A method for predicting the remaining life of lithium-ion batteries based on improved particle filtering

Abstract

The present invention discloses a method for predicting the remaining life of a lithium-ion battery based on an improved particle filter, belonging to the field of lithium-ion battery management systems. The present invention proposes a new particle filtering algorithm. By setting two particle weight thresholds, p1 and p2, particles with a weight greater than p1 are copied, particles with a weight less than p2 are eliminated, and the remaining particles are retained. This avoids repeated calculation of particles with small weights and, to a certain extent, preserves particle diversity and avoids particle degradation. The new particle filtering algorithm is used to determine the optimal parameters of a double-exponential empirical prediction model to predict the future capacity decay trend of lithium-ion batteries, thereby improving prediction accuracy and reliability. Furthermore, there is no need to statistically calculate the cumulative weight values ​​of similar or identical results, thus greatly reducing the amount of calculation.

Description

Technical Field

[0001] The invention relates to a method for predicting the remaining service life of a lithium-ion battery based on improved particle filtering, and belongs to the field of lithium-ion battery management systems. Background Art

[0002] With increasing concerns about fuel consumption and carbon emissions, low-emission, energy-efficient electric vehicles and microgrids have become a trend in energy transformation and supply. Lithium-ion batteries, with their low self-discharge rate and high energy density, are a prime candidate for chemical energy storage. However, lithium-ion batteries can experience material aging and capacity decay during the charge and discharge cycles, leading to performance degradation and even accidents. Therefore, it is necessary to research battery remaining useful life (RUL) prediction technology so that appropriate measures can be taken based on the predicted RUL to minimize performance degradation and accidents.

[0003] Research on predicting the remaining life of lithium-ion batteries has found that the estimation of the state of health (SOH) of lithium-ion batteries is an indispensable and important performance indicator in energy storage systems. Accurate SOH estimation can effectively reflect the health of lithium-ion batteries. SOH can usually be simply understood as the battery's current maximum capacity. Battery capacity, as a direct indicator of battery SOH, is used in many methods. Research has shown that the double exponential empirical model can better fit the degradation data of lithium-ion battery capacity. Its expression is as follows:

[0004] Q(k)=a*exp(b*k)+c*exp(d*k) (1)

[0005] Where a, b, c, and d are model parameters, a and c are internal impedances, b and d are degradation rates, k is the number of cycles, and Q is the battery capacity.

[0006] Particle filtering algorithms offer improved adaptability for battery SOH estimation and prediction. However, traditional particle filtering algorithms suffer from particle degradation, whereby correct particles are discarded and particle diversity is reduced, which limits prediction accuracy. Therefore, many researchers have explored various strategies to address these issues, such as improving particle filtering through resampling techniques. Commonly used resampling methods include random resampling and polynomial resampling. Random resampling is to randomly generate particles after discarding particles with small weights. This can ensure the diversity of particles as much as possible, but it will bring a lot of repeated calculations, mainly because the weights of randomly generated particles cannot be guaranteed, so it will still lead to the problem of low subsequent prediction accuracy; the difference between polynomial resampling and random resampling is that it will continuously record and copy the cumulative weight values ​​of similar or identical results to obtain the optimal development results. Theoretically, polynomial resampling balances the problems of particle diversity and accuracy to a certain extent, but its computational complexity is much higher than random resampling, so it has higher requirements for hardware equipment and computing power. It is usually used in laboratory research and is not applicable to actual production processes. Moreover, because the particles with similar or identical results are continuously recorded and copied during the polynomial resampling process, the particles with the largest weights will gradually increase, and eventually only a few particles with the largest weights will be left, losing particle diversity, which also affects the accuracy of subsequent prediction results. Summary of the Invention

[0007] In order to provide a battery remaining life prediction method applicable to actual production processes, the present invention provides a new particle filtering method, which realizes the prediction of the remaining life of lithium-ion batteries based on the proposed particle filtering method.

[0008] A method for predicting the remaining life of a lithium-ion battery based on an improved particle filter, the method comprising:

[0009] Step 1: Define the capacity Q of the lithium-ion battery to represent the remaining life of the battery. The normalized initial capacity is 1. When the capacity is less than the preset capacity threshold, the battery is considered to have reached the end of its service life.

[0010] Step 2: Fit the collected battery capacity degradation data using a double exponential empirical prediction model to determine the initial values ​​a0, b0, c0, and d0 of the four parameters a, b, c, and d of the double exponential empirical prediction model;

[0011] Step 3: Establish particle set X for improved particle filter algorithm m , filter state X pf , battery capacity observation Z, battery capacity Z predicted by the filter m , the battery capacity prediction value Z after filtering pf , particle importance weight W; among them, particle set Xm There are M particles in it, m=1,2,…,M; set the number of cycles k of the particle filter algorithm to end the cycle when it reaches N;

[0012] Add process noise to the initial parameters a0, b0, c0, and d0 to initialize the particle set state;

[0013] Step 4: Set the number of cycles of the particle filter algorithm to k = 2, perform particle initialization sampling at the cycle number k, substitute the particle sampling values ​​into the double exponential empirical prediction model, calculate the battery capacity prediction values ​​corresponding to M particles, calculate the importance weights of the particles based on the prediction values, and normalize the weights;

[0014] Step 5: Set thresholds p1 and p2 to resample the particles, p1>p2, copy the particles with weights greater than p1, eliminate the particles with weights less than p2, and retain the remaining particles; after copying, eliminating and retaining the particles accordingly, update the particle filter X pf , use the updated state to calculate the battery capacity prediction value Z after filtering pf ;

[0015] Step 6: Set k = k + 1, return to step 4, until k = N, and complete the particle filter X pf and the battery capacity prediction value Z after filtering pf Updates;

[0016] Step 7: Set the prediction start cycle S = N-FC, where FC represents the number of prediction cycles and N represents the total number of cycles; according to the updated particle filter X obtained in step 6 pf Determine the values ​​of the four parameters a, b, c, and d of the double exponential empirical prediction model, and use the double exponential empirical prediction model to predict the capacity Z of the lithium-ion battery within the cycle period. pf , predicting the remaining life of lithium-ion batteries based on their capacity.

[0017] Optionally, the double exponential empirical prediction model is:

[0018] Q(k)=a*exp(b*k)+c*exp(d*k) (1)

[0019] Among them, parameters a and c represent the internal impedance of the battery, b and d represent the degradation rate of the battery; k is the number of cycles, and Q is the battery capacity.

[0020] Optionally, the state of the double exponential empirical prediction model:

[0021] X(k)=[a(k) b(k) c(k) d(k)] (3)

[0022] Its state equation is:

[0023]

[0024] Among them, w a (k), w b (k), w(k), w d (k) represents the process noise corresponding to the four parameters; σ a , σ b , σ c , σ d They represent the corresponding noise variance respectively;

[0025] The observation equation is:

[0026] Q(k)=a(k)*exp(b(k)*k+c(k)*exp(d(k)*k)+v(k) (5)

[0027] The measurement noise v(k) has a mean of 0 and a variance of σ v Gaussian white noise, that is, v(k)~N(0,σ v ).

[0028] Optionally, initializing the particle set state in step 3 includes:

[0029] Initialize the prediction model state according to the initial values ​​a0, b0, c0, and d0 of the four parameters a, b, c, and d:

[0030] X0=[a0 b0 c0 d0] (6)

[0031] Then the particle set is initialized as:

[0032]

[0033] Among them, i is the particle number, X0 is the initial state of the prediction model, D is the process noise covariance, and randn is a 4-dimensional random number vector.

[0034] Optionally, the importance weight of the particles in step 4 is calculated using the Gaussian distribution principle:

[0035]

[0036] Where k is the number of cycles, i is the particle number, R is the observation noise covariance, R = 0.001, Z(k) is the capacity observation value of the lithium-ion battery at the kth cycle, Z m (i,k) is the predicted capacity value of the lithium-ion battery calculated by the i-th particle at the k-th cycle time, and W(i,k) represents the weight of the i-th particle at the k-th cycle time.

[0037] Optionally, resampling the particles in step 5 includes:

[0038]

[0039] Among them, X m (i) represents the state of the i-th particle, W(i) represents the weight of the i-th particle, p1 and p2 are two set thresholds, A represents the replication of the particle, and B represents the elimination of the particle.

[0040] Optionally, after the particles are copied, eliminated and retained accordingly in step 5, the particle filter X is updated. pf ,include:

[0041] Take the average of M particles and update the particle filter X pf :

[0042]

[0043] Among them, X pf (k) represents the state of the particle filter in the kth cycle, X m (i,k) represents the state of the i-th particle in the k-th cycle.

[0044] Optionally, in step 5, the updated state is used to calculate the battery capacity prediction value Z after filtering by the filter. pf ,include:

[0045]

[0046] Among them, X pf (k) represents the state of the particle filter in the kth cycle, Z pf (k) and Q(k) represent the predicted values ​​of the lithium-ion battery capacity at the kth cycle, and a(k), b(k), c(k), and d(k) represent the four parameter values ​​of the double exponential empirical model at the kth cycle.

[0047] Optionally, in step seven, the capacity Z of the lithium-ion battery in the cycle is predicted. f The calculation method is as follows:

[0048]

[0049] Among them, X f (k) represents the predicted state of the particle filter in the kth period, Z f (k) and Q(k) represent the predicted values ​​of the lithium-ion battery capacity at the kth cycle, and a(k), b(k), c(k), and d(k) represent the four parameters of the double exponential empirical model at the kth cycle.

[0050] The beneficial effects of the present invention are:

[0051] By proposing an improved particle filter algorithm, setting two thresholds p1 and p2, particles with weights greater than p1 are retained and copied, particles with weights less than p2 are eliminated, and particles with weights between p1 and p2 are retained. This not only avoids repeated calculations of particles with small weights, but also retains particle diversity to a certain extent, avoids particle degradation, and combines a fusion prediction model based on a double exponential empirical model and an improved particle filter algorithm to improve the accuracy of prediction of the remaining life of lithium-ion batteries. Secondly, the traditional particle filter algorithm has a particle degradation problem, which leads to certain limitations in measurement accuracy. This application integrates a double exponential empirical model and an improved particle filter algorithm, and proposes a new resampling method that effectively reduces the particle degradation phenomenon. After improving the particle filter, the final parameters of the double exponential empirical model are obtained, and the future capacity attenuation trend of the lithium-ion battery is predicted, which improves the prediction accuracy and reliability. In addition, there is no need to statistically calculate the weight cumulative value of similar or identical results, so the amount of calculation is greatly reduced. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0053] Figure 1 This is a flowchart of a method for predicting the remaining life of a lithium-ion battery based on improved particle filtering disclosed in one embodiment of the present invention.

[0054] Figure 2 This is a simulation diagram of the online prediction results of lithium-ion battery capacity decay using the method of the present application disclosed in one embodiment of the present invention.

[0055] Figure 3 This is a simulation diagram comparing the mean absolute errors of online prediction results of lithium-ion battery capacity decay using the method of the present application and two existing methods disclosed in one embodiment of the present invention.

[0056] Figure 4 This is a simulation diagram comparing the root mean square error of the online prediction results of lithium-ion battery capacity decay using the method of the present application and two existing methods disclosed in one embodiment of the present invention. DETAILED DESCRIPTION

[0057] To make the objectives, technical solutions and advantages of the present invention more clear, the embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0058] Example 1:

[0059] This embodiment provides a method for predicting the remaining life of a lithium-ion battery based on an improved particle filter. Figure 1 , the method comprising:

[0060] Step 1: Define the capacity Q of the lithium-ion battery to represent the remaining life of the battery. The normalized initial capacity is 1. When the capacity is less than the preset capacity threshold, the battery is considered to have reached the end of its service life.

[0061] Step 2: Fit the collected battery capacity degradation data using a double exponential empirical prediction model to determine the initial values ​​a0, b0, c0, and d0 of the four parameters a, b, c, and d of the double exponential empirical prediction model;

[0062] Step 3: Establish particle set X for improved particle filter algorithm m , filter state X pf , battery capacity observation Z, battery capacity Z predicted by the filter m , the battery capacity prediction value Z after filtering pf , particle importance weight W; among them, particle set X m There are M particles in it, m=1,2,…,M; set the number of cycles k of the particle filter algorithm to end the cycle when it reaches N;

[0063] Add process noise to the initial parameters a0, b0, c0, and d0 to initialize the particle set state;

[0064] Step 4: Set the number of cycles of the particle filter algorithm to k = 2, perform particle initialization sampling at the cycle number k, substitute the particle sampling values ​​into the double exponential empirical prediction model, calculate the battery capacity prediction values ​​corresponding to M particles, calculate the importance weights of the particles based on the prediction values, and normalize the weights;

[0065] Step 5: Set thresholds p1 and p2 to resample the particles, p1>p2, copy the particles with weights greater than p1, eliminate the particles with weights less than p2, and retain the remaining particles; after copying, eliminating and retaining the particles accordingly, update the particle filter X pf , use the updated state to calculate the battery capacity prediction value Z after filtering pf ;

[0066] Step 6: Set k = k + 1, return to step 4, until k = N, and complete the particle filter X pf and the battery capacity prediction value Z after filtering pf Updates;

[0067] Step 7: Set the prediction start cycle S = N-FC, where FC represents the number of prediction cycles and N represents the total number of cycles; according to the updated particle filter X obtained in step 6 pf Determine the values ​​of the four parameters a, b, c, and d of the double exponential empirical prediction model, and use the double exponential empirical prediction model to predict the capacity Z of the lithium-ion battery within the cycle period. pf , predicting the remaining life of lithium-ion batteries based on their capacity.

[0068] Example 2

[0069] This embodiment provides a method for predicting the remaining life of a lithium-ion battery based on an improved particle filter. The method combines a double exponential empirical model with an improved particle filter method to predict the degradation trend of the lithium-ion battery capacity in the future based on the lithium-ion battery capacity in the past period of time, thereby predicting the remaining life of the lithium-ion battery.

[0070] In the method of this embodiment, a double exponential empirical model is first used to fit the capacity degradation data of three batteries from the University of Maryland to obtain the four initial parameters a0, b0, c0, and d0 of the model; for a detailed introduction to the double exponential empirical model, please refer to "Zhang Ning, Xu Aidong, Wang Kai, et al. Research on the remaining life prediction method of lithium-ion batteries based on particle filter algorithm [J]. High Technology Communications, 2017, 27(08): 699-707."

[0071] According to the four initial parameters of the double exponential model and the process noise, M particles are initialized;

[0072] The particle filter method is used to sample particles, calculate the difference between the predicted value and the observed value, and calculate the importance weight of the particles in combination with the Gaussian distribution. The weight is normalized and then the particles are resampled.

[0073] Introducing the new resampling method proposed in this application:

[0074] Two thresholds, p1 and p2, are set. Particles with weights greater than p1 are replicated, particles with weights less than p2 are eliminated, and the remaining particles are retained. The M particles are averaged to obtain the final parameters a, b, c, and d of the biexponential model. Thresholds p1 and p2 are specified by a technician, and p1 is greater than p2. In practical applications, thresholds p1 and p2 can be set by a technician. The setting process can determine the optimal value through multiple experiments, that is, by setting different combinations of thresholds p1 and p2 and comparing the accuracy of the prediction results to determine the optimal value. Alternatively, the setting can be based on experience, and this application does not impose any restrictions on this.

[0075] According to the final parameters a, b, c, d, and substituting them into the double exponential model, a prediction model for lithium-ion battery capacity decay can be established:

[0076] Q(k)=a*exp(b*k)+c*exp(d*k) (1)

[0077] Where a, b, c, and d are model parameters, a and c are internal impedances, b and d are degradation rates, k is the number of cycles, and Q is the battery capacity.

[0078] The prediction curve of lithium-ion battery capacity decay is obtained based on the final parameters determined by the improved particle filter algorithm and the expression of the double exponential empirical model.

[0079] See also Figure 1 The method for predicting the remaining life of a lithium-ion battery based on improved particle filtering includes:

[0080] Step 1: Define the capacity Q of the lithium-ion battery to represent the remaining life of the battery. The normalized initial capacity is 1. When the capacity is less than 0.7, the battery is considered to have reached the end of its service life. The number of cycles N = 200, the total number of particles M = 200, and the prediction period FC = 20.

[0081] Step 2: Define the four initial parameters of the double exponential empirical model. Use the original capacity degradation data measured in the laboratory environment of the University of Maryland to perform curve fitting on three sets of data, and obtain the initial parameters a0 = -0.0000083499, b0 = 0.055237, c0 = 0.90097, and d0 = -0.00088543.

[0082] Table 1 Basic parameters of the model

[0083] describe parameter value Number of cycles N 200 Total number of particles M 200 Prediction start time Start 180 Predicted number of cycles Future_Cycle 20 Empirical model initial parameters 1 a0 -0.0000083499 Empirical model initial parameters 2 b0 0.055237 Empirical model initial parameters 3 c0 0.90097 Empirical model initial parameters 4 d0 -0.00088543 Prediction model state initialization X0 [a0,b0,c0,d0]

[0084] Step 3: Establish particle set X for improved particle filter algorithm m , filter state X pf , battery capacity observation Z, battery capacity Z predicted by the filter m , the battery capacity prediction value Z after filtering pf , particle importance weight W. Add process noise to the initial parameters a0, b0, c0, d0 to initialize the particle set state.

[0085] Table 2 Improved particle filter model parameters

[0086]

[0087]

[0088] Step 4: Set k = 2, perform particle initialization sampling at cycle number k, substitute the particle sampling values ​​into the double exponential empirical model, calculate the battery capacity prediction values ​​corresponding to M particles, and calculate the particle importance weights based on the prediction values ​​and the Gaussian distribution. Normalize the weights.

[0089] Step 5: Use the improved resampling method to resample the particles, set two thresholds p1 and p2, copy the particles with weights greater than p1, eliminate the particles with weights less than p2, and retain the remaining particles. Take the average value of M particles and update the particle filter X pf , use the updated state to calculate the battery capacity prediction value Z after filtering pf .

[0090] Step 6: Set k = k + 1, return to step 4, until k = N, and complete the particle filter X pf and the battery capacity prediction value Z after filtering pf Updates.

[0091] Step 7: Let the cycle period at the start of the prediction S = N-FC, such as N = 200, FC = 20, S = 180, (FC represents the number of predicted cycles, N represents the total number of cycles) then the predicted lithium-ion battery capacity Z from the 180th cycle to the 200th cycle is f , according to the above obtained X pf Substituting into the double exponential empirical model, we get Z f .

[0092] Step 8: Output particle filter X based on the result of step 6 pf , characterizing the changes in parameters a, b, c, and d in the double exponential empirical model with the cycle period. Based on the results of step 7, a predicted value of the lithium-ion battery capacity based on the double exponential empirical model and the improved particle filter method is output, and the remaining life of the lithium-ion battery is estimated.

[0093] In order to evaluate the prediction performance of the method of the present application, this embodiment compares the estimation results with those of two existing methods to judge the pros and cons of the method. The two existing methods are the random resampling particle filter method and the polynomial resampling particle filter method.

[0094] The comparison of battery remaining capacity prediction errors of different prediction methods is shown in Table 3:

[0095] Table 3 Comparison of battery capacity prediction errors under different prediction methods

[0096] Evaluation indicators This method Random resampling Polynomial resampling Mean Absolute Error (MAE) 0.0096 0.0115 0.0122 Root mean square error (RMSE) 0.0109 0.0129 0.0137 Maximum error (ME) 0.0435 0.0696 0.0771

[0097] To verify the accuracy and effectiveness of the method proposed in this application, the following simulation experiments were conducted using the method of this application and the existing random resampling particle filter and polynomial resampling particle filter methods. The accompanying figures show the battery capacity prediction and error of each method.

[0098] During the experiment, the simulation was conducted using raw data on battery capacity degradation measured in a laboratory environment at the University of Maryland. The data sample was the capacity degradation of an A12 battery over 200 cycles, with the first 180 cycles serving as training samples and the last 20 cycles serving as prediction validation samples.

[0099] Please refer to Figure 2 , where the broken line represents the actual value of the battery capacity, and the five-pointed star represents the prediction result of this method. Figure 2 It can be seen that the predicted value of the method of the present application is very close to the actual value of the battery capacity, which shows that the prediction result of the method is good and the error is small.

[0100] The three methods of this method, random resampling, and polynomial resampling were simulated 100 times, and the average absolute error between the predicted value and the true value of each simulation was recorded. The results are as follows Figure 3 As shown. The five-pointed star line represents this method, the ordinary line represents random resampling, and the circle line represents polynomial resampling. Figure 3 It can be seen that the average absolute error between the predicted value and the true value of the method of the present application is smaller overall, indicating that the average absolute error of the present method is smaller than that of the other two methods.

[0101] The three methods of this method, random resampling, and polynomial resampling were simulated 100 times, and the root mean square error between the predicted value and the true value of each simulation was recorded. The results are as follows Figure 4 The five-pointed star line represents this method, the ordinary line represents random resampling, and the circle line represents polynomial resampling, indicating that this method has a smaller root mean square error than the other two methods.

[0102] Comprehensive Table 3, Figure 2 、 Figure 3 、 Figure 4 , this method has a good effect on predicting the remaining life of lithium-ion batteries. Compared with random resampling and polynomial resampling, the mean absolute error (MAE), root mean square error (RMSE), and maximum error (ME) of this method are smaller, and the prediction effect is better. Compared with random resampling, the improvements are 19.79%, 18.34%, and 60%, respectively; compared with polynomial resampling, the improvements are 25%, 25.68%, and 77.24%, respectively. It can be seen that in the process of battery capacity attenuation prediction, the method based on the double exponential empirical model and improved particle filtering proposed in this application can further improve the prediction accuracy.

[0103] Some steps in the embodiments of the present invention may be implemented using software, and the corresponding software program may be stored in a readable storage medium, such as a CD or a hard disk.

[0104] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for predicting the remaining life of a lithium-ion battery based on an improved particle filter, characterized in that: The method comprises: Step 1: Define the capacity Q of the lithium-ion battery to represent the remaining life of the battery. The normalized initial capacity is 1. When the capacity is less than the preset capacity threshold, the battery is considered to have reached the end of its service life. Step 2: Fit the collected battery capacity degradation data using a double exponential empirical prediction model to determine the initial values ​​a0, b0, c0, and d0 of the four parameters a, b, c, and d of the double exponential empirical prediction model; Step 3: Establish particle set X for improved particle filter algorithm m , filter state X pf , battery capacity observation Z, battery capacity Z predicted by the filter m , the battery capacity prediction value Z after filtering pf , particle importance weight W; among them, particle set X m There are M particles in it, m=1,2,…,M; set the number of cycles k of the particle filter algorithm to end the cycle when it reaches N; Add process noise to the initial parameters a0, b0, c0, and d0 to initialize the particle set state; Step 4: Set the number of cycles of the particle filter algorithm to k = 2, perform particle initialization sampling at the cycle number k, substitute the particle sampling values ​​into the double exponential empirical prediction model, calculate the battery capacity prediction values ​​corresponding to M particles, calculate the importance weights of the particles based on the prediction values, and normalize the weights; Step 5: Set thresholds p1 and p2 to resample the particles, p1>p2, copy the particles with weights greater than p1, eliminate the particles with weights less than p2, and retain the remaining particles; after copying, eliminating and retaining the particles accordingly, update the particle filter X pf , use the updated state to calculate the battery capacity prediction value Z after filtering pf ; Step 6: Set k = k + 1, return to step 4, until k = N, and complete the particle filter X pf and the battery capacity prediction value Z after filtering pf Updates; Step 7: Set the prediction start cycle S = N-FC, where FC represents the number of prediction cycles and N represents the total number of cycles; according to the updated particle filter X obtained in step 6 pf Determine the values ​​of the four parameters a, b, c, and d of the double exponential empirical prediction model, and use the double exponential empirical prediction model to predict the capacity Z of the lithium-ion battery within the cycle period. pf , predicting the remaining life of lithium-ion batteries based on their capacity.

2. The method according to claim 1, characterized in that The double exponential empirical prediction model is: Q(k)=a*exp(b*k)+c*exp(d*k) (1) Among them, parameters a and c represent the internal impedance of the battery, b and d represent the degradation rate of the battery; k is the number of cycles, and Q is the battery capacity.

3. The method according to claim 2, characterized in that The double exponential empirical prediction model states: X(k)=[a(k) b(k) c(k) d(k)] (3) Its state equation is: Among them, w a (k), w b (k), w c (k), w d (k) represents the process noise corresponding to the four parameters; σ a , σ b , σ c , σ d They represent the corresponding noise variance respectively; The observation equation is: Q(k)=a(k)*exp(b(k)*k+c(k)*exp(d(k)*k)+v(k) (5) The measurement noise v(k) has a mean of 0 and a variance of σ v Gaussian white noise, that is, v(k)~N(0,σ v ).

4. The method according to claim 3, characterized in that The step 3 of initializing the particle set state includes: Initialize the prediction model state according to the initial values ​​a0, b0, c0, and d0 of the four parameters a, b, c, and d: X0=[a0 b0 c0 d0] (6) Then the particle set is initialized as: Among them, i is the particle number, X0 is the initial state of the prediction model, D is the process noise covariance, and randn is a 4-dimensional random number vector.

5. The method according to claim 4, characterized in that The importance weight of the particles in step 4 is calculated using the Gaussian distribution principle: Where k is the number of cycles, i is the particle number, R is the observation noise covariance, R = 0.001, Z(k) is the capacity observation value of the lithium-ion battery at the kth cycle, Z m (i,k) is the predicted capacity value of the lithium-ion battery calculated by the i-th particle at the k-th cycle time, and W(i,k) represents the weight of the i-th particle at the k-th cycle time.

6. The method according to claim 5, characterized in that The step 5 of resampling the particles includes: Among them, X m (i) represents the state of the i-th particle, W(i) represents the weight of the i-th particle, p1 and p2 are two set thresholds, A represents the replication of the particle, and B represents the elimination of the particle.

7. The method according to claim 6, characterized in that After the particles are copied, eliminated and retained in step 5, the particle filter X is updated. pf ,include: Take the average of M particles and update the particle filter X pf : Among them, X pf (k) represents the state of the particle filter in the kth cycle, X m (i,k) represents the state of the i-th particle in the k-th cycle.

8. The method according to claim 7, characterized in that In step 5, the updated state is used to calculate the battery capacity prediction value Z after filtering by the filter. pf ,include: Among them, X pf (k) represents the state of the particle filter in the kth cycle, Z pf (k) and Q(k) represent the predicted values ​​of the lithium-ion battery capacity at the kth cycle, and a(k), b(k), c(k), and d(k) represent the four parameter values ​​of the double exponential empirical model at the kth cycle.

9. The method according to claim 8, characterized in that The step 7 predicts the capacity Z of the lithium-ion battery in the cycle f The calculation method is as follows: Among them, X f (k) represents the predicted state of the particle filter in the kth period, Z f (k) and Q(k) represent the predicted values ​​of the lithium-ion battery capacity at the kth cycle, and a(k), b(k), c(k), and d(k) represent the four parameters of the double exponential empirical model at the kth cycle.

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