reliability curve; Figure 7 (b) is the life probability density curve.

[0102] From the reliability curves of the above working conditions at different SOC levels, it can be seen that the reliability evaluation curves at different SOC levels are slightly different, but generally similar. The battery reliability under the T35C2 working condition is the best, and it decreases the slowest with the increase of the cycle period; on the contrary, the battery reliability under the T35C4 and T25C4 working conditions is the worst, and it decreases the fastest with the increase of the cycle period; the overall reliability evaluation results are consistent with the test results. From the predicted life probability density curves under various working conditions, it can be seen that the predicted life probability density curves under different SOC levels are slightly different, but generally similar. The probability density curves under the T35C4, T25C4, and T45C4 working conditions reach the maximum probability in the early stage and drop rapidly, indicating that the battery life under these three working conditions is the shortest; while the probability density curves of T35C2, T35C1, T35C3, and T45C1 reach the maximum probability in the later stage of the cycle and drop slowly, indicating that the battery life under these four working conditions is longer, and the curve results are consistent with the measured results.

[0103] 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 the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution, which should be included in the scope of the claims of the present invention.

Claims

1. A battery life prediction method based on accelerated degradation test data, characterized in that: The method includes the following steps: S1: Perform battery performance degradation modeling on the battery performance parameter degradation process based on the Wiener random process model; S2: Determine the variation of the diffusion parameter and the drift parameter in the model with different stresses based on the principle of constant acceleration factor; S3: Measure the overall life result of the battery with the reliability curve and the life probability density curve of the battery.

2. The method for predicting battery life based on accelerated degradation test data according to claim 1, characterized in that: The said S1 includes: S11: Characteristic description of the Wiener process. The Wiener process has three major characteristics, including: The function representing the Wiener process is Y(t) = μ·Λ(t) + σ·B(Λ(t)) where μ represents the drift parameter and is greater than 0, σ represents the diffusion parameter and is greater than 0, B(·) represents the standard Brownian motion, and the introduced time function Λ(t) satisfies the initial condition Λ(0) = 0; (1) Y(t) is continuous at the starting point t = 0 and satisfies the condition Y(0) = 0 with probability 1; (2) For any non - negative and successively increasing time points 0 ≤ t1 < t2 ≤ t3 < t4, where t1, t2, t3, t4 respectively represent 4 increasing time nodes in the battery test or operation process, the increments Y(t2) - Y(t1) and Y(t4) - Y(t3) within two time periods are statistically independent of each other; (3) The independent time interval increment of the Wiener process ΔY(t) = Y(t+Δt)-Y(t) obeys the normal distribution, that is, ΔY(t) ~ N(μΔΛ(t), σ 2 ΔΛ(t)), where ΔA(t)=Λ(t+Δt)-Λ(t); S12: By continuously accumulating these independent increments, we can deduce Y(t)~N(μΛ(t), σ 2 Λ(t)), the specific form of the probability density function (PDF) of Y(t) is: S13: Set a performance failure threshold D; the service life ξ of the battery is the time point when the performance parameter first touches or exceeds the threshold D, that is, ξ is expressed as the first moment when Y(t) reaches or exceeds D: ξ = inf{t|Y(t) ≥ D}; the calculation formula for the cumulative distribution function (CDF) of the battery life ξ is: In the above formula, Φ(·) is the standard normal CDF; the calculation formula for the PDF of the battery is:

3. The method for predicting battery life based on accelerated degradation test data according to claim 1, characterized in that: In the said S2, the accelerated degradation modeling process is divided into: S21: Define the acceleration factor, with two different battery stress levels S k and S h , and for each stress level, the performance parameter degradation of the battery follows the above Wiener process degradation model; the battery at stress level S k The cumulative distribution function of the life span is expressed as F k (t k ), F k (t k ) gives the time t when the battery reaches or exceeds the life span at this stress level k probability; at higher stress levels S h The cumulative distribution function of battery life is expressed as F h (t h ), represents the battery under stress level S h The lower lifespan reaches at least time t h probability; When F k (t k )=F h (t h ), then the stress S k Equivalent to S h The acceleration factor A k，h Defined as: A k，h =t h / t k S22: Derivation after the acceleration factor unchanged principle is established. Let the acceleration factor unchanged principle be established, then A k，h Is a non-conformist h , t k Changes, only two stresses S k , S h The determined constants give the following relationship: f k (t k )=A k,h f h (t h ) Let Λ(t) = t, and obtain To ensure A k，h Is a non-conformist k The constant of change requires that t k The coefficient term is 0, that is Derive from the above formula: By A k，h ≠1, k≠h, we know μ and σ 2 All of them change with the change of stress, that is, it is assumed that the drift parameters and diffusion parameters in the Wiener process model are related to the accelerated stress level of the battery.

4. The method for predicting battery life based on accelerated degradation test data according to claim 1, characterized in that: In the said S3, overall life prediction: Based on the ohmic resistance data of the EIS test of the battery under each stress, establish the reliability function as: The predicted life probability density curve function is: The likelihood function used for model parameter estimation is:

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