Energy storage system parameter fitting method based on active learning Kriging model

Abstract

The invention discloses an energy storage system parameter fitting method based on an active learning Kriging model. The method comprises the following steps: extracting a plurality of sample points to construct an initial training set, and normalizing the training set; constructing a Kriging model taking the initial sample set or the added sample set as a training set; utilizing a predictor function to obtain a prediction result and an estimation variance of the Kriging model on the sample points of the verification set; respectively substituting the prediction result and the variance into the U active learning function for calculation to obtain a function value of the corresponding learning function; repeating according to a convergence condition to obtain an active learning Kriging model; according to the method, the Kriging model is utilized to establish the energy storage system parameter agent model, the energy storage system model can be dynamically fitted on the basis of limited experimental data, the energy storage system parameters are updated in real time, and the precision and adaptability of an energy storage system management system are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of energy storage system BMS, and in particular to a method for fitting model parameters of an energy storage system. Background Art

[0002] With the widespread application of electric vehicles and energy storage systems, the battery management system (BMS) plays a key role in the performance prediction and management of energy storage systems. The state parameters of the energy storage system, such as open circuit voltage (OCV), energy storage system inductance and capacitance, change dynamically with the changes in the energy storage system state, affecting the state of charge (SOC) estimation and energy storage system health management. However, existing energy storage system modeling methods based on physical models or data-driven models have certain limitations in terms of real-time performance, accuracy and adaptability. In particular, due to the complexity of the changes in energy storage system parameters with SOC, they often cannot provide efficient and accurate estimation.

[0003] Most existing technologies rely on traditional energy storage system models and filtering methods, such as Kalman filtering and particle filtering, to estimate the relationship between SOC and energy storage system parameters.

[0004] For example: Chinese patent CN110165707A proposes a photovoltaic storage system optimization control method based on Kalman filtering and model predictive control, uses an improved Kalman filtering algorithm to establish the time equation and state equation of the filter, establishes a mathematical model of the photovoltaic storage combined power generation system, and uses the model predictive control method to optimize the energy storage system. This method can achieve early prediction and timely control of the photovoltaic storage combined system to ensure that the output power of the photovoltaic power generation system is smoothed while optimizing the output and charge state of the energy storage system; however, it is not adaptable enough to modeling nonlinear or time-varying systems, which can easily lead to a decrease in prediction accuracy, and the real-time calculation complexity of the model predictive control is high, which can easily affect the dynamic response speed; Chinese patent CN118322931A discloses an intelligent control and management system for a chemical battery energy storage system for new energy vehicles, which uses the Kalman filtering method to evaluate the battery state value, monitor and analyze the charge and discharge state of the new energy vehicle battery, and uses different state estimation algorithms Mutual verification improves the accuracy of battery status analysis. Although multi-algorithm collaborative verification improves accuracy, it increases computing resource usage, affects real-time control efficiency, and does not fully consider the impact of time-varying parameters during battery aging on long-term estimation stability; Chinese patent CN115935206A proposes a SOC estimation method and device, equipment and storage medium for energy storage systems, which performs particle filtering on the interactive models separately to determine the estimated SOC of each interactive model, and uses particle filtering to estimate the SOC of high-frequency equivalent circuits and medium- and low-frequency equivalent circuits. The fused SOC is then calculated through an interactive multi-model algorithm to reduce the SOC calculation error caused by frequency band changes between high-frequency, medium- and low-frequency frequencies. Although particle filtering and multi-model fusion strategies can reduce the estimation error caused by frequency band switching, they are highly dependent on the accuracy of the equivalent circuit model parameters. At the same time, parallel calculation of high-frequency, medium- and low-frequency models will significantly increase the complexity of the algorithm, which may restrict real-time performance and increase hardware resource consumption of embedded systems.

[0005] In summary, these methods usually require a large amount of training data or assume that parameters remain unchanged, and cannot accurately respond to the dynamic changes in parameters of the energy storage system during actual use. They have problems such as poor real-time performance, low accuracy, and insufficient adaptability. Therefore, how to effectively model the relationship between the energy storage system SOC and parameters such as the energy storage system inductance, open-circuit voltage, and capacitance has become an important issue in improving the performance of energy storage system management systems. Summary of the Invention

[0006] The purpose of the present invention is to solve the problems in the prior art and propose a parameter fitting method for energy storage systems based on active learning Kriging model, which can more accurately predict battery parameters under limited experimental data and improve BMS performance.

[0007] To achieve the above object, the present invention proposes a parameter fitting method for an energy storage system based on an active learning Kriging model, which is characterized by comprising the following steps in sequence: a) Fully charge the energy storage system and let it stand until the internal state reaches equilibrium; b) After fully charging at constant current and constant voltage, set several SOC values ​​from 0 to 100%, and then discharge at constant current to the set SOC value; c) Apply a series of constant current pulses to perform HPPC testing, record the voltage and current changes during the pulses, and calculate the system parameter values ​​based on the voltage and current; d) determining whether it is the last SOC value, if yes, proceeding to step f), if no, proceeding to step e); e) Enter the next set SOC value and repeat steps b) to c) to obtain the corresponding system parameter values ​​under the SOC value; f) Using SOC as the research variable, a number of sample points were extracted from the sample space using the Latin hypercube sampling method, and the model parameter values ​​were calculated by table lookup to construct the initial training set and normalize the training set; g) Constructing a Kriging model with the initial sample set or the added sample set as the training set; h) Use Latin hypercube sampling in the sample space to extract several sample points as the validation set of the active learning function. After normalizing the validation set, use the predictor function to obtain the prediction results and estimated variance of the validation set sample points using the above Kriging model; i) The prediction results and variance are respectively brought into the U active learning function for calculation to obtain the function value of the corresponding learning function; j) Determine whether the function value of the learning function meets the convergence condition. If not, add the new sample point to the training set and return to step g); if yes, obtain the active learning Kriging model and end the program.

[0008] Preferably, the constant current pulse in step c) includes a discharge pulse and a charge pulse, and the system parameter values ​​include open circuit voltage (OCV), ohmic internal resistance (R0), polarization internal resistance (Rp) and polarization capacitance (Cp).

[0009] Preferably, the method for calculating the open circuit voltage (OCV), ohmic internal resistance (R0), polarization internal resistance (Rp) and polarization capacitance (Cp) corresponding to each SOC point in step c) is as follows: OCV: take the average voltage value in the static stage as OCV; R0: calculate based on the voltage mutation ΔV and current change ΔI at the moment of the start of the discharge or charging pulse, R0 = ΔV / ΔI; Rp and Cp: perform exponential fitting on the voltage decay curve after the pulse to obtain the time constant τ, then Rp = τ / Cp, where Cp can be estimated by other methods or empirical values ​​or obtained by model fitting.

[0010] Preferably, in step f), 28 sample points are extracted from the sample space using the Latin hypercube sampling method as an initial training set, and the corresponding SOC, open circuit voltage (OCV), ohmic internal resistance (R0), polarization internal resistance (Rp), and polarization capacitance (Cp) values ​​are extracted. The SOC input data is normalized to the [0,1] interval, and the dacefit function of the DACE toolbox is used to construct four independent Kriging models with SOC as input and open circuit voltage (OCV), ohmic internal resistance (R0), polarization internal resistance (Rp), and polarization capacitance (Cp) as outputs. The established Kriging model can be expressed as: (1); Where, is a vector containing m basis functions, is a vector containing m regression coefficients; To obey the normal distribution The covariance of the steady-state Gaussian process is: (2); Where, are any two sets of input parameters drawn from the sample space of the energy storage system. and The spatial correlation equation adopts the Gaussian equation, which is in the form of: (3); Where, is the input parameter vector No. A quantity, is the corresponding correlation parameter, obtained by maximum likelihood estimation, and expressed as follows: (4); Where R is the correlation matrix, ; After transformation, we can get the following global unconstrained minimum optimization problem, thereby determining the parameters : (5); At this point, the construction process of the Kriging model of the energy storage system is transformed into solving the optimization problem of formula (5). Using the least squares method, the polynomial parameters of the Kriging model of the energy storage system, that is, its regression coefficients, can be obtained: (6); Where F is ; Likewise, the estimate of the variance is: (7); For the sample space of energy storage system , the predicted value of the Kriging model of the energy storage system Normal distribution , where the best linear unbiased estimate and mean square error It can be expressed as: (8); (9); Where, Forecast point The correlation vector between all k samples in the sample set extracted from the sample space of the energy storage system .

[0011] Preferably, in step h), 500 sample points are extracted as a validation set using the Latin hypercube sampling method and normalized, and the open circuit voltage (OCV), ohmic internal resistance (R0), polarization internal resistance (Rp) and polarization capacitance (Cp) of the validation set sample points and the prediction variance are predicted using the predictor function, in the same manner as in step f).

[0012] Preferably, in step i), the U function is used to calculate the function value of each validation set sample point, and the U function is defined as follows: U(x)=|f(x)-y| / s(x), where f(x) is the predicted value, y is the target value, and since y is the validation set, y is known, s(x) is the predicted standard deviation, and the sample point with the largest U function value is selected and added to the training set. The Kriging model is rebuilt using the updated training set until the maximum value of the U function is less than 0.01 or the number of iterations reaches 100.

[0013] Beneficial effects of the present invention: The present invention uses an active learning Kriging model to establish a proxy model between the SOC of the energy storage system and the inductance, open-circuit voltage and capacitance of the energy storage system. Through this method, the energy storage system model can be dynamically fitted based on limited experimental data, and the energy storage system parameters can be updated in real time, thereby improving the accuracy and adaptability of the energy storage system management system and overcoming the shortcomings of traditional methods in dynamic parameter changes.

[0014] The features and advantages of the present invention will be described in detail through embodiments with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is a schematic diagram of the preparation process in the method of the present invention; Figure 2 It is a schematic diagram of the process of constructing the active learning Kriging model in the method of the present invention. DETAILED DESCRIPTION

[0016] Model selection: Taking into account both computational complexity and accuracy, the first-order PNGV model is selected to describe the energy storage system, and its state-space equation is established. System parameters include open-circuit voltage, ohmic internal resistance, polarization internal resistance, and polarization capacitance, which are related to the SOC value.

[0017] HPPC experiment design, obtain data samples: fully charge the energy storage system and let it stand until the internal equilibrium state is reached; its voltage and current are detected in real time through external sensors; it is discharged at a constant current, and paused every 0.1% drop in the SOC value to allow internal equilibrium to be reached. At this time, the SOC drop value is measured using the ampere-hour integration method; a series of constant current pulses of charge and discharge are applied at each pause point, and the voltage and current changes in this process are recorded. The system parameter values ​​at this time are calculated using the first-order PNGV model, including open circuit voltage, ohmic internal resistance, polarization internal resistance and polarization capacitance; based on the above experimental data, a table between SOC value and system parameters is established as a sample pool.

[0018] An active learning Kriging proxy model was constructed: SOC was used as the research variable, 28 sample points were extracted in the sample space using the Latin hypercube sampling method, and the model parameter values ​​were calculated by table lookup to construct an initial training set. The input parameters of the training set were normalized and the dacefit function of the dace toolkit was used to construct a Kriging model with the initial sample set as the training set. 500 sample points were extracted in the sample space using the Latin hypercube sampling method as the validation set of the active learning function. After normalizing the validation set, the predictor function of the dace toolkit was used to obtain the prediction results and estimated variance of the validation set sample points of the above Kriging model. The prediction results and variance were respectively substituted into the U active learning function for calculation to obtain the function value of the corresponding learning function. If the convergence condition was not met, the new sample point was added to the training set. The Kriging model was rebuilt using the expanded training set and the above steps were repeated until the convergence condition of the corresponding learning function was met. If the number of iterations exceeded 100, the iteration was considered to have failed.

[0019] See Figure 1 、 Figure 2 , the energy storage system parameter fitting method based on the active learning Kriging model includes the following steps in sequence: a) Fully charge the energy storage system and let it stand until the internal state reaches equilibrium; b) After fully charging at constant current and constant voltage, set several SOC values ​​from 0 to 100%, and then discharge at constant current to the set SOC value; c) Apply a series of constant current pulses to perform HPPC testing, record the voltage and current changes during the pulses, and calculate the system parameter values ​​based on the voltage and current; d) determining whether it is the last SOC value, if yes, proceeding to step f), if no, proceeding to step e); e) Enter the next set SOC value and repeat steps b) to c) to obtain the corresponding system parameter values ​​under the SOC value; f) Using SOC as the research variable, a number of sample points were extracted from the sample space using the Latin hypercube sampling method, and the model parameter values ​​were calculated by table lookup to construct the initial training set and normalize the training set; g) Constructing a Kriging model with the initial sample set or the added sample set as the training set; h) Use Latin hypercube sampling in the sample space to extract several sample points as the validation set of the active learning function. After normalizing the validation set, use the predictor function to obtain the prediction results and estimated variance of the validation set sample points using the above Kriging model; i) The prediction results and variance are respectively brought into the U active learning function for calculation to obtain the function value of the corresponding learning function; j) Determine whether the function value of the learning function meets the convergence condition. If not, add the new sample point to the training set and return to step g); if yes, obtain the active learning Kriging model and end the program.

[0020] Example 1: 1. Experimental equipment: Energy storage system battery cell: BYD-LFP40A lithium iron phosphate battery cell, nominal capacity 40Ah, nominal voltage 3.2V; battery testing system: BTS-5V100A battery testing system, which has constant current and constant voltage charging and discharging functions, current accuracy of ±0.1%FS, voltage accuracy of ±0.05%FS, and data acquisition frequency of 10Hz; constant temperature chamber: DHS-225A constant temperature chamber, temperature control accuracy of ±0.5℃, used to control the experimental temperature at 25℃; computer: desktop computer equipped with Intel i7-13700K processor, 16GB DDR5 memory, and Windows 11 Home Chinese version operating system, installed with Matlab 2023b and DACE toolbox.

[0021] 2. HPPC experimental steps: Preparation: Place the battery cell in a constant temperature box, set the temperature to 25°C, and let it stand for 2 hours to make its internal temperature uniform; Full charge: Use the BTS-5V100A battery test system to charge to 3.6V at a constant current of 1C (40A), then charge at a constant voltage of 3.6V until the current drops to 0.05C (2A), and let it stand for 1 hour; Discharge: Discharge at a constant current of 1C, and pause the discharge every time the SOC drops by 0.1%, and let it stand to allow the battery to reach equilibrium; Use the ampere-hour integration method to record the discharged capacity and calculate the current SOC; HPPC test: Perform an HPPC test at each SOC point, including the following steps: discharge at a constant current of 1C for 10 seconds, let it stand for 10 seconds, charge at a constant current of 1C for 10 seconds, and let it stand for 10 seconds; Record the voltage and current data throughout the process; Repeat: Repeat the discharge and HPPC test steps; Data save: Save all voltage, current and SOC data.

[0022] 3. Data processing and parameter extraction: Data filtering: Use a moving average filter to filter the voltage and current data to eliminate noise interference; Parameter calculation: Based on the first-order PNGV model, the open circuit voltage (OCV), ohmic internal resistance (R0), polarization internal resistance (Rp) and polarization capacitance (Cp) corresponding to each SOC point are calculated according to the HPPC test data; the specific calculation method is as follows: OCV: take the average voltage value of the static stage as OCV; R0: Calculate based on the voltage mutation ΔV and current change ΔI at the beginning of the discharge or charging pulse, R0=ΔV / ΔI; Rp and Cp: Perform exponential fitting on the voltage decay curve after the pulse to obtain the time constant τ, then Rp=τ / Cp, where Cp can be estimated by other methods or empirical values, or obtained by fitting a more complex model; in this embodiment, the voltage decay curve is fitted by the least squares method, and the values ​​of Rp and Cp are obtained at the same time; Establish a data table: The above SOC value-system parameters are stored in the data table to form a sample space for subsequent use.

[0023] 4. Build an active learning Kriging model: Initial training set: 28 sample points were extracted from the sample space as the initial training set using the Latin hypercube sampling method, and the corresponding SOC, OCV, R0, Rp, and Cp values ​​were extracted.

[0024] Data normalization: Normalize the SOC input data to the [0,1] range.

[0025] Kriging model construction: Use the dacefit function of the DACE toolbox, with SOC as input and OCV, R0, Rp, and Cp as output, to construct four independent Kriging models; the established Kriging model can be expressed as: (1); Where, is a vector containing m basis functions, is a vector containing m regression coefficients; To obey the normal distribution The covariance of the steady-state Gaussian process is: (2); Where, are any two sets of input parameters drawn from the sample space of the energy storage system. and The spatial correlation equation adopts the Gaussian equation, which is in the form of: (3); Where, is the input parameter vector No. A quantity, is the corresponding correlation parameter, obtained by maximum likelihood estimation, and expressed as follows: (4); Where R is the correlation matrix, ; After transformation, we can get the following global unconstrained minimum optimization problem, thereby determining the parameters : (5); At this point, the construction process of the Kriging model of the energy storage system is transformed into solving the optimization problem of formula (5). Using the least squares method, the polynomial parameters of the Kriging model of the energy storage system, that is, its regression coefficients, can be obtained: (6); Where F is ; Likewise, the estimate of the variance is: (7); For the sample space of energy storage system , the predicted value of the Kriging model of the energy storage system Normal distribution , where the best linear unbiased estimate and mean square error It can be expressed as: (8); (9); Where, Forecast point The correlation vector between all k samples in the sample set extracted from the sample space of the energy storage system .

[0026] Validation set: 500 sample points were extracted as the validation set using the Latin hypercube sampling method and normalized.

[0027] Active learning iteration: Use the predictor function to predict the OCV, R0, Rp, and Cp values ​​and prediction variance of the validation set sample points.

[0028] Use the U function to calculate the function value of each validation set sample point; the U function is defined as follows: U(x) = |f(x) - y| / s(x), where f(x) is the predicted value, y is the target value (in this case, since it is a validation set, y is known), and s(x) is the predicted standard deviation.

[0029] Select the sample point with the largest U function value and add it to the training set.

[0030] Rebuild the kriging model using the updated training set.

[0031] Repeat the above steps until the maximum value of the U function is less than 0.01 or the number of iterations reaches 100.

[0032] 5. Model validation: An independent test dataset (obtained by repeating the HPPC experiment but not used for training and validation) was used to evaluate the prediction accuracy of the final kriging model; the root mean square error (RMSE) and mean absolute percentage error (MAPE) were used as evaluation metrics.

[0033] 6. Expected Results: Through the above embodiments, a high-precision proxy model between battery SOC and parameters can be established; compared with traditional methods, this method can more accurately predict battery parameters under limited experimental data and improve the performance of the BMS.

[0034] Example 2: 1. Experimental equipment: Energy storage system battery cells: CATL-NMC811 cylindrical lithium-ion battery cells, nominal capacity 20Ah, nominal voltage 3.6V; Battery testing system: Digatron BTS-600HV high-precision battery testing system, supporting ±0.02% current accuracy and ±0.01% voltage accuracy, with data acquisition frequency increased to 50Hz; Constant temperature chamber: ESPEC PL-3KPF high and low temperature test chamber, with temperature control accuracy of ±0.3°C, and the experimental temperature set to -10°C to simulate low-temperature conditions; Computer: Equipped with an AMD Ryzen 9 7950X processor, 32GB DDR5 memory, and Windows 11 Home Chinese Edition operating system, and installed with Matlab 2023b and the DACE toolbox.

[0035] 2. HPPC experimental steps: Preparation: Place the battery cell in a constant temperature box, pre-cool it to -10℃, and then let it stand for 3 hours to ensure thermal equilibrium; Full charge: Use 2C constant current to charge to 4.2V, then switch to constant voltage charging until the current decays to 0.05C (1A), and let it stand for 2 hours to eliminate the polarization effect; Discharge: Discharge at a constant current of 0.5C, pause the discharge every time the SOC drops by 0.5%, and let it stand for 5 minutes to stabilize the internal state; Correct the SOC value by the open circuit voltage method combined with the ampere-hour integration; HPPC test: Perform a double pulse sequence at each SOC point: first discharge at 2C for 15 seconds, let it stand for 30 seconds, then charge at 1C for 10 seconds, and record the voltage and current response of the entire cycle; Repeat the above process until the SOC drops to 0%; Data storage: Synchronously store the original data to this SSD and back it up to the laboratory server in real time via FTP.

[0036] 3. Data processing and parameter extraction: Data filtering: Use discrete wavelet transform (Daubechies db4 mother wavelet) to perform multi-scale noise reduction on the voltage signal to eliminate high-frequency electromagnetic interference; OCV: Take the voltage average of the last 5s window during the static phase; R0: Calculate based on the voltage jump ΔV and current ΔI within 5ms of the discharge pulse. The formula is modified to R0 = ΔV / (ΔI×k), where k = 1.05 to compensate for the increase in SEI film impedance at low temperatures; Rp and Cp: Perform double exponential fitting on the voltage relaxation curve after the charge pulse to separate the interface polarization and diffusion polarization effects; Data table construction: The multi-dimensional parameter mapping relationship is stored in a CSV file to form an exclusive sample pool under low-temperature conditions.

[0037] 4. Active learning Kriging model: Initial training set: Using improved Latin hypercube sampling (Maximin optimization criterion), 35 sample points are extracted from the sample space, covering the non-uniform distribution of the SOC interval [0,1] (with a focus on encrypting the 30%-70% SOC area).

[0038] Kriging model construction: Use the dacefit function of the DACE toolbox, with SOC as input and OCV, R0, Rp, and Cp as output, to construct four independent Kriging models; the established Kriging model can be expressed as: (1); Where, is a vector containing m basis functions, is a vector containing m regression coefficients; To obey the normal distribution The covariance of the steady-state Gaussian process is: (2); Where, are any two sets of input parameters drawn from the sample space of the energy storage system. and The spatial correlation equation adopts the Gaussian equation, which is in the form of: (3); Where, is the input parameter vector No. A quantity, is the corresponding correlation parameter, obtained by maximum likelihood estimation, and expressed as follows: (4); Where R is the correlation matrix, ; After transformation, we can get the following global unconstrained minimum optimization problem, thereby determining the parameters : (5); At this point, the construction process of the Kriging model of the energy storage system is transformed into solving the optimization problem of formula (5). Using the least squares method, the polynomial parameters of the Kriging model of the energy storage system, that is, its regression coefficients, can be obtained: (6); Where F is ; Likewise, the estimate of the variance is: (7); For the sample space of energy storage system , the predicted value of the Kriging model of the energy storage system Normal distribution , where the best linear unbiased estimate and mean square error It can be expressed as: (8); (9); Where, Forecast point The correlation vector between all k samples in the sample set extracted from the sample space of the energy storage system .

[0039] Validation set: 600 sample points were extracted as the validation set using the Latin hypercube sampling method and normalized.

[0040] Active learning iteration: Use the predictor function to predict the OCV, R0, Rp, and Cp values ​​and prediction variance of the validation set sample points.

[0041] Use the U function to calculate the function value of each validation set sample point; the U function is defined as follows: U(x) = |f(x) - y| / s(x), where f(x) is the predicted value, y is the target value (in this case, since it is a validation set, y is known), and s(x) is the predicted standard deviation.

[0042] Select the sample point with the largest U function value and add it to the training set.

[0043] Rebuild the kriging model using the updated training set.

[0044] Repeat the above steps until the maximum value of the U function is less than 0.005 or the number of iterations reaches 150.

[0045] 5. Model Validation: The model robustness was evaluated using a 10-fold cross-validation method, and the MAE (mean absolute error) and R² coefficient of determination were calculated for each fold subset. Extreme Conditions Testing: Accelerated aging scenarios were designed at -20°C and 55°C, and the parameter prediction deviations of the traditional equivalent circuit model (ECM) and the proposed method were compared.

[0046] 6. Expected Results: Through the above embodiment, a high-precision proxy model between battery SOC and parameters can be established. At low temperature conditions of -10°C, the OCV prediction accuracy reaches ±2mV (1.5 times that of normal temperature conditions), meeting the BMS low-temperature compensation requirements.

[0047] Example 3: 1. Experimental Equipment: Energy Storage System Battery Cell: Lishen-LFP50Ah prismatic lithium-ion battery, nominal capacity 50Ah, nominal voltage 3.2V, cycle life ≥4000 cycles; Battery Testing System: NEWARE BTS-750V200A high-precision bidirectional test system, supporting ±0.01%FS current accuracy and ±0.02%FS voltage accuracy, with data acquisition frequency increased to 100Hz; Constant Temperature Chamber: Thermal Chambers TC-5KE high and low temperature test chamber, with temperature control accuracy of ±0.2°C, and the experimental temperature set to 60°C to simulate extreme thermal aging scenarios; Computer: Equipped with an AMD Ryzen 9 7950X processor, 64GB ECC DDR5 memory, and Windows 11 Home Chinese Edition operating system, with Matlab 2023b and the DACE toolbox installed.

[0048] 2. HPPC experimental steps: Preparation: Place the battery cell in a constant temperature chamber, preheat to 60°C, and let it stand for 5 hours to eliminate thermal stress; Full charge: Use 0.5C constant current to charge to 3.6V, then switch to constant voltage charging until the current decays to 0.02C (1A), and let it stand for 3 hours to eliminate electrochemical polarization effects; Discharge: Discharge at 0.2C constant current, pause discharge every 1% decrease in SOC, and let it stand for 10 minutes to allow internal concentration gradients to relax; SOC value is corrected using the open circuit voltage method combined with Kalman filtering.

[0049] HPPC test: High-frequency response: discharge at 3C for 5 seconds (Δt=10ms sampling rate) and stand for 2 seconds to capture ohmic polarization transients; medium-frequency response: charge at 1C for 30 seconds (Δt=100ms sampling rate) and stand for 60 seconds to observe the interface diffusion process; low-frequency response: discharge at 0.5C for 120 seconds (Δt=1s sampling rate) to record the concentration polarization steady-state recovery curve; data storage: synchronously store raw data in a RAID 0 array and transmit it to a cloud database in real time via the OPC UA protocol.

[0050] 3. Data Processing and Parameter Extraction: Data Filtering: An improved moving average filter (with an optimized window length of 15 sampling points) is used to preprocess the voltage signal to eliminate high-frequency electromagnetic interference. An adaptive Kalman filter algorithm is introduced for the current signal, and the signal-to-noise ratio is improved by dynamically adjusting the observation noise covariance matrix (Q value set to 0.02²). Parameter Calculation: OCV: The average voltage within a 5-second window after the static phase is taken as the open-circuit voltage reference value, and the temperature compensation coefficient K_T=1+α(T-T_0) is added, where α=0.0005 / °C (typical value for lithium iron phosphate batteries) to correct for the impact of ambient temperature differences. R0: The ohmic internal resistance is calculated based on the transient response within the initial 2ms of the discharge pulse, using the formula R0=ΔV peak / ΔI, eliminating the AD sampling delay effect through cubic spline interpolation; Rp and Cp: perform double exponential fitting on the voltage relaxation curve after the pulse (10s~120s interval), and use the least squares method to simultaneously solve the polarization resistance and capacitance parameters; SOC correction: use the ampere-hour integration method combined with OCV table correction to build a closed-loop feedback mechanism to suppress cumulative errors; data table construction: store the five-dimensional parameter mapping relationship of SOC-R0-Rp-Cp-OCV in a SQLite database, and attach a timestamp and temperature label to each set of data to support multi-dimensional query and analysis.

[0051] 4. Active learning Kriging model: Initial training set: Using the Sobol sequence + adaptive encryption strategy, 42 sample points are extracted in the SOC range [0,1], of which the 60%-80% SOC area is encrypted to 3 times the density (simulating the commonly used working range of BMS).

[0052] Kriging model construction: Use the dacefit function of the DACE toolbox, with SOC as input and OCV, R0, Rp, and Cp as output, to construct four independent Kriging models; the established Kriging model can be expressed as: (1); Where, is a vector containing m basis functions, is a vector containing m regression coefficients; To obey the normal distribution The covariance of the steady-state Gaussian process is: (2); Where, are any two sets of input parameters drawn from the sample space of the energy storage system. and The spatial correlation equation adopts the Gaussian equation, which is in the form of: (3); Where, is the input parameter vector No. A quantity, is the corresponding correlation parameter, obtained by maximum likelihood estimation, and expressed as follows: (4); Where R is the correlation matrix, ; After transformation, we can get the following global unconstrained minimum optimization problem, thereby determining the parameters : (5); At this point, the construction process of the Kriging model of the energy storage system is transformed into solving the optimization problem of formula (5). Using the least squares method, the polynomial parameters of the Kriging model of the energy storage system, that is, its regression coefficients, can be obtained: (6); Where F is ; Likewise, the estimate of the variance is: (7); For the sample space of energy storage system , the predicted value of the Kriging model of the energy storage system Normal distribution , where the best linear unbiased estimate and mean square error It can be expressed as: (8); (9); Where, Forecast point The correlation vector between all k samples in the sample set extracted from the sample space of the energy storage system .

[0053] Validation set: 600 sample points were extracted as the validation set using the Latin hypercube sampling method and normalized.

[0054] Active learning iteration: Use the predictor function to predict the OCV, R0, Rp, and Cp values ​​and prediction variance of the validation set sample points.

[0055] Use the U function to calculate the function value of each validation set sample point; the U function is defined as follows: U(x) = |f(x) - y| / s(x), where f(x) is the predicted value, y is the target value (in this case, since it is a validation set, y is known), and s(x) is the predicted standard deviation.

[0056] Select the sample point with the largest U function value and add it to the training set.

[0057] Rebuild the kriging model using the updated training set.

[0058] Repeat the above steps until the RMSE decreases to <0.05% after 10 consecutive iterations or the total number of iterations reaches 200.

[0059] 5. Model validation: A step-temperature experiment (25°C → 45°C → 60°C) was designed to compare the parameter prediction deviations of the traditional ECM and the proposed method under temperature transitions.

[0060] 6. Expected Results: Through the above embodiment, a high-precision proxy model between battery SOC and parameters can be established. Under high-temperature conditions of 60°C, the OCV prediction accuracy reaches ±1.5mV (1.2 times that under normal temperature conditions), meeting safety requirements.

[0061] The above embodiments are intended to illustrate the present invention, not to limit the present invention. Any solution that is a simple transformation of the present invention falls within the protection scope of the present invention.

Claims

1. A parameter fitting method for energy storage systems based on active learning Kriging model, characterized by: The following steps are included in sequence: a) Fully charge the energy storage system and let it stand until the internal state reaches equilibrium; b) After fully charging at constant current and constant voltage, set several SOC values ​​from 0 to 100%, and then discharge at constant current to the set SOC value; c) Apply a series of constant current pulses to perform HPPC testing, record the voltage and current changes during the pulses, and calculate the system parameter values ​​based on the voltage and current; d) determining whether it is the last SOC value, if yes, proceeding to step f), if no, proceeding to step e); e) Enter the next set SOC value and repeat steps b) to c) to obtain the corresponding system parameter values ​​under the SOC value; f) Using SOC as the research variable, a number of sample points were extracted from the sample space using the Latin hypercube sampling method, and the model parameter values ​​were calculated by table lookup to construct the initial training set and normalize the training set; g) Constructing a Kriging model with the initial sample set or the added sample set as the training set; h) Use Latin hypercube sampling in the sample space to extract several sample points as the validation set of the active learning function. After normalizing the validation set, use the predictor function to obtain the prediction results and estimated variance of the validation set sample points using the above Kriging model; i) The prediction results and variance are respectively brought into the U active learning function for calculation to obtain the function value of the corresponding learning function; j) Determine whether the function value of the learning function meets the convergence condition. If not, add the new sample point to the training set and return to step g); if yes, obtain the active learning Kriging model and end the program.

2. The energy storage system parameter fitting method based on the active learning Kriging model according to claim 1, characterized in that: The constant current pulse in step c) includes a discharge pulse and a charge pulse, and the system parameter values ​​include open circuit voltage (OCV), ohmic internal resistance (R0), polarization internal resistance (Rp) and polarization capacitance (Cp).

3. The energy storage system parameter fitting method based on the active learning Kriging model according to claim 2, characterized in that: The method for calculating the open circuit voltage (OCV), ohmic internal resistance (R0), polarization internal resistance (Rp) and polarization capacitance (Cp) corresponding to each SOC point in step c) is as follows: OCV: the average voltage value in the static stage is taken as OCV; R0: calculated based on the voltage mutation ΔV and current change ΔI at the beginning of the discharge or charge pulse, R0 = ΔV / ΔI; Rp and Cp: exponentially fit the voltage decay curve after the pulse to obtain the time constant τ, then Rp = τ / Cp, where Cp can be estimated by other methods or empirical values ​​or obtained by model fitting.

4. The energy storage system parameter fitting method based on the active learning Kriging model according to claim 3, characterized in that: In step f), 28 sample points are extracted from the sample space using the Latin hypercube sampling method as an initial training set, and the corresponding SOC, open circuit voltage (OCV), ohmic internal resistance (R0), polarization internal resistance (Rp), and polarization capacitance (Cp) values ​​are extracted. The SOC input data is normalized to the [0, 1] interval. The dacefit function of the DACE toolbox is used to construct four independent Kriging models with SOC as input and open circuit voltage (OCV), ohmic internal resistance (R0), polarization internal resistance (Rp), and polarization capacitance (Cp) as outputs. The established Kriging model can be expressed as: （1）； Where, is a vector containing m basis functions, is a vector containing m regression coefficients; To obey the normal distribution The covariance of the steady-state Gaussian process is: （2）； Where, are any two sets of input parameters drawn from the sample space of the energy storage system. and The spatial correlation equation adopts the Gaussian equation, which is in the form of: （3）； Where, is the input parameter vector No. A quantity, is the corresponding correlation parameter, obtained by maximum likelihood estimation, and expressed as follows: （4）； Where R is the correlation matrix, ; After transformation, we can get the following global unconstrained minimum optimization problem, thereby determining the parameters : （5）； At this point, the construction process of the Kriging model of the energy storage system is transformed into solving the optimization problem of formula (5). Using the least squares method, the polynomial parameters of the Kriging model of the energy storage system, that is, its regression coefficients, can be obtained: （6）； Where F is ; Likewise, the estimate of the variance is: （7）； For the sample space of energy storage system , the predicted value of the Kriging model of the energy storage system Normal distribution , where the best linear unbiased estimate and mean square error It can be expressed as: （8）； （9）； Where, Forecast point The correlation vector between all k samples in the sample set extracted from the sample space of the energy storage system .

5. The energy storage system parameter fitting method based on active learning Kriging model according to claim 4, characterized in that: In step h), 500 sample points are extracted as a validation set using the Latin hypercube sampling method and normalized. The open circuit voltage (OCV), ohmic internal resistance (R0), polarization internal resistance (Rp), and polarization capacitance (Cp) values ​​of the validation set sample points, as well as the prediction variance, are predicted using the predictor function, in the same manner as in step f).

6. The energy storage system parameter fitting method based on active learning Kriging model according to claim 5, characterized in that: In the step i), the U function is used to calculate the function value of each validation set sample point. The U function is defined as follows: U(x)=|f(x)-y| / s(x), where f(x) is the predicted value, y is the target value, and y is known because it is a validation set. s(x) is the predicted standard deviation. The sample point with the largest U function value is selected and added to the training set. The updated training set is used to reconstruct the Kriging model until the maximum value of the U function is less than 0.01 or the number of iterations reaches 100.

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