An Incremental Correlation Vector Machine-Based Online Prediction Method for Battery State of Charge (SOC) Based on Multi-Core Integration Strategy

Abstract

This invention discloses an online prediction method for battery SOC based on an incremental correlation vector machine (RVM) strategy using a multi-kernel ensemble approach. The method includes the following steps: Step 1, data preprocessing; Step 2, training set sampling; Step 3, kernel function selection; Step 4, model training; Step 5, model validation; Step 6, adaptive kernel parameters; Step 7, RVM model ensemble; Step 8, model prediction; Step 9, incremental learning strategy; and Step 10, online incremental prediction. From a practical perspective, this invention addresses the complexities and diverse needs of various applications. Drawing on the ideas of incremental learning and ensemble learning, it generates highly differentiated RVM individual learning models containing multiple kernel functions through dual perturbation of training samples and kernel functions. Combined with a novel incremental ensemble strategy, it avoids the problem of model overlearning, improves the model's generalization ability and robustness, and expands its application scope.

Description

Technical Field

[0001] This invention relates to the field of battery dynamic state assessment and performance prediction technology, specifically to an online prediction method for the state-of-the-art (SOC) of lithium-ion batteries based on the correlation vector machine algorithm, whale optimization algorithm, incremental learning concept, and multi-kernel function ensemble learning strategy. Background Technology

[0002] Electric vehicles have experienced rapid development in recent years. Power batteries are crucial for the development of new energy vehicles and represent the biggest bottleneck in their cost and technology. The State of Charge (SOC) directly reflects the battery's remaining capacity and is one of the most important parameters in a battery management system. Accurate SOC estimation provides a basis for ensuring stable battery operation, developing battery balancing strategies, and implementing intelligent charging. It effectively prevents battery damage caused by overcharging or over-discharging, extends battery life, improves energy efficiency, and reduces operating costs.

[0003] Currently, SOC prediction methods can be divided into two categories: model-based and data-driven. Model-based methods establish an equivalent circuit model or electrochemical model of the battery based on the internal electrochemical reactions. The prediction accuracy depends on the accuracy of the model, but it is difficult to accurately establish a battery model in practical applications. Data-driven methods do not require establishing a complex internal mechanism model of the battery and have strong nonlinear mapping capabilities, but they require a large number of data samples for training, model parameters are difficult to determine, and prediction results are greatly affected by noise, resulting in weak generalization ability and robustness. Therefore, how to improve the generalization performance and robustness of data-driven algorithms and establish parameter adaptive models when sample data is insufficient is an urgent problem to be solved in the application of data-driven algorithms for lithium battery state of charge assessment and prediction. Summary of the Invention

[0004] The technical problem this invention aims to solve is to provide an online prediction method for lithium-ion battery SOC based on an incremental relevance vector machine (RVM) strategy. It draws on incremental learning ideas and ensemble learning strategies, proposing an incremental multi-core weighted ensemble prediction method based on the Relevance Vector Machine (RVM) algorithm. First, a dual perturbation mechanism using the Bagging algorithm and multi-core function selection is employed to generate RVM individual models with distinct characteristics. Then, the Whale Optimization Algorithm (WOA) is used to globally optimize the kernel parameters of the RVM individual models. Second, the k-nearest neighbor method is used to select k groups of optimal individual learners of different types, transforming the selective ensemble problem into a combinatorial optimization problem, resulting in an RVM weighted ensemble prediction model combining k RVM individual learners. Finally, by incorporating incremental learning ideas, the features of newly added samples are continuously learned, achieving online incremental prediction of lithium-ion battery SOC.

[0005] To achieve the above technical objectives, the present invention is implemented through the following technical solution:

[0006] An incremental correlation vector machine-based online prediction method for battery SOC based on a multi-core ensemble strategy includes the following steps:

[0007] Step 1: Data Preprocessing

[0008] Given a dataset Data, normalize the dataset so that all data are in the range [-1, 1], and divide it into a training set DN and a test set DT;

[0009] Step 2: Training set sampling

[0010] For the training set DN, the Bagging bootstrap sampling algorithm is used to perform n samplings, resulting in n training subsets [A1, A2, ..., A] containing a samples each. n ] and n validation sets [B1, B2, ..., B] corresponding to the training subset, each containing b samples. n ];

[0011] Step 3: Kernel Function Selection

[0012] m kernel functions are selected as the core mapping functions of the algorithm, including linear kernel function, polynomial kernel function, Gaussian kernel function, exponential radial basis kernel function, Sigmoid kernel function, Cauchy kernel function, Fourier kernel function and wavelet kernel function;

[0013] Step 4: Model Training

[0014] Based on the n training sample subsets [A1, A2, ..., A2] obtained in step 2 nUsing the m kernel functions from step 3, and employing the fast sequential sparse Bayesian learning method, m×n RVM models are trained, resulting in corresponding m×n sets of related vectors [RV1, RV2, ..., RV...]. m×n ];

[0015] Step 5: Model Validation

[0016] Based on the n verification sets [B1, B2, ..., B] obtained in step 2 n ], respectively using the verification subset B j Validate training subset A j The predictive performance of the m trained RVM models is calculated, and the root mean square error [RMSE1, RMSE2, ..., RMSE] of the m×n model predictions is calculated. m×n ], where j∈[1,n];

[0017] Step 6: Adaptive Kernel Parameters

[0018] Using the whale optimization algorithm, the kernel parameter population is initialized. Then, in steps 4 and 5, the root mean square error of the model prediction values ​​corresponding to all kernel parameters is calculated and used as the fitness function of the whale optimization algorithm. The kernel parameters of the m×n RVM models are globally optimized respectively, and finally m×n RVM prediction models are obtained.

[0019] Step 7: RVM Model Integration

[0020] The test set is divided into c time-series correlated test subsets [DT1,…,DT] based on the prediction step size. i-1 ,DT i ,…,DT c [This refers to the test subset DT within the test set DT.] i Combined with the k-nearest neighbor method, calculate DT i With verification subset B j The Euclidean distance (j∈[1,n]) is used to find the k nearest neighbor validation subsets and the RVM prediction model with the minimum root mean square error for each validation subset. Based on the root mean square error of the model's predictions of the validation set data, corresponding weights are obtained, resulting in a weighted ensemble prediction model combining the k RVM models and the corresponding correlation vectors [RV1,RV2,…,RV]. k ];

[0021] Step 8: Model Prediction

[0022] Using the RVM weighted ensemble prediction model obtained in step 7, the test subset DT i The data is used to make predictions, and the predicted values ​​SOC and confidence intervals are output.

[0023] Step 9: Incremental Learning Strategy

[0024] Combining incremental learning principles, the newly added test subset DT... i Before making predictions based on the data, in order to obtain the changing trends of neighboring samples, the newly added test subset DT from the previous step is... i-1 and its predicted value SOC i-1 Reassemble the training samples containing input and output data from step i-1, and combine them with the relevant vector set [RV] obtained during model training in step i-2. 1,i-2 RV 2,i-2 ,…,RV k,i-2 Together, they form a new training set [ND1,ND2,…,ND] k The RVM ensemble prediction model obtained in step 7 is then used for training to obtain k sets of related vectors [RV]. 1,i-1 RV 2,i-1 ,…,RV k,i-1 ], and the relevant vector [RV] of each group belonging to the new samples. new1,i-1 RV new2,i-1 ,…,RV newk,i-1 Together they form the test subset DT i-1 eigenvectors RV new And add it to the historical correlation vector [RV1,RV2,…,RV] of the m×n group of RVM prediction models in step 6. m×n ]middle;

[0025] Step 10: Online Incremental Prediction

[0026] Repeat steps 7-9 to finally output the SOC estimate and confidence interval for the entire test set.

[0027] Furthermore, in step 1, the first 30% of the dataset is used as the training set, and 70% as the test set. The data is susceptible to noise interference or operational errors during collection, which may cause some abnormal data in the dataset. The dataset is normalized using the following formula to ensure that the voltage, current, and temperature data are all within the interval [-1, 1], where x... min Let x be the minimum value of the data to be processed. max The maximum value of the data to be processed;

[0028]

[0029] Furthermore, in step 2, the training data is perturbed using the Bagging sampling method. A certain number of training samples are randomly drawn from the training set with replacement to generate multiple sets of training data containing different data distribution information, thereby generating individual learners with greater differences. Each sampling generates 63.2% of the training set, and the remaining 36.8% of the data in the total training set DN can be used as the validation set, where the number of sampling times n is 10.

[0030] Furthermore, in addition to the eight commonly used kernel functions described in step 3, the remaining m-8 kernel functions, such as novel kernel functions and variants of commonly used kernel functions, can be added to the ensemble algorithm in future research to increase its scalability.

[0031] Furthermore, the training algorithm in step 4 employs the fast sequence sparse Bayesian learning algorithm, which includes the following steps:

[0032] Step 4.1: Initialize a base function And calculate the corresponding weight ω. i hyperparameter α i :

[0033]

[0034] Step 4.2: Calculate the covariance Σ and mean μ of ω:

[0035] ∑=(σ -2 φ T φ+A) -1

[0036] μ = σ -2 ∑φ T t

[0037] Where Σ is an m×m matrix, μ is an m×1 column vector, and μ = (μ1, μ2, ..., μ...). m ) T ,A=diag(α1,α2,…,α m );

[0038] Step 4.3: Obtain α using the Fast Sequence Sparse Bayesian Learning Algorithm. i and σ 2 ;

[0039] Step 4.4: Select the next candidate basis function, following the methods in steps 4.5 to 4.7;

[0040] Step 4.5: If q i 2 >s i , and α i <∞, then the basis functions in the model It already exists, and the hyperparameter α is updated. i =s i 2 / (q i 2 -s i Update according to the following calculation process:

[0041]

[0042]

[0043]

[0044]

[0045] Where β=σ -2 , Σ jj Let j be the j-th diagonal element of the covariance Σ;

[0046] Step 4.6: If q i 2 >s i , and α i If ∞, then a basis function is added to the model. And update the hyperparameter α i =s i 2 / (q i 2 -s i Update according to the following calculation process:

[0047]

[0048]

[0049]

[0050]

[0051] Step 4.7: If q i 2 ≤s i , and α i If the value is less than ∞, then the basis functions in the model are deleted. And update the hyperparameter α i =∞, update according to the following calculation process:

[0052]

[0053]

[0054]

[0055] Step 4.8: Update the noise variance σ 2 , where Ф contains only existing basis functions, and m is the number of columns of existing basis functions;

[0056]

[0057] Step 4.9: Delete with μ i The data in the training set corresponding to 0 are used to obtain the relevant vector set RS.

[0058] Furthermore, in step 6, a novel heuristic optimization algorithm—the whale optimization algorithm—is selected due to its simplicity, minimal parameter adjustments, and strong ability to escape local optima. The specific steps are as follows:

[0059] Step 6.1, Population Initialization: Each individual in the whale population is represented by a D-dimensional random vector, and the population size is represented by N. P The formula is shown below, where x min and x max X i The lower and upper bounds; rand(1,D) represents a random number between [0,1];

[0060] X i =x min +rand(1,D)(x max -x min )

[0061] i = 1, 2, ..., N p

[0062] Step 6.2: Substitute the kernel parameter population from Step 6.1 into Steps 4 and 5, and calculate the fitness function of all kernel parameter populations using the root mean square error between the predicted and actual SOC values ​​as the fitness function to obtain the optimal solution X. * ;

[0063] Step 6.3: If the judgment value p < 0.5, then proceed to step 6.4; otherwise, proceed to step 6.5.

[0064] Step 6.4: If |A| < 1, then jump to step 6.4.1; otherwise, jump to step 6.4.2.

[0065] Step 6.4.1, Encircling the Prey: Humpback whales can track, surround, and prey on prey based on its location. In the WOA (Way of the Prey), the prey's location is the solution space, and the current best candidate solution is the target prey or a near-optimal solution. During the encirclement phase, the whale population moves closer to the optimal solution and updates its position. This process is represented as follows:

[0066] D = |C·X * (t)-X(t)|

[0067] X(t+1)=X * (t)-A·D

[0068] Where: t is the current iteration number; X *(t) represents the position of the current optimal solution; X and D are position vectors; A and C are coefficient vectors, which change with the number of iterations. In each iteration, when a better solution appears, the current optimal solution X is updated. * ;

[0069] A = 2a·ra

[0070] C = 2·r

[0071] a decreases linearly from 2 to 0, and r is a random vector in the range [0,1].

[0072] Step 6.4.2, Searching for food: Humpback whales randomly search for prey based on each other's locations. rand The location of a whale randomly selected from the current population;

[0073] D = |C·X rand -X|

[0074] X(t+1)=X rand -A·D

[0075] Step 6.5, Bubble Net Foraging: Humpback whales generate bubble nets along circular or "9" shaped paths while foraging. Two strategies are designed as follows:

[0076] Shrinking encirclement mechanism: As the iteration proceeds, 'a' decreases linearly, and the range of values ​​for 'A' decreases accordingly. After the update, the position of the whale population can be obtained between the initial position and the current optimal position.

[0077] Position Spiral Update: To simulate the spiral motion of humpback whales, the following spiral equation representing the position between the humpback whale and its prey is established:

[0078] X(t+1)=D′·e bl ·cos(2πl)+X * (t)

[0079] D′=|X * (t)-X(t)|

[0080] Where: b defines the shape of the logarithmic spiral, b = 1; l is a random number between [-1, 1]; D′ is the distance from the i-th whale to its prey (current optimal position);

[0081] Step 6.6: Determine if the maximum number of iterations has been reached. If yes, update the optimal value and output it; otherwise, return to step 6.3.

[0082] Furthermore, the Euclidean distance calculation method and weight calculation method of the k-nearest neighbor method in step 7 are shown in the following two equations:

[0083]

[0084]

[0085] in, To verify the values ​​of the set elements, denoted as the test set element value, l as the number of elements, and RMSE as the root mean square error of the i-th RVM model prediction.

[0086] Furthermore, in step 9, an incremental learning strategy is used to retrain the SOC estimate of the previous step length during online training, and the trained correlation vectors are added to the historical correlation vector set to continuously learn the features of new samples and enhance the long-term prediction ability of the algorithm.

[0087] Compared with the prior art, the present invention has the following advantages:

[0088] (1) This invention establishes an RVM algorithm estimation model with the advantage of small sample prediction. This algorithm can obtain high estimation accuracy with only a small number of training samples, overcoming the limitation of large training data requirements of the data-driven method. The training algorithm adopts the fast sequence sparse Bayes learning algorithm, which reduces the complexity of matrix operations and greatly improves the computational efficiency of the algorithm.

[0089] (2) The present invention uses a novel heuristic optimization algorithm, the whale optimization algorithm, which is simple to operate, requires few parameters to be adjusted, and has a strong ability to escape local optima, to perform global optimization of the kernel parameters. This solves the problem of difficulty in determining the internal parameters of data-driven algorithms, saves a lot of trial parameter time, and improves the prediction accuracy and computational efficiency of the algorithm.

[0090] (3) From a practical perspective, this invention addresses the problem that the RVM algorithm, which often uses a single kernel function for modeling, has poor adaptability in the face of complex applications and diverse needs. Drawing on the idea of ​​ensemble learning, it proposes a multi-kernel weighted ensemble prediction method based on the Relevance Vector Machine algorithm. This method generates individual RVM learning models with significant differences by using both training samples and kernel functions for dual perturbation. This avoids the problem of overlearning, improves the model's generalization ability and robustness, and expands its application scope.

[0091] (4) This invention integrates the incremental learning concept into the ensemble learning strategy, proposing a novel incremental fusion method. It combines the feature vectors of new samples predicted by multiple individual RVM prediction models in the RVM ensemble prediction model into a newly added relevance vector set RV. new This addresses the problem that the correlation vector of a single prediction model is insufficient to reflect the overall sample characteristics. It adds the correlation vector to the historical correlation vectors of all RVM individual models, continuously learning the characteristics of new samples and improving the long-term prediction ability of the algorithm. Attached Figure Description

[0092] Figure 1 This is a flowchart of the incremental correlation vector machine algorithm based on a multi-core integration strategy.

[0093] Figure 2 This is a flowchart of the whale optimization algorithm based on the relevance vector machine. Detailed Implementation

[0094] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the embodiments and accompanying drawings. It should be noted that the embodiments described herein are illustrative, but not limiting, and therefore this invention is not limited to the above embodiments. Based on the principles of this invention, all other implementation methods obtained by those skilled in the art without creative effort are considered to be within the protection scope of this invention.

[0095] This invention focuses on the estimation of state of charge (SOC) of lithium-ion batteries. It establishes a data-driven model based on the correlation vector machine algorithm. Addressing the problems of large training sample requirements, difficulty in parameter determination, and poor generalization performance inherent in data-driven models, this invention proposes an online fusion prediction method for lithium-ion battery SOC, combining incremental learning, whale optimization algorithm, and multi-core ensemble strategy. The overall process is as follows: Figure 1 As shown, it includes the following steps:

[0096] Step 1: Data Preprocessing. Given a dataset Data, the first 30% of the data is used as the training set DN, and the remaining 70% is used as the test set DT. Data is susceptible to noise interference or erroneous operations during acquisition, which can lead to some abnormal data in the dataset. The dataset is normalized using equation (1) to ensure that the voltage, current, and temperature data are all within the range [-1, 1], where x... min Let x be the minimum value of the data to be processed. max This represents the maximum value of the data to be processed.

[0097]

[0098] Step 2: Training set sampling. For the training set DN, the Bagging bootstrap sampling algorithm is used to perform n sampling iterations to obtain n training subsets [A1, A2, ..., A...] containing a samples each. n ] and n validation sets [B1, B2, ..., B] corresponding to the training subset, each containing b samples. n This method generates 63.2% of the training set with each sampling, and the remaining 36.8% of the data in the total training set DN can be used as the validation set. The number of sampling times n is 10.

[0099] This invention uses the Bagging sampling method to perturb the training data, randomly drawing a certain number of training samples with replacement from the training set to generate multiple sets of training data containing different data distribution information, thereby generating individual learners with greater diversity and avoiding overlearning.

[0100] Step 3: Kernel Function Selection. This invention uses the correlation vector machine algorithm as the core prediction algorithm and selects m kernel functions as the core mapping functions of the algorithm, including linear kernel functions, polynomial kernel functions, Gaussian kernel functions, exponential radial basis kernel functions, sigmoid kernel functions, Cauchy kernel functions, Fourier kernel functions, and wavelet kernel functions, etc.

[0101] This invention establishes an RVM algorithm estimation model with the advantage of small sample prediction. This algorithm can obtain high estimation accuracy with only a small number of training samples, overcoming the limitation of large training data requirements of data-driven methods.

[0102] The mathematical expression for the Relevance Vector Machine (RVM) model is:

[0103] t=Φω+ε (2)

[0104] in Let m be the number of nonlinear basis functions. i = 1, 2, ..., m, K(x) is the kernel function, ω = (ω1, ..., ωm) m ) T The weights of the model are ε = (ε1, ε2, ..., ε3). n ) is Gaussian noise, and ε i ~N(0, σ 2 ), σ 2 Predict the noise variance of SOC for the RVM model.

[0105] The Relevance Vector Machine (RVM) algorithm maps nonlinear feature vectors from a low-dimensional space to a high-dimensional space through kernel functions, achieving efficient computation. This invention uses multiple kernel functions to establish an RVM ensemble prediction model.

[0106] Commonly used kernel functions are described below:

[0107] (1) Linear kernel function: K(x,x) j )=x i ·x′ j

[0108] This function has a simple form and is suitable for simple datasets.

[0109] (2) Polynomial kernel function: K(x) i ,x j )=((x i ·x′ j)+1) d

[0110] In a polynomial kernel function, the parameter d is the order (kernel parameter). The larger the value of d (the higher the VC dimension), the higher the dimension of the mapping, which enhances the learning ability and improves the prediction performance. However, this can easily lead to overfitting and requires a large amount of computation.

[0111] (3) Gaussian radial basis kernel function:

[0112] (4) Exponential radial basis kernel function:

[0113] The parameter σ in the radial base class kernel function is a kernel parameter that determines the generalization ability of the model.

[0114] (5) Sigmoid kernel function: K(x,x) j )=tanh(a*(x·x j ′)+c)

[0115] (6) Cauchy kernel function: K(x,x) j )=1 / (||xx j || 2 / g+1)

[0116] (7) Fourier kernel function: where x k It is the k-th dimension, and q is the regularization parameter, 0≤q≤1.

[0117]

[0118] (8) Wavelet kernel function:

[0119] In addition to the eight commonly used kernel functions mentioned above, this invention allows for the addition of m-8 other kernel functions (such as novel kernel functions and variants of commonly used kernel functions) to the ensemble algorithm in future research. All subsequent methods using this RVM ensemble prediction algorithm as a framework are within the scope of this invention. The purpose of selecting multiple kernel functions is to generate various individual RVM prediction models with significant differences, enabling them to possess both global and local fitting capabilities, thereby enhancing the model's applicability and generalization ability.

[0120] Step 4: Model Training. Based on the n training sample subsets [A1, A2, ..., A...] obtained in Step 2... n Using the m kernel functions from step 3, and employing the fast sequential sparse Bayesian learning method, m×n RVM models are trained, resulting in corresponding m×n sets of related vectors [RV1, RV2, ..., RV...]. m×n ].

[0121] The training algorithm employs a fast sequence sparse Bayesian learning algorithm, which includes the following steps:

[0122] Step 4.1: Initialize a base function And calculate the corresponding weight ω. i hyperparameter α i :

[0123]

[0124] All other hyperparameters α i For infinity, the corresponding ω i All are zero, meaning the model contains only A basis function;

[0125] Step 4.2: Calculate the covariance Σ and mean μ of ω:

[0126]

[0127] Where Σ is an m×m matrix, μ is an m×1 column vector, and μ = (μ1, μ2, ..., μ...). m ) T ,A=diag(α1,α2,…,α m );

[0128] Step 4.3: Obtain α using the Fast Sequence Sparse Bayesian Learning Algorithm. i and σ 2 ;

[0129] Calculate the sparsity factor s i and quality factor q i The sparsity factor is used to measure the basis functions. The quality factor measures the degree of overlap with all remaining basis functions in the model, and is used to measure the number of basis functions removed. Subsequent correction of model errors:

[0130]

[0131] Ф contains a basis function Right now Where B = σ -2 I. Then let each of them... Given j = 1, ..., n, and j ≠ i, calculate all S... j and Q j :

[0132]

[0133] Step 4.4: Select the next candidate basis function, following the methods in steps 4.5 to 4.7;

[0134] Step 4.5: If q i 2 >s i , and α i <∞, then the basis functions in the model It already exists, and the hyperparameter α is updated. i =s i 2 / (q i 2 -s i Update according to the following calculation process:

[0135]

[0136] Where β=σ -2 , Σ jj Let j be the j-th diagonal element of the covariance Σ;

[0137] Step 4.6: If q i 2 >s i , and α i If ∞, then a basis function is added to the model. And update the hyperparameter α i =s i 2 / (q i 2 -s i Update according to the following calculation process:

[0138]

[0139] Step 4.7: If q i 2 ≤s i , and α i If the value is less than ∞, then the basis functions in the model are deleted. And update the hyperparameter α i =∞, update according to the following calculation process:

[0140]

[0141] Step 4.8: Update the noise variance σ 2 , where Ф contains only existing basis functions, and m is the number of columns of existing basis functions;

[0142]

[0143] Step 4.9: Delete with μ i The data in the training set corresponding to 0 are used to obtain the relevant vector set RS.

[0144] In step 4, the RVM training algorithm uses the Fast Sequence Sparse Bayesian Learning Algorithm proposed by Professor Tipping in 2003. The number of basis functions in this algorithm starts from 1 and increases continuously. It selects basis functions that meet the conditions by re-estimation, addition and deletion. Moreover, the calculation of the model training result only includes the current basis function, which greatly reduces the dimension of the calculation matrix and improves the training speed.

[0145] Step 5: Model Validation. Based on the n validation sets [B1, B2, ..., B] obtained in Step 2... n ], respectively using the verification subset B j Validate training subset A j The prediction performance of the trained m RVM models is calculated by calculating the root mean square error (RMSE) of the predicted SOC values ​​of the m×n models, where j∈[1,n] and n=10; the prediction equation is shown in Equation (11) and the root mean square error is shown in Equation (12).

[0146]

[0147]

[0148] Where h is the prediction step size, y n+h The SOC prediction value is given by a step size of h. The variance of the predicted values, This is the actual SOC value.

[0149] Step 6: Adaptive Kernel Parameters. Using the whale optimization algorithm, initialize the kernel parameter population, then proceed to steps 4 and 5 to calculate the root mean square error of the model predictions corresponding to all kernel parameters. Use this error as the fitness function of the whale optimization algorithm to globally optimize the kernel parameters of the m×n RVM models, ultimately obtaining m×n RVM prediction models.

[0150] This invention employs a novel heuristic optimization algorithm—the whale optimization algorithm—that is simple to operate, requires few parameter adjustments, and has a strong ability to escape local optima. This algorithm performs global optimization of the kernel parameters, solving the problem of difficult parameter determination in data-driven algorithms, saving a significant amount of trial-and-error time, and improving the algorithm's prediction accuracy and computational efficiency.

[0151] The Whale Algorithm is inspired by the bubble-web hunting behavior of humpback whales. Humpback whales prefer to prey on schools of shrimp and small fish near the surface, creating a surrounding bubble web as they rise to the surface. In the WOA algorithm, the target prey is considered the optimal solution. The detailed process of the whale optimization algorithm based on relevance vector machines is as follows... Figure 2 As shown, its corresponding Figure 1 The WOA algorithm section in the document describes the algorithm steps as follows:

[0152] Step 6.1: Population Initialization. Each individual in the whale population is represented by a D-dimensional random vector, and the population size is represented by N. P The formula is shown in equation (13), where x min and x max X i The lower and upper bounds of the integer; rand(1,D) represents a random number between [0,1].

[0153]

[0154] Step 6.2: Substitute the kernel parameter population from Step 6.1 into Steps 4 and 5, and use the root mean square error between the SOC predicted value and the true value as the fitness function to calculate the fitness function of all kernel parameter populations, and obtain the optimal solution X*.

[0155] Step 6.3: If the judgment value p < 0.5, then proceed to step 6.4; otherwise, proceed to step 6.5.

[0156] Step 6.4: If |A|<1, then jump to step 6.4.1; otherwise, jump to step 6.4.2.

[0157] Step 6.4.1: Encircling the Prey. Humpback whales can track, surround, and prey on prey based on its location. In the WOA (Way of Attrition), the prey's location is the solution space, and the current best candidate solution is the target prey or a near-optimal solution. During the encirclement phase, the whale population moves closer to the optimal solution and updates its position. This process is represented as follows:

[0158] D = |C·X * (t)-X(t)| (14)

[0159] X(t+1)=X * (t)-A·D (15)

[0160] Where: t is the current iteration number; X * (t) represents the position of the current optimal solution; X and D are position vectors; A and C are coefficient vectors, which change with the number of iterations. In each iteration, when a better solution appears, the current optimal solution X is updated. * .

[0161] A = 2a·ra (16)

[0162] C = 2·r (17)

[0163] a decreases linearly from 2 to 0, and r is a random vector in the range [0,1].

[0164] Step 6.4.2: Searching for food. Humpback whales randomly search for prey based on each other's positions. X rand The location of a whale is randomly selected from the current population.

[0165] D = |C·X rand -X| (18)

[0166] X(t+1)=X rand -A·D (19)

[0167] Step 6.5: Bubble Web Foraging. Humpback whales generate bubble webs along circular or "9" shaped paths while foraging, with two strategies designed as follows.

[0168] Shrinking encirclement mechanism. As shown in equation (16), as the iteration proceeds, a decreases linearly, and the range of values ​​for A decreases accordingly. The updated whale population position can be obtained between the initial position and the current optimal position.

[0169] Position spiral update. To simulate the spiral motion of humpback whales, the spiral equation representing the position between the humpback whale and its prey is established as follows:

[0170] X(t+1)=D′·e bl ·cos(2πl)+X * (t) (20)

[0171] D′=|X * (t)-X(t)| (21)

[0172] Where: b defines the shape of the logarithmic spiral, b = 1; l is a random number between [-1, 1]; D′ is the distance from the i-th whale to its prey (current optimal position).

[0173] Step 6.6: Determine if the maximum number of iterations has been reached. If yes, update the optimal value and output it; otherwise, return to step 6.3.

[0174] Step 7: RVM Model Integration. Divide the test set into c time-series correlated test subsets [DT1,…,DT2] based on the prediction step size. i-1 ,DT i ,…,DT c [This refers to the test subset DT within the test set DT.] i Combined with the k-nearest neighbor method, calculate DT i With verification subset B j The Euclidean distance (j∈[1,n]) is used to find the k nearest neighbor validation subsets and the RVM prediction model with the minimum root mean square error for each validation subset. Based on the root mean square error of the model's predictions of the validation set data, corresponding weights are obtained, resulting in a weighted ensemble prediction model combining the k RVM models and the corresponding correlation vectors [RV1,RV2,…,RV]. k ].

[0175] The Euclidean distance calculation method of the k-nearest neighbor method is shown in Equation (22), and the weight calculation method is shown in Equation (23):

[0176]

[0177]

[0178] in, To verify the values ​​of the set elements, denoted as the test set element value, l as the number of elements, and RMSE as the root mean square error of the i-th RVM model prediction.

[0179] From a practical perspective, this invention addresses the issue of poor adaptability of the RVM algorithm, which often uses a single kernel function for modeling, in the face of complex applications and diverse needs. Drawing on the idea of ​​ensemble learning, it proposes a multi-kernel weighted ensemble prediction method based on the Relevance Vector Machine algorithm. This method generates individual RVM learning models with greater differences by using both training samples and kernel functions for dual perturbation. This avoids the problem of model overlearning, improves the model's generalization ability and robustness, and expands its application scope.

[0180] Step 8: Model Prediction. Using the RVM weighted ensemble prediction model obtained in Step 7, predict the test subset DT. i The data is used to make predictions, and the predicted values ​​SOC and confidence intervals are output.

[0181] Step 9: Incremental Learning Strategy. Combining the incremental learning approach, the newly added test subset DT... i Before making predictions based on the data, in order to obtain the changing trends of neighboring samples, the newly added test subset DT from the previous step is... i-1 and its predicted value SOC i-1 Reassemble the training samples containing input and output data from step i-1, and combine them with the relevant vector set [RV] obtained during model training in step i-2. 1,i-2 RV 2,i-2 ,…,RV k,i-2 Together, they form a new training set [ND1,ND2,…,ND] k The RVM ensemble prediction model obtained in step 7 is then used for training to obtain k sets of related vectors [RV]. 1,i-1 RV 2,i-1 ,…,RV k,i-1 ], and the relevant vector [RV] of each group belonging to the new samples. new1,i-1 RV new2,i-1 ,…,RV newk,i-1 Together they form the test subset DT i-1 eigenvectors RV newAnd add it to the historical correlation vector [RV1,RV2,…,RV] of the m×n group of RVM prediction models in step 6. m×n ]middle.

[0182] This invention incorporates the incremental learning concept into an ensemble learning strategy, combining the feature vectors of new samples predicted by multiple individual RVM prediction models in the RVM ensemble prediction model into a newly added relevance vector set RV. new This addresses the problem that the correlation vector of a single prediction model is insufficient to reflect the overall sample characteristics. It adds the correlation vector to the historical correlation vectors of all RVM individual models, continuously learning the characteristics of new samples and improving the long-term prediction ability of the algorithm.

[0183] Step 10: Online Incremental Prediction. Repeat steps 7-9 to finally output the SOC estimate and confidence interval for the entire test set.

Claims

1. A method for online prediction of battery SOC based on an incremental correlation vector machine with a multi-core ensemble strategy, characterized in that, Includes the following steps: Step 1: Data Preprocessing Given a dataset Data, normalize the dataset so that all data are in the range [-1, 1], and divide it into a training set DN and a test set DT; Step 2: Training set sampling For the training set DN, the Bagging bootstrap sampling algorithm is used to perform n samplings, resulting in n training subsets [A1, A2, ..., A] containing a samples each. n ] and n validation sets [B1, B2, ..., B] corresponding to the training subset, each containing b samples. n ]; Step 3: Kernel Function Selection m kernel functions are selected as the core mapping functions of the algorithm, including linear kernel function, polynomial kernel function, Gaussian kernel function, exponential radial basis kernel function, Sigmoid kernel function, Cauchy kernel function, Fourier kernel function and wavelet kernel function; Step 4: Model Training Based on the n training sample subsets [A1, A2, ..., A2] obtained in step 2 n Using the m kernel functions from step 3, and employing the fast sequential sparse Bayesian learning method, m×n RVM models are trained, resulting in corresponding m×n sets of related vectors [RV1, RV2, ..., RV...]. m×n ]; Step 5: Model Validation Based on the n verification sets [B1, B2, ..., B] obtained in step 2 n ], respectively using the verification subset B j Validate training subset A j The predictive performance of the m trained RVM models is calculated, and the root mean square error [RMSE1, RMSE2, ..., RMSE] of the m×n model predictions is calculated. m×n ], where j∈[1,n]; Step 6: Adaptive Kernel Parameters Using the whale optimization algorithm, the kernel parameter population is initialized. Then, in steps 4 and 5, the root mean square error of the model prediction values ​​corresponding to all kernel parameters is calculated and used as the fitness function of the whale optimization algorithm. The kernel parameters of the m×n RVM models are globally optimized respectively, and finally m×n RVM prediction models are obtained. Step 7: RVM Model Integration The test set is divided into c time-series correlated test subsets [DT1,…,DT] based on the prediction step size. i-1 ,DT i ,…,DT c [This refers to the test subset DT within the test set DT.] i Combined with the k-nearest neighbor method, calculate DT i With verification subset B j The Euclidean distance (j∈[1,n]) is used to find the k nearest neighbor validation subsets and the RVM prediction model with the minimum root mean square error for each validation subset. Based on the root mean square error of the model's predictions of the validation set data, corresponding weights are obtained, resulting in a weighted ensemble prediction model combining the k RVM models and the corresponding correlation vectors [RV1,RV2,…,RV]. k ]; Step 8: Model Prediction Using the RVM weighted ensemble prediction model obtained in step 7, the test subset DT... i The data is used to make predictions, and the predicted values ​​SOC and confidence intervals are output. Step 9: Incremental Learning Strategy Combining incremental learning principles, the newly added test subset DT... i Before making predictions based on the data, in order to obtain the changing trends of neighboring samples, the newly added test subset DT from the previous step is... i-1 and its predicted value SOC i-1 Reassemble the training samples containing input and output data from step i-1, and combine them with the relevant vector set [RV] obtained during model training in step i-2. 1,i-2 RV 2,i-2 ,…,RV k,i-2 Together, they form a new training set [ND1,ND2,…,ND] k The RVM ensemble prediction model obtained in step 7 is then used for training to obtain k sets of related vectors [RV]. 1,i-1 RV 2,i-1 ,…,RV k,i-1 ], and the relevant vector [RV] of each group belonging to the new samples. new1,i-1 RV new2,i-1 ,…,RV newk,i-1 Together they form the test subset DT i-1 eigenvectors RV new And add it to the historical correlation vector [RV1,RV2,…,RV] of the m×n group of RVM prediction models in step 6. m×n ]middle; Step 10: Online Incremental Prediction Repeat steps 7-9 to finally output the SOC estimate and confidence interval for the entire test set.

2. The online prediction method for battery SOC based on a multi-core ensemble strategy using incremental correlation vector machine as described in claim 1, characterized in that: In step 1, the first 30% of the dataset is used as the training set, and the remaining 70% as the test set. During data collection, the dataset is susceptible to noise interference or operational errors, which may cause some abnormal data. The dataset is normalized using the following formula to ensure that the voltage, current, and temperature data are all within the interval [-1, 1], where x... min Let x be the minimum value of the data to be processed. max The maximum value of the data to be processed; 。 3. The online prediction method for battery SOC based on a multi-core ensemble strategy using incremental correlation vector machine as described in claim 1, characterized in that: In step 2, the training data is perturbed using the Bagging sampling method. A certain number of training samples are randomly drawn from the training set with replacement to generate multiple sets of training data containing different data distribution information, thus generating individual learners with greater differences. Each sampling generates 63.2% of the training set, and the remaining 36.8% of the data in the total training set DN can be used as the validation set, where the number of sampling times n is 10.

4. The online prediction method for battery SOC based on a multi-core ensemble strategy using incremental correlation vector machine as described in claim 1, characterized in that: In step 6, a novel heuristic optimization algorithm—the whale optimization algorithm—is selected due to its simplicity, minimal parameter adjustments, and strong ability to escape local optima. The specific steps are as follows: Step 6.1, Population Initialization: Each individual in the whale population is represented by a D-dimensional random vector, and the population size is represented by N. P The formula is shown below, where x min and x max X i The lower and upper bounds; rand(1,D) represents a random number between [0,1]; ； Step 6.2: Substitute the kernel parameter population from Step 6.1 into Steps 4 and 5, and calculate the fitness function of all kernel parameter populations using the root mean square error between the predicted and actual SOC values ​​as the fitness function to obtain the optimal solution. ; Step 6.3: If the judgment value p < 0.5, then proceed to step 6.4; otherwise, proceed to step 6.

5. Step 6.4: If |A| < 1, then jump to step 6.4.1; otherwise, jump to step 6.4.

2. Step 6.4.1, Encircling the Prey: Humpback whales can track, surround, and prey on prey based on its location. In the WOA (Way of the Prey), the prey's location is the solution space, and the current best candidate solution is the target prey or a near-optimal solution. During the encirclement phase, the whale population moves closer to the optimal solution and updates its position. This process is represented as follows: ； ； Where: t is the current iteration number; X represents the position of the current optimal solution; X and D are position vectors; A and C are coefficient vectors, which change with the number of iterations. In each iteration, when a better solution appears, the current optimal solution is updated. ; ； ； a decreases linearly from 2 to 0, and r is a random vector in the range [0,1]. Step 6.4.2, Searching for food: Humpback whales randomly search for prey based on each other's locations. rand The location of a whale randomly selected from the current population; ； ； Step 6.5, Bubble Net Foraging: Humpback whales generate bubble nets along circular or "9"-shaped paths while foraging. Two strategies are designed as follows: Shrinking encirclement mechanism: As the iteration proceeds, 'a' decreases linearly, and the range of values ​​for 'A' decreases accordingly. After the update, the position of the whale population can be obtained between the initial position and the current optimal position. Position Spiral Update: To simulate the spiral motion of humpback whales, the following spiral equation representing the position between the humpback whale and its prey is established: ； ； Where: b defines the shape of the logarithmic spiral, b=1; l is a random number between [-1,1]; D′ is the distance from the i-th whale to its prey (current optimal position); Step 6.6: Determine if the maximum number of iterations has been reached. If yes, update the optimal value and output it; otherwise, return to step 6.

3.

5. The online prediction method for battery SOC based on a multi-core ensemble strategy using incremental correlation vector machine as described in claim 1, characterized in that: The Euclidean distance calculation method and weight calculation method of the k-nearest neighbor method in step 7 are shown in the following two equations: ； ； in, To verify the values ​​of the elements in the set, denoted as the test set element value, l as the number of elements, and RMSE as the root mean square error of the i-th RVM model prediction.

6. The online prediction method for battery SOC based on a multi-core ensemble strategy using incremental correlation vector machine as described in claim 1, characterized in that: In step 9, an incremental learning strategy is used to retrain the SOC estimate of the previous step length during online training, and the trained correlation vectors are added to the historical correlation vector set to continuously learn the features of new samples and enhance the long-term prediction ability of the algorithm.

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