Battery residual life prediction method considering capacity self-recovery

Abstract

The invention relates to a battery residual life prediction method considering capacity self-recovery. The method comprises the following steps: obtaining an original estimation error according to battery capacity data and a capacity predicted by adopting a double-index model; the method comprises the following steps: reconstructing an original error sequence through CEEMDAN, and selecting a strongly correlated intrinsic mode function; gaussian process regression is adopted to predict a new error sequence; using the prediction result of the GPR to correct the final capacity estimation; and using the corrected capacity estimation to predict the remaining service life of the lithium ion battery. The CEEMDAN can extract a representative intrinsic mode function according to the multi-scale characteristics of the battery capacity degradation data, and effectively preserves the long-term evolution information and important local fluctuation information of the system. And in combination with the GPR, prediction error local fluctuation caused by the capacity self-recovery effect can be accurately predicted and corrected, and confidence evaluation on the prediction result is provided, so that the prediction performance is more stable and accurate. Through the operation, the prediction precision of the RUL is obviously improved.

Description

Technical Field

[0001] The present invention relates to the technical field of battery health systems, and in particular to a method for predicting remaining battery life taking into account capacity self-recovery. Background Art

[0002] Due to the global energy crisis and environmental pollution, electric vehicles (EVs) have become a major trend in the automotive industry. Lithium-ion batteries are widely used in electric vehicles due to their high power density and long cycle life. Battery durability and cost are one of the main challenges in the commercialization of electric vehicles. RUL represents the time required from the current moment to the end of life (EOL), usually expressed in the number of cycles. If the current capacity is less than 80% of the nominal capacity, it is considered to have reached EOL, which means that the battery needs to be scrapped or replaced. Accurate prediction of the remaining useful life (RUL) and timely maintenance of the battery before an impending failure event can help extend the service life of lithium-ion batteries and reduce costs.

[0003] Predicting the remaining service life of lithium batteries is usually achieved through electrochemical models, capacity decay analysis, cycle life prediction, and advanced battery management system technology, combined with real-time monitoring and data-driven methods to accurately estimate the health status and remaining life of the battery. As the main method for predicting the remaining life of lithium batteries, the capacity decay model is favored because of its simplicity, direct practicality, and wide applicability in practical applications. By measuring the change in the charge and discharge capacity of the battery, the health status and remaining life of the battery can be quickly and effectively evaluated, providing a reliable basis for life prediction for electric vehicles. However, the existing methods are studied under the premise that the battery capacity decay process is irreversible. In fact, after discharge and rest, lithium batteries will show a short-term capacity recovery phenomenon due to electrolyte redistribution, changes in the solid electrolyte interface (SEI) layer, internal stress release, and reversal of side reactions. This phenomenon is the result of the complex electrochemical behavior of lithium batteries, which brings challenges to the prediction of the remaining service life of the battery and causes local fluctuations in the remaining service life prediction error.

[0004] The existing method of predicting the degradation state of lithium-ion batteries using random forest regression models involves determining the parameter features that characterize the self-recovery state of battery capacity. The selection of these features is crucial to the prediction results, and there are great challenges in how to accurately select and measure these features, and how to adjust the parameters of the model to optimize the prediction performance. When using the VMD-HGWO-SVR model to predict the remaining service life of lithium batteries, it is necessary to set a threshold based on the correlation coefficient analysis to select the appropriate modal function for reconstruction, which involves certain subjective judgments and experience accumulation. Different threshold selections may affect the final preprocessing effect and prediction results. When using the method combining CEEMDAN and Bi-LSTM to predict the remaining service life of lithium-ion batteries, since Bi-LSTM is a deep learning model with a complex internal structure and mechanism, it is usually regarded as a black box model, which makes it difficult to understand which features the model is based on when making decisions during predictions, and it is difficult to provide detailed confidence and uncertainty estimates. Summary of the invention

[0005] In view of the above-mentioned problems, the present invention proposes a method for predicting the remaining life of a battery taking into account capacity self-recovery.

[0006] Terminology explanation: EMD: Empirical Mode Decomposition is a signal processing technique used to decompose non-stationary and nonlinear signals into a series of intrinsic mode functions (IMFs). These IMFs represent the intrinsic oscillation modes of the signal at different time scales, and the decomposition is achieved by iteratively solving the local extrema and mean.

[0007] IMF: Intrinsic Mode Functions (IMF) are signal components generated during the empirical mode decomposition process. These components must have the same number of zeros and extreme points over the entire time scale or differ by at most one, and the local average value at any time is zero, that is, the average value of the upper and lower envelopes of the signal is zero. IMF is used to decompose complex signals so that each IMF represents a different scale or frequency component of the signal, which facilitates subsequent signal analysis and processing.

[0008] NLML: Negative log marginal likelihood NLML refers to the negative logarithm of the marginal likelihood. In statistics and machine learning, especially in Bayesian statistics and Gaussian processes, NLML is used to evaluate how well a model fits the data. It quantifies how well the model explains the observed data while taking into account parameter uncertainty. By minimizing NLML, the optimal model parameters can be found to better describe the data, which is a key tool for model selection and parameter estimation in complex statistical models such as Gaussian processes.

[0009] CEEMDAN: Complete Ensemble Empirical Mode Decomposition with Adaptive Noise is an improved version of EMD, which aims to solve some limitations of traditional EMD in dealing with nonlinear and non-stationary signals. CEEMDAN uses ensemble averaging technology to eliminate modal mixing and pseudo-modal problems between modes by adding random noise multiple times, making the decomposition results more stable and reliable.

[0010] GPR: Gaussian Process Regression (GPR) is a non-parametric regression method based on probability theory, used to predict continuous output variables. It assumes that the unknown function can be regarded as a Gaussian process, that is, the function value of any set of input variables obeys a multidimensional normal distribution. Through known training data, GPR can infer the probability distribution of the target function and use this distribution for prediction.

[0011] White Gaussian noise: White Gaussian noise is a random signal that obeys a Gaussian distribution in time or space and has uniform power spectral density at all frequencies.

[0012] To achieve the above object, the present invention provides the following technical solutions: A method for predicting remaining battery life taking into account capacity self-recovery, the method comprising the following steps: The original estimation error is obtained based on the battery capacity data and the capacity predicted using the double exponential model; The original error sequence is reconstructed through CEEMDAN, and strongly correlated intrinsic mode functions (IMFs) are selected; Use Gaussian process regression to predict new error sequences; Correct the final capacity estimate using the GPR predictions; Predict the remaining useful life of lithium-ion batteries using corrected capacity estimates.

[0013] As a further technical solution of the present invention, the step of reconstructing the original error sequence by CEEMDAN includes: The modal decomposition method is used to decompose the original error curve into a trend term reflecting the error change and a detail fluctuation term caused by the capacity self-recovery effect. There are some problems with traditional modal decomposition methods. For example, empirical mode decomposition (EMD) has characteristic components with different time scales in a single intrinsic mode function (IMF) component, which is the mode mixing problem. As an improved method of EMD, ensemble empirical mode decomposition (EEMD) reduces the mode mixing effect by adding white noise, but its decomposition process is incomplete, inefficient, and has large reconstruction errors. CEEMDAN was proposed to solve the above problems. It adds adaptive Gaussian white noise before each decomposition process and obtains each IMF component by calculating a unique residual signal. CEEMDAN implements a complete adaptive decomposition process, and the original data can be accurately reconstructed. Assuming the original signal is s(t), the CEEMDAN algorithm is described as follows: 1) Decomposition , the first eigenmode function is calculated as:

[0014] in represents the original error sequence, Represents different white Gaussian noises that satisfy the standard normal distribution; i=1,2,..., L is the number of times the white noise is added, represents the noise factor and is obtained in the same way as the EMD , represents the estimated value of the first intrinsic mode function IMF decomposed by the CEEMDAN algorithm, It represents the first intrinsic mode function IMF obtained by empirical mode decomposition EMD after adding Gaussian white noise for the i-th time. It is the result obtained by averaging the estimated value of the first IMF obtained by empirical mode decomposition (EMD) after adding Gaussian white noise multiple times; 2) Calculate the first residual when k=1, and the calculation formula is ; 3) Generate the first intrinsic mode function through EMD decomposition , and calculate the second eigenmode function as: ; 4) Calculate the kth residual ; 5) Generate the kth intrinsic mode function through EMD decomposition , and calculate the k+1th eigenmode function: ; ; in is the operator used to generate the kth IMFs, represents the i-th sample of different white Gaussian noise sequences that satisfy the standard normal distribution, where i From 1 to L The index of L In the process of adding different white Gaussian noises, each added white noise is independent and identically distributed. By adding noise multiple times and averaging the results, the stability and accuracy of the decomposition are improved. 6) Repeat steps 4) and 5) until the EMD process cannot decompose the residual; eventually, the residual Represents the global trend of capacity forecast error, residual represents the local fluctuation of the prediction error caused by the capacity self-recovery effect; 7) Use the Pearson correlation coefficient to measure the correlation between each IMF component and the error evolution information. By calculating the correlation coefficient between each IMF component and the error evolution information, determine which IMF components are useful and which are noise. The calculation formula of the Pearson correlation coefficient is as follows: ; The Pearson correlation coefficient was used to quantitatively evaluate the positive or negative correlation, and the correlation between the IMF and the original error was obtained, where a high correlation is represented by a value far from 0; Represents a series of intrinsic mode function IMF components, represents the average value of a series of intrinsic mode function IMF components, and represents the original error sequence, represents the average value of the original error series; Through correlation analysis, the appropriate intrinsic mode function is selected; since high-frequency IMF represents local fluctuations and has little impact on long-term predictions, it is removed from the reconstruction process. Since weakly correlated IMFs contribute little to error trend predictions, they are also removed from the reconstruction. IMFs with correlation coefficients greater than 0.4 are selected as effective components for error reconstruction. The reconstructed sequence reflects both the long-term trend of the original sequence and the degradation information of the original sequence. This lays the foundation for the successful prediction of data-driven algorithms that are sensitive to training data.

[0015] As a further technical solution of the present invention, the step of using Gaussian process regression (GPR) to predict a new error sequence includes: As a machine learning model based on statistical learning and Bayesian theory, GPR has been widely used in the field of regression prediction.

[0016] The probability density function is:

[0017] is the average function, is the covariance function called the kernel function K; The specific calculation process is: ; in, stands for mathematical expectation; The squared exponential covariance function is used as the kernel function of the covariance function: ; in is the signal variance, with output scaled magnitude, is a diagonal matrix; The observed output with Gaussian noise is: ; The observation vector Affected by noise Influence; The prior distribution of the observations is shown as: ; in is the n-dimensional identity matrix, represents the normal distribution, also called the Gaussian distribution, is the noise covariance matrix, expressed as: ; in Indicates the similarity of variables. and is used to calculate the kernel function The input parameter, P is a diagonal matrix, is the inverse matrix of the diagonal matrix, and the hyperparameter set It is formulated and optimized by minimizing the negative log marginal likelihood (NLML), which is expressed as: ; The calculation process of NLML is written as: ; in, is the negative log marginal likelihood, a measure of the probability that a given parameter set A scalar value that indicates how well the model fits the data. It is the negative logarithm of the marginal likelihood. is the conditional probability density function, which means that given the input and parameters Next, output The probability of is the observed output data vector, is the parameter set of the Gaussian process model, Is the input data The internal kernel function matrix, is the variance matrix of the noise; The maximum value of the objective function is obtained by taking the derivative of the log-likelihood function, which is calculated as follows: ; here is an element of the hyperparameter set; The GPR training process is carried out in the above manner, and then the GPR model is used for prediction tasks using the posterior distribution. , observed value and predicted values The joint prior distribution of is expressed as follows: ; according to The joint Gaussian distribution on derives the posterior distribution : ; Among them, the predicted mean and covariance The calculation formula is: ; in, Indicates that at the new input point The predicted output value at Represents a set of training data points The corresponding output value vector, Represents a set of input points With new input point The kernel function matrix between Represents a set of training data points The internal kernel matrix, represents the variance matrix of the noise, Indicates a new input point and its own kernel function value.

[0018] Compared with the prior art, the present invention has the following beneficial effects: First, CEEMDAN can adaptively extract intrinsic mode functions (IMFs) of different scales and frequencies according to the characteristics of the data, so as to better capture the long-term evolution information and local fluctuation information in the process of lithium battery capacity degradation. This data-driven feature enables the model to adapt to the working conditions and degradation characteristics of different batteries more effectively. In addition, using GPR to predict new error sequences to correct the original remaining service life prediction values ​​can effectively reduce the local fluctuations of the prediction error caused by the self-recovery effect of battery capacity. GPR can not only provide accurate prediction values, but also evaluate the uncertainty of the prediction results, thereby improving the accuracy and reliability of the prediction. In addition, Gaussian process regression, as a probability-based non-parametric regression method, can provide confidence and uncertainty estimates for the prediction results and has good model interpretability. This enables users to understand the prediction basis of the model and the contribution of each intrinsic mode function to the prediction. The method combined with CEEMDAN and GPR can better maintain the generalization ability and stability of the model when processing battery capacity degradation data. By effectively extracting and utilizing the intrinsic mode functions, the problem of model performance degradation caused by changes in data characteristics can be reduced. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 A flowchart of a method for predicting remaining battery life taking into account capacity self-recovery provided in an embodiment of the present invention.

[0020] Figure 2 This is the prediction result without considering the capacity self-recovery effect.

[0021] Figure 3 A diagram of prediction results using the prediction method of the present invention provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0022] The technical solution of the present invention is further described in detail below in conjunction with specific implementation methods.

[0023] After discharge and rest, lithium batteries will show a phenomenon of short-term capacity recovery due to electrolyte redistribution, changes in the solid electrolyte interface (SEI) layer, internal stress release, reversal of side reactions, etc. The self-recovery effect of battery capacity will cause the problem of local fluctuations in prediction errors. To address this problem, the present invention proposes to reconstruct a new error sequence using the complete ensemble empirical mode decomposition (CEEMDAN) of adaptive noise. By selecting strongly correlated intrinsic mode functions (IMFs), the long-term evolution information of the system and some important local fluctuation information are retained. Finally, Gaussian process regression (GPR) is used to predict the new error sequence to correct the final capacity estimate and thus predict the remaining service life of the lithium-ion battery.

[0024] See also Figure 1 As an embodiment of the present invention, a method for predicting the remaining life of a battery considering capacity self-recovery is provided, and the method comprises the following steps: The original estimation error is obtained based on the battery capacity data and the capacity predicted using the double exponential model; The original error sequence is reconstructed through CEEMDAN, and strongly correlated intrinsic mode functions (IMFs) are selected; Gaussian process regression (GPR) is used to predict new error sequences; Use the GPR predictions to correct the final capacity estimate; Predict the remaining useful life of lithium-ion batteries using corrected capacity estimates.

[0025] In this embodiment, the step of reconstructing the original error sequence by using CEEMDAN includes: The modal decomposition method is used to decompose the original error curve into a trend term reflecting the error change and a detail fluctuation term caused by the capacity self-recovery effect. There are some problems with traditional modal decomposition methods. For example, empirical mode decomposition (EMD) has characteristic components with different time scales in a single intrinsic mode function (IMF) component, which is the mode mixing problem. As an improved method of EMD, ensemble empirical mode decomposition (EEMD) reduces the mode mixing effect by adding white noise, but its decomposition process is incomplete, inefficient, and has large reconstruction errors. CEEMDAN was proposed to solve the above problems. It adds adaptive Gaussian white noise before each decomposition process and obtains each IMF component by calculating a unique residual signal. CEEMDAN implements a complete adaptive decomposition process, and the original data can be accurately reconstructed. Assuming the original signal is s(t), the CEEMDAN algorithm is described as follows: 1) Decomposition , the first eigenmode function is calculated as:

[0026] in represents the original error sequence, Represents different white Gaussian noises that satisfy the standard normal distribution; i=1,2,..., L is the number of times the white noise is added, represents the noise factor and is obtained in the same way as the EMD , represents the estimated value of the first intrinsic mode function IMF decomposed by the CEEMDAN algorithm, It represents the first intrinsic mode function IMF obtained by empirical mode decomposition EMD after adding Gaussian white noise for the i-th time. It is the result obtained by averaging the estimated value of the first IMF obtained by empirical mode decomposition (EMD) after adding Gaussian white noise multiple times; 2) Calculate the first residual when k=1, and the calculation formula is ; 3) Generate the first intrinsic mode function through EMD decomposition , and calculate the second eigenmode function as: ; 4) Calculate the kth residual ; 5) Generate the kth intrinsic mode function through EMD decomposition , and calculate the k+1th eigenmode function: ; ; in is the operator used to generate the kth IMFs, represents the i-th sample of different white Gaussian noise sequences that satisfy the standard normal distribution, where i From 1 to L The index of L In the process of adding different white Gaussian noises, each added white noise is independent and identically distributed. By adding noise multiple times and averaging the results, the stability and accuracy of the decomposition are improved. 6) Repeat steps 4) and 5) until the EMD process cannot decompose the residual; eventually, the residual Represents the global trend of capacity forecast error, residual represents the local fluctuation of the prediction error caused by the capacity self-recovery effect; 7) Eliminate some high-frequency components that do not contribute much to the evolution information through the Pearson correlation coefficient; high-frequency IMF components usually contain high-frequency noise and subtle fluctuations in the signal, which do not have much impact on the overall trend change of the error sequence. Therefore, these high-frequency components can be ignored when predicting and analyzing the evolution trend of the error sequence. By selecting those IMF components that contain the main error evolution information, a more representative error sequence can be reconstructed; these selected IMF components mainly contain low-frequency components and trend information in the signal, rather than high-frequency noise; in order to screen out the IMF components that contribute to the error evolution information, the Pearson correlation coefficient is used to measure the correlation between each IMF component and the error evolution information. By calculating the correlation coefficient between each IMF component and the error evolution information, it can be determined which IMF components are useful and which are noise; the calculation formula of the Pearson correlation coefficient is as follows:

[0027] The Pearson correlation coefficient was used to quantitatively evaluate the positive or negative correlation. The correlation between the IMF and the original error was obtained by the above method, where a high correlation is represented by a value far from 0; Represents a series of intrinsic mode function IMF components, represents the average value of a series of intrinsic mode function IMF components, and represents the original error sequence, represents the average value of the original error series; Through correlation analysis, suitable intrinsic mode functions (IMFs) are selected; since high-frequency IMFs represent local fluctuations and have little impact on long-term predictions, they are removed from the reconstruction process. Since weakly correlated IMFs contribute little to error trend predictions, they are also removed from the reconstruction. IMFs with correlation coefficients greater than 0.4 are selected as effective components for error reconstruction. The reconstructed sequence reflects both the long-term trend and the degradation information of the original sequence. This lays the foundation for the successful prediction of data-driven algorithms that are sensitive to training data.

[0028] In this example, the specific steps of using Gaussian process regression (GPR) to predict a new error sequence include: As a machine learning model based on statistical learning and Bayesian theory, GPR has been widely used in the field of regression prediction.

[0029] The probability density function is:

[0030] is the average function, is the covariance function called the kernel function K; The specific calculation process is: ; in, stands for mathematical expectation; The squared exponential covariance function is used as the kernel function of the covariance function: ; in is the signal variance, with output scaled magnitude, is a diagonal matrix; The observed output with Gaussian noise is: ; The observation vector Affected by noise Influence; The prior distribution of the observations is shown as: ; in is the n-dimensional identity matrix, represents the normal distribution, also called the Gaussian distribution, is the noise covariance matrix, expressed as: ; in Indicates the similarity of variables. and is used to calculate the kernel function The input parameter, P is a diagonal matrix, is the inverse matrix of the diagonal matrix, and the hyperparameter set It is formulated and optimized by minimizing the negative log marginal likelihood (NLML), which is expressed as: ; The calculation process of NLML is written as: ; in, is the negative log marginal likelihood, a measure of the probability that a given parameter set A scalar value that indicates how well the model fits the data. It is the negative logarithm of the marginal likelihood. is the conditional probability density function, which means that given the input and parameters Next, output The probability of is the observed output data vector, is the parameter set of the Gaussian process model, Is the input data The internal kernel function matrix, is the variance matrix of the noise; The maximum value of the objective function is obtained by taking the derivative of the log-likelihood function, which is calculated as follows: ; here is an element of the hyperparameter set; The GPR training process is carried out in the above manner, and then the GPR model is used for prediction tasks using the posterior distribution. , observed value and predicted values The joint prior distribution of is expressed as follows: ; according to The joint Gaussian distribution on derives the posterior distribution : ; Among them, the predicted mean and covariance The calculation formula is: ; in, Indicates that at the new input point The predicted output value at Represents a set of training data points The corresponding output value vector, Represents a set of input points With new input point The kernel function matrix between Represents a set of training data points The internal kernel matrix, represents the variance matrix of the noise, Indicates a new input point and its own kernel function value.

[0031] In this embodiment, in the step of predicting the remaining service life of the lithium-ion battery using the corrected capacity estimation, the battery capacity data set used is obtained by conducting experiments in a laboratory. Figure 2 and Figure 3 They are respectively a prediction result diagram without considering the capacity self-recovery effect and a prediction result diagram using the prediction method of the present invention. It can be seen that the prediction result of the present invention is more in line with the actual reference capacity of the battery, and can more accurately track the capacity change trend of the battery during the degradation process, thereby verifying the accuracy and effectiveness of the method proposed in the present invention.

[0032] It should be noted that, in this article, the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, an element defined by the sentence "comprises a ..." does not exclude the existence of other identical elements in the process, method, article or device including the element.

[0033] The above are only preferred embodiments of the present invention, and are not intended to limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made using the contents of the present invention specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A method for predicting remaining battery life considering capacity self-recovery, characterized in that: The method comprises the following steps: The original estimation error is obtained based on the battery capacity data and the capacity predicted using the double exponential model; The original error sequence is reconstructed through CEEMDAN, and strongly correlated intrinsic mode functions are selected; Use Gaussian process regression to predict new error sequences; Correct the final capacity estimate using the GPR predictions; Predict the remaining useful life of lithium-ion batteries using corrected capacity estimates.

2. A method for predicting remaining battery life taking into account capacity self-recovery according to claim 1, characterized in that: The step of reconstructing the original error sequence by CEEMDAN and selecting a strongly correlated intrinsic mode function comprises: Assuming the original signal is s(t), the CEEMDAN algorithm is described as follows: 1) Decomposition , the first eigenmode function is calculated as: ； in represents the original error sequence, Represents different white Gaussian noises that satisfy the standard normal distribution; i=1,2,..., L is the number of times the white noise is added, represents the noise factor and is obtained in the same way as the EMD , represents the estimated value of the first intrinsic mode function IMF obtained by decomposition using the CEEMDAN algorithm, It represents the first intrinsic mode function IMF obtained by empirical mode decomposition EMD after adding Gaussian white noise for the i-th time. It is the result obtained by averaging the estimated value of the first IMF obtained by empirical mode decomposition (EMD) after adding Gaussian white noise multiple times; 2) Calculate the first residual when k=1, and the calculation formula is ; 3) Generate the first intrinsic mode function through EMD decomposition , and calculate the second eigenmode function as: ； 4) Calculate the kth residual ; 5) Generate the kth intrinsic mode function through EMD decomposition , and calculate the k+1th eigenmode function: ； ； in is the operator used to generate the kth IMFs, represents the i-th sample of different white Gaussian noise sequences that satisfy the standard normal distribution, where i From 1 to L The index of L In the process of adding different white Gaussian noises, each added white noise is independent and identically distributed. By adding noise multiple times and averaging the results, the stability and accuracy of the decomposition are improved. 6) Repeat steps 4) and 5) until the EMD process cannot decompose the residual; eventually, the residual Represents the global trend of capacity forecast error, residual represents the local fluctuation of the prediction error caused by the capacity self-recovery effect; 7) Use the Pearson correlation coefficient to measure the correlation between each IMF component and the error evolution information. By calculating the correlation coefficient between each IMF component and the error evolution information, determine which IMF components are useful and which are noise. The calculation formula of the Pearson correlation coefficient is as follows: ； The Pearson correlation coefficient was used to quantitatively evaluate the positive or negative correlation, and the correlation between the IMF and the original error was obtained, where a high correlation is represented by a value far from 0; Represents a series of intrinsic mode function IMF components, represents the average value of a series of intrinsic mode function IMF components, and represents the original error sequence, represents the average value of the original error sequence; Through correlation analysis, the appropriate intrinsic mode function is selected; since high-frequency IMF represents local fluctuations and has little impact on long-term predictions, it is removed from the reconstruction process. Since weakly correlated IMFs contribute little to error trend predictions, they are also removed from the reconstruction. IMFs with correlation coefficients greater than 0.4 are selected as effective components for error reconstruction. The reconstructed sequence reflects both the long-term trend and the degradation information of the original sequence.

3. A method for predicting remaining battery life taking into account capacity self-recovery according to claim 1, characterized in that: The step of using Gaussian process regression to predict a new error sequence includes: The probability density function is: ； is the average function, is the covariance function called the kernel function K; The specific calculation process is: ； in, stands for mathematical expectation; The squared exponential covariance function is used as the kernel function of the covariance function: ； in is the signal variance, with output scaled magnitude, is a diagonal matrix; The observed output with Gaussian noise is: ； The observation vector Affected by noise Influence; The prior distribution of the observations is shown as: ； in is the n-dimensional identity matrix, represents the normal distribution, also called the Gaussian distribution, is the noise covariance matrix, expressed as: ； in Indicates the similarity of variables. and is used to calculate the kernel function The input parameter, P is a diagonal matrix, is the inverse matrix of the diagonal matrix, and the hyperparameter set It is formulated and optimized by minimizing the negative log marginal likelihood, which is expressed as: ； The calculation process of NLML is written as: ； in, is the negative log marginal likelihood, a measure of the probability that a given parameter set A scalar value that indicates how well the model fits the data; it is the negative logarithm of the marginal likelihood, is the conditional probability density function, which means that given the input and parameters Next, output The probability of is the observed output data vector, is the parameter set of the Gaussian process model, Is the input data The internal kernel function matrix, is the variance matrix of the noise; The maximum value of the objective function is obtained by taking the derivative of the log-likelihood function, which is calculated as follows: ； here is an element of the hyperparameter set; Perform the GPR training process, and then use the posterior distribution to use the GPR model for prediction tasks at the test point , observed value and predicted values The joint prior distribution of is expressed as follows: ； according to The joint Gaussian distribution on derives the posterior distribution : ； Among them, the predicted mean and covariance The calculation formula is: ； in, Indicates that at the new input point The predicted output value at Represents a set of training data points The corresponding output value vector, Represents a set of input points With new input point The kernel function matrix between Represents a set of training data points The internal kernel matrix, represents the variance matrix of the noise, Indicates a new input point and its own kernel function value.

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