SOC estimation method, system and device based on improved maximum correlation entropy EKF algorithm and medium

Abstract

An SOC estimation method, system, device and medium based on an improved maximum correlation entropy EKF algorithm, first, a second-order RC equivalent circuit model is adopted to describe transient and dynamic characteristics of a battery, that is, a state-space equation of a lithium ion battery is derived, curve fitting is performed on SOC and OCV data, and a mapping relational expression of SOC and OCV is obtained; then, on the basis of the second-order RC equivalent circuit model and the parameter data, state updating is carried out on the battery equivalent circuit model through a generalized mixed maximum correlation entropy extended Kalman filtering algorithm, and SOC estimation under different working conditions is achieved; according to the method, the Kalman filtering process is optimized, and the generalized mixed maximum correlation entropy criterion is introduced, so that the defects of a traditional method in a non-Gaussian noise environment are overcome, and the precision and robustness of SOC estimation are remarkably improved; compared with the prior art, the method can better adapt to complex noise and dynamic working conditions in the battery system, and a more advanced and reliable solution is provided for optimization of the battery management system.

Description

Technical Field

[0001] The present invention relates to the technical field of lithium-ion battery management systems, and in particular to a SOC estimation method, system, device and medium based on an improved maximum related entropy EKF algorithm. Background Art

[0002] In lithium-ion battery management systems, accurate estimation of the battery state of charge (SOC) helps improve system performance and reliability, and can also extend battery life. The SOC of a lithium-ion battery refers to an indicator that reflects the ratio of the battery's current remaining capacity to its total capacity, usually expressed as a percentage. Accurate estimation of the SOC can enable real-time monitoring and management of the battery's charge state, effectively avoiding overcharging and over-discharging of the battery and extending the battery's service life.

[0003] At present, the commonly used SOC estimation methods include the ampere-hour integration method, the open circuit voltage method, the Kalman filter method and the data-driven method. ① The ampere-hour integration method is the simplest SOC estimation method, but because it is a typical open-loop estimation system, it can only estimate the SOC by integrating the battery charge and discharge current, and does not use the feedback information of the actual output value such as the battery voltage to correct the estimation error; ② The open circuit voltage method infers the battery SOC by measuring the open circuit voltage of the battery. However, since it needs to be stationary for a long time to obtain a stable voltage value, it is not suitable for online estimation, and the relationship between the open circuit voltage and SOC is affected by factors such as temperature, charge and discharge rate, and battery health status. Therefore, there may be large errors under different working conditions; ③ The Kalman filter method is a combination of the first two methods and is a commonly used state estimation algorithm. The Kalman filter method obtains the optimal estimate of the state by weighted fusion of the system model and the observed data. In SOC estimation, the mathematical model of the battery and the measured current, voltage and other information can be combined with the Kalman filter algorithm to estimate the SOC. This method has high accuracy and robustness, but requires accurate system models and observation data, and has high computational complexity; ④ The data-driven method relies on a large number of data samples and often regards the battery as a black box model. Therefore, long-term historical data is required to establish a database to ensure the quality and availability of the data. Representative methods include support vector machine (SVM), neural network (BP) and its improved methods. However, these algorithms do have some limitations when dealing with nonlinear systems and need to be selected for different application scenarios. The most commonly used methods are the Kalman filter algorithm and its derivative algorithms, which have significant advantages in state estimation. However, these algorithms do have some limitations when dealing with nonlinear systems and need to be selected for different application scenarios. For example, PLETT G L. Extended Kalman filtering for battery management systems of LiPB-based HEV battery packs: part 3, state and parameter estimation [J]. Journal of Power Sources, 2004, 134: 277-292. The Extended Kalman Filter (EKF) is a classic nonlinear filtering method that Taylor expands the nonlinear function and retains the first-order linear terms. Although EKF performs well in processing nonlinear systems, it does not handle non-Gaussian noise well, which may lead to unsatisfactory filtering effects and reduced accuracy of state estimation. Summary of the invention

[0004] In order to overcome the shortcomings of the above-mentioned prior art, the purpose of the present invention is to provide a SOC estimation method, system, device and medium based on an improved maximum correlated entropy EKF algorithm. In order to solve the problems of inaccurate state of charge (SOC) estimation and poor robustness in a non-Gaussian noise environment, the generalized maximum mixed correlated entropy criterion and the extended Kalman filter algorithm are combined, which can more accurately estimate the SOC during continuous measurement and updating, and has stronger robustness to system noise and interference; the algorithm has improved its adaptability to various battery types and working conditions through improvements, and can provide more accurate SOC estimation under different temperatures and working conditions, and is suitable for a wide range of fields such as electric vehicles and energy storage systems.

[0005] In order to achieve the above object, the specific technical solution adopted by the present invention is as follows:

[0006] A SOC estimation method based on an improved maximum correlation entropy EKF algorithm, the specific steps are as follows:

[0007] Step 1: Use a second-order RC equivalent circuit model to describe the transient and dynamic characteristics of the battery, that is, derive the state space equation of the lithium-ion battery, perform curve fitting on the SOC and OCV data, and obtain the mapping relationship between SOC and OCV;

[0008] Step 2: Based on the second-order RC equivalent circuit model of step 1 and the mapping relationship between SOC and OCV, the state of the second-order RC equivalent circuit model is updated through the generalized hybrid maximum correlation entropy extended Kalman filter algorithm to achieve SOC estimation under different working conditions.

[0009] The specific method of step 1 is:

[0010] The second-order RC equivalent circuit model used is composed of an internal resistance R0 and two RC parallel branches. The internal resistance R0 reflects the voltage drop of the battery when current passes through it, and the RC parallel branches are used to simulate the polarization effect and dynamic voltage change of the battery.

[0011] According to Kirchhoff's law, the equivalent circuit of the second-order RC equivalent circuit model is expressed as:

[0012]

[0013] Where U OC is the open circuit voltage, U1 and U2 are the voltages of the two RC networks in the equivalent circuit, R0 is the ohmic internal resistance of the battery, R1 and R2 are the polarization resistances of the RC network, C1 and C2 are the polarization capacitances of the RC network, Ut is the terminal voltage, and I is the battery current. Based on the second-order RC equivalent circuit model, the state space equation of the lithium-ion battery is derived as follows:

[0014]

[0015] U t,k =U OC (SOC k )-U 1,k -U 2,k -I k R0+v k (3)

[0016] In the formula, SOC k represents the estimated state of charge (SOC) value at time k, Δt is the sampling time, ξ is the battery capacity, k is a discrete time variable, and U OC (SOC k ) is the value of open circuit voltage (OCV), w k is the system process noise, v k is the observation noise; there is a nonlinear relationship between SOC and OCV (state of charge and open circuit voltage). Use the toolbox to import SOC and OCV data for curve fitting to obtain the mapping relationship between SOC and OCV for subsequent analysis and calculation of the second-order equivalent circuit model of the battery:

[0017] The general expression of SOC-OCV mapping relationship is expressed in the following form: OC =f(SOC), where f(SOC) is the mapping function between SOC and OCV;

[0018] Using polynomial fitting, the form is: U OC (SOC) = A1 + A2gSOC + A3gSOC 2 +L+A n gSOC n , where A1, A2LL A n are the fitting coefficients.

[0019] The specific method of step 2 is:

[0020] 2.1 Construct a nonlinear characteristic mathematical model of lithium-ion batteries. The nonlinear model of lithium-ion batteries is described as follows:

[0021]

[0022] Among them, x k Represents the state variable at time k, with x k =[U 1,k ,U 2,k ,SOC k ] T To express; y k represents the observed value at time k; wk-1 represents process noise; v k represents the observation noise; f(g) represents the state function of the nonlinear system; h(g) represents the observation function of the nonlinear system; Q k-1 is the process noise w k-1 The covariance matrix of the prediction model itself represents the noise; R k-1 is the system observation noise v k The covariance matrix of represents the noise of the measurement equipment;

[0023] 2.2 Based on the maximum correlation entropy, generalized mixed entropy is introduced. Given two random variables X and Y, the maximum correlation entropy is defined as:

[0024] V(X,Y)=E[κ(X,Y)]=∫∫κ(x,y)p(x,y)dxdy (5)

[0025] Where E[g] represents the expected operation, κ(g) represents the Mercer kernel function, and p(x, y) represents the joint probability density function of x and y. Based on the maximum correlation entropy, the mixed correlation entropy is defined as:

[0026] M(X,Y)=E[θ1κ1(X,Y)+θ2κ2(X,Y)] (6)

[0027] Where 0<θ 1, θ2<1, θ1+θ2=1, and κ1(g) and κ2(g) are two different kernel functions; the joint probability density function of X and Y is unknown, so the sample mean of the mixed correlation entropy is used for estimation, and the calculation formula is:

[0028]

[0029] Where N is the number of samples, x i and i Represent the i-th element of random variables X and Y respectively; a flexible generalized Gaussian function is used as the kernel function, namely the generalized Gaussian kernel, which is shown below;

[0030]

[0031] Where 0<β is the kernel width parameter, 0<α is the shape parameter, τ=α / (2βΓ(1 / α)) is the normalization constant, and Γ(g) is the gamma function. In equation (7), both κ1(g) and κ2(g) use generalized Gaussian kernels. The error is defined as e i =x i -y i , then formula (9) can be simplified to

[0032]

[0033] When the error e i When is zero, formula (9) reaches its maximum value, which is called generalized mixed maximum correlation entropy (GMMCC);

[0034] 2.3 Based on the generalized mixed maximum correlation entropy obtained in step 2.2 combined with the extended Kalman filter algorithm, the recursive calculation time update and measurement update stages are optimized to perform SOC estimation:

[0035] According to equation (4), the discrete state equation and observation equation are established and linearized:

[0036]

[0037] in

[0038]

[0039] Among them, x k ,y k 、u k is the system state, output and measurement value at time k; A k With B k is the state dynamic characteristics of the system state space model at time k; C k With D k is the measured dynamic characteristics of the system state space model at time k;

[0040] The augmented state expression is reconstructed from formula (10):

[0041]

[0042] Where I is a 2×2 identity matrix; Represents the prior state estimation error and measurement error;

[0043] The error covariance expression is obtained by state reconstruction through formula (11):

[0044]

[0045] Among them, F k 、F p,k|k-1 、F R,k Respectively by P k|k-1 , R k Perform Cholesky decomposition to obtain; by multiplying both sides of equation (11) Obtain a simplified nonlinear recursive expression:

[0046] D k =Z k x k +Ek (13)

[0047]

[0048] Combining equation (9) and equation (16), the cost function is:

[0049]

[0050] Among them, e i,k =d i,k -w i,k x k , N = n + m;

[0051] According to the generalized mixed maximum correlation entropy GMMCC, the optimal posterior state estimate is defined as:

[0052]

[0053] Derivative equation (17) is taken and the derivative result is set to zero, that is, The optimal state estimate is:

[0054]

[0055] Solve equation (19):

[0056]

[0057] Formula (20) is about x k The nonlinear fixed point equation of i,k is the transformation matrix F k The inverse left multiplication of is the same as x in formula (13) k Related; write formula (20) into matrix form, expressed as

[0058]

[0059] in,

[0060]

[0061] Λ P,k =diag(Λ 1,k (e 1,k ),...,Λ n,k (e n,k )) (twenty four)

[0062] Λ R,k =diag(Λ n+1,k (e n+1,k ),...,Λ n+m,k (e n+m,k )) (25)

[0063] Among them, Λ P,k is the weight matrix of the error covariance, Λ R,k is the weight matrix of the measurement noise; according to the discrete state equation and observation equation in equation (10), n and m are the dimensions of the state vector and the measurement vector, respectively; the vector dimensions n and m are set to 3 and 1, respectively; the weight matrix is ​​used to correct the error covariance matrix:

[0064]

[0065] According to equation (26), the prior error covariance and measurement noise covariance optimized by generalized mixed maximum correlation entropy (GMMCC) are obtained:

[0066]

[0067]

[0068] The prior error covariance P is corrected according to the generalized mixed maximum correlation entropy GMMCC. k|k-1 and the measurement noise covariance R k , iteratively update the gain matrix, state and posterior error covariance matrix to complete the accurate estimation of battery SOC.

[0069] The prior error covariance P corrected by the generalized mixed maximum correlation entropy GMMCC in step 3 k|k-1 and the measurement noise covariance R k , iteratively update the gain matrix, state and posterior error covariance matrix, specifically:

[0070] (1) Initialization

[0071]

[0072] (2) One-step prediction of state variables and error covariance

[0073]

[0074] (3) Gain matrix update

[0075]

[0076] (4) State estimation update

[0077]

[0078] (5) Error covariance matrix update

[0079]

[0080] (6) Update of measurement noise variance and process noise variance

[0081]

[0082] A SOC estimation system based on an improved maximum correlation entropy EKF algorithm, comprising:

[0083] The data preprocessing module is used in step 1. It uses a second-order RC equivalent circuit model to describe the transient and dynamic characteristics of the battery, that is, to derive the state space equation of the lithium-ion battery, perform curve fitting on the SOC and OCV data, and obtain the mapping relationship between SOC and OCV to support the data in step 2.

[0084] The state prediction and correction update module is used in step 2. In the generalized hybrid maximum correlation entropy extended Kalman filter algorithm, the current SOC is first predicted using the dynamic model of the battery; the SOC estimate at the previous moment is recursively transferred to the current moment through the state equation to obtain the predicted SOC value and error covariance; then, according to the difference between the measured value and the predicted value, the Kalman gain is calculated using the measurement equation, and the measurement error is optimized based on the generalized hybrid correlation entropy criterion to update the SOC estimate and its error covariance, thereby achieving a more accurate state estimation.

[0085] A SOC estimation device based on an improved maximum correlation entropy EKF algorithm, comprising:

[0086] Memory for storing computer programs;

[0087] A processor is used to implement the SOC estimation method based on the improved maximum related entropy EKF algorithm described in steps 1 to 2 when executing the computer program.

[0088] A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, it can implement SOC estimation based on the improved maximum related entropy EKF algorithm based on the method described in steps 1 to 2.

[0089] Compared with the prior art, the present invention has the following beneficial effects:

[0090] 1. In actual battery management, especially under complex working conditions, the noise of the battery often exhibits non-Gaussian characteristics. This makes the traditional Kalman filtering method susceptible to interference from high noise when estimating SOC, resulting in estimation deviation. Since only one generalized kernel function is used, the performance may degrade when processing complex data and data that are insensitive to kernel parameters. In order to solve this problem, the present invention introduces a generalized hybrid maximum correlation entropy method into the Kalman filtering method, which reduces noise interference, improves the processing performance of complex data and data that are insensitive to kernel functions, reduces SOC estimation deviation, and effectively improves the accuracy of SOC estimation.

[0091] Second, the method of the present invention takes into account the impact of temperature changes on the battery model and noise characteristics. Under different temperature conditions (such as 10°C, 25°C and 40°C), these factors will affect the measurement signal and cause noise changes. The traditional method has poor robustness under these dynamic conditions, while the GMMCC-EKF method proposed in this invention can enable the algorithm to maintain good robustness in the face of complex noise and dynamic environments.

[0092] 3. The present invention obtains the generalized mixed entropy by adopting a kernel function composed of two generalized Gaussian functions, inherits the flexibility of the generalized Gaussian kernel, and uses statistical linearization technology to unify the state error and measurement error in the cost function, and then obtains the optimal estimate of the nonlinear equation through the fixed point iteration method. It has the advantages and innovations of significantly improving the SOC estimation accuracy, strong anti-noise performance, and adaptability to complex dynamic working conditions.

[0093] In summary, the SOC estimation method based on GMMCC-EKF proposed in the present invention solves the shortcomings of traditional methods in non-Gaussian noise environments by optimizing the Kalman filtering process and introducing the generalized mixed maximum correlation entropy criterion, and significantly improves the accuracy and robustness of SOC estimation. Compared with the prior art, this method can better adapt to the complex noise and dynamic conditions in the battery system. The experimental results show that under different temperatures, different battery types, and different operating conditions, the estimation accuracy of the GMMCC-EKF algorithm is improved compared to the extended Kalman filter algorithm (EKF) and the traditional maximum correlation entropy extended Kalman filter (MCC-EKF). Similarly, given the initial value error, the GMMCC-EKF algorithm can quickly converge to the true value. All of these show that the new algorithm provides a more advanced and reliable solution for the optimization of battery management systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0094] In order to more clearly illustrate the embodiments of the present invention, the drawings required for the embodiments will be briefly introduced below. The drawings 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.

[0095] Figure 1 It is the second-order RC equivalent circuit model of the present invention.

[0096] Figure 2 This is the current-voltage curve under DST conditions.

[0097] Figure 3 is the voltage-current curve under NEDC conditions; where: Figure 3 (a) is the current-voltage curve at 10°C; Figure 3 (b) is the current-voltage curve at 25°C; Figure 3 (c) is the current-voltage curve at 40°C.

[0098] Figure 4 are process noise and measurement noise; where, Figure 4 (a) is the network voltage process noise of R1C1; Figure 4 (b) is the network voltage process noise of R2C2; Figure 4 (c) is the process noise estimation of SOC; Figure 4 (d) is the measurement noise.

[0099] Figure 5 is the non-Gaussian noise in the measured current.

[0100] Figure 6 is the SOC estimation and SOC estimation error of GMMCC-EKF, EKF and MCC-EKF for battery No. 1 at 25°C; Figure 6 (a) is the estimated SOC value; Figure 6 (b) is the SOC estimation error value.

[0101] Figure 7 is the SOC estimation and SOC estimation error of GMMCC-EKF, EKF and MCC-EKF for battery No. 2 at 10°C; Figure 7 (a) is the estimated SOC value; Figure 7 (b) is the SOC estimation error value.

[0102] Figure 8 is the SOC estimation and SOC estimation error of GMMCC-EKF, EKF and MCC-EKF for battery No. 2 at 25°C; Figure 8 (a) is the estimated SOC value; Figure 8 (b) is the SOC estimation error value.

[0103] Fig. 9 is the SOC estimation and SOC estimation error of GMMCC-EKF, EKF and MCC-EKF for battery No. 2 at 40°C; Fig. 9 (a) is the estimated SOC value; Fig. 9 (b) is the SOC estimation error value.

[0104] Fig.10 is the SOC estimation and SOC estimation error of GMMCC-EKF, EKF and MCC-EKF for battery No. 2 at 25°C; Fig.10 (a) is the estimated SOC value; Fig.10 (b) is the SOC estimation error value.

[0105] Fig.11 is the SOC estimation and SOC estimation error of GMMCC-EKF, EKF and MCC-EKF for battery No. 2 at 25°C; Fig.11 (a) is the estimated SOC value; Fig.11 (b) is the SOC estimation error value.

[0106] Fig.12 is the SOC estimation result of GMMCC-EKF algorithm under different initial values ​​at 25℃; Fig.12 (a) is the estimated SOC value, Fig.12 (b) is the SOC estimation error value.

[0107] Fig.13 is the SOC estimation result of GMMCC-EKF algorithm under different initial values ​​at 25℃; Fig.13 (a) is the estimated SOC value, Fig.13 (b) is the SOC estimation error value. DETAILED DESCRIPTION

[0108] The present invention will be further described below in conjunction with the embodiments, but it does not constitute any limitation to the present invention. Any limited number of modifications made by anyone within the scope of the claims of the present invention are still within the scope of the claims of the present invention.

[0109] A SOC estimation method based on an improved maximum correlation entropy EKF algorithm, the specific steps are as follows:

[0110] Step 1: Use the second-order RC equivalent circuit model, such as Figure 1 , describing the transient and dynamic characteristics of the battery, that is, deriving the state space equation of the lithium-ion battery, performing curve fitting on the SOC and OCV data, and obtaining the mapping relationship between SOC and OCV;

[0111] Step 2: Based on the second-order RC equivalent circuit model of step 1 and the mapping relationship between SOC and OCV, the state of the second-order RC equivalent circuit model is updated through the generalized hybrid maximum correlation entropy extended Kalman filter algorithm to achieve SOC estimation under different working conditions.

[0112] The specific method of step 1 is:

[0113] The second-order RC equivalent circuit model used is composed of an internal resistance R0 and two RC parallel branches. The internal resistance R0 reflects the voltage drop of the battery when current passes through it, and the RC parallel branches are used to simulate the polarization effect and dynamic voltage change of the battery.

[0114] According to Kirchhoff's law, the equivalent circuit of the second-order RC equivalent circuit model is expressed as:

[0115]

[0116] In the formula, U OC is the open circuit voltage, U1 and U2 are the voltages of the two RC networks in the equivalent circuit, R0 is the ohmic internal resistance of the battery, R1 and R2 are the polarization resistances of the RC network, C1 and C2 are the polarization capacitances of the RC network, Ut is the terminal voltage, and I is the battery current. Based on the second-order RC equivalent circuit model, the state space equation of the lithium-ion battery is derived as follows:

[0117]

[0118] U t,k =U OC (SOC k )-U 1,k -U 2,k -I k R0+v k (3)

[0119] In the formula, SOC k represents the estimated state of charge (SOC) value at time k, Δt is the sampling time, ξ is the battery capacity, k is a discrete time variable, and U OC (SOC k ) is the value of open circuit voltage (OCV), w k is the system process noise, v k is the observation noise; there is a nonlinear relationship between SOC and OCV (state of charge and open circuit voltage). Use the toolbox to import SOC and OCV data for curve fitting to obtain the mapping relationship between SOC and OCV for subsequent analysis and calculation of the second-order equivalent circuit model of the battery:

[0120] The general expression of SOC-OCV mapping relationship is expressed in the following form: OC =f(SOC), where f(SOC) is the mapping function between SOC and OCV;

[0121] Using polynomial fitting, the form is: U OC (SOC) = A1 + A2gSOC + A3gSOC2 +L+A n gSOC n , where A1, A2LL A n are the fitting coefficients.

[0122] Here we select two different lithium-ion batteries with a nominal capacity / nominal voltage of 35Ah / 3.7V LiMn2O4 lithium-ion battery (named battery No. 1, the data of battery No. 1 was obtained by the Advanced Energy Storage Science and Application Research Group of Beijing Institute of Technology) and a 1.5Ah / 3.6V ICR18650 single battery (named battery No. 2, the data of battery No. 2 was measured by the Blue Power CT6001A battery tester) to operate under the dynamic stress test (Dynamic Stress Test, DST) and the New European Driving Cycle (New European Driving Cycle, NEDC) conditions. The temperature of battery No. 1 was measured to be 25℃, and the temperature of battery No. 2 was 10℃, 25℃ and 40℃. The current and voltage curves of DST and NEDC data are as follows Figure 2 and Figure 3 shown.

[0123] Then a sixth-order polynomial is used for fitting. After the fitting is completed, a mathematical expression for representing the relationship between SOC and OCV can be obtained;

[0124] The mapping relationship between SOC and OCV of battery No. 1 is as follows:

[0125] U OC (SOC) = 3.557 + 0.855z + 3.79z 2 -24.65z 3

[0126] +54.45z 4 -52.48z 5 +18.64z 6

[0127] The mapping relationship between SOC and OCV of battery No. 2 is as follows:

[0128] U OC (SOC) = 2.978 + 8.7z - 49.11z 2 +138.6z 3

[0129] -197z 4 +137.3z 5 -37.37z 6

[0130] Where z is the SOC of the battery.

[0131] The specific method of step 2 is:

[0132] 2.1 Construct a nonlinear characteristic mathematical model:

[0133] The nonlinear system of lithium-ion battery is described as

[0134]

[0135] Among them, x k Represents the state variable at time k, with x k =[U 1,k, U 2,k ,SOC k ] T To express; y k represents the observed value at time k; w k-1 represents process noise; v k represents the observation noise; f(g) represents the state function of the nonlinear system; h(g) represents the observation function of the nonlinear system; Q k-1 is the process noise w k-1 The covariance matrix of the prediction model itself represents the noise; R k-1 is the system observation noise v k The covariance matrix of represents the noise of the measurement equipment;

[0136] 2.2 Based on the maximum correlation entropy, generalized mixed entropy is introduced. Given two random variables X and Y, the maximum correlation entropy is defined as:

[0137] V(X,Y)=E[κ(X,Y)]=∫∫κ(x,y)p(x,y)dxdy (5)

[0138] Where E[g] represents the expected operation, κ(g) represents the Mercer kernel function, and p(x, y) represents the joint probability density function of x and y. Based on the maximum correlation entropy, the mixed correlation entropy is defined as:

[0139] M(X,Y)=E[θ1κ1(X,Y)+θ2κ2(X,Y)] (6)

[0140] Among them, 0<θ1,θ2<1,θ1+θ2=1, and κ1(g) and κ2(g) are two different kernel functions; the joint probability density function of X and Y is unknown, so in practical applications, the sample mean estimation of mixed correlation entropy is usually used, and the calculation formula is:

[0141]

[0142] Where N is the number of samples, x i and iRepresent the i-th element of random variables X and Y respectively; a flexible generalized Gaussian function is used as the kernel function, namely the generalized Gaussian kernel, which is shown below;

[0143]

[0144] Where 0<β is the kernel width parameter, 0<α is the shape parameter, τ=α / (2βΓ(1 / α)) is the normalization constant, and Γ(g) is the gamma function. In equation (7), both κ1(g) and κ2(g) use generalized Gaussian kernels. The error is defined as e i =x i -y i , then formula (9) can be simplified to

[0145]

[0146] When the error e i When is zero, formula (9) reaches its maximum value, which is called generalized mixed maximum correlation entropy (GMMCC);

[0147] 2.3 Based on the generalized mixed maximum correlation entropy obtained in step 2.2 combined with the extended Kalman filter algorithm, optimization is performed in the time update and measurement update stages of the recursive calculation to perform SOC estimation:

[0148] According to equation (4), the discrete state equation and observation equation are established and linearized:

[0149]

[0150] in

[0151] D k =-R0

[0152] Among them, x k ,y k 、u k is the system state, output and measurement value at time k; A k With B k is the state dynamic characteristics of the system state space model at time k; C k With D k is the measured dynamic characteristics of the system state space model at time k;

[0153] The augmented state expression is reconstructed from formula (10):

[0154]

[0155] Where I is a 2×2 identity matrix; Represents the prior state estimation error and measurement error;

[0156] The error covariance expression is obtained by state reconstruction of formula (11):

[0157]

[0158] Among them, F k 、F p,k|k-1 、F R,k Respectively by P k|k-1 , R k Perform Cholesky decomposition to obtain; by multiplying both sides of equation (11) Get the simplified nonlinear recursive expression:

[0159] D k =Z k x k +E k (13)

[0160]

[0161] Combining equation (9) and equation (16), the cost function is:

[0162]

[0163] Among them, e i,k =d i,k -w i,k x k , N = n + m;

[0164] According to the generalized mixed maximum correlation entropy GMMCC, the optimal posterior state estimate is defined as:

[0165]

[0166] Derivative equation (17) is taken and the derivative result is set to zero, that is, The optimal state estimate is:

[0167]

[0168] Solve equation (19):

[0169]

[0170] Formula (20) is about x k The nonlinear fixed point equation of i,k is the transformation matrix F k The inverse left multiplication of is the same as x in formula (13) k Related; write formula (20) into matrix form, expressed as

[0171]

[0172] in,

[0173]

[0174] Λ P,k =diag(Λ 1,k (e 1,k ),...,Λ n,k (e n,k )) (twenty four)

[0175] Λ R,k =diag(Λ n+1,k (e n+1,k ),...,Λ n+m,k (e n+m,k )) (25)

[0176] Among them, Λ P,k is the weight matrix of the error covariance, Λ R,k is the weight matrix of the measurement noise; according to the discrete state equation and observation equation in equation (10), n and m are the dimensions of the state vector and the measurement vector, respectively; the vector dimensions n and m are set to 3 and 1, respectively; the weight matrix is ​​used to correct the error covariance matrix:

[0177]

[0178] According to equation (26), the prior error covariance and measurement noise covariance optimized by generalized mixed maximum correlation entropy (GMMCC) are obtained:

[0179]

[0180] According to the GMMCC modified P k|k-1 and R k , iteratively update the gain matrix, state and posterior error covariance matrix to complete the accurate estimation of battery SOC:

[0181] (1) Initialization

[0182]

[0183] (2) One-step prediction of state variables and error covariance

[0184]

[0185] (3) Gain matrix

[0186]

[0187] (4) State estimation update

[0188]

[0189] (5) Error covariance matrix update

[0190]

[0191] (6) Update of measurement noise variance and process noise variance

[0192]

[0193] Simulation experiment and analysis

[0194] In order to verify the effectiveness of the SOC estimation method based on GMMCC-EKF proposed in this invention, the mean absolute error (MAE) and root mean square error (RMSE) evaluation indicators are used to evaluate the performance of the algorithm, which are expressed as follows:

[0195]

[0196] Where: SOC k is the true value; is the estimated value; N is the total number of sampling points.

[0197] Based on the data of battery No. 1 and battery No. 2, the proposed algorithm is compared with the EKF and MCC-EKF algorithms for SOC estimation under two different non-Gaussian noise interferences. This is to evaluate the performance of the algorithm. In order to illustrate the impact of current noise on algorithm estimation, Figure 4 and Figure 5 is the generated non-Gaussian noise as shown below. Figure 4 and Figure 5 , current noise is added.

[0198] In the following simulations, different noise types, temperatures, and initial SOC values ​​are considered to verify the effectiveness of the proposed method compared with the EKF and MCC-EKF methods.

[0199] (1) Battery SOC estimation in a uniform mixed noise environment

[0200] In this section, the mixed noise whose noise follows uniform distribution is called uniform mixed noise, and the mixed noise whose noise follows Laplace distribution is called Laplace mixed noise. Figure 4 and Figure 5 shows the plots of these two noises, and Figure 6 The SOC estimation results and estimation error curves obtained under these two types of noise are shown.

[0201] (2) Verification based on No. 1 battery under DST conditions

[0202] from Figure 6 It can be seen that when the initial value is correct, that is, the initial value is 1, the estimated curve of EKF fluctuates violently, which shows that EKF is very sensitive to non-Gaussian noise. In contrast, MCC-EKF has a certain inhibitory effect under non-Gaussian noise due to the existence of maximum correlation entropy, and the proposed GMMCC-EKF algorithm of the present invention has a more accurate SOC estimation result relative to the first two algorithms, that is, the SOC is closer to the true value because it has a more flexible kernel width selection method. For accurate quantitative analysis and comparison, Table 1 lists the operation time, MAE and RMSE results of all methods. Numerical analysis more intuitively proves that the proposed GMMCC-EKF has good robustness under non-Gaussian noise interference. The evaluation index results of each method under these two types of noise are shown in Table 1.

[0203] Table 1 is a comparison of the estimated performance of No. 1 batteries

[0204] Tab.1 Comparison of estimation performance of No.1 battery

[0205]

[0206] As can be seen from Table 1, although the operation time of the GMMCC-EKF algorithm of the present invention is slightly longer, it shows the best performance in terms of MAE and RMSE. Specifically, the MAE of the GMMCC-EKF algorithm is improved by about 90.3% and 86.0% compared with the EKF algorithm and the MCC-EKF algorithm, respectively. In terms of RMSE, the GMMCC-EKF algorithm is improved by about 90.1% and 83.9% compared with the EKF algorithm and the MCC-EKF algorithm, respectively. The results show that GMMCC-EKF significantly improves the accuracy in SOC estimation, making it more advantageous than EKF and MCC-EKF when processing battery estimation tasks.

[0207] (3) Verification based on No. 2 battery at different temperatures under NEDC conditions

[0208] The above results on battery No. 1 prove that the proposed algorithm can accurately estimate the SOC of lithium-ion batteries at a single temperature. In order to verify the applicability of the GMMCC-EKF algorithm of the present invention under different battery and temperature conditions, simulation tests were carried out at temperatures of 10°C, 25°C and 40°C. Figure 7 (a) and Figure 7 (b) shows the SOC estimation results and estimation errors at 10℃ respectively.

[0209] from Figure 7 It can be seen from (a) that the SOC estimation result based on the GMMCC-EKF algorithm of the present invention is closer to the true value, and the downward trend of the SOC estimation curve is basically consistent with the true SOC curve. Figure 7 From the SOC estimation error of (b), the SOC estimation error based on the GMMCC-EKF algorithm is closer to 0 than that of the other two algorithms, which shows that the proposed algorithm has good robustness.

[0210] Table 2 shows the estimated performance comparison of No. 2 batteries

[0211] Tab.2 Comparison of estimation performance of No.2 battery

[0212]

[0213] As can be seen from Table 2, the GMMCC-EKF algorithm of the present invention shows a significant improvement in accuracy in the SOC estimation of battery No. 2. Specifically, the MAE of the GMMCC-EKF algorithm is improved by about 76.3% and 69.2% compared with the EKF algorithm and the MCC-EKF algorithm, respectively. In terms of RMSE, the GMMCC-EKF algorithm is improved by about 77.4% and 68.2% compared with the EKF algorithm and the MCC-EKF algorithm, respectively. These results show that GMMCC-EKF provides higher accuracy than EKF and MCC-EKF when processing the SOC estimation of battery No. 2.

[0214] Figure 8 The SOC estimation result and estimation error of battery No. 2 at 25°C.

[0215] exist Figure 8 It is shown in the figure that in the initial stage, the SOC estimation values ​​of each algorithm show an increasing trend, which may be due to the dynamic characteristics of the initial battery charging and the influence of measurement noise. However, as time goes by, the GMMCC-EKF algorithm of the present invention gradually converges to the true value, which shows that the algorithm has significant advantages in suppressing noise and interference and optimizing the estimation process. Compared with EKF and MCC-EKF, the latter shows large error fluctuations during the estimation process and cannot be adjusted to the true value in time. Therefore, the GMMCC-EKF algorithm shows higher stability and accuracy in battery SOC estimation, and can better adapt to the complex dynamic behavior of the battery under actual working conditions.

[0216] Table 3 shows the estimated performance comparison of No. 2 batteries

[0217] Tab.3 Comparison of estimation performance of No.2 battery

[0218]

[0219] From the quantitative analysis in Table 3, it can be seen that the MAE of the GMMCC-EKF algorithm of the present invention is improved by about 76.3% and 57.3% compared with the EKF algorithm and the MCC-EKF algorithm, respectively. In terms of RMSE, the GMMCC-EKF algorithm is improved by about 72.4% and 47.4% compared with the EKF algorithm and the MCC-EKF algorithm, respectively. This shows that the GMMCC-EKF algorithm has higher accuracy than EKF and MCC-EKF.

[0220] Fig. 9 The SOC estimation result and estimation error of battery No. 2 at 40°C.

[0221] Fig. 9 The SOC estimation results and their errors of GMMCC-EKF, EKF and MCC-EKF algorithms at 40°C are shown. Fig. 9 In (a), the curve of GMMCC-EKF is closest to the true value and performs best, followed by MCC-EKF, while EKF has the largest deviation. Fig. 9 In (b), the error of GMMCC-EKF is the smallest and the fluctuation is small, which shows its superior accuracy and stability in noisy environment. Overall, GMMCC-EKF outperforms EKF and MCC-EKF in terms of estimation accuracy and error control at 40℃.

[0222] Table 4 shows the estimated performance comparison of No. 2 batteries.

[0223] Tab.4 Comparison of estimation performance of No.2 battery

[0224]

[0225] As can be seen from Table 4, the MAE of the GMMCC-EKF algorithm is improved by about 63.2% and 58.8% compared with the EKF algorithm and the MCC-EKF algorithm, respectively. In terms of RMSE, the GMMCC-EKF algorithm is improved by about 70.5% and 58.2% compared with the EKF algorithm and the MCC-EKF algorithm, respectively. The experimental results show that in a uniform mixed noise environment, the SOC estimation value of the GMMCC-EKF algorithm is closer to the true value, which can effectively improve the accuracy of battery SOC estimation.

[0226] SOC estimation in Laplace mixed noise environment

[0227] In order to further study the accuracy of the proposed algorithm in SOC estimation under different noise environments, the estimation performance of the algorithm in a complex noise environment was tested based on battery No. 1 and battery No. 2 at 25°C. By comparing and analyzing the SOC estimation results with the actual SOC curve, the robustness and accuracy of the algorithm under different noise levels were evaluated. Fig.10 and Fig.11 The SOC estimation results and error analysis under DST and NEDC conditions are shown respectively.

[0228] (1) Verification based on No. 1 battery under DST conditions

[0229] The verification results at 25°C showed that Fig.10 The SOC estimation of battery No. 1 and its estimation error under DST conditions are shown. Fig.10 (a) is the SOC estimation curve of GMMCC-EKF, EKF and MCC-EKF algorithms. The results show that the estimated value of GMMCC-EKF algorithm is more stable and closer to the true value. Fig.10 (b) shows the SOC estimation error. It is obvious that the estimation error of GMMCC-EKF is smaller, indicating that the algorithm has better accuracy and robustness under this condition. This further verifies the effectiveness of the GMMCC-EKF algorithm in battery SOC estimation.

[0230] Table 5 shows the estimated performance comparison of No. 1 battery

[0231] Tab.5 Comparison of estimation performance of No.1 battery

[0232]

[0233] From the results in Table 5, we can see that the MAE of the GMMCC-EKF algorithm is improved by about 79.5% and 64.5% compared with the EKF algorithm and the MCC-EKF algorithm, respectively. In terms of RMSE, the GMMCC-EKF algorithm is improved by about 79.2% and 58.1% compared with the EKF algorithm and the MCC-EKF algorithm, respectively. These data show that the GMMCC-EKF algorithm has obvious advantages in the accuracy of SOC estimation and can effectively improve the accuracy of battery SOC estimation.

[0234] (2) Verification based on No. 2 battery under NEDC conditions

[0235] Through Fig.11 From the analysis, we can see that at 25°C, the SOC estimation results of the GMMCC-EKF algorithm are significantly better than those of the EKF and MCC-EKF algorithms. Fig.11 In (a), the estimated curve of GMMCC-EKF is consistent with the true value, indicating that the algorithm performs well in capturing the dynamic changes of battery SOC. Fig.11 In (b), the error curve of GMMCC-EKF is more stable, and its error fluctuation is smaller than that of EKF and MCC-EKF, showing better estimation accuracy and robustness. These results show the application potential of GMMCC-EKF algorithm in battery SOC estimation.

[0236] Table 6 shows the estimated performance comparison of No. 2 batteries

[0237] Tab.6 Comparison of estimation performance of No.2 battery

[0238]

[0239] As shown in Table 6, the MAE of the GMMCC-EKF algorithm is improved by about 56.8% and 48.3% compared with the EKF algorithm and the MCC-EKF algorithm, respectively. In terms of RMSE, the GMMCC-EKF algorithm is improved by about 66.3% and 39.1% compared with the EKF algorithm and the MCC-EKF algorithm, respectively. In summary, the GMMCC-EKF algorithm has a significant performance improvement in battery SOC estimation compared with traditional algorithms, and can effectively improve the accuracy and stability of battery SOC estimation.

[0240] Robustness Analysis

[0241] The initial SOC has a significant impact on the Kalman filter and its derivative algorithms. Inaccurate initial SOC values ​​may increase the estimation error. This section studies the robustness analysis of different initial SOC values ​​(SOC(0)=1, 0.9, 0.8, 0.7, 0.6) in a uniform mixed noise environment. Fig.12 and Fig.13 They are the SOC estimation and SOC estimation error of battery 1 and battery 2 at 25 under different initial SOCs.

[0242] according to Fig.12 and Fig.13 It can be observed from the results that when the initial SOC setting is inaccurate, the SOC estimation result also converges relatively quickly. When the initial SOC error is smaller, the SOC estimation converges faster. Even when the initial SOC error is large, the SOC estimation curve can still closely follow the downward trend of the actual SOC curve.

[0243] The present invention significantly improves the estimation accuracy and robustness of the lithium-ion battery SOC estimation method based on GMMCC-EKF, especially in non-Gaussian noise environments. The Kalman filter process is optimized by the generalized hybrid maximum correlation entropy criterion, which effectively reduces the estimation error of the traditional method under complex noise. This method solves the accuracy and stability problems of the traditional extended Kalman filter in non-Gaussian noise and practical applications, and provides an innovative battery management optimization solution.

Claims

1. A SOC estimation method based on an improved maximum correlation entropy EKF algorithm, characterized in that: The specific steps are as follows: Step 1: Use a second-order RC equivalent circuit model to describe the transient and dynamic characteristics of the battery, that is, derive the state space equation of the lithium-ion battery, perform curve fitting on the SOC and OCV data, and obtain the mapping relationship between SOC and OCV; Step 2: Based on the second-order RC equivalent circuit model of step 1 and the mapping relationship between SOC and OCV, the state of the second-order RC equivalent circuit model is updated through the generalized hybrid maximum correlation entropy extended Kalman filter algorithm to achieve SOC estimation under different working conditions.

2. The SOC estimation method based on the improved maximum correlation entropy EKF algorithm according to claim 1 is characterized in that: The specific method of step 1 is: The second-order RC equivalent circuit model used is composed of an internal resistance R0 and two RC parallel branches. The internal resistance R0 reflects the voltage drop of the battery when current passes through it, and the RC parallel branches are used to simulate the polarization effect and dynamic voltage change of the battery. According to Kirchhoff's law, the equivalent circuit of the second-order RC equivalent circuit model is expressed as: Where U OC is the open circuit voltage, U1 and U2 are the voltages of the two RC networks in the equivalent circuit, R0 is the ohmic internal resistance of the battery, R1 and R2 are the polarization resistances of the RC network, C1 and C2 are the polarization capacitances of the RC network, Ut is the terminal voltage, and I is the battery current. Based on the second-order RC equivalent circuit model, the state space equation of the lithium-ion battery is derived as follows: U t,k =U OC (SOC k )-U 1,k -U 2,k -I k R0+v k (3) In the formula, SOC k represents the estimated state of charge (SOC) value at time k, Δt is the sampling time, ξ is the battery capacity, k is a discrete time variable, and U OC (SOC k ) is the value of open circuit voltage (OCV), w k is the system process noise, v k is the observation noise; there is a nonlinear relationship between SOC and OCV (state of charge and open circuit voltage). Use the toolbox to import SOC and OCV data for curve fitting to obtain the mapping relationship between SOC and OCV for subsequent analysis and calculation of the second-order equivalent circuit model of the battery: The general expression of SOC-OCV mapping relationship is expressed in the following form: OC =f(SOC), where f(SOC) is the mapping function between SOC and OCV; Using polynomial fitting, the form is: U OC (SOC) = A1 + A2gSOC + A3gSOC 2 +L+A n gSOC n , among which A1, A2L LA n are the fitting coefficients.

3. The SOC estimation method based on the improved maximum correlation entropy EKF algorithm according to claim 1 is characterized in that: The specific method of step 2 is: 2.1 Construct a nonlinear characteristic mathematical model of lithium-ion batteries. The nonlinear model of lithium-ion batteries is described as follows: Among them, x k Represents the state variable at time k, with x k =[U 1,k ,U 2,k ,SOC k ] T To express; y k represents the observed value at time k; w k-1 represents process noise; v k represents the observation noise; f(g) represents the state function of the nonlinear system; h(g) represents the observation function of the nonlinear system; Q k-1 is the process noise w k-1 The covariance matrix of the prediction model itself represents the noise; R k-1 is the system observation noise v k The covariance matrix of represents the noise of the measurement equipment; 2.2 Based on the maximum correlation entropy, generalized mixed entropy is introduced. Given two random variables X and Y, the maximum correlation entropy is defined as: V(X,Y)=E[κ(X,Y)]=∫∫κ(x,y)p(x,y)dxdy (5) Where E[g] represents the expected operation, κ(g) represents the Mercer kernel function, and p(x, y) represents the joint probability density function of x and y. Based on the maximum correlation entropy, the mixed correlation entropy is defined as: M(X,Y)=E[θ1κ1(X,Y)+θ2κ2(X,Y)] (6) Among them, 0<θ1,θ2<1,θ1+θ2=1, and κ1(g) and κ2(g) are two different kernel functions; the joint probability density function of X and Y is unknown, so the sample mean of the mixed correlation entropy is used for estimation, and the calculation formula is: Where N is the number of samples, x i and i Represent the i-th element of random variables X and Y respectively; a flexible generalized Gaussian function is used as the kernel function, namely the generalized Gaussian kernel, which is shown below; Where 0<β is the kernel width parameter, 0<α is the shape parameter, τ=α / (2βΓ(1 / α)) is the normalization constant, and Γ(g) is the gamma function. In equation (7), both κ1(g) and κ2(g) use generalized Gaussian kernels. The error is defined as e i =x i -y i , then formula (9) can be simplified to When the error e i When is zero, formula (9) reaches its maximum value, which is called generalized mixed maximum correlation entropy (GMMCC); 2.3 Based on the generalized mixed maximum correlation entropy obtained in step 2.2 combined with the extended Kalman filter algorithm, optimization is performed in the time update and measurement update stages of the recursive calculation to perform SOC estimation: According to equation (4), the discrete state equation and observation equation are established and linearized: in Among them, x k ,y k 、u k is the system state, output and measurement value at time k; A k With B k is the state dynamic characteristics of the system state space model at time k; C k With D k is the measured dynamic characteristics of the system state space model at time k; The augmented state expression is reconstructed from formula (10): Where I is a 2×2 identity matrix; Represents the prior state estimation error and measurement error; The error covariance expression is obtained by state reconstruction of formula (11): Among them, F k 、F p,k|k-1 、F R,k Respectively by P k|k-1 , R k Perform Cholesky decomposition to obtain; by multiplying both sides of equation (11) Obtain a simplified nonlinear recursive expression: D k =Z k x k +E k (13) Combining equation (9) and equation (16), the cost function is: Among them, e i,k =d i,k -w i,k x k , N = n + m; According to the generalized mixed maximum correlation entropy GMMCC criterion, the optimal posterior state estimate is defined as: Derivative equation (17) is taken and the derivative result is set to zero, that is, The optimal state estimate is: Solve equation (19): Formula (20) is about x k The nonlinear fixed point equation of i,k is the transformation matrix F k The inverse left multiplication of is the same as x in formula (13) k Related; write formula (20) into matrix form, expressed as in, L P,k =diag(Λ 1,k (e 1,k ),...,L n,k (e n,k )) (24) L R,k =diag(Λ n+1,k (e n+1,k ),...,L n+m,k (e n+m,k )) (25) Among them, Λ P,k is the weight matrix of the error covariance, Λ R,k is the weight matrix of the measurement noise; according to the discrete state equation and observation equation in equation (10), n and m are the dimensions of the state vector and the measurement vector, respectively; the vector dimensions n and m are set to 3 and 1, respectively; the weight matrix is ​​used to correct the error covariance matrix: According to equation (26), the prior error covariance and measurement noise covariance optimized by generalized mixed maximum correlation entropy (GMMCC) are obtained: The prior error covariance P is corrected according to the generalized mixed maximum correlation entropy GMMCC. k|k-1 and the measurement noise covariance R k , iteratively update the gain matrix, state and posterior error covariance matrix to complete the accurate estimation of battery SOC.

4. The SOC estimation method based on the improved maximum correlation entropy EKF algorithm according to claim 3 is characterized in that: The prior error covariance P corrected by the generalized mixed maximum correlation entropy GMMCC in step 3 k|k-1 and the measurement noise covariance R k , iteratively update the gain matrix, state and posterior error covariance matrix, specifically: (1) Initialization (2) One-step prediction of state variables and error covariance (3) Gain matrix update (4) State estimation update (5) Error covariance matrix update (6) Update of measurement noise variance and process noise variance 5. A SOC estimation system based on an improved maximum correlation entropy EKF algorithm, characterized in that: include: The data preprocessing module is used in step 1. It uses a second-order RC equivalent circuit model to describe the transient and dynamic characteristics of the battery, that is, to derive the state space equation of the lithium-ion battery, perform curve fitting on the SOC and OCV data, and obtain the mapping relationship between SOC and OCV to support the data in step 2. The state prediction and correction update module is used in step 2. In the generalized hybrid maximum correlation entropy extended Kalman filter algorithm, the current SOC is first predicted using the dynamic model of the battery; the SOC estimation value at the previous moment is recursively transferred to the current moment through the state equation to obtain the predicted SOC value and error covariance; Then, according to the difference between the measured value and the predicted value, the Kalman gain is calculated using the measurement equation, and the measurement error is optimized based on the generalized mixed correlation entropy criterion to update the SOC estimation value and its error covariance, thereby achieving a more accurate state estimation.

6. A SOC estimation device based on an improved maximum correlation entropy EKF algorithm, characterized in that: include: Memory for storing computer programs; A processor is used to implement the SOC estimation method based on the improved maximum related entropy EKF algorithm described in steps 1 to 2 when executing the computer program.

7. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the SOC estimation based on the improved maximum correlation entropy EKF algorithm can be implemented based on the method described in steps 1 to 2.

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