Lithium ion battery state-of-charge estimation method based on improved AO-EKF algorithm

Abstract

The invention discloses a lithium ion battery charge state estimation method based on an improved AO-EKF algorithm, and relates to a lithium ion battery, and the estimation method comprises the steps: building a lithium ion circuit equivalent model, obtaining a discretization state equation and a terminal voltage observation equation corresponding to the circuit equivalent model, and carrying out different battery characteristic tests, identifying parameters in the circuit equivalent model; introducing Tent chaotic mapping to initialize a cluster of the eagle optimization algorithm, setting a dynamic switching condition of a cluster search strategy of the eagle optimization algorithm, and further optimizing a noise covariance matrix and an observation covariance matrix of the system in the EKF algorithm process by combining with the circuit equivalent model after parameter identification; and based on the optimized noise covariance matrix and observation covariance matrix, optimizing to obtain a state vector updating equation and an error covariance updating equation so as to output a final SOC estimation value. According to the method, the accuracy of the lithium ion SOC can be improved, and estimation errors caused by environment changes and battery characteristic changes are avoided.

Description

Technical Field

[0001] This application generally relates to the technical field of lithium-ion batteries, and specifically relates to a method for estimating the state of charge of a lithium-ion battery based on an improved AO-EKF algorithm. Background Art

[0002] With the wide application of electric vehicles, as the core power source of electric vehicles, the performance management of lithium-ion batteries has become crucial. In current battery research, the ampere-hour integration method, open-circuit voltage method, Kalman filtering method and its improved methods are mainly used to estimate the battery SOC. The ampere-hour integration method estimates the change in battery capacity by integrating the charge and discharge current, but there are cumulative errors; the open-circuit voltage method estimates the SOC by matching the voltage-SOC curve, but the battery needs to be fully static; the Kalman filtering method combines the battery state and the observation equation, which can meet the online estimation requirements, but the non-linear characteristics of the battery will affect its accuracy, so the extended Kalman filter (EFK) is derived to improve the estimation accuracy and robustness.

[0003] Traditional EKF has extremely high requirements for the accuracy of the battery model and the noise covariance matrix. Parameters of the battery model, such as internal resistance and capacity, will change with the aging of the battery, temperature changes and the increase in the number of charge and discharge cycles. Under actual working conditions, small deviations in these parameters may lead to large error accumulations in the EKF estimation results, thereby affecting the estimation accuracy of the SOC. Secondly, the EKF algorithm is highly dependent on the initial SOC value. If the initial SOC value is inaccurate, during the subsequent estimation process, the convergence speed of the EKF will be significantly slowed down, and the final estimation accuracy will also be greatly reduced; it can be seen that in these cases, due to the limitations of its algorithm itself, the traditional EKF method is difficult to adapt to this complex dynamic working condition and can no longer guarantee the stability and accuracy of the SOC estimation. Summary of the Invention

[0004] In view of the above-mentioned defects or deficiencies in the prior art, it is desirable to provide a method for estimating the state of charge of a lithium-ion battery based on an improved AO-EKF algorithm.

[0005] This application provides a method for estimating the state of charge of a lithium-ion battery based on an improved AO-EKF algorithm, including the following steps: Establish an equivalent model of the lithium-ion circuit, obtain the discretized state equation and the terminal voltage observation equation corresponding to the circuit equivalent model, and identify the parameters in the circuit equivalent model through different battery characteristic tests; Introduce the Tent chaotic map to initialize the population of the eagle optimization algorithm, and set the dynamic switching conditions for the population search strategy of the eagle optimization algorithm. Then, combined with the circuit equivalent model after parameter identification, optimize the system noise covariance matrix and the observation covariance matrix in the EKF algorithm process; Based on the optimized noise covariance matrix and observation covariance matrix, the state vector update equation and the error covariance update equation are optimized to output the final SOC estimation value.

[0006] According to the technical solution provided by the present application, by conducting different battery characteristic tests, the parameters in the circuit equivalent model are identified, specifically including: Conduct a battery open-circuit voltage characteristic test at a preset temperature to obtain the fitting curve data of the open-circuit voltage and the state of charge; Complete the HPPC test on the battery test platform according to the test standard to obtain the test current and voltage data; According to the fitting curve data and the test current and voltage data, the least squares method with a genetic factor is used to identify the parameters in the circuit equivalent model.

[0007] According to the technical solution provided by the present application, the Tianying optimization algorithm includes at least four search strategies; Introduce the Tent chaotic map to initialize the population of the Tianying optimization algorithm, and set the dynamic switching conditions of the population search strategies of the Tianying optimization algorithm, specifically including: Select multiple different initial values within the preset initial value range, respectively establish multiple groups of chaotic sequences, and map each chaotic sequence to the corresponding theoretical parameter range, so as to initialize the population of the Tianying optimization algorithm, making the population individuals evenly distributed in the solution space; Based on the population diversity index, fitness improvement rate and search efficiency associated with the initialized population, set the dynamic switching conditions required for each search strategy to switch to each other.

[0008] According to the technical solution provided by the present application, the four search strategies are: the first strategy, the second strategy, the third strategy and the fourth strategy; each search strategy sequentially uses the next strategy as the target switching strategy, and the target switching strategy of the fourth strategy is to maintain its own strategy; When the current search strategy meets the corresponding dynamic switching conditions, enter the corresponding target switching strategy; judge that if the current search strategy does not meet the corresponding dynamic switching conditions, then fallback to the previous search strategy; among them, when the fourth strategy does not meet the corresponding dynamic switching conditions, then fallback to the first strategy.

[0009] According to the technical solution provided by the present application, in combination with the circuit equivalent model after parameter identification, the noise covariance matrix and the observation covariance matrix of the system in the EKF algorithm process are optimized, specifically including: Based on the EKF algorithm, construct the initial state equation and the initial observation equation for the dynamic change of the battery system state, and substitute the discretized state equation and the terminal voltage observation equation in the circuit equivalent model after parameter identification into the general form of the nonlinear system; Design a fitness function, and with the minimization of the root mean square error between the SOC estimated value and the true value as the optimization goal, use the initialized Tianying optimization algorithm to optimize the noise covariance matrix and the observation covariance matrix corresponding to the extended initial state equation and the initial observation equation respectively.

[0010] According to the technical solution provided by the present application, based on the optimized noise covariance matrix and observation covariance matrix, optimize to obtain the state vector update equation and the error covariance update equation, so as to output the final SOC estimated value, specifically including: Using the optimized noise covariance matrix and observation covariance matrix as the initial value reference, establish the initialized state vector and error covariance matrix; Based on the circuit equivalent model and dynamic characteristics of the battery, through system identification and mathematical derivation, obtain the state vector prediction equation and the error covariance prediction equation; By updating the state vector prediction equation and the error covariance prediction equation, obtain the state vector update equation and the error covariance update equation, so as to output the final SOC estimated value from the state vector update equation and the error covariance update equation.

[0011] According to the technical solution provided by the present application, by updating the state vector prediction equation and the error covariance prediction equation, obtain the state vector update equation and the error covariance update equation, specifically including: Calculate the Kalman gain matrix according to the error covariance prediction matrix, the observation covariance matrix and the observation matrix; Based on the Kalman gain matrix, the observation matrix and the terminal voltage observation value, update the state vector prediction equation and the error covariance prediction equation to obtain the state vector update equation and the error covariance update equation.

[0012] According to the technical solution provided by the present application, after outputting the final SOC estimated value, the method further includes: using preset working condition data to experimentally verify the output results of the state vector update equation and the error covariance update equation.

[0013] In summary, the present technical solution specifically discloses a method for estimating the state of charge of a lithium-ion battery based on an improved AO-EKF algorithm, including: establishing an equivalent model of the lithium-ion circuit, obtaining a discretized state equation and a terminal voltage observation equation corresponding to the circuit equivalent model, and identifying the parameters in the circuit equivalent model by conducting different battery characteristic tests; introducing the Tent chaotic map to initialize the population of the Tianying optimization algorithm, and setting the dynamic switching condition of the population search strategy of the Tianying optimization algorithm, and then combining the circuit equivalent model after parameter identification to optimize the system noise covariance matrix and the observation covariance matrix in the EKF algorithm process; based on the optimized noise covariance matrix and observation covariance matrix, optimizing to obtain a state vector update equation and an error covariance update equation to output the final SOC estimated value.

[0014] Most of the existing SOC estimation methods use the traditional EKF method. In this case, due to the limitations of its algorithm itself, it is difficult to adapt to such complex dynamic working conditions, resulting in insufficient robustness and unable to ensure the stability and accuracy of SOC estimation. In this application, by introducing the Tent chaotic map to initialize the population and setting a dynamic strategy selection mechanism, the initial global search ability and optimization efficiency are significantly improved, and at the same time, the problem of local optimum is avoided. This method not only improves the convergence speed of the algorithm, but also enhances its stability in complex optimization problems, providing a more reliable optimization basis for the subsequent estimation of SOC using the EKF algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Other features, objects, and advantages of the present application will become more apparent by reading the detailed description of the non-limiting embodiments with reference to the following drawings: Figure 1 It is a schematic flow chart of a method for estimating the state of charge of a lithium-ion battery based on an improved AO-EKF algorithm.

[0016] Figure 2 It is an expanded schematic flow chart of step S100 in the method for estimating the state of charge of the battery.

[0017] Figure 3 It is an expanded schematic flow chart of step S200 in the method for estimating the state of charge of the battery.

[0018] Figure 4 It is an expanded schematic flow chart of step S300 in the method for estimating the state of charge of the battery.

[0019] Figure 5 It is a schematic structural diagram of the lithium-ion circuit equivalent model.

[0020] Figure 6 It is a schematic curve diagram of the partial open-circuit voltage test voltage and current.

[0021] Figure 7 It is a schematic diagram of the OCV-SOC fitting curve in the OCV test.

[0022] Figure 8 It is the current and terminal voltage curve in the HPPC test.

[0023] Figure 9 It is a schematic diagram of the simulation model structure.

[0024] Figure 10 It is the SOC estimation curve under US06 driving cycle.

[0025] Figure 11 It is a comparison chart of SOC estimation error curves. Specific embodiments

[0026] The following further elaborates on the present application in conjunction with the accompanying drawings and embodiments. It can be understood that the specific embodiments described herein are merely for explaining the related invention and not for limiting the invention. Additionally, it should be noted that for the sake of description, only the parts related to the invention are shown in the drawings.

[0027] It should be noted that, without conflict, the embodiments in the present application and the features in the embodiments can be combined with each other. The following will detail the present application with reference to the accompanying drawings and embodiments.

[0028] Embodiment 1 To make the technical solutions of the embodiments of the present application clearer and easier to understand, the application background provided by the embodiments of the present application is introduced below.

[0029] With the widespread application of electric vehicles, as the core power source of electric vehicles, the performance management of lithium-ion batteries has become crucial. The SOC (State of Charge) of lithium-ion batteries is the core parameter of the battery management system. Accurate SOC estimation is beneficial to the energy distribution and management of electric vehicles. At the same time, reliable SOC estimation can also avoid overcharging or over-discharging of the battery, ensuring that users can meet the power demand without damaging the battery. Therefore, researching and developing efficient and accurate SOC estimation methods is of great significance for improving the performance and user experience of electric vehicles.

[0030] In current battery research, the ampere-hour integration method, open-circuit voltage method, Kalman filtering method and their improved methods are mainly used to estimate the battery SOC. The ampere-hour integration method estimates the battery capacity change by integrating the charge and discharge current, but there are cumulative errors; the open-circuit voltage method estimates the SOC by matching the voltage-SOC curve, but the battery needs to be fully static; the Kalman filtering method combines the battery state and the observation equation, which can meet the on-line estimation requirements, but the non-linear characteristics of the battery will affect its accuracy. Therefore, the extended Kalman filter (EFK) is derived to improve the estimation accuracy and robustness.

[0031] Traditional EKF has extremely high requirements for the accuracy of the battery model and the noise covariance matrix. Parameters of the battery model, such as internal resistance and capacity, will change with the aging of the battery, temperature change and the increase of charge and discharge cycle times. Under actual working conditions, small deviations of these parameters may lead to large error accumulation in the EKF estimation results, thereby affecting the estimation accuracy of SOC. Secondly, the EKF algorithm is highly dependent on the initial SOC value. If the initial SOC value is inaccurate, during the subsequent estimation process, the convergence speed of EKF will be significantly slowed down, and the final estimation accuracy will also be greatly reduced. During the actual driving process of an electric vehicle, the battery faces complex and changeable working conditions, making the charge and discharge process of the battery show significant non-linear characteristics. In this case, due to the limitations of its algorithm itself, the traditional EKF method is difficult to adapt to this complex dynamic working condition, resulting in insufficient robustness and unable to ensure the stability and accuracy of SOC estimation.

[0032] In view of this, this application proposes a method for estimating the state of charge of a lithium-ion battery based on an improved AO-EKF algorithm. Please combine Figure 1 with the schematic diagram of the estimation method flow shown in the figure. The purpose of this invention is to propose a lithium-ion SOC estimation method with high precision and strong robustness. By improving the AO algorithm, the noise covariance matrix and initial parameters of EKF are optimized to solve the problems of sensitivity to model errors and poor adaptability to dynamic working conditions of traditional methods.

[0033] Specifically, the estimation method proposed in the embodiment of this application includes the following steps: S100. Establish an equivalent model of the lithium-ion circuit, obtain the discretized state equation and terminal voltage observation equation corresponding to the circuit equivalent model, and identify the parameters in the circuit equivalent model by conducting different battery characteristic tests; In the estimation of the battery state of charge, the equivalent circuit model can simplify the complex circuit system into circuit elements, describe the dynamic response using linear relationships, and optimize and adjust the elements according to the battery characteristics. Generally, the higher the order of the model, the better it can reflect the dynamic characteristics of the battery, but the complexity of the model will also be higher. In this application, a second-order equivalent model is used. It takes into account the hysteresis effect inside the battery and the polarization phenomenon of the chemical reaction, and can better describe the dynamic and static characteristics of battery charging and discharging. It is a choice that balances complexity and accuracy. For the specific second-order equivalent model, please refer to Figure 5 . Among them, R 0 is the ohmic internal resistance; R 1 , R 2 are the polarization resistances; C 1 , C 2 are the polarization capacitances; U oc represents the open-circuit voltage; U t represents the battery terminal voltage, where U 1 (t) and U 2 (t) correspond to the polarization voltages of different RC links in the second-order RC equivalent circuit model respectively); I is the output current.

[0034] Based on the establishment of the above lithium-ion circuit equivalent model, taking the discharge direction as the reference direction, the Kirchhoff's Voltage Law (KVL) equation is listed for this equivalent circuit, and the system state equation of formula (1) below and the observation equation of formula (2) below can be obtained.

[0035] Formula (1); Formula (2); In the above formulas, Q is the actual battery capacity; is the charge-discharge efficiency, which is generally less than 1 during the charging process and equal to 1 during discharging; SOC is the state of charge , SOC 0 is the initial state of charge.

[0036] Based on the above formulas (1) and (2), discretization can be performed to obtain the following formulas (3) and (4), which are the discretized state equation and the discretized terminal voltage observation equation.

[0037] Formula (3); Formula (4); In the above Formulas (3) and (4), the current I is used as the input variable; the terminal voltage U t is used as the output variable; t is the sampling time, taking 0.1 s; k and k+1 is the sampling time t at k moment and k+1 the physical quantities corresponding to the moment.

[0038] Furthermore, referring to Figure 2 , after obtaining the equivalent model of the lithium-ion circuit, it is necessary to accurately identify the parameters in the model to ensure the accuracy of the equivalent model of the lithium-ion circuit, and at the same time determine the accuracy of the physical meaning of the EKF algorithm. In the embodiment of the present application, through experimental tests (OCV test, HPPC test) and data fitting (FFRLS algorithm), 5 parameters to be identified in the model ( R 0 、R 1 , R 2、 C 1 , C 2 ) are determined, and the OCV-SOC curve is fitted. Referring to Figure 7 , the specific steps are as follows: S101. Conduct the battery open-circuit voltage characteristic test at a preset temperature to obtain the fitting curve data of the open-circuit voltage and the state of charge; The OCV test is also called the battery open-circuit voltage characteristic test. It is necessary to conduct the battery open-circuit voltage characteristic test at 25°C, regard the battery terminal voltage that tends to be stable during the static process as the OCV of the lithium-ion battery, and perform six-term fitting on the test data. Finally, the corresponding relationship between the open-circuit voltage and the SOC is obtained (the relevant data can be referred to Figure 6 and Figure 7 ). Then, the SOC of the battery, that is, the percentage of the remaining power, can be estimated according to the measured OCV value, laying a foundation for establishing a non-linear mapping.

[0039] S102. Complete the HPPC test on the battery test platform according to the test standard to obtain the test current and voltage data; The HPPC test is also called the pulse charge and discharge test. It obtains the test current and voltage data for parameter identification by completing the HPPC test on the battery test platform according to the test standard, such as Figure 8It is a cyclic voltage-current curve graph. Specifically, for the second-order RC equivalent circuit model, by analyzing and processing the voltage and current data of these stages and using the corresponding circuit theory and mathematical formulas, the polarization internal resistance can be calculated. R 0 , R 1 , R 2 and the polarization capacitance C 1 , C 2 . Usually, tools such as the curve fitting toolbox of MATLAB are used to solve these parameters.

[0040] S103. According to the fitting curve data, test current and voltage data, use the least squares method with a genetic factor to identify the parameters in the circuit equivalent model.

[0041] After obtaining the fitting curve data, test current and voltage data, identify the RC network parameters through the least squares method with a forgetting factor (FFRLS, forgetting factor generally takes 0.95 - 1.00, and takes 0.99 in the embodiments of the present application) to reduce the saturation of cumulative data, better adapt to the changes of system parameters, improve the sensitivity of the model to new data, and significantly enhance the adaptability of the model to parameter time-variation (such as aging, temperature).

[0042] Based on the above description, it can be seen that due to the dynamic changes of the battery internal resistance ( R 0 , R 1 , R 2 ) and capacitance ( C 1 , C 2 ) with aging, temperature, and the number of charge and discharge cycles, the traditional EKF algorithm assumes that the model parameters are fixed, and the parameter deviation will cause the prediction error of the state equation to gradually amplify, ultimately resulting in the deviation of the SOC estimation from the true value. Then, in this application, the circuit equivalent model is parameter-identified through OCV testing and HPPC testing, and the model parameters are updated in real time, no longer relying on fixed identification parameters, which can effectively ensure the accuracy of the circuit equivalent model.

[0043] S200. Introduce the Tent chaotic mapping to initialize the population of the Tianying optimization algorithm, and set the dynamic switching conditions of the population search strategy of the Tianying optimization algorithm. Then, combined with the circuit equivalent model after parameter identification, optimize the system noise covariance matrix and observation covariance matrix in the EKF algorithm process; Noise covariance matrix Q and observation covariance matrixR It is a key parameter of the EKF, which directly affects the calculation of the Kalman gain. Therefore, in the embodiments of this application, the Aquila Optimizer (AO) is used to optimize the noise covariance matrix and the observation covariance matrix. However, due to the problem that the population distribution of the Aquila Optimizer itself is prone to be uneven during initialization, Tent chaos mapping is introduced to initialize the population on the basis of the Aquila Optimizer, and a dynamic strategy selection is proposed to improve the problem that the AO algorithm may prematurely enter local development in the initial iteration or still over-explore globally in the later stage. Finally, based on the optimized AO algorithm and the circuit equivalent model after precise parameter identification, the noise covariance matrix and the observation covariance matrix of the system in the EKF algorithm process are optimized.

[0044] In a preferred embodiment, referring to Figure 3 , the Aquila Optimizer in the embodiments of this application includes at least four search strategies; the specific expansion steps of "introducing Tent chaos mapping to initialize the population of the Aquila Optimizer and setting the dynamic switching conditions of the population search strategy of the Aquila Optimizer" in the above steps are as follows: S201. Select multiple different initial values within the preset initial value range, respectively establish multiple groups of chaotic sequences, and map each chaotic sequence to the corresponding theoretical parameter range, so as to initialize the population of the Aquila Optimizer, making the population individuals evenly distributed in the solution space; Introducing Tent chaos mapping to initialize the population of the Aquila Optimizer aims to make the initial solutions of the population evenly distributed. The chaotic sequences generated by Tent mapping have good distribution and randomness, making the population individuals more evenly distributed in the solution space, thereby improving the global search ability and optimization efficiency of the algorithm, and reducing the dependence of the EKF algorithm on the initial Q / R. The specific process needs to be randomly initialized within the search range when establishing the mathematical model, and its specific mathematical expression is as follows formula (5): Formula (5); In formula (5), rand is a random number between 0 and 1 in the Gaussian distribution; LB j is the j th lower bound of the given problem; UB j is the upper bound of the given problem; N is the population size; D is the size of the dimension.

[0045] The mathematical expression of Tent chaos mapping is as follows formula (6): Formula (6); In formula (6), and The n -th and n+1 -th chaotic values respectively. When the chaotic sequences a ∈ [0, 1] and ∈ [0, 1], the system is in a chaotic state.

[0046] Introduce the Tent chaotic map to initialize the population. Select multiple different initial values within the preset initial value range [0, 1] to obtain chaotic sequences a with different initial values, which are used to replace the random numbers for initializing the population of the AO algorithm rand , as shown in the following formula (7). At the same time, linearly map the chaotic sequence to the theoretical parameter range to complete the initialization of the population, so that the individuals in the population are evenly distributed in the solution space.

[0047] Formula (7).

[0048] S202. Based on the population diversity index, fitness improvement rate, and search efficiency associated with the initialized population, set the dynamic switching conditions required for each search strategy to switch with each other.

[0049] The basic setting of the Tianying optimization algorithm itself is to simulate the hunting behavior of Tianying and output the best individual position through the set dynamic search strategy. In the embodiment of this application, the Tianying optimization algorithm includes four search strategies, namely the first strategy, the second strategy, the third strategy, and the fourth strategy (the four strategies can be respectively understood as expanding exploration, shrinking exploration, expanding exploitation, and shrinking exploitation), and will be dynamically adjusted according to the iteration stage and population situation during the execution of the algorithm to balance the global search and local search capabilities.

[0050] The following is an elaboration on the four search strategies: (1) Expanding exploration: In this strategy, Tianying flies at a high altitude and widely explores the search space to identify the area where the prey is located. The mathematical model of this behavior is expressed as the following formula (8): Formula (8); Further, is the solution for the (t + 1)-th iteration of this stage; is the current global best solution at the t-th iteration; T and t respectively represent the maximum number of iterations and the current number of iterations; is t the average value of the solutions in the iteration; represents t the position of the i -th individual at time

[0051] (2) Shrinking exploration Among them, after Tianying determines the target area, it continues to explore within the selected area to narrow down the target area where the prey is located. The mathematical expression of this behavior is as follows in formula (9): Formula (9); Among them, , ; In formula (9), is the solution of the (t + 1)-th iteration in this stage, is the Lévy flight distribution function, taking values that decrease from 2 to 0, s is the control factor with a value of 1.5, is the flight step length, and v are random variables between 0 and 1, is the Gamma function, is the stable distribution exponent with a value of 1.5; is the random solution obtained within the range of [1, N] at the t-th iteration; y and x represent the spiral form in the search, r 1 is the fixed radius, with a value between 1 and 20; U is 0.00565; is 0.005; D 1 is from 1-D of an integer; = 1.5 π .

[0052] (3) Expanded development When the area where the prey is located is accurately locked, Tianying slowly conducts development within the search space, approaching the target in a low-altitude flight manner to conduct a preliminary attack to detect the prey's reaction. The mathematical expression of this behavior is as follows in formula (10): Formula (10); In formula (10), is the solution of the t+1 -th iteration in this stage, , are development adjustment parameters in (0, 1).

[0053] (4) Narrowed development When Tianying approaches the prey, it attacks the prey according to random motion. The mathematical expression of this behavior is as follows in formula (11): Formula (11); Among them, ; In formula (11), For this stage t+1 the solution of the i-th iteration; is the quality function used to balance the search strategy during iteration; G 1 is used to track various movements of prey AO during the search for prey; G 2 is a decreasing value from 2 to 0, indicating A 0 the flight speed of; X(t) is the t current value of the i-th iteration.

[0054] In the traditional AO algorithm, if the strategy selection stage is divided according to a fixed iteration ratio, it is easy to cause premature entry into local development in the early stage of iteration, or excessive global exploration in the later stage. At the same time, the fixed ratio cannot be dynamically adjusted according to the optimization process, and it is easy to fall into local optimum or slow convergence speed. Facing the dynamic parameter changes in the SOC estimation of lithium-ion batteries, the algorithm has insufficient robustness. Therefore, in this application, based on the population diversity index (DI), fitness improvement rate (FIR), and search efficiency (SIF), dynamic switching conditions required for each search strategy to switch with each other are set; for example, according to the population diversity index, if the degree of difference (diversity) among individuals in the population is low, it indicates that it may have fallen into a local area, and the algorithm may adjust the search strategy and adopt a more exploratory strategy to increase diversity; the fitness improvement rate reflects the ability of the algorithm to find a better solution. When the improvement rate is low, it will also prompt the algorithm to change the strategy.

[0055] Specifically, the population diversity index (DI) is used to measure the degree of dispersion of individual distribution. The smaller the value, the more convergent the population. Its specific mathematical expression is shown in the following formula (12): Formula (12); where N is the population size, is the current global best solution at the t-th iteration; is the norm.

[0056] The fitness improvement rate (FIR) is used to reflect the convergence speed. When the value tends to zero, it indicates that the convergence has stagnated, triggering the stage switching mechanism. Its specific mathematical expression is shown in the following formula (13).

[0057] Formula (13); where is the statistical window, and the value can be selected as 8; represents that when the algorithm runs to the t t-th iteration, the fitness value (objective function value) corresponding to the currently found optimal solution.

[0058] The higher the Search Efficiency (SIF) value, the more effective the current strategy is, which is used to reflect the speed and quality of the algorithm in finding better solutions during the search process. It comprehensively considers the convergence speed of the algorithm and the quality of the found solutions. Its specific mathematical expression is as follows in formula (14): Formula (14); Wherein, is the updated individual position, is the indicator function, taking 1 when the condition is met and 0 otherwise. Finally, we obtain the search strategy switching conditions as shown in Table 1 below.

[0059] Table 1 Search Strategy Switching Conditions

[0060] Next, we give a simple explanation of the design of the switching conditions in Table 1 above: The switching conditions corresponding to Stage 1: (1) The selection of the 25% threshold can be set based on the test results. For example, assuming that the DI value obtained in the CEC2017 test is 30%, but considering the characteristics of the EKF's noise covariance matrix and observation covariance matrix optimization, such as high dimensionality, non-linearity, and parameter coupling, the threshold can be reduced to 25% to extend the exploration stage. At the same time, through simulation experiments, the state estimation error, algorithm convergence speed, and parameter estimation stability of different DI thresholds (20%, 25%, 30%) are compared. The results show that the optimization effect is the best when the threshold is 25%; (2) t >0.25 T max , ensuring that even if the diversity does not reach the threshold, the algorithm is forced to enter the next stage after 25% of the iterations are completed, avoiding the algorithm from staying for a long time due to misjudgment of indicators, and ensuring that the algorithm progresses according to the typical optimization process of "exploration → exploitation", providing a basic time-driven guarantee.

[0061] The switching conditions corresponding to Stage 2 and Stage 3: (1) FIR The threshold (δ) is used as the convergence stagnation detection. When the fitness improvement rate approaches zero ( δ =1e −5 ), it indicates that the local search in the current stage has entered a stagnation stage and the quality of the solution cannot be further improved. For most optimization problems, the magnitude of the fitness change is at 1e −5The following can be regarded as convergence stagnation; (2) The search efficiency SIF(t) represents the proportion of new solutions that are better than the parent solutions, and can also be set based on experimental verification of test functions such as CEC2017. For example, experimental verification of test functions such as CEC2017 shows that thresholds of 0.2 and 0.1 can effectively distinguish high and low search efficiency in most scenarios. However, considering the high-dimensional characteristics of EKF parameter optimization, in a high-dimensional space, the probability of finding a better solution is significantly reduced, and the SIF value may generally be lower than that in the standard test function scenario. If the SIF in stage 2 is 0.2, it may be too strict, resulting in frequent backtracking to the exploration stage and wasting computing resources. Therefore, in the embodiments of this application, the thresholds are adjusted from 0.2 and 0.1 to 0.1 and 0.05 to match the low search efficiency characteristics in the high-dimensional space. And through simulation experiment comparison, it shows that when the thresholds are 0.1 and 0.05, the algorithm in the high-dimensional EKF parameter optimization task can not only avoid premature convergence to local optima but also effectively reduce unnecessary exploration backtracking times, ensuring the rationality and effectiveness of the search in high-dimensional complex optimization scenarios.

[0062] The switching condition corresponding to stage 4: If FIR(t) < δ continue K generations, it indicates that the algorithm may fall into deep local optima or the search space structure is complex, then force a restart of stage 1; in the embodiments of this application K the threshold is selected as 10 generations, which is more suitable for the slow convergence characteristics of the high-dimensional space compared to 5 generations in the standard optimization algorithm. And when forcing a restart of stage 1, elite individuals are retained to avoid complete loss of historical information.

[0063] Based on Table 1 above, each search strategy sequentially uses the next strategy as the target switching strategy, and the target switching strategy of the fourth strategy is to maintain its own strategy, that is, the target stage of expanding exploration is to narrow exploration, the target stage of narrowing exploration is to expand exploitation, the target stage of expanding exploitation is to narrow exploitation, and narrowing exploitation is to maintain its own search strategy.

[0064] Further, when the current search strategy meets the corresponding dynamic switching condition, enter the corresponding target switching strategy; judge that if the current search strategy does not meet the corresponding dynamic switching condition, then backtrack to the previous search strategy; among them, when the fourth strategy does not meet the corresponding dynamic switching condition, then backtrack to the first strategy.

[0065] For example, during the process of expanding exploration, it is found that the population diversity index reaches the following at this time, it means that further search can enter the stage of narrowing exploration. When in the process of narrowing exploration, if the fitness improvement rate appears at this time, then backtrack to expanding exploration, indicating that the exploitation efficiency is low at this time, otherwise enter the stage of expanding exploitation.

[0066] It should be noted that: is the diversity value of the initial population; under such a strategy design, a fallback mechanism is added so that when the development efficiency is low, it can actively fallback to the previous stage to avoid ineffective iterations. Finally, when is reached, the output result ; by monitoring these metrics, the algorithm can dynamically adjust the search strategy, balance the capabilities of global search and local search, and increase the probability of finding the global optimal solution, that is, the search for the optimal individual position is completed; combined with the next step, based on the improvement of the Tianying optimization algorithm, and then by combining the circuit equivalent model after parameter identification, the noise covariance matrix and the observation covariance matrix of the system in the EKF algorithm can be optimized, that is, the optimal solutions for the noise covariance matrix Q and the observation covariance matrix R are found; It should be noted that under different working conditions of the battery (such as temperature changes, different charge and discharge rates, etc.), the characteristics of model errors and measurement errors will change. The fixed noise covariance matrix Q and the observation covariance matrix R may not be able to accurately describe these changes, resulting in a decrease in the estimation accuracy of the EKF algorithm. The improved AO algorithm can make the EKF algorithm better adapt to different working conditions and improve the accuracy of battery state estimation by dynamically adjusting Q and R matrices. Specifically, using the improved AO algorithm to optimize Q and R matrices specifically includes the following steps: S203. Based on the EKF algorithm, construct the initial state equation and the initial observation equation for the dynamic change of the battery system state, and substitute the discretized state equation and the terminal voltage observation equation in the circuit equivalent model after parameter identification into the general form of the nonlinear system; When the EKF algorithm is used for SOC estimation, the ampere-hour integration method and the RC loop polarization voltage calculation formula are used to measure the internal state of the battery, accurately express the relationship between the state variables such as the state of charge and voltage inside the battery, and construct the state equation and the observation equation for the dynamic change of the battery system state as formula (15) below: Formula (15); Substituting the discretized state equation and the terminal voltage observation equations (3) and (4) into the general form of the nonlinear system can obtain a mathematical model with physical significance, which can more accurately describe various physical and chemical processes inside the battery. The corresponding parameters are as follows: is the state variable, is the terminal voltage is the observed value; ; ; ; It can be determined according to the relationship between the fitted open-circuit voltage and SOC; ; is the observation noise, representing the measurement error of the sensor for the measurable signal; is the system process noise, representing the model error and quantization error.

[0067] S204. Design the fitness function, and take the minimization of the root mean square error between the SOC estimated value and the true value as the optimization goal, and use the initialized Tianying optimization algorithm to optimize the noise covariance matrix and the observation covariance matrix in the EKF algorithm respectively.

[0068] In practical applications, when using the improved AO algorithm to dynamically adjust the noise covariance matrix Q and the observation covariance matrix R in the process of the EKF algorithm, first set Q , R to be in the form of a diagonal matrix, that is, the following formula (16): Formula (16); Secondly, it is also necessary to design the fitness function ; In the embodiment of the present application, taking the minimization of the root mean square error (RMSE) between the SOC estimated value and the true value as the optimization goal, where is the filtered SOC estimated value, is the true SOC value. Under such an optimization goal, use the initialized Tianying optimization algorithm according to the above search strategy to optimize the noise covariance matrix Q and the observation covariance matrix R to obtain Q and R the optimal optimization results.

[0069] S300. Based on the optimized noise covariance matrix and observation covariance matrix, optimize to obtain the state vector update equation and the error covariance update equation to output the final SOC estimated value.

[0070] As can be seen from the foregoing description, the noise covariance matrix Q and the observation covariance matrix R are the key parameters of the EKF algorithm. After obtaining the optimal noise covariance matrix Q and the observation covariance matrix RAfter that, it is equivalent to obtaining the improved AO-EKF algorithm. Subsequently, the improved AO-EKF algorithm can be used to estimate the battery SOC, that is, the state vector update equation and the error covariance update equation are optimized. Finally, the final SOC estimation value is output using the state vector update equation and the error covariance update equation.

[0071] In a preferred embodiment, referring to Figure 4 , the expansion of step S300 further includes the following steps: S301. With the optimized noise covariance matrix and observation covariance matrix as the initial reference, establish the initial state vector and error covariance matrix; First of all, what needs to be done is initialization. The optimal noise covariance matrix Q optimized by using the improved AO algorithm and the observation covariance matrix R are used as the initial values to provide a reasonable starting point for the filtering iteration. Finally, the state vector and error covariance matrix in the EKF algorithm are initialized as follows in formula (17): Formula (17).

[0072] Among them, represents the expected value (mean) of the initial state , and the initial state is set to

[0073] the statistical average value of; Similarly, P 0 is the error covariance matrix of the initial state, usually defined as the expected value of the product of the state error and its transpose.

[0074] S302. Based on the circuit equivalent model and dynamic characteristics of the battery, through system identification and mathematical derivation, obtain the state vector prediction equation and the error covariance prediction equation;; Starting the EKF recursion algorithm with the initialized state vector and error covariance, substituting into the discretized formula (15), the state vector prediction equation and the error covariance prediction equation at k time can be obtained. Specifically, see the following formula (18): Formula (18); Among them, is the process noise covariance matrix.

[0075] S303. By updating the state vector prediction equation and the error covariance prediction equation, obtain the state vector update equation and the error covariance update equation, so as to output the final SOC estimation value from the state vector update equation.

[0076] First, the data output by the state vector prediction equation and the error covariance prediction equation are the basis for the correction process of SOC estimation. Therefore, in order to optimize the prediction results using the observation information, in the embodiments of the present application, based on the state vector prediction equation and the error covariance prediction equation, a state vector update equation and an error covariance update equation for outputting the final SOC estimation value are further obtained through correction means. Specifically, this step includes the following steps: Step 1: Calculate the Kalman gain matrix according to the error covariance prediction matrix, the observation covariance matrix, and the observation matrix; The Kalman gain matrix can balance the weights of the predicted value and the observed value. In the embodiments of the present application, according to the error covariance prediction matrix, the observation covariance matrix, and the observation matrix, the Kalman gain matrix of the following formula (19) can be calculated: Formula (19); Wherein, is k the observation matrix at time is k-1 the observation covariance matrix at time

[0077] Step 2: Update the state vector prediction equation and the error covariance prediction equation based on the Kalman gain matrix, the observation matrix, and the terminal voltage observation value to obtain the state vector update equation and the error covariance update equation.

[0078] According to k the terminal voltage at time and the Kalman gain matrix k at time Formula (20).

[0079] Furthermore, combining the foregoing content, it can be seen that by continuously repeating the above prediction and update steps, the EKF algorithm can gradually adjust the estimation of SOC according to the dynamic characteristics of the system and the observation information, making it closer to the true value more accurately. When any of the following conditions is met, the update ends: (1) Reaching the pre-set number of iterations, that is, completing a predetermined number of prediction and update steps; (2) The error covariance matrix of the state estimation converges, that is, the uncertainty of the estimated value is reduced to a certain extent; (3) The system reaches a steady state, that is, the change of the state variable tends to be stable.

[0080] Therefore, the entire process of the EKF algorithm and the related formulas work together to achieve the estimation and prediction of SOC.

[0081] In addition, after the final SOC estimation value is output, the method further includes: experimentally verifying the output results of the state vector update equation and the error covariance update equation using preset operating condition data.

[0082] To evaluate the performance of this estimation method, during the design process, experimental verification was also carried out by using US06 operating condition data. In the experiment, the voltage and current information of the operating condition was obtained by precise measurement equipment, and the SOC value was directly measured by the ampere-hour integration method, which is simple, reliable, and not affected by model errors, and can be regarded as the true value. During the experiment, the current information of the US06 test and the parameter identification results were input into the Simulink simulation model (as Figure 9 shown). To better evaluate the performance and reliability of the SOC estimation and prediction algorithm at a higher state of charge, and to cover a larger range of SOC changes in the experiment, finally, the SOC estimation curve and the estimation error curve of the US06 operating condition were obtained as shown in Figure 10 and Figure 11 shown; from Figure 10 and Figure 11 it can be seen that Figure 10 in the SOC estimation curve of Figure 11 after optimizing the parameters using the improved algorithm, there is a good estimation effect on SOC, and the improved algorithm can converge to a steady state faster;

[0083] Based on the above description, the present application proposes a method for estimating the state of charge of a lithium-ion battery based on an improved AO-EKF algorithm. On the one hand, this method initializes the population by introducing Tent chaotic mapping, solves the problem of uneven population distribution during the initialization of the traditional Albatross Optimization (AO) algorithm, and significantly improves the global search ability and optimization efficiency. At the same time, a dynamic strategy selection mechanism is proposed to dynamically adjust the optimization strategy according to population diversity and fitness improvement rate, avoiding the problem of local optimum. This method not only improves the convergence speed of the algorithm but also enhances its stability in complex optimization problems, providing a more reliable optimization basis for subsequent SOC estimation. On the other hand, the improved Albatross Optimization (IAO) algorithm is combined with the Extended Kalman Filter (EKF). By dynamically optimizing the key parameters of EKF through AO, the accuracy and robustness of SOC estimation are significantly improved. Moreover, by designing a fitness function with the goal of minimizing the Root Mean Square Error (RMSE), the optimization process becomes more efficient and targeted. This method solves the problem that the traditional EKF algorithm is sensitive to model errors and adapts to the dynamic characteristic changes of the battery. Finally, by dynamically adjusting the noise covariance matrix, the algorithm can adapt to complex conditions such as battery aging and temperature changes, solving the problem that the traditional method is sensitive to model errors. At the same time, based on battery characteristic tests, multiple parameter tables (such as parameters at different temperatures) can be pre-stored, and the optimization initial values can be automatically switched in low-temperature or high-temperature environments to ensure the stability of SOC estimation. This method significantly improves the adaptability and robustness of the algorithm under complex working conditions, avoiding error accumulation caused by environmental changes.

[0084] The above description is only a preferred embodiment of the present application and an explanation of the applied technical principles. Those skilled in the art should understand that the scope of the invention involved in the present application is not limited to the technical solution formed by the specific combination of the above technical features, but should also cover other technical solutions formed by any combination of the above technical features or their equivalent features without departing from the inventive concept. For example, the technical solutions formed by mutually replacing the above features with (but not limited to) technical features with similar functions disclosed in the present application.

Claims

1. A method for estimating the state of charge of a lithium-ion battery based on an improved AO-EKF algorithm, characterized in that: The steps include: Establishing a lithium-ion circuit equivalent model, obtaining a discretized state equation and a terminal voltage observation equation corresponding to the circuit equivalent model, and identifying parameters in the circuit equivalent model by conducting different battery characteristic tests; The Tent chaotic map is introduced to initialize the population of the Eagle optimization algorithm, and the dynamic switching conditions of the Eagle optimization algorithm population search strategy are set, and then the noise covariance matrix and the observation covariance matrix of the system in the EKF algorithm process are optimized by combining the circuit equivalent model after parameter identification; Based on the optimized noise covariance matrix and observation covariance matrix, the state vector update equation and the error covariance update equation are optimized to output the final SOC estimation value.

2. The method for estimating the state of charge of a lithium-ion battery based on the improved AO-EKF algorithm according to claim 1, characterized in that: By carrying out different battery characteristic tests, the parameters in the circuit equivalent model are identified, including: Conducting a battery open circuit voltage characteristic test at a preset temperature to obtain fitting curve data of open circuit voltage and state of charge; Complete HPPC test on the battery test platform according to the test standards and obtain test current and voltage data; According to the fitting curve data and the test current and voltage data, the least square method with genetic factors is used to identify the parameters in the circuit equivalent model.

3. The method for estimating the state of charge of a lithium-ion battery based on an improved AO-EKF algorithm according to claim 1, characterized in that: The Sky Eagle optimization algorithm includes at least four search strategies; The Tent chaotic map is introduced to initialize the population of the Eagle optimization algorithm, and the dynamic switching conditions of the Eagle optimization algorithm population search strategy are set, including: Selecting multiple different initial values ​​within a preset initial value range, respectively establishing multiple groups of chaotic sequences, and mapping each of the chaotic sequences to a corresponding theoretical parameter range, thereby initializing the population of the Sky Eagle optimization algorithm so that the individuals of the population are evenly distributed in the solution space; Based on the population diversity index, fitness improvement rate and search efficiency associated with the initialized population, dynamic switching conditions that need to be triggered when each of the search strategies switches to each other are set.

4. The method for estimating the state of charge of a lithium-ion battery based on the improved AO-EKF algorithm according to claim 3, characterized in that: The four search strategies are: a first strategy, a second strategy, a third strategy and a fourth strategy; each of the search strategies takes the next strategy as the target switching strategy in turn, and the target switching strategy of the fourth strategy is to maintain the own strategy; When the current search strategy meets the corresponding dynamic switching conditions, enter the corresponding target switching strategy; if it is determined that the current search strategy does not meet the corresponding dynamic switching conditions, then fall back to the previous search strategy; wherein, when the fourth strategy does not meet the corresponding dynamic switching conditions, then fall back to the first strategy.

5. The method for estimating the state of charge of a lithium-ion battery based on an improved AO-EKF algorithm according to claim 1, characterized in that: Combined with the circuit equivalent model after parameter identification, the noise covariance matrix and observation covariance matrix of the system in the EKF algorithm process are optimized, specifically including: Based on the EKF algorithm, the initial state equation and initial observation equation of the dynamic change of the battery system state are constructed, and the discretized state equation and the terminal voltage observation equation in the circuit equivalent model after parameter identification are substituted into the general form of the nonlinear system; A fitness function is designed, and the root mean square error between the estimated SOC value and the true value is minimized as the optimization goal. The initialized Sky Eagle optimization algorithm is used to optimize and expand the noise covariance matrix and the observation covariance matrix corresponding to the initial state equation and the initial observation equation respectively.

6. The method for estimating the state of charge of a lithium-ion battery based on the improved AO-EKF algorithm according to claim 5, characterized in that: Based on the optimized noise covariance matrix and observation covariance matrix, the state vector update equation and the error covariance update equation are optimized to output the final SOC estimation value, specifically including: Using the optimized noise covariance matrix and observation covariance matrix as initial value references, the initialization state vector and error covariance matrix are established; Based on the circuit equivalent model and dynamic characteristics of the battery, the state vector prediction equation and error covariance prediction equation are obtained through system identification and mathematical derivation; By updating the state vector prediction equation and the error covariance prediction equation, a state vector update equation and an error covariance update equation are obtained, and thus the final SOC estimation value is output by the state vector update equation and the error covariance update equation.

7. The method for estimating the state of charge of a lithium-ion battery based on the improved AO-EKF algorithm according to claim 6, characterized in that: By updating the state vector prediction equation and the error covariance prediction equation, a state vector update equation and an error covariance update equation are obtained, which specifically include: Calculating a Kalman gain matrix based on the error covariance prediction matrix, the observation covariance matrix and the observation matrix; Based on the Kalman gain matrix, the observation matrix and the terminal voltage observation value, the state vector prediction equation and the error covariance prediction equation are updated to obtain the state vector update equation and the error covariance update equation.

8. The method for estimating the state of charge of a lithium-ion battery based on an improved AO-EKF algorithm according to claim 1, characterized in that: After outputting the final SOC estimation value, the method further includes: experimentally verifying the output results of the state vector update equation and the error covariance update equation using preset operating condition data.

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