Lithium ion battery state-of-charge estimation method based on GRU-FOEKF joint algorithm

Abstract

The invention relates to the technical field of battery state estimation, in particular to a battery state of charge (SOC) estimation algorithm combining a gated cycle unit (GRU) and a fractional order extended Kalman filter (FOEKF). Aiming at the problem that a traditional fractional order SOC estimation algorithm is highly dependent on an initial value, the initial value can be preliminarily estimated, the precision of a fractional order model is ensured, and the stability and adaptability of the algorithm are enhanced. According to the method, the time sequence features in the battery operation process are extracted through the GRU, dynamic error correction is carried out in combination with the FOEKF, and estimation deviation caused by improper selection of initial values is effectively reduced. Experiments show that under the environment of large temperature change, compared with a traditional GRU and a fractional order improved algorithm, the method has higher estimation precision under the condition of the same initial value, even if the initial noise error is large, the average absolute error is still lower than 0.017, the method can be widely applied to a battery management system, and the SOC estimation precision and robustness of an electric vehicle and an energy storage system are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of batteries, and particularly to a method for estimating the state of charge of a lithium-ion battery based on a GRU-FOEKF combined algorithm. Background Art

[0002] With the continuous popularization of fuel-powered vehicles, the problems of fossil energy consumption and environmental pollution caused by them have become global challenges. In this situation, efficient transportation vehicles integrating clean energy technologies are leading the global automotive industry towards a sustainable development model. As the core power unit of new energy vehicles, the lithium-ion battery system has become the preferred solution for energy storage devices of electric transportation equipment due to its significant energy density advantages, optimized charge and discharge performance, compact structure design, and excellent cycle stability and other key characteristics.

[0003] In the battery state assessment system, the method for predicting the state of charge (SOC) occupies a core position. High-precision and fast-converging SOC estimation can provide more accurate range prediction, expand the available range of SOC, and effectively avoid the damage to the battery caused by overcharging and over-discharging. This not only prolongs the battery life but also reduces safety hazards such as performance degradation, overheating, or fire and explosion.

[0004] Model-based SOC estimation strategies include integer-order and fractional-order types. The traditional integer-order modeling framework has dominated past research due to its high parameter identification ability, low state variable dimension, and strong compatibility with filtering algorithms. Among them, the second-order RC equivalent model has become a typical implementation due to its simple topological structure and convenient experimental verification. Based on this framework, extended Kalman filter systems (such as EKF, AEKF) and unscented Kalman filter systems (such as UKF, AUKF) have been derived, forming a complete time-domain state observer technology chain. However, the polarization capacitance exhibits non-integer-order characteristics during the battery discharge process, prompting researchers to introduce fractional-order calculus theory to reconstruct the state equation and replace the traditional integer-order model with a fractional-order model to achieve precise matching of the dynamic characteristics of the capacitor voltage and the electrochemical response. Based on this theoretical breakthrough, fractional-order estimation algorithms such as FOEKF and FOAEKF have been developed.

[0005] In the two types of methods proposed above, a large number of researchers have found that neural networks can be combined with modeling algorithms to further improve the accuracy of the final estimation results and avoid some of the more difficult problems. However, there are still problems with traditional integration of integer-order models and neural networks: First, the fractional-order relaxation characteristics of polarization capacitance are not considered, resulting in quantization errors in the output voltage values of the model, which in turn leads to an error accumulation effect; Second, due to the introduction of fractional-order coefficients in the fractional-order state correction equation, its correction process is different from that of integer-order, resulting in the state estimation value deviating from the true operating conditions. The above technical defects together lead to significant systematic errors in the traditional fusion strategy in the fractional-order dynamic response scenario. Summary of the Invention

[0006] To solve the above problems, this paper proposes an estimation method strategy that combines the GRU algorithm and the FOEKF algorithm, combines the neural network estimation results with the fractional-order model, and improves the final estimation accuracy by modifying the proportionality coefficient K_k and the state transition matrix.

[0007] An estimation method combining GRU and FOEKF proposed by the present invention adopts the technical solution including the following steps:

[0008] Step a, conduct hybrid power pulse characteristic experiments (HPPC) at 15°C, 25°C, and 35°C, collect battery discharge data, and fit the relationship diagram between the open-circuit voltage and SOC;

[0009] Step b, establish a second-order fractional-order model based on the second-order RC equivalent circuit to obtain the mathematical expression and state-space equation of the second-order fractional-order model;

[0010] Step c, use the whale algorithm to identify the parameters of the second-order fractional-order model;

[0011] Step d, use the GRU algorithm to estimate the initial state of charge of the battery, and introduce the FOEKF algorithm after the GRU algorithm to filter and correct errors.

[0012] As a further improvement of the present invention, in step a, when conducting the hybrid power pulse characteristic experiment and collecting battery discharge data, the specific steps are as follows:

[0013] Step a1, in a constant-temperature test environment, set three temperature gradients of 15°C, 25°C, and 35°C respectively, and conduct hybrid power pulse characteristic experiments on lithium-ion batteries;

[0014] Step a2, the GRU algorithm uses any three of the experiments for mutual training and randomly mixes them with each other in the loop drive;

[0015] Step a3: Based on the least squares support vector machine algorithm, use the obtained test data to fit the relationship graph between the open circuit voltage and SOC of the battery.

[0016] As a further improvement of the present invention, in step b, a second-order fractional-order model is established based on the second-order RC equivalent circuit to obtain the mathematical expression and state-space equation of the second-order fractional-order model. The specific formulas are as follows:

[0017] Mathematical expression:

[0018]

[0019] State-space equation:

[0020]

[0021] Combining the above formula with the ampere-hour integration method gives a discrete and decentralized second-order RC model:

[0022]

[0023] U k =C k x k -I k R0+E+v k

[0024] Where C k =[-1,-1,0], state vector x k =[U1(k),U2(k),SOC(k)] T , and fractional-order factor w k is the system noise, v k is the measurement noise, both obey the normal distribution and are independent zero-mean Gaussian white noises, and the covariance matrices are Q k and R k .

[0025] As a further improvement of the present invention, in step c, the whale algorithm is used to identify the parameters of the second-order fractional-order model. The specific formula is as follows:

[0026] Error minimization objective function:

[0027]

[0028] Where, y true (t i ) is the experimental data, y model (t i ,θ) is the simulation output of the fractional-order model

[0029] Parameter optimization steps:

[0030] Step c1, set the whale population size: N, individual position: X i =(x i1 ,x i2 ,...,x iD ), maximum number of iterations: T max , parameters: α, spiral shape constant b;

[0031] Step c2, calculate the fitness value f(X i ) of each whale individual based on the experimental data, and record the current optimal solution X * ;

[0032] Step c3, update the whale individual positions using the following three stages:

[0033] Encircling prey (p < 0.5, |A| < 1), the whale approaches the current optimal individual:

[0034] D = |C·X * (t) - X(t)|,

[0035] X(t + 1) = X * (t) - A·D

[0036] Bubble-net attack (p < 0.5, |A| < 1), the whale approaches the prey along a spiral path:

[0037] X(t + 1) = D′·e bl ·cos(2πl) + X * (t)

[0038] Random search (|A| ≥ 1), randomly select other whales as a reference for global search:

[0039] D = |C·X rand (t) - X(t)|,

[0040] X(t + 1) = X rand (t) - A·D

[0041] Step c4, repeat the search until convergence or the maximum number of iterations is reached, and output the optimal parameter combination.

[0042] As a further improvement of the present invention, in step d, the preprocessed battery data is input into the constructed GRU algorithm, and the battery SOC estimated value is output through its dual-gate coupling mechanism. The output SOC estimated value is used as the input of the FOEKF, and through the dynamic adjustment of the process noise covariance and the state prediction equation, the Kalman gain is calculated to correct the error of the estimated value, and the optimized final state of charge value SOC is output. The specific steps are as follows;

[0043] Step d1, GRU algorithm:

[0044] z t = σ(W z x t + U z h t-1 + b z )

[0045] r t = σ(W r x t + U r h t-1 + b r )

[0046]

[0047] where σ is the Sigmoid activation function, ⊙ represents element-wise multiplication, and W, U, b are the trainable parameters of the network.

[0048] Step d2, FOEKF algorithm:

[0049] System modeling:

[0050] Dαx k - f(x k , u k , w k )

[0051] y k - h(x k , v k )

[0052] where D α x k is the fractional derivative, α is the fractional order (0 < α ≤ 1), x k is the state variable, u k is the control input, w k and v k are the process noise and measurement noise respectively, y k is the observed value, and f(·) and h(·) are the state transition and observation functions of the system respectively.

[0053] Predicted state value:

[0054] x k|k-1 = f(x k-1 , u k-1 )

[0055] Predicted error covariance:

[0056]

[0057] Among them: F k is the Jacobian matrix of the state transition matrix.

[0058] Calculate the observation error:

[0059] y k - h(x k|k-1 )

[0060] Calculate the Jacobian matrix of the observation matrix:

[0061]

[0062] Calculate the Kalman gain:

[0063]

[0064] Update the state estimate:

[0065] x k = x k|k-1 + K k (y k - h(x k|k-1 ))

[0066] Update the error covariance:

[0067] P k = (I - K k H k )P k|k-1

[0068] Step d3, GRU - FOEKF joint algorithm:

[0069] Obtain the initial variable SOC+ of the state equation of the filtering algorithm through the basic training of the neural network. Therefore, the mathematical model in the above second - order model becomes the mathematical model:

[0070]

[0071] U k = C k x k - I k R0 + E + v k

[0072] Among them C k = [-1, -1, 0], the state vector x k = [U1(k), U2(k), SOC + (k)] T , and the fractional - order factor w k is the system noise, v kFor measuring noise, all obey the normal distribution.

[0073] The Kalman gain K_k also changes specifically with the change of the fractional order, from the basic;

[0074]

[0075] becomes;

[0076]

[0077] Compared with the prior art, the technical solution of the present invention has the following advantages:

[0078] (1) Combining the strategies of GRU and FOEKF effectively solves the problem of large initial error of FOEKF.

[0079] (2) Adopting the combined strategy of GRU and FOEKF solves the problem of increased training time when improving the accuracy of the neural network.

[0080] (3) Through the algorithm combined strategy, the problem of error accumulation in the estimation process of the FOEKF algorithm is overcome. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] Figure 1 is the system block diagram of the present invention;

[0082] Figure 2 is the open-circuit voltage and SOC fitting diagram of the present invention;

[0083] Figure 3 is the schematic diagram of the second-order fractional equivalent circuit model of the lithium battery of the present invention;

[0084] Figure 4 is the schematic diagram of the GRU-FOEKF combined algorithm flow of the present invention;

[0085] Figure 5 is the comparison diagram of SOC estimation results under the 25°C HPPC working condition of the present invention;

[0086] Figure 6 is the comparison diagram of SOC estimation errors under the 25°C HPPC working condition of the present invention; DETAILED DESCRIPTION OF THE INVENTION

[0087] The following will further describe in detail the specific embodiments of the present invention with reference to the drawings Specific Embodiment 1

[0089] A method for estimating the state of charge of a lithium-ion battery based on the GRU-FOEKF combined algorithm in this specific embodiment, as Figure 1 shown, includes the following steps:

[0090] Step a: Conduct mixed power pulse characteristic experiments at 15°C, 25°C, and 35°C, collect battery discharge data, and fit the relationship expression between the open-circuit voltage and SOC.

[0091] Step b: Establish a second-order fractional-order model based on the second-order RC equivalent circuit, and obtain the mathematical expression and state-space equation of the second-order fractional-order model.

[0092] Step c: Use the whale algorithm to identify the parameters of the second-order fractional-order model.

[0093] Step d: Use the GRU algorithm to estimate the initial state of charge of the battery, and introduce the FOEKF algorithm after the GRU algorithm for filtering and error correction. Specific Embodiment 2

[0095] A method for estimating the state of charge of a lithium-ion battery based on the GRU-FOEKF joint algorithm in this specific embodiment further limits on the basis of Specific Embodiment 1:

[0096] As Figure 2 shown, in step a for conducting the mixed power pulse characteristic experiment, collecting battery discharge data, and fitting the relationship expression between the open-circuit voltage and SOC, the specific steps are as follows:

[0097] Step a1: In a constant-temperature test environment, set three temperature gradients of 15°C, 25°C, and 35°C respectively, and conduct the mixed power pulse characteristic experiment on the lithium-ion battery.

[0098] Step a2: The GRU algorithm uses any three of the experiments for mutual training and randomly mixes them with each other in the cyclic drive.

[0099] Step a3: Based on the least squares support vector machine algorithm, use the obtained test data to fit the relationship graph between the open-circuit voltage and SOC of the battery. Specific Embodiment 3

[0101] A method for estimating the state of charge of a lithium-ion battery based on the GRU-FOEKF joint algorithm in this specific embodiment further limits on the basis of Specific Embodiment 2:

[0102] As Figure 3 shown, in step b for establishing a second-order fractional-order model based on the second-order RC equivalent circuit and obtaining the mathematical expression and state-space equation of the second-order fractional-order model, the specific formulas are as follows:

[0103] Mathematical expression:

[0104]

[0105] Space state equation:

[0106]

[0107] Combining the above equation with the ampere-hour integration method gives a discrete and decentralized second-order RC model:

[0108]

[0109] U k =C k x k -I k R0+E+v k

[0110] where C k =[-1,-1,0], the state vector x k =[U1(k),U2(k),SOC(k)] T , and the fractional-order factor w k is the system noise, v k is the measurement noise, both follow a normal distribution, and are independent zero-mean Gaussian white noises, with covariance matrices Q k and R k . Specific implementation method four:

[0112] A method for estimating the state of charge of a lithium-ion battery based on the GRU-FOEKF joint algorithm in this specific implementation method further limits on the basis of the specific implementation method three:

[0113] In step c, the whale algorithm is used to identify the parameters of the second-order fractional-order model, and the specific formula is as follows:

[0114] Error minimization objective function:

[0115]

[0116] where, y true (t i ) is the experimental data, y model (t i ,θ) is the simulation output of the fractional-order model

[0117] Parameter optimization steps:

[0118] Step c1, set the whale population size: N, the individual position: X i =(x i1 ,x i2 ,...,x iD ), the maximum number of iterations: T max, Parameters: α, helical shape constant b;

[0119] Step c2, calculate the fitness value f(X i ) of each whale individual based on the experimental data, and record the current optimal solution X * ;

[0120] Step c3, update the positions of whale individuals using the following three stages:

[0121] Encircling the prey (p < 0.5, |A| < 1), the whale approaches the current optimal individual:

[0122] D = |C·X * (t) - X(t)|,

[0123] X(t + 1) = X * (t) - A·D

[0124] Bubble-net attack (p < 0.5, |A| < 1), the whale approaches the prey along a spiral path:

[0125] X(t + 1) = D′·e bl ·cos(2πl) + X * (t)

[0126] Random search (|A| ≥ 1), randomly select other whales as references for global search:

[0127] D = |C·X rand (t) - X(t)|,

[0128] X(t + 1) = X rand (t) - A·D

[0129] Step c4, repeat the search until convergence or the maximum number of iterations is reached, and output the optimal parameter combination. Specific implementation method five:

[0131] A lithium-ion battery state of charge estimation method based on the GRU-FOEKF joint algorithm in this specific implementation method is further limited on the basis of the specific implementation method four:

[0132] As Figure 4 shown, in step d, the preprocessed battery data is input into the constructed GRU algorithm, and the battery SOC estimation value is output through its dual-gate coupling mechanism. The output SOC estimation value is used as the input quantity of the FOEKF. After dynamically adjusting the process noise covariance and the state prediction equation, the Kalman gain is calculated to correct the error of the estimation value, and the optimized final state of charge value SOC is output. The specific steps are as follows;

[0133] Step d1, GRU algorithm:

[0134] z t = σ(W z x t + U z h t-1 + b z )

[0135] r t = σ(W r x t + U r h t-1 + b r )

[0136]

[0137] where σ is the Sigmoid activation function, ⊙ represents element-wise multiplication, and W, U, and b are the trainable parameters of the network.

[0138] Step d2, FOEKF algorithm:

[0139] System modeling:

[0140] Dαx k - f(x k , u k , w k )

[0141] y k - h(x k , v k )

[0142] where D α x k is the fractional derivative, α is the fractional order (0 < α ≤ 1), x k is the state variable, u k is the control input, w k and v k are the process noise and measurement noise respectively, y k is the observation value, and f(·) and h(·) are the state transition and observation functions of the system respectively.

[0143] Predicted state value:

[0144] x k|k-1 = f(x k-1 , u k-1 )

[0145] Predicted error covariance:

[0146]

[0147] where: F kis the Jacobian matrix of the state transition matrix.

[0148] Calculate the observation error:

[0149] y k -h(x k|k-1 )

[0150] Calculate the Jacobian matrix of the observation matrix:

[0151]

[0152] Calculate the Kalman gain:

[0153]

[0154] Update the state estimate:

[0155] x k =x k|k-1 +K k (y k -h(x k|k-1 ))

[0156] Update the error covariance:

[0157] P k =(I-K k H k )P k|k-1

[0158] Step d3, GRU-FOEKF joint algorithm:

[0159] Obtain the initial variable SOC+ of the state equation of the filtering algorithm through the basic training of the neural network. Therefore, the mathematical model in the above second-order model becomes the mathematical model:

[0160]

[0161] U k =C k x k -I k R0+E+v k

[0162] where C k =[-1,-1,0], the state vector x k =[U1(k),U2(k),SOC + (k)] T , and the fractional-order factor w k is the system noise, v k is the measurement noise, both of which follow a normal distribution.

[0163] The Kalman gain K_k also changes specifically with the variation of the fractional order, starting from the basic;

[0164]

[0165] becomes;

[0166]

[0167] The experimental results are as Figure 5 and Figure 6 shown. It can be seen from the figure that under the HPPC working condition, compared with the traditional neural network algorithm and the fractional-order extended Kalman filter algorithm, the accuracy of this algorithm has been significantly improved. At the same time, from the results obtained under the HPPC working conditions at three different temperatures of 15°C, 25°C, and 35°C, it can be seen that within a wide temperature range, the robustness and accuracy of this algorithm have still been significantly improved.

[0168] It should be noted that the above specific implementation manners only exemplarily illustrate the principles and effects of the present invention, rather than limiting the present invention. Any person familiar with this technology can modify or change the above specific implementation manners without departing from the spirit and scope of the present invention. Therefore, all equivalent modifications or changes completed by those with ordinary knowledge in the technical field without departing from the spirit and technical ideas disclosed by the present invention should still be covered by the claims of the present invention.

Claims

1. A method for estimating the state of charge of a lithium-ion battery based on the GRU-FOEKF joint algorithm, characterized in that The method includes the following steps: a) Conduct mixed power pulse characteristic experiments at 15°C, 25°C, and 35°C, collect battery discharge data, and fit a relationship graph between the open-circuit voltage and the SOC; b) Establish a second-order fractional-order model based on the second-order RC equivalent circuit, and obtain the mathematical expression and state-space equation of the second-order fractional-order model; c) Use the whale algorithm to identify the parameters of the second-order fractional-order model; d) Use the GRU algorithm to estimate the initial state of charge of the battery, and introduce the FOEKF algorithm after the GRU algorithm for filtering and error correction.

2. A method for estimating the state of charge of a lithium-ion battery based on the GRU-FOEKF joint algorithm according to claim 1, wherein in step a, when conducting the mixed power pulse characteristic experiment and collecting the battery discharge data, the specific steps are as follows: Step a1, in a constant-temperature test environment, set three temperature gradients of 15°C, 25°C, and 35°C respectively, and conduct mixed power pulse characteristic experiments on the lithium-ion battery; Step a2, the GRU algorithm uses any three of the experiments for mutual training and randomly mixes with each other in the cyclic drive; Step a3, based on the least squares support vector machine algorithm, use the obtained test data to fit a relationship graph between the open-circuit voltage and the SOC of the battery.

3. A method for estimating the state of charge of a lithium-ion battery based on the GRU-FOEKF joint algorithm according to claim 2, wherein the mathematical expression and state-space equation of the second-order fractional-order model in step b are as follows: Mathematical expression: V(t) = E - R0I(t) - R1I(t)α1 - R2I(t)α2 State-space equation: Combining the above formula with the ampere-hour integration method to obtain a discrete second-order RC model: U k = C k x k - I k R0 + E + v k where C k = [-1, -1, 0], the state vector x k = [U1(k), U2(k), SOC(k)] T , and the fractional order factor w k is the system noise, v k is the measurement noise, both of which follow a normal distribution and are independent zero-mean Gaussian white noises, with covariance matrices Q k and R k .

4. A method for estimating the state of charge of a lithium-ion battery based on the GRU-FOEKF joint algorithm according to claim 3, wherein in step c, an error minimization objective function is adopted and the whale algorithm is used for parameter optimization. The specific formula is as follows: Error minimization objective function: where y true (t i ) is the experimental data, and y model (t i , θ) is the simulation output of the fractional-order model Parameter optimization steps: Step c1, set the whale population size: N, individual position: X i =(x i1 ,x i2 ,...,x iD ), maximum number of iterations: T max , parameters: α, spiral shape constant b; Step c2, calculate the fitness value f(X i ) of each whale individual based on the experimental data, and record the current optimal solution X * ; Step c3, update the position of the whale individual in the following three stages: Surrounding the prey (p < 0.5, |A| < 1), the whale approaches the current optimal individual; D = |C·X * (t) - X(t)|, X(t + 1) = X * (t) - A·D Bubble net attack (p < 0.5, |A| < 1), the whale approaches the prey in a spiral path; X(t + 1) = D′·e bl ·cos(2πl) + X * (t) Random search (|A| ≥ 1), randomly select other whales as references for global search; D = |C·X rand (t) - X(t)|, X(t + 1) = X rand (t) - A·D Step c4, repeat the search until convergence or reach the maximum number of iterations, and output the optimal parameter combination.

5. A method for estimating the state of charge of a lithium-ion battery based on the GRU-FOEKF joint algorithm according to claim 4, wherein in step d, the GRU algorithm is used to estimate the initial state of charge of the battery, and the FOEKF algorithm is introduced after the GRU algorithm for filtering and error correction. The specific steps are as follows: Step d1, GRU algorithm: z t = σ(W z x t + U z h t-1 + b z ) r t = σ(W r x t + U r h t-1 + b r ) where σ is the Sigmoid activation function, ⊙ represents element-wise multiplication, and W, U, b are the trainable parameters of the network. Step d2, FOEKF algorithm: System modeling: D α x k -f(x k ,u k ,w k ) y k -h(x k ,v k ) Among them, D α x k is the fractional derivative, α is the fractional order (0 < α ≤ 1), x k is the state variable, u k is the control input, w k and v k are the process noise and measurement noise respectively, y k is the observation value, f(·) and h(·) are the state transition and observation functions of the system respectively. Predicted state value: x k|k-1 = f(x k-1 , u k-1 ) Prediction error covariance: where: F k is the Jacobian matrix of the state transition matrix. Calculate the observation error: y k -h(x k|k-1 ) Calculate the Jacobian matrix of the observation matrix: Calculate the Kalman gain: Update the state estimate: x k = x k|k-1 + K k (y k - h(x k|k-1 )) Update the error covariance: P k = (I - K k H k )P k|k-1 Step d3, GRU-FOEKF joint algorithm: The initial variable SOC+ of the state equation of the filtering algorithm is obtained through the basic training of the neural network. Therefore, the mathematical model in the above second-order model becomes the mathematical model: U k = C k x k - I k R0 + E + v k Among them C k = [-1, -1, 0], the state vector x k = [U1(k), U2(k), SOC + (k)] T , and the fractional-order factor w k is the system noise, v k is the measurement noise, both of which follow a normal distribution. The Kalman gain K_k will also change specifically with the change of the fractional order. From the basic; Becomes;

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