Battery Life Prediction Method Based on Accelerated Degradation Test Data

Abstract

This invention relates to a battery life prediction method based on accelerated degradation test data, belonging to the field of energy storage health management. The method includes: using a Wiener stochastic process to model battery performance degradation using battery performance degradation parameters to determine the cumulative distribution function and probability density function of battery life; determining the changes of diffusion and drift parameters in the model parameters with acceleration stress based on the principle of invariant acceleration factor; and measuring the overall battery life prediction result using reliability curves and probability density curves. This invention uses a Wiener stochastic process to model battery performance degradation data under different accelerated stresses, ultimately obtaining the overall battery life prediction result under different accelerated stress degradation conditions.

Description

Technical Field

[0001] This invention belongs to the field of energy storage health management and relates to a method for predicting battery life based on accelerated degradation test data. Background Technology

[0002] Currently, with increasing global emphasis on energy conservation, emission reduction, and sustainable development, lithium batteries, as important energy storage devices, are finding increasingly wider applications. However, the lifespan of lithium batteries remains a key factor restricting their development. Accurately predicting the lifespan of lithium batteries is of great significance for reducing operating costs, improving resource utilization, and effectively managing the recycling of used batteries.

[0003] The shortcomings of existing technology:

[0004] Most existing methods for predicting lithium battery life are based on empirical formulas or simple mathematical models, resulting in low prediction accuracy and difficulty in meeting the needs of practical applications.

[0005] Some lifespan prediction methods rely primarily on actual battery usage data, while accelerated degradation test data can provide richer information on battery degradation, helping to improve prediction accuracy.

[0006] Different operating conditions and stress levels can significantly affect battery life, and existing life prediction methods have not adequately considered this factor.

[0007] The purpose of this 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 prediction accuracy, and provide more reliable data support for battery manufacturers and end users. Summary of the Invention

[0008] In view of this, 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.

[0009] To achieve the above objectives, the present invention provides the following technical solution:

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

[0011] S1: Battery performance degradation modeling based on Wiener stochastic process model;

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

[0013] S3: The overall lifespan of the battery is measured by the battery's reliability curve and life probability density curve.

[0014] Furthermore, the said S1 includes:

[0015] S11: Characteristic description 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, and B(·) represents the standard Brownian motion. At the same time, 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 (Probability Density Function, PDF) of Y(t) is deduced as follows:

[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 (Cumulative Distribution Function, CDF) of the battery life ξ is:

[0025]

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

[0027]

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

[0029] S21: Defines the acceleration factor, with two different battery stress levels S. k and S h Furthermore, for each stress level, the battery's performance parameters degrade according to the Wiener process degradation model described above; the battery at stress level S k The cumulative distribution function of the lower lifetime is expressed as F k (t k ), F k (t k Give the time t under this stress level when the battery life reaches or exceeds the specified value. k The probability at higher stress levels S h Under these conditions, the cumulative distribution function of battery life is expressed as F h (t h ), representing the battery under stress level S. h The minimum lifespan is t. h The probability of;

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

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

[0032] S22: Derivation after the principle of constant acceleration factor holds. Let the principle of constant acceleration factor hold, then A k,h It is not a follower of t h , t k The change is caused by only two stresses S k S h The determined constants yield the following relationship:

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

[0034] Let Λ(t) = t, then we get

[0035]

[0036] To ensure A k,h It is not a follower of t k The constant of change requires that t in the above formula k The coefficient term is 0, that is...

[0037]

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

[0039]

[0040] By A k,h ≠1, k≠h, know μ and σ 2 Both parameters change with stress, meaning that the drift and diffusion parameters in the Wiener process model are assumed to be related to the battery acceleration stress level.

[0041] Furthermore, in S3, the overall lifetime prediction is as follows:

[0042] Based on the ohmic resistance data of the battery under various stresses obtained from EIS tests, the reliability function is established as follows:

[0043]

[0044] The probability density curve function for predicting lifetime is:

[0045]

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

[0047]

[0048] The beneficial effects of this invention are as follows: This 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 the Wiener process model from the perspective of performance degradation modeling. In the accelerated degradation modeling process, it is determined that both drift and diffusion parameters change with stress. Using the ohmic resistance obtained by fitting EIS test data from characteristic testing as a performance degradation parameter, a Wiener stochastic process model is established. Maximum likelihood function estimation is performed using the fmincon function to solve for the model parameter values ​​corresponding to different operating conditions and SOC levels. Using the Wiener stochastic process model, a reliability evaluation function and a predicted life probability density function are determined as indicators for reliable life prediction. Reliability curves and probability density curves are plotted for batteries under different operating conditions. Based on the reliability curves, the battery under the T35C2 condition exhibits the best reliability, while the batteries under the T35C4 and T25C4 conditions show the worst reliability. The reliability curves for each condition are consistent with the actual experimental results. From the battery predicted life probability density curves for each condition, it can be seen that the probability density curves for T35C4, T25C4, and T45C4 conditions reach their maximum probability values ​​early on and then rapidly decline, indicating that these three conditions have shorter lifespans. Conversely, the probability density curves for T35C2, T35C1, T35C3, and T45C4 conditions reach their maximum probability values ​​later in the cycle and then slowly decline, indicating that these four conditions have longer lifespans. All of these results are consistent with experimental measurements.

[0049] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0050] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

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

[0052] Figure 2 Reliability curves and lifetime probability density curves at a SOC of 10%; Figure 2 (a) is the reliability curve; Figure 2 (b) is the lifetime probability density curve;

[0053] Figure 3 Reliability curves and lifetime probability density curves at a SOC of 20%; Figure 3 (a) is the reliability curve; Figure 3 (b) is the lifetime probability density curve;

[0054] Figure 4 Reliability curves and lifetime probability density curves at a SOC of 40%; Figure 4 (a) is the reliability curve; Figure 4 (b) is the lifetime probability density curve;

[0055] Figure 5 Reliability curves and lifetime probability density curves at a SOC of 60%; Figure 5 (a) is the reliability curve; Figure 5 (b) is the lifetime probability density curve;

[0056] Figure 6 The reliability curve and lifetime probability density curve are shown at an SOC of 80%. Figure 6 (a) is the reliability curve; Figure 6 (b) is the lifetime probability density curve;

[0057] Figure 7 The reliability curve and lifetime probability density curve are shown at a SOC of 100%. Figure 7 (a) is the reliability curve; Figure 7 (b) is the lifetime probability density curve. Detailed Implementation

[0058] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed 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 are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0059] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0060] In the 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 drawings. It 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 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 changes 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 increments ΔY(t) = Y(t+Δt)-Y(t) of the Wiener process follow a normal distribution, i.e., 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, Y(t) ~ N(μΛ(t),σ 2 Therefore, the specific form of the probability density function (PDF) of Y(t) can be derived as follows:

[0074]

[0075] S13: Set a performance failure threshold D. Battery life ξ can be understood as the time required for the performance parameter to first reach or exceed the threshold D, i.e., ξ represents the first moment when Y(t) reaches or exceeds D: ξ = inf{t|Y(t)≥D}. The cumulative distribution function (CDF) formula for battery life ξ is:

[0076]

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

[0078]

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

[0080] S21: Define the acceleration factor, assuming two different battery stress levels S k and S h Furthermore, for each stress level, the battery's performance parameters degrade according to the Wiener process degradation model described above. Correspondingly, the battery at stress level S... k The cumulative distribution function of the lower lifetime is expressed as F k (t k In other words, F k (t k The given information indicates the time t during which the battery's lifespan reaches or exceeds this stress level. k The probability; similarly, at higher stress levels S h Under these conditions, the cumulative distribution function of battery life is expressed as F h (t h This represents the battery's stress level S. hThe minimum lifespan is t. h The probability of.

[0081] when

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

[0083] When, the stress S can be... k Equivalent to S h Acceleration factor A k,h Defined as

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

[0085] S22: Derivation after the principle of constant acceleration factor holds. Let the principle of constant acceleration factor hold, then A k,h It should be a non-t h , t k The change is caused by only two stresses S k S h The constant determined by this. The resulting relation is:

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

[0087] Let Λ(t) = t, then we get

[0088]

[0089] To ensure A k,h It is not a follower of t k The constant of change requires that t in the above formula k The coefficient term is 0, that is...

[0090]

[0091] From the above formula, we can derive

[0092]

[0093] By A k,h Given that ≠1 (k≠h), we can know that μ and σ 2 Both parameters change with stress, meaning that the drift and diffusion parameters in the Wiener process model are assumed to be related to the battery acceleration stress level.

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

[0095] Based on the ohmic resistance data of the battery under various stresses obtained from EIS tests, the reliability function is established as follows:

[0096]

[0097] The probability density curve function for predicting lifetime is:

[0098]

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

[0100]

[0101] The reliability curve shows the relationship between battery usage time and reliability under different operating conditions; the lifetime probability density curve shows the probability of battery failure per unit time near a specific lifetime moment under different operating conditions, and the overall shape of each curve reflects the distribution characteristics of the lifetime of the same batch of batteries under that operating condition. Figures 2-7 The image shows the overall battery life prediction results. Figure 2 Reliability curves and lifetime probability density curves at a SOC of 10%; Figure 2 (a) is the reliability curve; Figure 2 (b) is the lifetime probability density curve; Figure 3 Reliability curves and lifetime probability density curves at a SOC of 20%; Figure 3 (a) is the reliability curve; Figure 3 (b) is the lifetime probability density curve; Figure 4 Reliability curves and lifetime probability density curves at a SOC of 40%; Figure 4 (a) is the reliability curve; Figure 4 (b) is the lifetime probability density curve; Figure 5 Reliability curves and lifetime probability density curves at a SOC of 60%; Figure 5 (a) is the reliability curve; Figure 5 (b) is the lifetime probability density curve; Figure 6 The reliability curve and lifetime probability density curve are shown at an SOC of 80%. Figure 6 (a) is the reliability curve; Figure 6 (b) is the lifetime probability density curve; Figure 7 The reliability curve and lifetime probability density curve are shown at a SOC of 100%. Figure 7 (a) is the reliability curve; Figure 7 (b) is the lifetime probability density curve.

[0102] As can be seen from the reliability curves under different SOC levels for each operating condition, the reliability assessment curves differ slightly but are generally similar. The battery reliability is best under the T35C2 condition, and the decrease is slowest with increasing cycle time; conversely, the battery reliability is worst under the T35C4 and T25C4 conditions, and the decrease is fastest with increasing cycle time; the overall reliability assessment results are consistent with the experimental results. As can be seen from the predicted lifetime probability density curves for each operating condition, the predicted lifetime probability density curves differ slightly under different SOC levels but are generally similar. The probability density curves for T35C4, T25C4, and T45C4 conditions reach their maximum probability in the early stages and then decrease rapidly, indicating that the battery life is shortest under these three conditions; while the probability density curves for T35C2, T35C1, T35C3, and T45C1 reach their maximum probability in the later stages of cycling and then decrease slowly, indicating that the battery life is longer under these four conditions. 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 solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within 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 invariant acceleration factor; S3: Measure the overall life result of the battery with the reliability curve and the life probability density curve of the battery; The 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 sequentially increasing time points 0 ≤ t1 < t2 ≤ t3 < t4, where t1, t2, t3, t4 represent 4 increasing time nodes in the battery test or operation process, the increments Y(t2) - Y(t1) and Y(t4) - Y(t3) in the two time periods are statistically independent of each other; (3) The independent time interval increments ΔY(t) = Y(t+Δt)-Y(t) of the Wiener process follow a normal distribution, i.e., ΔY(t) ~ N(μΔΛ(t), σ 2 ΔΛ(t)), where ΔΛ(t)=Λ(t+Δt)-Λ(t); S12: By continuously accumulating these independent increments, Y(t) ~ N(μΛ(t),σ 2 From Λ(t), we can derive the specific form of the probability density function PDF of Y(t): 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 cumulative distribution function CDF calculation formula of the battery life ξ is: In the above formula, Φ(·) is the standard normal CDF; the PDF calculation formula of the battery is: In the S2, the accelerated degradation modeling process is divided into: S21: Defines the acceleration factor, with two different battery stress levels S. k and S h Furthermore, for each stress level, the battery's performance parameters degrade according to the Wiener process degradation model described above; the battery at stress level S k The cumulative distribution function of the lower lifetime is expressed as F k (t k ), F k (t k Give the time t under this stress level when the battery life reaches or exceeds the specified value. k The probability at higher stress levels S h Under these conditions, the cumulative distribution function of battery life is expressed as F h (t h ), representing the battery under stress level S. h The minimum lifespan is t. h The probability of; When F k (t k ) = F h (t h When ), then the stress S k Equivalent to S h Acceleration factor A k,h Defined as: A k,h =t h / t k S22: Derivation after the principle of constant acceleration factor holds. Let the principle of constant acceleration factor hold, then A k,h It is not a follower of t h , t k The change is caused by only two stresses S k S h The determined constants yield the following relationship: f k (t k )=A k,h f h (t h ) Let Λ(t) = t, and we get To ensure A k,h It is not a follower of t k The constant of change requires that t in the above formula k The coefficient term is 0, that is... Derived from the above formula: By A k,h ≠1, k≠h, know μ and σ 2 Both parameters change with stress, meaning that the drift and diffusion parameters in the Wiener process model are assumed to be related to the battery acceleration stress level.

2. The battery life prediction method based on accelerated degradation test data according to claim 1, characterized in that: In the S3, overall life prediction: Based on the ohmic resistance data of the EIS test of the battery under various stresses, 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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