Lithium ion battery remaining life prediction method and system based on GM-PFF
By combining grey model and particle flow filtering, the accuracy and stability issues of lithium-ion battery remaining life prediction under small sample and uncertainty conditions are solved, achieving high-precision battery life prediction and health status assessment, and optimizing battery usage strategies and system operation.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- FUJIAN NORMAL UNIV
- Filing Date
- 2026-05-18
- Publication Date
- 2026-07-03
AI Technical Summary
Existing methods for predicting the remaining lifespan of lithium-ion batteries lack accuracy and stability under conditions of small sample size and uncertainty in observational information, making it difficult to achieve high-precision predictions.
A combined approach based on grey model (GM) and particle flow filter (PFF) is adopted. The grey model is used to fit and predict historical data, and the particle flow filter algorithm is used to update the model parameters. The sliding window technique is combined to dynamically adapt to different stages of battery capacity decay and output the probability density distribution of the remaining battery life.
It improves the accuracy and stability of lithium-ion battery remaining life prediction, reduces the root mean square error of prediction, can dynamically adapt to different stages of battery capacity decay, provides a reliable tool for battery health status assessment and cascade utilization, reduces operation and maintenance costs, and improves system safety and economy.
Smart Images
Figure CN122330718A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of lithium-ion battery technology, and in particular to a method and system for predicting the remaining life of lithium-ion batteries based on GM-PFF. Background Technology
[0002] With the advancement of the global energy transition, lithium-ion batteries, as core energy storage components, are increasingly widely used in electric vehicles, large-scale energy storage systems, and other fields. Irreversible aging occurs during battery use, leading to capacity decay. Accurate prediction of their remaining useful life (RUL) is crucial for implementing predictive health management and ensuring the safe and economical operation of systems.
[0003] Currently, lithium-ion battery RUL prediction methods are mainly divided into two categories: model-based methods and data-based methods. Model-based methods (such as those combining Kalman filtering and particle filtering) describe capacity decay by establishing mathematical models, but the internal chemical degradation mechanism of the battery is complex, making accurate modeling difficult. Data-based methods (such as support vector regression and neural networks) can uncover data patterns, but their performance heavily relies on a large amount of historical data, which is often insufficient for practical applications. Particle filtering is an effective Bayesian filtering method for handling nonlinear, non-Gaussian systems, but it suffers from the "particle degradation" problem, where only a few high-weight particles are effective after multiple iterations, wasting a large amount of computational resources. Particle flow filtering (PFF) introduces homotopy theory, allowing particles to "flow" from the prior distribution to the posterior distribution, ensuring all particles have equal weights and eliminating the need for resampling, thus theoretically solving the particle degradation problem. However, the prediction accuracy of PFF is highly dependent on the accuracy of the observation information, and its performance will significantly decrease when there is noise or fluctuation in the battery monitoring data.
[0004] Therefore, how to achieve high-precision and high-stability prediction of the RUL of lithium-ion batteries under conditions of small sample size and uncertainty in observation information remains a technical challenge that urgently needs to be solved in this field. Summary of the Invention
[0005] The purpose of this invention is to provide a method and system for predicting the remaining life of lithium-ion batteries based on GM-PFF. By embedding the grey model (GM) into the particle flow filter (PFF) framework, the root mean square error of the remaining life prediction of lithium-ion batteries is effectively reduced, and the prediction accuracy is improved.
[0006] The technical solution adopted in this invention is:
[0007] A method for predicting the remaining life of lithium-ion batteries based on GM-PFF includes the following steps:
[0008] S1. Obtain the historical capacity decay data sequence of lithium-ion batteries; use the least squares method to fit the first k periods of the historical capacity decay data sequence to obtain the initial parameters of the degradation model; and initialize the model parameters of the gray model used as the degradation model.
[0009] S2. Taking the (k+1)th cycle as the starting point of the battery capacity prediction stage, the predicted battery capacity value for the current prediction cycle i is obtained using the grey model, and the predicted battery capacity value is used as the observation value of the particle flow filter in the current prediction cycle. ;
[0010] S3. Based on the observations, the particle flow filtering algorithm is used to calculate the particle flow, so that all particles flow from the prior probability distribution to the posterior probability distribution to update the parameters of the degenerate model.
[0011] S4. Using the updated degradation model, predict the battery capacity for the next m cycles from the initial prediction cycle. Predicted battery capacity The predicted capacity is compared with the preset failure threshold FT. If the predicted capacity is higher than the failure threshold FT, the value of the predicted future cycle number m is increased one by one. The comparison process in step S4 is repeated until the predicted capacity is lower than or equal to the failure threshold, and the time point corresponding to the current predicted capacity is taken as the predicted end point of battery life. The remaining battery life (RUL) is obtained by calculating the number of cycles from the start point of the battery capacity prediction stage to the predicted end point of battery life.
[0012] S5. Repeat steps S2 to S4 to obtain multiple predicted values of remaining battery life (RUL) based on the predicted trajectories of all particles, and generate the probability density function of remaining life.
[0013] Furthermore, the implementation of initializing the model parameters of the gray model as the degradation model in step S1 includes: setting the total number of particles in the particle flow filter, the variance of measurement noise and observation noise; and setting the sliding window length t of the gray model GM(1,1).
[0014] Furthermore, the sliding window length t ranges from 10 to 20 cycles.
[0015] Furthermore, the specific implementation of predicting the current cycle battery capacity value using the grey model in step S2 includes:
[0016] The generated sequence is obtained by accumulating the historical capacity decay data sequence within the sliding window of the gray model.
[0017] A whitening differential equation is constructed based on the generated sequence, and the development coefficient of the whitening differential equation is solved using the least squares method. and internal generation control of grayscale b;
[0018] Solving parameters The predicted battery capacity for the current period i is obtained by restoring the prediction using the time response function. .
[0019] Furthermore, the particle flow filtering algorithm in step S3 adopts the extended Daum-Huang filtering algorithm.
[0020] Furthermore, the preset failure threshold FT in step S4 is set to a value range of 65% to 85% of the rated capacity of the lithium-ion battery.
[0021] Furthermore, the formula for calculating the remaining battery life (RUL) in step S4 is: RUL = m - ST - k, where RUL is the remaining battery life, m is the predicted number of cycles, ST is the starting predicted cycle point of the battery capacity, and k is the number of cycles of the fitted historical capacity decay data sequence.
[0022] Furthermore, in step S5, the prediction stage of lithium-ion battery life is divided into three stages: early, middle and late. The remaining lifespan is predicted based on the training data of each stage to verify the predictive adaptability of the model under different aging conditions.
[0023] Furthermore, it also includes step S6: calculating the performance evaluation metrics of the predicted battery remaining life (RUL), the performance evaluation metrics including at least one of root mean square error (RMSE), absolute error (AE), and accuracy metric (PI).
[0024] Among them, the accuracy index PI is defined as the difference between the upper and lower limits of the probability density interval, and is used to quantify the range of uncertainty of the prediction results.
[0025] This invention also discloses a lithium-ion battery remaining life prediction system, comprising:
[0026] The data acquisition module is used to acquire historical capacity decay data sequences of lithium-ion batteries;
[0027] The initialization module is used to fit the first k periods of the historical capacity decay data sequence using the least squares method to obtain the initial parameters of the degradation model; and to initialize the model parameters of the gray model, which serves as the degradation model.
[0028] The grey prediction module uses the (k+1)th cycle as the starting point for the battery capacity prediction stage. It uses a grey model to predict the battery capacity for the current prediction cycle i, and then uses this predicted battery capacity as the observation value of the particle flow filter in the current prediction cycle. ;
[0029] The particle flow filtering update module is used to calculate the particle flow based on the observations using the particle flow filtering algorithm, so that all particles flow from the prior probability distribution to the posterior probability distribution to update the parameters of the degenerate model.
[0030] The lifetime prediction module is used to predict the battery capacity m cycles ahead of the initial prediction cycle using an updated degradation model. Predicted battery capacity The predicted capacity is compared with the preset failure threshold FT. If the predicted capacity is higher than the failure threshold FT, the value of the predicted future cycle number m is increased one by one. The battery predicted capacity calculation and comparison process is repeated until the predicted capacity is lower than or equal to the failure threshold, and the time point corresponding to the current predicted capacity is taken as the predicted end of the battery life. The remaining battery life (RUL) is obtained by calculating the number of cycles from the start of the battery capacity prediction stage to the predicted end of the battery life.
[0031] The output module is used to summarize the predicted values of multiple battery remaining lifetimes (RUL) based on the predicted trajectories of all particles, and generate the probability density function of the remaining lifetime to characterize the range of uncertainty in the prediction.
[0032] The present invention adopts the above technical solution and has the following beneficial effects compared with the prior art:
[0033] (1) By embedding the grey model (GM) into the particle flow filter (PFF) framework, the superior ability of GM to predict trends in small sample data is utilized to provide a more robust and reliable "observation value" input for PFF. Compared with the traditional PFF, the method of this invention (GM-PFF) effectively reduces the root mean square error of the prediction of the remaining life of lithium-ion batteries and improves the prediction accuracy. (2) This invention uses a sliding window grey model for online local prediction, which enables it to dynamically adapt to different trends in the early, middle and late stages of battery capacity decay. This invention does not rely on a large amount of historical battery data and can achieve high-precision trend tracking in the early stage of prediction, providing a reliable tool for early health status assessment and tiered utilization value judgment of batteries. (3) This invention finally outputs the probability density distribution of RUL rather than a single-point estimate, which intuitively shows the uncertainty range of the prediction result of battery life in a quantitative form. It can provide richer and more reliable information for battery maintenance, replacement and system redundancy design, which helps to optimize battery usage strategies, reduce operation and maintenance costs, and improve the safety and economy of the entire energy storage system or electrical equipment. Attached Figure Description
[0034] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments;
[0035] Figure 1This is a schematic diagram of the principle architecture of the lithium-ion battery remaining life prediction method based on GM-PFF of the present invention.
[0036] Figure 2 A schematic diagram of the CALCE lithium-ion battery degradation dataset;
[0037] Figure 3 A schematic diagram of the NASA PCoE lithium-ion battery degradation dataset;
[0038] Figure 4 This invention aims to fit the grayscale model of the grayscale model to the A1 battery using 70 training cycles of data.
[0039] Figure 5 This invention aims to fit the grayscale model of the grayscale model to the A1 battery using 80 cycles of training data.
[0040] Figure 6 This is the intention of fitting the grayscale model of the present invention to the A1 battery with 90 cycles of training data;
[0041] Figure 7 This is the battery capacity degradation prediction result for the first 70 cycles of battery A1 in this invention during the early prediction phase.
[0042] Figure 8 This is the predicted battery capacity degradation result for the first 80 cycles of battery A1 in this invention during the mid-term prediction phase.
[0043] Figure 9 This is the battery capacity degradation prediction result for the late prediction stage of the first 90 cycles of battery A1 of the present invention.
[0044] Figure 10 This is the battery capacity degradation prediction result for the first 70 cycles of battery B06 of the present invention during the early prediction stage.
[0045] Figure 11 This is the battery capacity degradation prediction result for the first 80 cycles of battery B06 of the present invention during the mid-term prediction phase.
[0046] Figure 12 This is the battery capacity degradation prediction result for the late prediction stage of the first 90 cycles of battery B06 of the present invention. Detailed Implementation
[0047] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings.
[0048] like Figures 1 to 12 As shown, this invention discloses a method for predicting the remaining life of lithium-ion batteries based on GM-PFF, comprising the following steps:
[0049] S1. Obtain the historical capacity decay data sequence of lithium-ion batteries; use the least squares method to fit the first k periods of the historical capacity decay data sequence to obtain the initial parameters of the degradation model; and initialize the model parameters of the gray model used as the degradation model, including: setting the total number of particles for particle flow filtering, and the variance of measurement noise and observation noise. As a feasible implementation method, initialize the number of particles to 100, and the measurement noise... , , , and observation noise Set the sliding window length t of the gray model GM(1,1). As an optional implementation, the sliding window length t can range from 10 to 20 periods.
[0050] Furthermore, the gray model described above lies between the white and black models, representing a system where some internal information is known and some is unknown. Gray models have a unique advantage in predicting data quality with small sample sizes, exhibiting good predictive performance. The most typical example is the GM(1,1) model; the process of establishing the GM(1,1) model is as follows:
[0051] For a set of historical data, (1);
[0052] in, It is a historical data array; Historical data array The first historical data; Historical data array The nth historical data; n is the number of historical data in the historical data array;
[0053] The first-order cumulative generation sequence (1-AGO) is obtained from the historical data array sequence. Represented as:
[0054] (2);
[0055] The whitening differential equation is:
[0056] (3);
[0057] in, 'b' represents the grayscale development, and 'b' represents the internal grayscale generation control, satisfying the following requirements:
[0058] ;
[0059] ;
[0060] (4);
[0061] Where B is the lithium-ion battery capacity degradation data matrix; Y is the data vector generated by the first-order cumulative generation sequence; This is the nth data point in the first-order cumulative generation sequence;
[0062] The restored data and predicted values are as follows:
[0063] ;
[0064] (5);
[0065] in, The predicted value of the first-order cumulative generation sequence at time t; The predicted value of the first-order cumulative generation sequence at time t+1; The predicted value is the original historical data at time t+1.
[0066] Grey models are suitable for situations with small sample sizes and incomplete data, and can perform trend prediction well.
[0067] S2. Take the (k+1)th cycle as the starting point of the battery capacity prediction stage, i.e., set the starting time ST=k+1; obtain the actual capacity as training data, use the grey model to predict the battery capacity value of the current prediction cycle i, and use the battery capacity prediction value as the observation value of the particle flow filter in the current prediction cycle. ;
[0068] S3. Based on the observations, a particle flow filtering algorithm is used to calculate the particle flow, so that all particles flow from the prior probability distribution to the posterior probability distribution to update the parameters of the degenerate model; as a feasible implementation method, the particle flow filtering algorithm adopts the extended Daum-Huang filtering algorithm.
[0069] S4. Using the updated degradation model, predict the battery capacity for the next m cycles from the initial prediction cycle. Predicted battery capacity The predicted capacity is compared with the preset failure threshold FT. If the predicted capacity is higher than the failure threshold FT, the value of the predicted future cycle number m is increased one by one. The comparison process in step S4 is repeated until the predicted capacity is lower than or equal to the failure threshold, and the time point corresponding to the current predicted capacity is taken as the predicted end point of battery life. The remaining battery life (RUL) is obtained by calculating the number of cycles from the start point of the battery capacity prediction stage to the predicted end point of battery life. The calculation expression is: RUL=m-ST-k, where RUL is the remaining battery life, m is the predicted number of cycles, ST is the start prediction cycle point of battery capacity, and k is the number of cycles of the fitted historical capacity decay data sequence.
[0070] Specifically, a degradation model is used to predict battery capacity. Comparison of predicted battery capacity and failure threshold FT, if If the predicted future period number m is incremented by 1, the prediction is repeated until... As a feasible implementation, the preset failure threshold FT is set to a value range of 65% to 85% of the rated capacity of the lithium-ion battery.
[0071] S5. Repeat steps S2 to S4 to obtain multiple predicted values of remaining battery life (RUL) based on the predicted trajectories of all particles, and generate the probability density function of remaining life.
[0072] Furthermore, the specific implementation of predicting the current cycle battery capacity value using the grey model in step S2 includes:
[0073] The generated sequence is obtained by accumulating the historical capacity decay data sequence within the sliding window of the gray model.
[0074] A whitening differential equation is constructed based on the generated sequence, and the development coefficient of the whitening differential equation is solved using the least squares method. and internal generation control of grayscale b;
[0075] Solving parameters The predicted battery capacity for the current period i is obtained by restoring the prediction using the time response function. .
[0076] Furthermore, as a preferred technical solution, in the specific implementation of this invention, the prediction stage of lithium-ion battery life in step S5 is divided into three stages: early, middle and late. The remaining service life is predicted based on the training data of different stages to verify the predictive adaptability of the model under different aging conditions.
[0077] Furthermore, it also includes step S6: calculating the performance evaluation metrics of the predicted battery remaining life (RUL), the performance evaluation metrics including at least one of root mean square error (RMSE), absolute error (AE), and accuracy metric (PI).
[0078] Specifically, the root mean square error (RMSE) is the error between the actual battery capacity and the predicted battery capacity, expressed as follows:
[0079] (6);
[0080] Absolute Error (AE) is the absolute value of the difference between the actual remaining battery life and the predicted remaining battery life, expressed as follows:
[0081] (7);
[0082] The precision index (PI) is the relative width of the probability density interval, where... and Let represent the upper and lower bounds of the probability density interval, respectively, and their expressions are as follows:
[0083] (8);
[0084] Furthermore, as an optional implementation, the lithium-ion battery degradation dataset used for the training dataset of the degradation model in the specific implementation of the present invention comes from the Center for Advanced Life Cycle Engineering (CALCE) at the University of Maryland and the National Aeronautics and Space Administration Prognostics Center of Excellence (NASA PCoE).
[0085] like Figure 1 As shown, the present invention also discloses a lithium-ion battery remaining life prediction system, comprising:
[0086] The data acquisition module is used to acquire historical capacity decay data sequences of lithium-ion batteries;
[0087] The initialization module is used to fit the first k periods of the historical capacity decay data sequence using the least squares method to obtain the initial parameters of the degradation model; and to initialize the model parameters of the gray model, which serves as the degradation model.
[0088] The grey prediction module uses the (k+1)th cycle as the starting point for the battery capacity prediction stage. It uses a grey model to predict the battery capacity for the current prediction cycle i, and then uses this predicted battery capacity as the observation value of the particle flow filter in the current prediction cycle. ;
[0089] The particle flow filtering update module is used to calculate the particle flow based on the observations using the particle flow filtering algorithm, so that all particles flow from the prior probability distribution to the posterior probability distribution to update the parameters of the degenerate model.
[0090] The lifetime prediction module is used to predict the battery capacity m cycles ahead of the initial prediction cycle using an updated degradation model. Predicted battery capacity The predicted capacity is compared with the preset failure threshold FT. If the predicted capacity is higher than the failure threshold FT, the value of the predicted future cycle number m is increased one by one. The battery predicted capacity calculation and comparison process is repeated until the predicted capacity is lower than or equal to the failure threshold, and the time point corresponding to the current predicted capacity is taken as the predicted end of the battery life. The remaining battery life (RUL) is obtained by calculating the number of cycles from the start of the battery capacity prediction stage to the predicted end of the battery life.
[0091] The output module is used to summarize the predicted values of multiple battery remaining lifetimes (RUL) based on the predicted trajectories of all particles, and generate the probability density function of the remaining lifetime to characterize the range of uncertainty in the prediction.
[0092] Effect Experiment: Further, as an optional implementation method, such as Figure 2 As shown in Figure 3, the lithium-ion battery degradation dataset used in the training dataset of the degradation model of the present invention comes from the Center for Advanced Life Cycle Engineering (CALCE) at the University of Maryland and the National Aeronautics and Space Administration Prognostics Center of Excellence (NASA PCoE).
[0093] To demonstrate the specific effects of this invention, CALCE prediction was performed using training data from battery A1 at cycles 70, 80, and 90. The grey model predicted the capacity degradation trajectory as an approximately straight line, as shown below. Figure 4 , 5As shown in Figure 6, experimental results demonstrate its ability to effectively capture the early-stage stable degradation trend of lithium-ion batteries. This stems from GM's enhanced monotonicity through cumulative sequence generation, which aligns with the linear aging mechanism of battery capacity. However, the model lacks sufficient sensitivity to stochastic factors such as charge / discharge noise and operating condition fluctuations, resulting in the failure to reflect short-term capacity anomalies (e.g., capacity recovery caused by local voltage fluctuations). This characteristic makes GM suitable for degradation baseline modeling and rough lifetime prediction, but it needs to be combined with hybrid models (such as GM-PFF) to improve the predictive completeness for complex scenarios.
[0094] The nonlinear and stochastic characteristics of lithium-ion battery capacity degradation trajectories highlight the significant advantages of grey models in handling small samples and nonlinear systems. It can provide a preliminary estimate of battery capacity, offering strong support for subsequent refined predictions.
[0095] Table 1. Prediction results of GM (1,1) parameters
[0096]
[0097] Table 1 shows the grey model prediction results for the three battery groups, with the parameter estimates as follows: The development coefficient and b (grey action) together determine the slope and intercept of the capacity degradation trend. The model accuracy was verified by the posterior error ratio c (the ratio of the predicted residual variance to the original data variance). The results showed that the c value for battery A1 remained consistently below 0.5 throughout the process (maximum 0.48), indicating a high degree of agreement between its predicted curve and the actual capacity decay trajectory. This verified the strong adaptability of GM to linearly dominant degradation (such as the uniform growth mode of the SEI film in A1). Battery A2 exhibited stage-specific differences; the c value exceeded 0.65 in the early stages, indicating insufficient accuracy, while the c value decreased to 0.63 in the later stages, which was basically acceptable. This reflects the non-stationary fluctuations in the early stages of aging (such as local capacity recovery caused by lithium deposition), making it difficult for GM to capture short-term random terms. However, as degradation entered a steady-state period, the model accuracy significantly improved. GM's predictive performance is strongly correlated with the characteristics of battery degradation stages. It is more robust to predicting stages with a high proportion of trend components in historical data (such as the entire A1 cycle and the late A2 stage), but it is prone to bias in the early stages of degradation dominated by noise (such as the early A2 stage).
[0098] Therefore, based on the battery aging mechanism, a suitable prediction range for GM was selected. The experiment in this chapter uses a sliding window (15 cycles) to predict the capacity of lithium-ion batteries.
[0099] from Figures 8 to 12It can be clearly observed that the prediction results of the GM-PFF model are highly consistent with the actual measured capacity degradation trend. This trend indicates that the proposed method can accurately track the degradation process of lithium-ion batteries and make reasonable predictions about their remaining lifespan. To more systematically analyze the predictive performance of the model, three key prediction stages were set to correspond to different stages of battery lifespan development.
[0100] In the early prediction phase (the first 70 cycles), the main objective of the GM-PFF model is to capture the initial performance degradation trend of the battery. Predictions in this phase are particularly crucial, as they determine the accuracy and stability of subsequent predictions. The results show that the model can fit the battery capacity decline trajectory well in the early stages, demonstrating good predictive ability. The mid-term prediction phase (the first 80 cycles) further analyzes the mid-term degradation pattern of battery performance. In this phase, the battery capacity decline gradually accelerates, and nonlinear characteristics become more pronounced. GM-PFF maintains high prediction accuracy and successfully reflects this trend. This indicates that the model can not only adapt to early linear degradation characteristics but also capture mid-term nonlinear degradation behavior, laying the foundation for reliable battery life prediction. In the late prediction phase (the first 90 cycles), the battery capacity approaches the failure threshold, significantly increasing the difficulty of prediction. However, GM-PFF can still accurately characterize the battery degradation characteristics and reasonably predict the battery life endpoint. In particular, when the battery is close to failure, the predicted curve and the actual capacity curve have a high degree of overlap, further validating the effectiveness of the model.
[0101] Regarding end-of-life prediction, the blue solid line represents the probability density distribution, used to predict possible battery lifetime distributions. Observing the probability density curves reveals that the GM-PFF prediction results not only possess high accuracy but also good stability. The relatively concentrated probability distribution further indicates that this method effectively reduces uncertainty, making the prediction results more reliable. The GM-PFF model's prediction results highly match the actual end-of-life, and the prediction interval is mainly concentrated near the predicted end-of-life, reflecting the model's stability and accuracy. CALCE's prediction interval spans 2-3 cycles, while NASAPCoE's spans 5-7 cycles. This indicates that the particle distribution in GM-PFF is more concentrated, further corroborating the model's accuracy and stability in lifetime prediction.
[0102] from Figures 8 to 12Analysis shows that the black markers represent the actual capacity degradation of lithium-ion batteries, while the red markers represent the GM-PFF model's prediction of the remaining capacity. The high degree of overlap between the two intuitively demonstrates the superiority of GM-PFF in predicting battery capacity degradation trends. Furthermore, the solid red line represents the battery failure threshold, which corresponds to 0.72 Ah for the CALCE dataset and 1.4 Ah for the NASA PCoE dataset, providing clear reference standards for battery life assessment.
[0103] Comparative Analysis: A systematic validation study of lithium-ion battery capacity degradation prediction based on the GM-PFF and PFF models using the CALCE and NASA PCoE datasets reveals the significant advantages of the novel fusion model. As shown in Tables 2 and 3, under strict control of experimental variables (100 particles, consistent parameter configuration and environmental conditions), the GM-PFF model demonstrates breakthrough improvements in the three core indicators: root mean square error, absolute error, and accuracy.
[0104] Taking battery A1 in the CALCE dataset as an example, in the early prediction phase (first 70 cycles), the RMSE value of GM-PFF dropped to 0.0568, a 31% reduction compared to the 0.0825 error of the PFF model. This improvement showed an increasing trend as the prediction phase progressed. In particular, under complex conditions on the NASA dataset, the RMSE reduction of GM-PFF exceeded 6%, fully validating the model's adaptability to nonlinear degradation processes.
[0105] The model's advantages are even more pronounced in the later prediction stages. Taking battery B06 from the NASA dataset as an example, when the prediction stage reaches the late stage of capacity degradation, the absolute error of GM-PFF is only 3 cycles, compared to 14 cycles for the PFF model, representing a 79% improvement in prediction accuracy. This significant improvement stems from the innovative design of the model architecture: GM-PFF effectively corrects the prediction bias caused by the mismatch in proposal distribution in traditional particle filtering by using prior information constraints constructed through a grey model. The fitting characteristics of the grey model provide degradation trend guidance for the particles, making the particle flow process more closely resemble the actual degradation trajectory.
[0106] Accuracy index (PI), as a key indicator for evaluating model uncertainty, has a dual nature in battery capacity degradation prediction: it reflects both the model's own prediction confidence and the stochastic characteristics of the battery degradation mechanism. The data in the table shows that the PI value of GM-PFF is lower than or equal to that of PFF in most cases, indicating superior prediction accuracy and stability. PI is related to RMSE and AE; generally, a lower RMSE and AE result in a lower PI. For example, in the middle stage of B05, the PI of GM-PFF is 3, while that of PFF is 4, reflecting the more accurate prediction of GM-PFF. However, in some cases, such as the later stage of B06, the PI value of GM-PFF is higher, possibly due to increased prediction uncertainty. This indicates that PI is not only affected by error but also constrained by factors such as prediction stability. Therefore, GM-PFF performs better in the early and middle stages, but there is still room for optimization in later predictions to further improve stability and reliability.
[0107] From an engineering application perspective, the low-error characteristics and high-deterministic prediction capabilities exhibited by GM-PFF provide a new technological path for battery health management. Its early prediction stage can achieve capacity estimation errors within 6% (CALCE) and 4% (NASA PCoE), which is of significant value for scenarios such as the evaluation of the secondary use of power batteries and the formulation of maintenance strategies for energy storage systems.
[0108] Table 2 Comparison of CALCE prediction results between GM-PFF and PFF
[0109]
[0110] Table 3 Comparison of NASA PCoE prediction results between GM-PFF and PFF
[0111]
[0112] This invention introduces a combined approach of grey model and particle flow filtering to improve the accuracy of RUL prediction for lithium-ion batteries. The grey model captures the uncertainties in the battery performance degradation process, while its predicted values guide particle state updates, thereby achieving a more accurate estimate of the battery's RUL.
[0113] To comprehensively evaluate the performance of the GM-PFF method at different stages, root mean square error, absolute error, and accuracy were selected as performance indicators, and the GM-PFF prediction results for the early, middle, and late stages were analyzed in detail. Furthermore, the uncertainty of the prediction results was quantified by the probability density distribution range, providing decision-makers with richer information support.
[0114] Experimental results on two commonly used datasets show that, compared to particle flow filtering, the GM-PFF method effectively reduces the uncertainty range of the prediction results and exhibits lower error when predicting the RUL of lithium-ion batteries. However, the prediction accuracy of particle flow filtering still depends to some extent on the degradation trend of empirical models. For batteries under different operating conditions, multiple empirical models can be used in combination to improve the reliability and accuracy of predictions.
[0115] The present invention adopts the above technical solution and has the following beneficial effects compared with the prior art:
[0116] (1) By embedding the grey model (GM) into the particle flow filter (PFF) framework, the superior ability of GM to predict trends in small sample data is utilized to provide a more robust and reliable "observation value" input for PFF. Compared with the traditional PFF, the method of this invention (GM-PFF) effectively reduces the root mean square error of the prediction of the remaining life of lithium-ion batteries and improves the prediction accuracy. (2) This invention uses a sliding window grey model for online local prediction, which enables it to dynamically adapt to different trends in the early, middle and late stages of battery capacity decay. This invention does not rely on a large amount of historical battery data and can achieve high-precision trend tracking in the early stage of prediction, providing a reliable tool for early health status assessment and tiered utilization value judgment of batteries. (3) This invention finally outputs the probability density distribution of RUL rather than a single-point estimate, which intuitively shows the uncertainty range of the battery life prediction results in a quantitative form. It can provide richer and more reliable information for battery maintenance, replacement and system redundancy design, which helps to optimize battery usage strategies, reduce operation and maintenance costs, and improve the safety and economy of the entire energy storage system or electrical equipment.
[0117] Obviously, the described embodiments are only a part of the embodiments of this application, not all of them. Without conflict, the embodiments and features in the embodiments of this application can be combined with each other. The components of the embodiments of this application described and illustrated herein can generally be arranged and designed in various different configurations. Therefore, the detailed description of the embodiments of this application is not intended to limit the scope of the claimed application, but merely to illustrate selected embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.
Claims
1. A method for predicting the remaining life of a lithium-ion battery based on GM-PFF, characterized in that, Includes the following steps: S1. Obtain the historical capacity decay data sequence of lithium-ion batteries; use the least squares method to fit the first k periods of the historical capacity decay data sequence to obtain the initial parameters of the degradation model; and initialize the model parameters of the gray model used as the degradation model. S2, taking the k+1th cycle as a starting cycle point of a prediction stage of the battery capacity, predicting the battery capacity prediction value of the current prediction cycle i by using the grey model, and taking the battery capacity prediction value as an observation value of the particle flow filtering in the current prediction cycle ; S3. Based on the observations, the particle flow filtering algorithm is used to calculate the particle flow, so that all particles flow from the prior probability distribution to the posterior probability distribution to update the parameters of the degenerate model. S4. Using the updated degradation model, predict the battery capacity for the next m cycles from the initial prediction cycle. Predicted battery capacity The predicted capacity is compared with the preset failure threshold FT. If the predicted capacity is higher than the failure threshold FT, the value of the predicted future cycle number m is increased one by one. The comparison process in step S4 is repeated until the predicted capacity is lower than or equal to the failure threshold, and the time point corresponding to the current predicted capacity is taken as the predicted end point of battery life. The remaining battery life is obtained by calculating the number of cycles from the start point of the battery capacity prediction stage to the predicted end point of battery life. S5. Repeat steps S2 to S4 to obtain multiple predicted battery remaining lifetime (RUL) values based on the predicted trajectories of all particles, and generate the probability density function of the remaining lifetime.
2. The method for predicting the remaining life of lithium-ion batteries based on GM-PFF according to claim 1, characterized in that, The implementation of initializing the model parameters of the gray model as the degradation model in step S1 includes: setting the total number of particles in the particle flow filter, the variance of measurement noise and observation noise; and setting the sliding window length t of the gray model GM(1,1).
3. The method for predicting the remaining life of lithium-ion batteries based on GM-PFF according to claim 2, characterized in that, The sliding window length t ranges from 10 to 20 cycles.
4. The method for predicting the remaining life of lithium-ion batteries based on GM-PFF according to claim 1, characterized in that, The implementation of step S2, which uses a grey model to predict the battery capacity value for the current cycle, specifically includes: The generated sequence is obtained by accumulating the historical capacity decay data sequence within the sliding window of the gray model. A whitening differential equation is constructed based on the generated sequence, and the development coefficient of the whitening differential equation is solved using the least squares method. and internal generation control of grayscale b; Solving parameters The predicted battery capacity for the current period i is obtained by restoring the prediction using the time response function. .
5. The method for predicting the remaining life of lithium-ion batteries based on GM-PFF according to claim 1, characterized in that, In step S3, the particle flow filtering algorithm uses the extended Daum-Huang filtering algorithm.
6. The method for predicting the remaining life of a lithium-ion battery based on GM-PFF according to claim 1, characterized in that, In step S4, the preset failure threshold FT is set to a value range of 65% to 85% of the rated capacity of the lithium-ion battery.
7. The method for predicting the remaining life of a lithium-ion battery based on GM-PFF according to claim 1, characterized in that, The formula for calculating the remaining battery life in step S4 is: RUL=m-ST-k, where RUL is the remaining battery life, m is the predicted number of cycles, ST is the starting predicted cycle point of battery capacity, and k is the number of cycles of the fitted historical capacity decay data sequence.
8. The method for predicting the remaining life of lithium-ion batteries based on GM-PFF according to claim 1, characterized in that, In step S5, the prediction stage of lithium-ion battery life is divided into three stages: early, middle and late. The remaining lifespan is predicted based on the training data of each stage.
9. The method for predicting the remaining life of a lithium-ion battery based on GM-PFF according to claim 1, characterized in that, It also includes step S6: calculating the performance evaluation index of the battery remaining life prediction result, the performance evaluation index including at least one of root mean square error RMSE, absolute error AE and accuracy index PI.
10. A lithium-ion battery remaining life prediction system, employing the lithium-ion battery remaining life prediction method based on GM-PFF as described in any one of claims 1 to 9, characterized in that the system... include: The data acquisition module is used to acquire historical capacity decay data sequences of lithium-ion batteries; The initialization module is used to fit the first k periods of the historical capacity decay data sequence using the least squares method to obtain the initial parameters of the degradation model; and to initialize the model parameters of the gray model, which serves as the degradation model. The grey prediction module uses the (k+1)th cycle as the starting point for the battery capacity prediction stage. It uses a grey model to predict the battery capacity for the current prediction cycle i, and then uses this predicted battery capacity as the observation value of the particle flow filter in the current prediction cycle. ; The particle flow filtering update module is used to calculate the particle flow based on the observations using the particle flow filtering algorithm, so that all particles flow from the prior probability distribution to the posterior probability distribution to update the parameters of the degenerate model. The lifetime prediction module is used to predict the battery capacity m cycles ahead of the initial prediction cycle using an updated degradation model. Predicted battery capacity The predicted capacity is compared with the preset failure threshold FT. If the predicted capacity is higher than the failure threshold FT, the value of the predicted future cycle number m is increased one by one. The battery predicted capacity calculation and comparison process is repeated until the predicted capacity is lower than or equal to the failure threshold, and the time point corresponding to the current predicted capacity is taken as the predicted battery life end point. The remaining battery life is obtained by calculating the number of cycles from the start of the battery capacity prediction stage to the predicted battery life end point. The output module is used to summarize the predicted values of the remaining battery life based on the predicted trajectories of all particles, and generate the probability density function of the remaining life to characterize the range of uncertainty in the prediction.