A method for synergistic estimation of lithium battery state of energy with strong robustness to temperature and noise

Abstract

The application discloses a lithium battery energy state cooperative estimation method with strong robustness to temperature and noise, and belongs to the technical field of battery state estimation. A pre-established open-circuit voltage-energy state-temperature nonlinear relationship is acquired, and dynamic measurement data under a running working condition are collected in real time. A second-order fractional equivalent circuit model is established, a constant-phase element is used to replace an integer-order ideal capacitor, and the electrochemical dispersion effect inside a lithium battery is more accurately depicted. A parameter identification window mechanism is combined with CVPPSO, a double-population cooperative search strategy of global exploration of a main population and local development of a slave population and a speed pause mechanism are used, and the local development capability of the algorithm in a low-energy state strong nonlinear region is enhanced. An adaptive particle filtering algorithm and a residual error driven feedback mechanism are used, noise variance is dynamically updated according to observation residual error, stable energy state estimation can be maintained under non-Gaussian noise interference and wide temperature range change, and strong robustness to temperature and noise is realized.

Description

Technical Field

[0001] This application relates to the field of battery state estimation technology, specifically to a collaborative method for estimating the energy state of lithium batteries that is robust to temperature and noise. Background Technology

[0002] Lithium-ion batteries, as a high-energy-density battery type, have advantages such as small size and light weight, and are widely used in new energy vehicles, energy storage, and other fields. State of energy (SGE), defined as the ratio of remaining energy to rated energy, is one of the core states of a lithium-ion battery. Unlike state of charge (SOC), SGE focuses more on the battery's remaining energy, and accurate SGE estimation is crucial for guiding energy allocation. Therefore, it is necessary to perform real-time, accurate, and stable estimation of SGE.

[0003] Existing energy state estimation methods mainly include power integration methods, open-circuit voltage methods, data-driven methods, and model-based methods. Methods based on equivalent circuit models are widely used in online state estimation due to their rigorous electrochemical physical meaning and low computational cost. Typical model-based energy state estimation methods involve three key steps: equivalent modeling, parameter identification, and state estimation. However, existing technologies still have the following technical shortcomings in practical applications: The accuracy of equivalent circuit models is limited: Traditional equivalent circuit models often use integer-order ideal capacitance to describe the polarization and diffusion processes of the battery, which makes it difficult to accurately characterize the inherent electrochemical dispersion effect inside the lithium battery. This causes the model to deviate from the actual electrochemical behavior, limiting the upper limit of accuracy for subsequent parameter identification and state estimation.

[0004] Multidimensional parameter identification suffers from poor real-time performance and is prone to getting trapped in local optima: Battery equivalent parameters are nonlinear and time-varying, and are affected by factors such as charge / discharge rate, temperature, and aging degree; traditional parameter identification methods such as Kalman filtering have strong real-time performance but limited accuracy, while the more accurate particle swarm optimization algorithm has poor local exploitation ability when faced with multidimensional parameter coupling and is prone to getting trapped in local false optima, especially under low energy conditions where parameter identification is prone to large deviations.

[0005] Poor robustness of state estimation: Traditional state estimation algorithms, such as extended Kalman filtering, unscented Kalman filtering, and particle filtering, typically treat the system measurement noise variance as a fixed constant. In industrial environments, when the system faces sudden non-Gaussian noise interference or drastic temperature changes, the fixed noise variance can lead to a mismatch between the initial particle distribution and the true posterior distribution, causing the algorithm to diverge or the estimation accuracy to drop sharply.

[0006] Therefore, how to solve the problems of poor real-time performance of multidimensional parameter identification, easy getting trapped in local optima, and poor robustness of state estimation in the existing technology, so as to achieve high-precision and robust estimation of energy state, has become a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0007] To address the aforementioned technical problems, this application proposes the following technical solution: Firstly, embodiments of this application provide a collaborative estimation method for the energy state of a lithium battery that exhibits strong robustness against temperature and noise, comprising the following steps: The pre-established OCV-SOE-T (Open Circuit Voltage-State of Energy-Temperature) nonlinear relationship of the lithium battery is obtained, and dynamic measurement data of the lithium battery under operating conditions are collected in real time. A second-order FECM (Fractional-order Equivalent Circuit Model) is established to describe the electrochemical dispersion effect of the battery. The dynamic measurement data is input into the model to establish the physical parameter boundaries for parameter identification. Combining the PIW (Parameter Identification Window) mechanism, the CVPPSO (Coevolutionary Velocity Pause Particle Swarm Optimization) algorithm is used to identify the second-order FECM online and obtain accurate model parameters in real time. By combining the identified model parameters, the noise variance is dynamically updated using the APF (Adaptive Particle Filter) algorithm and residual-driven feedback mechanism to suppress measurement uncertainty and output SOE estimation results that are robust to temperature and noise.

[0008] In one possible implementation, acquiring the pre-established OCV-SOE-T nonlinear relationship of the lithium battery and collecting dynamic measurement data of the lithium battery under operating conditions in real time includes: The lithium battery was subjected to a charge-discharge-rest cycle test at multiple preset temperature levels. Calculate the SOE value at the resting point based on the energy released in each discharge stage and record the corresponding OCV. After obtaining multiple sets of OCV-SOE data, fit the data according to temperature to obtain the nonlinear relationship between OCV-SOE-T. The dynamic measurement data of the lithium battery under operating conditions is collected in real time by the charge and discharge test equipment. The dynamic measurement data includes terminal voltage, load current and corresponding temperature.

[0009] In one possible implementation, establishing a second-order FECM to describe the electrochemical dispersion effect inside the battery, inputting the dynamic measurement data into the model, and establishing physical parameter boundaries for parameter identification include: The second-order FECM is established by replacing the two integer-order capacitors in the equivalent circuit model with two constant-phase elements. The second-order FECM is pre-identified offline using dynamic measurement data at different temperatures to obtain the variation range of each parameter to be identified within the corresponding temperature range. The variation range is then used as the physical parameter boundary for online parameter identification.

[0010] In one possible implementation, the second-order FECM is composed of an ohmic internal resistance R0, a first polarization branch, and a second polarization branch connected in series; the first polarization branch is formed by a first polarization resistor R1 connected in parallel with a first constant-phase element CPE1, representing the electrochemical polarization process of the battery; the second polarization branch is formed by a second polarization resistor R2 connected in parallel with a second constant-phase element CPE2, representing the concentration polarization process of the battery; the fractional orders of the first constant-phase element CPE1 and the second constant-phase element CPE2 are fixed as those obtained from offline identification. and .

[0011] In one possible implementation, the combination of the PIW mechanism and the CVPPSO algorithm for online identification of the second-order FECM to obtain accurate model parameters in real time includes: Set the PIW length and sampling step size, and extract the actual terminal voltage and load current data sequence within the PIW at each sampling step size; The parameters to be identified in the second-order FECM Pars This is mapped to the optimization objective of the particle swarm optimization. At each sampling time, PIW slides once, and CVPPSO completes one evolution, updating only one parameter in each evolution; After completing one parameter identification, slide PIW to update historical data and output the current real-time equivalent battery parameters. Parameter identification is performed by... Pars The parameters are processed sequentially and cyclically until the sampling ends.

[0012] In one possible implementation, for open-circuit voltage Slowly changing physical properties are treated approximately linearly within PIW, as shown in the following formula: in:k Sampling time, For PIW k The estimated open-circuit voltage at each sampling time. This represents the open-circuit voltage at the initial sampling time within the PIW. The length of PIW This represents the change in open-circuit voltage.

[0013] In one possible implementation, a velocity pause mechanism is introduced in the particle optimization iteration, giving the particle a certain probability to maintain the search pace of the previous moment, so that the search process generates three detection modes: slow, fast and uniform, in order to avoid the parameters getting trapped in local pseudo-optima.

[0014] In one possible implementation, two populations are divided to maintain particle diversity, wherein: the main population explores the global physical boundary with the goal of minimizing the root mean square error of the terminal voltage; the secondary population does not perform independent velocity calculations, but directly focuses on the optimal physical parameter boundary currently discovered by the main population, and uses a decreasing shrinkage mechanism to perform fine-grained local updates of polarization parameters in the neighborhood of this boundary.

[0015] In one possible implementation, the step of combining the identified model parameters, utilizing the APF algorithm and residual-driven feedback mechanism to dynamically update the noise variance, suppress measurement uncertainty, and output SOE estimation results that are robust to temperature and noise includes: During the state prediction phase, the state space equation is updated based on the real-time second-order FECM equivalent parameters, and the particle swarm is driven by the current load current to perform nonlinear propagation of the prior state. During the weight calculation and normalization stage, the observation residual between the terminal voltage predicted by the second-order FECM and the actual acquired terminal voltage is extracted in real time. The weight value of each particle is calculated based on the observation residual and the current observation noise variance, and the weight value is normalized. During the resampling and state output phase, resampling is performed based on the normalized weight values. When the resampling conditions are met, the effective particles are resampled and their states are weighted, and the updated results are output. During the noise variance update phase, the noise variance is dynamically updated based on the observed residuals through the residual-driven feedback mechanism, and the updated noise variance is used for weight calculation at the next time step.

[0016] In one possible implementation, the step of extracting the observation residual between the terminal voltage predicted by the second-order FECM model and the actual acquired terminal voltage in real time during the observation update phase includes: When encountering sudden non-Gaussian noise interference, the noise variance is relaxed, and the weight of abnormally abrupt measurement values ​​is actively reduced to prevent severe degradation of the filtered particle swarm. Conversely, when the operating current is stable, the noise variance is reduced to lock in high-precision state of energy (SOE) tracking.

[0017] In the embodiments of this application, the beneficial effects include: (1) This application establishes a second-order fractional-order equivalent circuit model and uses constant-phase elements to replace integer-order ideal capacitors, which can more accurately characterize the electrochemical dispersion effect inside the lithium battery and improve the model's accuracy in representing the battery's real electrochemical behavior. (2) This application combines the parameter identification window mechanism with the co-evolutionary velocity pause particle swarm algorithm. Through the dual-population cooperative search strategy of global exploration of the main population and local development from the population, and the velocity pause mechanism, the algorithm enhances the local development capability of the algorithm in the low-energy state and strong nonlinear region, and suppresses the search from getting trapped in local false optimum while ensuring the real-time performance of online identification. (3) This application adopts an adaptive particle filter algorithm and a residual-driven feedback mechanism to dynamically update the noise variance based on the observed residual. It can maintain a stable energy state estimate under non-Gaussian noise interference and wide temperature range variation, thus achieving strong robustness to temperature and noise. Attached Figure Description

[0018] Figure 1 A flowchart illustrating a collaborative energy state estimation method with strong robustness to temperature and noise, provided for an embodiment of this application; Figure 2 A three-dimensional diagram of the open-circuit voltage-energy state-temperature nonlinear relationship provided in the embodiments of this application; Figure 3 This is a schematic diagram of load current and injected non-Gaussian noise provided in an embodiment of this application, wherein (a) is the load current and (b) is the artificially injected non-Gaussian noise; Figure 4 The second-order fractional-order equivalent circuit model diagram provided in the embodiments of this application; Figure 5 A schematic diagram illustrating the working principle of the co-evolutionary velocity-pause particle swarm optimization algorithm provided in this application embodiment; Figure 6 A schematic diagram illustrating the working principle of the parameter identification window provided in this application embodiment; Figure 7 The parameter identification results provided in the embodiments of this application are shown in the following figure: (a) is the identification result of the resistance of the co-evolutionary velocity pause particle swarm optimization algorithm, (b) is the identification result of the capacitance, (c) is the identification result of the open circuit voltage, and (d) is the identification result of the change in open circuit voltage. Figure 8The terminal voltage fitting error and error distribution diagram provided in the embodiments of this application are shown, wherein (a) is the terminal voltage fitting error identified by the parameters of the co-evolutionary velocity pause particle swarm optimization algorithm, and (b) is the error distribution histogram of the fitting error. Figure 9 The fitness change trend of the co-evolutionary velocity-pause particle swarm optimization algorithm under 6 random energy state points provided in the embodiments of this application; Figure 10 The flowchart of the adaptive particle filter algorithm provided in the embodiments of this application is shown. Figure 11 A comparison diagram of energy state estimation results of different methods provided in the embodiments of this application is shown, wherein (a) is the energy state estimation result, and (b) is the energy state estimation error result; Figure 12 The diagram shows the energy state estimation results of different methods under noise injection provided in the embodiments of this application, where (a) is the energy state estimation result and (b) is the energy state estimation error result. Figure 13 The energy state estimation error of the collaborative estimation method disclosed in this application is given under four typical temperatures; Figure 14 The diagram shows the energy state estimation results of different methods in the ablation test provided in the embodiments of this application, where (a) is the energy state estimation result and (b) is the energy state estimation error result. Detailed Implementation

[0019] The present solution will now be described in conjunction with the accompanying drawings and specific embodiments.

[0020] Figure 1 This is a flowchart illustrating a collaborative energy state estimation method with strong robustness to temperature and noise disclosed in this application. The SOE collaborative estimation method disclosed in this application includes: S101, acquire the pre-established OCV-SOE-T nonlinear relationship of the lithium battery, and collect dynamic measurement data of the lithium battery under operating conditions in real time.

[0021] In this embodiment, to verify the effectiveness of the above algorithm, the lithium battery characteristics were tested at different temperatures using a specific experimental platform. Specifically, the battery used in the experiment was a single lithium iron phosphate battery, model LFP18650E. In the OCV-SOE-T nonlinear relationship test, the temperature of the constant temperature chamber was increased from 10℃ to 40℃, with each temperature setting in 5℃ increments. In the DST dynamic operating condition test, four typical temperatures of 15℃, 25℃, 30℃, and 35℃ were selected for verification. Detailed parameters are shown in Table 1. The experimental platform consisted of a Xinwei CE-4008Q-5V15A-S1 charge-discharge test device, a matching CT-4001-ZWJPLUS-1U intermediate computer, a PC-based host computer, and the lithium battery. By defining low-rate discharge and DST load conditions using a central computer, charge-discharge testing equipment was used to collect battery terminal voltage, load current, and corresponding temperature. The collected data was pre-processed by the central computer and then sent to a PC (Intel Core i5-12490F CPU, 3.00GHz, 16GB, 64bit, Windows 11) for data storage. After the raw experimental data was tested and stored, MATLAB (R2023b) was used to verify the SOE collaborative estimation algorithm.

[0022] Table 1. Main technical parameters of the test battery Lithium battery characteristic tests: (1) OCV-SOE-T nonlinear relationship test. First, adjust the temperature of the constant temperature chamber to 10℃, and use 0.5 C rated The constant current charging method charges the battery until the terminal voltage reaches 3.6V, then switches to constant voltage charging, and continues charging until the current decreases to 0.01V. C rated Power off and leave for 5 hours. At 0.1 C rated The battery was discharged for 30 minutes, then disconnected, and left to stand for 8 hours. This discharge pattern was repeated until the voltage dropped to 2.5 V, then disconnected again and left to stand for 8 hours. The SOE value corresponding to each resting point was calculated based on the energy released in each discharge stage. The temperature of the constant temperature chamber was increased by 5°C, and this charge-discharge pattern was repeated until the temperature of the constant temperature chamber reached 40°C. The nonlinear relationship between OCV-SOE-T is as follows: Figure 2 As shown.

[0023] (2) Dynamic operating condition test. At four typical temperatures of 15℃, 25℃, 30℃, and 35℃, the lithium battery was subjected to dynamic operating condition testing using the DST standard. The test data was sorted according to the sampling time, with a sampling interval of 0.5s, for algorithm verification and analysis. The time cycle for completing one DST test is 720s, and its load current is as follows: Figure 3As shown in (a). To verify the algorithm's anti-interference capability, non-Gaussian noise was artificially injected into the measurement data, with a maximum noise amplitude of 18.3mV, as shown in (a). Figure 3 As shown in (b).

[0024] S102, establish a second-order FECM to describe the internal electrochemical dispersion effect of the battery, input the dynamic measurement data into the model, and establish physical parameter boundaries for parameter identification.

[0025] The electrochemical impedance spectroscopy of lithium iron phosphate batteries exhibits obvious fractional-order characteristics. Therefore, this application utilizes constant-phase elements with fractional-order characteristics to replace the capacitors in integer-order circuits, constructing a fractional-order equivalent circuit model to describe the electrochemical dispersion effect inside the battery.

[0026] In this embodiment, two constant-phase elements are used. CPE 1 and CPE 2. Replace the two integer-order capacitors in the equivalent circuit model and establish a second-order FECM as follows: Figure 4 As shown.

[0027] In this embodiment, dynamic measurement data obtained by DST dynamic operating condition testing at four typical temperatures of 15℃, 25℃, 30℃ and 35℃ are used to perform offline parameter pre-identification of the second-order FECM, obtain the variation range of each parameter to be identified, and use the variation range as the physical parameter boundary for subsequent online parameter identification.

[0028] exist Figure 4 middle, R 0 represents the ohmic internal resistance of the lithium battery; R 1 and constant phase elements CPE 1. Parallel connection indicates the electrochemical polarization process of the battery; R 2 with constant phase elements CPE 2. Parallel connection indicates the concentration polarization process of the battery; i Indicates the load current; u p1 and u p2 Indicates polarization voltage; u oc Indicates the open-circuit voltage of the battery; u L This represents the battery's terminal voltage. To reduce the computational cost of online identification, the fractional order of the two constant-phase elements is fixed to the order obtained from offline identification. α = 0.75 and β = 0.99.

[0029] S103, combined with the PIW mechanism, uses CVPPSO algorithm. Law The second-order FECM is identified online to obtain accurate model parameters in real time.

[0030] The CVPPSO algorithm is characterized by: addressing the problems of poor real-time performance and susceptibility to local false optima in biomimetic optimization algorithms; utilizing a dual-population strategy and a velocity pause mechanism to increase particle diversity and improve the algorithm's local exploitation capability; and achieving real-time online updating of the parameters to be identified through PIW sliding. Its working principle is as follows: Figure 5 As shown.

[0031] In this embodiment, the parameters to be identified include: .

[0032] in, For the first polarization resistor, For the first constant phase element CPE The equivalent capacitance corresponding to 1, This is the second polarization resistor. For the second constant phase element CPE The equivalent capacitance corresponding to 2.

[0033] In this embodiment, the schematic diagram of PIW is as follows: Figure 6 As shown in the figure, PIW( k ) represents the identification window at the current sampling time, PIW( k+ 1) Represents the identification window for the next sampling time; u L,k and u L,k+1 This represents the terminal voltage data of the identification window. The PIW length is set to... L p At each sampling step, the actual terminal voltage and load current data sequence within the PIW are extracted. The parameters to be identified in the second-order FECM are then... Pars Mapped to the optimization objective of particle swarm optimization, the PIW slides once at each sampling time, and CVPPSO completes one evolution. Each evolution updates only one parameter. After completing one parameter identification, the PIW slides to update historical data and outputs the real-time equivalent battery parameters at the current time. Parameter identification is performed according to... Pars The parameters are processed sequentially and cyclically until sampling is complete. This applies to open-circuit voltages. u oc Slowly changing physical properties are treated approximately linearly within PIW, and the formula is as follows: in: k Sampling time, For PIW k The estimated open-circuit voltage at each sampling time. This represents the open-circuit voltage at the initial sampling time within the PIW. The length of PIW This represents the change in open-circuit voltage.

[0034] In this embodiment, a velocity update pause mechanism is introduced in the particle optimization iteration, giving particles a certain probability of maintaining the search pace from the previous moment. This mechanism is specifically designed to address the characteristic of lithium batteries exhibiting a sharp increase in multidimensional nonlinear polarization in the low SOE region, effectively preventing parameters from getting trapped in local pseudooptima.

[0035] The particle velocity update formula is: Among them, velocity disturbance intensity coefficient With speed update probability They are respectively: In the above formula, t Let the current iteration algebra be... i Indicates the current evolutionary particle number; Indicates the first t During the nth iteration i The velocity of each particle; Indicates the first t During the nth iteration i The position vector of each particle, i.e., the current combination of parameters of the battery model to be identified.

[0036] Pbest It is the historical best position of a single particle. Gbest It is the optimal position among all particles. Pbest and Gbest In each iteration, the main group update formula and the slave group update formula are compared and updated according to the formula described later. c 1 represents the individual learning factor, used to control the particle's trajectory towards itself. Pbest The degree of proximity reflects the particle's autonomous search capability; c 2 is the global learning factor, used to control the direction of particle movement. Gbest The degree of proximity reflects the group's collaborative search capability; both values ​​are 2. Controlling the intensity of particle velocity perturbations, The probability of controlling particle velocity updates: when η When =1, the speed update will not pause, and the algorithm degenerates into a co-evolutionary particle swarm optimization algorithm; when η When the velocity is 0, the particle remains at a constant speed and will not update its velocity. This represents the maximum number of iterations for a particle, with a value of 12. It is a constant with a value of 2.5.

[0037] rand, rand1, and rand2 are all random numbers uniformly distributed between 0 and 1. rand1 and rand2 are used to increase the randomness of particle motion and avoid particles getting trapped in local false optima. rand is a random variable for mode selection, used to determine whether the current particle should perform a velocity update.

[0038] Based on the above formula, the search process naturally forms three detection modes: slow, fast, and constant speed: when rand ≥ η When (t), the current particle maintains uniform motion; when rand < η (t) and λ When (t) is large, particle velocity changes rapidly, suitable for large-scale global exploration in the early stages of a search; when rand < η (t) and λ When (t) is small, the particle velocity changes slowly, which is suitable for fine-grained local searches in the later stages of the search. As the number of iterations increases... t Increase η (t) gradually decreases λ (t) gradually decreases, thus allowing the particle to smoothly transition from an early, large-scale, rapid search to a later, local, slow, and refined search.

[0039] In this embodiment, two populations are used to maintain particle diversity. The main population explores the global physical boundary with the goal of minimizing the root mean square error of the terminal voltage. The secondary population does not perform independent velocity calculations but directly focuses on the optimal physical parameter boundary currently discovered by the main population, using a decreasing shrinkage mechanism to perform refined local updates of polarization parameters within the neighborhood of this boundary. The new position update formula is: Main group update: Update from the group: In this embodiment, the fitness function of the CVPPSO algorithm is: Here, fitness represents the particle's fitness level. This represents the estimated terminal voltage. This indicates the measured value of the terminal voltage.

[0040] The parameter identification results of the CVPPSO algorithm are basically continuous and fluctuate slowly over long time scales, which is consistent with the long-term variation law of the equivalent parameters of lithium batteries. The CVPPSO algorithm was used to identify the parameters of the second-order FECM established in this application under DST conditions, and the results are as follows: Figure 7 As shown. Figure 7 In the middle (a), the resistance identification result is shown. Figure 7 (b) represents the capacitor identification result. Figure 7 (c) represents the open-circuit voltage. u oc The identification results Figure 7 In the middle (d), it represents the change in open-circuit voltage Δ. u oc The identification results. Figure 7 (a) and Figure 7 (b) The results show that R The identification results for 0 show an almost slightly upward linear trend. Although R 1 and R The identification results of 2 show local small-amplitude oscillations, but the overall results still maintain the characteristic of continuous and slow fluctuations. C 1 and C The fluctuation characteristics of 2 and R 0 Similar, but the main difference is that it shows a downward trend most of the time. Figure 7 (c) and Figure 7 (d) The results show that u oc The identification results can accurately track the terminal voltage. u L The changing trend, its changing pattern and u oc The general pattern of change is consistent.

[0041] Compared to the CPSO algorithm, the CVPPSO algorithm achieves higher terminal voltage fitting accuracy, especially in the low SOE range, while the computational cost remains almost unchanged. To investigate the roles of the dual-population strategy and the speed pause mechanism, parameter identification was performed using both the CPSO and CVPPSO algorithms under DST conditions. The terminal voltage fitting results are as follows: Figure 8 As shown in Table 2. Figure 8 In the middle (a), the fitting error of the terminal voltage is represented. Figure 8 In Figure (b), the error distribution histogram of the fitting error is shown. The results show that, under the same equivalent model, the root mean square error (RMSE) of CVPPSO is 2.10 × 10⁻³V, which is 27.5% lower than that of CPSO. Figure 9The results show the fitness trend of the CVPPSO algorithm at six random SOE points. The results indicate that CVPPSO exhibits a smoother decrease in fitness and a lower final convergence value across different SOE intervals, particularly in the low SOE intervals (e.g., SOE = 15.37% and 5.29%), where the differences are more pronounced. This is because battery polarization is more significant in the low SOE interval, increasing model nonlinearity. Traditional CPSO is more prone to getting trapped in local optima in this region, while CVPPSO, through an improved particle update mechanism, enhances population diversity and search direction stability, thus achieving better voltage fitting results. This demonstrates that CVPPSO possesses stronger local optimization capabilities in complex nonlinear search spaces and maintains good convergence performance in the highly coupled low SOE interval.

[0042] Table 2. Test results of parameter identification for CPSO and CVPPSO algorithms S104 combines the identified model parameters and utilizes the APF algorithm and residual-driven feedback mechanism to dynamically update the noise variance, suppress measurement uncertainty, and output SOE estimation results that are robust to temperature and noise.

[0043] The APF algorithm is characterized by: addressing the low accuracy and poor robustness of traditional Kalman filtering algorithms by using a set of discrete random sampling points to approximate the probability density function, replacing integration with the sample mean to improve estimation accuracy, and adaptively updating the noise variance to cope with complex operating conditions and interference, thus enhancing robustness. Its algorithm flowchart is shown below. Figure 10 As shown.

[0044] In this embodiment, during the state prediction phase, the APF algorithm updates the state space equation based on the real-time second-order FECM equivalent parameters and combines the current load current to drive the particle swarm to perform nonlinear propagation of the prior state.

[0045] In this embodiment, during the weight calculation and normalization stage, based on the prior state particles obtained in the state prediction stage, the predicted terminal voltage corresponding to each particle is calculated using a second-order FECM model. The predicted terminal voltage is then compared with the actual acquisition terminal voltage to obtain the observation residual. A particle likelihood function is constructed based on the observation residual, and the weight value of each particle is calculated in conjunction with the current observation noise variance to characterize the degree of matching between different predicted states and actual observation data. The weight calculation and normalization are performed according to the following formula: in, Represents particle weights. This represents the normalized weight of the particles; This represents the measurement noise variance, and N is the number of particles used in the APF algorithm.

[0046] In this embodiment, during the resampling and state update phase, after the aforementioned adaptive weight adjustment, the effective particles are resampled and their states are weighted, and the updated result is output. The resampling determination is performed according to the following formula: in, N The number of particles used in the APF algorithm.

[0047] In this embodiment, during the noise variance update stage, the APF algorithm extracts the observation residual between the terminal voltage predicted by the FECM model and the actual acquired terminal voltage in real time. When encountering sudden non-Gaussian noise interference, this observation residual will undergo abnormal abrupt changes. At this time, the state feedback mechanism is triggered, and the algorithm will dynamically expand the effective boundary of the system observation noise variance matrix based on the moving average of historical residuals. By relaxing the noise variance, the weight of abnormally abrupt measurement values ​​is actively reduced to prevent severe degradation of the filter particle swarm; conversely, when the operating current is stable, the system automatically shrinks the noise variance to lock in high-precision SOE tracking. The noise variance update method is as follows: in, Indicates the change in state; Indicates the attenuation factor; The standard deviation represents the variance of the noise.

[0048] Ultimately, under the synergistic effect of the FECM-CVPPSO-APF three components disclosed in this application, the system outputs a lithium battery state of energy estimation result that is highly robust to temperature and noise.

[0049] The SOE estimation results of the FECM-CVPPSO-APF collaborative estimation method described in this application have high accuracy and fast convergence speed. To explore the role of particle filtering and adaptive theory in improving SOE estimation accuracy, based on the parameter identification results of the second-order FECM and CVPPSO algorithms, SOE estimation was performed under DST conditions using extended Kalman filter (EKF), unscented Kalman filter (UKF), particle filter (PF), and APF, respectively. The estimation results are as follows: Figure 11 As shown in Table 3. Figure 11 In the middle (a), the SOE estimation results of the four methods are shown. Figure 11 In the middle (b), the SOE estimation error results of the four methods are shown.

[0050] The results show that the collaborative estimation method disclosed in this application has the smallest SOE estimation error, with an RMSE of only 0.32%. Furthermore, with an initial SOE bias of 10%, its convergence time is only 9 seconds, significantly better than other methods, indicating that it can quickly enter the stable region even with a large initial bias. This is because they handle the nonlinear state-space model differently. EKF and UKF rely on linearization or higher-order approximations, which easily generate model approximation errors in the strongly nonlinear mapping region of OCV-SOE, resulting in slow convergence speed and large steady-state errors. Although PF avoids the linearization problem, the fixed noise variance leads to insufficient matching between the initial particle distribution and the true posterior distribution, affecting convergence efficiency. In contrast, APF adjusts the particle distribution in real time through adaptive updates of the noise variance, making it better match the system uncertainty. Therefore, the collaborative estimation method disclosed in this application shows significant advantages in both accuracy and convergence speed. Finally, although its computational cost is slightly higher than other methods, it still falls within the low computational cost category.

[0051] Table 3. Test results of SOE estimation accuracy using the collaborative estimation method The collaborative estimation method disclosed in this application exhibits strong filtering capability against non-Gaussian noise. To explore the role of adaptive theory in enhancing the algorithm's noise robustness, non-Gaussian noise was artificially injected into the measurement data. Then, under DST conditions, SOE estimation was performed using EKF, UKF, PF, and APF, respectively. The estimation results are as follows: Figure 12 As shown in Table 4. Figure 12 In the middle (a), the SOE estimation results of the four methods are shown under the condition of artificial non-Gaussian noise injection. Figure 12 In the middle (b), the SOE estimation error results of the four methods are shown under the condition of artificial non-Gaussian noise injection.

[0052] The results show that after the injection of non-Gaussian noise, the estimation errors of all algorithms increased, with EKF and UKF exhibiting significant oscillations in their estimation errors, while APF remained stable at the lowest error level. Table 4 shows that the RMSE of the collaborative estimation method disclosed in this application is 0.42%, an increase of only 0.1% compared to before the noise injection. Simultaneously, its convergence time is only 6 seconds, without significant oscillations. This is because non-Gaussian noise typically exhibits suddenness and heavy-tailed characteristics. When abnormal fluctuations occur in the observed signal, EKF and UKF, based on the Gaussian assumption, struggle to accurately describe the statistical characteristics of the noise, leading to a rapid amplification of errors. APF has less dependence on the noise distribution model and can adaptively adjust the noise variance, allowing the particle distribution range to dynamically adjust with changes in system uncertainty. Therefore, even under non-Gaussian noise conditions, the collaborative estimation method disclosed in this application can still maintain good SOE estimation accuracy and stability. This further illustrates that the inclusion of adaptive theory significantly enhances the system's robustness to noise interference.

[0053] Table 4. Noise robustness test results of the collaborative estimation method The collaborative estimation method disclosed in this application demonstrates high SOE estimation accuracy under various typical temperatures. To investigate the role of adaptive theory in enhancing the algorithm's temperature robustness, the algorithm was tested at four typical temperatures: 15℃, 25℃, 30℃, and 35℃. The test results are as follows: Figure 13 As shown in Table 5, the SOE estimation error of the collaborative estimation method disclosed in this application remained at a low level under four typical temperatures, with RMSE values ​​of 0.30%, 0.32%, 0.11%, and 0.11%, respectively. The maximum error did not exceed 0.6%, and the convergence time was within 10 seconds, with no performance degradation observed. Temperature changes affect the battery's internal resistance and polarization characteristics, thereby altering the system's state propagation characteristics. The APF further compensates for changes in model uncertainty through an adaptive adjustment mechanism. Therefore, even under different temperature environments, the collaborative estimation method disclosed in this application can still maintain stable SOE estimation performance.

[0054] Table 5. Temperature robustness test results of the collaborative estimation method Ablation studies have shown that accurate physical modeling (FECM), precise online parameter identification (CVPPSO), and a highly robust filtering method (APF) are all essential for improving the accuracy and robustness of SOE estimation. To rigorously quantify the respective contributions of FECM, CVPPSO, and APF to SOE estimation, SOE estimation was performed under harsh conditions of 25℃, artificially injected non-Gaussian noise, and an initial SOE error of 10%, using IECM-CPSO-PF, FECM-CPSO-APF, FECM-CVPPSO-PF, and FECM-CVPPSO-APF respectively. The test results are as follows: Figure 14 As shown in Table 6. Figure 14 In the middle (a), the SOE estimation results of the four methods in the ablation test are shown. Figure 14 (b) represents the SOE estimation error results for the four methods in the ablation test.

[0055] The results show that using the baseline method for SOE estimation results in large modeling errors and fails to filter non-Gaussian noise, with a steady-state RMSE as high as 3.41%. Introducing FECM effectively improves the model representation accuracy, reducing the RMSE to 1.55%. Further introduction of CVPPSO enhances the algorithm's local exploitation capabilities, improving parameter identification accuracy and thus enhancing the model's tracking and prediction capabilities, reducing the RMSE to 0.98%. However, the curve still oscillates due to unfiltered noise. The collaborative estimation method disclosed in this application effectively suppresses non-Gaussian noise interference through real-time adaptive updates of noise variance, ultimately reducing the SOE estimation RMSE to a stable 0.42%. The collaborative system of the FECM-CVPPSO-APF components systematically reduces the interference caused by modeling errors, parameter errors, and observation noise, thus verifying the necessity of the proposed SOE collaborative estimation method.

[0056] Table 6. Test results of ablation study using the collaborative estimation method This application proposes a collaborative estimation method for SOE of lithium batteries based on a three-component architecture of FECM-CVPPSO-APF, exhibiting strong robustness against temperature and noise, belonging to the field of lithium battery state estimation. This method abandons the simple stacking of pure mathematical optimization algorithms, deeply embedding them within the real physical data stream and time slices of the battery. It fundamentally solves the complex engineering challenges of poor real-time performance in multi-dimensional parameter identification, susceptibility to local optima, and weak anti-interference capability of state estimation, which lead to low accuracy and robustness in the final SOE estimation. The effectiveness of this collaborative mechanism for lithium battery SOE estimation is verified under conditions of significant non-Gaussian noise interference and wide temperature range variations. The results show that: (1) The CVPPSO algorithm, which deeply integrates PIW, accurately breaks through the bottleneck of real-time tracking of multidimensional variable parameters. By performing dimensionality reduction physical mapping within the PIW sliding window and combining the velocity pause mechanism of the main population with the local boundary development of the secondary population, the premature convergence phenomenon of polarization parameters is successfully suppressed. The verification results show that the fitting accuracy of the terminal voltage is improved by 27.5% compared with the traditional CPSO algorithm, and the online computational load is perfectly controlled while achieving high-precision tracking of multiple parameters.

[0057] (2) The observation residual-driven APF algorithm completely and effectively overcomes the vulnerability of the system to sudden disturbances. By monitoring the terminal voltage in real time to predict the residual and dynamically expanding or contracting the boundary of the system noise covariance matrix, the interference of non-Gaussian noise is effectively isolated. The verification results show that under multiple adverse conditions such as superimposed severe non-Gaussian noise injection, severe mismatch of SOE initial value and ambient temperature drift, the SOE collaborative estimation method disclosed in this application can not only achieve rapid state convergence within 10 seconds, but also stabilize the RMSE of SOE at an extremely low level of 0.42%, fully demonstrating its strong anti-disturbance robustness and excellent engineering application value.

[0058] In this application embodiment, "at least one" refers to one or more, and "more than one" refers to two or more. "And / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent the existence of A alone, the simultaneous existence of A and B, or the existence of B alone. A and B can be singular or plural. The character " / " generally indicates that the preceding and following related objects have an "or" relationship. "At least one of the following" and similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one of a, b, and c can represent: a, b, c, ab, ac, bc, or abc, where a, b, and c can be single or multiple.

[0059] The above description is merely a specific embodiment of this application. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the protection scope of this application. The protection scope of this application should be determined by the protection scope of the claims.

Claims

1. A collaborative estimation method for the state of energy of lithium batteries with strong robustness to temperature and noise, characterized in that, Includes the following steps: The pre-established open-circuit voltage-state of energy-temperature (OCV-SOE-T) nonlinear relationship of the lithium battery is obtained, and dynamic measurement data of the lithium battery under operating conditions are collected in real time. A second-order fractional equivalent circuit model (FECM) is established to describe the electrochemical dispersion effect of the battery. The dynamic measurement data is input into the model to establish the physical parameter boundaries for parameter identification. Combining the parameter identification window (PIW) mechanism, the Co-evolutionary Speed ​​Pause Particle Swarm Optimization (CVPPSO) algorithm is used to identify the second-order FECM online and obtain accurate model parameters in real time. By combining the identified model parameters, the adaptive particle filter algorithm (APF) and residual-driven feedback mechanism are used to dynamically update the noise variance, suppress measurement uncertainty, and output SOE estimation results that are robust to temperature and noise.

2. The method according to claim 1, characterized in that, The process of acquiring the pre-established open-circuit voltage-state of energy-temperature (OCV-SOE-T) nonlinear relationship of the lithium battery and collecting dynamic measurement data of the lithium battery under operating conditions in real time includes: The lithium battery was subjected to charge-discharge-rest cycle tests at multiple preset temperature levels. Calculate the SOE value at the resting point based on the energy released in each discharge stage and record the corresponding OCV. After obtaining multiple sets of OCV-SOE data, fit the data according to temperature to obtain the nonlinear relationship between OCV-SOE-T. The dynamic measurement data of the lithium battery under operating conditions is collected in real time by the charge and discharge test equipment. The dynamic measurement data includes terminal voltage, load current and corresponding temperature.

3. The method according to claim 1, characterized in that, The establishment of a second-order fractional equivalent circuit model (FECM) to describe the battery electrochemical dispersion effect involves inputting the dynamic measurement data into the model to establish physical parameter boundaries for parameter identification, including: The second-order FECM is established by replacing the two integer-order capacitors in the equivalent circuit model with two constant-phase elements. The second-order FECM is pre-identified offline using dynamic measurement data at different temperatures to obtain the variation range of each parameter to be identified within the corresponding temperature range. The variation range is then used as the physical parameter boundary for online parameter identification.

4. The method according to claim 3, characterized in that, The second-order FECM consists of an ohmic internal resistance R0, a first polarization branch, and a second polarization branch connected in series. The first polarization branch is formed by a first polarization resistor R1 connected in parallel with a first constant-phase element CPE1, representing the electrochemical polarization process of the battery. The second polarization branch is formed by a second polarization resistor R2 connected in parallel with a second constant-phase element CPE2, representing the concentration polarization process of the battery. The fractional orders of the first constant-phase element CPE1 and the second constant-phase element CPE2 are fixed as those obtained from offline identification. and .

5. The method according to claim 1, characterized in that, The combined parameter identification window (PIW) mechanism employs the Co-evolutionary Speed ​​Paused Particle Swarm Optimization (CVPPSO) algorithm to perform online identification of the second-order FECM, obtaining accurate model parameters in real time, including: Set the PIW length and sampling step size, and extract the actual terminal voltage and load current data sequence within the PIW at each sampling step size; The parameters to be identified in the second-order FECM Pars This is mapped to the optimization objective of the particle swarm optimization. At each sampling time, PIW slides once, and CVPPSO completes one evolution. Each evolution only updates one parameter. After completing one parameter identification, slide PIW to update historical data and output the current real-time equivalent battery parameters. Parameter identification is performed by... Pars The parameters are processed sequentially and cyclically until the sampling ends.

6. The method according to claim 5, characterized in that, For open circuit voltage Slowly changing physical properties are treated approximately linearly within PIW, as shown in the following formula: in: k Sampling time, For PIW k The estimated open-circuit voltage at each sampling time. This represents the open-circuit voltage at the initial sampling time within the PIW. The length of PIW This represents the change in open-circuit voltage.

7. The method according to claim 5 or 6, characterized in that, In the particle optimization iteration, a velocity pause mechanism is introduced, which gives the particle a certain probability to maintain the search pace of the previous moment, so that the search process generates three detection modes: slow, fast and uniform speed, in order to avoid the parameters from getting trapped in local pseudo-optima.

8. The method according to claim 7, characterized in that, To maintain particle diversity, two populations are divided: the main population explores the global physical boundary with the goal of minimizing the root mean square error of the terminal voltage; the secondary population does not perform independent velocity calculations, but directly focuses on the optimal physical parameter boundary currently discovered by the main population, and uses a decreasing shrinkage mechanism to perform fine-grained local updates of polarization parameters in the neighborhood of this boundary.

9. The method according to claim 1, characterized in that, By combining the identified model parameters, the Adaptive Particle Filter (APF) algorithm and residual-driven feedback mechanism are used to dynamically update the noise variance, suppress measurement uncertainty, and output SOE estimation results that are robust to temperature and noise, including: During the state prediction phase, the state space equation is updated based on the real-time second-order FECM equivalent parameters, and the particle swarm is driven by the current load current to perform nonlinear propagation of the prior state. During the weight calculation and normalization stage, the observation residual between the terminal voltage predicted by the second-order FECM and the actual acquired terminal voltage is extracted in real time. The weight value of each particle is calculated based on the observation residual and the current observation noise variance, and the weight value is normalized. During the resampling and state output phase, resampling is performed based on the normalized weight values. When the resampling conditions are met, the effective particles are resampled and their states are weighted, and the updated results are output. During the noise variance update phase, the noise variance is dynamically updated based on the observed residuals and the residual-driven feedback mechanism. The updated noise variance is then used for weight calculation at the next time step.

10. The method according to claim 9, characterized in that, In the weight calculation and normalization stage, the observation residual between the terminal voltage predicted by the second-order FECM model and the actual acquired terminal voltage is extracted in real time, including: When encountering sudden non-Gaussian noise interference, the noise variance is relaxed, and the weight of abnormally abrupt measurement values ​​is actively reduced to prevent severe degradation of the filtered particle swarm. Conversely, when the operating current is stable, the noise variance is reduced to lock in high-precision state of energy (SOE) tracking.

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