An adaptive high-low magnification lithium ion battery state of charge estimation method and system

Abstract

The application provides a self-adaptive high-low rate lithium ion battery state of charge estimation method and system, which comprises three steps: step one: obtaining offline parameters of a gas-liquid heat electric coupling model; step two: self-adaptive high-low rate gas-liquid heat electric coupling model parameter and state of charge online estimation method; and step three: developing a self-adaptive high-low rate lithium ion battery state of charge online estimation system. The application introduces an adaptive coefficient L related to the charging and discharging rate, so that the model itself can automatically adjust the output characteristics according to the current rate, and the wide rate range working conditions from low rate to high rate can be adapted without changing the model structure, overcoming the defect that the precision of the traditional fixed parameter model suddenly decreases when the rate changes.

Description

Technical Field

[0001] This invention relates to the field of lithium-ion battery state estimation technology, specifically to an adaptive method and system for estimating the state of charge of high and low rate lithium-ion batteries, which is particularly suitable for online accurate estimation of battery state of charge in battery management systems. Background Technology

[0002] Lithium-ion batteries have been widely used in new energy vehicles and energy storage due to their advantages, including being environmentally friendly, having high energy density, long cycle life, low self-discharge rate, and lower purchase cost resulting from large-scale production. Because the electrodes and electrolytes of lithium-ion batteries are extremely sensitive to oxygen and water vapor in the air, they are typically sealed in a sealed environment. During battery operation, sensors can only directly collect voltage, current, and temperature, but cannot directly obtain implicit battery parameters and the state of charge (SOC). However, these SOC parameters are crucial for the accurate online detection of lithium-ion battery parameters and SOC, which are essential for predicting battery aging, estimating remaining life, equalizing charge levels, estimating remaining energy, controlling charging, diagnosing faults, and determining actual and reliable capacity.

[0003] Existing methods for detecting latent state quantities in batteries mainly include the ampere-hour integration method, the equivalent circuit model method, and the electrochemical model method. The ampere-hour integration method, due to its low computational cost and ease of implementation, was a commonly used method for predicting the state of charge, actual capacity, and reliable capacity of early lithium-ion batteries. However, this method cannot effectively distinguish between sampling noise and errors during the integration process, leading to a continuous increase in accumulated errors and a gradual decrease in prediction accuracy over time, making it difficult to meet the high-precision detection requirements of current electric vehicles for latent state quantities. The equivalent circuit model is an empirical model that does not need to consider the complex electrochemical processes inside the battery. It has fewer and easier-to-identify model parameters, thus it is widely used in engineering. However, this model suffers from insufficient mechanistic description and lacks parameters that directly reflect the temperature characteristics of lithium-ion batteries. Since battery parameters and state of charge are significantly affected by temperature, the traditional equivalent circuit model does not perform well in fitting wide current and temperature ranges, resulting in decreased adaptability of the method in high and low temperature environments. Introducing a temperature correction term further increases computational complexity. Electrochemical models are typical mechanistic models, with advantages such as high accuracy and clear mechanisms. However, they also have problems such as difficulty in solving partial differential equations, numerous and complex parameters, and difficulty in ensuring real-time calculation. At present, they are still rarely used for online estimation of implicit parameters and state of charge in the working process of lithium-ion batteries.

[0004] In addition to the traditional models and methods mentioned above, the recently proposed gas-liquid thermoelectric coupling model serves as a novel analytical model for lithium-ion batteries. By analyzing the physical similarity between gas-liquid dynamics and electricity, it studies the intrinsic relationship between diffusion / equilibrium between gas molecules and lithium ions, establishing a gas-liquid dynamic battery model that directly couples temperature characteristics. This model features a simple structure, fewer parameters, and ease of identification, and can accommodate both long-term concentration polarization and short-term electrochemical polarization. However, existing technical solutions based on the gas-liquid thermoelectric coupling model mostly employ offline parameter identification or single-filter combined parameter identification methods, lacking an adaptive adjustment mechanism for changes in charge / discharge rate. This weakens the adaptability of the gas-liquid thermoelectric coupling model to dynamic charge / discharge conditions, and it has not yet achieved accurate online co-estimation of lithium-ion battery parameters and state of charge across a wide range of operating conditions, from high to low rates. To address this, this invention proposes an adaptive method and system for estimating the state of charge (SOC) of lithium-ion batteries at high and low rates. By introducing adaptive coefficients related to the charge / discharge rate, a dual-filter collaborative estimation architecture for parameters and states is constructed to achieve online joint identification and high-precision SOC estimation. This aims to solve the problems of insufficient accuracy and poor model adaptability in SOC estimation under dynamic operating conditions at high and low rates in existing technologies, and to improve the robustness and accuracy of online estimation of latent state variables of lithium-ion batteries. Summary of the Invention

[0005] The technical solution of this invention is: an adaptive method and system for estimating the state of charge of high and low rate lithium-ion batteries, characterized by comprising the following steps:

[0006] Step 1: Obtain the offline parameters of the gas-liquid thermoelectric coupling model;

[0007] Step 2: Online estimation method for parameters and state of charge of adaptive high and low magnification gas-liquid thermoelectric coupling model;

[0008] Step 3: Develop an adaptive online state-of-charge estimation system for high and low rate lithium-ion batteries.

[0009] In the above scheme, the first step of obtaining the offline parameters of the gas-liquid thermoelectric coupling model is as follows: the open-circuit voltage prediction equation of the gas-liquid thermoelectric coupling model is Formula 1, and the terminal voltage prediction equation is Formula 2. The superscript and subscript of the letters in the formula are used to distinguish the state of the parameters. The subscript k represents the current sampling time, k-1 represents the previous sampling time, and k+1 represents the next sampling time.

[0010] Formula 1

[0011] Formula 2

[0012] In the formula, V represents the terminal voltage; U represents the open-circuit voltage; V1 represents the electrochemical polarization voltage; T represents the Kelvin temperature; R0, R1, τ, k1, and k2 represent five parameters to be identified; b and c are intermediate variables; Δt is the sampling period; I represents the current (positive for discharging and negative for charging); L is the adaptive coefficient, related to the battery charge / discharge rate; β is the battery matching factor; C is the charge / discharge rate; and Q... T This represents the actual capacity.

[0013] The open-circuit voltage of the lithium-ion battery under different states of charge (SOC) was obtained through intermittent charge-discharge tests, along with the corresponding terminal voltage, current, and temperature. Based on optimization algorithms and Formula 1, five parameters to be identified in the gas-liquid thermoelectric coupling model were used as initial values ​​θ0 for the online parameter identification method. The optimization algorithms used in the online parameter identification included genetic algorithm, least squares method, ant colony algorithm, particle filter algorithm, and neural network algorithm. The mapping function U=g(SOC) between the open-circuit voltage U and the SOC of the lithium-ion battery was obtained through HPPC testing.

[0014] The second step, the online estimation method for parameters and state of charge of the gas-liquid thermoelectric coupling model with adaptive high and low magnification, specifically involves: estimating the parameters and state of charge of the gas-liquid thermoelectric coupling model online based on the dual extended Kalman filter algorithm, with the parameter vector θ defined by Formula 3, the state vector x defined by Formula 4, and the discretized state equation defined by Formula 5.

[0015] Formula 3

[0016] Formula 4

[0017] Formula 5

[0018] In the formula, T in the upper right corner represents the transpose operation, SOC is the state of charge, f is the state equation, η is the Coulomb efficiency, r is the system noise which follows a multivariate normal distribution and the system noise covariance matrix is ​​Q.

[0019] Equation 1 is transformed into Equation 6, the observation equation;

[0020] Formula Six

[0021] In the formula, v is the measurement noise and follows a multivariate normal distribution, and the variance of the measurement noise is R.

[0022] Calculate the state Jacobian matrix F x k :

[0023] Formula 7

[0024] Calculate the state observation Jacobian vector Hx k :

[0025] Formula 8

[0026] In the formula, g'(SOC) k ) indicates SOC k Find the derivative. This indicates the calculation of partial derivatives.

[0027] The parameters of a lithium-ion battery are slow variables. The parameter state transition is that the posterior parameter at sampling time k-1 is assigned to the prior parameter at sampling time k.

[0028] Calculate the parameter observation Jacobian vector H θ k :

[0029] Formula Nine

[0030] Standard steps for performing the double extended Kalman filter algorithm:

[0031] Step S0: Initialization

[0032] Formula 10

[0033] Step S1: Obtain the prior values ​​of the state and parameters

[0034] Formula Eleven

[0035] Step S2: Obtain the prior values ​​of the state and parameter covariance matrix.

[0036] Formula 12

[0037] Step S3: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full and Predicting by substituting into Formula Six

[0038] Formula Thirteen

[0039] Step S4: Calculate the Kalman gain of the state and parameters.

[0040] Formula Fourteen

[0041] Step S5: Obtain the state and parameter posterior values

[0042] Formula Fifteen

[0043] Step S6: Obtain the posterior values ​​of the state and parameter covariance matrix

[0044] Formula Sixteen

[0045] In the formula, the superscript "¯" indicates the prior value of the parameter, and the superscript "^" indicates the posterior value of the parameter. This represents the initial value of the state vector. The initial values ​​of the parameter vector are represented, where T0 represents the initial temperature. This represents the initial value of the state covariance matrix. This represents the initial value of the parameter covariance matrix. The initial values ​​of the system noise covariance matrix represent the state. This represents the initial value of the system noise covariance matrix of the parameters. This represents the initial value of the variance of the state measurement noise. U0 represents the initial value of the parameter measurement noise variance, and y represents the initial value of the open-circuit voltage. k,采样 Let E represent the battery terminal voltage sampled at time k, and let E represent the identity matrix with the numbers in parentheses indicating the matrix dimension.

[0046] Repeat steps S1 to S6 to achieve online parameter and state of charge (SOC) of the gas-liquid thermoelectric coupling model, and the SOC in the state vector x. k The state of charge (SOC) of the battery is defined as β, which is the battery matching factor in the parameter vector θ and is identified online, enabling adaptive SOC estimation for high and low rate lithium-ion batteries.

[0047] Step three involves developing an adaptive online state-of-charge estimation system for high and low rate lithium-ion batteries, comprising a data acquisition module, a battery latent state estimation module, a data storage module, and a display module.

[0048] The data acquisition module's signal acquisition unit is connected to a current sensor, a voltage sensor, and a temperature sensor to acquire the lithium-ion battery's current, terminal voltage, and temperature, respectively. The data acquisition module is connected to the battery latent state estimation module and the data storage module, and sends the acquired terminal voltage, temperature, and current signals to both modules. The battery latent state estimation module integrates the adaptive high / low rate gas-liquid thermoelectric coupling model parameters and the online state of charge estimation method from step two. It accurately estimates the parameters of the gas-liquid thermoelectric coupling model and the lithium-ion battery's state of charge online, and sends the estimation results to the data storage module. The display module is connected to the battery latent state estimation module and displays the lithium-ion battery's predicted state of charge.

[0049] In the above scheme, the online estimation method for parameters and state of charge of the gas-liquid thermoelectric coupling model with adaptive high and low magnification in step two includes, in addition to the double extended Kalman filter algorithm, genetic algorithm, least squares algorithm, particle filter algorithm, simulated annealing algorithm, ant colony algorithm, observer, neural network algorithm, and artificial intelligence algorithm.

[0050] Compared with the prior art, the beneficial effects of the present invention are as follows.

[0051] 1. This invention realizes real-time estimation of online parameters and state of charge of lithium-ion batteries based on a gas-liquid thermoelectric coupling model and a dual extended Kalman filter algorithm. By introducing an adaptive coefficient φ related to the charge / discharge rate, the model itself can automatically adjust its output characteristics according to the current rate. It can adapt to a wide range of operating conditions from low to high rates without changing the model structure, overcoming the defect of the traditional fixed parameter model where the accuracy drops sharply when the rate changes.

[0052] 2. This invention employs the DEKF algorithm to run the state filter and parameter filter in parallel, achieving collaborative online estimation of SOC and model parameters through shared voltage residuals. The parameter filter uses the current residual to correct the model parameters in each sampling period, enabling the parameters to adaptively adjust in real time according to battery aging, temperature changes, and rate switching. This completely avoids the high-cost work of traditional methods requiring extensive offline experiments to calibrate model parameters under different operating conditions, while also solving the problem that fixed-parameter models cannot track battery performance degradation.

[0053] 3. A dual extended Kalman filter algorithm is used to achieve online collaborative prediction of model parameters and state of charge. It can decompose high-dimensional matrix operations into two lower-dimensional matrix operations, which significantly simplifies the structural complexity of the prediction method, reduces computational cost, and is easy to implement on embedded systems, thus solving the problem of poor prediction timeliness in engineering. Attached Figure Description

[0054] Figure 1 This is the flowchart of an adaptive high- and low-rate lithium-ion battery state-of-charge estimation method according to the present invention.

[0055] Figure 2 This document presents the open-circuit voltage and state of charge data of the lithium-ion battery of this invention, along with polynomial fitting curves.

[0056] Figure 3 This is the CDFU operating current acquisition data curve of the lithium-ion battery of this invention.

[0057] Figure 4 This is the CDFU terminal voltage acquisition data curve of the lithium-ion battery of the present invention.

[0058] Figure 5This is the temperature acquisition data curve of the CDFU operating condition of the lithium-ion battery of this invention.

[0059] Figure 6 This is the CDFU (Concentration-Delayed-Full-Age) state-of-charge prediction data curve for the lithium-ion battery of this invention.

[0060] Figure 7 This invention provides a flowchart of an adaptive high- and low-rate lithium-ion battery state-of-charge estimation system. Detailed Implementation

[0061] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments, but the scope of protection of the present invention is not limited thereto.

[0062] The technical solution of this invention is: an adaptive method and system for estimating the state of charge of high and low rate lithium-ion batteries, characterized in that, referring to... Figure 1 This includes the following steps:

[0063] Step 1: Obtain the offline parameters of the gas-liquid thermoelectric coupling model;

[0064] Step 2: Online estimation method for parameters and state of charge of adaptive high and low magnification gas-liquid thermoelectric coupling model;

[0065] Step 3: Develop an adaptive online state-of-charge estimation system for high and low rate lithium-ion batteries.

[0066] In the above scheme, the first step of obtaining the offline parameters of the gas-liquid thermoelectric coupling model is as follows: the open-circuit voltage prediction equation of the gas-liquid thermoelectric coupling model is Formula 1, and the terminal voltage prediction equation is Formula 2. The superscript and subscript of the letters in the formula are used to distinguish the state of the parameters. The subscript k represents the current sampling time, k-1 represents the previous sampling time, and k+1 represents the next sampling time.

[0067] Formula 1

[0068] Formula 2

[0069] In the formula, V represents the terminal voltage; U represents the open-circuit voltage; V1 represents the electrochemical polarization voltage; T represents the Kelvin temperature; R0, R1, τ, k1, and k2 represent five parameters to be identified; b and c are intermediate variables; Δt is the sampling period; I represents the current (positive for discharging and negative for charging); L is the adaptive coefficient, related to the battery charge / discharge rate; β is the battery matching factor; C is the charge / discharge rate; and Q... T This represents the actual capacity.

[0070] The open-circuit voltage of the lithium-ion battery under different states of charge (SOC) was obtained through intermittent charge-discharge testing, along with the corresponding terminal voltage, current, and temperature. Based on the method and formula in the published invention patent ZL201711337881.6, five parameters to be identified for the gas-liquid thermoelectric coupling model were used as the initial values ​​for the online parameter identification method: θ0 = [0.016 0.0048 0.101 2.74 0.62 1]. The optimization algorithms used in the online parameter identification included genetic algorithm, least squares method, ant colony algorithm, particle filter algorithm, and neural network algorithm. The mapping function U = g(SOC) between the open-circuit voltage U and the SOC of the lithium-ion battery was obtained through HPPC testing. Figure 2 As shown.

[0071] The second step, the online estimation method for parameters and state of charge of the gas-liquid thermoelectric coupling model with adaptive high and low magnification, specifically involves: estimating the parameters and state of charge of the gas-liquid thermoelectric coupling model online based on the dual extended Kalman filter algorithm, with the parameter vector θ defined by Formula 3, the state vector x defined by Formula 4, and the discretized state equation defined by Formula 5.

[0072] Formula 3

[0073] Formula 4

[0074] Formula 5

[0075] In the formula, T in the upper right corner represents the transpose operation, SOC is the state of charge, f is the state equation, η is the Coulomb efficiency, r is the system noise which follows a multivariate normal distribution and the system noise covariance matrix is ​​Q.

[0076] Equation 1 is transformed into Equation 6, the observation equation;

[0077] Formula Six

[0078] In the formula, v is the measurement noise and follows a multivariate normal distribution, and the variance of the measurement noise is R.

[0079] Calculate the state Jacobian matrix F x k :

[0080] Formula 7

[0081] Calculate the state observation Jacobian vector H x k :

[0082] Formula 8

[0083] In the formula, g'(SOC)k ) indicates SOC k Find the derivative. This indicates the calculation of partial derivatives.

[0084] The parameters of a lithium-ion battery are slow variables. The parameter state transition is that the posterior parameter at sampling time k-1 is assigned to the prior parameter at sampling time k.

[0085] Calculate the parameter observation Jacobian vector H θ k :

[0086] Formula Nine

[0087] The CDFU operating condition is a sequential combination of 5-minute constant current discharge, DST, FUDS, and UDDS operating conditions, which is closer to the actual driving conditions of a car. Figure 3 Displays the CDFU operating current acquisition data curve of the lithium-ion battery. Figure 4 Displays the voltage acquisition data curve of the CDFU terminal of the lithium-ion battery under operating conditions. Figure 5 Displays the CDFU operating temperature acquisition data curve of the lithium-ion battery; according to Figures 2 to 5 The standard steps for performing the double extended Kalman filter algorithm on the data are as follows:

[0088] Step S0: Initialization

[0089] Formula 10

[0090] Step S1: Obtain the prior values ​​of the state and parameters

[0091] Formula Eleven

[0092] Step S2: Obtain the prior values ​​of the state and parameter covariance matrix.

[0093] Formula 12

[0094] Step S3: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full and Predicting by substituting into Formula Six

[0095] Formula Thirteen

[0096] Step S4: Calculate the Kalman gain of the state and parameters.

[0097] Formula Fourteen

[0098] Step S5: Obtain the state and parameter posterior values

[0099] Formula Fifteen

[0100] Step S6: Obtain the posterior values ​​of the state and parameter covariance matrix

[0101] Formula Sixteen

[0102] In the formula, the superscript "¯" indicates the prior value of the parameter, and the superscript "^" indicates the posterior value of the parameter. This represents the initial value of the state vector. The initial values ​​of the parameter vector are represented, where T0 represents the initial temperature. This represents the initial value of the state covariance matrix. This represents the initial value of the parameter covariance matrix. The initial values ​​of the system noise covariance matrix represent the state. This represents the initial value of the system noise covariance matrix of the parameters. This represents the initial value of the variance of the state measurement noise. U0 represents the initial value of the parameter measurement noise variance, and y represents the initial value of the open-circuit voltage. k,采样 Let E represent the battery terminal voltage sampled at time k, and let E represent the identity matrix with the numbers in parentheses indicating the matrix dimension.

[0103] Repeat steps S1 to S6 to achieve online parameter and state of charge (SOC) of the gas-liquid thermoelectric coupling model, and the SOC in the state vector x. k This refers to the battery's state of charge. Figure 6 The data curves of the state of charge prediction under CDFU conditions for lithium-ion batteries are displayed. β in the parameter vector θ is the battery matching factor and is identified online, realizing adaptive state of charge estimation for high and low rate lithium-ion batteries.

[0104] Step three describes the development of an adaptive online state-of-charge estimation system for high and low rate lithium-ion batteries, such as... Figure 7 As shown, it includes a data acquisition module, a battery latent state estimation module, a data storage module, and a display module.

[0105] The data acquisition module's signal acquisition unit is connected to a current sensor, a voltage sensor, and a temperature sensor to acquire the lithium-ion battery's current, terminal voltage, and temperature, respectively. The data acquisition module is connected to the battery latent state estimation module and the data storage module, and sends the acquired terminal voltage, temperature, and current signals to both modules. The battery latent state estimation module integrates the adaptive high / low rate gas-liquid thermoelectric coupling model parameters and the online state of charge estimation method from step two. It accurately estimates the parameters of the gas-liquid thermoelectric coupling model and the lithium-ion battery's state of charge online, and sends the estimation results to the data storage module. The display module is connected to the battery latent state estimation module and displays the lithium-ion battery's predicted state of charge.

[0106] In the above scheme, the online estimation method for parameters and state of charge of the gas-liquid thermoelectric coupling model with adaptive high and low magnification in step two includes, in addition to the double extended Kalman filter algorithm, genetic algorithm, least squares algorithm, particle filter algorithm, simulated annealing algorithm, ant colony algorithm, observer, neural network algorithm, and artificial intelligence algorithm.

Claims

1. The technology of this invention is: an adaptive method and system for estimating the state of charge of high and low rate lithium-ion batteries, characterized in that, Includes the following steps: Step 1: Obtain the offline parameters of the gas-liquid thermoelectric coupling model; Step 2: Online estimation method for parameters and state of charge of adaptive high and low magnification gas-liquid thermoelectric coupling model; Step 3: Develop an adaptive online state-of-charge estimation system for high and low rate lithium-ion batteries; The first step of obtaining the offline parameters of the gas-liquid thermoelectric coupling model is as follows: the open-circuit voltage prediction equation of the gas-liquid thermoelectric coupling model is Formula 1, and the terminal voltage prediction equation is Formula 2. The superscript and subscript of the letters in the formula are used to distinguish the state of the parameters. The subscript k represents the current sampling time, k-1 represents the previous sampling time, and k+1 represents the next sampling time. Formula 1 Formula 2 In the formula, V represents the terminal voltage; U represents the open-circuit voltage; V1 represents the electrochemical polarization voltage; T represents the Kelvin temperature; R0, R1, τ, k1, and k2 represent five parameters to be identified; b and c are intermediate variables; Δt is the sampling period; I represents the current (positive for discharging and negative for charging); L is the adaptive coefficient, related to the battery charge / discharge rate; β is the battery matching factor; C is the charge / discharge rate; and Q... T This refers to the actual capacity. The open-circuit voltage of a lithium-ion battery under different states of charge (SOC) is obtained, along with the corresponding terminal voltage, current, and temperature. Based on optimization algorithms and Formula 1, five parameters to be identified in the gas-liquid thermoelectric coupling model are used as initial values ​​θ0 for the online parameter identification method. The optimization algorithms used in the online parameter identification include genetic algorithm, least squares method, ant colony algorithm, particle filter algorithm, and neural network algorithm. The mapping function U=g(SOC) between the open-circuit voltage U and the state of charge (SOC) of the lithium-ion battery is obtained through HPPC testing. The second step, the online estimation method for parameters and state of charge of the gas-liquid thermoelectric coupling model with adaptive high and low magnification, is specifically as follows: the parameters and state of charge of the gas-liquid thermoelectric coupling model are estimated online based on the dual extended Kalman filter algorithm. Let the parameter vector θ be Equation 3, the state vector x be Equation 4, and the discretized state equation be Equation 5. Formula 3 Formula 4 Formula 5 In the formula, T in the upper right corner represents the transpose operation, SOC is the state of charge, f is the state equation, η is the Coulomb efficiency, r is the system noise which follows a multivariate normal distribution and the system noise covariance matrix is ​​Q; Equation 1 is transformed into Equation 6, the observation equation; Formula Six In the formula, v is the measurement noise that follows a multivariate normal distribution and the variance of the measurement noise is R; Calculate the state Jacobian matrix F x k : Formula 7 Calculate the state observation Jacobian vector H x k : Formula 8 In the formula, g'(SOC) k ) indicates SOC k Find the derivative. This indicates the calculation of partial derivatives; The parameters of a lithium-ion battery are slow variables. The parameter state transition is that the posterior parameter at sampling time k-1 is assigned to the prior parameter at sampling time k. Calculate the parameter observation Jacobian vector H θ k : Formula Nine Standard steps for performing the double extended Kalman filter algorithm: Step S0: Initialization Formula 10 Step S1: Obtain the prior values ​​of the state and parameters Formula Eleven Step S2: Obtain the prior values ​​of the state and parameter covariance matrix Official Twelve Step S3: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full context.] and Substitute into Formula Six for prediction Formula Thirteen Step S4: Calculate the Kalman gain of the state and parameters. Formula Fourteen Step S5: Obtain the state and parameter posterior values Formula Fifteen Step S6: Obtain the posterior values ​​of the state and parameter covariance matrix Formula Sixteen In the formula, the superscript "¯" indicates the prior value of the parameter, and the superscript "^" indicates the posterior value of the parameter. This represents the initial value of the state vector. The initial values ​​of the parameter vector are represented, where T0 represents the initial temperature. This represents the initial value of the state covariance matrix. This represents the initial value of the parameter covariance matrix. The initial values ​​of the system noise covariance matrix represent the state. This represents the initial value of the system noise covariance matrix of the parameters. This represents the initial value of the variance of the state measurement noise. U0 represents the initial value of the parameter measurement noise variance, and y represents the initial value of the open-circuit voltage. k,采样 Let E represent the terminal voltage sampled by the battery at time k, and let E represent the identity matrix with the numbers in parentheses indicating the dimension of the matrix. Repeat steps S1 to S6 to achieve online parameter and state of charge (SOC) of the gas-liquid thermoelectric coupling model, and the SOC in the state vector x. k The state of charge (SOC) of the battery is defined as β, where β in the parameter vector θ is the battery matching factor and is identified online, enabling adaptive SOC estimation for high and low rate lithium-ion batteries.

2. The adaptive high- and low-rate lithium-ion battery state-of-charge estimation method and system according to claim 1, characterized in that, Step 3: Develop an adaptive online state-of-charge estimation system for high and low rate lithium-ion batteries, including a data acquisition module, a battery latent state estimation module, a data storage module, and a display module; The data acquisition module's signal acquisition unit is connected to a current sensor, a voltage sensor, and a temperature sensor to acquire the current, terminal voltage, and temperature of the lithium-ion battery, respectively. The data acquisition module is connected to the battery latent state estimation module and the data storage module, and sends the acquired terminal voltage, temperature, and current signals to both the battery latent state estimation module and the data storage module. The battery latent state estimation module integrates the parameters of the adaptive high and low rate gas-liquid thermoelectric coupling model and the online estimation method of state of charge from step two. It is used to accurately estimate the parameters of the gas-liquid thermoelectric coupling model and the state of charge of the lithium-ion battery online, and sends the estimation results to the data storage module. The display module is connected to the battery latent state estimation module and is used to display the state of charge of the lithium-ion battery predicted by the battery latent state estimation module.

3. The adaptive high- and low-rate lithium-ion battery state-of-charge estimation method and system according to claim 1, characterized in that, Step 2, the online estimation method for parameters and state of charge of the gas-liquid thermoelectric coupling model with adaptive high and low magnification, includes, in addition to the aforementioned double extended Kalman filter algorithm, genetic algorithm, least squares algorithm, particle filter algorithm, simulated annealing algorithm, ant colony algorithm, observer, neural network algorithm, and artificial intelligence algorithm.

4. The method and system for reliable lithium-ion battery capacity prediction with low computational cost according to claim 1, characterized in that, r represents system noise, including other distributions, and v represents measurement noise, including other distributions.

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