Sample size self-adaptive battery reliability evaluation method

Abstract

The invention provides a sample size adaptive battery reliability evaluation method, which comprises the following steps of: firstly, establishing a battery capacity degradation model based on a random process; secondly, adaptive augmentation of battery capacity degradation data is carried out by adopting an augmentation amplitude adaptive generative adversarial network; then, constructing a battery life distribution model based on Gaussian kernel density estimation, and extracting reliability indexes under a given confidence coefficient by using a Delta method, including reliability, failure rate, average pre-failure time and reliable life; and finally, carrying out capacity degradation data augmentation p (p is greater than or equal to 3) times by taking a fixed augmentation sample size h (h is greater than or equal to 10) as an increment, when the change rate of each reliability index after three times of augmentation is less than 1%, judging that the reliability index obtained by evaluation is in a convergence state, and taking the corresponding reliability index at the moment as a final evaluation result. According to the method, under the condition of limited data, a reasonable reliability evaluation result is determined, and support is provided for forward design of the reliability of the battery.

Description

Technical Field

[0001] The present invention relates to the technical field of battery reliability assessment, and in particular to a battery reliability assessment method with adaptive sample size, which is particularly suitable for battery reliability assessment under conditions of limited degradation data. Background Art

[0002] Batteries inevitably experience inconsistent capacity degradation over long-term use, resulting in a decrease in reliability and safety. Therefore, a reasonable and accurate reliability assessment based on battery capacity degradation data is of great practical significance for improving battery performance, extending service life, and reducing maintenance costs. Battery reliability assessment methods rely heavily on extensive experimental data. However, in practical applications, due to high experimental costs and time constraints, only limited capacity degradation data is typically available. This makes it difficult for traditional methods to accurately assess battery reliability when processing small sample sizes. To address these issues, generative adversarial networks (GANs) have been widely used as an effective data augmentation technique. However, traditional GAN ​​models often rely on completely random or manually predetermined augmentation amplitudes during training, lacking adaptability to dynamic data changes. This limitation leads to a mismatch between the augmentation method and actual training requirements, increasing the risk of underfitting or overfitting, compromising the effectiveness of data augmentation, and ultimately reducing the accuracy of reliability assessments. Therefore, there is an urgent need for a new method that can adaptively adjust the augmentation amplitude to effectively assess battery reliability under limited degradation data conditions. Summary of the Invention

[0003] The present invention addresses the technical problems existing in the prior art and provides a battery reliability assessment method with adaptive sample size, comprising:

[0004] Step 1: construct a battery capacity degradation model based on a random process and calculate the life of each battery in a given battery sample to form an initial battery life data set;

[0005] Step 2: Adopting an augmentation-adaptive generative adversarial network, the strategy network dynamically adjusts the augmentation amplitude based on the loss feedback of the target network, controls the generative network to adaptively augment the parameters of the battery capacity degradation model, and calculates the corresponding battery life based on the established battery capacity degradation model to expand the battery life dataset.

[0006] Step 3: Based on the expanded battery life data set, a battery life distribution model is established using the Gaussian kernel density estimation method to calculate the battery reliability indicators, including reliability, failure rate, mean time before failure, and reliable life;

[0007] Step 4: Use the Delta method to calculate the lower confidence limit of each reliability index under a given confidence level;

[0008] In step 5, the capacity degradation data is augmented p times (p ≥ 3) with a fixed augmented sample size h (h ≥ 10) as an increment. When the change rate of each reliability indicator after three consecutive augmentations is less than 1%, the reliability indicator obtained by the evaluation is determined to be in a convergence state, and the corresponding reliability indicator at this time is used as the final evaluation result.

[0009] In response to the defects in the prior art, the present invention provides a battery reliability evaluation method with adaptive sample size. Compared with traditional methods, the present invention effectively solves the problem of insufficient samples by establishing a battery capacity degradation model based on a random process and adaptively augmenting the limited battery capacity degradation data with an augmentation amplitude adaptive generative adversarial network. Furthermore, the battery life distribution model is constructed using Gaussian kernel density estimation, and the reliability index under a given confidence level is extracted with the help of the Delta method to ensure the scientificity and accuracy of the evaluation results. In addition, with a fixed augmentation sample size h (h ≥ 10) as an increment, p (p ≥ 3) times of capacity degradation data augmentation is performed, and the rate of change of the reliability index after three consecutive augmentations is less than 1% as the convergence condition, thereby determining the final reliability evaluation result, making the evaluation result more reasonable. The present invention provides support for the forward design of battery reliability under limited data conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Figure 1 A flow chart of a battery reliability assessment method with adaptive sample size provided by the present invention;

[0011] Figure 2 The reliability index changes of batteries under different augmented sample sizes; DETAILED DESCRIPTION

[0012] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0013] Figure 1 The present invention provides a flow chart of a sample size adaptive battery reliability assessment method, which mainly includes:

[0014] Step 1: construct a battery capacity degradation model based on a random process and calculate the life of each battery in a given battery sample to form an initial battery life data set;

[0015] Specifically, the process of constructing the battery capacity degradation model and forming the initial battery life data set in step 1 includes:

[0016] In step 1.1, a nonlinear Wiener process combined with an exponential function is used as a random process to construct a battery capacity degradation model, which is expressed as follows:

[0017]

[0018] Among them, C i (t) is the capacity of the i-th battery at time t, C 0i is the initial capacity of the i-th battery, β i1 , β i2 is the exponential function parameter of the i-th battery, σ i is the error parameter, and B(t) is the standard Brownian motion.

[0019] Combined with the capacity degradation data set C, the parameters of the degradation model are estimated, and the battery capacity degradation model parameter set under the initial sample size n is obtained.

[0020] In step 1.2, based on the battery capacity degradation model parameter set B, the capacity degradation failure threshold is defined as 80% of its initial value (i.e., SOH = 80%), and the life of the i-th battery is calculated. The expression is:

[0021]

[0022] Finally, the initial battery life data set is formed

[0023] Step 2: Adopting an augmentation-adaptive generative adversarial network, the strategy network dynamically adjusts the augmentation amplitude based on the loss feedback of the target network, controls the generative network to adaptively augment the parameters of the battery capacity degradation model, and calculates the corresponding battery life based on the established battery capacity degradation model to expand the battery life dataset.

[0024] Specifically, the augmented amplitude adaptive generative adversarial network in step 2 includes:

[0025] The generative network receives the input noise vector z and the augmentation amplitude m adjusted by the policy network, and outputs the augmented sample, which is expressed as:

[0026] x ada =G(z,m) (3)

[0027] Among them, m∈[0,1], G represents the generator in the generative network.

[0028] Then, the discriminator D is used to distinguish between the real sample x and the augmented sample x ada The adversarial training objectives of the generator G and the discriminator D are defined as:

[0029]

[0030] Among them, D(x) and D(G(z,m)) are the discriminator D for the real sample x and the augmented sample x respectively. ada Output.

[0031] The target network is trained based on the augmented data generated by the generator network and provides task feedback to the policy network to guide sample generation. This is achieved through the cross entropy loss function, which is expressed as:

[0032]

[0033] Among them, f t (·) represents the output of the target network, y i Represents sample x i The real output.

[0034] Specifically, L full represents the cross entropy loss when the augmentation is maximum (m=1), L ada represents the cross entropy loss of adaptive augmented samples (m∈(0,1)), L none It represents the cross entropy loss when the augmentation is minimum (m=0).

[0035] The policy network uses the A2C reinforcement learning algorithm to dynamically and adaptively adjust the augmentation amplitude m based on the loss function feedback provided by the target network and the preset reward function r. Its expression is:

[0036] m=p θ (s) (6)

[0037] Among them, p θ (·) represents the parameterized form of the policy network; s is the sample state, and its expression is:

[0038] s=[f t (x),f t (x ada )] (7)

[0039] The A2C reinforcement learning algorithm consists of an Actor network and a Critic network, and their loss functions are:

[0040] L Actor =-logp θ (s none )(r+γV φ (s ada )-Vφ (s none )) (8)

[0041]

[0042] Where γ represents the discount factor; V φ (·) represents the state value function estimated by the Critic network; r represents the reward function, which is expressed as:

[0043] r=μ(L full -L ada )+(1-μ)(L ada -L none ) (10)

[0044] Here, μ represents the adjustment factor, which has an initial value of 1 and gradually decreases to 0 during the training process.

[0045] Step 2.1, set the initial battery capacity degradation model parameter set Input into the augmented amplitude adaptive generative adversarial network and set the augmented sample size m. Through the iterative interaction of the above network, the expanded capacity degradation model parameter set is generated

[0046] Step 2.2, based on the expanded capacity degradation model parameter set Β a Repeat step 1.2 to update the corresponding battery life and obtain the expanded battery life data set

[0047] Step 3: Based on the expanded battery life data set, a battery life distribution model is established using the Gaussian kernel density estimation method to calculate the battery reliability indicators, including reliability, failure rate, mean time before failure, and reliable life;

[0048] Specifically, the process of establishing a battery life distribution model and calculating reliability indicators in step 3 includes:

[0049] Step 3.1, the Gaussian kernel function K is expressed as:

[0050]

[0051] Therefore, according to the expanded battery life dataset L a , the Gaussian kernel density estimation method is used to establish the battery life distribution model, and its expression is:

[0052]

[0053] in, is the battery life distribution model, n is the number of battery samples, ti is the life data of the i-th battery sample, and h is the bandwidth of the Gaussian distribution.

[0054] Usually, the bandwidth h is determined by the Silverman criterion, which is expressed as:

[0055]

[0056] in, is the sample standard deviation.

[0057] Step 3.2, based on the established battery life distribution model Combining the number of battery samples n, bandwidth h, battery specified operating time t and specified reliability level R, the reliability indicators such as reliability, failure rate, mean time before failure and reliable life are solved by probability statistics method. The expression is:

[0058]

[0059]

[0060] in, is reliability, the probability that the battery will work properly within a specified time t; The failure rate is the probability that a battery that is operating normally over a period of time will fail per unit time. MTTF is the mean time to failure, which indicates the average working time of the battery before failure. Reliable life is the maximum working time of the battery under the specified reliability R; is the reliability function The inverse function of .

[0061] Step 4: Use the Delta method to calculate the lower confidence limit of each reliability index under a given confidence level;

[0062] Specifically, the process of estimating the approximate variance of the reliability index and calculating the lower confidence limit of the reliability index in step 4 includes:

[0063] Step 4.1, use the second-order Taylor expansion to estimate the approximate variance of the reliability index, which is expressed as:

[0064]

[0065] Combine The variance of Then the approximate variance of each reliability index is:

[0066]

[0067]

[0068] in, Var[MTTF] and is the approximate variance of reliability, failure rate, mean time before failure and reliable life; for The first derivative of .

[0069] Step 4.2: Based on the given confidence level 1-α and the reliability index obtained, calculate the confidence lower limit of each reliability index under the confidence level. The expression is:

[0070]

[0071] in, and is the confidence limit of reliability, failure rate, mean time before failure and reliable life under given confidence level, Z 1-α is the quantile of the standard normal distribution.

[0072] In step 5, the capacity degradation data is augmented p times (p ≥ 3) with a fixed augmented sample size h (h ≥ 10) as an increment. When the change rate of each reliability indicator after three consecutive augmentations is less than 1%, the reliability indicator obtained by the evaluation is determined to be in a convergence state, and the corresponding reliability indicator at this time is used as the final evaluation result.

[0073] Specifically, the process of determining the convergence state and analyzing the reliability index in step 5 includes:

[0074] Assume that the reliability index after the pth augmentation is Y p , then the reliability index change rate after the pth and p-1th augmentation ΔY p for:

[0075]

[0076] If the change rate of each reliability index after three consecutive augmentations satisfies:

[0077]

[0078] It is determined that the reliability index has reached a convergence state, and the corresponding reliability index at this time is used as the final evaluation result.

[0079] Assume that the battery's specified operating time t is 600 cycles, the specified reliability level R is 90%, the confidence level 1-α is 90%, and the augmented sample size h is 10. Repeat steps 2-4 to generate a series of reliability index data under different augmented sample sizes m (m=p·h), and observe its change pattern with the increase of augmented sample size m.

[0080] like Figure 2As shown in Table 1, within the current augmented sample size range (10≤m≤90), the reliability index shows significant volatility with increasing sample size and no convergence trend is observed. Furthermore, the change rates of the reliability index after the last three augmentations are calculated.

[0081] Table 1 Reliability index change rate

[0082]

[0083] According to Table 1, as the augmented sample size m increases, the change rate of each reliability indicator and its lower confidence limit is greater than 1% in three consecutive augmentations, which does not meet the convergence state. This indicates that the existing capacity degradation dataset is insufficient to support reasonable reliability assessment. Therefore, the augmented sample size m needs to be further increased.

[0084] Gradually increase the sample size m until the change rate of each reliability index is less than 1% after the last three augmentations, indicating that the reliability index has reached convergence. This indicates that as the sample size increases, the improvement in the reliability assessment results becomes less significant. At this point, it can be considered that a reasonable reliability assessment result has been achieved, that is, the most reasonable reliability index has been determined based on the initial sample size n.

[0085] It is understandable that the above method can be used to comprehensively evaluate the reliability indicators of the battery, including but not limited to the battery's reliability, failure rate, mean time before failure, and reliable life.

[0086] This invention enables a reasonable assessment of battery reliability even with limited capacity degradation data. By adaptively adjusting the sample size and data augmentation, it effectively addresses the difficulty of traditional methods in accurately assessing battery reliability with small sample sizes. This adaptive approach not only significantly improves the credibility of assessment results but also reduces assessment costs, representing a significant improvement over traditional reliability assessment methods.

[0087] It should be noted that, in the above embodiments, the description of each embodiment has its own focus. If a part of an embodiment is not elaborated in detail, reference can be made to the relevant content of other embodiments for supplementary understanding.

[0088] Although the preferred embodiments of the present invention have been described in detail herein, those skilled in the art may make further changes and modifications thereto after understanding the core inventive concepts. Therefore, the appended claims should be interpreted as covering the preferred embodiments and all changes and modifications thereof within the scope of the present invention.

[0089] Obviously, those skilled in the art may make various modifications and variations to the present invention without departing from the spirit and scope of the present invention. As long as such modifications and variations fall within the scope of the claims of the present invention and their equivalents, they shall be considered part of the present invention.

Claims

1. A sample size adaptive battery reliability assessment method, characterized in that: include: Step 1: construct a battery capacity degradation model based on a random process and calculate the life of each battery in a given battery sample to form an initial battery life data set; Step 2: Adopting an augmentation-adaptive generative adversarial network, the strategy network dynamically adjusts the augmentation amplitude based on the loss feedback of the target network, controls the generative network to adaptively augment the parameters of the battery capacity degradation model, and calculates the corresponding battery life based on the established battery capacity degradation model to expand the battery life dataset. Step 3: Based on the expanded battery life data set, a battery life distribution model is established using the Gaussian kernel density estimation method to calculate the battery reliability indicators, including reliability, failure rate, mean time before failure, and reliable life; Step 4: Use the Delta method to calculate the lower confidence limit of each reliability index under a given confidence level; In step 5, the capacity degradation data is augmented p times (p ≥ 3) with a fixed augmented sample size h (h ≥ 10) as an increment. When the change rate of each reliability indicator after three consecutive augmentations is less than 1%, the reliability indicator obtained by the evaluation is determined to be in a convergence state, and the corresponding reliability indicator at this time is used as the final evaluation result.

2. The battery reliability evaluation method according to claim 1, wherein: The augmented magnitude adaptive generative adversarial network consists of a generation network, a target network, and a strategy network, including: The generative network receives the input noise vector z and the augmentation amplitude m adjusted by the policy network, and outputs the augmented sample, which is expressed as: x ada =G(z,m) (1) Among them, m∈[0,1], G represents the generator in the generation network; The target network is trained based on the augmented data generated by the generator network and provides task feedback to the policy network to guide sample generation. This is achieved through the cross entropy loss function, which is expressed as: Among them, f t (·) represents the output of the target network, y i Represents sample x i The real output of The policy network uses the A2C reinforcement learning algorithm to dynamically and adaptively adjust the augmentation amplitude m based on the loss function feedback provided by the target network and the preset reward function r. Its expression is: m=p θ (s) (3) Among them, p θ (·) represents the parameterized form of the policy network, s is the sample state, and its expression is: s=[f t (x),f t (x ada )] (4) The A2C reinforcement learning algorithm consists of an Actor network and a Critic network, and their loss functions are: L Actor =-logp θ (s none )(r+γV φ (s ada )-V φ (s none )) (5) Where γ represents the discount factor, V φ (·) represents the state value function estimated by the Critic network, and r represents the reward function, which is expressed as: r=μ(L full -L ada )+(1-μ)(L ada -L none ) (7) Among them, μ represents the adjustment factor, the initial value is 1, and it gradually decreases to 0 during the training process. full represents the cross entropy loss when the augmentation is maximum (m=1), L ada represents the cross entropy loss of adaptive augmented samples (m∈(0,1)), L none It represents the cross entropy loss when the augmentation is minimum (m=0).

3. The battery reliability evaluation method according to claim 1, wherein: The specific process of the Gaussian kernel density estimation method includes: Step 3.1, establish battery life distribution model: in, is the battery life distribution model, n is the number of battery samples, t i is the life data of the i-th battery sample, h is the bandwidth, is the sample standard deviation; Step 3.2, based on the established battery life distribution model Combining the number of battery samples n, bandwidth h, specified battery operating time t and specified reliability level R, the battery reliability indicators such as reliability, failure rate, mean time before failure and reliable life are solved through probability statistics method.

4. The battery reliability evaluation method according to claim 1, wherein: The specific process of the Delta method includes: Step 4.1, use the second-order Taylor expansion to estimate the approximate variance of the reliability index, which is expressed as: in, Var[MTTF] and is the approximate variance of reliability, failure rate, mean time before failure and reliable life, for The first derivative of . Step 4.2: Based on the given confidence level 1-α and the reliability index obtained, calculate the confidence lower limit of each reliability index under the confidence level. The expression is: in, and is the confidence limit of reliability, failure rate, mean time before failure and reliable life under given confidence level, Z 1-α is the quantile of the standard normal distribution.

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