Lithium battery modeling method based on fractional order neural network

Abstract

The invention relates to the technical field of lithium battery modeling, in particular to a lithium battery modeling method based on a fractional order neural network. The method comprises the following steps: performing electrochemical impedance spectroscopy processing on a lithium battery to obtain preprocessed impedance data; obtaining structure and material data of the lithium battery; performing SEI film structure dynamic analysis according to the preprocessed impedance data to obtain SEI film growth process dynamic data; constructing a fractional order impedance model according to the dynamic data of the SEI film growth process to obtain fractional order impedance model parameters; and performing parameter physical significance analysis on the parameters of the fractional order impedance model to obtain parameter physical significance data. According to the method, the precision of the model is improved by more accurately describing the fractional order characteristics in the lithium battery, the limitation that a traditional integer order model is difficult to accurately describe the process is overcome by performing fractional order modeling on the SEI film growth process, and the explanatory property and applicability of the model are enhanced by introducing microscopic information.

Description

Technical Field

[0001] The present invention relates to the technical field of lithium battery modeling, and in particular to a lithium battery modeling method based on a fractional-order neural network. Background Art

[0002] Lithium batteries are widely used in new energy vehicles, portable electronic devices and other fields due to their high energy density and long cycle life. In order to achieve efficient utilization and safe management of lithium batteries, it is necessary to establish an accurate lithium battery model. Traditional lithium battery modeling methods mainly include equivalent circuit model method and electrochemical model method.

[0003] The equivalent circuit model method selects appropriate circuit elements to construct an equivalent circuit similar to the input and output characteristics of lithium batteries, thereby achieving the description of lithium battery characteristics. Commonly used equivalent circuit models include the Rint model, the Thevenin model, the PNGV model, etc. This type of model has a simple structure, high computational efficiency, and is easy to apply online, but it is difficult to accurately describe the complex electrochemical processes inside lithium batteries, resulting in insufficient model accuracy. The electrochemical model method is based on the physical and chemical processes inside lithium batteries to establish partial differential equations that describe lithium ion concentration distribution, potential distribution, etc., such as porous electrode theory, pseudo-two-dimensional (P2D) model, etc. The electrochemical model has a clear physical meaning, but the model is highly complex and difficult to solve, and is not easy to apply to real-time control. Existing methods have the defects of insufficient model accuracy and lack of microscopic scale information.

[0004] Manifestations of insufficient model accuracy: Integer-order equivalent circuit models are difficult to accurately describe the complex electrochemical processes inside lithium batteries, especially processes with fractional-order characteristics such as SEI film growth. This leads to insufficient model accuracy and makes it difficult to meet the needs of high-precision lithium battery management.

[0005] Lack of microscopic information: Most lithium battery modeling methods are based on macroscopic test data, such as voltage and current, and lack consideration of the microscopic physical processes inside lithium batteries. The performance of lithium batteries is closely related to the microstructure and properties of their internal materials. Models lacking microscopic information are difficult to accurately reflect the internal state of lithium batteries, resulting in insufficient model applicability and robustness. Summary of the invention

[0006] Based on this, it is necessary to provide a lithium battery modeling method based on a fractional-order neural network to solve at least one of the above technical problems.

[0007] To achieve the above purpose, a lithium battery modeling method based on fractional-order neural network includes the following steps:

[0008] Step S1: Perform electrochemical impedance spectroscopy processing on the lithium battery to obtain pre-processed impedance data; obtain lithium battery structure and material data; perform SEI film structure dynamic analysis based on the pre-processed impedance data to obtain SEI film growth process dynamic data; construct a fractional impedance model based on the SEI film growth process dynamic data to obtain fractional impedance model parameters;

[0009] Step S2: Analyze the physical meaning of the parameters of the fractional impedance model to obtain physical meaning data of the parameters; perform micro-scale simulation according to the lithium battery structure and material data to obtain micro-scale simulation data; generate a parameter mapping relationship table for the micro-scale simulation data and the physical meaning data of the parameters to obtain a parameter mapping relationship table; generate an equivalent circuit model according to the parameter mapping relationship table to obtain a fractional equivalent circuit model;

[0010] Step S3: Establishing a fractional-order state space expression according to the fractional-order equivalent circuit model to obtain a fractional-order state space expression;

[0011] Step S4: selecting a network structure according to the fractional-order state space expression to obtain neural network structure data; performing fractional-order operator embedding analysis according to the neural network structure data to obtain fractional-order operator embedding data; generating a fractional-order neural network according to the neural network structure data and the fractional-order operator embedding data to obtain fractional-order neural network data;

[0012] Step S5: training the fractional-order neural network parameters on the fractional-order neural network data to obtain an initial fractional-order neural network model; optimizing the model performance indicators of the initial fractional-order neural network model to obtain a fractional-order neural network model; and deploying the fractional-order neural network model on the hardware platform of the lithium battery management system to implement lithium battery management operations.

[0013] The present invention conducts electrochemical impedance spectrum analysis and SEI film structure dynamic analysis on lithium batteries, and constructs a fractional impedance model in combination with fractional calculus theory, which can more accurately describe the complex electrochemical process inside the battery, especially the dynamic characteristics of the SEI film, and lay the foundation for the subsequent construction of a more accurate battery model. By correlating the parameters of the macroscopic fractional impedance model with the parameters obtained by microscopic scale simulation, and establishing a parameter mapping relationship table, the physical information of the microscopic scale can be integrated into the macroscopic model, and a more accurate and comprehensive fractional equivalent circuit model can be constructed to improve the physical meaning and prediction accuracy of the model. The fractional equivalent circuit model is converted into a fractional state space expression, and the relationship between the input, output and state variables of the battery system can be expressed in a concise and unified mathematical form, which is convenient for the subsequent design of the controller, system analysis and simulation. By constructing a reasonable neural network structure and embedding the fractional operator into the neural network, the neural network model can be equipped with the ability to describe fractional-order dynamics, thereby more accurately describing the complex electrochemical behavior of the battery and improving the prediction accuracy and generalization ability of the model. By training, evaluating, optimizing and deploying the fractional-order neural network model, a lithium battery model with high precision and strong generalization ability can be obtained, and it can be applied to the actual battery management system to realize the functions of real-time monitoring of battery status, life prediction, fault diagnosis, etc., improve the safety and reliability of the battery management system, and extend the service life of the battery. Therefore, the present invention provides a lithium battery modeling method based on a fractional-order neural network, which is used to solve the defects of the existing method in terms of insufficient model accuracy and lack of microscopic scale information. By introducing fractional-order differential equations, constructing fractional-order impedance models and equivalent circuit models, the fractional-order characteristics inside the lithium battery can be more accurately described, and the accuracy of the model is improved. By performing fractional-order modeling on the SEI film growth process, the limitation that the traditional integer-order model is difficult to accurately describe the process is overcome. The multi-scale physical mechanism information is integrated, the microscopic physical parameters of the material are obtained through microscopic simulation, and a mapping relationship is established with the fractional-order model parameters, so that the model has a clear physical meaning. The introduction of microscopic information enhances the interpretability and applicability of the model.

[0014] Preferably, step S1 comprises the following steps:

[0015] Step S11: performing electrochemical impedance spectroscopy test on the lithium battery to obtain raw impedance data; performing impedance data preprocessing on the raw impedance data to obtain preprocessed impedance data;

[0016] Step S12: performing electrochemical characteristic analysis on the pre-processed impedance data to obtain electrochemical characteristic data;

[0017] Step S13: obtaining lithium battery structure and material data; performing a dynamic analysis of the SEI film structure according to the lithium battery structure and material data and electrochemical characteristic data to obtain dynamic data of the SEI film growth process;

[0018] Step S14: performing fractional capacitance analysis on the dynamic data of the SEI film growth process to obtain fractional capacitance data;

[0019] Step S15: performing fractional impedance modeling according to the dynamic data of the SEI film growth process and the fractional capacitance data to obtain a fractional impedance model;

[0020] Step S16: Utilize the preprocessed impedance data to perform model verification on the fractional-order impedance model to obtain the fractional-order impedance model parameters.

[0021] The present invention can improve the quality and reliability of data by preprocessing the original impedance data, such as removing noise, smoothing, etc., and provide more accurate input for subsequent analysis and modeling, thereby improving the accuracy of the model. Electrochemical characteristic analysis of the preprocessed impedance data can extract key parameters reflecting the electrochemical process inside the battery, such as ohmic resistance, charge transfer resistance, etc., to provide a basis for subsequent dynamic analysis of SEI film structure, which helps to understand the reaction mechanism inside the battery more deeply. Combining lithium battery structure and material data and electrochemical characteristic data to perform dynamic analysis of SEI film structure can more accurately describe the growth process of SEI film, such as changes in SEI film thickness and density, and provide a more practical physical model for subsequent fractional impedance modeling. By performing fractional-order capacitance analysis on the dynamic data of SEI film growth process, the capacitance of SEI film can be more accurately described, overcoming the limitations of traditional integer-order capacitance models, more accurately reflecting the complex electrochemical behavior of SEI film, and improving the accuracy of the model. Based on the dynamic data of SEI film growth process and fractional capacitance data, fractional impedance modeling can be used to build a model that more accurately describes the dynamic behavior of lithium batteries, especially to better capture the complex electrochemical process of SEI film and improve the prediction accuracy of the model. The fractional impedance model can be verified using preprocessed impedance data to evaluate the accuracy and reliability of the model, and the model parameters can be optimized based on the verification results to further improve the accuracy and generalization ability of the model.

[0022] Preferably, step S13 comprises the following steps:

[0023] Step S131: extracting SEI film structure data according to the lithium battery structure and material data and the pre-processed impedance data to obtain SEI film structure data;

[0024] Step S132: performing electrochemical performance correlation analysis on the SEI film structure data according to the electrochemical characteristic data to obtain structural parameters affecting the electrochemical performance;

[0025] Step S133: performing SEI film structure correlation according to the electrochemical performance-influencing structural parameters and the electrochemical characteristic data to obtain SEI film structure correlation data;

[0026] Step S134: Perform a dynamic analysis of the SEI film growth process based on the SEI film structure correlation data to obtain the SEI film growth process dynamic data.

[0027] The present invention can more accurately extract the structural information of the SEI film, such as the thickness, density, pore structure, etc. of the SEI film, by combining the lithium battery structure and material data and the pre-processed impedance data, so as to provide a more reliable data basis for the subsequent analysis of the influence of the SEI film on the battery performance. By performing correlation analysis on the SEI film structure data and the electrochemical characteristic data, it is possible to identify which SEI film structure parameters have a significant influence on the electrochemical performance of the battery, such as the influence of the thickness and density of the SEI film on the internal resistance of the battery, thereby providing guidance for the subsequent optimization of battery design and improvement of battery performance. By establishing a correlation model between the SEI film structure parameters and the battery electrochemical performance indicators, the intrinsic connection between the SEI film structure and the battery performance can be more deeply understood, such as establishing a relationship model between the SEI film thickness and the battery capacity attenuation, thereby providing a theoretical basis for predicting the battery life and optimizing the battery use strategy. By analyzing the SEI film structure correlation data, the dynamic process of the SEI film evolving over time during the charge and discharge process can be predicted, such as the SEI film thickness gradually increases with the increase in the number of charge and discharge cycles, thereby providing data support for optimizing the battery charging strategy and extending the battery life.

[0028] Preferably, step S2 comprises the following steps:

[0029] Step S21: performing characteristic parameter analysis on the fractional-order impedance model parameters to obtain key characteristic parameters; performing parameter physical meaning analysis on the key characteristic parameters to obtain parameter physical meaning data;

[0030] Step S22: performing micro-scale simulation according to the lithium battery structure and material data to obtain micro-scale simulation data;

[0031] Step S23: performing parameter correlation analysis on the micro-scale simulation data and the parameter physical meaning data to obtain parameter correlation data;

[0032] Step S24: deriving a mapping relationship for the parameter association data to obtain mapping relationship derived data; generating a parameter mapping relationship table according to the mapping relationship derived data to obtain a parameter mapping relationship table;

[0033] Step S25: performing component model corresponding processing according to the parameter mapping relationship table to obtain component model corresponding data; performing initial circuit topology analysis according to the component model corresponding data to obtain initial circuit topology data;

[0034] Step S26: using the fractional-order impedance model parameters to assign circuit parameters to the initial circuit topology data to obtain a component circuit model;

[0035] Step S27: simplifying and optimizing the component circuit model and generating an equivalent circuit model to obtain a fractional-order equivalent circuit model.

[0036] The present invention can link the abstract model parameters with the specific physical processes inside the battery by analyzing the characteristic parameters and interpreting the physical meaning of the fractional impedance model parameters, for example, interpreting a certain parameter as the ionic conductivity of the SEI membrane, thereby enhancing the interpretability and physical meaning of the model. By performing microscopic scale simulation, the internal microscopic parameters of the battery that are difficult to measure directly, such as the diffusion coefficient of lithium ions in the electrolyte, can be obtained, providing a data basis for establishing the connection between macroscopic parameters and microscopic parameters. By correlating and analyzing macroscopic parameters and microscopic parameters, the influence of the microscopic mechanism inside the battery on the macroscopic performance can be revealed, such as analyzing the relationship between the ionic conductivity of the SEI membrane and the lithium ion diffusion coefficient, providing theoretical guidance for optimizing battery materials and structures. By establishing a parameter mapping relationship table, the macroscopic model parameters can be linked to the microscopic simulation parameters, and a cross-scale model bridge can be established, laying the foundation for building a more accurate and comprehensive battery model. By applying the parameter mapping relationship table to the construction of the equivalent circuit model, the physical information at the microscopic scale can be integrated into the macroscopic model. For example, the value of the SEI film resistance in the equivalent circuit can be determined according to the microstructural parameters of the SEI film, thereby improving the physical accuracy and prediction accuracy of the model. By using the parameters of the fractional impedance model to assign parameters to the initial circuit topology, the experimental measurement data can be combined with the model parameters to make the constructed equivalent circuit model more consistent with the characteristics of the actual battery. By simplifying and optimizing the component circuit model, the complexity of the model can be reduced while ensuring the accuracy of the model, the computational efficiency of the model can be improved, and the application and promotion of the model can be facilitated.

[0037] Preferably, step S22 comprises the following steps:

[0038] Step S221: constructing a molecular dynamics model according to the lithium battery structure and material data to obtain a molecular dynamics model;

[0039] Step S222: using a molecular dynamics model to simulate the operation of battery materials and obtain simulation operation result data; visualizing the lithium ion atomic trajectory of the simulation operation result data and obtain atomic trajectory visualization data;

[0040] Step S223: performing lithium ion average displacement analysis according to the atomic trajectory visualization data to obtain lithium ion average displacement data;

[0041] Step S224: extracting the lithium ion diffusion coefficient according to the lithium ion average displacement data to obtain the lithium ion diffusion coefficient;

[0042] Step S225: performing micro-scale analysis of simulation parameters on the lithium ion diffusion coefficient to obtain micro-scale simulation data.

[0043] The present invention constructs a molecular dynamics model based on the structure and material data of the lithium battery, and can introduce real battery material information, such as atomic arrangement, interaction force, etc., into the simulation calculation, providing a reliable model basis for subsequent simulation analysis. Using the constructed molecular dynamics model for simulation operation, the dynamic evolution process of battery materials at a microscopic scale, such as the diffusion process of lithium ions in the electrolyte, can be simulated, and these processes can be intuitively observed through visualization technology, providing intuitive image information for a deep understanding of the microscopic mechanism inside the battery. By analyzing the atomic trajectory of lithium ions, the average displacement of lithium ions can be calculated, and the migration ability of lithium ions in battery materials can be quantitatively described, providing a data basis for the subsequent calculation of the lithium ion diffusion coefficient. According to the average displacement data of lithium ions, the diffusion coefficient of lithium ions in battery materials can be calculated using theoretical formulas such as the Einstein relationship. This parameter is one of the key parameters for evaluating battery performance and reflects the transmission efficiency of lithium ions inside the battery. By performing microscopic scale analysis on the simulation parameters of the lithium ion diffusion coefficient, such as studying the effects of temperature, electrolyte concentration and other factors on the diffusion coefficient, we can gain an in-depth understanding of the microscopic factors that affect the lithium ion transmission efficiency and provide theoretical guidance for optimizing the design of battery materials and electrolytes.

[0044] Preferably, step S3 comprises the following steps:

[0045] Step S31: Establishing circuit equations using Kirchhoff's voltage law according to the fractional-order equivalent circuit model to obtain a circuit equation group;

[0046] Step S32: constructing a fractional-order differential equation for the fractional-order component data in the circuit equation group to obtain a fractional-order differential equation;

[0047] Step S33: selecting state variables according to the fractional-order differential equation to obtain state variable data; constructing a state equation according to the state variable data to obtain a fractional-order state equation;

[0048] Step S34: constructing an output equation according to the fractional-order state equation to obtain the output equation; constructing a fractional-order state space expression for the output equation and the fractional-order state equation to obtain the fractional-order state space expression.

[0049] The present invention uses Kirchhoff's voltage law to establish a circuit equation group of a fractional equivalent circuit model, which can convert the circuit model into a mathematical expression, providing a basis for subsequent analysis and solution using fractional calculus theory. Converting the fractional-order component data in the circuit equation group into a fractional-order differential equation can more accurately describe the complex electrochemical processes inside the battery, such as the formation of the SEI film and the ion transport process, because these processes often show fractional-order kinetic characteristics, which are difficult to accurately describe with traditional integer-order models. By selecting appropriate variables as state variables and rewriting the fractional-order differential equations into the form of state equations, high-order differential equations can be converted into a set of first-order differential equations, which is more convenient for numerical solution and analysis, and also lays the foundation for the subsequent construction of state space expressions. Establishing a fractional-order state space expression can express the relationship between the input, output and state variables of the battery system in a concise and unified mathematical form, which provides convenience for subsequent design of controllers, system analysis and simulation.

[0050] Preferably, step S4 comprises the following steps:

[0051] Step S41: Acquire actual working condition data of the lithium battery; construct a fractional-order neural network data set according to the fractional-order state space expression and the actual working condition data of the lithium battery to obtain a fractional-order neural network data set;

[0052] Step S42: selecting a network structure according to the fractional-order neural network data set to obtain neural network structure data;

[0053] Step S43: performing fractional-order operator embedding analysis according to the neural network structure data to obtain fractional-order operator embedding data;

[0054] Step S44: setting hyperparameters for the neural network structure data to obtain network hyperparameters;

[0055] Step S45: Generate a fractional-order neural network according to the neural network structure data, the fractional-order operator embedding data and the network hyperparameters to obtain fractional-order neural network data.

[0056] The present invention obtains the actual working condition data of the lithium battery and constructs a data set in combination with the fractional-order state space expression, so that the trained neural network model can be closer to the actual working state of the battery, and the prediction accuracy and generalization ability of the model can be improved. According to the characteristics of the data set, a suitable neural network structure is selected, and the data information can be fully utilized, such as selecting a recurrent neural network (RNN) to process time series data, thereby improving the learning efficiency and prediction accuracy of the model. By embedding fractional-order operators into the neural network, the neural network model can be equipped with the ability to describe fractional-order dynamics, thereby more accurately describing the complex electrochemical behavior of the battery and improving the prediction accuracy of the model. The neural network structure is set with hyperparameters, such as learning rate, batch size, etc., which can optimize the training process of the model and improve the convergence speed and generalization ability of the model. According to the determined network structure, fractional-order operator embedding information and network hyperparameters, a fractional-order neural network model is generated, which provides a basis for subsequent model training and optimization.

[0057] Preferably, step S43 includes the following steps:

[0058] Step S431: performing operator embedding position selection of a neuron activation function on the neural network structure data to obtain operator embedding position data;

[0059] Step S432: selecting a fractional-order derivative operator according to the operator embedding position data to obtain a fractional-order derivative operator;

[0060] Step S433: determining the operator order of the fractional-order derivative operator to obtain the fractional-order operator order;

[0061] Step S434: performing discretization operator calculation according to the fractional-order operator order and the fractional-order operator to obtain discretization operator calculation method data;

[0062] Step S435: Perform fractional-order operator embedding on the neural network structure data according to the discretization operator calculation method data to obtain fractional-order operator embedding data.

[0063] The present invention can more effectively utilize the characteristics of fractional-order operators and improve the model's ability to describe the nonlinear dynamic behavior of batteries by selecting a suitable embedding position of the neuron activation function, such as embedding in the hidden layer or output layer neurons. According to the embedding position of the operator and the specific application scenario, a suitable fractional-order derivative operator is selected, such as selecting Caputo fractional-order derivatives to describe a system with initial conditions, which can improve the accuracy and efficiency of the model. By determining the order of the fractional-order derivative operator, the degree of memory of the model for historical information can be controlled. For example, a smaller order corresponds to a longer memory time, so that the model can better capture the long-term behavior characteristics of the battery and improve the prediction accuracy of the model. The fractional-order derivative operator is discretized, and the fractional-order model of the continuous-time system can be converted into the form of a discrete-time system, so as to facilitate implementation and calculation on a digital computer, and provide convenience for subsequent model training and application. The discretized fractional-order operator is embedded in the neural network structure, so that the neural network model has the ability to describe fractional-order dynamics, thereby more accurately describing the complex electrochemical behavior of the battery and improving the prediction accuracy of the model.

[0064] Preferably, step S5 comprises the following steps:

[0065] Step S51: outputting expression data using a fractional-order state space expression according to actual operating condition data of the lithium battery to obtain fractional-order neural network training data and fractional-order neural network test data;

[0066] Step S52: using the fractional-order neural network training data to perform fractional-order network parameter training on the fractional-order neural network data to obtain an initial fractional-order neural network model;

[0067] Step S53: using the fractional-order neural network test data to calculate the model performance index of the initial fractional-order neural network model to obtain model performance index data;

[0068] Step S54: performing performance indicator verification analysis on the model performance indicator data to obtain performance indicator verification data; optimizing the model performance indicator of the initial fractional-order neural network model according to the performance indicator verification data to obtain a fractional-order neural network model;

[0069] Step S55: deploying the fractional-order neural network model onto the hardware platform of the lithium battery management system to implement lithium battery management operations.

[0070] The present invention uses fractional-order state space expressions and actual working condition data to construct training and test data sets, which can ensure that the trained model can be effectively applied to actual scenarios and improve the practical value of the model. The model can be trained using fractional-order neural network training data, and the model parameters can be adjusted so that it can accurately fit the characteristics of the training data, providing a basis for subsequent model evaluation and optimization. The performance of the initial model is evaluated using test data, and the prediction accuracy and generalization ability of the model can be objectively evaluated, providing a direction for subsequent model optimization. According to the model performance index data, analysis and optimization are performed, such as adjusting the model structure, parameters, etc., which can improve the prediction accuracy and generalization ability of the model and make it more suitable for actual application scenarios. The optimized fractional-order neural network model is deployed on the hardware platform of the lithium battery management system, which can realize the functions of real-time monitoring of the battery status, life prediction, fault diagnosis, etc., improve the safety and reliability of the battery management system, and extend the service life of the battery.

[0071] Preferably, step S52 includes the following steps:

[0072] Step S521: using a preset damage function to perform fractional-order algorithm optimization on the fractional-order neural network data to obtain fractional-order neural network optimization data;

[0073] Step S522: using the fractional-order neural network training data to train the network parameters of the fractional-order neural network optimization data and perform overfitting suppression to obtain a fractional-order neural network training network;

[0074] Step S523: performing network performance evaluation on the fractional-order neural training network to obtain network performance evaluation data;

[0075] Step S524: Generate a fractional-order neural network model based on the network performance evaluation data to obtain an initial fractional-order neural network model.

[0076] The present invention optimizes the fractional-order neural network data by using a preset damage function and a fractional-order algorithm, and can find better network parameters, such as connection weights and biases, so as to reduce the prediction error of the model and improve the accuracy of the model. The optimized network parameters are trained using training data, and overfitting suppression measures such as regularization and Dropout are taken, so that the model can achieve high accuracy on the training set while also having good generalization ability, and can also maintain good prediction performance on the test set. The performance evaluation of the trained fractional-order neural training network can objectively evaluate the model's prediction accuracy, generalization ability and other indicators, and provide a basis for subsequent judgment of whether the model meets the requirements. The initial fractional-order neural network model is generated according to the network performance evaluation results. If the model performance meets expectations, the model can be used for subsequent battery management tasks; otherwise, it is necessary to return to step S521, adjust the optimization algorithm, damage function and other parameters, and retrain and optimize until the model performance meets the requirements.

[0077] The present invention conducts electrochemical impedance spectrum analysis and SEI film structure dynamic analysis on lithium batteries, and constructs a fractional impedance model in combination with fractional calculus theory, which can more accurately describe the complex electrochemical process inside the battery, especially the dynamic characteristics of the SEI film, and lay the foundation for the subsequent construction of a more accurate battery model. By correlating the parameters of the macroscopic fractional impedance model with the parameters obtained by microscopic scale simulation, and establishing a parameter mapping relationship table, the physical information of the microscopic scale can be integrated into the macroscopic model, and a more accurate and comprehensive fractional equivalent circuit model can be constructed to improve the physical meaning and prediction accuracy of the model. The fractional equivalent circuit model is converted into a fractional state space expression, and the relationship between the input, output and state variables of the battery system can be expressed in a concise and unified mathematical form, which is convenient for the subsequent design of the controller, system analysis and simulation. By constructing a reasonable neural network structure and embedding the fractional operator into the neural network, the neural network model can be equipped with the ability to describe fractional-order dynamics, thereby more accurately describing the complex electrochemical behavior of the battery and improving the prediction accuracy and generalization ability of the model. By training, evaluating, optimizing and deploying the fractional-order neural network model, a lithium battery model with high precision and strong generalization ability can be obtained, and it can be applied to the actual battery management system to realize the functions of real-time monitoring of battery status, life prediction, fault diagnosis, etc., improve the safety and reliability of the battery management system, and extend the service life of the battery. Therefore, the present invention provides a lithium battery modeling method based on a fractional-order neural network, which is used to solve the defects of the existing method in terms of insufficient model accuracy and lack of microscopic scale information. By introducing fractional-order differential equations, constructing fractional-order impedance models and equivalent circuit models, the fractional-order characteristics inside the lithium battery can be more accurately described, and the accuracy of the model is improved. By performing fractional-order modeling on the SEI film growth process, the limitation that the traditional integer-order model is difficult to accurately describe the process is overcome. The multi-scale physical mechanism information is integrated, the microscopic physical parameters of the material are obtained through microscopic simulation, and a mapping relationship is established with the fractional-order model parameters, so that the model has a clear physical meaning. The introduction of microscopic information enhances the interpretability and applicability of the model. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] Figure 1 A schematic diagram of the steps of a lithium battery modeling method based on a fractional-order neural network;

[0079] Figure 2 for Figure 1 Detailed implementation steps of step S1 in FIG.

[0080] Figure 3 for Figure 1 Detailed implementation steps of step S2 in FIG.

[0081] The purpose, features and advantages of the present invention will be further described with reference to the accompanying drawings in conjunction with the embodiments. DETAILED DESCRIPTION

[0082] The technical method of the present invention is described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by technicians in this field without creative work are within the scope of protection of the present invention.

[0083] In addition, the accompanying drawings are only schematic illustrations of the present invention and are not necessarily drawn to scale. The same reference numerals in the figures represent the same or similar parts, and their repeated description will be omitted. Some of the block diagrams shown in the accompanying drawings are functional entities and do not necessarily correspond to physically or logically independent entities. The functional entities can be implemented in software form, or implemented in one or more hardware modules or integrated circuits, or implemented in different networks and / or processor methods and / or microcontroller methods.

[0084] It should be understood that, although the terms "first", "second", etc. may be used herein to describe various units, these units should not be limited by these terms. These terms are used only to distinguish one unit from another unit. For example, without departing from the scope of the exemplary embodiments, the first unit may be referred to as the second unit, and similarly the second unit may be referred to as the first unit. The term "and / or" used herein includes any and all combinations of one or more of the listed associated items.

[0085] To achieve this, please refer to Figures 1 to 3 , a lithium battery modeling method based on fractional-order neural network, comprising the following steps:

[0086] Step S1: Perform electrochemical impedance spectroscopy processing on the lithium battery to obtain pre-processed impedance data; obtain lithium battery structure and material data; perform SEI film structure dynamic analysis based on the pre-processed impedance data to obtain SEI film growth process dynamic data; construct a fractional impedance model based on the SEI film growth process dynamic data to obtain fractional impedance model parameters;

[0087] Step S2: Analyze the physical meaning of the parameters of the fractional impedance model to obtain physical meaning data of the parameters; perform micro-scale simulation according to the lithium battery structure and material data to obtain micro-scale simulation data; generate a parameter mapping relationship table for the micro-scale simulation data and the physical meaning data of the parameters to obtain a parameter mapping relationship table; generate an equivalent circuit model according to the parameter mapping relationship table to obtain a fractional equivalent circuit model;

[0088] Step S3: Establishing a fractional-order state space expression according to the fractional-order equivalent circuit model to obtain a fractional-order state space expression;

[0089] Step S4: selecting a network structure according to the fractional-order state space expression to obtain neural network structure data; performing fractional-order operator embedding analysis according to the neural network structure data to obtain fractional-order operator embedding data; generating a fractional-order neural network according to the neural network structure data and the fractional-order operator embedding data to obtain fractional-order neural network data;

[0090] Step S5: training the fractional-order neural network parameters on the fractional-order neural network data to obtain an initial fractional-order neural network model; optimizing the model performance indicators of the initial fractional-order neural network model to obtain a fractional-order neural network model; and deploying the fractional-order neural network model on the hardware platform of the lithium battery management system to implement lithium battery management operations.

[0091] In the embodiment of the present invention, reference Figure 1 The above is a schematic diagram of the steps of the lithium battery modeling method based on the fractional order neural network of the present invention. In this example, the lithium battery modeling method based on the fractional order neural network includes the following steps:

[0092] Step S1: Perform electrochemical impedance spectroscopy processing on the lithium battery to obtain pre-processed impedance data; obtain lithium battery structure and material data; perform SEI film structure dynamic analysis based on the pre-processed impedance data to obtain SEI film growth process dynamic data; construct a fractional impedance model based on the SEI film growth process dynamic data to obtain fractional impedance model parameters;

[0093] In an embodiment of the present invention, the lithium battery is first subjected to an electrochemical impedance spectroscopy (EIS) test, and the raw data is preprocessed, such as removing noise, smoothing, etc., to obtain preprocessed impedance data. At the same time, the structure and material data of the lithium battery, such as information on electrode materials, electrolytes, etc., are collected. Then, based on the preprocessed impedance data, combined with electrochemical principles and fractional calculus theory, the dynamic growth process of the SEI film is analyzed, such as the changes in SEI film thickness and composition over time. Finally, based on the dynamic data of the growth process of the SEI film, a fractional impedance model describing the battery impedance characteristics is established, and the fractional impedance model parameters are obtained by model fitting.

[0094] Step S2: Analyze the physical meaning of the parameters of the fractional impedance model to obtain physical meaning data of the parameters; perform micro-scale simulation according to the lithium battery structure and material data to obtain micro-scale simulation data; generate a parameter mapping relationship table for the micro-scale simulation data and the physical meaning data of the parameters to obtain a parameter mapping relationship table; generate an equivalent circuit model according to the parameter mapping relationship table to obtain a fractional equivalent circuit model;

[0095] In an embodiment of the present invention, the physical meaning of the fractional impedance model parameters obtained in step S1 is analyzed, for example, the parameters are associated with the electrochemical processes inside the battery, such as the formation of the SEI film, ion transport, etc. At the same time, according to the structure and material data of the lithium battery, a microscopic scale simulation is performed, for example, using molecular dynamics simulation to obtain microscopic parameters such as the lithium ion diffusion coefficient. Then, a mapping relationship table between macroscopic parameters and microscopic parameters is established, for example, the ionic conductivity of the SEI film is associated with the lithium ion diffusion coefficient. Finally, according to the parameter mapping relationship table, a fractional equivalent circuit model is constructed, which can more intuitively reflect the electrochemical process inside the battery.

[0096] Step S3: Establishing a fractional-order state space expression according to the fractional-order equivalent circuit model to obtain a fractional-order state space expression;

[0097] In the embodiment of the present invention, based on the fractional-order equivalent circuit model obtained in step S2, Kirchhoff's voltage law is applied to write the circuit equation, and the circuit equation is converted into the form of a fractional-order differential equation using the fractional-order calculus theory. Then, appropriate variables are selected as state variables, and the fractional-order differential equation is rewritten into the form of a state equation. Finally, according to actual needs, the output variable is selected and the output equation is established. The state equation and the output equation are combined to obtain a fractional-order state space expression describing the input-output relationship of the system.

[0098] Step S4: selecting a network structure according to the fractional-order state space expression to obtain neural network structure data; performing fractional-order operator embedding analysis according to the neural network structure data to obtain fractional-order operator embedding data; generating a fractional-order neural network according to the neural network structure data and the fractional-order operator embedding data to obtain fractional-order neural network data;

[0099] In an embodiment of the present invention, first, actual operating data of lithium batteries under different operating conditions, such as charge and discharge current, voltage, temperature, etc., are collected. Then, based on the fractional-order state space expression and the collected actual operating condition data, a data set for training and testing the fractional-order neural network is constructed. According to the characteristics of the data set, a suitable neural network structure is selected, and the embedding position, type and order of the fractional-order operator are determined. Finally, a fractional-order neural network model is constructed based on the selected neural network structure, the embedding information of the fractional-order operator and the network hyperparameters.

[0100] Step S5: training the fractional-order neural network parameters on the fractional-order neural network data to obtain an initial fractional-order neural network model; optimizing the model performance index of the initial fractional-order neural network model to obtain a fractional-order neural network model; deploying the fractional-order neural network model on the hardware platform of the lithium battery management system to implement lithium battery management operations;

[0101] In an embodiment of the present invention, the initial fractional-order neural network model is trained using fractional-order neural network training data, and overfitting suppression measures such as regularization technology and Dropout technology are taken to finally obtain a trained fractional-order neural network model. The performance of the trained model is evaluated using test data, and the model is optimized based on the evaluation results, such as adjusting the network structure and hyperparameters. Finally, the optimized fractional-order neural network model is deployed on the hardware platform of the lithium battery management system for real-time monitoring of the battery status, prediction of the remaining battery life, etc., thereby realizing lithium battery management operations.

[0102] Preferably, step S1 comprises the following steps:

[0103] Step S11: performing electrochemical impedance spectroscopy test on the lithium battery to obtain raw impedance data; performing impedance data preprocessing on the raw impedance data to obtain preprocessed impedance data;

[0104] Step S12: performing electrochemical characteristic analysis on the pre-processed impedance data to obtain electrochemical characteristic data;

[0105] Step S13: obtaining lithium battery structure and material data; performing a dynamic analysis of the SEI film structure according to the lithium battery structure and material data and electrochemical characteristic data to obtain dynamic data of the SEI film growth process;

[0106] Step S14: performing fractional capacitance analysis on the dynamic data of the SEI film growth process to obtain fractional capacitance data;

[0107] Step S15: performing fractional impedance modeling according to the dynamic data of the SEI film growth process and the fractional capacitance data to obtain a fractional impedance model;

[0108] Step S16: Utilize the preprocessed impedance data to perform model verification on the fractional-order impedance model to obtain the fractional-order impedance model parameters.

[0109] As an example of the present invention, refer to Figure 2 As shown, in this example, step S1 includes:

[0110] Preferably, step S1 comprises the following steps:

[0111] Step S11: performing electrochemical impedance spectroscopy test on the lithium battery to obtain raw impedance data; performing impedance data preprocessing on the raw impedance data to obtain preprocessed impedance data;

[0112] In the embodiment of the present invention, first, an electrochemical impedance spectroscopy (EIS) test is performed on a lithium battery using an electrochemical workstation to obtain raw impedance data. The test frequency range is usually set to 100kHz to 0.01Hz, and a small-amplitude AC voltage signal is applied. The obtained raw data contains the impedance information of the battery, but there are noise and errors. Therefore, it is necessary to preprocess the raw impedance data, such as removing outliers, smoothing, and data interpolation, to improve the accuracy and reliability of the data, and finally obtain preprocessed impedance data.

[0113] Step S12: performing electrochemical characteristic analysis on the pre-processed impedance data to obtain electrochemical characteristic data;

[0114] In the embodiment of the present invention, the pre-processed impedance data is used to perform electrochemical characteristic analysis. This can be achieved by methods such as equivalent circuit fitting or distribution function analysis. For example, the impedance spectrum can be fitted using Zview software to obtain parameters such as the battery's ohmic resistance, charge transfer resistance, SEI membrane resistance, and Warburg impedance. These parameters can reflect information such as the battery's internal resistance, reaction kinetics, and ion transport characteristics, and constitute electrochemical characteristic data.

[0115] Step S13: obtaining lithium battery structure and material data; performing a dynamic analysis of the SEI film structure according to the lithium battery structure and material data and electrochemical characteristic data to obtain dynamic data of the SEI film growth process;

[0116] In an embodiment of the present invention, the structure and material data of the lithium battery are collected, such as the type of electrode material, particle size distribution, porosity, and the composition and concentration of the electrolyte. Combined with electrochemical characteristic data, such as changes in SEI film resistance, the structural evolution of the SEI film is analyzed. For example, an increase in SEI film resistance corresponds to a thickening or composition change of the SEI film. Through a comprehensive analysis of this information, dynamic data of the SEI film growth process can be obtained, such as changes in SEI film thickness over time, changes in SEI film composition over time, etc.

[0117] Step S14: performing fractional capacitance analysis on the dynamic data of the SEI film growth process to obtain fractional capacitance data;

[0118] In the embodiment of the present invention, the dynamic data of the SEI film growth process is used to analyze the capacitance characteristics of the SEI film. Traditional capacitance models usually use integer-order capacitance elements, but the capacitance behavior of the SEI film exhibits fractional-order characteristics. Therefore, it is necessary to adopt a fractional-order capacitance model to more accurately describe the capacitance behavior of the SEI film. By analyzing the dynamic data of the SEI film growth process, such as the changes in the thickness and composition of the SEI film, the change data of the SEI film fractional capacitance over time can be obtained.

[0119] Step S15: performing fractional impedance modeling according to the dynamic data of the SEI film growth process and the fractional capacitance data to obtain a fractional impedance model;

[0120] In the embodiment of the present invention, a fractional impedance model of a lithium battery is constructed based on the dynamic data of the SEI film growth process and the fractional capacitance data. The model can use fractional calculus theory to describe the electrochemical process inside the battery, such as the formation of the SEI film and the ion transport process. The fractional impedance model can more accurately describe the dynamic behavior of lithium batteries, especially the complex electrochemical process of the SEI film.

[0121] Step S16: using the preprocessed impedance data to perform model verification on the fractional-order impedance model to obtain the fractional-order impedance model parameters;

[0122] In the embodiment of the present invention, the fractional impedance model is verified by using the preprocessed impedance data. By comparing the error between the model prediction value and the experimental measurement value, the accuracy and reliability of the model can be evaluated. At the same time, according to the result of the model verification, the parameters of the fractional impedance model are adjusted and optimized, and finally the parameters of the fractional impedance model are obtained.

[0123] Preferably, step S13 comprises the following steps:

[0124] Step S131: extracting SEI film structure data according to the lithium battery structure and material data and the pre-processed impedance data to obtain SEI film structure data;

[0125] Step S132: performing electrochemical performance correlation analysis on the SEI film structure data according to the electrochemical characteristic data to obtain structural parameters affecting the electrochemical performance;

[0126] Step S133: performing SEI film structure correlation according to the electrochemical performance-influencing structural parameters and the electrochemical characteristic data to obtain SEI film structure correlation data;

[0127] Step S134: Perform a dynamic analysis of the SEI film growth process based on the SEI film structure correlation data to obtain the SEI film growth process dynamic data.

[0128] In an embodiment of the present invention, the structural information of the SEI film is extracted based on the structure and material data of the lithium battery, such as the particle size and porosity of the electrode material, and the electrochemical impedance spectrum data after pretreatment. For example, the SEI film resistance and capacitance parameters obtained by impedance spectrum fitting can be used, combined with information such as the specific surface area and porosity of the electrode material, to estimate the thickness, density and pore structure of the SEI film, and finally obtain the SEI film structure data. The SEI film structure data is correlated using electrochemical characteristic data, such as the internal resistance and exchange current density of the battery. For example, the relationship between parameters such as SEI film thickness, density and pore structure and the internal resistance and exchange current density of the battery is analyzed. Through statistical analysis and data mining and other methods, it can be determined which SEI film structure parameters have a significant effect on the electrochemical performance of the battery, and the electrochemical performance-affecting structural parameters are obtained. Based on the electrochemical performance-affecting structural parameters and electrochemical characteristic data, the structural information of the SEI film is associated with the electrochemical performance of the battery. For example, a mathematical model between parameters such as SEI film thickness, density, pore structure and electrochemical performance indicators such as battery internal resistance and exchange current density is established. The model can be a linear model, a nonlinear model or a machine learning model, etc., depending on the results of the data analysis. Finally, the SEI film structure associated data is obtained, that is, data that can reflect the relationship between the SEI film structure and the electrochemical performance of the battery. Based on the SEI film structure associated data, the dynamic process of the SEI film evolving over time during the charge and discharge process is analyzed. For example, according to the battery's charge and discharge regime, such as current density, cut-off voltage, etc., and the SEI film structure associated data, the change trend of parameters such as SEI film thickness, density, and pore structure over time can be predicted. Finally, the dynamic data of the SEI film growth process is obtained, such as the curve of the SEI film thickness changing over time, the curve of the SEI film composition changing over time, etc.

[0129] Preferably, step S2 comprises the following steps:

[0130] Step S21: performing characteristic parameter analysis on the fractional-order impedance model parameters to obtain key characteristic parameters; performing parameter physical meaning analysis on the key characteristic parameters to obtain parameter physical meaning data;

[0131] Step S22: performing micro-scale simulation according to the lithium battery structure and material data to obtain micro-scale simulation data;

[0132] Step S23: performing parameter correlation analysis on the micro-scale simulation data and the parameter physical meaning data to obtain parameter correlation data;

[0133] Step S24: deriving a mapping relationship for the parameter association data to obtain mapping relationship derived data; generating a parameter mapping relationship table according to the mapping relationship derived data to obtain a parameter mapping relationship table;

[0134] Step S25: performing component model corresponding processing according to the parameter mapping relationship table to obtain component model corresponding data; performing initial circuit topology analysis according to the component model corresponding data to obtain initial circuit topology data;

[0135] Step S26: using the fractional-order impedance model parameters to assign circuit parameters to the initial circuit topology data to obtain a component circuit model;

[0136] Step S27: simplifying and optimizing the component circuit model and generating an equivalent circuit model to obtain a fractional-order equivalent circuit model.

[0137] As an example of the present invention, refer to Figure 3 As shown, in this example, step S2 includes:

[0138] Step S21: performing characteristic parameter analysis on the fractional-order impedance model parameters to obtain key characteristic parameters; performing parameter physical meaning analysis on the key characteristic parameters to obtain parameter physical meaning data;

[0139] In the embodiment of the present invention, the parameters of the fractional impedance model are first analyzed to identify the key characteristic parameters that have the greatest impact on the model output. Then, the physical meaning of these key characteristic parameters is analyzed by combining electrochemical principles and fractional calculus theory, such as how they are related to the electrochemical process inside the battery. Finally, the physical meaning data of the parameters are obtained, such as a certain parameter representing the ionic conductivity of the SEI membrane.

[0140] Step S22: performing micro-scale simulation according to the lithium battery structure and material data to obtain micro-scale simulation data;

[0141] In the embodiment of the present invention, the structure and material data of the lithium battery, such as the crystal structure of the electrode material, the molecular structure of the electrolyte, etc., are used to perform microscopic simulation. For example, molecular dynamics simulation or first principle calculation methods can be used to study the transmission process of lithium ions inside the battery, the formation process of the SEI film, etc. Finally, microscopic simulation data, such as the diffusion coefficient of lithium ions, the growth rate of the SEI film, etc., are obtained.

[0142] Step S23: performing parameter correlation analysis on the micro-scale simulation data and the parameter physical meaning data to obtain parameter correlation data;

[0143] In the embodiment of the present invention, the physical meaning data of the parameters are correlated with the microscopic simulation data. For example, the relationship between the ionic conductivity of the SEI membrane and the diffusion coefficient of lithium ions in the SEI membrane is analyzed. Through data analysis and model building, the law that can correlate the macroscopic parameters and the microscopic parameters is found to obtain parameter correlation data.

[0144] Step S24: deriving a mapping relationship for the parameter association data to obtain mapping relationship derived data; generating a parameter mapping relationship table according to the mapping relationship derived data to obtain a parameter mapping relationship table;

[0145] In the embodiment of the present invention, based on the parameter association data, the mapping relationship between the macroscopic parameters and the microscopic parameters is derived. For example, a functional relationship between the ionic conductivity of the SEI membrane and the lithium ion diffusion coefficient is established. And these mapping relationships are organized into a parameter mapping relationship table.

[0146] Step S25: performing component model corresponding processing according to the parameter mapping relationship table to obtain component model corresponding data; performing initial circuit topology analysis according to the component model corresponding data to obtain initial circuit topology data;

[0147] In the embodiment of the present invention, each element in the fractional impedance model is matched to a specific physical process according to the parameter mapping relationship table. For example, a fractional capacitance element in the model is matched to the capacitance characteristic of the SEI film. Then, according to the physical meaning of the element, a suitable circuit topology structure is selected, such as an RC circuit, an RCR circuit, etc., to construct the initial circuit topology data.

[0148] Step S26: using the fractional-order impedance model parameters to assign circuit parameters to the initial circuit topology data to obtain a component circuit model;

[0149] In the embodiment of the present invention, the parameters of the fractional impedance model are used to assign parameters to the initial circuit topology data. For example, the ionic conductivity of the SEI film is mapped to the corresponding resistance value in the circuit model. Finally, a component circuit model containing specific parameter values ​​is obtained.

[0150] Step S27: simplifying and optimizing the component circuit model and generating an equivalent circuit model to obtain a fractional-order equivalent circuit model;

[0151] In the embodiment of the present invention, the component circuit model is simplified and optimized. For example, components of the same type are merged, components with little influence on the model output are removed, etc. Finally, a simplified fractional-order equivalent circuit model is obtained, which can more intuitively reflect the electrochemical process inside the battery while maintaining a high model accuracy.

[0152] Preferably, step S22 comprises the following steps:

[0153] Step S221: constructing a molecular dynamics model according to the lithium battery structure and material data to obtain a molecular dynamics model;

[0154] Step S222: using a molecular dynamics model to simulate the operation of battery materials and obtain simulation operation result data; visualizing the lithium ion atomic trajectory of the simulation operation result data and obtain atomic trajectory visualization data;

[0155] Step S223: performing lithium ion average displacement analysis according to the atomic trajectory visualization data to obtain lithium ion average displacement data;

[0156] Step S224: extracting the lithium ion diffusion coefficient according to the lithium ion average displacement data to obtain the lithium ion diffusion coefficient;

[0157] Step S225: performing micro-scale analysis of simulation parameters on the lithium ion diffusion coefficient to obtain micro-scale simulation data.

[0158] In an embodiment of the present invention, based on the structure and material data of the lithium battery, such as the crystal structure of the electrode material, the molecular structure of the electrolyte, etc., appropriate molecular dynamics simulation software and force field parameters are selected to construct a molecular dynamics model of the battery system. The model should contain a sufficient number of atoms to reflect the real battery structure and behavior. Using the constructed molecular dynamics model, simulation parameters such as temperature, pressure, simulation time, etc. are set to run the molecular dynamics simulation. During the simulation process, the position and velocity information of all atoms in the system are recorded to obtain the simulation operation result data. At the same time, the simulation result data is processed, for example, using visualization software such as VMD and Ovito to visualize the motion trajectory of lithium ions during the simulation process to obtain atomic trajectory visualization data. The atomic trajectory visualization data is analyzed to calculate the average displacement of each lithium ion during the simulation time. The average displacement data of lithium ions can be obtained by counting the displacement data of all lithium ions and calculating their mean. According to the average displacement data of lithium ions, the diffusion coefficient of lithium ions in the battery material is calculated. The diffusion coefficient reflects the migration ability of lithium ions in the battery material and is an important parameter for evaluating battery performance. The lithium ion diffusion coefficient is analyzed and associated with other simulation parameters such as temperature and electrolyte concentration. For example, the relationship between the lithium ion diffusion coefficient and temperature, or the effect of different electrolyte concentrations on the lithium ion diffusion coefficient, can be analyzed. Finally, microscopic simulation data can be obtained, such as the change curve of the lithium ion diffusion coefficient at different temperatures.

[0159] Preferably, step S3 comprises the following steps:

[0160] Step S31: Establishing circuit equations using Kirchhoff's voltage law according to the fractional-order equivalent circuit model to obtain a circuit equation group;

[0161] Step S32: constructing a fractional-order differential equation for the fractional-order component data in the circuit equation group to obtain a fractional-order differential equation;

[0162] Step S33: selecting state variables according to the fractional-order differential equation to obtain state variable data; constructing a state equation according to the state variable data to obtain a fractional-order state equation;

[0163] Step S34: constructing an output equation according to the fractional-order state equation to obtain the output equation; constructing a fractional-order state space expression for the output equation and the fractional-order state equation to obtain the fractional-order state space expression.

[0164] In an embodiment of the present invention, according to the simplified fractional-order equivalent circuit model, Kirchhoff's voltage law (KVL) is applied to write the voltage equations of each loop in the circuit. Since the circuit contains fractional-order components, the obtained circuit equation group will contain fractional-order calculus terms. The fractional-order component data in the circuit equation group, such as the value and order of the fractional-order capacitor, are substituted into the expression of the fractional-order differential equation. For example, using the Caputo fractional-order derivative definition, the current-voltage relationship of the fractional-order capacitor is expressed in the form of a fractional-order differential equation. Finally, a group of fractional-order differential equations describing the dynamic behavior of the circuit system is obtained. According to the group of fractional-order differential equations, appropriate variables are selected as state variables. Variables that can reflect the energy storage state of the system are usually selected, such as the voltage across the capacitor, the current in the inductor, etc. According to the definition of the state variable, the group of fractional-order differential equations is rewritten into the form of a state equation with the state variable and its fractional-order derivative as the variable. According to actual needs, the variables that need to be predicted or controlled are selected as output variables, such as the terminal voltage and current of the battery. According to the definition of output variables and fractional-order state equations, the output equations of the relationship between output variables and state variables are established. Finally, the fractional-order state equations and output equations are combined to obtain the fractional-order state space expression that describes the input-output relationship of the system.

[0165] Preferably, step S4 comprises the following steps:

[0166] Step S41: Acquire actual working condition data of the lithium battery; construct a fractional-order neural network data set according to the fractional-order state space expression and the actual working condition data of the lithium battery to obtain a fractional-order neural network data set;

[0167] Step S42: selecting a network structure according to the fractional-order neural network data set to obtain neural network structure data;

[0168] Step S43: performing fractional-order operator embedding analysis according to the neural network structure data to obtain fractional-order operator embedding data;

[0169] Step S44: setting hyperparameters for the neural network structure data to obtain network hyperparameters;

[0170] Step S45: Generate a fractional-order neural network according to the neural network structure data, the fractional-order operator embedding data and the network hyperparameters to obtain fractional-order neural network data.

[0171] In an embodiment of the present invention, actual operating data of a lithium battery under different operating conditions, such as charge and discharge current, voltage, temperature, etc., are collected. According to the fractional state space expression, the collected actual operating condition data is used to generate a data set for training and testing a fractional neural network. The data set usually includes input data, such as the charge and discharge current, temperature, etc. of the battery, and corresponding output data, such as the terminal voltage, SOC, etc. of the battery. According to the characteristics of the fractional neural network data set, such as data scale, input and output dimensions, etc., a suitable neural network structure is selected, such as a multilayer perceptron (MLP), a recurrent neural network (RNN), etc. The structural parameters such as the number of layers of the neural network and the number of neurons in each layer are determined to obtain the neural network structure data. According to the neural network structure, how to embed fractional operators, such as fractional calculus operators, etc., in the neural network is analyzed. The embedding position of the fractional operator is determined, such as embedding in the activation function of the neuron, or embedding in the connection weight of the network. Select a suitable fractional operator type, such as Caputo fractional derivative, Greenwald-Letnikov fractional derivative, etc., and determine the order of the fractional operator. Finally, the fractional-order operator embedding data is obtained, such as the type, order, and embedding position of the fractional-order operator. According to the neural network structure data and the fractional-order operator embedding data, the hyperparameters of the neural network are set, such as the learning rate, batch size, and regularization coefficient. The selection of these hyperparameters will affect the training speed and generalization ability of the neural network. According to the neural network structure data, the fractional-order operator embedding data, and the network hyperparameters, a fractional-order neural network model is constructed. During the construction process, the fractional-order operator is embedded into the specified position of the neural network, such as using a fractional-order activation function or a fractional-order weight, and finally the fractional-order neural network data is obtained, such as the initial values ​​of the network's connection weights, bias terms, and other parameters.

[0172] Preferably, step S43 includes the following steps:

[0173] Step S431: performing operator embedding position selection of a neuron activation function on the neural network structure data to obtain operator embedding position data;

[0174] Step S432: selecting a fractional-order derivative operator according to the operator embedding position data to obtain a fractional-order derivative operator;

[0175] Step S433: determining the operator order of the fractional-order derivative operator to obtain the fractional-order operator order;

[0176] Step S434: performing discretization operator calculation according to the fractional-order operator order and the fractional-order operator to obtain discretization operator calculation method data;

[0177] Step S435: Perform fractional-order operator embedding on the neural network structure data according to the discretization operator calculation method data to obtain fractional-order operator embedding data.

[0178] In an embodiment of the present invention, the neural network structure data, such as the neuron type, the number of network layers, etc., is analyzed to determine in which neurons the activation function of which the fractional-order operator is embedded. For example, the fractional-order operator can be selected to be embedded in the activation function of the hidden layer neurons or the output layer neurons. Finally, the operator embedding position data is obtained, such as "embedded in the activation function of all neurons in the second layer of the network". Based on the operator embedding position, the appropriate fractional-order derivative operator type is selected. It is necessary to select a suitable operator according to the specific application scenario and the characteristics of the fractional-order neural network model. For example, the Caputo fractional-order derivative is suitable for the case where the initial conditions are known, while the Greenwald-Letnikov fractional-order derivative is suitable for discrete time systems. Finally, the fractional-order derivative operator is obtained, such as "select Greenwald-Letnikov fractional-order derivative". Determine the order of the fractional-order derivative operator. The order of the fractional-order operator determines the model's ability to remember historical information, and the appropriate order needs to be selected according to the specific problem and data characteristics. For example, optimization algorithms such as grid search and genetic algorithms can be used to determine the optimal order. Finally, the order of the fractional operator is obtained, such as "determine that the order of the fractional derivative is 0.5". Since neural network training is usually performed on a digital computer, the fractional derivative operator and the fractional operator order need to be discretized to obtain a discretized formula that can be numerically calculated on a computer. For example, the fractional derivative operator can be discretized using a difference method, a convolution method, etc. Finally, the discretized operator calculation method data is obtained, such as "the fractional derivative is discretized using the backward difference method to obtain a specific calculation formula". According to the discretized operator calculation method data, the fractional operator is embedded into the neural network structure data. For example, the discretized fractional derivative operator is embedded into the expression of the neuron activation function, or it is used to construct a new fractional neural network layer. Finally, the fractional operator embedding data is obtained, such as "the discretized Greenwald-Letnikov fractional derivative is embedded into the sigmoid activation function of all neurons in the second layer of the network to obtain a new activation function expression".

[0179] Preferably, step S5 comprises the following steps:

[0180] Step S51: outputting expression data using a fractional-order state space expression according to actual operating condition data of the lithium battery to obtain fractional-order neural network training data and fractional-order neural network test data;

[0181] Step S52: using the fractional-order neural network training data to perform fractional-order network parameter training on the fractional-order neural network data to obtain an initial fractional-order neural network model;

[0182] Step S53: using the fractional-order neural network test data to calculate the model performance index of the initial fractional-order neural network model to obtain model performance index data;

[0183] Step S54: performing performance indicator verification analysis on the model performance indicator data to obtain performance indicator verification data; optimizing the model performance indicator of the initial fractional-order neural network model according to the performance indicator verification data to obtain a fractional-order neural network model;

[0184] Step S55: deploying the fractional-order neural network model onto the hardware platform of the lithium battery management system to implement lithium battery management operations.

[0185] In an embodiment of the present invention, the actual operating condition data of the lithium battery is input into the fractional state space expression, and the corresponding output data, such as the terminal voltage and SOC of the battery, are calculated. The input data and the output data are divided into a training set and a test set for subsequent neural network training and testing, and the fractional neural network training data and the test data are obtained. The initial fractional neural network model is trained using the fractional neural network training data. During the training process, the connection weights and bias terms of the neural network are updated using optimization algorithms such as the back propagation algorithm, so that the error between the predicted output and the actual output of the model is minimized. Finally, the trained initial fractional neural network model is obtained. The initial fractional neural network model is tested using the fractional neural network test data. The performance indicators of the model on the test set, such as the mean square error (MSE), the mean absolute error (MAE), the coefficient of determination (R-squared), etc., are calculated to evaluate the prediction accuracy and generalization ability of the model. The model performance indicator data is analyzed, such as observing the error curve of the model on the training set and the test set, to determine whether the model has problems such as overfitting or underfitting. According to the results of the performance indicator verification analysis, the initial fractional-order neural network model is optimized, such as adjusting the network structure, hyperparameters, regularization methods, etc., to improve the prediction accuracy and generalization ability of the model. Finally, the optimized fractional-order neural network model is obtained. The optimized fractional-order neural network model is deployed on the hardware platform of the lithium battery management system, such as an embedded system. The deployed model can be used to monitor the battery status in real time, predict the remaining battery life, optimize the battery charging strategy, etc., so as to realize the lithium battery management operation.

[0186] Preferably, step S52 includes the following steps:

[0187] Step S521: using a preset damage function to perform fractional-order algorithm optimization on the fractional-order neural network data to obtain fractional-order neural network optimization data;

[0188] Step S522: using the fractional-order neural network training data to train the network parameters of the fractional-order neural network optimization data and perform overfitting suppression to obtain a fractional-order neural network training network;

[0189] Step S523: performing network performance evaluation on the fractional-order neural training network to obtain network performance evaluation data;

[0190] Step S524: Generate a fractional-order neural network model based on the network performance evaluation data to obtain an initial fractional-order neural network model.

[0191] In an embodiment of the present invention, a preset damage function, such as mean square error (MSE), cross entropy, etc., is selected to evaluate the prediction error of the fractional neural network model. The fractional neural network data is optimized using a fractional algorithm, such as the Adam algorithm, the RMSprop algorithm, etc., such as updating the connection weights and bias terms of the network to minimize the preset damage function. Finally, the optimized fractional neural network data, such as the updated network parameters, are obtained. The network parameters of the fractional neural network data are trained using the fractional neural network training data. During the training process, overfitting suppression measures are taken, such as regularization technology (L1, L2 regularization), Dropout technology, Early Stopping, etc., to prevent the model from overfitting on the training set and improve the generalization ability of the model. Finally, a trained fractional neural network training network is obtained. The performance of the fractional neural network training network is evaluated using the fractional neural network test data. For example, the performance indicators such as the mean square error (MSE), mean absolute error (MAE), and coefficient of determination (R-squared) of the model on the test set are calculated to evaluate the prediction accuracy and generalization ability of the model and obtain network performance evaluation data. According to the network performance evaluation data, determine whether the model meets the preset performance requirements. If the model performance meets the requirements, save the fractional-order neural network training network as the initial fractional-order neural network model; otherwise, return to step S521, adjust the parameters such as the fractional-order algorithm or the damage function, and re-optimize and train until the model performance meets the requirements.

[0192] Therefore, the embodiments should be regarded as illustrative and non-restrictive from all points, and the scope of the present invention is limited by the appended claims rather than the above description, and it is therefore intended that all changes falling within the meaning and range of equivalent elements of the application documents are included in the present invention.

[0193] The above description is only a specific embodiment of the present invention, so that those skilled in the art can understand or implement the present invention. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but should conform to the widest scope consistent with the principles and novel features invented herein.

Claims

1. A lithium battery modeling method based on fractional-order neural network, characterized in that: The following steps are involved: Step S1: Perform electrochemical impedance spectroscopy on the lithium battery to obtain pre-processed impedance data; obtain lithium battery structure and material data; Perform dynamic analysis on the SEI film structure based on the pre-processed impedance data to obtain the dynamic data of the SEI film growth process; construct a fractional impedance model based on the dynamic data of the SEI film growth process to obtain the parameters of the fractional impedance model; Step S2: Perform parameter physical meaning analysis on the parameters of the fractional-order impedance model to obtain parameter physical meaning data; Perform micro-scale simulation according to lithium battery structure and material data to obtain micro-scale simulation data; generate a parameter mapping relationship table for the micro-scale simulation data and parameter physical meaning data to obtain a parameter mapping relationship table; generate an equivalent circuit model according to the parameter mapping relationship table to obtain a fractional-order equivalent circuit model; Step S3: Establishing a fractional-order state space expression according to the fractional-order equivalent circuit model to obtain a fractional-order state space expression; Step S4: Selecting a network structure according to the fractional-order state space expression to obtain neural network structure data; Performing fractional-order operator embedding analysis according to the neural network structure data to obtain fractional-order operator embedding data; performing fractional-order neural network generation according to the neural network structure data and the fractional-order operator embedding data to obtain fractional-order neural network data; Step S5: training the fractional-order neural network parameters on the fractional-order neural network data to obtain an initial fractional-order neural network model; optimizing the model performance indicators of the initial fractional-order neural network model to obtain a fractional-order neural network model; and deploying the fractional-order neural network model on the hardware platform of the lithium battery management system to implement lithium battery management operations.

2. The lithium battery modeling method based on fractional order neural network according to claim 1 is characterized in that: Step S1 includes the following steps: Step S11: performing electrochemical impedance spectroscopy test on the lithium battery to obtain raw impedance data; performing impedance data preprocessing on the raw impedance data to obtain preprocessed impedance data; Step S12: performing electrochemical characteristic analysis on the pre-processed impedance data to obtain electrochemical characteristic data; Step S13: obtaining lithium battery structure and material data; performing a dynamic analysis of the SEI film structure according to the lithium battery structure and material data and electrochemical characteristic data to obtain dynamic data of the SEI film growth process; Step S14: performing fractional capacitance analysis on the dynamic data of the SEI film growth process to obtain fractional capacitance data; Step S15: performing fractional impedance modeling according to the dynamic data of the SEI film growth process and the fractional capacitance data to obtain a fractional impedance model; Step S16: Utilize the preprocessed impedance data to perform model verification on the fractional-order impedance model to obtain the fractional-order impedance model parameters.

3. The lithium battery modeling method based on fractional order neural network according to claim 2 is characterized in that: Step S13 includes the following steps: Step S131: extracting SEI film structure data according to the lithium battery structure and material data and the pre-processed impedance data to obtain SEI film structure data; Step S132: performing electrochemical performance correlation analysis on the SEI film structure data according to the electrochemical characteristic data to obtain structural parameters affecting the electrochemical performance; Step S133: performing SEI film structure correlation according to the electrochemical performance-influencing structural parameters and the electrochemical characteristic data to obtain SEI film structure correlation data; Step S134: Perform a dynamic analysis of the SEI film growth process based on the SEI film structure correlation data to obtain the SEI film growth process dynamic data.

4. The lithium battery modeling method based on fractional order neural network according to claim 1 is characterized in that: Step S2 includes the following steps: Step S21: performing characteristic parameter analysis on the fractional-order impedance model parameters to obtain key characteristic parameters; performing parameter physical meaning analysis on the key characteristic parameters to obtain parameter physical meaning data; Step S22: performing micro-scale simulation according to the lithium battery structure and material data to obtain micro-scale simulation data; Step S23: performing parameter correlation analysis on the micro-scale simulation data and the parameter physical meaning data to obtain parameter correlation data; Step S24: deriving a mapping relationship for the parameter association data to obtain mapping relationship derived data; generating a parameter mapping relationship table according to the mapping relationship derived data to obtain a parameter mapping relationship table; Step S25: performing component model corresponding processing according to the parameter mapping relationship table to obtain component model corresponding data; performing initial circuit topology analysis according to the component model corresponding data to obtain initial circuit topology data; Step S26: using the fractional-order impedance model parameters to assign circuit parameters to the initial circuit topology data to obtain a component circuit model; Step S27: simplifying and optimizing the component circuit model and generating an equivalent circuit model to obtain a fractional-order equivalent circuit model.

5. The lithium battery modeling method based on fractional order neural network according to claim 4 is characterized in that: Step S22 includes the following steps: Step S221: constructing a molecular dynamics model according to the lithium battery structure and material data to obtain a molecular dynamics model; Step S222: using a molecular dynamics model to simulate the operation of battery materials and obtain simulation operation result data; visualizing the lithium ion atomic trajectory of the simulation operation result data and obtain atomic trajectory visualization data; Step S223: performing lithium ion average displacement analysis according to the atomic trajectory visualization data to obtain lithium ion average displacement data; Step S224: extracting the lithium ion diffusion coefficient according to the lithium ion average displacement data to obtain the lithium ion diffusion coefficient; Step S225: performing micro-scale analysis of simulation parameters on the lithium ion diffusion coefficient to obtain micro-scale simulation data.

6. The lithium battery modeling method based on fractional order neural network according to claim 1, characterized in that: Step S3 includes the following steps: Step S31: Establishing circuit equations using Kirchhoff's voltage law according to the fractional-order equivalent circuit model to obtain a circuit equation group; Step S32: constructing a fractional-order differential equation for the fractional-order component data in the circuit equation group to obtain a fractional-order differential equation; Step S33: selecting state variables according to the fractional-order differential equation to obtain state variable data; constructing a state equation according to the state variable data to obtain a fractional-order state equation; Step S34: constructing an output equation according to the fractional-order state equation to obtain the output equation; constructing a fractional-order state space expression for the output equation and the fractional-order state equation to obtain the fractional-order state space expression.

7. The lithium battery modeling method based on fractional order neural network according to claim 1 is characterized in that: Step S4 includes the following steps: Step S41: Acquire actual working condition data of the lithium battery; construct a fractional-order neural network data set according to the fractional-order state space expression and the actual working condition data of the lithium battery to obtain a fractional-order neural network data set; Step S42: selecting a network structure according to the fractional-order neural network data set to obtain neural network structure data; Step S43: performing fractional-order operator embedding analysis according to the neural network structure data to obtain fractional-order operator embedding data; Step S44: setting hyperparameters for the neural network structure data to obtain network hyperparameters; Step S45: Generate a fractional-order neural network according to the neural network structure data, the fractional-order operator embedding data and the network hyperparameters to obtain fractional-order neural network data.

8. The lithium battery modeling method based on fractional order neural network according to claim 7 is characterized in that: Step S43 includes the following steps: Step S431: performing operator embedding position selection of a neuron activation function on the neural network structure data to obtain operator embedding position data; Step S432: selecting a fractional-order derivative operator according to the operator embedding position data to obtain a fractional-order derivative operator; Step S433: determining the operator order of the fractional-order derivative operator to obtain the fractional-order operator order; Step S434: performing discretization operator calculation according to the fractional-order operator order and the fractional-order operator to obtain discretization operator calculation method data; Step S435: Perform fractional-order operator embedding on the neural network structure data according to the discretization operator calculation method data to obtain fractional-order operator embedding data.

9. The lithium battery modeling method based on fractional order neural network according to claim 1, characterized in that: Step S5 includes the following steps: Step S51: outputting expression data using a fractional-order state space expression according to actual operating condition data of the lithium battery to obtain fractional-order neural network training data and fractional-order neural network test data; Step S52: using the fractional-order neural network training data to perform fractional-order network parameter training on the fractional-order neural network data to obtain an initial fractional-order neural network model; Step S53: using the fractional-order neural network test data to calculate the model performance index of the initial fractional-order neural network model to obtain model performance index data; Step S54: performing performance indicator verification analysis on the model performance indicator data to obtain performance indicator verification data; optimizing the model performance indicator of the initial fractional-order neural network model according to the performance indicator verification data to obtain a fractional-order neural network model; Step S55: deploying the fractional-order neural network model onto the hardware platform of the lithium battery management system to implement lithium battery management operations.

10. The lithium battery modeling method based on fractional order neural network according to claim 1, characterized in that: Step S52 includes the following steps: Step S521: using a preset damage function to perform fractional-order algorithm optimization on the fractional-order neural network data to obtain fractional-order neural network optimization data; Step S522: using the fractional-order neural network training data to train the network parameters of the fractional-order neural network optimization data and perform overfitting suppression to obtain a fractional-order neural network training network; Step S523: performing network performance evaluation on the fractional-order neural training network to obtain network performance evaluation data; Step S524: Generate a fractional-order neural network model based on the network performance evaluation data to obtain an initial fractional-order neural network model.

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