A lithium battery residual life prediction method based on VMD and improved BiGRU

Abstract

The application relates to the field of lithium battery life prediction, and discloses a lithium battery residual life prediction method based on VMD and an improved BiGRU, capacity attenuation time series are constructed by acquiring lithium battery charging and discharging data; the VMD algorithm is used to pretreat the capacity data, a plurality of intrinsic mode function (IMF) components and a residual term are acquired; the improved eagle algorithm is used to determine the key parameters of VMD decomposition; for each IMF component and the residual term, an improved BiGRU neural network prediction model is constructed, independent training and prediction are carried out on each component prediction model, linear superposition is carried out on the prediction results of the components, a final battery capacity prediction sequence is obtained, and the residual life of the lithium battery is calculated.

Description

Technical Field

[0001] This invention relates to the field of lithium battery life prediction, and specifically to a method for predicting the remaining life of lithium batteries based on VMD and an improved BiGRU. Background Technology

[0002] Lithium-ion batteries, as high-efficiency energy storage devices, are widely used in electric vehicles and energy storage systems. However, batteries undergo performance degradation during cycling, such as capacity decay and internal resistance increase. Accurately predicting the remaining useful life (RUL) of a battery is a critical aspect of battery management.

[0003] In existing technologies, data-driven RUL prediction methods, such as recurrent neural networks and long short-term memory networks, directly model the original capacity decay sequence. However, due to the non-stationarity, nonlinearity, and noise interference of the battery capacity sequence, traditional methods struggle to effectively extract multi-scale features and capture long-term dependencies, resulting in limited prediction accuracy. Furthermore, the models are sensitive to hyperparameters, easily leading to training instability and convergence failure. Deep learning combined with VMD decomposition prediction methods can further improve prediction accuracy and stability, but VMD suffers from data non-stationarity and modal mixing, resulting in poor extraction of health status features. Therefore, there is an urgent need for a prediction method that can improve these aspects, further enhance prediction accuracy, and provide higher stability and reliability, offering a new solution for lithium battery health management and lifespan prediction. Summary of the Invention

[0004] Purpose of the invention: To address the problems mentioned in the background art, this invention discloses a method for predicting the remaining life of lithium batteries based on VMD and an improved BiGRU. The method uses VMD and an improved Tianying algorithm to perform parameter decomposition and dynamically optimize information extraction. The improved BiGRU optimizes the extraction of health status features, solves the problems of insufficient high-dimensional exploration and low-dimensional convergence oscillation, and improves the accuracy and reliability of lithium battery remaining life prediction.

[0005] Technical solution:

[0006] This invention discloses a method for predicting the remaining life of lithium batteries based on VMD and an improved BiGRU, the method comprising the following steps:

[0007] S1 acquires lithium battery charge and discharge data and constructs a capacity decay time series;

[0008] S2 preprocesses the capacity data using the VMD algorithm to obtain multiple intrinsic mode function (IMF) components and residual terms;

[0009] S3 uses an improved Skyhawk algorithm to determine the key parameters of VMD decomposition;

[0010] S4 constructs an improved BiGRU neural network prediction model for each IMF component and residual term, trains and predicts each component prediction model independently, and linearly superimposes the prediction results of each component to obtain the final battery capacity prediction sequence and calculates the remaining life of the lithium battery.

[0011] Furthermore, the core parameters of the VMD algorithm include:

[0012] Penalty factor α, number of modes Noise margin τ, DC component DC, initialization method init, and convergence accuracy tol, along with the penalty factor α (which has no fixed empirical value) and the number of modes. The penalty factor α, which has no fixed empirical value, is related to the number of modes. This was determined by improving the Skyhawk algorithm.

[0013] Furthermore, the optimization fitness function of the improved Skyhawk algorithm is:

[0014]

[0015] in, This is for normalized reconstruction error; This is a weighting factor used to balance the magnitudes of the two terms; here, it is set to 0.5. The average component aliasing degree; Calculate the L2 norm; The original signal vector; To reconstruct the signal vector; The number of modal components; The modal component index (n=1, 2, 3...K); For the first The center frequency of each component; For the first The center frequency of each component, the reconstruction error measures the difference between the sum of all components and the original signal, and the component aliasing measures the degree of overlap of the center frequencies of adjacent IMF components. The weighted quantization of the two measures the VMD decomposition effect.

[0016] Furthermore, in the early stages of each iteration, the improved Skyhawk algorithm uses dynamic weights to perturb the global optimal position, providing guidance for a smooth transition into different stages of the algorithm. The dynamic weight formula is as follows:

[0017]

[0018] In the formula, Dynamic weights; This represents the current iteration number; This represents the maximum number of iterations.

[0019] The formula for the global optimal position is adjusted as follows:

[0020]

[0021] In the formula, This is the globally optimal position in the t-th iteration after improvement; This is the global optimal position in the original t-th iteration.

[0022] Furthermore, the improved Skyhawk algorithm incorporates a dual-memory pool collaborative guidance strategy for individual position updates in the X1 / X2 phase of the exploration phase and the X3 / X4 phase of the development phase, i.e., constructing a global memory pool. and individual local memory pool To store historical optimal solutions, during the algorithm's position update process, a historical optimal solution randomly selected from the dual memory pool is introduced. and Compared with the current population average position During the coordinated guidance process, the X1 and X3 phase positions are updated as follows:

[0023]

[0024]

[0025] In the formula, The improved algorithm X1 stage shows the position of the individual Skyhawk; To improve the individual position of Skyhawks in the X3 stage; and The numbers are independent, uniformly distributed random numbers in the interval [0,1]. The global historical optimal solution is randomly selected from the global memory pool; The local historical optimal solution is randomly selected from the individual's local memory pool; The random numbers are uniformly distributed between [0,1]. , To find the upper and lower limits of the parameters.

[0026] Furthermore, the improved Skyhawk algorithm dynamically adapts the step size in the shrinking exploration phase X2 and the shrinking development phase X4, which rely on the Levy flight step size. It improves the algorithm's position through dynamic weights and a dual-memory pool guidance strategy. The position updates in phases X2 and X4, combined with the dynamic step size, are as follows:

[0027]

[0028]

[0029] In the formula, The improved algorithm X2 stage shows the individual positions of the Skyhawks. To improve the individual positions of Skyhawks in the later stages 4; Let be the position of the individual randomly selected in the t-th iteration; , These are the parameters for the spiral trajectory; To balance the quality function of the search; For the eagle's movement factor; This is the slope factor for the eagle's flight path.

[0030] Furthermore, the S4-improved BiGRU neural network prediction model is as follows:

[0031] A multi-head self-attention layer and a feature fusion layer are added. The multi-head self-attention layer performs global long-term dependency capture on the temporal features of the injected location information, and its output is processed by residual connection and layer normalization to obtain self-attention features. The feature fusion layer concatenates the self-attention features with the forward and backward temporal features output by the bidirectional GRU layer in the feature dimension, and the resulting hybrid feature is used as the core feature for regression prediction.

[0032] Furthermore, S5 independently trains and predicts for each IMF component and residual term by dividing each component into training and test sets and normalizing them separately. Then, an independent Transformer-BiGRU prediction model is built for each component. Each component model uses the same network architecture but trains parameters independently. The Adam optimizer is used for parameter optimization, with an initial learning rate of 0.001-0.01. Dropout layers are used to prevent overfitting, with a dropout rate set to 0.1-0.4. The number of training epochs is set to 500-2000.

[0033] Beneficial effects:

[0034] 1. This invention adaptively separates high-frequency noise and trend terms from battery capacity sequences through variational mode decomposition (VMD), and combines this with an improved Tianying MAO algorithm to search for optimal parameters of the penalty factor α and the number of modes K, effectively reducing data non-stationarity and mode aliasing. The fitness function that minimizes reconstruction error and component aliasing is used to quantify the VMD decomposition effect, providing cleaner input features for the prediction model and optimizing health status feature extraction.

[0035] 2. This invention uses dynamic weight perturbation of the global optimal solution to avoid getting trapped in local optima in the early stages of iteration due to directly using the global optimal solution, and to avoid convergence instability during the fixed threshold switching stage in the middle stages. It adopts a dual memory pool to guide the entire iteration process, with global and individual historical optimal information guiding position updates to avoid the population losing high-quality solutions. The algorithm is specifically optimized to reduce the step size in the exploration and development stages, solving the problems of insufficient high-dimensional exploration and low-dimensional convergence oscillation caused by the fixed step size of the original Lévy flight.

[0036] 3. This invention combines the advantages of Transformer in capturing long-term dependencies with the improved BiGRU in extracting local temporal features for hybrid modeling; finally, it superimposes the prediction results of each component to achieve fitting of the decay trajectory, thereby further improving the accuracy and reliability of the prediction. Attached Figure Description

[0037] Figure 1 This is a diagram illustrating the overall framework of the method of this invention.

[0038] Figure 2 The flowchart illustrates the specific method of combining the improved Skyhawk algorithm with VMD decomposition in an embodiment of the present invention.

[0039] Figure 3 This is a schematic diagram showing the test comparison of the improved Skyhawk Algorithm (MAO) in this invention.

[0040] Figure 4 This is a time-domain diagram of the MAO-VMD decomposition of battery capacity decay in embodiment B0005 of the present invention.

[0041] Figure 5 This is a diagram showing the final battery capacity sequence results in an embodiment of the present invention. Detailed Implementation

[0042] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0043] like Figure 1 As shown, this invention discloses a method for predicting the remaining life of lithium batteries based on VMD and an improved BiGRU. The method steps are as follows:

[0044] S1: Obtain historical charge-discharge cycle data of lithium batteries and construct a capacity decay time series;

[0045] S2: The capacity data is preprocessed by using the Variational Mode Decomposition (VMD) algorithm to decompose the original capacity signal into multiple Intrinsic Mode Function (IMF) components and residual terms to separate high-frequency noise and residual trend terms. The key parameters of the VMD decomposition are determined using an improved Skyhawk Optimization (MAO) algorithm.

[0046] The S3 improved Skyhawk algorithm has the following specific improvement steps:

[0047] S3.1 In the early stages of each iteration, dynamic weights are used to perturb the global optimal position, providing guidance for a smooth transition of the algorithm into different stages;

[0048] S3.2 Incorporate a dual-memory pool collaborative guidance strategy into the position update formula in all stages (including X1 / X2 in the exploration stage and X3 / X4 in the development stage) to perform individual position updates;

[0049] S3.3 performs dynamic adaptation of the step size during the scaling-out exploration phase (X2) and scaling-out development phase (X4) of the algorithm, which depends on the Levy flight step size.

[0050] S4: For each IMF component and residual term, an improved BiGRU neural network prediction model is constructed. A Transformer multi-head self-attention mechanism is embedded in the bidirectional GRU and a feature fusion layer is added. The self-attention features and the temporal features of the bidirectional GRU are fused through the feature fusion layer to achieve joint prediction.

[0051] S5: Train and predict each component prediction model independently, and then linearly superimpose the prediction results of each component to obtain the final battery capacity prediction sequence.

[0052] S6: Calculate the remaining lifespan of the lithium battery based on the predicted capacity sequence and the preset failure threshold.

[0053] Specifically, the parameter settings for the variational mode decomposition algorithm in S2 are as follows: The core parameters of VMD include the penalty factor α and the number of modes. The parameters to be considered include noise margin τ, DC component DC, initialization method init, and convergence accuracy tol. Here, battery data has no significant noise, so τ is set to 0; battery capacity has no DC component, so DC is set to 0; to ensure decomposition stability, init is set to 1; and the convergence accuracy tol is 1e-7, which is a commonly used industrial value. Additionally, the penalty factor α and the number of modes are considered as parameters that have the greatest impact on the decomposition effect and have no fixed empirical value. An improved Skyhawk algorithm is used to automatically determine the fitness function, which is optimized as follows:

[0054]

[0055] In the formula, This is for normalized reconstruction error; This is a weighting factor used to balance the magnitudes of the two terms; here, it is set to 0.5. The average component aliasing degree; Calculate the L2 norm; The original signal vector; To reconstruct the signal vector; The number of modal components; The modal component index (n=1, 2, 3...K); For the first The center frequency of each component; For the first The center frequencies of each component. Reconstruction error measures the difference between the sum of all components and the original signal, avoiding excessive information loss; component aliasing measures the degree of overlap of the center frequencies of adjacent IMF components, avoiding information redundancy. The weighted quantization of the two measures improves the VMD decomposition effect.

[0056] Specifically, such as Figure 2 As shown in the figure, the specific process of the improved Skyhawk algorithm in this embodiment to find the optimal combination of VMD mode number K and penalty factor α is as follows:

[0057] Initialize the core parameters of the MAO algorithm, including population size, maximum number of iterations T, and parameter search range: K∈[2,10], α∈[1000,2000]); at the same time, initialize the dual memory pool of MAO and randomly generate the initial population individuals.

[0058] Substitute [K,α] of each initial population individual into the VMD algorithm to decompose the target signal; calculate the fitness value of the decomposed IMF component, and update the global optimal position and individual optimal position of MAO based on the fitness, while adjusting the global optimal position with adaptive weights.

[0059] During the iteration phase, the parameters for the exploration and development phases are updated. The updated individual parameters are then substituted back into VMD to calculate the fitness value after decomposition. The new fitness is compared with the current best fitness. If the new value is smaller, the global best parameters are updated.

[0060] Determine if the termination condition is met: If the maximum number of iterations is reached or the optimal fitness value is stable, terminate the iteration and output the optimal parameter combination; if not, increment the iteration count by 1 and return to step 3 to continue iterating.

[0061] The optimal parameters are output, and the optimal K and α obtained by MAO are substituted into VMD to complete the final decomposition of the battery capacity decay sequence.

[0062] Specifically, in the early stages of each iteration, S3.1 uses dynamic weights to perturb the global optimal position, providing guidance for a smooth transition into different stages of the algorithm. The dynamic weight formula is as follows:

[0063]

[0064] In the formula, Dynamic weights; This represents the current iteration number; This represents the maximum number of iterations.

[0065] The formula for the global optimal position is adjusted as follows:

[0066]

[0067] In the formula, This is the globally optimal position in the t-th iteration after improvement; This is the global optimal position in the original t-th iteration.

[0068] Specifically, the position update formula for all stages in S3.2 (including X1 and X2 in the exploration stage, and X3 and X4 in the development stage) incorporates a dual-memory pool collaborative guidance strategy for individual position updates:

[0069] Build a global memory pool and individual local memory pool To store historical optimal solutions, during the algorithm's position update process, a historical optimal solution randomly selected from the dual memory pool is introduced. and Compared with the current population average position This approach employs collaborative guidance, unlike traditional methods that rely solely on the current best and random individuals. The position update formulas for stages X1 and X3 are:

[0070]

[0071]

[0072] In the formula, The improved algorithm X1 stage shows the position of the individual Skyhawk; To improve the individual position of Skyhawks in the X3 stage; and The numbers are independent, uniformly distributed random numbers in the interval [0,1]. The global historical optimal solution is randomly selected from the global memory pool; The local historical optimal solution is randomly selected from the individual's local memory pool; The random numbers are uniformly distributed between [0,1]. , To find the upper and lower limits of the parameters.

[0073] Specifically, in the reduction exploration phase (X2) and reduction development phase (X4) of the S3.3 algorithm, which rely on the Levy flight step size, dynamic adaptation of the step size is performed. The step size is dynamically adjusted based on individual fitness, iteration progress, and problem dimension. The step size formula is:

[0074]

[0075] In the formula, Let be the random step size vector of Levi's flight; The dimension of the problem corresponds to the number of variables required to solve the optimization problem; here, we take 2. and These are random numbers that follow a normal distribution. Iteration progress factor; Fitness factor; The objective function is the current fitness value of the individual Skyhawk. This is the minimum fitness value found in the entire population. This represents the maximum fitness value found in the entire current population. Dimension factor.

[0076] Based on the improvements to the algorithm's position using dynamic weights and a dual memory pool guidance strategy, the position update formulas for the remaining X2 and X4 stages, combined with the dynamic step size, are as follows:

[0077]

[0078]

[0079] In the formula, The improved algorithm X2 stage shows the individual positions of the Skyhawks. To improve the individual positions of Skyhawks in the later stages 4; Let be the position of the individual randomly selected in the t-th iteration; , These are the parameters for the spiral trajectory; To balance the quality function of the search; For the eagle's movement factor; This is the slope factor for the eagle's flight path.

[0080] Specifically, the improved BiGRU network model in S4 includes the following hierarchical structure:

[0081] Input and Embedding Layer: Receives IMF component time-series data and maps it to a high-dimensional feature space through a fully connected linear layer to obtain the initial feature representation H(0).

[0082] Positional encoding layer: The positional encoding matrix P generated by sine and cosine functions is element-wise summed with the initial feature representation H(0) to inject absolute and relative positional information of the sequence into the model, resulting in H. p =H(0)+P.

[0083] Multi-head self-attention layer: for H p Multi-head self-attention computation is performed, with four attention heads, each with a 32-dimensional key vector. The output is processed through residual connections and layer normalization to obtain the feature H that captures global dependencies. a .

[0084] Bidirectional GRU layer: H a The input is fed into a bidirectional gated recurrent unit layer to encode the sequence in both forward and backward directions. Finally, the forward and backward hidden states at each time step are concatenated to obtain the feature H containing bidirectional context information.b .

[0085] Feature fusion layer: Combines the output H of the multi-head self-attention layer a With the output H of the bidirectional GRU layer b The features are concatenated along the feature dimension to form a hybrid feature H. f =[H a ;H b ].

[0086] Predictive output layer: Represents the hybrid features H f Through one or more fully connected layers, the final regression output is the predicted value of the IMF component at the next time step.

[0087] Independent prediction and training for each IMF component included: dividing each component into separate training and test sets and normalizing them separately; then building an independent Transformer-BiGRU prediction model for each component, with each model using the same network architecture but training parameters independently. The Adam optimizer was used for parameter optimization, with an initial learning rate of 0.001-0.01; Dropout layers were used to prevent overfitting, with a dropout rate set to 0.1-0.4; and the number of training epochs was set to 500-2000.

[0088] like Figure 3 As shown in the figure, the improved Eagle Algorithm (MAO) of this invention is compared with other algorithms in performance testing. AO is the original Eagle Algorithm, and IAO is the Eagle Algorithm with dynamically weighted perturbation. The test function is an unconstrained unimodal convex function to verify the convergence and optimization accuracy of the algorithms. As can be seen from the figure, the convergence performance of the Eagle Algorithm is better than other algorithms. Compared with the original AO, the Eagle Algorithm IAO with dynamically weighted perturbation achieves a smooth transition when the number of iterations reaches 2 / 3 of the maximum number of iterations, i.e., when the search behavior transitions from the exploration phase to the development phase. Based on this, the addition of a dual-memory pool guidance mechanism and adaptive multi-scale Lévy flight further ensures that MAO has both fast convergence and ultra-high optimization accuracy in terms of function, and its overall performance is significantly better than that of the compared algorithms such as AO, PSO, WOA, and GWO.

[0089] To further demonstrate the effectiveness of the method of this invention, this embodiment uses the NASA battery dataset, employing the capacity decay sequence of battery B0005 as the training set and the capacity decay sequence of battery B0006 as the test set. MAO-VMD searches for the optimal parameter combination [8, 1000]. After finding the optimal parameters, the time-domain plot of the capacity decay of battery B0005 is shown in the figure. Figure 4As shown, the capacity decay signal is decomposed into 8 IMF components and 1 residual, covering different features from long-term trends to high-frequency noise. For each IMF component and residual term, an independent improved BiGRU neural network prediction model is constructed. The prediction results of each component are linearly superimposed to obtain the final battery capacity prediction sequence. The actual value of battery B0006 obtained from the model with k=8 and α=1000 is compared with the predicted value, and the results are as follows. Figure 5 As shown in Table 1, the experimental data are compared when K is 7, 8, and 9, respectively. The results show the mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination (R²). 2 .

[0090] Table 1

[0091] MAE RMSE <![CDATA[R 2 ]]> K=7 0.0341 0.0430 0.9691 K=8 0.0331 0.0412 0.9718 K=9 0.0355 0.0466 0.9638

[0092] The data in the table shows that when K is 8, the prediction effect is better than that of two similar values, indicating that the improved optimization algorithm and the construction of the fitness function can achieve a good prediction effect.

[0093] The above embodiments are only for illustrating the technical concept and features of the present invention, and are intended to enable those skilled in the art to understand the content of the present invention and implement it accordingly. They should not be construed as limiting the scope of protection of the present invention. All equivalent transformations or modifications made in accordance with the spirit and essence of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A method for predicting the remaining life of a lithium battery based on VMD and an improved BiGRU, characterized in that, The method includes the following steps: S1 acquires lithium battery charge and discharge data and constructs a capacity decay time series; S2 preprocesses the capacity data using the VMD algorithm to obtain multiple intrinsic mode function (IMF) components and residual terms; S3 uses an improved Skyhawk algorithm to determine the key parameters of VMD decomposition; S4 constructs an improved BiGRU neural network prediction model for each IMF component and residual term, trains and predicts each component prediction model independently, and linearly superimposes the prediction results of each component to obtain the final battery capacity prediction sequence and calculates the remaining life of the lithium battery.

2. The lithium battery remaining life prediction method based on VMD and improved BiGRU according to claim 1, characterized in that, The core parameters of the VMD algorithm include: Penalty factor α, number of modes Noise margin τ, DC component DC, initialization method init, and convergence accuracy tol, along with the penalty factor α (which has no fixed empirical value) and the number of modes. The penalty factor α, which has no fixed empirical value, is related to the number of modes. This was determined by improving the Skyhawk algorithm.

3. The lithium battery remaining life prediction method based on VMD and improved BiGRU according to claim 2, characterized in that, The optimized fitness function of the improved Skyhawk algorithm is: ； in, This is for normalized reconstruction error; This is a weighting factor used to balance the magnitudes of the two terms; here, it is set to 0.

5. The average component aliasing degree; Calculate the L2 norm; The original signal vector; To reconstruct the signal vector; The number of modal components; The modal component index (n=1, 2, 3...K); For the first The center frequency of each component; For the first The center frequency of each component, the reconstruction error measures the difference between the sum of all components and the original signal, and the component aliasing measures the degree of overlap of the center frequencies of adjacent IMF components. The weighted quantization of the two measures the VMD decomposition effect.

4. The lithium battery remaining life prediction method based on VMD and improved BiGRU according to claim 1, characterized in that, The improved Skyhawk algorithm uses dynamic weights to perturb the global optimal position in the early stages of each iteration, providing guidance for a smooth transition into different stages of the algorithm. The dynamic weight formula is as follows: ； In the formula, Dynamic weights; This represents the current iteration number; This represents the maximum number of iterations. The formula for the global optimal position is adjusted as follows: ； In the formula, This is the globally optimal position in the t-th iteration after improvement; This is the global optimal position in the original t-th iteration.

5. The lithium battery remaining life prediction method based on VMD and improved BiGRU according to claim 1, characterized in that, The improved Skyhawk algorithm introduces a dual-memory pool collaborative guidance strategy for individual position updates in the X1 / X2 phase of the exploration phase and the X3 / X4 phase of the development phase, i.e., constructing a global memory pool. and individual local memory pool To store historical optimal solutions, during the algorithm's position update process, a historical optimal solution randomly selected from the dual memory pool is introduced. and Compared with the current population average position During the coordinated guidance process, the X1 and X3 phase positions are updated as follows: ； ； In the formula, The improved algorithm X1 stage shows the position of the individual Skyhawk; To improve the individual position of Skyhawks in the X3 stage; and The numbers are independent, uniformly distributed random numbers in the interval [0,1]. The global historical optimal solution is randomly selected from the global memory pool; The local historical optimal solution is randomly selected from the individual's local memory pool; The random numbers are uniformly distributed between [0,1]. , To find the upper and lower limits of the parameters.

6. The lithium battery remaining life prediction method based on VMD and improved BiGRU according to claim 5, characterized in that, The improved Skyhawk algorithm dynamically adapts the step size in the shrinking exploration phase X2 and the shrinking development phase X4, which rely on the Levy flight step size. It improves the algorithm's position using dynamic weights and a dual-memory pool guidance strategy. The position updates in phases X2 and X4, combined with the dynamic step size, are as follows: ； ； In the formula, The improved algorithm X2 stage shows the individual positions of the Skyhawks. To improve the individual positions of Skyhawks in the later stages 4; Let be the position of the individual randomly selected in the t-th iteration; , These are the parameters for the spiral trajectory; To balance the quality function of the search; For the eagle's movement factor; This is the slope factor for the eagle's flight path.

7. The lithium battery remaining life prediction method based on VMD and improved BiGRU according to claim 1, characterized in that, The S4-improved BiGRU neural network prediction model is as follows: A multi-head self-attention layer and a feature fusion layer are added; the multi-head self-attention layer performs global long-term dependency capture on the temporal features of the injected location information, and its output is processed by residual connection and layer normalization to obtain self-attention features; The feature fusion layer concatenates the self-attention features with the forward and backward temporal features output by the bidirectional GRU layer along the feature dimension, and the resulting hybrid feature serves as the core feature for regression prediction.

8. The lithium battery remaining life prediction method based on VMD and improved BiGRU according to claim 7, characterized in that, S5 trains and predicts independently for each IMF component and residual term. This involves dividing each component into training and test sets, normalizing them separately, and then building an independent Transformer-BiGRU prediction model for each component. Each component model uses the same network architecture but trains independently with parameters. The Adam optimizer is used for parameter optimization, with an initial learning rate of 0.001-0.

01. Dropout layers are used to prevent overfitting, with a dropout rate set to 0.1-0.

4. The number of training rounds is set to 500-2000 rounds.

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