A Lithium-ion Remaining Lifetime Prediction Method Based on an Improved Particle Filter Model

Abstract

This invention relates to a lithium-ion battery remaining life prediction method based on an improved particle filter model, belonging to the field of battery technology. Addressing the issues of random current variations and incomplete charge / discharge during lithium-ion battery use due to random load, resulting in significant differences in battery degradation rates and insufficient battery degradation data, this invention proposes a method for estimating the health status of lithium-ion batteries and constructing a neural network model for remaining life prediction. Specifically, the method involves: extracting health factors from historical data; obtaining a complete sequence of health factors through Bayesian-optimized multi-kernel RVM mapping; establishing a sequence-to-sequence LSTM model to estimate the true capacity of the lithium-ion battery; establishing a bi-exponential model for lithium-ion battery degradation based on IPSO-PF-LSTM; and predicting the remaining life. Optimizing multiple algorithms together better leverages the advantages of the bi-exponential model, thereby improving the accuracy of life prediction.

Description

Technical Field

[0001] This invention belongs to the field of battery technology and relates to a method for predicting the remaining lifetime of lithium-ion batteries based on an improved particle filter model. Background Technology

[0002] After repeated charge-discharge cycles, the performance of a battery will be irreversibly affected. Problems such as battery leakage, insulation damage, and partial short circuits can all lead to catastrophic accidents. Therefore, accurate estimation of battery status information is essential to avoid safety hazards caused by lithium-ion battery aging and performance degradation.

[0003] The health status and remaining lifespan of a battery are closely related to its historical usage. In practical applications, batteries are often not under standard charge and discharge conditions. Random discharge in reality can lead to large differences in battery degradation rates and insufficient battery degradation data. In this case, we should consider extracting an optimized complete health factor sequence and using sequence-to-sequence LSTM and an improved particle filter model to estimate the health status and predict the remaining lifespan. Summary of the Invention

[0004] In view of this, the purpose of this invention is to provide a lithium-ion battery remaining lifetime prediction method based on an improved particle filter model. Addressing the issues of significant differences in battery degradation rates and insufficient battery degradation data, a multi-kernel RVM is used for health factor mapping, combined with a sequence-to-sequence LSTM model to obtain capacity estimates for multiple future cycles.

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

[0006] A lithium-ion battery remaining lifetime prediction method based on an improved particle filter model includes the following steps:

[0007] S1: Extract and optimize health factors: Extract health factors from lithium-ion battery charge and discharge data curves, and optimize the parameters of some health factors to obtain the health factors with the highest correlation to capacity decay.

[0008] S2: Health factor mapping of multi-core RVM: Using the correlation vector machine (RVM) optimized by Bayes as a tool, the mapping relationship between charging health factors and discharging health factors is learned to obtain a complete health factor sequence;

[0009] S3: Sequence-to-sequence LSTM model: Construct sequence input based on the complete battery health factors extracted in S2, and train the LSTM neural network using battery capacity data as labels;

[0010] S4: Establish a dual-exponential model for lithium-ion battery degradation based on IPSO-PF: The parameters of the dual-exponential model are continuously optimized using an improved particle swarm optimization algorithm and particle filtering algorithm to fit the battery capacity degradation trend.

[0011] S5: Lifetime Prediction: Train the model built in S4 and perform lifetime prediction.

[0012] Optionally, S1 specifically involves selecting the time difference HF1 of the equal voltage interval during constant current charging, the time difference HF2 of the equal current interval during constant voltage charging, and the temperature difference HF3 of the equal voltage interval during constant current charging as health factors, based on the charging stage curve. The specific calculation formula is as follows:

[0013]

[0014] in For constant current charging, the voltage reaches V. upper absolute time, For constant current charging, the voltage reaches V. lower Absolute time; For constant voltage charging, the voltage reaches I. upper absolute time, For constant voltage charging, the voltage reaches I. lower Absolute time; For constant current charging, the voltage reaches V. upper temperature, For constant current charging, the voltage reaches V. lower Temperature;

[0015] Based on the battery's random discharge curve, the integral value of random discharge current HF4, the sample entropy of random discharge voltage HF5, and the standard deviation of random discharge temperature HF6 are extracted as health factors. The specific calculation formula is as follows:

[0016]

[0017] SampEn is an estimate of the conditional probability that a window of length m will maintain similarity and match the next electrical event within a tolerance r. The window of length m is a subsequence of a time series of length Nc; T K is the Kth temperature value of the battery in a random discharge cycle; u is the average temperature of the random discharge cycle; and n is the number of temperatures measured.

[0018] Six health factors were extracted from the charge-discharge curves of lithium-ion batteries under random discharge conditions. Then, a particle swarm optimization algorithm was used to optimize these extracted health factors during the charging process. Specifically, the V of HF1 was optimized. upper V lower HF2's I upper I lowerAnd HF3's V upper V lower As parameters to be optimized, the Pearson correlation coefficients between each health factor and capacity are used as the fitness function of the PSO, i.e.:

[0019] F(x)=ρ(HF,capacity) (3)

[0020] Where F(x) is the particle swarm fitness function, HF is the corresponding health factor sequence, capacity is the capacity sequence, and ρ is the Pearson correlation coefficient function.

[0021] Optionally, S2 specifically involves: taking the charging health factors HF1, HF2, and HF3 from incomplete charge-discharge cycles as input, and the discharging health factors HF4, HF5, and HF6 as outputs; for the dataset... x i ∈R,t i ∈R where x i For the input of the sample, t i Let R represent the target output value, and D represent the set of real numbers. The relationship between the model input and output is as follows:

[0022] t i =y(x i ,w i )+ε i (4)

[0023] Where K(x,x) i The kernel function is represented as w = (w1, w2, K, w). D ) T Here, w0 is the weight vector corresponding to the kernel function, and w0 is the bias parameter.

[0024] To address the different degradation trends of health factors, linear kernel functions, polynomial kernel functions, Gaussian kernel functions, and Sigmoid kernel functions are selected and linearly combined. The weight coefficients of the four combined kernel functions need to be manually determined.

[0025] The optimization of the RVM model using the Bayesian optimization algorithm consists of two steps: Gaussian process regression and sampling using a sampling function. The posterior distribution of the objective function is updated by continuously adding sampling points until it matches the true distribution. First, an initial hyperparameter set x is selected in the domain space χ. Then, the probability distribution of f(x) is calculated based on the properties of the sampling set and the Gaussian distribution, and the position of the next sampling point is obtained using the sampling function. Finally, f(x) is calculated and the objective function f is updated to reach the required number of iterations or meet the convergence condition.

[0026] The specific implementation process of the Bayesian optimized multi-kernel RVM algorithm is as follows: preparation of training set and prediction set; determination of the hyperparameters to be optimized and their range; construction and training of Bayesian optimized RVM model.

[0027] Optionally, S3 specifically includes:

[0028] S32: Constructing the dataset: Based on the multi-core RVM framework in S2, obtain the complete health factor sequence, normalize it, construct the input data, extract the capacity data, and calculate the battery health state (SOH), which is the label corresponding to the input; the constructed dataset is:

[0029]

[0030] Y = {Y1,Y2,Y3,…,Y} m} (6)

[0031] For the LSTM model, with a step size of 10, the capacity value {x} is obtained through the current 10 consecutive loops. 41 ,x 42 ,…,x 49 ,x 50 A single prediction outputs capacity estimates for the next 10 cycles. These 10 estimates are then used for the next prediction. This sequence-to-sequence LSTM method requires fewer iterations and has a smaller cumulative error; Y i Let be the SOH value in the i-th cycle; m be the cycle number.

[0032] S32: Offline training of the model: First, determine the parameters that need to be optimized for the LSTM algorithm: time step, number of hidden layer nodes, and number of training iterations; input the optimized parameters of particle swarm optimization into the LSTM model, initialize other parameters, divide the dataset obtained in ① into training set and test set, and then train the LSTM model.

[0033] S33: Online prediction: Extract the charging data of the current cycle and combine it with past data to construct the input, and input it into the trained model to obtain the SOH prediction value for multiple consecutive cycles.

[0034] Optionally, in step S4, a double-exponential model is used as an empirical model for lithium-ion batteries to fit the battery capacity degradation trend; the established model is as follows:

[0035]

[0036] Where k is the number of charge-discharge cycles, Q kLet a1, a2, a3, and a4 be the capacity of the battery in the kth cycle. a1, a2, a3, and a4 are the aging parameters to be identified in the double exponential model, which are related to the internal characteristics of the battery. Among them, a1 and a3 are related to the internal resistance of the battery in the current cycle, and a2 and a4 are related to the degradation rate of the battery.

[0037] Choose x r,k =[x 1,k x 2,k x 3,k x 4,k ] T The state variables of the battery capacity decay model in the k-th cycle are discretized, and the state equation and observation equation based on particle filtering are as follows:

[0038] Q k =a 1,k ·exp(a 2,k ·k)+a 3,k ·exp(a 4,k ·k) (8)

[0039]

[0040]

[0041] In the formula, x 1,k x 2,k x 3,k x 4,k The initial values ​​are the bi-exponential model parameters a1, a2, a3, a4; y k It is the output of the model, Q k For the capacity of lithium-ion batteries, γ k =[γ 1,k γ 2,k γ 3,k γ 4,k ] T For process noise, It measures noise;

[0042] To mitigate particle degradation and enable particles to better adapt to the battery aging trend under random discharge conditions, the IPSO-PF algorithm is used to predict capacity based on the established battery aging model.

[0043] The specific steps of the IPSO-PF algorithm are as follows:

[0044] ① Initialization

[0045] Let the current charge / discharge cycle number be k; when performing particle filtering, take k=0, based on the initial prior probability density p(x r,0 Extract n initial state particles

[0046] ② Importance Sampling

[0047] When k = 1, 2, ..., N, the prior PDF is selected as the state PDF, that is...

[0048]

[0049] New samples are drawn based on importance probability density. Then, an improved particle swarm optimization algorithm was used to process the particle set. The iterative optimization process involves the following steps:

[0050] Step 11: Set the maximum number of iterations T max The population size n is chosen to be consistent with the number of particles in particle filtering, and the particle range R and maximum velocity V are set. max Initial parameters include inertia weight ω, acceleration factors c1 and c2, etc.; the fitness function for particle swarm optimization is:

[0051]

[0052] Where K is the number of training set samples, and L is the step size of the sequence-to-sequence LSTM. This represents the LSTM's estimate of the future L capacities from the previous section;

[0053] Step 12: Set the iteration number t = 1, and set the initial position of the particle as the initialization parameter of the particle in particle filtering. Set the current position as the individual's historical best pBest, the best individual in the population as the population's historical best gBest, and calculate the fitness function value of each particle.

[0054] Step 13: In the current iteration loop, if the current fitness function value is better than the historical best value, then update the individual historical best value; if the current fitness function is better than the global historical best value, then update the population historical best value. At the end of one loop, update the velocity and position of the d-th dimension of each particle i, as shown below:

[0055]

[0056]

[0057] In the formula, c1 and c2 are learning factors, with a fixed value of 2.0; ω is the inertia weight, initialized to 0.9, and improved using a linear differential decreasing strategy, the algorithm of which is as follows:

[0058]

[0059]

[0060] Step 14: Determine if the maximum number of iterations or the set optimization limit has been reached. If so, the optimization is complete. Let the particles in PF... Otherwise, proceed to step 2;

[0061] ③ Particle weight update

[0062] The particle weight formula is reconstructed, and the weight judgment for multiple time ranges is performed using the first iteration result of LSTM sequence-to-sequence and combined with the aging model. The specific formula is as follows:

[0063]

[0064] in, It is the weight of the i-th particle. For the first iteration result of the sequence-to-sequence LSTM, y k The aging model output value takes noise into account, where R is the variance of the measured noise and N is the total number of charge-discharge cycles of the battery.

[0065] ④ Resampling

[0066] First, it is necessary to determine whether resampling is required in this iteration; let the number of effective particles be N. eff for:

[0067]

[0068] If N eff <N threshold For particles Perform random resampling to obtain a new particle set. Otherwise, resampling will not be performed;

[0069] ⑤ State estimation

[0070] By performing a weighted calculation on the particles in the particle set, the estimated value is obtained:

[0071]

[0072] ⑥ Battery RUL Prediction

[0073] Assuming the battery is currently in the k-th cycle, based on the state equation and observation equation of the particle filter, the capacity prediction for each particle in the current cycle for the next j cycles is calculated as follows:

[0074]

[0075] The prediction capacity for the next j iterations at the k-th iteration is:

[0076]

[0077] A posteriori PDF approximation of battery capacity:

[0078]

[0079] The predicted RUL value for the battery is calculated as follows:

[0080]

[0081] Optionally, in step S5, the test set data is input into the model established in step S4, and after obtaining the parameters of the double exponential model, the model is trained based on particle filtering and lifetime prediction is performed.

[0082] The beneficial effects of this invention are as follows: Addressing the problems of varying rates of battery degradation in the later stages due to random discharge current and the limitations of data-driven Remaining Life (RUL) prediction methods, this invention proposes an improved RUL prediction method based on particle filtering and LSTM neural networks. First, a dual-exponential model of lithium-ion battery degradation is established. The parameters of the dual-exponential model are optimized through particle filtering. Specifically, for particle degradation phenomena in the power swarm optimization (PF), an improved particle swarm optimization algorithm is used for optimization. Regarding the impact of random discharge current on the degree of late-stage battery degradation, the importance sampling step and particle weight update step in the PF are improved. The health status estimation results based on sequence-to-sequence LSTM are used for particle filtering importance sampling and particle weight updates. A fitness function and weight judgment formula considering the future capacity change trend of the battery are established, thereby improving the accuracy of remaining life prediction.

[0083] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0084] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0085] Figure 1 This is a structural framework diagram of the present invention;

[0086] Figure 2 Correlation analysis diagrams of health factor sequences and capacity sequences; (a) Comparison diagram of charging health factors and capacity; (b) Comparison diagram of discharging health factors and capacity;

[0087] Figure 3 Flowchart for optimizing health factor parameters in particle swarm optimization algorithm;

[0088] Figure 4 Figure 1 shows the estimation results of health factor for RW4 in 60% of incomplete charge-discharge cycles; (a) estimation of HF4 for HF1, HF2, and HF3; (b) absolute error of HF4 estimation; (c) estimation of HF5 for HF1, HF2, and HF3; (d) absolute error of HF5 estimation; (e) estimation of HF6 for HF1, HF2, and HF3; (f) absolute error of HF6 estimation.

[0089] Figure 5 A diagram illustrating the overall framework of battery health state estimation methods;

[0090] Figure 6 This is a graph showing the predicted remaining lifespan of lithium-ion batteries under standard operating conditions.

[0091] Figure 7 This is a graph showing the predicted remaining lifespan of a lithium-ion battery under random discharge conditions. Detailed Implementation

[0092] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0093] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0094] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0095] like Figure 1 As shown, the implementation process of the present invention includes:

[0096] S1: Extract and optimize health factors: Extract health factors from lithium-ion battery charge and discharge data curves, and optimize the parameters of some health factors to obtain the health factors with the highest correlation to capacity decay.

[0097] S2: Health Factor Mapping of Multi-Kernel RVM: Using a Bayesian-optimized Relevance Vector Machine (RVM) as a tool, the mapping relationship between charging health factors and discharging health factors is learned to obtain a complete health factor sequence.

[0098] S3: Sequence-to-sequence LSTM model: Construct sequence input based on the complete battery health factors extracted in S2, and train the LSTM neural network using battery capacity data as labels.

[0099] S4: Establish a dual-exponential model for lithium-ion battery degradation based on IPSO-PF: The parameters of the dual-exponential model are continuously optimized using an improved particle swarm optimization algorithm and a particle filter algorithm to fit the battery capacity degradation trend.

[0100] S5: Lifetime Prediction: Train the model built in S4 and perform lifetime prediction.

[0101] experiment

[0102] This example combines the battery aging datasets provided by NASA's Ames Prediction Center and the Oxford Battery Aging Dataset to conduct research on battery aging analysis, health status estimation under random discharge conditions, and RUL prediction of lithium-ion batteries under random discharge conditions. The Oxford dataset contains battery aging data for eight 0.74Ah lithium-ion pouch batteries. All data were collected in a 40°C constant-temperature chamber using a constant-current-constant-voltage charging mode, while the discharge mode was based on repeated Urban Artemis driving cycles, with a standard charge-discharge cycle performed every 100 charge-discharge cycles to determine battery characteristics. The NASA random discharge dataset simulates different styles of discharge current conditions. The battery charge-discharge experiment went through three stages: random discharge cycle experiment, reference charge-discharge experiment, and pulse discharge experiment. Using RW4 battery data as an example, the remaining life of the lithium-ion battery was predicted.

[0103] S1: Extract and optimize health factors. First, extract the characteristics of the battery charging stage based on the characteristic curve changes during constant current-constant voltage charging.

[0104] The time difference between equal voltage intervals during constant current charging (HF1), the time difference between equal current intervals during constant voltage charging (HF2), and the temperature difference between equal voltage intervals during constant current charging (HF3) are selected as health factors based on the charging stage curves. The specific calculation formulas are as follows:

[0105]

[0106] in For constant current charging, the voltage reaches V. upper absolute time, For constant current charging, the voltage reaches V. lower Absolute time; For constant voltage charging, the voltage reaches I. upper absolute time, For constant voltage charging, the voltage reaches I. lower Absolute time; For constant current charging, the voltage reaches V. upper temperature, For constant current charging, the voltage reaches V. lower Temperature;

[0107] In addition, the integral value of random discharge current (HF4), the sample entropy of random discharge voltage (HF5), and the standard deviation of random discharge temperature (HF6) need to be extracted as health factors based on the random discharge curve of the battery. The specific calculation formula is as follows:

[0108]

[0109] SampEn is an estimate of the conditional probability that a window of length m (a subsequence of a time series of length Nc) maintains similarity within tolerance r and also matches the next electrical event; T K This is the Kth temperature value from a random discharge cycle of the battery. u is the average temperature of the random discharge cycle, and n is the number of temperatures measured. For example... Figure 2 The figure shown is a comparison chart of health factors and capacity obtained from the RW4 dataset. Figure 2 In the figure, (a) is a comparison chart of charging health factors and capacity; (b) is a comparison chart of discharging health factors and capacity.

[0110] After extracting six health factors from the charge-discharge curves of lithium-ion batteries under random discharge conditions, particle swarm optimization (PSO) algorithm can be used to optimize these extracted health factors during the charging process. Specifically, the V of HF1 is optimized. upper V lower HF2's I upper I lower And HF3's V upper V lowerAs parameters to be optimized, the Pearson correlation coefficients between each health factor and capacity are used as the fitness function of PSO. In this case, the population size is chosen to be 50, and the number of iterations is chosen to be 20.

[0111] F(x)=ρ(HF,capacity) (3)

[0112] Where F(x) is the particle swarm fitness function, HF is the corresponding health factor sequence, capacity is the capacity sequence, and ρ is the Pearson correlation coefficient function. Figure 3 The diagram shown is a flowchart of the particle swarm optimization algorithm for optimizing health factor parameters.

[0113] S2: The charging health factors HF1, HF2, and HF3 from incomplete charge-discharge cycles are taken as input, and the discharging health factors HF4, HF5, and HF6 are taken as output. For the dataset... x i ∈R,t i ∈R where x i For the input of the sample, t i Let R represent the target output value, and D represent the set of real numbers, where D is the total number of samples. The relationship between the model input and output is as follows:

[0114] t i =y(x i ,w i )+ε i (4)

[0115] Where K(x,x) i The kernel function is represented as w = (w1, w2, K, w). D ) T is the weight vector corresponding to the kernel function, and w0 is the bias parameter.

[0116] To address the different degradation trends of health factors, this paper selects linear kernel functions, polynomial kernel functions, Gaussian kernel functions, and Sigmoid kernel functions for linear combination. The weight coefficients of the four combined kernel functions need to be determined manually.

[0117] Furthermore, the process of optimizing the RVM model using the Bayesian optimization algorithm mainly consists of two steps: Gaussian process regression and sampling of the acquisition function. The posterior distribution of the objective function is updated by continuously adding sampling points until the posterior distribution is consistent with the true distribution.

[0118] When mapping health factors, the ratio of incomplete charge / discharge cycles in the training set to the total number of training sets significantly impacts the accuracy of health factor estimation. To demonstrate the estimation performance of multi-core RVM, battery RW4 is used as an example, employing random current discharge and representing 60% of the cycles as incomplete discharge cycles to illustrate the experiment. These incomplete discharge cycles are randomly distributed throughout the discharge cycle. Figure 4 The figure shown is the estimation result of the health factor of RW4 with 60% incomplete charge-discharge cycle ratio. Figure 4 In the example, (a) estimates HF4 for HF1, HF2, and HF3; (b) estimates the absolute error of HF4; (c) estimates HF5 for HF1, HF2, and HF3; (d) estimates the absolute error of HF5; (e) estimates HF6 for HF1, HF2, and HF3; and (f) estimates the absolute error of HF6.

[0119] S3: Based on the multi-core RVM framework obtained in S2, the complete health factor sequence is obtained, normalized, and input data is constructed. Capacity data is extracted, and the battery state of health (SOH), i.e., the label corresponding to the input, is calculated. The constructed dataset is as follows:

[0120]

[0121] Y = {Y1,Y2,Y3,…,Y} m} (6)

[0122] For the LSTM model, assuming a step size of 10, that is, the capacity value {x} passing through the current 10 consecutive loops. 41 ,x 42 ,…,x 49 ,x 50 A single prediction can output capacity estimates for the next 10 cycles. These 10 estimates are then used for the next prediction. This sequence-to-sequence LSTM method requires fewer iterations and has a smaller cumulative error. i Let m be the SOH value of the i-th iteration. m is the iteration number. ② Offline Model Training: First, determine the parameters that need optimization for the LSTM algorithm: time step, number of hidden layer nodes, and number of training iterations. Input the optimized parameters from particle swarm optimization into the LSTM model, initialize other parameters, divide the dataset obtained in ① into training and test sets, and then train the LSTM model. ③ Online Prediction: Extract the charging data of the current iteration and combine it with past data to construct the input, and input it into the trained model to obtain the SOH prediction values ​​for multiple consecutive iterations. For example... Figure 5 The diagram shown is an overall framework diagram of the battery health state estimation method.

[0123] S4: A double-exponential model is used as an empirical model for lithium-ion batteries to fit the battery capacity degradation trend. The established model is as follows:

[0124]

[0125] Where k is the number of charge-discharge cycles, Q k Let be the capacity of the battery in the k-th cycle. a1, a2, a3, and a4 are the aging parameters to be identified in the double exponential model, which are related to the internal characteristics of the battery. Among them, a1 and a3 are related to the internal resistance of the battery in the current cycle, and a2 and a4 are related to the degradation rate of the battery.

[0126] Choose x r,k =[x 1,k x 2,k x 3,k x 4,k ] T The state variables of the battery capacity decay model in the k-th cycle are discretized, and the state equation and observation equation based on particle filtering are as follows:

[0127] Q k =a 1,k ·exp(a 2,k ·k)+a 3,k ·exp(a 4,k ·k) (8)

[0128]

[0129]

[0130] In the formula, x 1,k x 2,k x 3,k x 4,k The initial values ​​are the bi-exponential model parameters a1, a2, a3, and a4. k It is the output of the model, Q k For the capacity of lithium-ion batteries, γ k =[γ 1,k γ 2,k γ 3,k γ 4,k ] T For process noise, It measures noise.

[0131] To mitigate particle degradation and enable particles to better adapt to battery aging trends under random discharge conditions, the IPSO-PF algorithm is used to predict capacity based on the established battery aging model. The specific steps of the IPSO-PF algorithm are as follows:

[0132] ① Initialization: Let the current charge / discharge cycle number be k. When performing particle filtering, first set k = 0, based on the initial prior probability density p(x r,0 Extract n initial state particles Increasing the number of particles in particle filtering can effectively slow down particle degradation, but it will increase the computational load.

[0133] ② Importance sampling: When k = 1, 2, ..., N, the prior PDF is selected as the state PDF, i.e.

[0134]

[0135] New samples are drawn based on importance probability density. Then, an improved particle swarm optimization algorithm was used to process the particle set. The iterative optimization process involves the following steps:

[0136] Step 11: Set the maximum number of iterations T max The population size n is chosen to be consistent with the number of particles in particle filtering, and the particle range R and maximum velocity V are set. max Initial parameters include inertia weight ω, acceleration factors c1 and c2, etc. Let the fitness function for particle swarm optimization be:

[0137]

[0138] Where K is the number of training set samples, and L is the step size of the sequence-to-sequence LSTM. This is the estimate of the future L capacities by LSTM from the previous section.

[0139] Step 12: Set the iteration number t = 1, and set the initial position of the particle as the initialization parameter of the particle in particle filtering. Set the current position as the individual's historical best pBest, and the best individual in the population as the population's historical best gBest, and calculate the fitness function value of each particle.

[0140] Step 13: In the current iteration loop, if the current fitness function value is better than the historical best value, then update the individual historical best value; if the current fitness function is better than the global historical best value, then update the population historical best value. At the end of one loop, update the velocity and position of the d-th dimension of each particle i, as shown below:

[0141]

[0142]

[0143] In the formula, c1 and c2 are learning factors, with a fixed value of 2.0. ω is the inertia weight, initialized to 0.9. Given that a linear decreasing strategy for ω during iteration may lead to local optima and loss of particle diversity, this paper adopts a linear differential decreasing strategy for improvement. The algorithm is as follows:

[0144]

[0145]

[0146] Step 14: Determine if the maximum number of iterations or the set optimization limit has been reached. If so, the optimization is complete. Let the particles in PF... Otherwise, proceed to step 2.

[0147] ③ Particle weight update: The particle weight formula is reconstructed to focus on judging the future trend of particles, and improved upon. By using the first iteration result of LSTM sequence to sequence, it can reflect the future trend more deeply. Combined with the aging model, weight judgment is performed for multiple time ranges. The specific formula is as follows:

[0148]

[0149] in, It is the weight of the i-th particle. For the first iteration result of the sequence-to-sequence LSTM, y k The aging model output value takes noise into account, where R is the variance of the measured noise and N is the total number of charge-discharge cycles of the battery.

[0150] ④ Resampling: Resampling is mainly to address the particle scarcity problem in the classical Monte Carlo method. If the number of effective particles generated in the current loop is low, resampling is necessary to avoid getting trapped in a local optimum due to too few active particles, and to avoid wasting computation on particles with small weights. First, it's necessary to determine whether resampling is needed for this loop. Let the number of effective particles be N. eff for:

[0151]

[0152] If N eff <N threshold For particles Perform random resampling to obtain a new particle set. Otherwise, resampling is not performed. Generally, select...

[0153] ⑤ State estimation: By performing weighted calculations on the particles in the particle set, an estimated value is obtained:

[0154] ⑥ Battery RUL Prediction: Assuming the battery is currently in the kth cycle, based on the state equation and observation equation of the particle filter, the capacity prediction for each particle in the current cycle for the next j cycles is calculated as follows:

[0155]

[0156] Therefore, the prediction capacity for the next j cycles at the k-th cycle is:

[0157]

[0158] The posterior PDF of battery capacity can be approximated as:

[0159]

[0160] The predicted RUL value for the battery is calculated as follows:

[0161]

[0162] After obtaining the parameters of the double-exponential model, particle filter-based model training and prediction can be performed. Based on the algorithm flow in 4), this invention sets the number of particles in the particle filter to 200 and the LSTM estimation sequence length to 15. To verify that the proposed IPSO-PF-LSTM algorithm can achieve RUL prediction of lithium-ion batteries under standard operating conditions and random discharge conditions, and its applicability to different battery packs, experiments were conducted to compare several different algorithms. The results show that the algorithm's errors on the random current aging test dataset and the standard operating condition aging test dataset are within 6.2% and 7.0%, respectively, and its performance indicators are superior to other RUL prediction methods. Figure 6 and Figure 7 The figures shown are the predicted remaining lifespan of lithium-ion batteries under standard operating conditions and random discharge conditions, respectively.

[0163] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for predicting the remaining life of a lithium-ion battery based on an improved particle filter model, characterized in that: The method includes the following steps: S1: Extract and optimize health factors: Extract health factors from lithium-ion battery charge and discharge data curves, and optimize the parameters of some health factors to obtain the health factors with the highest correlation to capacity decay. S2: Health factor mapping of multi-core RVM: Using the correlation vector machine RVM optimized by Bayes as a tool, the mapping relationship between charging health factors and discharging health factors is learned to obtain a complete health factor sequence; S3: Sequence-to-sequence LSTM model: Construct sequence input based on the complete battery health factors extracted in S2, and train the LSTM neural network using battery capacity data as labels; S4: Establish a dual-exponential model for lithium-ion battery degradation based on IPSO-PF: The parameters of the dual-exponential model are continuously optimized using an improved particle swarm optimization algorithm and particle filtering algorithm to fit the battery capacity degradation trend. In step S4, a double-exponential model is used as an empirical model for lithium-ion batteries to fit the battery capacity degradation trend; the established model is as follows: （7） wherein, is the number of cycles for the charge-discharge cycle, is the capacity of the battery at the first cycle, is the capacity of the battery at the second cycle, , , , are the aging parameters to be identified for the double exponential model, related to the internal characteristics of the battery, wherein , is related to the internal resistance of the battery at the current cycle, , is related to the degradation rate of the battery; Select For the battery capacity decay model in the first The state variables of the next cycle are discretized, and the state equation and observation equation based on the particle filter are as follows: （8） （9） （10） In the formula, , , , The initial values ​​are the parameters of the double exponential model. , , , ; It is the output of the model. This refers to the capacity of lithium-ion batteries. For process noise, It measures noise; To mitigate particle degradation and enable particles to better adapt to the battery aging trend under random discharge conditions, the IPSO-PF algorithm is used to predict capacity based on the established battery aging model. The specific steps of the IPSO-PF algorithm are as follows: ① Initialization Let the current charge / discharge cycle number be... When performing particle filtering, take According to the initial prior probability density extract Initial state particles ; ② Importance Sampling when When choosing the prior probability density function as the state probability density function, that is... （11） New samples are drawn based on importance probability density. Then, an improved particle swarm optimization algorithm was used to process the particle set. The iterative optimization process involves the following steps: Step 11: Set the maximum number of iterations Population size The particle number is selected in the same way as in particle filtering, and the particle range is set. Maximum speed Inertia weight Accelerator , Initial parameters are equal; let the fitness function for particle swarm optimization be: （12） in, The number of samples in the training set. The step size for a sequence-to-sequence LSTM. For the previous section on LSTM for the future An estimated capacity; Step 12: Set the number of iterations The initial position of the particles is set as the initialization parameter for the particles in the particle filter. Set the current position as the individual's historical best. The best individual in the population is the population's historical best. And calculate the fitness function value of each particle; Step 13: In the current iteration loop, if the current fitness function value is better than the historical best value, then update the individual historical best value; if the current fitness function is better than the global historical best value, then update the population historical best value; at the end of one loop, for each particle... The The velocity and position of each dimension are updated separately, as shown below: （13） （14） In the formula , The learning factor is set to a fixed value of 2.

0. It is the inertia weight, initialized to 0.9, and improved using a linear differential decreasing strategy. The algorithm is as follows: （15） （16） Step 14: Determine if the maximum number of iterations or the set optimization limit has been reached. If so, the optimization is complete. Let the particles in PF... =[Optimal individual particles in the particle swarm]; otherwise, go to step 2; ③ Particle weight update The particle weight formula is reconstructed, and the weight judgment for multiple time ranges is performed using the first iteration result of LSTM sequence-to-sequence and combined with the aging model. The specific formula is as follows: （17） in, It is the first The weight of each particle, This is the result of the first iteration of the sequence-to-sequence LSTM. The aging model output value takes noise into account. To measure the variance of noise, This represents the total number of charge-discharge cycles of the battery. ④ Resampling First, it is necessary to determine whether resampling is required in this iteration; let the number of effective particles be... for: （18） if For particles Perform random resampling to obtain a new particle set. Otherwise, resampling will not be performed. ; ⑤ State estimation By performing a weighted calculation on the particles in the particle set, the estimated value is obtained: （19） ⑥ Battery RUL Prediction Assuming the battery is currently at the [number]th [position], In each cycle, based on the state equation and observation equation of the particle filter, each particle predicts the future in the current cycle. The capacity of each loop is calculated as follows: （20） In the The cycle point for the future The prediction capacity for each cycle is: （21） A posteriori PDF approximation of battery capacity: （22） The predicted RUL value for the battery is calculated as follows: （23） S5: Lifetime Prediction: Train the model built in S4 and perform lifetime prediction.

2. The lithium-ion remaining lifetime prediction method based on the improved particle filter model according to claim 1, characterized in that: Specifically, S1 involves selecting the time interval of the constant voltage period during constant current charging based on the charging phase curve. HF 1. Time difference of equal current interval during constant voltage charging HF 2. Temperature difference during constant current charging at equal voltage intervals HF As a health factor, the specific calculation formula for 3 is as follows: （1） in For constant current charging voltage to reach absolute time, For constant current charging voltage to reach Absolute time; For constant voltage charging, the voltage reaches absolute time, For constant voltage charging, the voltage reaches Absolute time; For constant current charging voltage to reach temperature, For constant current charging voltage to reach Temperature; Extract the integral value of random discharge current based on the battery's random discharge curve. HF 4. Random discharge voltage sample entropy HF 5. Standard deviation of random discharge temperature HF As a health factor, 6 is calculated using the following formula: （2） SampEn is a term with a length of m The window in tolerance r The estimate of the conditional probability that maintains similarity and also matches the next electric current, with a length of [length missing]. m The window is of length Nc A subsequence of a time series; T K It is the first random discharge cycle of the battery. K A temperature value; u It is the average degree of random discharge cycles. n It is the number of temperatures measured; Six health factors were extracted from the charge-discharge curves of lithium-ion batteries under random discharge conditions. Then, particle swarm optimization (PSO) was used to optimize these extracted health factors during the charging process. Specifically, the health factors extracted during the charging process were... HF 1 of , , HF 2 of , as well as HF 3 , As parameters to be optimized, the Pearson correlation coefficients between each health factor and capacity are used as the fitness function of the PSO, i.e.: （3） in, F(x) Let be the particle swarm fitness function. HF For the corresponding health factor sequence, capacity It is a capacity sequence. This is the Pearson correlation coefficient function.

3. The lithium-ion remaining lifetime prediction method based on the improved particle filter model according to claim 2, characterized in that: Specifically, S2 involves: incorporating charging health factors from incomplete charge-discharge cycles. HF 1. HF 2. HF 3 together serve as inputs, discharging health factors HF 4. HF 5. HF 6 are used as outputs respectively; for the dataset , , in For the input of the sample, Let R represent the target output value, D represent the set of real numbers, and D represent the total number of samples. The relationship between the model input and output is as follows: （4） in Represented as a kernel function, The weight vector corresponding to the kernel function. These are bias parameters; To address the different degradation trends of health factors, linear kernel functions, polynomial kernel functions, Gaussian kernel functions, and Sigmoid kernel functions are selected and linearly combined. The weight coefficients of the four combined kernel functions need to be manually determined. The optimization of the RVM model using the Bayesian optimization algorithm consists of two steps: Gaussian process regression and sampling of the acquisition function. The posterior distribution of the objective function is updated by continuously adding sampling points until the posterior distribution matches the true distribution. First, in the domain space... Select an initial hyperparameter set x; then calculate based on the properties of the sampling set and the Gaussian distribution. The probability distribution is used to obtain the position of the next sampling point using the acquisition function; finally, the probability distribution is calculated. And update the objective function. To reach the required number of iterations or to satisfy the convergence condition; The specific implementation process of the Bayesian optimized multi-kernel RVM algorithm is as follows: preparation of training set and prediction set; determination of the hyperparameters to be optimized and their range; construction and training of Bayesian optimized RVM model.

4. The lithium-ion remaining lifetime prediction method based on the improved particle filter model according to claim 3, characterized in that: Specifically, S3 is: S32: Constructing the dataset: Based on the multi-core RVM framework in S2, obtain the complete health factor sequence, normalize it, construct the input data, extract the capacity data, and calculate the battery health state (SOH), which is the label corresponding to the input; the constructed dataset is: （5） （6） For the LSTM model, with a step size of 10, the capacity value is obtained from the current 10 consecutive loops. A single prediction outputs capacity estimates for the next 10 cycles. Then, these 10 estimates are used for the next prediction. This sequence-to-sequence LSTM method has fewer iterations and smaller cumulative error. For the first SOH value for the next cycle; This represents the number of loop iterations. S32: Offline training of the model: First, determine the parameters that need to be optimized for the LSTM algorithm: time step, number of hidden layer nodes, and number of training iterations; input the optimized parameters of particle swarm optimization into the LSTM model, initialize other parameters, divide the dataset obtained in ① into training set and test set, and then train the LSTM model. S33: Online prediction: Extract the charging data of the current cycle and combine it with past data to construct the input, and input it into the trained model to obtain the SOH prediction value for multiple consecutive cycles.

5. The lithium-ion remaining lifetime prediction method based on the improved particle filter model according to claim 1, characterized in that: S5 inputs the test set data into the model established in S4, and after obtaining the parameters of the double exponential model, performs model training based on particle filtering and performs lifetime prediction.

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