Lithium-ion battery soc estimation method fusing grid search and adaptive filtering

Abstract

This application relates to the field of battery management technology, and in particular to a lithium-ion battery SOC estimation method that integrates grid search and adaptive filtering. The method includes constructing an equivalent circuit model of the lithium-ion battery; identifying parameters of the equivalent circuit model based on AFFRLS and dynamically correcting the parameter values; performing filtering operations on the SOC using an improved filtering algorithm; maintaining an innovation sequence composed of voltage estimation errors through a sliding window; and dynamically updating the process noise covariance matrix based on the innovation sequence. Q The grid search (GS) algorithm is used to optimize within a predefined parameter space to determine the process noise covariance matrix. Q The optimal initial value is obtained; by fusing the parameter identification results, the filtering estimation results of the improved filtering algorithm, and the optimal initial value, the final state of charge estimate is output. This achieves high accuracy, strong robustness, and wide adaptability to various operating conditions in the state of charge estimation of lithium-ion batteries, effectively avoiding estimation divergence and initial value deviation problems.

Description

Technical Field

[0001] This application relates to the field of battery management technology, and more specifically, to a method for estimating the state of charge (SOC) of a lithium-ion battery that integrates grid search and adaptive filtering. Background Technology

[0002] State of Charge (SOC), as a core indicator of the Battery Management System (BMS), directly determines the safety and reliability of lithium-ion batteries. Currently, mainstream SOC estimation methods can be divided into three categories: The first category is traditional methods, including the coulomb counting method and the open-circuit voltage method. However, the coulomb counting method relies on the initial SOC value and integral calculations, and the error accumulates over time. The open-circuit voltage method requires a long period of rest, which cannot meet the needs of online estimation. The second category is data-driven methods, such as neural networks (NN) and support vector machines (SVM). While these can handle nonlinear problems, they rely on a large amount of high-quality training data, and their generalization ability is limited by operating conditions. The third category is model-driven methods, based on equivalent circuit models and filtering algorithms, which are currently the mainstream solutions in the industry. Among them, Recursive Least Squares (RLS) is used to identify battery parameters online, but the fixed forgetting factor can easily lead to lag in parameter updates; EKF is difficult to adapt to system nonlinearity and time-varying noise; AEKF can adjust the process noise covariance matrix Q online, but the selection of the initial Q matrix depends on experience, which can easily cause estimation divergence or decrease in accuracy.

[0003] Furthermore, existing technologies suffer from several common drawbacks: First, they are sensitive to initial parameters. The initial value of the Q matrix in EKF and AEKF significantly affects convergence, and improper values ​​can easily lead to divergence in SOC estimation under complex conditions. Second, parameter tracking is lagging. Traditional fixed forgetting factor RLS cannot dynamically adapt to the time-varying characteristics of parameters such as resistance and capacitance during charge-discharge cycles, increasing identification errors and affecting SOC estimation accuracy. Third, they have poor adaptability to operating conditions. A single algorithm cannot simultaneously adapt to high-dynamic operating conditions (such as US06) and wide temperature ranges, resulting in significant errors in low-temperature and high-current fluctuation scenarios. Therefore, how to avoid errors caused by improper selection of the initial Q matrix and provide a lithium-ion battery state-of-charge estimation method with high estimation accuracy, robustness, and wide adaptability to operating conditions has become an urgent technical problem to be solved. Summary of the Invention

[0004] In view of this, this application provides a lithium-ion battery SOC estimation method that integrates grid search and adaptive filtering to solve the above-mentioned technical problems.

[0005] The technical solution provided in this application is as follows: A lithium-ion battery SOC estimation method integrating grid search and adaptive filtering includes: Construct an equivalent circuit model for a lithium-ion battery; The equivalent circuit model is parameter identified and the parameter values ​​are dynamically corrected based on the adaptive forgetting factor recursive least squares method (AFFRLS). An improved filtering algorithm is used to filter the State of Charge (SOC). A sliding window is used to maintain the innovation sequence composed of voltage estimation errors, and the process noise covariance matrix is ​​dynamically updated based on the innovation sequence. Q ; The grid search (GS) algorithm is used to optimize within a preset parameter space to determine the process noise covariance matrix. Q The optimal initial value; By integrating the parameter identification results, the filtering estimation results of the improved filtering algorithm, and the optimal initial value, the final state of charge estimate is output.

[0006] In one possible implementation, the equivalent circuit model is a second-order RC equivalent circuit model; After constructing the second-order RC equivalent circuit model of a lithium-ion battery, the method further includes: Based on the aforementioned second-order RC equivalent circuit model, establish the state equations and observation equations of the second-order RC model system. Determine the time-varying parameters and state vectors to be identified in the second-order RC equivalent circuit model; wherein, the time-varying parameters include ohmic resistance. R 0. Electrochemical polarization resistance R 1. Concentration polarization resistance R 2. Capacitor C 1. C 2; The state vector is represented as In the formula, V 1 and V 2 represents the electrochemical polarization voltage and the concentration polarization voltage, respectively.

[0007] One possible implementation involves using the Adaptive Forgetting Factor Recursive Least Squares (AFFRLS) method to identify parameters of the equivalent circuit model and dynamically adjust the parameter values, including: Collect the actual measured value and the model estimated value of the battery terminal voltage, and determine the voltage estimation error; The forgetting factor in AFFRLS is dynamically adjusted based on the voltage estimation error, and based on the adjusted forgetting factor... λThe system assigns weights to historical data and current measurement data, and performs identification calculations and value corrections on time-varying parameters in the equivalent circuit model. Specifically, when the voltage error increases, the forgetting factor is reduced and the weight of the current measurement data is increased; when the voltage error decreases, the forgetting factor is increased and the weight of the current measurement data is decreased.

[0008] In one possible implementation, the forgetting factor in the algorithm is dynamically adjusted based on the voltage estimation error. λ It also includes: Introducing adjustable gain η and voltage offset factor ε Forgetting factor through continuous mapping function λ Smoothing adjustment, adjusted forgetting factor λ Represented as:

[0009] In the formula, This indicates the voltage estimation error. This represents the smoothing factor for different voltage estimation errors before adjustment.

[0010] In one possible implementation, the noise covariance matrix of the process is dynamically updated based on the innovation sequence. Q ,include: The innovation sequence is defined as the deviation between the actual measured value and the model estimate of the battery terminal voltage. Configure a fixed-length sliding window to store the latest generated information data in real time; Calculate the covariance of all new data within the sliding window; By introducing a decay memory factor and calculating the covariance using an exponential weighting method, the updated process noise covariance matrix is ​​obtained. Q .

[0011] In one possible implementation, before using the grid search (GS) algorithm to optimize within a preset parameter space, the method further includes: By systematically searching the optimal parameter space under different operating conditions and temperature conditions. Q = [ Q 1, Q 2, Q 3] ; among which, Q 1 represents the variance of capacitor voltage noise in a first-order RC network. Q 2 represents the variance of the capacitor voltage noise in the second-order RC network. Q 3 represents the SOC state noise variance.

[0012] In one possible implementation, the optimization objective of the grid search GS algorithm is to minimize the root mean square error (RMSE) of the state of charge estimation, and the process noise covariance matrix... Q The parameter space includes the first-order RC network capacitor voltage noise variance. Q 1. Variance of capacitor voltage noise in a second-order RC network Q 2 and SOC state noise Q 3; The determination process noise covariance matrix Q The optimal initial values ​​include Based on prior knowledge and preliminary experimental results, in logarithmic space... Q 1. Q 2. Q Define the boundaries of the parameter range for parameter 3; Set the sampling density ρ for the grid search, perform a systematic traversal within the parameter space, and determine the root mean square error (RMSE) of the state of charge estimation as the objective. Q The optimal initial value of the matrix.

[0013] Compared with the prior art, the technical solution provided in this application has the following beneficial effects: This application improves the battery time-varying parameter tracking capability by optimizing the initial value of the noise covariance matrix through grid search and combining it with the adaptive forgetting factor recursive least squares method, thus significantly improving the estimation accuracy; relying on the innovation sequence-based... Q The online matrix adjustment mechanism and parameter pre-convergence mechanism effectively avoid the estimation divergence problem that is prone to occur in traditional methods, while offsetting the negative impact of initial value deviation, giving the scheme strong robustness. In addition, the linkage between the second-order RC equivalent circuit model and each algorithm module allows the scheme to adapt to a variety of dynamic operating conditions and temperature environments, with wide operating condition adaptability, and can stably meet the battery state of charge estimation requirements in different scenarios. Attached Figure Description

[0014] Figure 1 This is a flowchart of a lithium-ion battery SOC estimation method that integrates grid search and adaptive filtering, provided in Embodiment 1 of this application.

[0015] Figure 2 The 2RC equivalent circuit diagram is provided for Embodiment 1 of this application.

[0016] Figures 3-4 This is a flowchart of a lithium-ion battery SOC estimation method that integrates grid search and adaptive filtering, provided in Embodiment 2 of this application.

[0017] Figure 5 This is a schematic diagram showing the comparison of voltage estimation based on different operating conditions under different temperature conditions, as provided in Embodiment 3 of this application.

[0018] Figure 6 This is a schematic diagram of convergence analysis for different initial SOC values ​​provided in Embodiment 4 of this application.

[0019] Figure 7 This is a schematic diagram of RMSE and MAE analysis under the same density with different spatial parameters provided in Embodiment 5 of this application.

[0020] Figure 8 This is a schematic diagram of RMSE and MAE analysis under different densities with the same spatial parameters provided in Embodiment 5 of this application.

[0021] Figure 9 This is a schematic diagram comparing SOC estimation under different temperature conditions and different operating conditions using different algorithms provided in Embodiment Six of this application. Detailed Implementation

[0022] The technical solutions in the embodiments of this application will be clearly and completely described below with reference to the embodiments of this application. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0023] Example 1 See Figure 1 This is a flowchart of a lithium-ion battery SOC estimation method that integrates grid search and adaptive filtering, provided in Embodiment 1 of this application. Figure 1 As shown, the specific implementation steps of the above method include: Step 101: Construct an equivalent circuit model of a lithium-ion battery.

[0024] The equivalent circuit model described above is a second-order RC equivalent circuit model, and the time-varying parameters of the model include ohmic resistance. R 0. Electrochemical polarization resistance R 1 and capacitor C 1. Concentration polarization resistance R 2 and capacitor C 2. See also Figure 2 This is provided for Embodiment 1 of this application. 2RC equivalent circuit diagram. Wherein, Indicates open-circuit voltage. Indicates the battery terminal voltage. Indicates ohmic resistance. R 1 and C 1 represents the electrochemical polarization equivalent circuit. R 2 and C 2 represents the equivalent circuit of the corresponding concentration polarization. and These represent the electrochemical polarization voltage and the concentration polarization voltage, respectively. This indicates the battery's current; a positive value indicates discharge.

[0025] Step 102: Based on the adaptive forgetting factor recursive least squares method (AFFRLS), the equivalent circuit model is parameter identified and the parameter values ​​are dynamically corrected.

[0026] This application addresses the inherent contradiction between parameter tracking agility and noise robustness in traditional recursive least squares (RLS) algorithms with a fixed forgetting factor. It proposes a voltage error-driven adaptive forgetting factor mechanism to improve the parameter estimation performance of dynamic systems. This mechanism establishes a negative correlation between voltage estimation error and the forgetting factor. When the voltage estimation error increases, the forgetting factor is automatically reduced to enhance the response to current data and improve the tracking speed of time-varying parameters. When the voltage estimation error decreases, the forgetting factor is increased to suppress noise interference and ensure estimation smoothness. The voltage estimation error refers to the error between the actual measured value and the model estimated value of the battery terminal voltage.

[0027] Step 103: Perform filtering operations on the State of Charge (SOC) using an improved filtering algorithm. Maintain the innovation sequence composed of voltage estimation errors through a sliding window, and dynamically update the process noise covariance matrix based on the above innovation sequence. Q。

[0028] To improve the EKF algorithm, this application designs a process noise covariance matrix based on the innovation sequence. Q Online adjustment mechanism. This mechanism uses voltage estimation error as the information and maintains the latest information sequence in real time through a sliding window of fixed length. By combining circular indexes to achieve window scrolling updates, outdated information can be avoided as interference, and the ability to track the time-varying characteristics of the system can be enhanced.

[0029] Step 104: Use the grid search (GS) algorithm to optimize within the preset parameter space and determine the process noise covariance matrix. Q The optimal initial value.

[0030] Specifically, this application systematically searches the optimal parameter space under different operating conditions and temperature conditions, and initializes the initial parameter space. Q The matrix selection problem is transformed into an explicit GS optimization problem. This method not only reduces the difficulty of parameter selection, but also ensures the best accuracy of SOC estimation through scientific optimization.

[0031] Step 105: Combine the parameter identification results, the filtering estimation results of the improved filtering algorithm, and the above optimal initial values ​​to output the final state of charge estimate.

[0032] This application utilizes historically collected battery current, terminal voltage, state of charge (SOC), and temperature data to perform a joint estimation algorithm combining an improved adaptive forgetting factor recursive least squares method (AFFRLS) and an adaptive extended Kalman filter (AEKF). Simultaneously, a grid search (GS) algorithm is introduced to estimate the noise covariance matrix. Q The parameter space of the matrix is ​​globally traversed to find the optimal matrix that minimizes the error of the joint estimation algorithm. Q Matrix parameter combination. Then, the resulting optimal... Q The matrix, along with the latest real-time battery current, terminal voltage, and temperature data, are input into the improved AFFRLS-AEKF joint estimation algorithm. Through iterative calculations and data fusion, the algorithm ultimately outputs a high-precision estimate of the battery state of charge (SOC).

[0033] Compared with the prior art, the beneficial effects of the technical solution provided in Embodiment 1 of this application are as follows: This application provides a high-precision, robust, and complex-condition-adaptive solution for lithium-ion battery SOC estimation. It utilizes the Adaptive Forgotten Factor Recursive Least Squares (AFFRLS) method to dynamically identify parameters of the equivalent circuit model and can adjust model parameters in real time according to the battery's operating state, ensuring the model always closely matches the actual electrochemical characteristics of the battery, thus providing an accurate model foundation for SOC estimation. Secondly, the improved filtering algorithm uses a sliding window-maintained information sequence to realize the process noise covariance matrix. Q The dynamic update effectively improves the dynamic response capability and stability of the filter estimation; at the same time, the grid search algorithm... Q The precise optimization of the matrix initial value avoids the drawbacks of traditional filtering algorithms, such as slow convergence and large errors caused by improper selection of initial parameters, which greatly shortens the convergence time of the algorithm and reduces the estimation bias in the initial stage.

[0034] Example 2 Embodiment 2 of this application is a further refinement and supplement to the technical solution of Embodiment 1 above, so as to fully disclose the technical solution claimed in this application. See also Figures 3-4 This is a flowchart of a lithium-ion battery SOC estimation method that integrates grid search and adaptive filtering, provided in Embodiment 2 of this application. Figures 3-4 As shown, the specific implementation steps of the above method include: Step 201: Construct a second-order RC equivalent circuit model, and establish the state equation and observation equation of the second-order RC model system based on the above second-order RC equivalent circuit model.

[0035] Specifically, the above second-order RC equivalent circuit model The state equations of the above second-order RC model system are expressed as follows:

[0036] In the formula, U 1( k） Indicates time k The equivalent circuit voltage of electrochemical polarization at the point, U 2( k） Indicates time k The concentration polarization equivalent circuit voltage at point SOC. k） Indicates time k The state of charge at that point. I This indicates the battery's current; a positive value indicates discharge. I ( k） Indicates time k The system input current at that location. C n Indicates capacity, Δ t That is the sampling time. R Indicates ohmic resistance. R 1 and C 1 represents the electrochemical polarization equivalent circuit. R 2 and C 2 represents the equivalent circuit of the corresponding concentration polarization.

[0037] The above observation equation is expressed as: Ut ( k ) = U oc(SOC( k ))- U 1( k )- U 2( k )- I ( k ) R 0 In the formula, U oc represents the open-circuit voltage. Ut This indicates the battery terminal voltage.

[0038] Step 202: Determine the parameters to be identified and the state vector of the above second-order RC equivalent circuit model.

[0039] Among them, the parameters to be identified include R 0、 R 1. R 2. C 1. C 2. The above state vector is represented as follows: In the formula, V 1 and V 2 represents the electrochemical polarization voltage and the concentration polarization voltage, respectively.

[0040] In this embodiment of the application, regarding the above-mentioned parameters to be identified... R0、 R 1. R 2. C 1. C 2. First, select approximate initial values, then update them online using the Adaptive Forgetting Factor Recursive Least Squares (AFFRLS) method. The specific implementation is as follows: Step 203: Based on the adaptive forgetting factor recursive least squares method (AFFRLS), the equivalent circuit model is parameter identified, a forgetting factor adjustment mechanism based on voltage estimation error is set, and the above-mentioned parameters to be identified are adjusted in combination with the continuous mapping function.

[0041] Specifically, the voltage estimation error mentioned above refers to the error between the actual measured value and the model estimated value of the battery terminal voltage. Based on this voltage estimation error, the forgetting factor in AFFRLS is dynamically adjusted. The weights of historical data and current measurement data are assigned based on the adjusted forgetting factor, and the time-varying parameters in the equivalent circuit model are identified, calculated, and corrected. Specifically, when the voltage error increases, the forgetting factor is automatically reduced, and the weight of the current measurement data is increased to enhance the response to the current data and improve the tracking speed of time-varying parameters; when the voltage error decreases, the forgetting factor is increased, and the weight of the current measurement data is decreased to suppress noise interference and ensure estimation smoothness.

[0042] Furthermore, to optimize the dynamic response process, this application sets a three-level error threshold to trigger the segmented adjustment of the forgetting factor, which can be specifically expressed as follows:

[0043] In the formula, This indicates the voltage estimation error. This represents the smoothing factor for different voltage estimation errors.

[0044] At the same time, the gain adjustment is introduced. η and voltage offset factor ε Forgetting factor through continuous mapping function λ Perform a smoothing adjustment. The adjusted forgetting factor. λ Represented as:

[0045] In the formula, =0.01 indicates that the gain is adjusted. =0.5 represents the voltage offset factor. Compared to discrete control methods, this method can improve response smoothness and control accuracy, thus enabling the AFFRLS algorithm to balance convergence speed and estimation accuracy under different operating conditions and optimize parameter identification performance.

[0046] Step 204: Using the Adaptive Extended Kalman Filter (AEKF), with the voltage estimation error mentioned above as the innovation sequence, dynamically update the process noise covariance matrix. Q .

[0047] This application proposes a process noise covariance matrix based on an information sequence. Q Online adjustment mechanism. This mechanism uses voltage estimation error as the information and maintains the latest information sequence in real time through a sliding window of length n=25. By combining circular indexes to achieve window scrolling updates, outdated information can be avoided as interference, and the ability to track the time-varying characteristics of the system can be enhanced.

[0048] To achieve the process noise covariance matrix Q Online optimization is performed by calculating the covariance of all innovation data within the sliding window, introducing a decaying memory factor, and using an exponential weighting method to optimize the process noise covariance matrix. Q Dynamic updates are performed. The improved Q-matrix expression is as follows:

[0049]

[0050]

[0051] In the formula, Indicates length in n The voltage estimation error stored at that location. Indicates length is n A sliding window of 25 is used to maintain the latest information sequence in real time. This represents the average value of the news sequence within the window. This represents the new information covariance. =0.75 represents the decay memory factor. express k Kalman gain at time step. This represents the updated state noise covariance matrix. This strategy balances historical information with current innovation contributions by using a decaying memory factor, enabling the state noise covariance matrix to dynamically track changes in system noise characteristics, thus improving the algorithm's stability and estimation accuracy. T This indicates transpose.

[0052] Step 205: Systematically search for the optimal parameter space under different operating conditions and temperature conditions. Based on prior knowledge and preliminary experimental results, define the boundary of the above parameter space in the logarithmic space.

[0053] Among them, the different working conditions and temperature conditions mentioned above include, but are not limited to, the use of US06 and FUDS high dynamic stress test conditions at temperatures of -10℃, 0℃, and 10℃.

[0054] In setting the parameter space, the search range was systematically determined based on prior knowledge and pre-experiments. Considering that the parameter matrix needs to cover multiple orders of magnitude, a logarithmic space was used for boundary definition to improve computational efficiency. The parameter space boundary was set as follows: Each element of the matrix, including the voltage-noise variance of the first-order RC network capacitor. Q 1. Variance of capacitor voltage noise in a second-order RC network Q 2 and SOC state noise variance Q 3. Used for traversal optimization to find the optimal solution. Matrix. The parameter space boundary settings can be expressed as:

[0055] This application embodiment systematically searches the optimal parameter space Q=[Q1,Q2,Q3] under different operating conditions and temperature conditions, and initializes the parameter space. The matrix selection problem is transformed into an explicit GS optimization problem. This method not only reduces the difficulty of parameter selection, but also ensures the best accuracy of SOC estimation through scientific optimization.

[0056] Step 206: Set the sampling density ρ of the grid search, perform a systematic traversal within the parameter space, and determine the root mean square error (RMSE) of the state of charge estimation as the objective. Q The optimal initial value of the matrix.

[0057] Specifically, the Q matrix is ​​optimized using GS, with the optimization objective being to find the parameter vector that minimizes the SOC estimation error. The search point density is determined based on the balance between accuracy and computational efficiency. In this embodiment, the sampling density ρ=5 effectively balances the requirements of estimation accuracy and computational efficiency.

[0058] The optimization objective uses the root mean square error (RMSE) to effectively penalize larger deviations, and is expressed as:

[0059] In optimizing the objective function This represents the final judgment value RMSE, where N represents the total number of data points. Indicates the use of different Q The value is the estimated SOC at point k. This represents the reference value of SOC at the current k data points. The optimal RMSE is obtained through iterative optimization with a density of 5 points in the parameter space, leading to the optimal Q matrix.

[0060] Step 207: Use the SOC estimated by AFFRLS-GS-AEKF as the final estimate.

[0061] Compared with the prior art, the technical solution provided in Embodiment 2 of this application has the following beneficial effects: (1) High estimation accuracy: Under temperature conditions of -10℃, 0℃, and 10℃, the embodiments of this application were verified using two high dynamic stress test conditions, US06 and FUDS, respectively. The root mean square error (RMSE) of the state of charge (SOC) estimation was always controlled below 0.75%, and the mean absolute error (MAE) did not exceed 0.76%. This high accuracy advantage is due to the synergistic effect of grid search (GS) and adaptive forgetting factor recursive least squares (AFFRLS). GS optimizes the initial value of the process noise covariance matrix (Q) with the goal of minimizing RMSE, thereby avoiding estimation errors caused by improper selection of the initial Q matrix. AFFRLS can dynamically adjust the forgetting factor through voltage error, effectively improving the tracking accuracy of battery time-varying parameters. The combination of the two significantly reduces the overall estimation deviation.

[0062] (2) Strong robustness: Under various complex working conditions, traditional estimation methods are prone to estimation divergence. However, this scheme, through the deep integration of GS, AFFRLS, and AEKF algorithms, can always ensure stable convergence of the estimation results. Even when the initial SOC value is in a large deviation range of 20%-100%, the RMSE of the SOC estimation can still be maintained below 0.073%, and the MAE is below 0.072%. This strong robustness relies on the online adjustment mechanism of the Q matrix based on the innovation sequence and the AFFRLS parameter pre-convergence mechanism. The former updates the innovation sequence in real time through a sliding window, which can dynamically adapt to changes in system noise. The latter can quickly stabilize the model parameters in the initial stage, effectively avoiding the adverse effects of initial value deviation on the final estimation results.

[0063] (3) Wide adaptability to operating conditions: The technical solution of this application can be well adapted to different dynamic operating conditions such as US06 and FUDS, as well as multiple temperature environments such as -10℃, 0℃, and 10℃. It also exhibits the characteristic that the voltage estimation accuracy gradually increases with the increase of temperature. Under the FUDS operating condition at 10℃, the voltage estimation RMSE can be as low as 0.34%. This advantage comes from the coordinated cooperation of multiple algorithm running software modules. The second-order RC equivalent circuit model can accurately characterize the dynamic characteristics of the battery, AFFRLS can adapt to the time-varying characteristics of battery parameters, and GS and AEKF can work together to optimize the noise processing and filtering process. The joint action of multiple modules ensures the stability of the solution under various operating conditions and meets the needs of battery SOC estimation in different application scenarios.

[0064] Example 3 In Embodiment 3 of this application, verification was performed using two high dynamic stress test conditions, US06 and FUDS, at temperatures of -10℃, 0℃, and 10℃. The battery sample used was a lithium iron phosphate A123 battery with a rated capacity of 1100mAh, which was used to provide experimental data support. The relevant data came from the open-source dataset from the University of Maryland.

[0065] Compare voltage estimates based on US06 operating condition (i) and FUDS operating condition (ii) under different temperatures: (a) -10℃, (b) 0℃, and (c) 10℃. Figure 5 As shown, the voltage estimation accuracy obtained by the AFFRLS-GS-AEKF method in this application shows a gradual improvement trend with increasing temperature. The AFFRLS-GS-AEKF method provided in this application, by integrating an adaptive forgetting factor and an online adjustment mechanism for process noise covariance, not only ensures estimation convergence under low temperature and complex operating conditions, but also achieves high SOC estimation accuracy, demonstrating good robustness and adaptability.

[0066] To further verify the beneficial effects of the above-described technical solution of this application, this embodiment also provides the following alternative technical solutions. A specific comparison is as follows: The Particle Swarm Optimization (PSO) method replaces the grid search (GS) optimization of the Q matrix. The PSO algorithm optimizes within the Q matrix parameter space, minimizing the RMSE through particle position updates, with 50-100 iterations. The final result achieves optimization accuracy similar to GS, with a SOC RMSE deviation of <0.02%, and a 30% reduction in computational complexity. However, comparative experiments show that the PSO algorithm is prone to getting trapped in local optima and exhibits lower robustness than GS in high-dimensional parameter spaces (e.g., Q matrix dimension > 3).

[0067] A strong tracking Kalman filter (STKF) is used instead of the AEKF. The STKF enhances the tracking ability for system abrupt changes by introducing a fading factor to adjust the filter gain, eliminating the need for a sliding window to update the information sequence. Compared to the technical solution in this application, this method reduces the SOC estimation error by 10%-15% during periods of abrupt changes in operating conditions (such as the peak current in the US06 operating condition). However, its adaptability to stable operating conditions is poor, and the voltage estimation error is 5%-8% higher than that of the AEKF in this application.

[0068] Least Squares Support Vector Machine (LSSVM) is used instead of AFFRLS for parameter identification. LSSVM achieves nonlinear parameter fitting based on kernel function mapping, eliminating the need for iterative updates to the forgetting factor, and the training sample size is set to 500-1000 sets (optimal 800 sets). In comparison, the offline parameter identification accuracy is higher than AFFRLS (error reduction of 0.5%-1%). However, this method has poor online real-time performance (computation time increases by 2-3 times) and is not suitable for highly dynamic operating conditions.

[0069] Example 4 The accuracy of the initial SOC value directly affects the estimation performance. To verify the robustness of the AFFRLS-GS-AEKF algorithm to the initial value, Example 4 of this application tested five initial SOC values ​​of 0.2, 0.4, 0.6, 0.8, and 1.0 under the conditions of 0℃ and US06, with the actual initial SOC being 0.5. Other parameters were the same as in Example 3 above.

[0070] The SOC estimation curve and error distribution are as follows: Figure 6 As shown, the step phenomenon in the initial stage of the SOC curve originates from the pre-convergence process of the AFFRLS algorithm on the model parameters. This stage rapidly stabilizes the system parameters to a reasonable range before initiating SOC estimation. The results show that the algorithm can quickly converge to near the true value after the parameters are fixed.

[0071] Further analysis of the corresponding RMSE and MAE results (Table 1) reveals that although deviations from the true initial SOC lead to a decrease in accuracy (the greater the deviation, the greater the relative error), the RMSE remains below 0.073% and the MAE below 0.072% under all test conditions. This result not only verifies the algorithm's adaptability under different initial SOCs but also demonstrates that its accuracy indicators are comprehensively superior to traditional methods, fully meeting the dual requirements of robustness to initial values ​​and estimation accuracy in practical applications. Table 1: RMSE and MAE for different initial SOC values

[0072] Example 5 Grid Search GS Optimization Q The effect of a matrix largely depends on the setting of the parameter space boundaries and density; the boundary conditions determine... Q The search range of the matrix is ​​determined by the sampling density, which directly affects the coverage of candidate points within that range. Both factors together determine the optimization accuracy and efficiency of the grid search.

[0073] In this regard, Example 5 of this application conducts an analysis of different parameter spaces and different density selections.

[0074] For spatial boundaries with the same density but different parameters, the influence of different parameter spatial boundaries and sampling density was considered, and the following was selected. Figure 7 The boundary ranges of groups a, b, and c in the middle correspond to

[10] respectively. -12 , 10 -1 ] 、[10 -8 , 10 -1 ] and [10 -4 , 10 -1 A comparative analysis was conducted. Figure 7 This paper demonstrates the impact of different boundary settings on estimation accuracy under the same sampling density ρ = 10, where color depth represents the RMSE and size reflects the MAE value. The results show that expanding the parameter space boundary helps improve estimation accuracy. Under the same density conditions, a larger search range corresponds to better RMSE and MAE indices. This indicates that, given sufficient computational resources, appropriately expanding the parameter space boundary can effectively improve the accuracy of SOC estimation, but a balance between computational efficiency and accuracy requirements must be maintained. The main distribution analysis is as follows: Figure 7 .

[0075] For different densities at the same parameter boundary, within the same parameter spatial boundary

[10] -12 10 -1 Under the condition, the following were selected Figure 8 The three density groups ρ (a, b, and c) were compared and analyzed for values ​​of 5, 10, and 15, respectively. Color depth represents the RMSE value, and size reflects the MAE value. Figure 8 The results show that both RMSE and MAE indices improve with increasing density. While a density of 5 minimizes computation and speeds up the process, it may miss the global optimum; conversely, increasing the density effectively improves the accuracy of SOC estimation. The main distribution analysis is as follows: Figure 8 Comprehensive boundary and density analysis shows that insufficient parameter space boundaries will affect convergence and estimation accuracy, while insufficient density only affects accuracy and not convergence.

[0076] Example 6 To evaluate the performance difference between this method and existing technologies, four typical algorithms were selected and compared with the AFFRLS-GS-AEKF algorithm provided by the final improvement in this technical solution. Existing technologies were used as comparative examples to illustrate that the solution in this application solves the problems of existing technologies and achieves unexpected technical effects.

[0077] The four typical algorithms selected in Embodiment Six of this application include the FFRLS-EKF algorithm, the FFRLS-AEKF algorithm, the AFFRLS-EKF algorithm, and the AFFRLS-AEKF algorithm. Comparative experiments were conducted under US06 and FUDS operating conditions at temperatures of -10℃, 0℃, and 10℃, including comparisons of voltage and SOC estimates before and after the AFFRLS improvement, comparisons of voltage and SOC estimates before and after the AEKF improvement, and comparisons of voltage and SOC estimates before and after introducing GS in the AFFRLS-AEKF algorithm. Figure 9 As shown in the image.

[0078] Under US06 and FUDS conditions, the estimated voltage and estimated SOC at -10℃, 0℃, and 10℃ are shown in Tables 2 and 3.

[0079] Table 2: Estimated RMSE and MAE at -10℃, 0℃, and 10℃ under US06 and FUDS operating conditions.

[0080] Table 3: Estimated RMSE and MAE of SOC at -10℃, 0℃, and 10℃ under US06 and FUDS operating conditions.

[0081] This application compares voltage and SOC using recursive least squares (FFRLS) and AFFRLS with a fixed forgetting factor under different temperatures and operating conditions. As shown in columns A, C, and E of Tables 2 and 3, introducing AFFRLS improves voltage estimation accuracy, while introducing adaptive methods slightly decreases accuracy. This is because SOC estimation is the optimization objective, reflecting the trade-off between voltage and SOC estimation objectives. For SOC estimation, introducing AFFRLS improves accuracy, and the voltage estimation is better due to the inclusion of voltage error assessment of the operating environment.

[0082] The voltage and SOC of the EKF and the improved AEKF are compared under different temperatures and operating conditions. Comparing columns A, B, and E of Tables 2 and 3, it can be seen that introducing AEKF into voltage estimation reduces the accuracy of voltage estimation because... Q Matrix changes, in order to meet SOC estimation requirements, will decrease voltage accuracy. This reflects the trade-off between voltage and the SOC estimation objective. For SOC estimation, introducing AEKF improves its accuracy. Because the voltage error assessment of the operating conditions is incorporated, the voltage estimation is generally better.

[0083] The voltage and SOC of AFFRLS-AEKF and the improved AFFRLS-GS-AEKF under different temperatures and operating conditions are compared. Comparing columns D and E of Tables 2 and 3, it can be seen that introducing GS slightly reduces the voltage estimation accuracy. This is because the grid search (GS) optimizes by minimizing the RMSE of the SOC estimation, reflecting the trade-off between voltage and SOC estimation objectives. For SOC estimation, introducing GS improves its accuracy. Since the voltage error is assessed based on the operating conditions, the voltage estimation is better.

[0084] Based on the above comparative analysis, the performance of each algorithm shows significant differences. The introduction of the AFFRLS method effectively reduced voltage estimation error, while the introduction of AEKF, although enabling the process noise covariance matrix to adaptively adjust with the Kalman gain, reduced voltage estimation accuracy to some extent. The complete algorithm AFFRLS-GS-AEKF has slightly lower voltage estimation accuracy than AFFRLS-AEKF. This is because the grid search optimizes by minimizing the RMSE of the SOC estimation, reflecting the trade-off between voltage and SOC estimation objectives. Furthermore, the voltage estimation accuracy of all algorithms shows a gradual improvement trend with increasing temperature.

[0085] Analysis shows that at -10℃, the AEKF method alone exhibits divergence at the end of the estimation process. However, by introducing the AFFRLS mechanism, the SOC estimation accuracy of both the EKF and AEKF algorithms is significantly improved. The proposed AFFRLS-GS-AEKF algorithm demonstrates excellent estimation performance under various conditions: at 10℃, RMSE is below 0.76% and MAE is below 0.75%; at 0℃, both RMSE and MAE are below 0.22%; and at -10℃, RMSE and MAE are below 0.12% and MAE is below 0.11%.

[0086] The results show that AFFRLS-GS-AEKF, by integrating the adaptive forgetting factor and the online adjustment mechanism of process noise covariance, not only ensures estimation convergence under low temperature and complex working conditions, but also achieves high SOC estimation accuracy, demonstrating good robustness and adaptability.

[0087] Although embodiments of this application have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principles and spirit of this application, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for estimating the state of charge (SOC) of a lithium-ion battery that integrates grid search and adaptive filtering, characterized in that, include: Construct an equivalent circuit model for a lithium-ion battery; The equivalent circuit model is parameter identified and the parameter values ​​are dynamically corrected based on the adaptive forgetting factor recursive least squares method (AFFRLS). An improved filtering algorithm is used to filter the State of Charge (SOC). A sliding window is used to maintain the innovation sequence composed of voltage estimation errors, and the process noise covariance matrix is ​​dynamically updated based on the innovation sequence. Q ; The grid search (GS) algorithm is used to optimize within a preset parameter space to determine the process noise covariance matrix. Q The optimal initial value; By integrating the parameter identification results, the filtering estimation results of the improved filtering algorithm, and the optimal initial value, the final state of charge estimate is output.

2. The lithium-ion battery SOC estimation method integrating grid search and adaptive filtering according to claim 1, characterized in that, The equivalent circuit model is a second-order RC equivalent circuit model; After constructing the second-order RC equivalent circuit model of a lithium-ion battery, the method further includes: Based on the aforementioned second-order RC equivalent circuit model, establish the state equations and observation equations of the second-order RC model system. Determine the time-varying parameters and state vectors to be identified in the second-order RC equivalent circuit model; wherein, the time-varying parameters include ohmic resistance. R 0. Electrochemical polarization resistance R 1. Concentration polarization resistance R 2. Capacitor C 1. C 2; The state vector is represented as In the formula, V 1 and V 2 represents the electrochemical polarization voltage and the concentration polarization voltage, respectively.

3. The lithium-ion battery SOC estimation method integrating grid search and adaptive filtering according to claim 1, characterized in that, The equivalent circuit model is parameter identified and its parameter values ​​are dynamically corrected based on the adaptive forgetting factor recursive least squares method (AFFRLS), including: Collect the actual measured value and the model estimated value of the battery terminal voltage, and determine the voltage estimation error; The forgetting factor in AFFRLS is dynamically adjusted based on the voltage estimation error, and the weights of historical data and current measurement data are assigned based on the adjusted forgetting factor. The time-varying parameters in the equivalent circuit model are identified, calculated, and corrected. Specifically, when the voltage error increases, the forgetting factor is reduced and the weight of the current measurement data is increased; when the voltage error decreases, the forgetting factor is increased and the weight of the current measurement data is decreased.

4. The lithium-ion battery SOC estimation method integrating grid search and adaptive filtering according to claim 3, characterized in that, The forgetting factor in the dynamic adjustment algorithm based on the voltage estimation error is used. λ It also includes: Introducing adjustable gain η and voltage offset factor ε Forgetting factor through continuous mapping function λ Smoothing adjustment, adjusted forgetting factor λ Represented as: In the formula, This indicates the voltage estimation error. This represents the smoothing factor for different voltage estimation errors before adjustment.

5. The lithium-ion battery SOC estimation method integrating grid search and adaptive filtering according to claim 1, characterized in that, Based on the noise covariance matrix of the dynamic update process of the aforementioned information sequence Q ,include: The innovation sequence is defined as the voltage estimation error between the actual measured value and the model estimate of the battery terminal voltage. Configure a fixed-length sliding window to store the latest generated information data in real time; Calculate the covariance of all new data within the sliding window; By introducing a decay memory factor and calculating the covariance using an exponential weighting method, the updated process noise covariance matrix is ​​obtained. Q .

6. The lithium-ion battery SOC estimation method integrating grid search and adaptive filtering according to claim 1, characterized in that, Before using the grid search (GS) algorithm to find the optimal solution within the preset parameter space, the method further includes: Systematically search the optimal parameter space under different operating conditions and temperature conditions. Q = [ Q 1, Q 2, Q 3] ; among which, Q 1 represents the variance of capacitor voltage noise in a first-order RC network. Q 2 represents the variance of the capacitor voltage noise in the second-order RC network. Q 3 represents the SOC state noise variance.

7. The lithium-ion battery SOC estimation method integrating grid search and adaptive filtering according to claim 1, characterized in that, The optimization objective of the grid search GS algorithm is to minimize the root mean square error (RMSE) of the state of charge estimation, and the process noise covariance matrix... Q The parameter space includes the first-order RC network capacitor voltage noise variance. Q 1. Variance of capacitor voltage noise in a second-order RC network Q 2 and SOC state noise Q 3; The determination process noise covariance matrix Q The optimal initial values ​​include Based on prior knowledge and preliminary experimental results, in logarithmic space... Q 1. Q 2. Q Define the boundaries of the parameter range for parameter 3; Set the sampling density ρ for the grid search, perform a systematic traversal within the parameter space, and determine the optimal parameters with the goal of minimizing the root mean square error (RMSE) of the state of charge estimation. Q The optimal initial value of the matrix.

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