Battery health state prediction method based on variational feature extraction and composite kernel function optimization Gaussian process regression

Abstract

The invention discloses a battery health state prediction method based on variational feature extraction and composite kernel function optimization Gaussian process regression. The method comprises the following steps: firstly, collecting battery cycle data, extracting features by utilizing VAE, screening out an optimal feature set by adopting PCC, and jointly dividing the optimal feature set and SOH data into a training set and a test set; in the training process, the optimal modal number K of the VMD is determined through the envelope entropy, a composite kernel function CKFGPR model fusing a linear kernel, a radial basis kernel and a periodic kernel is constructed, and hyper-parameters are optimized through maximum likelihood estimation. In the test stage, the features are decomposed into K intrinsic mode components by using VMD, the K intrinsic mode components are respectively input into the CKFGPR model for prediction and reconstruction, and finally the CKFGPR model is input again to realize SOH prediction. According to the method, the feature robustness is enhanced through cooperative application of the VAE and the VMD, the fitting capability of the GPR to the battery degradation behavior is improved in combination with the composite kernel function, and the SOH prediction precision is effectively improved.

Description

Technical Field

[0001] This invention relates to the field of lithium-ion battery technology, specifically to a method for predicting battery health status based on variational feature extraction and composite kernel function optimized Gaussian process regression. Background Technology

[0002] Lithium-ion batteries, as important energy storage devices, are widely used in electric vehicles, portable electronic devices, and energy storage systems. State of Health (SOH) is a key indicator for measuring the degree of battery performance degradation, and accurate SOH prediction is crucial for safe battery operation, lifespan assessment, and maintenance strategy development.

[0003] Currently, existing methods in state-of-health (SOH) estimation still face several key challenges. According to the review in "Areview of lithium-ion battery state-of-health estimation and prediction methods," traditional physical model-based methods typically require in-depth understanding of the internal electrochemical processes of the battery, leading to high modeling complexity and difficulty in accurately obtaining key parameters. Furthermore, the study also points out that single data-driven methods (such as standard Gaussian process regression) still have limited predictive ability when dealing with the non-stationary and nonlinear characteristics exhibited during battery degradation. In addition, "State of health estimation of lithium-ion batteries based on multi-feature extraction and temporal convolutional network" further demonstrates that existing methods have significant shortcomings in feature extraction, making it difficult to effectively identify key features closely related to performance degradation from high-dimensional battery data. On the other hand, as described in "Modified Gaussian Process Regression Models for Cyclic Capacity Prediction of Lithium-Ion Batteries", the selection of kernel functions in Gaussian process regression still mainly relies on empirical settings, and there is a lack of dedicated kernel functions designed specifically for battery degradation characteristics, which restricts further improvement of model performance. Summary of the Invention

[0004] This invention introduces variational feature extraction and composite kernel function optimization techniques, combined with historical battery degradation data, to achieve accurate prediction of the health status of lithium-ion batteries. The purpose of this invention is to provide a battery health status prediction method based on variational feature extraction and composite kernel function optimized Gaussian process regression. This method extracts nonlinear deep features using a variational autoencoder (VAE), selects the optimal feature subset using the Pearson coefficient (PCC), determines the optimal number of modes in variational mode decomposition (VMD) using the envelope entropy function, and constructs a Gaussian process regression (CKFGPR) model that integrates linear kernels, radial basis kernels, and periodic kernels. This enables accurate prediction of battery health status and assessment of remaining life, improving the reliability of the battery management system.

[0005] To achieve the above technical objectives, the present invention adopts the following technical solution:

[0006] A battery health state prediction method based on variational feature extraction and composite kernel function optimized Gaussian process regression includes the following steps:

[0007] Step 1: Data Acquisition and Preprocessing Steps:

[0008] Obtain historical operating data of lithium-ion batteries and construct a dataset containing battery characteristic parameters (voltage, current, and temperature) and SOH labels;

[0009] Step 2: Training Phase

[0010] (1) VAE feature extraction steps: Use the VAE model to perform nonlinear feature extraction and dimensionality reduction on the original battery data;

[0011] (2) Feature optimization step: PCC analysis is used to analyze the correlation between each high-order feature and the battery health status, and the optimal feature subset is selected;

[0012] (3) VMD signal decomposition steps: Adaptively update the optimal mode number K of VMD using the envelope entropy function method. opt ;

[0013] (4) CKFGPR modeling steps: Construct a Gaussian process regression model based on a composite kernel function, which includes a combination of linear kernel, radial basis kernel and periodic kernel, and use the maximum likelihood function method to adaptively update the hyperparameter matrix;

[0014] Step 3: Testing Phase

[0015] (1) Multi-component parallel prediction and reconstruction steps: The battery health state sequence is decomposed into K intrinsic mode components using the VMD algorithm, and the CKFGPR model is input to predict each IMF component. The prediction results of each IMF component are then superimposed and reconstructed.

[0016] (3) Health status prediction steps: The CKFGPR model combines reconstructed features to predict SOH and evaluates the accuracy of the results.

[0017] Furthermore, charge-discharge cycle data of lithium-ion batteries throughout their complete life cycle are collected, including voltage, current, temperature curves and corresponding capacity decay data. After data cleaning and standardization, a feature database is constructed. Nonlinear deep features of the battery data are extracted using VAE, and the latent representation of the data is learned through a composite network structure of encoder-decoder-regressor.

[0018] Furthermore, the variational autoencoder employs a multi-layer one-dimensional convolutional neural network as the encoder, mapping the input battery data to the mean μ and logvariance logvar of the latent space; it generates latent variable z from the latent distribution through reparameterization technology; the decoder reconstructs the input data using a multi-layer one-dimensional transposed convolutional neural network; the regressor predicts the battery health state value from the latent variable z; and the total loss function L... VAE Includes reconstruction loss L xent and KL divergence term L KL The weighted combination.

[0019] Furthermore, the reparameterization process is implemented using the following formula:

[0020]

[0021] Where z represents the latent feature vector obtained after reparameterization, μ represents the mean vector of the encoder output, σ represents the standard deviation vector of the encoder output, and ε is a single random sample value from an n-dimensional independent standard Gaussian distribution. Represents the element product.

[0022] Furthermore, the L VAE This can be achieved through the following formula:

[0023]

[0024]

[0025] L VAE =αL xent +βL KL ;

[0026] Among them, L xent The cross-entropy loss represents the reconstruction loss, used to measure the difference between the decoder output and the original input; m represents the dimension of the input sample, x... i Let x represent the i-th element of the original input vector. i ′ L represents the i-th element of the reconstructed vector. KLThe KL divergence between the latent distribution of the encoder output and the standard Gaussian distribution is represented by μ, where n represents the dimension of the latent space. i and σ i Let L and β represent the i-th elements of the vectors containing the mean and standard deviation of the latent variable distribution, respectively. α and β are trade-off parameters that control L. KL and L xent The importance of.

[0027] Furthermore, in the feature optimization step, PCC is used to determine feature relevance.

[0028] The calculation formula is as follows:

[0029]

[0030] Where, x i With y i Let x and y represent the i-th sample values, respectively. and This represents the average of variables x and y.

[0031] Furthermore, in the VMD signal decomposition step, the envelope entropy function is used as the evaluation...

[0032] Price index determines the optimal number of modes K opt The formula for calculating the envelope entropy is:

[0033]

[0034] Among them, E k Let a be the envelope entropy of the k-th IMF component. k (i) is the envelope signal of the k-th IMF component, p i The normalized probability distribution of the envelope signal is obtained by minimizing the average envelope entropy. Determine the optimal number of modes K opt .

[0035] Furthermore, the specific form of the composite kernel function is as follows:

[0036]

[0037] Among them, K linear K is a linear kernel function. rbf K is the radial basis kernel function. periodic Let X1 and X2 be the input feature matrices, l be the length scale parameter, p be the period parameter, σ1, σ2 and σ3 be the corresponding amplitude parameters, and ⊙ denote element-wise multiplication.

[0038] Furthermore, in the composite kernel function Gaussian process regression modeling step, the maximum likelihood estimation method is used for hyperparameter optimization, and the likelihood function is:

[0039]

[0040] Where L(θ) represents the logarithmic marginal likelihood function value to be maximized, θ is a hyperparameter vector, K is the kernel matrix, and I represents the identity matrix with the same dimensions as the kernel matrix K. Let represent the noise variance, y be the corresponding observation vector in the training set, and n be the number of training samples.

[0041] Furthermore, in the variational mode decomposition optimization step, the constructed constrained variational problem is expressed as:

[0042]

[0043] The constraints are: Where u k (t) represents the IMF component, ω k The center frequency.

[0044] Furthermore, the feature reconstruction step is achieved by linearly superimposing the predicted values ​​of each IMF component:

[0045]

[0046] Compared with the prior art, the present invention has the following technical advantages:

[0047] 1. This invention achieves deep mining and extraction of battery degradation features through a variational autoencoder (VAE). Traditional methods often rely on linear or shallow feature extraction techniques, which struggle to capture the complex nonlinear degradation patterns in battery data. The VAE model employed in this invention, through its encoder-decoder-regressor composite structure, automatically learns the probability distribution of data in the latent space, thereby extracting more representative and robust deep features. This deep learning-based feature extraction method not only preserves key data information but also, through joint optimization of the regressors, directly addresses the health status prediction task, significantly improving the discriminative power of the features.

[0048] 2. In terms of signal decomposition, this invention innovatively employs the envelope entropy index to achieve adaptive optimization of variational mode decomposition parameters. Traditional VMD methods often rely on expert experience to determine the number of modes, lacking objective optimization criteria. This invention, by constructing an envelope entropy evaluation system, can automatically determine the optimal number of decomposed modes, overcoming the subjectivity and limitations of manually set parameters. This adaptive optimization mechanism ensures optimal signal decomposition results, making the extracted intrinsic mode components purer and more stable, providing a high-quality data foundation for subsequent prediction modeling.

[0049] 3. To address the complex dynamic characteristics exhibited during battery degradation, this invention designs a composite kernel function Gaussian process regression model that integrates multiple kernel functions. Compared to traditional models with a single kernel function, this invention organically combines the overall trend capture capability of a linear kernel, the local nonlinear fitting capability of a radial basis kernel, and the cyclic characteristic representation capability of a periodic kernel, forming a comprehensive model of battery degradation behavior. Furthermore, by combining the hyperparameter adaptive learning mechanism of the maximum likelihood estimation method, the model can accurately match battery data features, significantly improving the model's fitting accuracy and generalization ability.

[0050] 4. The end-to-end collaborative prediction framework constructed in this invention embodies the systematic advantages of multi-technology integration. Through a technical chain of "feature extraction - feature selection - signal decomposition - accurate prediction," an organic whole is formed where each link complements the others. Variational autoencoders provide deep features, Pearson coefficients select and optimize feature subsets, adaptive variational mode decomposition enhances feature stability, and finally, accurate prediction is achieved through composite kernel function Gaussian process regression. This collaborative design significantly improves the prediction accuracy and stability of the entire system, effectively suppresses noise interference, and adapts to different battery operating conditions. Attached Figure Description

[0051] Figure 1 A schematic diagram of the battery health status prediction process based on variational feature extraction and composite kernel function optimization of Gaussian process regression. Detailed Implementation

[0052] like Figure 1 As shown, a battery health state prediction method based on variational feature extraction and composite kernel function optimized Gaussian process regression includes the following steps:

[0053] Step 1: Battery Data Preprocessing

[0054] After the process begins, battery data preprocessing is performed first. Time-series data of voltage, current, and temperature from lithium-ion battery charge-discharge cycles are acquired, and the raw data undergoes systematic cleaning and standardization. During the data cleaning phase, outliers and noisy data are removed through statistical analysis and threshold judgment to ensure data quality meets modeling requirements. Standardization is then performed using the Z-score standardization method to normalize each feature parameter to a standard normal distribution, effectively eliminating the influence of different units on model training. Based on this, the continuous time-series data is segmented into independent samples according to charge-discharge cycles, ensuring that each sample contains complete charge-discharge process data, laying the foundation for subsequent feature extraction.

[0055] Step 2: VAE Deep Feature Extraction

[0056] The preprocessed multi-source data is input into the VAE for deep feature extraction. First, a composite network structure of encoder-decoder-regressor is constructed. The encoder uses a three-layer one-dimensional convolutional network, extracting temporal features layer by layer through convolution operations with a kernel size of 5 and a stride of 2, mapping the input data to the mean μ and logvariance logvar in the latent space. Then, a latent variable z is generated by sampling from the latent distribution using a reparameterization technique, which is achieved through the following formula:

[0057]

[0058] Where z represents the latent feature vector obtained after reparameterization, μ represents the mean vector of the encoder output, σ represents the standard deviation vector of the encoder output, and ε is a single random sample value from an n-dimensional independent standard Gaussian distribution. The decoder employs a symmetric three-layer transposed convolutional structure to reconstruct the input data from the latent variables. The regressor predicts the battery health status value from the latent variables, using the total loss function L. VAE Optimization is performed to output deep features with strong representational capabilities. The formula is expressed as follows:

[0059]

[0060] L VAE =αL xent +βL KL ;

[0061] Among them, L xent This represents the reconstruction cross-entropy loss, used to measure the difference between the decoder output and the original input. m represents the dimension of the input sample, x... i Let x represent the i-th element of the original input vector. i ′ L represents the i-th element of the reconstructed vector. KL The KL divergence between the latent distribution of the encoder output and the standard Gaussian distribution is represented by μ, where n represents the dimension of the latent space. i and σ i Let L and β represent the i-th elements of the vectors containing the mean and standard deviation of the latent variable distribution, respectively. α and β are trade-off parameters that control L. KL and L xent The importance of.

[0062] Step 3: PCC Feature Optimization

[0063] A systematic Pearson correlation coefficient analysis was performed on multiple features extracted by the VAE network. By calculating the correlation coefficient between each feature and the SOH label, the linear correlation strength between each feature and the battery health state was quantitatively assessed. The calculation formula is as follows:

[0064]

[0065] Where, x i With y i Let x and y represent the i-th sample values, respectively. and This represents the average of variables x and y.

[0066] Based on the calculation results, a reasonable correlation threshold (usually 0.9) is set to select a subset of features that are strongly correlated with SOH, ensuring that the selected features have significant characterization ability for the battery degradation process. Furthermore, the features are sorted according to the absolute value of their correlation coefficients, and the top n most relevant features are selected to form the optimal feature subset. This retains the most discriminative feature information while effectively reducing the feature dimensionality.

[0067] Step 4: VMD signal decomposition

[0068] The VMD algorithm is used to adaptively decompose the battery health state sequence into multiple intrinsic mode functions. First, the optimal number of modes K is determined based on the envelope entropy minimization criterion. Then, the envelope entropy E of each IMF component is calculated. k and average envelope entropy With K opt Determine the optimal decomposition parameters. Their specific calculation formulas are as follows:

[0069]

[0070] Among them, E k Let a be the envelope entropy of the k-th IMF component. k (i) is the envelope signal of the k-th IMF component, p i The normalized probability distribution of the envelope signal is obtained by minimizing the average envelope entropy. Determine the optimal number of modes K opt Then, the constrained variational problem is solved:

[0071]

[0072] The constraints are: Where u k (t) represents the IMF component, ω k The center frequency.

[0073] By introducing a quadratic penalty factor α and Lagrange multipliers λ(t), an augmented Lagrange function is constructed. The IMF components, center frequency, and Lagrange multipliers are updated alternately using the alternating direction algorithm of multipliers. Finally, the non-stationary feature sequence is decomposed into K relatively stationary band-limited eigenmode functions.

[0074] Step 5: CKFGPR Modeling and Prediction

[0075] A CKFGPR model is constructed for SOH prediction. First, a fusion linear kernel Kf model is designed. linear Radial base nucleus K rbf and periodic kernel K periodic The composite kernel function K total :

[0076]

[0077] Where σ1, σ2, and σ3 are the corresponding amplitude parameters, and ⊙ represents element-wise multiplication. K linear Capturing long-term decay trends, K rbf Capturing local fluctuation characteristics, K periodic Capture capacity regeneration phenomena.

[0078] Subsequently, the maximum likelihood estimation method is used to optimize the hyperparameters by maximizing the marginal likelihood function. Determine the optimal parameter combination. Input each IMF component obtained from VMD decomposition into the corresponding GPR model for parallel prediction, and finally reconstruct the final health feature prediction value through linear superposition.

[0079] Step 6: Predictive Performance Evaluation

[0080] A comprehensive evaluation of the model's predictive performance is conducted. This is achieved by calculating the root mean square error. Mean Absolute Error Mean absolute percentage error Multiple evaluation indicators are used to quantitatively analyze the estimation accuracy and stability of the model. Simultaneously, the uncertainty quantification capability of the model is analyzed through prediction confidence intervals to comprehensively evaluate the effectiveness and reliability of the method in predicting the health status of lithium-ion batteries.

[0081] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A battery state of health prediction method based on variational feature extraction and composite kernel function optimized Gaussian process regression, characterized in that, The method comprises the following steps: Step 1: data acquisition and pretreatment step: Obtain the historical operation data of the lithium ion battery, and construct a data set containing battery characteristic parameters and SOH labels; Step 2: training stage: (1) VAE feature extraction step: using VAE model to perform nonlinear feature extraction and dimension reduction processing on the original battery data; (2) feature optimization step: using PCC to analyze the correlation between each high-order feature and the battery health status, and screening out the optimal feature subset; (3) VMD signal decomposition step: adopt envelope entropy function method to adaptively update the optimal modal number K of VMD opt ; (4) CKFGPR modeling step: constructing a Gaussian process regression model based on a composite kernel function, the composite kernel function comprising a combination of a linear kernel, a radial basis kernel and a periodic kernel, and using a maximum likelihood function method to adaptively update a hyperparameter matrix; Step 3: test stage: (1) multi-component parallel prediction and reconstruction step: using VMD algorithm to decompose the battery health status sequence into K intrinsic mode components, and inputting the CKFGPR model to predict each IMF component, and superimposing the prediction results of each IMF component to reconstruct; (3) health status prediction step: the CKFGPR model realizes SOH prediction in combination with the reconstructed features, and the result is subjected to accuracy evaluation. 2.The battery state of health prediction method based on variational feature extraction and composite kernel function optimized Gaussian process regression according to claim 1, wherein, The VMD adopts a composite network structure of encoder-decoder-regressor; wherein the encoder is composed of a multi-layer one-dimensional convolutional neural network, which maps the input battery data to the mean value μ and the logarithmic variance logvar of the latent space; the reparameterization module generates the latent variable z from the latent distribution by random sampling; the decoder is composed of a multi-layer one-dimensional transposed convolutional neural network, which reconstructs the input data from the latent variable z; the regressor predicts the battery health state value from the latent variable z; and the total loss function L VAE includes a reconstruction loss L xent and a weighted combination of KL divergence term L KL . 3.The battery state of health prediction method based on variational feature extraction and composite kernel function optimized Gaussian process regression according to claim 2, characterized in that, The reparameterization process is realized by the following formula: Wherein, z represents the latent feature vector obtained after reparameterization, μ represents the mean vector output by the encoder, σ represents the standard deviation vector output by the encoder, and ε is a random sampling value of n-dimensional independent standard Gaussian distribution, denotes an element product.

4. The battery state of health prediction method based on variational feature extraction and composite kernel function optimized Gaussian process regression according to claim 2, characterized in that, The L VAE By the following equation: L VAE = aL xent + bL KL ; where L xent represents the reconstruction cross-entropy loss, measuring the difference between the decoder output and the original input; m represents the dimension of the input sample, x i represents the i-th element of the original input vector, x i ′ represents the i-th element of the reconstruction vector, L KL represents the KL divergence between the latent distribution of the encoder output and the standard Gaussian distribution, n represents the dimension of the latent space, μ i and σ i respectively represent the i-th element of the mean and standard deviation vectors of the latent variable distribution, and α and β are weighting parameters controlling the importance of L KL and L xent , respectively.

5. The battery state of health prediction method based on variational feature extraction and composite kernel function optimized Gaussian process regression according to claim 1, characterized in that, In the feature optimization step, PCC is used to judge the correlation of the features, and the calculation formula is: where x i and y i denote the ith sample value of the variables x and y, respectively, and denote the mean value of the variables x and y.

6. The battery state of health prediction method based on variational feature extraction and composite kernel function optimized Gaussian process regression according to claim 1, characterized in that, In the VMD signal decomposition step, an envelope entropy function is used as an evaluation index to determine an optimal modal number K opt The calculation formula of the envelope entropy is: where E k is the envelope entropy of the kth IMF component, a k (i) is the envelope signal of the kth IMF component, p i is the normalized probability distribution of the envelope signal, by minimizing the average envelope entropy determines the optimal mode number K opt .

7. The battery state of health prediction method based on variational feature extraction and composite kernel function optimized Gaussian process regression according to claim 1, characterized in that, The specific form of the composite kernel function is: where K linear is a linear kernel function, K rbf is a radial basis kernel function, K periodic is a periodic kernel function, X1, X2 are input feature matrices, l is a length scale parameter, p is a period parameter, σ1, σ2, and σ3 are corresponding amplitude parameters, and ⊙ represents element-wise multiplication. 8.The battery state of health prediction method based on variational feature extraction and composite kernel function optimized Gaussian process regression according to claim 1, characterized in that, In the composite kernel function Gaussian process regression modeling step, the maximum likelihood estimation method is used for hyperparameter optimization, and the likelihood function is: where L(0) represents the log marginal likelihood function value to be maximized, 0 is a hyperparameter vector, K is a kernel matrix, and I represents an identity matrix of the same dimension as the kernel matrix K, is the noise variance, y is the corresponding observation vector in the training set, and n is the number of training samples. 9.The battery state of health prediction method based on variational feature extraction and composite kernel function optimized Gaussian process regression according to claim 1, characterized in that, In the variational mode decomposition optimization step, the constructed constrained variational problem is represented as: The constraint condition is: where u k (t) is the IMF component, ω k is the center frequency.

10. The battery state of health prediction method based on variational feature extraction and composite kernel function optimized Gaussian process regression according to claim 1, characterized in that, The feature reconstruction step is realized by linearly superimposing the predicted values of each IMF component:

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