SOC estimation method for low-temperature lithium battery based on kan-ukf

Abstract

The present application relates to the technical field of lithium battery state of charge estimation, and particularly relates to a low-temperature lithium battery SOC estimation method based on KAN-UKF, comprising: performing pulse discharge experiments on lithium batteries at different temperatures; using a forgetting factor recursive least squares method to identify parameters of dynamic open-circuit voltage and polarization voltage of the battery, and analyzing errors between the identified dynamic open-circuit voltage and actual open-circuit voltage; obtaining a polarization compensation factor and a voltage scaling factor, and performing temperature compensation on the polarization voltage and the dynamic open-circuit voltage at different temperatures, so as to map a low-temperature battery response to a normal-temperature equivalent response; constructing a KAN model, training the KAN model; combining the KAN model with UKF, and dynamically updating an SOC estimation value; the present application solves problems of low-temperature adaptability absence, strong data dependency, and model complexity and precision contradiction of current SOC estimation methods.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of lithium battery state of charge estimation, and particularly relates to a low-temperature lithium battery SOC estimation method based on KAN-UKF. BACKGROUND

[0002] Lithium-ion battery state estimation (especially state of charge SOC) is the core function of the battery management system, directly affecting the system safety and energy efficiency in low-temperature scenarios such as energy storage stations, new energy vehicles, aerospace, etc. The internal electrochemical reaction rate of the battery decreases in low-temperature environments, resulting in a significant deterioration in the accuracy of traditional SOC estimation methods, and it is urgent to break through the low-temperature adaptability bottleneck. Currently, SOC estimation techniques are mainly divided into two directions: model-based estimation and black-box model (data-driven) estimation, but both types of technology have obvious limitations and are difficult to meet the high-precision estimation requirements in low-temperature environments, as follows:

[0003] 1. Model-based filtering estimation method, Kalman filter (KF) family (such as extended Kalman filter EKF, unscented Kalman filter UKF) combined with equivalent circuit model (ECM). Advantages: EKF and UKF have self-correcting characteristics, and UKF does not need to calculate the Jacobian matrix, and has higher accuracy in state vector estimation. Limitations: ECM model has insufficient fitting capability in low-temperature, high-current, low-SOC, and other actual working conditions, and is difficult to capture the dynamic changes of polarization voltage; the OCV curve of some batteries (such as lithium iron phosphate) is flattened, resulting in failure of model correction and exacerbation of error accumulation.

[0004] 2. Data-driven black-box model method, neural network (NN), support vector machine, and other data-driven methods directly learn the SOC mapping relationship through a large amount of historical data. Advantages: Avoids relying on internal battery mechanism models and can fit highly nonlinear systems. Limitations: Requires a large amount of full-temperature working condition data for training, and the cost of low-temperature data acquisition is high; the network structure is complex (such as deep neural networks), requiring large computing resources, and having poor interpretability; the generalization ability is limited, and the performance significantly degrades in untrained temperatures or working conditions.

[0005] Therefore, the internal electrochemical reaction rate of the battery decreases in low-temperature environments, resulting in a significant deterioration in the accuracy of traditional SOC estimation methods, and it is urgent to break through the low-temperature adaptability bottleneck. SUMMARY

[0006] In order to solve the problems in the prior art, the present application provides a low-temperature lithium battery SOC estimation method based on KAN-UKF, to solve the problems of low-temperature adaptability, strong data dependence, and model complexity and precision contradiction in current SOC estimation methods.

[0007] To solve the above problems, the technical scheme of the present application is as follows: a low-temperature lithium battery SOC estimation method based on KAN-UKF, comprising the following steps:

[0008] S1, at different temperatures The HPPC pulse discharge experiment of the lithium battery is carried out, and the original terminal voltage , the original load current of the lithium battery is collected, and the actual open circuit voltage and the actual direct current resistance at different temperatures are extracted, which represent the values of voltage, current and resistance at continuous time , discrete time and temperature ;

[0009] S2, based on the first-order RC equivalent circuit model, the forgetting factor recursive least square method (FFRLS) is used to identify the open circuit voltage , the polarization voltage and the direct current resistance of the battery, and the error between the identified open circuit voltage and the actual open circuit voltage, i.e. OCV identification error is analyzed;

[0010] S3, based on the OCV identification error obtained in S2, the polarization compensation factor and the voltage scaling factor are obtained, the polarization voltage, open circuit voltage and terminal voltage at different temperatures are temperature compensated, and the compensated open circuit voltage , the compensated polarization voltage and the compensated terminal voltage are obtained, and the low-temperature battery response is mapped to the normal-temperature equivalent response;

[0011] S4, based on the Kolmogorov-Arnold network, a data-driven KAN model is constructed, and the KAN model is trained, the KAN model comprises an input layer: model input voltage , i.e. the voltage at the last time; model input current , i.e. the current at the current time; model input SOC , i.e. the current SOC; hidden layer; and output layer, the output layer outputs the next time terminal voltage prediction value, i.e. model predicted voltage ;

[0012] S5, taking the KAN model as the observation equation of UKF, and taking the ampere-hour integral method as the state transition equation, the SOC estimation value is dynamically updated .

[0013] Further, S2 comprises,

[0014] S21. Construct a first-order RC equivalent circuit model:

[0015] ,

[0016] wherein, is the original terminal voltage of the battery, is the identified open-circuit voltage, is the identified polarization voltage, is the identified DC internal resistance, is the original load current;

[0017] S22. Discretize the first-order RC equivalent circuit model to balance the estimation accuracy and computational complexity;

[0018] S23. FFRLS algorithm iteration, and then calculate the identified open-circuit voltage and the identified polarization voltage .

[0019] Further, in S22, the discretization includes:

[0020] Constructing a continuous domain equation of the polarization voltage, and converting the model equation in the continuous time domain into the discrete time domain:

[0021] wherein, is the polarization capacitance, is the polarization resistance, is the differential symbol in calculus, used to represent a small change, is the polarization resistance, is the time change rate;

[0022] Taking Laplace transform on it, with the initial condition being 0, to obtain the s-domain expression: ;

[0023] wherein, is the representation in the s-domain, is the representation in the s-domain, is the Laplace operator;

[0024] Adopting bilinear transformation to convert the s-domain into the z-domain to avoid frequency aliasing in the discretization process, and the transformation formula is: wherein, is the sampling period, is the unit delay operator, indicating the data at the previous time;

[0025] Obtain the discrete domain terminal voltage, and Input to KVL equation, through bilinear transformation and arrangement, finally get the discrete time domain of the terminal voltage expression:

[0026] ,

[0027] Wherein, 、 is the k time, k-1 time of the terminal voltage measurement value, 、 is the k time, k-1 time of the open circuit voltage, 、 is the k time, k-1 time of the load current respectively; 、 、 is the discretization coefficient,

[0028] By identifying the DC resistance, polarization resistance, polarization capacitance, sampling period together: ; ; ;

[0029] Further simplified as:

[0030] ,

[0031] Let as the input vector,

[0032] as the parameter vector, then the equation can be expressed in the form of linear regression:

[0033] .

[0034] Further, in S23, the FFRLS algorithm iteration comprises:

[0035] Set the starting point of parameter estimation, based on the prior knowledge of the full state of the battery to initialize the open circuit voltage, the rest of the parameters by default no contribution:

[0036] Set the initial parameter estimate value , wherein, is the initial value of the open circuit voltage, the initial covariance matrix , is a larger positive number, I is the 4 order unit matrix;

[0037] Recursive update: for each sampling time k, the following calculation is performed: calculate the gain matrix: ; update the parameter estimate: ;

[0038] Update the covariance matrix: ; wherein, For the forgetting factor, both the tracking speed and stability are considered;

[0039] Extract core parameters from the identification of Open-circuit voltage and polarization voltage are extracted from the , , The first element, the second element; the polarization voltage According to the KVL equation:

[0040] ,

[0041] , , , The third, fourth elements of ;

[0042] Error analysis: compare the identified with the actual open-circuit voltage directly measured in the experiment , calculate the open-circuit voltage identification error, and provide the basis for subsequent temperature compensation.

[0043] Further, in S3, the voltage scaling factor includes extracting the DC internal resistance at different temperatures from the HPPC experimental data of S1 , The change of terminal voltage before and after the pulse, The pulse current amplitude;

[0044] Get the scaling ratio of polarization voltage at low temperature relative to normal temperature , The DC internal resistance at normal temperature;

[0045] Using the MATLAB parameter identification toolbox, based on the comparison of voltages before and after compensation at different temperatures and the voltage at normal temperature, fine-tune to ensure that the scaled polarization voltage can best match the polarization characteristics at normal temperature, and finally optimize the value.

[0046] Further, in S3, the polarization compensation factor includes describing the change law of the polarization compensation dynamic quantity based on the first-order RC circuit:

[0047] , The polarization compensation dynamic quantity at time n, R and C are the RC parameters of the compensation model, The load current at time n;

[0048] The static compensation coefficient The polarization compensation dynamic quantity Combining, the polarization compensation factor is obtained:

[0049] ;

[0050] Parameter fitting: through a large number of low-temperature experiments, the error data of the identified open-circuit voltage and the actual OCV are collected, and the least square method is used to fit the values of a, R and C, so as to ensure that The identified deviation of OCV can be completely offset.

[0051] Further, in S4, the mapping from the input layer to the hidden layer includes: the input vector , is the voltage at the last moment , the current at the current moment and the current , the output of the first hidden layer is obtained by the composition of the input transformation matrix and the weight spline function: , wherein is the one-dimensional spline function of the first hidden neuron to the nth input feature, , is the spline coefficient, is the B-spline basis function, is the number of B-spline basis functions, and the output of the first hidden layer is: , wherein represents the function composition, that is, the output of each hidden neuron is the sum of the effects of the corresponding spline function on the input features;

[0052] Mapping between hidden layers: the output of the subsequent hidden layer is obtained by the composition of the interlayer transformation matrix , and the output of the second hidden layer is , and so on.

[0053] Output layer mapping: the output of the last hidden layer is obtained by the composition of the output transformation matrix , and the final predicted terminal voltage is obtained: , The mathematical expression of the overall KAN model is: .

[0054] Further, S5 includes:

[0055] S51, taking SOC as the only state variable of UKF, and using the ampere-hour integration method to describe the dynamic change of SOC:

[0056] ,

[0057] wherein: is the prior SOC estimate at time k, is the posterior SOC estimate at time k-1, is the charge-discharge efficiency, is the state transition current, is the process noise;

[0058] S52, establish an observation equation with the voltage prediction value of the KAN model as the observation value:

[0059] ,

[0060] wherein, is the terminal voltage observation value at time k (i.e. the compensated terminal voltage measured by the sensor in real time ),

[0061] is the output of the KAN model (i.e. ), is the observation noise;

[0062] S53, SOC estimation iteration of UKF, including:

[0063] initialize UKF parameters;

[0064] generate Sigma points, according to the current state mean and covariance , generate 2n+1=3 Sigma points, the Sigma points include:

[0065] ,

[0066] ,

[0067] ;

[0068] state prediction of Sigma points;

[0069] observation prediction of Sigma points;

[0070] S54, Kalman gain calculation and state update, calculate Kalman gain , update the SOC estimate value and covariance , output the SOC estimate value at time k.

[0071] Further, in S5, the state prediction of Sigma points includes, for each Sigma point , substitute the state equation to calculate the predicted Sigma point ,

[0072]

[0073] The predicted state mean is calculated by weighted summation and the predicted covariance wherein is the mean weight, is the covariance weight, is the covariance matrix of the process noise,

[0074]

[0075]

[0076]

[0077] is a scaling factor controlling the spread of the distribution of control sigma points, wherein takes a value between 0.01 and 0.1, controlling the distance of the sigma points from the mean; takes a value between 3-n, ensuring the positive definiteness of the sigma points.

[0078] Further, in S5, the observation prediction of the Sigma points comprises, for each predicted Sigma point substituting into the KAN model to calculate the observation predicted Sigma point,

[0079]

[0080] The observation predicted mean is calculated by weighted summation

[0081] The observation covariance

[0082] The state-observation cross covariance

[0083] wherein is the covariance matrix of the observation noise.

[0084] Compared with the prior art, the present application has the following beneficial effects:

[0085] ​​​​​​​​Significant improvement in low-temperature estimation accuracy: Through HPPC experiments combined with FFRLS algorithm, the open-circuit voltage, polarization voltage and DC internal resistance of the battery at different temperatures are accurately identified, the polarization compensation factor and voltage scaling factor are innovatively introduced, the identification deviation of the identified open-circuit voltage and the distortion of the identified polarization voltage at low temperature are effectively corrected, the low-temperature battery response is equivalently mapped to the normal-temperature characteristics, and the KAN model is combined with the high-precision fitting capability of the nonlinear relationship, the anti-noise and dynamic tracking advantages of UKF, the SOC estimation error is less than or equal to 2.5% in the low-temperature interval of-20℃ to 10℃, and the core pain points of the insufficient low-temperature fitting capability of the traditional ECM model and the poor generalization of the data-driven model are solved.

[0086] Reduce the cost of data collection and training: KAN model only needs normal temperature (25℃) working condition data to complete training, without collecting a large amount of low-temperature working condition data, greatly reducing the time and equipment cost of battery test in low-temperature environment, and the temperature compensation strategy avoids the need for full-temperature range data training, and KAN model is constructed by learnable spline function weight, only 4 layers of hidden layer (5 neurons per layer) are needed to achieve the fitting effect of deep neural network, which significantly reduces the model complexity and computing resource consumption, and adapts to the real-time operation demand of embedded BMS.

[0087] Strong model robustness and adaptability: The first-order RC equivalent circuit model is discretized to achieve an optimal balance between precision and computational complexity, and the forgetting factor feature of the FFRLS algorithm can dynamically track the time-varying characteristics of battery parameters, adapt to batteries of different aging degrees, KAN model does not need traditional activation function, and directly optimizes nonlinear mapping relationship through function composition, which has good adaptability to different types of lithium batteries (ternary material, lithium iron phosphate, lithium cobaltate) and different shapes (square, cylindrical, soft square), and UKF avoids linearization error through sigma point sampling, which can still maintain stable estimation accuracy in complex conditions such as large current and low SOC.

[0088] High engineering application value and sufficient safety guarantee: The method can be directly integrated into the battery management system of energy storage stations, new energy vehicles, aerospace and other low-temperature scenarios, and the estimation result of the posterior SOC estimation value can be deeply fused with the charge and discharge control, thermal management and fault warning module of BMS, through accurate grasp of the battery state of charge, the battery life attenuation or safety hazards caused by overcharge and overdischarge at low temperature can be avoided, and the system operation safety and reliability are improved; at the same time, the simplified model structure and data requirement reduce the engineering landing difficulty and cost, and have wide application prospect. BRIEF DESCRIPTION OF DRAWINGS

[0089] Figure 1 The whole system flowchart of the present application is shown in the figure;

[0090] Figure 2This is the equivalent model of the lithium battery ECM of the present invention;

[0091] Figure 3 This is a graph showing the relationship between the actual open-circuit voltage, actual DC internal resistance, and SOC value of the lithium battery identified in the HPPC experiment of this invention.

[0092] Figure 4 For the identification open-circuit voltage of FFRLS in this invention and actual open circuit voltage The resulting curves, a, b, c, and d, represent the relationship between curves at different temperatures, and the X-axis represents time (s).

[0093] Figure 5 The OCV identification error under the FFRLS algorithm of this invention The graph shows the relationship between curves at different temperatures or ranges, with a, b, c, and d representing the curves. The X-axis represents time (s).

[0094] Figure 6 This is a schematic diagram of the temperature compensation method of the present invention;

[0095] Figure 7 This refers to the KAN model that has been trained according to this invention. and reality Error graph;

[0096] Figure 8 The KAN model trained according to this invention is tested at a temperature of 25 degrees Celsius. Prediction and reality Prediction results chart;

[0097] Figure 9 The KAN model trained according to this invention is tested at a temperature of 10 degrees Celsius. Prediction and reality Prediction results chart;

[0098] Figure 10 The KAN model trained according to this invention is at a temperature of 0 degrees Celsius. Prediction and reality Prediction results chart;

[0099] Figure 11 The KAN model trained according to this invention is tested at a temperature of -10 degrees Celsius. Prediction and reality Prediction results chart. Detailed Implementation

[0100] The following is in conjunction with the appendix Figures 1-11With the detailed description of the specific embodiments of the present application, the present embodiment takes ternary material lithium ion battery (rated capacity 20 Ah, nominal voltage 3.6 V, discharge cut-off voltage 2.0 V) as the test object, the low-temperature applicable range is-20℃~10℃, and the real-time operation requirements of the battery management system of the energy storage station are adapted.

[0101] S1, experimental equipment and environment construction

[0102] Core equipment: high-precision constant temperature oven (temperature control accuracy ± 0.5℃, temperature range-40℃~85℃), battery charge and discharge tester (sampling frequency 10 Hz, voltage measurement accuracy ± 0.001V, current measurement accuracy ± 0.01A), data acquisition software (supporting real-time storage of voltage, current and temperature data).

[0103] Battery pretreatment: the ternary lithium battery is full charged and placed for 24h to ensure that the internal electrochemical state of the battery is stable and the initial polarization effect is eliminated.

[0104] HPPC pulse discharge experiment is performed, and the temperature is set: the temperature of the constant temperature oven is adjusted to 25℃ (normal temperature reference), 10℃, 0℃, -10℃, -20℃ in turn, the battery is placed for 4h at each temperature, and the battery temperature is consistent with the environment temperature (verified by the built-in temperature sensor).

[0105] Discharge procedure: according to the HPPC experiment standard, the following operations are performed at each temperature: 0.5C constant current discharge for 10min, record the voltage , current data during discharge ; apply a 5s 2C pulse discharge current, record the change of terminal voltage , current amplitude before and after the pulse , calculate ; stand for 30min to make the battery polarization fully recover, record the terminal voltage after standing (as the

[0106] of this SOC node K); repeat the above steps until the battery SOC decreases to 0% (the terminal voltage reaches 2.0V), and complete the HPPC data acquisition in the full SOC range. Data preprocessing: the collected raw data is subjected to outlier rejection (3σ criterion) and moving average filtering (window size 5), and the Figure 3 and DC internal resistance data of each SOC node k at different temperatures are extracted, the results are shown in , which significantly increases with the decrease of temperature, changes gently.

[0107] S2, parameter identification based on FFRLS

[0108] S21, the battery dynamic characteristics are described by a first-order RC equivalent circuit model, and an ECM equivalent model is shown in Figure 2 The terminal voltage equation is: ,

[0109] wherein, is the original terminal voltage of the battery, is the identified open-circuit voltage, is the identified polarization voltage, is the identified DC internal resistance, is the original load current;

[0110] S22, model discretization processing

[0111] Continuous domain equation is established, and the continuous domain dynamic equation of the polarization voltage is:

[0112] ,

[0113] wherein, is the polarization capacitance, is the polarization resistance, is the time change rate;

[0114] Laplace transform and bilinear transform, the continuous domain equation is subjected to Laplace transform (initial condition is 0), and the s-domain expression is obtained: ;

[0115] The s-domain is converted into z-domain by bilinear transform (avoiding frequency aliasing), and the transform formula is: wherein, is the sampling period, is the unit delay operator, indicating the data at the previous time;

[0116] Discrete domain terminal voltage equation derivation

[0117] Substitute into the KVL equation, and the discrete domain terminal voltage expression is obtained after arrangement:

[0118] ,

[0119] wherein, is the terminal voltage measurement value at k time, is the open-circuit voltage at k time, , are the load currents at k time and k-1 time respectively; , , is the discretization coefficient,

[0120] It is determined by the identified DC internal resistance, polarization resistance, polarization capacitance and sampling period: ; ; ;

[0121] For short time ≈ , further simplified as linear regression form:

[0122] ,

[0123] Let as input vector,

[0124] as parameter vector, the equation can be expressed as linear regression form:

[0125] .

[0126] S23, FFRLS algorithm iteration includes,

[0127] Initialization parameters, initial parameter estimation value: set the starting point of parameter estimation, initialize the open circuit voltage based on the prior knowledge of battery full state, and the rest of the parameters are default: set the initial parameter estimation value , where is the initial value of open circuit voltage, and the initial covariance matrix , is a larger positive number, and I is a 4-order unit matrix;

[0128] Recursive update: for each sampling time k, the following calculation is performed: calculate the gain matrix: ; Update parameter estimation: ;

[0129] Update the covariance matrix: ; Wherein is the forgetting factor, which takes into account the parameter tracking speed and stability;

[0130] Extract core parameters, extract open circuit voltage and polarization voltage from the identified : open circuit voltage , where is the first element and the second element of ; Polarization voltage According to KVL equation:

[0131] ,

[0132] Where , , are the third and fourth elements of , respectively;

[0133] Error analysis: compare the identified OCV with the actual OCV measured in the experiment , calculate the OCV identification error, and obtain the OCV identification error curve, as shown in , the OCV identified by FFRLS is lower than the actual measured OCV at low temperature Figure 5 , which is due to the polarization voltage identified by FFRLS at low temperature .

[0134] Error analysis: compare the identified OCV with the actual OCV measured in the experiment , calculate the OCV identification error, and obtain the OCV identification error curve, as shown in , the OCV identified by FFRLS is lower than the actual measured OCV at low temperature

[0135] S3, temperature compensation implementation,

[0136] Voltage scaling factor is calculated, since the instantaneous fluctuation of voltage is caused by internal resistance , so the scaling factor at different temperatures is calculated based on the resistance at 25 degrees , and the polarization voltage at different temperatures is scaled to the voltage of the battery at 25 degrees under the same current excitation. As shown in Figure 4 , the OCV identified by FFRLS at low temperature is lower than the actual measured OCV, which is due to the slowing down of the charge transfer process and ion migration process in the battery at low temperature, resulting in the OCV identified by FFRLS being doped with a part of the polarization voltage, causing the identified OCV voltage to be lower than the actual measured OCV.

[0137] Extract the DC internal resistance at different temperatures (the change of terminal voltage before and after the pulse discharge by HPPC pulse and the pulse current amplitude Calculation: ;

[0138] Definition , as the DC internal resistance at room temperature 25℃, in this embodiment =0.01Ω;

[0139] Based on MATLAB parameter identification toolbox optimization , ensure that the scaled polarization voltage matches the normal temperature characteristics, and the final optimization results are as follows:

[0140]

[0141] Polarization compensation factor Calculation

[0142] Static compensation coefficient and polarization compensation dynamic quantity​ Combining, the polarization compensation factor is obtained:

[0143] ;

[0144] Parameter fitting: through a large number of low-temperature experiments, collect Data, use the least square method to fit the values of a, R, C, ensure that B0 can completely offset the recognition deviation of open circuit voltage, the results are as follows:

[0145]

[0146] Voltage compensation is performed, and the polarization voltage and the open circuit voltage at each temperature are compensated. The compensation process is shown in Figure 6 After compensation, the low-temperature battery voltage response is equivalent to the normal temperature (25℃) characteristics:

[0147] Polarization voltage after compensation: ;

[0148] Open circuit voltage after compensation: ;

[0149] End voltage after compensation: .

[0150] S4, construction and training of KAN model

[0151] Training data preparation, data source: US06 and UDDS charge-discharge data of the battery at 25℃ normal temperature, covering SOC0%~100%, current 0.1C~2C;

[0152] Data dimension: input features are , and the output is the current voltage ;

[0153] Data preprocessing: min-max normalization is used to map input and output data to the interval [0,1], the formula is , , is the minimum and maximum value of the data.

[0154] KAN model structure setting

[0155] Input layer: 3 neurons (corresponding to 3 input features);

[0156] Hidden layer: 4 layers, 5 neurons in each layer (balance fitting accuracy and computational complexity);

[0157] Output layer: 1 neuron (corresponding to voltage prediction value );

[0158] Activation mechanism: using cubic B-spline function as learnable weights, no need for traditional activation function, number of spline basis functions M=10.

[0159] Model training process

[0160] Loss function: mean squared error (MSE), (N is the number of samples);

[0161] Optimizer: Adam optimizer, learning rate 1e-4, weight decay 1e-5;

[0162] Training iterations: batch size 32, training rounds 100, verify every 10 rounds, verification set accounts for 20%, stop training when the verification loss does not decrease for 5 consecutive rounds.

[0163] Model performance verification

[0164] Verification conditions: UDDS conditions (not involved in training);

[0165] Error indicators: mean absolute error (MAE)=0.009V, root mean square error (RMSE)=0.013V, voltage prediction error curve as Figure 7 shown;

[0166] Result analysis: KAN model predicted voltage deviation from actual voltage ≤0.1V, still maintains high accuracy in low SOC interval (0%~20%), indicating that the model can accurately capture the dynamic characteristics of the battery.

[0167] S5, KAN-UKF fusion SOC estimation

[0168] UKF parameter initialization, state variable: (SOC is the only state variable, n=1);

[0169] Initial SOC: (full charge state);

[0170] Initial covariance matrix: ;

[0171] UKF core parameters: , calculate scaling factor ;

[0172] Noise variance: process noise variance Q=1e-5, observation noise variance R=1e-4 (calibrated by experiment).

[0173] State equation and observation equation definition:

[0174] State equation (ampere-hour integral method): wherein: is the SOC estimate at time k, is the SOC estimate at time k-1, is the charge-discharge efficiency, is the sampling period, is the actual capacity of the battery, (state transition current), is the process noise;

[0175] Observation equation (KAN model output):

[0176]

[0177] wherein, , is the trained KAN model, is the observation noise.

[0178] UKF iterative estimation procedure:

[0179] Generate Sigma points, according to the current state mean and covariance , generate 2n+1=3 sigma points, sigma points include:

[0180] ,

[0181] ,

[0182] ;

[0183] Sigma point state prediction, substitute each sigma point into the state equation to get the predicted sigma point: ;

[0184] Weighted sum to calculate the predicted state mean and covariance:

[0185] ;

[0186] ;

[0187] wherein, is the mean weight, is the covariance weight, ;

[0188] ; , Take 2, corresponding to the optimal Gaussian distribution, is the scaling parameter, take 0.05.

[0189] Sigma point observation prediction

[0190] Substitute the predicted sigma points into the KAN model to obtain the observation prediction sigma points:

[0191] ;

[0192] Calculate the observation prediction mean value by weighted summation: ;

[0193] Observation covariance: ;

[0194] State-observation cross covariance: ;

[0195] Kalman gain calculation and state update include,

[0196] Calculate the Kalman gain (reflecting the correction weight of the observation value to the state estimate): , n = 1, is a scalar, and its inverse is its reciprocal;

[0197] Update the SOC estimate value and covariance , ,

[0198] ,

[0199] Output the SOC estimate value at time k , and constrain its range to [0%, 100%] to avoid SOC exceeding the physical range due to noise;

[0200] Estimate performance verification, in different low temperature environments (10℃, 0℃, -10℃), use US06 working condition data to verify the SOC estimation accuracy of KAN-UKF:

[0201] At 25℃: The estimation error is ≤1% (as shown in Figure 8 );

[0202] At 10℃: The estimation error is ≤1.5% (as shown in Figure 9 );

[0203] At 0℃: The estimation error is ≤2% (as shown in Figure 10 );

[0204] At -10℃: The estimation error is ≤2.5% (as shown in Figure 11 );

[0205] All errors in low-temperature scenarios meet the requirements of engineering applications (usually allowing errors ≤3%) and remain stable in dynamic conditions with rapid current changes.

[0206] The present application has the following advantages:

[0207] Strong low-temperature adaptability: temperature compensation converts low-temperature voltage into normal-temperature voltage, solving the problem of inaccurate parameter identification of traditional models at low temperatures, without the need for KAN model learning of full-temperature data, reducing data acquisition costs.

[0208] High estimation accuracy: KAN model accurately fits the nonlinear characteristics of the battery, and UKF effectively fuses the predicted value and the observed value, suppressing noise interference, with an SOC estimation error ≤2.5% at low temperatures.

[0209] Low computational complexity: the first-order ECM model and the four-layer KAN network balance accuracy and computational load, and UKF does not require a Jacobian matrix, making it suitable for real-time operation of embedded battery management systems (BMS).

[0210] Wide adaptability: supports various types of lithium batteries such as ternary materials and lithium iron phosphate, as well as various shapes such as square and cylindrical, and can be applied to scenarios such as energy storage stations, new energy vehicles, aerospace, etc.

[0211] The above specific embodiments are only used to illustrate the technical solutions of the present application and not to limit it. Although the present application has been described in detail with reference to the examples, those skilled in the art should understand that the technical solutions of the present application can be modified or replaced equivalently without departing from the scope of the technical solutions of the present application, and all should be included in the scope of the claims of the present application.

Claims

1. A method for estimating the state of charge (SOC) of a low-temperature lithium battery based on KAN-UKF, characterized in that, The method comprises the following steps; S1, at different temperatures The HPPC pulse discharge experiment of lithium battery was carried out, and the original terminal voltage of lithium battery was collected , the original load current , the actual open circuit voltage at different temperatures was extracted and the actual direct current resistance , the values of voltage, current and resistance at continuous time , discrete time , temperature ; S2, based on a first-order RC equivalent circuit model, using forgetting factor recursive least squares (FFRLS) to identify the open-circuit voltage of the battery , identify the polarization voltage , identify the DC internal resistance Parameter identification and analysis of the error between the identified open-circuit voltage and the actual open-circuit voltage, i.e. OCV identification error ; S3, identifying error based on OCV obtained in S2 , obtaining polarization compensation factor and voltage scaling factor , temperature compensation of polarization voltage, open circuit voltage, terminal voltage at different temperatures to obtain compensated open circuit voltage , compensated polarization voltage , compensated terminal voltage , mapping low-temperature battery response to normal-temperature equivalent response; S4. constructing a data-driven KAN model based on a Kolmogorov-Arnold network, training the KAN model, the KAN model comprising an input layer: model input voltage , i.e. voltage at the previous moment; model input current , i.e. current at the current moment; model input SOC , i.e. current SOC; a hidden layer; and an output layer outputting a next-moment terminal voltage prediction value, i.e. model predicted voltage ; S5, the KAN model is taken as the observation equation of UKF, the ampere-hour integration method is taken as the state transition equation, and the SOC estimation value is dynamically updated .

2. The method of estimation of claim 1, wherein: S2 comprises, S21. Constructing a first-order RC equivalent circuit model: ， wherein, is the original terminal voltage of the battery, is the identified open circuit voltage, is the identified polarization voltage, is the identified DC internal resistance, is the original load current; S22. Discretizing the first-order RC equivalent circuit model to balance the estimation accuracy and the calculation complexity; S23. Forgetting factor recursive least squares algorithm iteration, further to calculate the open circuit voltage and the polarization voltage .

3. The method of estimation of claim 2, wherein, In S22, the discretization comprises: Constructing a continuous domain equation of the polarization voltage, and converting the model equation in the continuous time domain into the discrete time domain: ， wherein, is the polarization capacitance, is the differential operator in calculus, used to denote a small change in quantity, is the polarization resistance, is the time rate of change; Taking Laplace transform on the equation, and taking 0 as the initial condition to obtain an expression in the s domain: ， wherein is In the s-domain representation, is In the s-domain representation, is the Laplacian operator; The s-domain is converted into the z-domain by using a bilinear transformation to avoid frequency aliasing in the discretization process, and the conversion formula is: , wherein, is a sampling period, is a unit delay operator, representing the data at the previous time instant; To obtain the discrete-domain terminal voltage, Inputting the KVL equations, after bilinear transformation and simplification, we finally obtain the discrete-time domain expression for the terminal voltage: ， in, , These are the measured terminal voltage values ​​at time k and time k-1. , Let K be the open-circuit voltage at time k and time k-1. , , respectively, are the load currents at time k and time k-1; , , These are the discretization coefficients. The expression is determined by the identified DC internal resistance, polarization resistance, polarization capacitance and sampling period: ； ； ； It is further simplified as: , let as the input vector, as the parameter vector, then the equation can be expressed in linear regression form: 。 4. The method of estimation according to claim 3, characterized in that, In S23, the forgetting factor recursive least square algorithm iteration comprises: Setting a starting point of parameter estimation, initializing the open circuit voltage based on the prior knowledge of the full state of the battery, and defaulting the remaining parameters to have no contribution: Let the initial parameter estimate value wherein, is the open circuit voltage initial value, the initial covariance matrix , is a positive number, and I is a 4-order unit matrix; Recursive update: For each sampling time k, perform the following calculations: Compute the gain matrix: ; Update the parameter estimate: ; Updating the covariance matrix: ; wherein, is a forgetting factor, taking into account the parameter tracking speed and stability; Extract core parameters from the identified Extract open circuit voltage and polarization voltage from the identified wherein, is the first element, the second element; polarization voltage Derivation from KVL equation: ， wherein , are respectively third, fourth elements; Error analysis: The identified open-circuit voltage is compared with the actual open-circuit voltage directly measured in the experiment , and the error of open-circuit voltage identification is calculated to provide a basis for subsequent temperature compensation.

5. The method of claim 4, wherein: S3, the voltage scaling factor The obtaining includes extracting the direct current resistance under different temperatures from the HPPC experimental data of S1 , is the change of the terminal voltage before and after the pulse, is the pulse current amplitude; obtaining a scaling of the polarization voltage at low temperature with respect to the normal temperature , is the direct current internal resistance at normal temperature; Using the MATLAB parameter identification toolbox, based on a comparison of the voltage before and after compensation at different temperatures with the voltage at room temperature, the following parameters were determined: Fine-tuning was performed to ensure that the scaled polarization voltage best matched the polarization characteristics at room temperature, resulting in the final optimized voltage. value.

6. The method of estimation of claim 5, wherein: In S3, the polarization compensation factor The obtaining includes describing a change rule of the polarization compensation dynamic quantity based on a first-order RC circuit. ， wherein, is the polarization compensation dynamic quantity at time n, R and C are RC parameters of the compensation model, is the load current at time n; The static compensation coefficient is combined with the dynamic quantity of polarization compensation to obtain the polarization compensation factor: ； Parameter fitting: through low temperature experiments, collect error data of open circuit voltage and actual OCV, use least square method to fit the values of a, R and C, ensure that the identification deviation of OCV can be completely offset.

7. The method of estimation of claim 6, wherein: In S4, the mapping from the input layer to the hidden layer includes: the input vector , is the voltage at the previous time , the current and the current , the output of the first layer hidden layer is obtained by the input transformation matrix and the weight spline function: , wherein, is a univariate spline function for the 1st hidden neuron to the n-th input feature, , is a spline coefficient, is a B-spline basis function, is the number of B-spline basis functions, the first layer hidden layer output: wherein, denotes the function composition, i.e. the output of each hidden neuron is the sum of the actions of the corresponding spline functions on the input features; Mapping between hidden layers: the output of a subsequent hidden layer is transformed by a layer-to-layer transformation matrix The composite is obtained, the second layer hidden layer output and so on; Output layer mapping: the output of the last hidden layer by an output transformation matrix Composite, get the final prediction end voltage : , The mathematical expression of the overall KAN model is: .

8. The method of estimation according to claim 7, characterized by S5 Comprises: S51. Taking the SOC as the only state variable of the UKF, and adopting the ampere-hour integral method to describe the dynamic change of the SOC: ， wherein: is the prior SOC estimate at time k, is the posterior SOC estimate at time k - 1, is the charge-discharge efficiency, is the state transition current, is the process noise; S52. Taking the voltage prediction value of the KAN model as an observation value, and establishing an observation equation: ， wherein, is the terminal voltage observation at time k, is the output of the KAN model, is the observation noise; S53. The SOC estimation iteration of the UKF comprises: Initializing the UKF parameters; generating sigma points, based on the current state mean , and a covariance , generating 2n+1=3 sigma points, the sigma points comprising: ， ， ； State prediction of the Sigma point; Observation prediction of the Sigma point; S54, Kalman gain calculation and state update, calculate Kalman gain , update SOC estimate and covariance , output SOC estimate at time k.

9. The method of estimation of claim 8, wherein: In S53, the state prediction of the sigma point includes, for each sigma point , substituting the state equation to calculate the predicted sigma point , ， The predicted state mean is calculated by a weighted sum and the predicted covariance wherein is the mean weight, is the covariance weight, is the covariance matrix of the process noise, ， wherein, is a scaling factor to control the spread of the sigma points, , take 0.01~0.1, control the distance between sigma points and mean; take 3-n, ensure the positive definiteness of the sigma points.

10. The method of estimation of claim 9, wherein: In S53, the observation prediction of the sigma point includes, for each predicted sigma point , substituting the KAN model to calculate the observation prediction sigma point: ， Calculating an observed prediction mean by a weighted sum , Observation covariance , state-observation cross-covariance , wherein is the covariance matrix of the observation noise.

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