Lithium ion battery residual life prediction method considering dynamic temperature influence

Abstract

The invention belongs to the technical field of battery residual life prediction, and particularly relates to a lithium ion battery residual life prediction method considering dynamic temperature influence, and the method specifically comprises the steps: building a lithium ion battery capacity degradation model, and obtaining a state space model under the dynamic temperature influence; a filtering method based on a Bayesian framework is used for predicting the capacity degradation state estimation value and the residual life of the lithium ion battery, a time-varying fading factor is introduced in the importance sampling process, and adaptive kernel density estimation is used in the resampling process. According to the method, a Wiener process is adopted to model a battery capacity degradation process in a nonlinear and time-varying temperature environment, and meanwhile, a time-varying fading factor and adaptive kernel density estimation are introduced to construct an importance density function and a resampling process of a filtering algorithm based on a Bayesian framework, so that the capacity degradation state change tracking capability of the filtering is improved, and the filtering efficiency is improved. And the battery residual life prediction error under the influence of the external environment is reduced.

Description

Technical Field

[0001] This invention belongs to the field of battery remaining life prediction technology, specifically relating to a method for predicting the remaining life of lithium-ion batteries that takes into account the effects of dynamic temperature. Background Technology

[0002] The global energy and environmental systems are facing unprecedented challenges. New energy technologies, with their green, clean, and sustainable characteristics, have become an important way to solve the energy crisis and environmental problems. Lithium-ion batteries, as a core component of new energy technologies, are widely used in key areas such as electric vehicles, photovoltaic energy storage, and military equipment. However, lithium-ion batteries inevitably age during use, severely affecting their health and overall performance. With increasing usage time, battery capacity gradually decreases, internal resistance increases, and eventually, battery failure may occur. More seriously, battery failure can trigger power outages or even catastrophic safety accidents. Faced with increasingly stringent reliability and safety requirements for lithium-ion battery application systems, the role of Predictive Fault Management (PHM) technology is becoming increasingly important. The core of PHM technology lies in accurately predicting the remaining battery life, providing a scientific basis for developing effective energy management strategies and lifespan extension plans.

[0003] However, in real-world operating environments, lithium-ion batteries are affected by both dynamic changes in the external environment and the complexity of their internal electrochemical reaction mechanisms. The temperature environment in which the battery operates exhibits significant dynamic variations, and these temperature fluctuations directly cause nonlinearity and uncertainty in battery capacity decay. Furthermore, in practical applications, this time-varying temperature not only accelerates battery performance degradation but also significantly increases the complexity and potential risks of system maintenance. Therefore, in-depth exploration of the capacity decay mechanism of lithium-ion batteries under dynamic temperature environments, and methods for predicting the remaining life of lithium-ion batteries that consider the influence of dynamic temperature, has significant theoretical and practical value for enhancing the reliability of battery systems and ensuring operational safety. Summary of the Invention

[0004] To address the shortcomings of the existing technology, this invention provides a method for predicting the remaining life of lithium-ion batteries that takes into account the effects of dynamic temperature, thereby solving the problems existing in the background technology.

[0005] This invention provides a method for predicting the remaining life of lithium-ion batteries considering the effects of dynamic temperature, specifically including: S1. Collect historical degradation data of lithium-ion batteries and perform preprocessing. The historical degradation data of lithium-ion batteries includes temperature, voltage, current and capacity. S2. Establish a lithium-ion battery capacity degradation model and obtain a state-space model under the influence of dynamic temperature. This degradation model not only considers the influence of dynamic temperature on the battery capacity degradation rate, but also considers the joint correlation between degradation rate and volatility. S3. Estimate the prior values ​​of model parameters in the state-space model under the influence of dynamic temperature based on the maximum likelihood estimation method; S4. Based on the state-space model under the influence of dynamic temperature and the prior values ​​of model parameters, a filtering method based on a Bayesian framework is used to predict the estimated value of lithium-ion battery capacity degradation state and remaining life. Among them, a time-varying fading factor is introduced to optimize the importance density function during the importance sampling process, and an adaptive kernel density is used to estimate the posterior probability density function during the resampling process. S5. Input the degradation data of the lithium-ion battery under test into step S4 after preprocessing to obtain the estimated value of the capacity degradation state and the remaining life of the lithium-ion battery under test.

[0006] Preferably, preprocessing includes data selection, data transformation, and feature selection.

[0007] Preferably, step S2 specifically includes: S21. Establish a Wiener degradation model that considers the effect of dynamic temperature on battery capacity degradation rate, as shown in the following expression: , In the formula, t represents time. Let t be the state variable representing the capacity degradation of the lithium-ion battery at time t. This represents the initial state variable indicating the capacity degradation of the lithium-ion battery. The drift coefficient reflects the degradation rate. Indicates dependence on dynamic temperature The time-varying degradation rate, To represent the diffusion coefficient of the degradation process, Represents standard Brownian motion; Represents a vector with unknown parameters It is used to characterize the nonlinear properties of components; S22. Determine the joint correlation between degradation rate and volatility under the influence of dynamic temperature, as shown in the following expression: , In the formula, z is the sample index. For acceleration coefficient, It is a fixed parameter that reflects the equivalence of the degradation mechanism; S23. Combining steps S21 and S22, a lithium-ion battery capacity degradation model is obtained. This degradation model not only considers the influence of dynamic temperature on the battery capacity degradation rate, but also the joint correlation between degradation rate and volatility. The expression is as follows: , In the formula, Indicates dynamic temperature. Represents the long-term average temperature. This represents the standard deviation fluctuation of temperature. Represents the regression rate. Brownian motion under time scale transformation, These are model parameters; S24, Known Degradation Monitoring Time The corresponding degradation observation state is ,use{ If k = 1, 2, ..., m, then it can be simplified to: The dynamic temperature data at the monitoring time points are ,Right now Therefore, the state-space model expression under the influence of dynamic temperature is as follows: , In the formula, for Dynamic temperature at any given moment for Estimated capacity degradation status of lithium-ion batteries at any given time; for and The difference, ; for and The difference, ; The parameters are nonlinear functions of time, representing unknown parameter vector at time ; for and The difference, .

[0008] Preferably, step S3 specifically includes: S31. Determine the model parameters in the state-space model under the influence of dynamic temperature. The model parameters include the model parameters in the temperature model. Model parameters in capacity degradation model , , ; S32. Estimating model parameters in a temperature model based on the maximum likelihood estimation method. The prior values ​​are as follows: S321. Based on the state-space model under the influence of dynamic temperature, it can be seen that... Under these conditions, dynamic temperature It follows a Gaussian distribution with a mean, i.e. obey Therefore, for The log-likelihood function yields: , In the formula, N represents a Gaussian distribution. Represents the log-likelihood function; S322. Taking the partial derivative of the log-likelihood function, we get: , ; S323. Substituting the formula obtained in step S322 into the formula in step S321, we get: , In the formula, , ; S324. Estimate the parameters based on the formula in step S323. Then Substituting into the formula in step S322, we can calculate... , ; S33. Estimating model parameters in a capacity degradation model based on the maximum likelihood estimation method. The prior values ​​are as follows: S331, Based on the measured temperature and state-space model, let , ,but Subsequently, based on the state-space model under the influence of dynamic temperature, it can be seen that... It follows a Gaussian distribution with a mean, i.e. obey ; S332, Let For model parameters, then The probability density function is shown below: ; S333, Based on the formula obtained in step S332 The log-likelihood function is shown below: ; S334, based on The log-likelihood function is obtained by maximizing it in a four-dimensional search. The maximum likelihood estimate.

[0009] Preferably, step S4 specifically includes: S41. Estimation and prediction of lithium-ion battery capacity degradation status, including: S411. Initialization: From the initial distribution Mid-sampling generation Particle sample And initialize weights for all particles. , ; S412. Calculate auxiliary variables: from the given... Auxiliary variables were calculated. Auxiliary variables from Obtained in; S413, Update the time-varying fading factor: Update the time-varying fading factor based on the suboptimal solution of the time-varying fading factor; S414. Importance Sampling and Weighting: An importance density function is generated based on auxiliary variables and a time-varying fading factor. Importance sampling is then performed based on this function. The first-order weight of each particle obtained after importance sampling is calculated and normalized to obtain the particle set. ; S415, Smoothing: Calculate the adaptive bandwidth and use an adaptive kernel density estimate based on the adaptive bandwidth to smooth the particles. Smoothing is performed to form a continuous posterior probability density function, i.e. ; S416, Perturbation Sampling: From Sampling Marked as To obtain the same weight A set of particles ,in For the magnitude of the disturbance, obey , The adaptive bandwidth for the i-th particle; S417. Prediction: Based on a state-space model under the influence of dynamic temperature, from... Get from A set of particles ; S418, Update: Calculate the second-order weights for each particle to obtain the particle set. ; S419. Resampling: Calculate the effective number of particles. ;like Less than the threshold Repeat steps S416-S419 to resample; S410, Obtain an estimate of the capacity degradation state of the lithium-ion battery; S42, Lithium-ion battery remaining life prediction, including: S421. In the state-space model under the influence of dynamic temperature, the remaining lifespan of the lithium-ion battery is defined as the time when the system state reaches or exceeds the predetermined fault threshold. S422, The updated model parameters based on the state-space model under dynamic temperature influence and the filtering method based on the Bayesian framework. To determine the dynamic temperature and capacity degradation trajectory; S423. Based on the dynamic temperature and capacity degradation state trajectory, obtain the remaining lifetime estimate for each particle; S424. Based on the remaining lifetime estimate of each particle, obtain the point estimate of the remaining lifetime of the lithium-ion battery and the probability density function of the remaining lifetime of the lithium-ion battery.

[0010] Preferably, the suboptimal solution of the time-varying fading factor is derived based on the residual orthogonality principle and the strong filtering idea, and the expression of the suboptimal solution of the time-varying fading factor is as follows: , , In the formula, k is the sample index. It is the transpose symbol. This represents the suboptimal solution with a time-varying fading factor. Represents the trace of a matrix. Let be the covariance matrix of the residuals. Measure the variance of noise. For measuring equations Jacobian matrix, This is state transition noise. Forgetting factor, The residual between the first true value and the estimated value; Let covariance matrix be the variance matrix. , Represents the expectation operator; The residual between the k-th true value and the estimated value. , for Real-time lithium-ion battery capacity; Known Based on time information, An estimate of the time measurement.

[0011] Preferably, the first-order weight expression is as follows: , , In the formula, for The first-order weights of the i-th particle at time i can be used to derive the sample set. ,in i , j For particle indexing, The marker indicating the particle at time k-1; To represent a direct proportion, for The weight of the i-th particle at time i. For measurement function, Indicates measurement noise. To assist in calculating the values ​​of the particle measurement equations, express The measured or estimated capacity of the lithium-ion battery at any given time; The second-order weight expression is shown below: , In the formula, for The second-order weight of the j-th particle at time j, for Time of the first The weight of each particle, express arrive Measurement of lithium-ion battery capacity at any given time.

[0012] Preferably, the adaptive bandwidth calculation formula is as follows: , , In the formula, The adaptive bandwidth for the i-th particle; For fixed bandwidth, , Let n be the standard deviation of the sample data, and n be the sample size. For local bandwidth factor, For sensitivity parameters; This is a preliminary nuclear density estimate of the i-th particle at point... The value at that location, G is The geometric mean ; Based on adaptive bandwidth, adaptive kernel density estimation is used for particle... Smoothing is performed to form a continuous posterior probability density function, i.e. The expression is as follows: , In the formula, express KDE, For kernel functions; The estimated value of the capacity degradation state of a lithium-ion battery is expressed as follows: , In the formula, for Estimated capacity degradation status of lithium-ion batteries at any given time. for The estimated value of the degenerate state of the j-th particle at time j.

[0013] The preferred expression for the dynamic temperature and capacity degradation state trajectory is as follows: , , The estimated remaining lifetime for each particle is given by the following formula: , In the formula, ; for The remaining lifespan of a lithium-ion battery when it reaches a critical threshold. express Time of the first i The remaining lifetime of each particle. Indicates the first i The lifetime of an individual particle.

[0014] Preferably, the point estimate of the remaining life of a lithium-ion battery is expressed as follows: , The probability density function expression for the remaining lifespan of a lithium-ion battery is shown below: , In the formula, express Point estimate of the remaining lifespan of a lithium-ion battery at a given time. Indicates the state given Temperature status The probability of remaining lifespan of a lithium-ion battery under certain conditions; express The weight of the i-th particle at time i; Let be the Dirac function, representing the probability density at a specific point.

[0015] Compared with the prior art, the present invention has the following beneficial effects: 1. This invention uses the Wiener process to model the battery capacity degradation process under nonlinear and time-varying temperature conditions. It not only considers the influence of dynamic temperature changes on the battery capacity decay rate and the joint correlation between degradation rate and volatility, but also overcomes the shortcomings of existing methods that usually treat dynamic temperature factors as constants or given values, ignoring their randomness, and thus failing to meet the complex and ever-changing operating conditions in reality.

[0016] 2. Based on the Bayesian framework, this invention introduces a time-varying fading factor to construct the importance density function of the filtering algorithm, achieving real-time adjustment of particle states, strengthening the orthogonality of residual sequences, and adaptively adjusting estimation errors, effectively improving the filtering's ability to track changes in capacity degradation state. Simultaneously, by introducing adaptive kernel density estimation to construct the resampling process of the filtering algorithm, it effectively alleviates the degradation and depletion problems among particles and reduces the prediction error of battery remaining life under the influence of the external environment. Attached Figure Description

[0017] Figure 1 Flowchart of the lithium-ion battery remaining life prediction method considering the dynamic temperature effect provided by the present invention. Figure 2 The temperature fluctuation curve and capacity degradation curve of battery B0018 in this embodiment of the invention; Figure 3 This is a comparison chart of the one-step prediction results and estimation errors of the capacity degradation state of battery B0018 under the traditional auxiliary particle filtering method and the improved filtering method of this application in the embodiments of the present invention. Figure 4 This section compares the predicted capacity of battery B0018 in the NASA battery dataset with the actual capacity at different initial prediction points. Figure 4 The starting point for a is the 60th cycle. Figure 4 b starts at the 70th cycle; Figure 5 This is a point prediction result of the remaining lifetime of battery B0018 in this embodiment of the invention from the 40th cycle to the 90th cycle; Figure 6 The remaining life prediction curves of battery B0018 in this embodiment of the invention at different cycle times are shown. Detailed Implementation

[0018] In the application research of lithium-ion batteries, time-varying temperature conditions have a significant and undeniable impact on battery discharge capacity and aging patterns. Therefore, accurately modeling the degradation process of batteries under dynamic temperatures is crucial for the optimized design of battery management systems and the accurate prediction of remaining battery life. Firstly, regarding the influence of time-varying temperature, this application employs the Wiener process to model the capacity degradation process of lithium-ion batteries under nonlinear, time-varying temperature environments, obtaining a lithium-ion battery capacity degradation model. This model considers the impact of dynamic temperature changes on the battery capacity decay rate, as well as the joint correlation between the degradation rate and volatility, and also provides a state-space model under the influence of dynamic temperature. Subsequently, the prior values ​​of the model parameters in the state-space model under the influence of dynamic temperature are estimated using the maximum likelihood estimation method. Secondly, addressing the issue that dynamic temperature environments increase model uncertainty, leading to particle filter depletion and decreased prediction accuracy, this application proposes a Bayesian-based filtering method to predict battery remaining life under dynamic temperature conditions. Specifically, a time-varying fading factor is introduced during importance sampling to adjust particle states in real time, thereby improving the filter's ability to track capacity changes. During resampling, adaptive kernel density estimation is used to estimate the posterior probability density function, transforming discrete particle samples into continuous probability density functions, thus optimizing the resampling strategy. Finally, this application also verifies the feasibility and effectiveness of the constructed model and algorithm in predicting battery remaining life through research and application of lithium-ion battery capacity degradation data under time-varying temperature conditions.

[0019] like Figure 1 As shown, this invention provides a method for predicting the remaining life of lithium-ion batteries considering the effects of dynamic temperature, specifically including: S1. Collect historical degradation data of lithium-ion batteries and perform preprocessing. The historical degradation data of lithium-ion batteries includes temperature, voltage, current and capacity.

[0020] In this application, preprocessing includes data selection, data transformation, and feature selection.

[0021] In this embodiment, data selection, data transformation, and feature selection are performed to ensure that the input data has the same format and distribution as the training data so that the model can process the data correctly.

[0022] S2. Establish a lithium-ion battery capacity degradation model to obtain a state-space model under the influence of dynamic temperature. This degradation model not only considers the influence of dynamic temperature on the battery capacity degradation rate, but also the joint correlation between degradation rate and volatility.

[0023] It should be noted that existing technologies establish a nonlinear Wiener process model and determine the battery remaining lifetime function and its probability density function based on this model. Unlike existing technologies, this application considers the impact of dynamic temperature on the lithium-ion battery capacity degradation rate, as well as the joint dependence of degradation rate and volatility under time-varying operating conditions, when establishing the lithium-ion battery capacity degradation model. By introducing time-varying drift coefficients and diffusion coefficients and establishing the proportional relationship between them, a more accurate Wiener degradation model is constructed.

[0024] The expression for the nonlinear Wiener process model established in the prior art is shown below: , In the formula, t represents time. Let t be the state variable representing the capacity degradation of the lithium-ion battery at time t. This represents the initial state variable indicating the capacity degradation of the lithium-ion battery. The drift coefficient reflects the degradation rate. To represent the diffusion coefficient of the degradation process, Represents standard Brownian motion; Represents a vector with unknown parameters It is used to characterize the nonlinear properties of components.

[0025] It is important to note that it is generally assumed that the battery's initial state has not degraded, i.e. . The most widely used form is the power function form, i.e. .like Then it is a linear Wiener process model.

[0026] In the existing technology, when A battery is considered to be inoperable when it reaches a predefined critical threshold. Therefore, based on the concept of first-reach time, the remaining battery life in the prior art can be defined as the time when it first crosses the predefined critical threshold, and its functional expression is as follows: , In the formula, L The remaining battery life indicates the time from the current moment until the battery fails. The infimum represents the minimum time value required to satisfy the condition; D For a predefined critical threshold, This indicates that the initial state has not reached the failure threshold.

[0027] In the prior art, the probability density function of the remaining battery life is derived based on the nonlinear Wiener process model and the remaining battery life function, as shown in the following expression: , In the formula, Let be the probability density function of the remaining battery life; As auxiliary symbols, .

[0028] It is important to note that In Formula 3, it has no specific meaning; it is merely a temporary auxiliary symbol used only in the process of simplifying the formula.

[0029] In this application, step S2 specifically includes: S21. Establish a Wiener degradation model that considers the influence of dynamic temperature on battery capacity degradation rate, specifically as follows: S211. Based on the OU process, dynamic temperature is modeled, and the expression is as follows: , In the formula, Indicates dynamic temperature. Represents the long-term average temperature. This represents the standard deviation fluctuation of temperature. Represents the regression rate. This refers to Brownian motion under time scale transformations.

[0030] It should be noted that the actual operating environment of many devices is essentially constant, such as the temperature and humidity of lithium-ion batteries. However, due to environmental disturbances and the interaction between the device and the environment, this environment can change over time, even randomly. Therefore, considering a stochastic degradation rate to describe the volatility of the actual dynamic temperature is more appropriate. As a continuous-time stochastic process, the OU process has wide applications, especially in financial markets, where it is used to characterize stock price volatility. The most significant characteristics of the OU process are its mean regression and stationarity, making it an ideal mathematical tool for describing stable but stochastic phenomena. Therefore, this application assumes the existence of a measurable dynamic temperature that affects the capacity degradation process of lithium-ion batteries and models the dynamic temperature based on the OU process.

[0031] It can be clearly seen from Formula 4 that... The randomness comes from .

[0032] S212. Use an exponential function to relate temperature to the battery capacity degradation rate, as shown in the following expression: , In the formula, Indicates dependence on dynamic temperature The time-varying degradation rate, These are the model parameters.

[0033] Considering that battery capacity degradation is typically affected by dynamic temperature, the temperature effect needs to be taken into account in the degradation model. A common approach is to assume that some parameters in the degradation model are functions of temperature; in this application, we consider using an exponential function to relate temperature to the degradation rate.

[0034] S213. Based on Formulas 1, 4, and 5, a Wiener degradation model considering the influence of dynamic temperature on battery capacity degradation rate is established, as shown in the following expression: .

[0035] S22. Determine the joint correlation between degradation rate and volatility under the influence of dynamic temperature.

[0036] Typically, the diffusion parameter reflecting degradation changes is assumed to be a constant and does not change with updates to monitoring data or variations in dynamic temperature. In reality, this assumption violates the true degradation process, because faster capacity degradation is accompanied by greater fluctuations in degradation over time, meaning components with larger drift parameters are expected to have larger diffusion parameters as well. Therefore, this application establishes a Wiener degradation model that considers the joint correlation between degradation rate and fluctuations under the influence of dynamic temperature.

[0037] In this application, step S22 specifically includes: S221. Assume that the lithium-ion battery operates under two different time-varying temperature conditions, i.e. and For different temperature conditions, then and The cumulative distribution function of the remaining battery life under temperature conditions is expressed as follows: and .if Then the acceleration coefficient The definition is as follows: , In the formula, z is the sample index. They are respectively the zth, At that moment; For the first The temperature at that moment Let Z be the temperature at time z. , .

[0038] S222. According to the principle of constant acceleration factor, if the failure mechanism of a lithium-ion battery remains unchanged throughout its operation, the acceleration factor will only be determined by the stress of the external environment. Therefore, for any given time... It should satisfy the following equation: .

[0039] S223, Regarding Formula 8 Taking the partial derivative, we get: , In the formula, and They are respectively and The probability density function of the remaining battery life under temperature conditions.

[0040] S224. Substitute Formula 3 into Formula 9, and let... The joint correlation between the degradation rate and volatility under the influence of dynamic temperature can be obtained, as shown in the following expression: , In the formula, It is a fixed parameter that reflects the equivalence of the degradation mechanism.

[0041] It is clear from Formula 10 that under different temperature conditions, and The ratio remains unchanged.

[0042] It is important to note that the above formula assumes the invariance of the failure mechanism, which is also a fundamental assumption of predictive science. If the failure mechanism changes, it becomes impossible to accurately predict the remaining battery life based on historical data, as the degradation trend may be inconsistent.

[0043] S23. Combining steps S21 and S22, a lithium-ion battery capacity degradation model is obtained. This degradation model not only considers the influence of dynamic temperature on the battery capacity degradation rate, but also the joint correlation between degradation rate and volatility. The expression is as follows: .

[0044] It should be noted that in Formula 11, Replace with , Replace with .

[0045] S24, Known Degradation Monitoring Time The corresponding degradation observation state is ,use{ If k = 1, 2, ..., m, then it can be simplified to: The dynamic temperature data at the monitoring time points are ,Right now Therefore, the state-space model expression under the influence of dynamic temperature is as follows: , In the formula, for Dynamic temperature at any given moment for Estimated capacity degradation status of lithium-ion batteries at any given time; for and The difference, ; for and The difference, ; The parameters are nonlinear functions of time, representing unknown parameter vector at time ; for and The difference, .

[0046] S3. Estimate the prior values ​​of model parameters in the state-space model under the influence of dynamic temperature based on the maximum likelihood estimation method.

[0047] In this application, step S3 specifically includes: S31. Determine the model parameters in the state-space model under the influence of dynamic temperature. The model parameters include the model parameters in the temperature model. Model parameters in capacity degradation model , , .

[0048] In this application, in the constructed state-space model under the influence of dynamic temperature, the temperature model corresponds to the temperature state variable. The expression is given by the capacity degradation model, which corresponds to the degradation state variable. The expression is given. Furthermore, in this application, based on historical degradation data from measurements, the model parameters in the temperature model are estimated using maximum likelihood estimation. Prior values ​​and model parameters in the capacity degradation model The prior value.

[0049] S32. Estimating model parameters in a temperature model based on the maximum likelihood estimation method. The prior values ​​are as follows: S321. Based on Formula Twelve, it can be seen that... Under these conditions, dynamic temperature It follows a Gaussian distribution with a mean, i.e. obey Therefore, for The log-likelihood function yields: , In the formula, N represents a Gaussian distribution. This represents the log-likelihood function.

[0050] S322. Taking the partial derivative of the log-likelihood function, we get: , .

[0051] S323. Substituting Formula XIV and Formula XV into Formula XIII, we get: , In the formula, , .

[0052] S324. Estimate parameters based on Formula Sixteen. Then Substituting into formulas fourteen and fifteen, we can find the answer. , .

[0053] S33. Estimating model parameters in a capacity degradation model based on the maximum likelihood estimation method. The prior values ​​are as follows: S331, Based on the measured temperature and state-space model, let , ,but Then, based on formula twelve, it can be seen that... It follows a Gaussian distribution with a mean, i.e. obey .

[0054] S332, Let For model parameters, then The probability density function is shown below: .

[0055] S333, Based on Formula Seventeen The log-likelihood function is shown below: .

[0056] S334. Based on Formula 18, four-dimensional search maximizes the result. The maximum likelihood estimate.

[0057] S4. Based on the state-space model under the influence of dynamic temperature and the prior values ​​of the model parameters, a filtering method based on a Bayesian framework is used to predict the estimated value of the capacity degradation state and the remaining life of lithium-ion batteries. Specifically, a time-varying fading factor is introduced to optimize the importance density function during the importance sampling process, and an adaptive kernel density is used to estimate the posterior probability density function during the resampling process.

[0058] When considering complex and variable external operating conditions, traditional particle filtering methods may lead to particle degradation and depletion, thus affecting the accuracy of state estimation and battery remaining lifetime prediction. This application proposes a filtering method based on a Bayesian framework, utilizing a time-varying fading factor and adaptive kernel density estimation (AKDE) to optimize the importance density function and resampling process.

[0059] In this application, the state transition equation and measurement equation of lithium-ion battery capacity during the aging process are determined based on a lithium-ion battery capacity degradation model, wherein the expression of the state transition equation is as follows: , The expression for the measurement equation is shown below: , In the formula, , They represent , Estimated capacity degradation status of lithium-ion batteries at any given time. express The measured or estimated capacity of a lithium-ion battery at any given time. For measurement function, This indicates measurement noise.

[0060] It should be noted that in Formula 20, when For known data, When the data is unknown, according to Derivation ,at this time express Lithium-ion battery capacity measurement value at any time; when For unknown data, When the data is known, according to Derivation ,at this time express Estimated capacity of lithium-ion batteries at any given time. (See below for details in this application.) Whether it represents a measured value or an estimated value needs to be determined based on the specific application.

[0061] In this embodiment of the application, h=1.

[0062] It should be noted that the degradation process is subject to uncertainties due to temperature variations, and the parameters... It is time-varying.

[0063] In traditional methods, unknown state vectors are derived based on a Bayesian framework. The specific steps are as follows: ① Prediction step: Assume the posterior probability density function at time k-1. Having obtained this, the prior probability density function at time k is shown in the following equation: , In the formula, The state transition equation in Formula 19 is obtained as follows: express arrive Measurement of lithium-ion battery capacity at any given time.

[0064] ② Update step: Once new measurements are obtained , The posterior probability density function is then updated to: , In the formula, It is the likelihood function; The normalization constant is , express arrive Measurement of lithium-ion battery capacity at any given time.

[0065] The optimal Bayesian estimate can be recursively obtained using formulas 21 and 22. However, for complex high-dimensional integrals, analytical solutions are often difficult to obtain. To approximate the system state, a series of filtering algorithms have been proposed, among which particle filtering (PF) is considered a practical method for solving nonlinear / non-Gaussian problems. The main idea of ​​particle filtering is to obtain an approximate estimate from the probability density function... Samples collected in China By using weighted samples to represent the posterior probability density, the state estimate of the target can be obtained.

[0066] Obtained based on the Bayesian framework The posterior probability density function is used, and particle filtering is employed to determine the posterior probability density at time k and the weight update equation, where the posterior probability density at time k is approximately: , The weight update equation at time k is: , In the formula, Indicates the number of particles. This represents the weight of the i-th particle at time k. To represent a direct proportion, This represents the capacity degradation state estimate of the i-th particle at time k; Let be the Dirac function, representing the probability density at a specific point.

[0067] For computational convenience, traditional particle filtering uses the importance density function. Set as Next, the particles are resampled by creating new particle samples by copying the current particles with larger weights, and then the weights are assigned accordingly. However, the importance density function of traditional particle filtering is independent of the measured value. Therefore, this type of filtering is inefficient and sensitive to external interference, and the diversity of particles is lost as resampling proceeds. Therefore, this application uses the Auxiliary Particle Filter (APF) importance density function proposed by Pitt and Shephard to reconstruct the importance density function at time k obtained by the traditional particle filter, that is, the posterior probability density at time k, in order to solve this problem.

[0068] In this application, the importance density function at time k is reconstructed using the importance density function of the auxiliary particle filter (APF), and the expression of the importance density function of the APF is as follows: , The importance density function expression for the reconstructed time k is shown below: , In the formula, i For particle indexing; The auxiliary variable for the i-th particle is, in the known... hour The representation of it, its mean can be regarded as a sample value. from Obtained from.

[0069] However, due to uncertainties such as external environment, model error, and interference noise, the battery capacity degradation state can easily change suddenly, leading to reduced estimation accuracy and robustness, and weakened tracking ability. When the estimated battery capacity degradation state deviates from the system state, it will destroy the orthogonality of the output residual sequence. Therefore, this application applies the idea of ​​a strong tracking algorithm, introducing a time-varying fading factor in the importance sampling process to adjust the particle state in real time, forcing the residual sequence to maintain orthogonality and adaptively adjusting the estimation error to improve the filtering algorithm's ability to track state changes. In this way, the filter can generate particles that are closer to the true posterior distribution at each step, thereby improving the filtering effect and sample efficiency.

[0070] Based on the strong tracking filtering principle, a filtering algorithm should have the minimum mean square error, and the residual sequences at different times should be orthogonal. If a filtering algorithm can simultaneously satisfy both conditions, then it is considered to possess optimal estimation performance and strong tracking capability. The expression for the minimum mean square error is shown in Equation 27, and the expression for the orthogonality of the residual sequences at different times is shown in Equation 28. , , In the formula, for The actual value of the capacity degradation state of the lithium-ion battery at any given time. Represents the expectation operator, Here, k and g are the transpose symbols, and k and g are the sample indices. The residual between the k-th true value and the estimated value. , for Real-time lithium-ion battery capacity; Known Based on time information, An estimate of the time measurement.

[0071] In this application, the suboptimal solution of the time-varying fading factor is derived based on the residual orthogonality principle and the strong filtering idea. The expression of the suboptimal solution of the time-varying fading factor is as follows: , , In the formula, This represents the suboptimal solution with a time-varying fading factor. Represents the trace of a matrix. Let be the covariance matrix of the residuals. Measure the variance of noise. For measuring equations Jacobian matrix, This is state transition noise. Forgetting factor, The residual between the first true value and the estimated value; Let covariance matrix be the variance matrix. .

[0072] It should be noted that state transition noise and measurement noise are independent of each other. Additionally, the forgetting factor is typically set to 0.95.

[0073] In this application, the time-varying fading factor is introduced into Formula 26, and the expression for the importance density function with the time-varying fading factor is as follows: , make Then formula thirty-one can be transformed into: .

[0074] In this application, the first-order weights are obtained based on the importance density function with an introduced time-varying fading factor. The expression for the first-order weights is as follows: , In the formula, To assist in calculating the values ​​of the particle measurement equations, for The weight of the i-th particle at time i; for The first-order weights of the i-th particle at time i can be used to derive the sample set. ,in i , j For particle indexing, This indicates the marker of the particle at time k-1.

[0075] In filtering algorithms, the calculation of particle weights fundamentally depends on the likelihood that each particle is correlated with the actual measurement result. In this application, a time-varying fading factor is introduced to adjust the particle weights, making the influence of recent measurements on the weights greater.

[0076] As can be seen from Formula 33, the updated weights take into account both the latest measurements. This also makes the most recent measurement data play a more important role in the weight update process, thereby enhancing the particle filter's responsiveness to changes in the external environment. To ensure the stability of the filtering process, this application sets the time-varying fading factor to be greater than 1, i.e. .

[0077] Due to the importance density function Sample sets can be exported. The filtered sampling is mainly obtained from the probability density function. This way we can ignore it. The mark in From the probability density function Sample generation Therefore, in this application, according to Give each sample Assign corresponding weights; these weights are called second-order weights, and their expressions are as follows: , In the formula, for The second-order weight of the j-th particle at time j, for Time of the first The weight of each particle.

[0078] In this application, the estimated value of the lithium-ion battery capacity degradation state is obtained based on the second-order weight, and the expression for the estimated value of the lithium-ion battery capacity degradation state is as follows: , In the formula, for The estimated value of the degenerate state of the j-th particle at time j.

[0079] To avoid the loss of diversity among particles, this application uses adaptive kernel density estimation to estimate the posterior probability density function, where the kernel function can be viewed as a smoothing function used to transform discrete particle samples into a continuous probability density function. In this way, not only can a continuous estimate of the system state be obtained, but the impoverishment problem can also be solved.

[0080] In this application, the continuous estimates of the capacity degradation state of lithium-ion batteries are estimated based on adaptive kernel density estimation, specifically as follows: (1) Using adaptive kernel density estimation for particles Smooth the signal to form a continuous posterior probability density function: , In the formula, express KDE, The adaptive bandwidth for the i-th particle; For kernel functions, the commonly used kernel function is the Gaussian kernel function, whose expression is: .

[0081] In practical kernel density estimation, if the bandwidth is fixed across the entire interval, it can easily lead to overfitting in areas with abundant sample data and underfitting in areas with scarce sample data. To improve the goodness of fit and make the bandwidth more consistent with the needs of actual sample data, this application adaptively selects the bandwidth based on a function that reflects the density of sample points—the local bandwidth factor.

[0082] (2) Calculate the adaptive bandwidth, as shown in the following expression: , , In the formula, For fixed bandwidth, , Let n be the standard deviation of the sample data, and n be the sample size. For local bandwidth factor, For sensitivity parameters; This is a preliminary nuclear density estimate of the i-th particle at point... The value at that location, G is The geometric mean .

[0083] It should be noted that the sensitivity parameter The value is usually taken as The most common value is 0.5.

[0084] (3) Based on adaptive bandwidth, adaptive kernel density estimation is used for particle... Smoothing is performed to form a continuous posterior probability density function, as shown below: .

[0085] It should be noted that adaptive kernel density estimation is used for particles When smoothing, These are the normalized first-order weights.

[0086] (4) Perturbation sampling is used to sample the smooth probability density function. The magnitude of the perturbation can be determined by the bandwidth of AKDE, i.e. obey ,in For the magnitude of the disturbance, therefore from New samples from China One particle is .

[0087] This application proposes a filtering method based on a Bayesian framework. It uses a non-parametric method—Adaptive Kernel Density Estimation (AKDE)—to approximate the true posterior probability distribution, transforming discrete particles into continuous PDFs. This improves the resampling strategy, increases particle diversity, and solves the uncertainty problem in the filtering process.

[0088] In this application, step S4 specifically includes: S41. Estimation and prediction of lithium-ion battery capacity degradation status, including: S411. Initialization: From the initial distribution Mid-sampling generation Particle sample And initialize weights for all particles. , ; S412. Calculate auxiliary variables: from the given... Auxiliary variables were calculated. Auxiliary variables from Obtained in; S413, Update the time-varying fading factor: Update the time-varying fading factor based on the suboptimal solution of the time-varying fading factor; S414. Importance Sampling and Weighting: An importance density function (Equation 33) is generated based on auxiliary variables and a time-varying fading factor. Importance sampling is then performed based on this function. The first-order weight of each particle obtained after importance sampling is calculated and normalized to obtain the particle set. The normalization formula is as follows: ; S415, Smoothing: Calculate the adaptive bandwidth and use an adaptive kernel density estimate based on the adaptive bandwidth to smooth the particles. Smoothing is performed to form a continuous posterior probability density function, i.e. ; S416, Perturbation Sampling: From Sampling Marked as To obtain the same weight A set of particles ,in For the magnitude of the disturbance, obey ; S417. Prediction: Based on a state-space model under the influence of dynamic temperature, from... Get from A set of particles ; S418, Update: Calculate the second-order weight of each particle based on Formula 34 to obtain the particle set. ; S419. Resampling: Calculate the effective number of particles. ;like Less than the threshold Repeat steps S416-S419 to resample; S410. Based on Formula 35, obtain the estimated value of the capacity degradation state of the lithium-ion battery.

[0089] It should be noted that during particle filtering, the weights are immediately replaced by the new weights after the update is completed. Therefore, for both sides of the normalization formula... This application does not distinguish between them.

[0090] S42, Lithium-ion battery remaining life prediction, including: S421. In the state-space model under the influence of dynamic temperature, the remaining lifespan of a lithium-ion battery is defined as the time when the system state reaches or exceeds a predetermined fault threshold, as shown in the following expression: , In the formula, L represents the remaining lifespan of the lithium-ion battery, which is related to the failure time. t The following relationship exists: ; The remaining lifespan of a lithium-ion battery when it reaches a critical threshold. yes The battery capacity degradation status at any given moment.

[0091] S422, The updated model parameters based on the state-space model under dynamic temperature influence and the filtering method based on the Bayesian framework. The dynamic temperature and capacity degradation trajectory is determined as follows: , , In the formula, ; for The remaining lifespan of a lithium-ion battery when it reaches a critical threshold.

[0092] S423. Based on the dynamic temperature and capacity degradation trajectory, the remaining lifetime estimate of each particle is obtained, as shown in the following expression: , In the formula, express Time of the first i The remaining lifetime of each particle. Indicates the first i The lifetime of an individual particle.

[0093] S424. Based on the remaining lifetime estimate of each particle, obtain the point estimate of the remaining lifetime of the lithium-ion battery and the probability density function of the remaining lifetime of the lithium-ion battery, wherein the expression for the point estimate of the remaining lifetime of the lithium-ion battery is as follows: , The probability density function expression for the remaining lifespan of a lithium-ion battery is shown below: , In the formula, express Point estimate of the remaining lifespan of a lithium-ion battery at a given time. Indicates the state given Temperature status The probability of remaining lifespan of a lithium-ion battery under certain conditions; express The weight of the i-th particle at time i; Let be the Dirac function, representing the probability density at a specific point.

[0094] S5. Input the degradation data of the lithium-ion battery under test into step S4 after preprocessing to obtain the estimated value of the capacity degradation state and the remaining life of the lithium-ion battery under test.

[0095] This application validates the proposed lithium-ion battery capacity degradation model and remaining life prediction method using a battery dataset provided by NASA Ames Research Center. The dataset contains four 18650 lithium-ion batteries, numbered B0005, B0006, B0007, and B0018, each with a rated capacity of 2 Ah. The four batteries were operated in three modes: charging mode, discharging mode, and impedance testing mode. The experiment was stopped when the batteries reached their end-of-life (EOL) standard, at which point the battery capacity decreased from 2 Ahr to 1.4 Ahr, representing a 30% reduction in rated capacity. Battery B0018 was used as an example for validation.

[0096] As is well known, operating temperature is a significant factor influencing capacity degradation. This application uses battery B0018 as an example. During verification, the particle size was set to N=400. The initial value was subtracted from the original data, and then the opposite value was taken, resulting in an initial value of 0. This increased the degradation trend, thus achieving data transformation. Figure 2 a represents the temperature fluctuation curve of battery B0018. Figure 2 b represents the capacity degradation curve of battery B0018. (From the figure...) Figure 2 As can be clearly seen from the temperature fluctuation curve of a, it is stable but exhibits random fluctuations, which is consistent with the conditions required by the degradation model proposed in this application.

[0097] First, to verify the effectiveness of this method, the lithium-ion battery capacity degradation model constructed in this application was compared with three other models in this experiment. The lithium-ion battery capacity degradation model constructed in this application is denoted as M0, and the other three models are as follows: (1) A basic nonlinear Wiener process proposed by Si, denoted as M1, is expressed as follows: , In the formula, v is a constant parameter used to control the intensity of random disturbances.

[0098] (2) Compared with model M0, the influence of temperature is ignored. The model M0 proposed in this application degenerates into a Wiener process model with adaptive drift, denoted as M2, and the expression is as follows: .

[0099] (3) Only the effect of time-varying temperature on the degradation rate is considered, while the interaction between the degradation rate and fluctuation under the influence of time-varying temperature is ignored, denoted as M3, and the expression is as follows: .

[0100] Based on the "Preliminary values ​​of model parameters in the state-space model under the influence of dynamic temperature based on the maximum likelihood estimation method" proposed in this application, the prior values ​​of the model parameters of battery B0018 in model M0 in this application are estimated as follows: .

[0101] In this experiment, the log-likelihood and AIC values ​​of the four models M0-M3 when fitting degradation data for battery B0018 are given, as shown in Table 1.

[0102]

[0103] As can be clearly seen from Table 1, model M0, which considers the effect of temperature on the capacity degradation rate and the interaction between degradation rate and volatility under the influence of time-varying temperature, has a greater likelihood and a smaller AIC, which means it has better performance when modeling degradation data.

[0104] To compare the one-step prediction accuracy of these models, this experiment also calculated... and The mean absolute error (MAE) between the values ​​is calculated, and the results are shown in Table 2. The formula for calculating MAE is as follows: .

[0105]

[0106] As can be clearly seen from Table 2, model M0 has the lowest MAE value, at 0.0068. This may be attributed to the fact that the model M0 proposed in this application fully considers the uncertainty of temperature factors in the battery capacity degradation process, and also indicates that the degradation path fitted by the algorithm proposed in this application is very good. It is precisely because of the optimization in these two key aspects that the prediction accuracy has been significantly improved, thereby effectively reducing the MAE in one prediction step.

[0107] Secondly, taking battery B0018 as an example, this experiment compares the one-step prediction results and estimation errors of the battery capacity degradation state obtained by the traditional auxiliary particle filtering method and the improved filtering method of this application, as shown in the comparison results. Figure 3 As shown, where Figure 3 a is a comparison chart of the one-step prediction results for the capacity degradation state of battery B0018. Figure 3 b is a comparison chart of the estimation error of battery B0018.

[0108] Again, such as Figure 4 As shown, to verify the battery remaining life prediction performance of this method, different prediction starting points (60, 70) and the same battery failure threshold were set in the experimental analysis. Figure 4This section compares the predicted capacity and actual capacity of battery B0018 in the NASA battery dataset at different starting prediction points. Figure 4 The starting point for a is the 60th cycle. Figure 4 b starts at the 70th cycle.

[0109] from Figure 3-4 It is evident from the data that the improved filtering method of this application maintains excellent estimation ability and strong robustness. Traditional auxiliary particle filtering methods, on the other hand, cannot effectively address the particle depletion problem caused by fluctuations in the external environment, resulting in significant fluctuations and estimation errors.

[0110] Furthermore, taking batteries B0005, B0006, and B0018 as examples, to better demonstrate the superiority of this method, the absolute error of this method was compared with that of some existing methods at the 60th and 70th cycles in this experiment. These methods included Auxiliary Particle Filter (APF), Extended Kalman Particle Filter-Autoregressive EKPF-AR, Kalman Filter-Rauch-Tung-Striebel Expected Maximum Value (KF-EM-RTS), and Particle Filter-Time Attention Mechanism-Bidirectional Gated Recursive Unit (PF-BiGRU-TSAM). The comparison results are shown in Table 3. It should be noted that the capacity fault threshold used in this experiment was the same when comparing the absolute error of this method with some existing methods at the 60th and 70th cycles.

[0111]

[0112] As can be clearly seen from Table 3, compared with existing methods, the proposed filtering method based on the Bayesian framework has significant advantages in predicting battery remaining life.

[0113] In addition, such as Figure 5-6 As shown, this experiment also uses battery B0018 as an example to present the predicted battery life after applying this prediction method. Figure 5 Point prediction results for the remaining lifetime of battery B0018 from the 40th cycle to the 90th cycle. Figure 6 The remaining life prediction curves for battery B0018 at different cycle times. Figure 5 As can be seen, with the increase of sample data, the absolute error between the estimated value and the actual value gradually decreases. From... Figure 6 As can be seen, as the sample data increases, the capacity performance of lithium batteries degrades, the probability density function gradually narrows over time, and the estimated remaining lifespan gets closer to the true value.

[0114] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for predicting the remaining life of lithium-ion batteries considering the effects of dynamic temperature, characterized in that, Specifically, it includes: S1. Collect historical degradation data of lithium-ion batteries and perform preprocessing. The historical degradation data of lithium-ion batteries includes temperature, voltage, current and capacity. S2. Establish a lithium-ion battery capacity degradation model and obtain a state-space model under the influence of dynamic temperature. This degradation model not only considers the influence of dynamic temperature on the battery capacity degradation rate, but also considers the joint correlation between degradation rate and volatility. S3. Estimate the prior values ​​of model parameters in the state-space model under the influence of dynamic temperature based on the maximum likelihood estimation method; S4. Based on the state-space model under the influence of dynamic temperature and the prior values ​​of model parameters, a filtering method based on a Bayesian framework is used to predict the estimated value of lithium-ion battery capacity degradation state and remaining life. Among them, a time-varying fading factor is introduced to optimize the importance density function during the importance sampling process, and an adaptive kernel density is used to estimate the posterior probability density function during the resampling process. S5. Input the degradation data of the lithium-ion battery under test into step S4 after preprocessing to obtain the estimated value of the capacity degradation state and the remaining life of the lithium-ion battery under test.

2. The method for predicting the remaining life of a lithium-ion battery considering the influence of dynamic temperature according to claim 1, characterized in that, Preprocessing includes data selection, data transformation, and feature selection.

3. The method for predicting the remaining life of a lithium-ion battery considering the influence of dynamic temperature according to claim 1, characterized in that, Step S2 is as follows: S21. Establish a Wiener degradation model that considers the effect of dynamic temperature on battery capacity degradation rate, as shown in the following expression: ， In the formula, t represents time. Let t be the state variable representing the capacity degradation of the lithium-ion battery at time t. This represents the initial state variable indicating the capacity degradation of the lithium-ion battery. The drift coefficient reflects the degradation rate. Indicates dependence on dynamic temperature The time-varying degradation rate, To represent the diffusion coefficient of the degradation process, Represents standard Brownian motion; Represents a vector with unknown parameters It is used to characterize the nonlinear properties of components; S22. Determine the joint correlation between degradation rate and volatility under the influence of dynamic temperature, as shown in the following expression: ， In the formula, z is the sample index. For acceleration coefficient, It is a fixed parameter that reflects the equivalence of the degradation mechanism; S23. Combining steps S21 and S22, a lithium-ion battery capacity degradation model is obtained. This degradation model not only considers the influence of dynamic temperature on the battery capacity degradation rate, but also the joint correlation between degradation rate and volatility. The expression is as follows: ， In the formula, Indicates dynamic temperature. Represents the long-term average temperature. This represents the standard deviation fluctuation of temperature. Represents the regression rate. Brownian motion under time scale transformation, These are model parameters; S24, Known Degradation Monitoring Time The corresponding degradation observation state is ,use{ If k = 1, 2, ..., m, then it can be simplified to: The dynamic temperature data at the monitoring time points are ,Right now Therefore, the state-space model expression under the influence of dynamic temperature is as follows: ， In the formula, for Dynamic temperature at any given moment for Estimated capacity degradation status of lithium-ion batteries at any given time; for and The difference, ; for and The difference, ; The parameters are nonlinear functions of time, representing unknown parameter vector at time ; for and The difference, .

4. The method for predicting the remaining life of a lithium-ion battery considering the influence of dynamic temperature according to claim 1, characterized in that, Step S3 is as follows: S31. Determine the model parameters in the state-space model under the influence of dynamic temperature. The model parameters include the model parameters in the temperature model. Model parameters in capacity degradation model , , ; S32. Estimating model parameters in a temperature model based on the maximum likelihood estimation method. The prior values ​​are as follows: S321. Based on the state-space model under the influence of dynamic temperature, it can be seen that... Under these conditions, dynamic temperature It follows a Gaussian distribution with a mean, i.e. obey Therefore, for The log-likelihood function yields: ， In the formula, N represents a Gaussian distribution. Represents the log-likelihood function; S322. Taking the partial derivative of the log-likelihood function, we get: ， ； S323. Substituting the formula obtained in step S322 into the formula in step S321, we get: ， In the formula, , ; S324. Estimate the parameters based on the formula in step S323. Then Substituting into the formula in step S322, we can calculate... , ; S33. Estimating model parameters in a capacity degradation model based on the maximum likelihood estimation method. The prior values ​​are as follows: S331, Based on the measured temperature and state-space model, let , ,but Subsequently, based on the state-space model under the influence of dynamic temperature, it can be seen that... It follows a Gaussian distribution with a mean, i.e. obey ; S332, Let For model parameters, then The probability density function is shown below: ； S333, Based on the formula obtained in step S332 The log-likelihood function is shown below: ； S334, based on The log-likelihood function is obtained by maximizing it in a four-dimensional search. The maximum likelihood estimate.

5. The method for predicting the remaining life of a lithium-ion battery considering the influence of dynamic temperature according to claim 1, characterized in that, Step S4 is as follows: S41. Estimation and prediction of lithium-ion battery capacity degradation status, including: S411. Initialization: From the initial distribution Mid-sampling generation Particle sample And initialize weights for all particles. , ; S412. Calculate auxiliary variables: from the given... Auxiliary variables were calculated. Auxiliary variables from Obtained; S413, Update the time-varying fading factor: Update the time-varying fading factor based on the suboptimal solution of the time-varying fading factor; S414. Importance Sampling and Weighting: An importance density function is generated based on auxiliary variables and a time-varying fading factor. Importance sampling is then performed based on this function. The first-order weight of each particle obtained after importance sampling is calculated and normalized to obtain the particle set. ; S415, Smoothing: Calculate the adaptive bandwidth and use an adaptive kernel density estimate based on the adaptive bandwidth to smooth the particles. Smoothing is performed to form a continuous posterior probability density function, i.e. ; S416, Perturbation Sampling: From Sampling Marked as To obtain the same weight A set of particles ,in For the magnitude of the disturbance, obey , The adaptive bandwidth for the i-th particle; S417. Prediction: Based on a state-space model under the influence of dynamic temperature, from... Get from A set of particles ; S418, Update: Calculate the second-order weights for each particle to obtain the particle set. ; S419, Resampling: Calculating the effective number of particles ;like Less than the threshold Repeat steps S416-S419 to resample; S410, Obtain an estimate of the capacity degradation state of the lithium-ion battery; S42, Lithium-ion battery remaining life prediction, including: S421. In the state-space model under the influence of dynamic temperature, the remaining lifespan of the lithium-ion battery is defined as the time when the system state reaches or exceeds the predetermined fault threshold. S422, The updated model parameters based on the state-space model under dynamic temperature influence and the filtering method based on the Bayesian framework. To determine the dynamic temperature and capacity degradation trajectory; S423. Based on the dynamic temperature and capacity degradation state trajectory, obtain the remaining lifetime estimate for each particle; S424. Based on the remaining lifetime estimate of each particle, obtain the point estimate of the remaining lifetime of the lithium-ion battery and the probability density function of the remaining lifetime of the lithium-ion battery.

6. The method for predicting the remaining life of a lithium-ion battery considering the influence of dynamic temperature according to claim 5, characterized in that, Based on the principle of residual orthogonality and the idea of ​​strong filtering, the suboptimal solution of the time-varying fading factor is derived, and the expression of the suboptimal solution of the time-varying fading factor is as follows: ， ， In the formula, k is the sample index. It is the transpose symbol. This represents the suboptimal solution with a time-varying fading factor. Represents the trace of a matrix. Let be the covariance matrix of the residuals. Measure the variance of noise. For measuring equations Jacobian matrix, This is state transition noise. Forgetting factor, The residual between the first true value and the estimated value; Let covariance matrix be the variance matrix. , Represents the expectation operator; The residual between the k-th true value and the estimated value. , for Real-time lithium-ion battery capacity; Known Based on time information, An estimate of the time measurement.

7. The method for predicting the remaining life of a lithium-ion battery considering the influence of dynamic temperature according to claim 5, characterized in that, The first-order weight expression is shown below: ， ， In the formula, for The first-order weights of the i-th particle at time i can be used to derive the sample set. ,in i , j For particle indexing, The marker indicating the particle at time k-1; To represent a direct proportion, for The weight of the i-th particle at time i. For measurement function, Indicates measurement noise. To assist in calculating the values ​​of the particle measurement equations, express The measured or estimated capacity of the lithium-ion battery at any given time; The second-order weight expression is shown below: ， In the formula, for The second-order weight of the j-th particle at time j, for Time of the first The weight of each particle, express arrive Measurement of lithium-ion battery capacity at any given time.

8. The method for predicting the remaining life of a lithium-ion battery considering the influence of dynamic temperature according to claim 5, characterized in that, The adaptive bandwidth calculation formula is as follows: ， ， In the formula, The adaptive bandwidth for the i-th particle; For fixed bandwidth, , Let n be the standard deviation of the sample data, and n be the sample size. For local bandwidth factor, For sensitivity parameters; This is a preliminary nuclear density estimate of the i-th particle at point... The value at that location, G is The geometric mean ; Based on adaptive bandwidth, adaptive kernel density estimation is used for particles. Smoothing is performed to form a continuous posterior probability density function, i.e. The expression is as follows: ， In the formula, express KDE, For kernel functions; The estimated value of the capacity degradation state of a lithium-ion battery is expressed as follows: ， In the formula, for Estimated capacity degradation state of lithium-ion batteries at any given time. for The estimated value of the degenerate state of the j-th particle at time j.

9. The method for predicting the remaining life of a lithium-ion battery considering the influence of dynamic temperature according to claim 5, characterized in that, The expressions for the dynamic temperature and capacity degradation state trajectory are shown below: ， ， The remaining lifetime estimate for each particle is given by the following formula: ， In the formula, ; for The remaining lifespan of a lithium-ion battery when it reaches a critical threshold. express Time of the first i The remaining lifetime of each particle. Indicates the first i The lifetime of an individual particle.

10. The method for predicting the remaining life of a lithium-ion battery considering the influence of dynamic temperature according to claim 5, characterized in that, The point estimate of the remaining life of a lithium-ion battery is expressed as follows: ， The probability density function expression for the remaining lifespan of a lithium-ion battery is shown below: ， In the formula, express Point estimate of the remaining lifespan of a lithium-ion battery at a given time. Indicates the state given Temperature status The probability of remaining lifespan of a lithium-ion battery under certain conditions; express The weight of the i-th particle at time i; Let be the Dirac function, representing the probability density at a specific point.

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