Parameter identification method of lithium battery fractional order model, medium and equipment

Abstract

The invention provides a parameter identification method of a lithium battery fractional order model, a medium and equipment, which can determine output data of the fractional order model according to open-circuit voltage correction data and initial values of model parameters, and determine a target function value according to the output data and data used for fitting under various working conditions. Determining a used model optimization algorithm and a search range corresponding to the model parameters according to the convergence trend of the target function value, adjusting the initial values of the model parameters according to the search range, and continuously fitting the model parameters of the fractional order model according to the open-circuit voltage correction data and the data used for fitting under various working conditions, according to the method, the precision and the stability of the model in the state of charge estimation process can be improved, the internal real electrochemical reaction environment can be better reflected through optimization and adjustment of the model parameters, the local precision and the global optimal performance can be considered, and the method is suitable for large-scale popularization and application. And the optimization convergence speed is accelerated.

Description

Technical Field

[0001] The present invention relates to the technical field of battery management, and in particular to a parameter identification method, medium and equipment for a lithium battery fractional-order model. Background Art

[0002] Lithium-ion batteries are widely used in the new energy vehicle industry. To safely and efficiently manage lithium-ion batteries, it is necessary to simulate them and establish corresponding simulation models. The fractional-order model of a lithium battery is a mathematical model established using fractional-order calculus. It is used to more accurately describe the complex electrochemical processes within lithium batteries, particularly the non-idealities and memory effects in charge transfer and diffusion. However, modeling fractional-order models and identifying the relevant model parameters remain challenging tasks.

[0003] The improved fractional-order model of lithium-ion batteries proposed in Chinese patent application CN108519555A replaces the linear relationship of polarization internal resistance in the traditional equivalent circuit model with the Butler-Volmer equation, introduces a hyperbolic sine function to describe the nonlinear charge transfer process, and replaces the polarization capacitor with a constant phase angle element to improve the accuracy of voltage and state of charge estimation under dynamic conditions. The disadvantage is that it relies on the nonlinear correction of the Butler-Volmer equation, resulting in high parameter identification complexity and the need for a large amount of experimental data calibration. In addition, the additional parameters introduced by the hyperbolic sine function increase the optimization dimension.

[0004] The frequency domain-time domain joint parameter identification method proposed in Chinese patent application CN112069739A achieves high-precision parameter estimation by decomposing the battery fractional-order model into an OCV model and an RC equivalent model, parsing the RC parameters and performing temperature correction, and adopting a hybrid strategy combined with a joint objective function to optimize parameter identification. However, the disadvantage is that the joint objective function has high computational cost and relies on electrochemical impedance spectroscopy data, which limits its practicality. The parameter dimension explosion caused by the hybrid strategy leads to slow convergence.

[0005] Chinese patent application CN113671378A proposes a fractional-order PNGV model that improves convergence speed and continuity by deriving discretized system identification equations and combining them with an improved ant colony optimization algorithm for online parameter identification. It is superior to traditional swarm intelligence algorithms in terminal voltage prediction and parameter curve smoothness, and is suitable for real-time battery management scenarios. However, the improved ant colony algorithm relies on the principle of short-term memory to simplify equations, which may lose long-term dynamic characteristics, and the parameter curve smoothness requirement limits the optimization freedom. The model's ability to describe low-frequency polarization processes is reduced, and the randomness of the ant colony algorithm may lead to unstable parameter identification results.

[0006] Therefore, current fractional-order models all have problems such as high complexity in model parameter identification, high computational cost, limited practicality due to reliance on experimental data, sacrifice of dynamic characteristics description capability due to model simplification or data truncation, and possible instability or slow convergence of the optimization process. Therefore, a new method for parameter identification in fractional-order models is needed. Summary of the Invention

[0007] One purpose of the present application is to provide a parameter identification method for a fractional-order model of a lithium battery, so as to solve the problems of complex model parameter identification, insufficient coverage of real test data, difficulty in thermal effect modeling, sensitivity to initial values, complex hysteresis effect and open-circuit voltage correction, slow convergence speed of optimization algorithm, and high computational cost in the existing technology.

[0008] To achieve the above objectives, some embodiments of the present application provide a parameter identification method for a fractional-order lithium battery model, the method comprising:

[0009] Determining the output data of the fractional-order model according to the open-circuit voltage correction data and the initial values ​​of the model parameters;

[0010] Determine the objective function value based on the output data and the data used for fitting under various preset working conditions;

[0011] According to the convergence trend of the objective function value, determine the model optimization algorithm to be used and the search range corresponding to the model parameters;

[0012] Adjust the initial values ​​of the model parameters according to the model optimization algorithm and the search range corresponding to the model parameters;

[0013] Continuously fitting the model parameters of the fractional-order model based on the open-circuit voltage correction data and the data used for fitting under various working conditions until the preset fitting stop condition is met;

[0014] Output the calibration quantity obtained by fitting corresponding to the model parameters.

[0015] Furthermore, the method for generating the open circuit voltage correction data includes:

[0016] Based on the open circuit voltage experimental data and reference performance test data, the mapping relationship data between the open circuit voltage and the state of charge is constructed by linearly interpolating the open circuit voltage plateau period and the non-plateau period respectively;

[0017] According to the experimental error compensation item, the mapping relationship data is error compensated to generate open circuit voltage correction data.

[0018] Furthermore, the data for fitting under various working conditions are obtained by:

[0019] Determine the corresponding working condition based on the step number and step name in the reference performance test data. The reference performance test data includes time, cell voltage, current, tab temperature, end face temperature, side face temperature, capacity, energy, step number and step name. The working conditions include short pulse test, long pulse test, rate discharge test and dynamic working condition cycle.

[0020] According to the corresponding working conditions, the data used for fitting under various working conditions are determined through the adaptive threshold discrimination algorithm.

[0021] Furthermore, according to the corresponding working conditions, the data for fitting under various working conditions is determined by an adaptive threshold discrimination algorithm, which also includes:

[0022] The time, cell voltage, current, tab temperature, end face temperature and side face temperature under various operating conditions are input into a one-dimensional heat conduction model to determine the internal core temperature of the battery in the data used for fitting under various operating conditions.

[0023] Furthermore, the objective function is a weighted least squares method, and the weights corresponding to the errors under different working conditions are determined according to the data characteristics of the working conditions.

[0024] Furthermore, the initial values ​​of the model parameters are normalized values ​​centered around 1.

[0025] Furthermore, based on the convergence trend of the objective function value, the model optimization algorithm to be used is determined, including:

[0026] When the objective function value is less than the preset optimization switching threshold, the model optimization algorithm used is switched from the global search algorithm to the gradient-based optimization algorithm.

[0027] Furthermore, according to the convergence trend of the objective function value, the search range corresponding to the model parameters is determined, including:

[0028] When the decrease in the objective function value is greater than a preset search range reduction threshold, the search range corresponding to the model parameter is reduced, and the search range corresponding to the model parameter is determined according to the lower boundary coefficient and the upper boundary coefficient corresponding to the model parameter;

[0029] When the decrease in the objective function value is less than a preset search range enlargement threshold, the search range corresponding to the model parameter is expanded.

[0030] Some embodiments of the present application further provide a computer-readable medium having computer-readable instructions stored thereon, wherein the computer-readable instructions can be executed by a processor to implement the parameter identification method of the aforementioned lithium battery fractional-order model.

[0031] Some embodiments of the present application also provide an electronic device, which includes a memory for storing computer program instructions and a processor for executing the computer program instructions, wherein when the computer program instructions are executed by the processor, the electronic device executes the aforementioned parameter identification method of the lithium battery fractional-order model.

[0032] Compared with the prior art, the solution provided in the present application can determine the output data of the fractional-order model based on the open-circuit voltage correction data and the initial values ​​of the model parameters, determine the objective function value based on the output data and the data used for fitting under various working conditions, determine the model optimization algorithm to be used and the search range corresponding to the model parameters based on the convergence trend of the objective function value, adjust the initial values ​​of the model parameters based on the model optimization algorithm and the search range corresponding to the model parameters, and continuously fit the model parameters of the fractional-order model based on the open-circuit voltage correction data and the data used for fitting under various working conditions until the preset fitting stop conditions are met, and then output the calibration quantity obtained by fitting corresponding to the model parameters, thereby realizing a dynamic correction mechanism for the open-circuit voltage-state of charge mapping relationship that combines static open-circuit voltage test and reference performance test dynamic data, and generating a corrected open-circuit voltage-state of charge mapping relationship through segmented interpolation and error compensation, which is more in line with the open-circuit voltage modeling under actual operating conditions and can improve the model in the state of charge estimation process. Accuracy and stability, it also implements an adaptive data interception method based on the current working condition characteristics, which can avoid manually setting thresholds and significantly improve the effectiveness and automation of fitting data. It also realizes the correction of external temperature test data by introducing a simplified heat conduction model, which can make the optimization adjustment of model parameters better reflect the internal real electrochemical reaction environment, thereby enhancing the robustness of the fractional-order model to temperature disturbances. At the same time, it also realizes a dynamic switching mechanism between the gradient-free global search algorithm and the gradient-based optimization algorithm, which can automatically select the optimization strategy according to the current error shape and the convergence trend of the model parameters, thereby taking into account local accuracy and global optimal performance, and accelerating the optimization convergence speed. It also realizes a dynamic adjustment mechanism of the upper and lower limits of the model parameters, and automatically adjusts the search space according to the gradient trend of the model parameters, thereby avoiding local minimum traps, improving search efficiency and final fitting accuracy, and finally realizing high-precision model parameter identification and fractional-order model construction for actual reference performance test dynamic data, with good generalization ability and engineering portability. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Other features, objects and advantages of the present application will become more apparent upon reading the detailed description of non-limiting embodiments made with reference to the following drawings:

[0034] Figure 1 A flowchart of a parameter identification method for a lithium battery fractional-order model is provided in some embodiments of the present application.

[0035] Figure 2 A schematic diagram comparing the actual test voltage and the output voltage of the fractional-order model provided in some embodiments of the present application. DETAILED DESCRIPTION

[0036] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0037] Here, the parameter identification method of the lithium battery fractional-order model in the embodiment of the present application is suitable for scenarios such as fractional-order model parameter modeling, battery status monitoring, and battery status estimation in the battery management process of various lithium-ion batteries.

[0038] The parameter identification method of the lithium battery fractional-order model provided in the present application can determine the output data of the fractional-order model based on the open-circuit voltage correction data and the initial values ​​of the model parameters, determine the objective function value based on the output data and the data used for fitting under various working conditions, determine the model optimization algorithm to be used and the search range corresponding to the model parameters based on the convergence trend of the objective function value, adjust the initial values ​​of the model parameters based on the model optimization algorithm and the search range corresponding to the model parameters, and continuously fit the model parameters of the fractional-order model based on the open-circuit voltage correction data and the data used for fitting under various working conditions until the preset fitting stop conditions are met, and then output the calibration quantity obtained by fitting corresponding to the model parameters, thereby realizing a dynamic correction mechanism for the open-circuit voltage-state of charge mapping relationship that combines static open-circuit voltage test and reference performance test dynamic data, and generating a corrected open-circuit voltage-state of charge mapping relationship through segmented interpolation and error compensation, which is more in line with the open-circuit voltage modeling under actual operating conditions and can improve the model in the state of charge estimation process. The accuracy and stability of the process are improved, and an adaptive data interception method based on the current working condition characteristics is realized, which can avoid manually setting thresholds and significantly improve the effectiveness and automation of fitting data. It also realizes the correction of external temperature test data by introducing a simplified heat conduction model, which can make the optimization adjustment of model parameters better reflect the internal real electrochemical reaction environment, thereby enhancing the robustness of the fractional-order model to temperature disturbances. At the same time, a dynamic switching mechanism between the gradient-free global search algorithm and the gradient-based optimization algorithm is realized, which can automatically select the optimization strategy according to the current error shape and the convergence trend of the model parameters, thereby taking into account local accuracy and global optimal performance and accelerating the optimization convergence speed. It also realizes the dynamic adjustment mechanism of the upper and lower limits of the model parameters, and automatically adjusts the search space according to the gradient trend of the model parameters, thereby avoiding local minimum traps, improving search efficiency and final fitting accuracy, and finally realizing high-precision model parameter identification and fractional-order model construction for actual reference performance test dynamic data, with good generalization ability and engineering portability.

[0039] Figure 1 The flow chart of the parameter identification method of the lithium battery fractional-order model executed by the electronic device in some embodiments of the present application is shown. The electronic device is the execution subject of the method, such as Figure 1 As shown, the method may include the following steps:

[0040] Step S101 : determining output data of the fractional-order model according to open-circuit voltage correction data and initial values ​​of model parameters.

[0041] It will be understood that electronic devices may include but are not limited to laptop computers, desktop computers, tablet computers, mobile phones, wearable devices, head-mounted displays, servers, mobile email devices, portable game consoles, portable music players, reader devices, televisions with one or more processors embedded or coupled thereto, or other electronic devices capable of accessing a network.

[0042] Here, the open circuit voltage correction data is data obtained by dynamically correcting the OCV-SOC mapping relationship data established based on actual test data.

[0043] In some embodiments of the present application, a method for generating open circuit voltage correction data may include the following steps:

[0044] (1) Based on the open circuit voltage experimental data and reference performance test data, the mapping relationship data between the open circuit voltage and the state of charge is constructed by linearly interpolating the open circuit voltage plateau period and non-plateau period respectively.

[0045] Here, the open circuit voltage experimental data and reference performance test data (RPT) are data obtained from actual laboratory tests of this model of lithium-ion cells or lithium-ion batteries. The reference performance test data includes test data under various operating conditions such as multi-rate discharge and pulse load.

[0046] The open circuit voltage test data and reference performance test data may include but are not limited to: time, cell voltage, current, tab temperature, end face temperature, side face temperature, capacity, energy, process step number and process step name and other data.

[0047] By dividing the open circuit voltage experimental data into two segments according to the plateau period and non-plateau period of the open circuit voltage, and constructing the mapping relationship data between the open circuit voltage and the state of charge by segmented linear interpolation, the interpolation result can be made more accurate.

[0048] (2) According to the experimental error compensation item, the mapping relationship data is error compensated to generate open circuit voltage correction data.

[0049] Here, an error compensation mechanism is introduced to dynamically correct the open-circuit voltage using experimental error compensation terms. This generates open-circuit voltage correction data, which represents the mapping relationship between the corrected open-circuit voltage and state of charge. This improves the robustness of the fractional-order model across different state-of-charge ranges. Each coordinate point in the open-circuit voltage correction data curve consists of the open-circuit voltage and state-of-charge data at 25°C.

[0050] Here, the experimental error compensation term can be obtained in a variety of ways, for example, by smoothing the original SOC-OCV curve through a mathematical function or a machine learning model, or by looking up a table combined with interpolation correction. The embodiments of the present application do not impose specific restrictions on this.

[0051] In some embodiments, the experimental error compensation term is calculated as follows:

[0052] (a) Find the SOC segment that requires error compensation;

[0053] (b) remapping the reference performance test experimental benchmark SOC-OCV mapping relationship data to the current SOC segment;

[0054] (c) interpolating to obtain new open circuit voltage error compensation data;

[0055] (d) Handling null values;

[0056] (e) Compensating the open circuit voltage error compensation data to the original mapping relationship data between the open circuit voltage and the state of charge.

[0057] In some embodiments, correcting the SOC-OCV mapping relationship data using an experimental error compensation term may include the following steps:

[0058] (a) Find the first and last non-zero OCV correction values ​​and convert the baseline OCV values ​​corresponding to these correction points to the current OCV curve by interpolation to obtain the corresponding starting and ending SOC points;

[0059] (b) Construct a new SOC reference axis that matches the current SOC range and interpolate the original OCV correction value (converted from millivolts to volts) onto the current SOC to adapt the correction value to the current SOC distribution; during the interpolation process, any NaN values ​​that may appear are automatically processed and replaced with 0;

[0060] (c) The interpolated OCV correction value is superimposed on the original OCV data to complete the correction of the OCV curve, making it closer to the baseline curve. The entire process achieves dynamic alignment and error correction between different SOC benchmarks through interpolation and linear mapping.

[0061] By introducing a dynamic open-circuit voltage correction mechanism, the fitting accuracy of the SOC-OCV mapping relationship and the response capability of the fractional-order model to nonlinear behaviors such as hysteresis and rate effect can be significantly improved, thereby enhancing the simulation and prediction accuracy of lithium-ion cells or batteries under different operating conditions.

[0062] Here, a lithium-ion cell or battery is modeled using a preset fractional-order model. This pre-established fractional-order model includes multiple model parameters, which are subsequently subjected to continuous fitting, identification, and optimization to ultimately determine the optimal model parameter values, i.e., the calibration values ​​obtained by fitting the corresponding model parameters. The preset fractional-order model is a special equivalent circuit model.

[0063] In some embodiments of the present application, the state space expression of the fractional-order model can be expressed as follows:

[0064] x k+1 =A d x k +B d I k+1 ,

[0065]

[0066] Among them, T s is the sampling time, X0 is the initial state vector, which is usually determined by the actual test data or the state of charge data after open circuit voltage correction. X0 may include but is not limited to the initial state of charge, initial temperature and other state data. k+1 is the state vector at the next moment, which is the current state vector X k and input current I k+1 Through recursion of fractional differential equations, we can get X k+1 It may include but is not limited to state of charge, polarization voltage, temperature and other status data.

[0067] K i is a gain coefficient, determined based on the model parameters ohmic internal resistance, reference charge transfer resistance, reference exchange current density, activation energy, fractional order corresponding to the first temperature range, fractional order corresponding to the second temperature range, fractional order corresponding to the third temperature range, fractional order corresponding to the fourth temperature range, SOC dependency coefficient, and BVK current scaling factor. In some embodiments, K i The calculation formula can be expressed as follows:

[0068] K i =ROhm+Rct0_ref·f Tct (T)·fI(I,T)·f SOC (SOC).

[0069] Where ROhm is the ohmic internal resistance, Rct0_ref is the reference charge transfer resistance, fI(I,T) is the function of the reference exchange current density and temperature, and f Tct (T) is the temperature-related function, f SOC (SOC) is a function related to the state of charge.

[0070] The above model parameters are expressed through different functions such as fI(I,T), f Tct (T), f SOC (SOC) and correction items affect K i , which indirectly affects the internal processing process and output data of the fractional-order model. For example, the activation energy of the model parameter affects the charge transfer resistance. The first temperature range corresponds to the fractional order, the second temperature range corresponds to the fractional order, the third temperature range corresponds to the fractional order, and the fourth temperature range corresponds to the fractional order, which affects the fractional order of the fractional-order model. This is reflected through a table lookup. The SOC dependency coefficient affects the SOC nonlinear correction, and the BVK current scaling factor affects the current nonlinear correction.

[0071] τ i is a time constant, determined based on the model parameter fractional order, the first thermal model proportional coefficient, the second thermal model proportional coefficient, the charge transfer resistance activation energy, and the charge transfer resistance reference temperature. In some embodiments, τ i It can be calculated as follows: Calculate the poles and zeros of fractional calculus through digital filtering algorithms such as Oustaloup approximation, and finally get τ i =1 / ω i ,p,ω i ,p is the i-th ω p ,ω i , where p is the pole angular frequency of the i-th RC link in the Oustaloup algorithm. Furthermore, the fractional order can be obtained based on the difference in the current temperature lookup table. The dynamic response of the lithium-ion battery diffusion process can also be positively adjusted by combining the first thermal model proportional coefficient, the second thermal model proportional coefficient, and the charge transfer resistance activation energy.

[0072] In some embodiments of the present application, the model parameters may include but are not limited to: ohmic internal resistance, reference charge transfer resistance, reference exchange current density, activation energy, fractional order corresponding to the first temperature range, fractional order corresponding to the second temperature range, fractional order corresponding to the third temperature range, fractional order corresponding to the fourth temperature range, SOC dependence coefficient, BVK current scaling factor, charge transfer resistance activation energy, charge transfer resistance reference temperature, first thermal model proportional coefficient and second thermal model proportional coefficient, etc.

[0073] Ohmic internal resistance describes the DC resistance of the battery itself and directly affects the fundamental gain of the voltage drop. Reference charge transfer resistance describes the charge reaction impedance at the electrode interface and determines the initial impedance of the charge transfer process. Reference exchange current density describes the activity term that controls the reaction rate and affects the nonlinear correction of the current to the charge transfer resistance. Activation energy describes the strength of the temperature effect and is an exponential term that controls the temperature variation of the charge transfer resistance. Fractional orders corresponding to the first temperature range describe the fractional orders corresponding to the first temperature range and adjust the double exponential correction of the reference charge transfer resistance to the temperature. Fractional orders corresponding to the second temperature range describe the fractional orders corresponding to the second temperature range. Fractional orders corresponding to the third temperature range describe the fractional orders corresponding to the third temperature range. Fractional orders corresponding to the fourth temperature range describe the fractional orders corresponding to the fourth temperature range. The SOC dependency coefficient describes the nonlinear dependence of battery performance on SOC (State of Charge). The BVK current scaling factor is used to model charge-discharge asymmetry and is a scaling factor that distinguishes charge-discharge asymmetry. BVK is the core controller (Batterie-Verwaltungs-Knoten). The charge transfer resistance activation energy describes the temperature-dependent activation energy of the charge transfer resistance. The charge transfer resistance reference temperature describes the base temperature for temperature scaling adjustments, typically based on 298.15K. The first thermal model scale factor describes the scale factor associated with heat transfer characteristics in the thermal model. The second thermal model scale factor describes another scale factor associated with heat capacity or thermal resistance in the thermal model.

[0074] In some embodiments of the present application, the initial values ​​corresponding to the model parameters, namely the initial calibration values, are normalized to obtain normalized initial values, which are dimensionless data.

[0075] Specifically, the actual initial value of each model parameter (such as resistance, current density) can be divided by a preset reference value or its initial value to convert it into a dimensionless number centered on "1". This dimensionless number is the initial value of the model parameter and is a normalized value centered on 1.

[0076] For example, the initial value of the battery's ohmic internal resistance is Rohmic_Ohm=0.002Ω.

[0077] The initial value of the model parameter = 1.0 (ie, the normalized space is set to vary around the original value ±).

[0078] By normalizing the initial values ​​of the model parameters, the following goals can be achieved:

[0079] (1) Maintaining the consistency of optimization scale, converting different physical quantities (such as Ω, A, J / mol) to the same order of magnitude range (such as 0.1 to 10) to avoid the optimizer from failing due to scale differences;

[0080] (2) Improve numerical stability to avoid the problem of some parameters being too small (such as 10 -6 ) or very large (such as 10 5 ) causes gradient descent or search step size to get out of control;

[0081] (3) Accelerate the convergence speed. After normalization, the sensitivity of each parameter change to the objective function is balanced, and the optimizer can more easily find the descent direction.

[0082] Here, initial values ​​are determined for the model parameters, and the fractional-order model is calculated according to the initial values ​​of the model parameters to obtain initial output data of the fractional-order model.

[0083] In some embodiments of the present application, the initial values ​​of the model parameters are shown in Table 1 below:

[0084] Serial number Parameter name Parameter initial value 1 Ohmic internal resistance 0.0002944Ω 2 Reference charge transfer resistance 0.0037Ω 3 Reference exchange current density 2.0753A 4 activation energy 117.595 J / mol 5 First temperature range 0.02 6 Second temperature range 0.02 7 The third temperature range 0.02 8 Fourth temperature range 0.02 9 SOC dependency coefficient 7.2554 10 BVK current scaling factor 300 11 Charge transfer resistance activation energy 2000J / mol 12 Charge transfer resistance reference temperature 300K 13 First thermal model scale factor 1 14 Second thermal model scale factor 1

[0085] Table 1

[0086] In some embodiments of the present application, the output data of the fractional-order model is the voltage of a lithium-ion cell or a lithium-ion battery.

[0087] In some embodiments of the present application, the simulation sampling rate can also be pre-set. The simulation sampling rate refers to the time step when the corresponding time axis is discretized during the iterative identification of the model parameters of the fractional-order model. The unit is usually seconds. The simulation sampling rate determines the number of points calculated per second during the iterative identification of the model parameters of the fractional-order model.

[0088] In some embodiments of the present application, a fitting SOC range can also be pre-set. The fitting SOC range refers to the SOC interval used to fit the actual test data during the iterative identification and optimization process of the model parameters of the fractional-order model. For example, the fitting SOC range can be set to 0.1~0.9. The relevant data outside this range is given zero weight and will not participate in the iterative identification and optimization process of the model parameters of the fractional-order model.

[0089] Step S102 : determining the objective function value based on the output data and the data used for fitting under various preset working conditions.

[0090] In addition, lithium-ion cells or batteries can operate under a variety of operating conditions, including but not limited to: short pulse testing, long pulse testing, rate discharge testing, dynamic operating cycle, etc.

[0091] The data used for fitting under various working conditions are actual measurement data of lithium-ion cells or batteries under different working conditions, which are used to fit the output data of the fractional-order model to obtain corresponding errors, and the fractional-order model is optimized and adjusted based on the errors.

[0092] In some embodiments of the present application, a method for obtaining data for fitting under various working conditions may include the following steps:

[0093] (1) Determine the corresponding working condition based on the step number and step name in the reference performance test data.

[0094] (2) According to the corresponding working conditions, the data used for fitting under various working conditions are determined through an adaptive threshold discrimination algorithm.

[0095] Here, typical operating conditions such as short pulse test, long pulse test and rate discharge test are determined mainly to obtain relevant model parameters such as high-frequency response, low-frequency response, diffusion polarization, etc. from these calibration data.

[0096] Adaptive thresholding algorithms dynamically set thresholds based on the statistical characteristics of the data or local trends, and then automatically extract valid data fragments. The thresholds are not fixed but dynamically adjusted based on the data characteristics.

[0097] The adaptive threshold determination algorithm may be, for example, a Diff-based threshold algorithm, a Std-based threshold algorithm, a Moving Average and sliding window detection-based threshold algorithm, and the like.

[0098] The Diff-based threshold algorithm can determine whether it is the start or end point of a pulse based on whether the speed of current and voltage changes exceeds the local threshold. It is suitable for capturing short-term pulses and dynamic segments.

[0099] The standard deviation-based threshold algorithm can calculate the standard deviation of the data in the current time window. If the standard deviation exceeds the average level by a certain multiple, it is considered to have entered the valid data segment. It can adapt to changes in noise levels and is particularly suitable for dynamic loads.

[0100] The threshold algorithm based on moving average and sliding window detection can use a sliding window to smooth the original data, detect places where the mean deviation exceeds a certain threshold, filter out occasional spikes, and is suitable for continuous small pulse extraction.

[0101] The following is an example of the "short pulse test" condition:

[0102] (1) On the current curve, detect the section where the current rises to a value greater than 30A and subsequently stabilizes between 10A and 40A → determine the starting point of the short pulse;

[0103] (2) The detection current drops to less than -150A and changes dramatically, which is recognized as the end point of the short pulse;

[0104] (3) The values ​​of the relevant parameters in the short pulse test condition where the current is between the threshold values ​​(30A, -150A) are determined as the data for fitting. The relevant parameters may be, for example, voltage, current, temperature, and time.

[0105] Here, the threshold value (30A, -150A) is an empirical value, but it can be dynamically adjusted according to different types of lithium-ion cells or batteries. In other words, it has adaptive logic, so that identification can be based on the current change trend rather than simply taking a fixed time period.

[0106] For example, in the reference performance test file of CATL's 314Ah battery cell, typical operating conditions such as short pulse test, long pulse test and rate discharge test can be automatically identified, and about 9 segments of sample data for effective fitting can be extracted based on current fluctuations, duration and temperature changes.

[0107] In some embodiments of the present application, when determining the data for fitting under various operating conditions using an adaptive threshold discrimination algorithm based on the corresponding operating conditions, the time, cell voltage, current, tab temperature, end face temperature, and side face temperature under various operating conditions can also be input into a one-dimensional heat conduction model to determine the internal core temperature of the battery within the data used for fitting under various operating conditions. Here, the one-dimensional heat conduction model estimates the internal core temperature of the lithium-ion cell or battery based on the input data, achieving dynamic correction of the temperature state, thereby improving the sensitivity of the fractional-order model to temperature changes and more realistically reflecting the reaction environment in the battery.

[0108] By preprocessing the operating condition data accordingly and combining it with the compensation mechanism of the one-dimensional heat conduction model, the robustness of the fractional-order model under uncertain conditions such as temperature fluctuations, SOC drift, and noise interference can be improved, ensuring the reliability and stability in the actual operation of electric vehicles or energy storage equipment.

[0109] Step S103: determining the model optimization algorithm to be used and the search range corresponding to the model parameters according to the convergence trend of the objective function value.

[0110] In some embodiments of the present application, the objective function is a weighted least squares method, and the weights corresponding to the errors under different working conditions are determined according to the data characteristics of the working conditions.

[0111] The objective function can be expressed as follows:

[0112]

[0113] Among them, J(θ) is the optimization objective function, θ is the model parameter vector composed of multiple model parameters, N is the total number of data points in all fitting sample time points, ω i is the weight of the i-th time point, assigned according to importance, U exp,i is the actual measured voltage value at the i-th time point, U sim,i (θ) is the output voltage value obtained by calculating the fractional-order model based on the open-circuit voltage correction data and the current values ​​of multiple model parameters at the i-th time point.

[0114] In lithium-ion cell or battery modeling, different operating conditions, such as short-pulse test, long-pulse test, rate discharge test, and dynamic operating cycle, correspond to different data characteristics, and therefore have different contributions and requirements for the accuracy of the final fractional-order model. In order to allow fractional-order model optimization to focus on more critical data segments, a method of setting differentiated weight factors is adopted.

[0115] Specifically, the weighting depends on which data or parameter-related characteristics contribute to the overall error during fractional-order model optimization. For example, larger weights are assigned to data segments corresponding to parameters with significant dynamic response and physical significance, such as charge transfer resistance and ohmic internal resistance, to enhance fitting accuracy. Smaller weights are assigned to hysteresis segments, static segments, or noise-susceptible segments to suppress noise interference and avoid overfitting, thereby achieving a dynamic balance between overall fitting accuracy and robustness.

[0116] For example, for energy storage batteries, based on the characteristics of long-term constant power charging and discharging of energy storage, the following weights can be set for different working conditions to obtain the best effect: for short pulse testing, set a low weight, such as 0.3; for long pulse testing, set a medium weight, such as 0.5; for rate discharge testing, set a high weight, such as 1.0; for dynamic working condition cycles, set a relatively high weight, such as 0.75.

[0117] In some embodiments of the present application, the model optimization algorithm used is determined based on the convergence trend of the objective function value. Specifically, when the objective function value is less than a preset optimization switching threshold, the model optimization algorithm used is switched from the global search algorithm to the gradient-based optimization algorithm.

[0118] The convergence trend of the objective function value may include but is not limited to the following situations: whether the optimization is being carried out effectively, whether it is close to convergence, whether there are signs of oscillation, stagnation or overfitting, whether it is necessary to trigger step size adjustment, search strategy switching or optimization termination, etc.

[0119] Here, in the initial stage of iterative adjustment of the model parameters in the fractional-order model, a global search algorithm is used for rough search. When the objective function value converges to a certain extent, that is, less than the preset optimization switching threshold, a gradient-based optimization algorithm is used for fine adjustment.

[0120] Global search algorithms are used to globally optimize the values ​​of model parameters. They explore along a predefined pattern near the current point and control the step size and search grid density based on whether the objective function value decreases, ultimately achieving convergence. Global search algorithms can include, but are not limited to, pattern search algorithms, particle swarm optimization algorithms, and genetic algorithms.

[0121] The optimization switching threshold can usually be determined based on the absolute error limit and the relative change limit. The absolute error limit is to set the absolute value of the objective function to be lower than a certain decimal, such as 1×10 -4 , the fitting is considered good enough. The relative change limit is determined based on the fact that the change in the objective function value between two consecutive iterations is very small.

[0122] Gradient-based optimization algorithms are used to finely control the convergence of objective function values, and may include but are not limited to: classical gradient descent methods, momentum methods, and specialized constrained optimization methods.

[0123] Gradient-based optimization algorithms can control the convergence of the objective function value through the gradient norm, the change in the objective function value, the change in the model parameter vector, or the number of iterations, and stop iteration after reaching the corresponding preset threshold. For example, when the gradient norm is less than 10 -4 The iteration can also be stopped when the change in the objective function value is less than 10 -6 Stop iteration when .

[0124] In some embodiments of the present application, the search range corresponding to the model parameters is determined based on the convergence trend of the objective function value. Specifically, when the decrease in the objective function value is greater than a preset search range reduction threshold, the search range corresponding to the model parameters is reduced; when the decrease in the objective function value is less than a preset search range expansion threshold, the search range corresponding to the model parameters is expanded.

[0125] Here, the search range corresponding to the model parameter is determined by the lower boundary coefficient and upper boundary coefficient corresponding to the model parameter. The lower boundary coefficient corresponding to the model parameter refers to the minimum allowable reduction factor, that is, the number of times the value of the model parameter can be reduced compared to the initial value. The upper boundary coefficient corresponding to the model parameter refers to the maximum allowable expansion factor, that is, the number of times the value of the model parameter can be increased compared to the initial value.

[0126] In some embodiments, the lower boundary coefficients and upper boundary coefficients corresponding to the model parameters are shown in Table 2 below:

[0127] Serial number Parameter name Lower boundary coefficient Upper boundary coefficient 1 Ohmic internal resistance 0.02 5.0 2 Reference charge transfer resistance 0.02 5.0 3 Reference exchange current density 0.02 10.0 4 activation energy 0.03 1.5 5 First temperature range 0.05 1.99 6 Second temperature range 0.05 1.99 7 The third temperature range 0.05 1.99 8 Fourth temperature range 0.05 1.99 9 SOC dependency coefficient 0.01 25.0 10 BVK current scaling factor 0.01 10.0 11 Charge transfer resistance activation energy 0.1 10 12 Charge transfer resistance reference temperature 0.9 1.1 13 First thermal model scale factor 0.01 10.0 14 Second thermal model scale factor 0.01 10.0

[0128] Table 2

[0129] For example, the initial value of the model parameter ohmic internal resistance Rohmic_Ohm is 0.002Ω. In the corresponding search range, the lower boundary coefficient is 0.02 and the upper boundary coefficient is 5.0, which means that the value of the model parameter ohmic internal resistance can vary from 0.002×0.02=0.00004Ω to 0.002×5.0=0.01Ω.

[0130] In some embodiments, the search range corresponding to the model parameters is dynamically adjusted based on the residual error of each iteration to avoid falling into a local optimum. By introducing a certain degree of search perturbation or expanding the search range, the optimization process has the opportunity to escape the local minimum region and continue to explore a more globally optimal solution. The residual error of each iteration is the difference between the actual measured voltage data and the output voltage data calculated by the fractional-order model based on the current model parameter values. It can be used to measure the current fitting accuracy of the fractional-order model and guide the optimization direction of the model parameters.

[0131] Specifically, the upper and lower boundary coefficients of the model parameters are dynamically adjusted according to the changes in the residuals of each round of iterative optimization, thereby changing the allowable search range corresponding to the values ​​of the model parameters.

[0132] For example, after each round of iterative model parameter adjustment and optimization is completed, the residual of the current round is calculated, and then the rate of change of the residual of the current round is compared with the residual of the previous round. If the residual decreases obviously, such as the decrease is greater than the preset search range reduction threshold, such as 10%, the search range needs to be narrowed. If the residual decreases very slowly or stagnates, such as the decrease is less than the preset search range expansion threshold, such as 1%, the search range needs to be expanded to prevent falling into the local optimum, and then the upper boundary coefficient and lower boundary coefficient corresponding to each model parameter are adjusted accordingly according to the expansion or reduction of the search range.

[0133] By monitoring the trend of residual changes in each round of optimization and based on the set convergence judgment criteria, we decide how often to update the upper and lower boundary coefficients of the model parameters, as well as the ratio of the upper and lower boundary coefficients of the model parameters for each contraction or expansion, thereby dynamically adjusting the search range.

[0134] Specifically, when the decrease in the objective function value in multiple consecutive iterations is lower than the preset threshold, the contraction update of the upper and lower boundary coefficients of the model parameters is triggered, and a fixed contraction ratio such as 0.9 is used to adjust the search range. When residual oscillation or stagnation of the decline is detected, an expansion update is triggered, and an expansion ratio such as 1.1 is used to relax the search range, thereby achieving a dynamic balance between optimizing the convergence speed and the global exploration capability.

[0135] By using the global search algorithm and the gradient-based optimization algorithm in stages and combining it with a dynamic search range adjustment strategy, it is possible to effectively avoid falling into the local optimal solution and accelerate the optimization convergence speed, making it suitable for large-scale modeling and batch processing scenarios.

[0136] Step S104: adjusting the initial values ​​of the model parameters according to the model optimization algorithm and the search range corresponding to the model parameters.

[0137] After determining the search range corresponding to the model optimization algorithm and model parameters, the corresponding model optimization algorithm and search range are used to adjust and optimize the values ​​of the model parameters of the fractional-order model to obtain the optimized values ​​of the model parameters, completing an iterative optimization of the fractional-order model. The optimized values ​​of the model parameters, that is, the current calibration values ​​corresponding to the model parameters, are used as the calibration values ​​of the model parameters in the next iteration.

[0138] For example, in each iteration, by calculating the change in the objective function value, analyzing its sensitivity or local downward trend with respect to each model parameter, and then adjusting the direction and magnitude of the model parameter values, the objective function value is gradually reduced, and the optimization process continuously converges to the optimal model parameter combination. Specifically, the gradient, or partial derivative, of the objective function with respect to each model parameter can be calculated, and the model parameter values ​​can be adjusted along the negative gradient direction.

[0139] Step S105 , continuously fitting the model parameters of the fractional-order model according to the open-circuit voltage correction data and the data used for fitting under various working conditions until a preset fitting stop condition is met.

[0140] The fitting optimization process of the fractional-order model is performed multiple times, and each fitting process executes the above steps S101 to S104. After the preset fitting stop condition is met, the fitting optimization of the fractional-order model is stopped.

[0141] The fitting stop condition can be a variety of conditions, including but not limited to: reaching a preset number of iterations, a preset stop judgment variable being less than a preset threshold, etc. For example, if the maximum number of iterations is set to 250, then the optimization of the fractional-order model will stop after 250 iterations.

[0142] In some embodiments of the present application, error convergence monitoring and intermediate parameter storage mechanisms are used during the fitting and optimization process of fractional-order models. Error convergence monitoring refers to real-time tracking of the changing trend of the objective function in each iteration during the model parameter optimization process, which is used to dynamically evaluate whether the optimization is progressing effectively and whether it is close to convergence.

[0143] The intermediate parameter preservation mechanism refers to the periodic preservation of the current optimal model parameter set, the current minimum objective function value, and the related fitting status during the model parameter optimization process. This prevents the loss of the optimization results of the fractional-order model due to program interruption, timeout, or convergence failure, and facilitates subsequent optimization or resumption of training.

[0144] In addition, the search range of model parameters can be narrowed or enlarged according to the changing trend of the objective function value, i.e., the residual, during each round of fitting optimization, and then dynamically judged in combination with the preset residual change threshold and convergence monitoring rules to ensure that the optimization process can converge quickly and escape from the local minimum.

[0145] Step S106: outputting the calibration values ​​obtained by fitting the model parameters.

[0146] After the fitting optimization process of the fractional-order model stops, the current calibration quantity of the model parameters is output as the calibration quantity obtained by the corresponding fitting. The calibration quantity is the optimal value of the model parameters obtained after the model parameter identification of the fractional-order model.

[0147] In an actual production environment, executing steps S101 to S106 above ultimately yields a set of optimal values ​​for model parameters. The root mean square (RMSE) of the voltage error between the obtained fractional-order model and the actual reference performance test data is less than 10 mV, and the maximum error is less than 25 mV. The fitting accuracy is significantly better than that of the traditional integer-order model, and the fractional-order model maintains good consistency at different rates and temperatures (0°C to 40°C), thereby verifying the effectiveness and universality of this method in parameter modeling of high-capacity lithium-ion cells or batteries.

[0148] Figure 2 Schematic diagram showing the comparison between the actual test voltage and the output voltage of the fractional-order model in some embodiments of the present application. Figure 2 As shown, there are 4 sub-graphs from top to bottom. The first sub-graph shows how the current loaded on the lithium-ion battery changes with time during the test. The second sub-graph shows how the temperature of three points on the surface of the lithium-ion battery, namely the tab, end face and side face, changes with time. The third sub-graph shows how the voltage changes with time, where the solid line represents the voltage between the positive and negative electrodes of the battery obtained by the test, and the dotted line represents the voltage between the positive and negative electrodes of the battery output by the fractional-order model. The fourth sub-graph shows how the difference between the test voltage of the lithium-ion battery and the output voltage of the fractional-order model changes with time. It can be seen that the difference between the actual test voltage of the lithium-ion battery and the output voltage predicted by the fractional-order model in the embodiment of the present application remains within a small range, and the fit is good.

[0149] Some embodiments of the present application further provide a computer-readable medium having computer-readable instructions stored thereon, wherein the computer-readable instructions can be executed by a processor to implement the parameter identification method of the aforementioned lithium battery fractional-order model.

[0150] Some embodiments of the present application also provide an electronic device, which includes a memory for storing computer program instructions and a processor for executing the computer program instructions, wherein when the computer program instructions are executed by the processor, the electronic device executes the aforementioned parameter identification method of the lithium battery fractional-order model.

[0151] In summary, the solution provided in the present application can determine the output data of the fractional-order model based on the open-circuit voltage correction data and the initial values ​​of the model parameters, determine the objective function value based on the output data and the data used for fitting under various working conditions, determine the model optimization algorithm used and the search range corresponding to the model parameters based on the convergence trend of the objective function value, adjust the initial values ​​of the model parameters based on the model optimization algorithm and the search range corresponding to the model parameters, and continuously fit the model parameters of the fractional-order model based on the open-circuit voltage correction data and the data used for fitting under various working conditions until the preset fitting stop conditions are met, and then output the calibration quantity obtained by fitting corresponding to the model parameters, thereby realizing a dynamic correction mechanism for the open-circuit voltage-state of charge mapping relationship that combines static open-circuit voltage test and reference performance test dynamic data, and generating a corrected open-circuit voltage-state of charge mapping relationship through segmented interpolation and error compensation, which is more in line with the open-circuit voltage modeling under actual operating conditions and can improve the accuracy of the model in the state of charge estimation process. In addition, an adaptive data capture method based on the current working condition characteristics is implemented, which can avoid manually setting thresholds and significantly improve the effectiveness and automation of fitting data. In addition, a simplified heat conduction model is introduced to correct external temperature test data, which can make the optimization adjustment of model parameters better reflect the internal real electrochemical reaction environment, thereby enhancing the robustness of the fractional-order model to temperature disturbances. At the same time, a dynamic switching mechanism between the gradient-free global search algorithm and the gradient-based optimization algorithm is implemented, which can automatically select the optimization strategy according to the current error shape and the convergence trend of the model parameters, thereby taking into account local accuracy and global optimal performance and accelerating the optimization convergence speed. In addition, a dynamic adjustment mechanism for the upper and lower limits of the model parameters is implemented, which automatically adjusts the search space according to the gradient trend of the model parameters, thereby avoiding local minimum traps, improving search efficiency and final fitting accuracy, and finally realizing high-precision model parameter identification and fractional-order model construction for actual reference performance test dynamic data, with good generalization ability and engineering portability.

[0152] It should be noted that the application can be implemented in software and / or a combination of software and hardware, for example, can be implemented using an application specific integrated circuit (ASIC), a general purpose computer or any other similar hardware device. In one embodiment, the software program of the application can be executed by a processor to realize the steps or functions described above. Similarly, the software program of the application (including relevant data structures) can be stored in a computer-readable recording medium, for example, a RAM memory, a magnetic or optical drive or a floppy disk and similar devices. In addition, some steps or functions of the application can be implemented using hardware, for example, as a circuit that cooperates with a processor to perform each step or function.

[0153] In a typical configuration of the present application, the terminal and the network device each include one or more processors (CPU), input / output interfaces, network interfaces and memory.

[0154] Memory may include non-permanent storage in a computer-readable medium, random access memory (RAM) and / or non-volatile memory in the form of read-only memory (ROM) or flash RAM. Memory is an example of a computer-readable medium.

[0155] Computer-readable media include permanent and non-permanent, removable and non-removable media that can be implemented by any method or technology to store information. The information can be computer-readable instructions, data structures, program modules or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, compact disc-read only memory (CD-ROM), digital versatile disc (DVD) or other optical storage, magnetic cassettes, magnetic disk storage or other magnetic storage devices or any other non-transmission media that can be used to store information that can be accessed by a computing device. As defined herein, computer-readable media does not include non-transitory media such as modulated data signals and carrier waves.

[0156] In addition, a part of the present application may be applied as a computer program product, such as computer program instructions, which, when executed by a computer, can call or provide the method and / or technical solution according to the present application through the operation of the computer. The program instructions for calling the method of the present application may be stored in a fixed or removable recording medium, and / or transmitted through a data stream in a broadcast or other signal-carrying medium, and / or stored in a working memory of a computer device that runs according to the program instructions. Here, according to an embodiment of the present application, a device is included, which includes a memory for storing computer program instructions and a processor for executing program instructions, wherein, when the computer program instructions are executed by the processor, the device is triggered to run the method and / or technical solution based on the aforementioned multiple embodiments of the present application.

[0157] It is obvious to those skilled in the art that the present application is not limited to the details of the above-mentioned exemplary embodiments, and that the present application can be implemented in other specific forms without departing from the spirit or basic characteristics of the present application. Therefore, from any point of view, the embodiments should be regarded as exemplary and non-restrictive, and the scope of the present application is defined by the appended claims rather than the above description, and it is intended that all changes that fall within the meaning and scope of the equivalent elements of the claims are included in the present application. Any figure mark in the claims should not be regarded as limiting the claims involved. In addition, it is obvious that the word "comprising" does not exclude other units or steps, and the singular does not exclude the plural. Multiple units or devices stated in the device claim can also be implemented by one unit or device through software or hardware. Words such as first and second are used to indicate names and do not indicate any particular order.

Claims

1. A parameter identification method for a lithium battery fractional-order model, characterized in that: The method includes: Determining the output data of the fractional-order model according to the open-circuit voltage correction data and the initial values ​​of the model parameters; Determining an objective function value based on the output data and data for fitting under a plurality of preset working conditions; Determining the model optimization algorithm to be used and the search range corresponding to the model parameters according to the convergence trend of the objective function value; Adjusting the initial values ​​of the model parameters according to the model optimization algorithm and the search range corresponding to the model parameters; Continuously fitting the model parameters of the fractional-order model according to the open circuit voltage correction data and the data for fitting under the multiple working conditions until a preset fitting stop condition is met; Output the calibration quantity obtained by fitting corresponding to the model parameters.

2. The method according to claim 1, characterized in that The method for generating the open circuit voltage correction data includes: Based on the open circuit voltage experimental data and reference performance test data, the mapping relationship data between the open circuit voltage and the state of charge is constructed by linearly interpolating the open circuit voltage plateau period and the non-plateau period respectively; According to the experimental error compensation item, error compensation is performed on the mapping relationship data to generate open circuit voltage correction data.

3. The method according to claim 1, characterized in that Methods for obtaining data for fitting under various working conditions include: Determine the corresponding working condition based on the step number and step name in the reference performance test data, wherein the reference performance test data includes time, cell voltage, current, tab temperature, end surface temperature, side surface temperature, capacity, energy, step number and step name, and the working condition includes short pulse test, long pulse test, rate discharge test, and dynamic working condition cycle; According to the corresponding working conditions, the data used for fitting under various working conditions are determined by an adaptive threshold discrimination algorithm.

4. The method according to claim 3, characterized in that According to the corresponding working conditions, the data for fitting under various working conditions are determined by an adaptive threshold discrimination algorithm, further comprising: The time, cell voltage, current, tab temperature, end surface temperature and side surface temperature under various operating conditions are input into a one-dimensional heat conduction model to determine the internal core temperature of the battery in the data used for fitting under various operating conditions.

5. The method according to claim 1, wherein The objective function is a weighted least squares method, and the weights corresponding to the errors under different working conditions are determined according to the data characteristics of the working conditions.

6. The method according to claim 1, wherein The initial values ​​of the model parameters are normalized values ​​centered around 1.

7. The method according to claim 1, characterized in that Determine the model optimization algorithm to be used based on the convergence trend of the objective function value, including: When the objective function value is less than a preset optimization switching threshold, the model optimization algorithm used is switched from the global search algorithm to a gradient-based optimization algorithm.

8. The method according to claim 1, characterized in that Determining the search range corresponding to the model parameters according to the convergence trend of the objective function value includes: When the decrease in the objective function value is greater than a preset search range reduction threshold, reducing the search range corresponding to the model parameter, wherein the search range corresponding to the model parameter is determined according to the lower boundary coefficient and the upper boundary coefficient corresponding to the model parameter; When the decrease in the objective function value is less than a preset search range enlargement threshold, the search range corresponding to the model parameter is expanded.

9. A computer-readable medium having computer-readable instructions stored thereon, wherein the computer-readable instructions can be executed by a processor to implement the method according to any one of claims 1 to 8.

10. An electronic device comprising a memory for storing computer program instructions and a processor for executing the computer program instructions, wherein: When the computer program instructions are executed by the processor, the electronic device is caused to perform the method according to any one of claims 1 to 8.

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