CN115470742B - Lithium ion battery modeling method, system, equipment and storage medium - Google Patents

Lithium ion battery modeling method, system, equipment and storage medium Download PDF

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CN115470742B
CN115470742B CN202211342111.1A CN202211342111A CN115470742B CN 115470742 B CN115470742 B CN 115470742B CN 202211342111 A CN202211342111 A CN 202211342111A CN 115470742 B CN115470742 B CN 115470742B
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王冰川
戴聪玲
王勇
吉振东
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Central South University
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Abstract

The invention discloses a lithium ion battery modeling method, a system, equipment and a storage medium, wherein the method obtains a partial differential equation of a lithium ion battery according to a charge conservation law and an ohm law, and defines boundary conditions and initial conditions according to the partial differential equation; constructing a network prediction model based on a physical information neural network; constructing a first loss function, and performing iterative update on parameters of the network prediction model by adopting a gradient descent algorithm to complete first training of the network prediction model; constructing a second loss function, and performing iterative updating on parameters of the network prediction model by adopting a gradient descent algorithm to complete second training of the network prediction model; constructing a third loss function, and performing iterative updating on parameters of the network prediction model by adopting a gradient descent algorithm to finish third training of the network prediction model; and predicting parameters of the lithium ion battery through the network prediction model after three times of training. The invention can improve the prediction precision of the network prediction model.

Description

Lithium ion battery modeling method, system, equipment and storage medium
Technical Field
The invention relates to the technical field of battery modeling, in particular to a lithium ion battery modeling method, a lithium ion battery modeling system, lithium ion battery modeling equipment and a storage medium.
Background
The lithium ion battery becomes one of the first choices of the energy storage element of the new energy automobile due to a series of outstanding characteristics of high energy density, high voltage, low self-discharge rate, good stability and the like. In order to better understand the characteristics of the battery and to make reasonable use strategies, modeling of lithium ion batteries has become an important research direction. The performance of the battery electrodes is affected by the aspect ratio, the placement of the current collector tabs, and the total amount of current flowing through the electrodes. If one electrode is not optimally designed, the potential and current density will be non-uniform, as will the utilization of the active material on the electrode. This effect becomes more pronounced as the size of the electrode becomes larger, which may lead to accelerated degradation of the electrode due to excessive local utilization of active material on the electrode. Therefore, the optimal design of the electrode is very meaningful for the production of large-scale lithium ion batteries, and plays an important role in the modeling research of the lithium ion batteries.
In the existing battery modeling technology, a modeling method based on traditional numerical calculation, such as a finite element method or a finite difference method, solves a partial differential equation, and a large amount of computing resources and computing time are consumed. In the machine learning modeling method based on data driving, the electrode reaction of the battery is regarded as a black box model, only the relation between the input and the output of the model is concerned, and the training of the model is completed by updating network parameters by using input and output data obtained by actual testing. Although this method no longer needs complete equation information and a large amount of calculation, its accuracy depends on the precision and scale of the sampled data, and the cost of obtaining enough high-precision test data is also very large.
Disclosure of Invention
The present invention is directed to solving at least one of the problems of the prior art. Therefore, the invention provides a lithium ion battery modeling method, system, equipment and storage medium, which can improve the prediction precision of a network prediction model and reduce the calculation amount of the network prediction model.
In a first aspect, an embodiment of the present invention provides a lithium ion battery modeling method, where the lithium ion battery modeling method includes:
according to the law of conservation of charge and the ohm law, obtaining a partial differential equation of the lithium ion battery, and defining a boundary condition and an initial condition according to the partial differential equation;
constructing a network prediction model based on a physical information neural network, wherein the network prediction model comprises a positive electrode network, a DOD network, a flux network and a negative electrode network;
constructing a first loss function of the anode network, the DOD network, the flux network and the cathode network according to data driving, and iteratively updating parameters of the network prediction model by adopting a gradient descent algorithm until a preset first maximum iteration frequency is reached or the first loss function is stably converged, thereby completing first training of the network prediction model;
constructing second loss functions of the anode network, the DOD network, the flux network and the cathode network according to the data drive, the boundary condition and the initial condition, and iteratively updating parameters of the network prediction model by adopting a gradient descent algorithm until a preset second maximum iteration time is reached or the second loss functions are stably converged, thereby completing second training of the network prediction model;
constructing a third loss function of the positive pole network, the DOD network, the flux network and the negative pole network according to the data drive, the partial differential equation, the boundary condition and the initial condition, and constructing a total loss function according to the third loss function of the positive pole network, the DOD network, the flux network and the negative pole network; iteratively updating the parameters of the network prediction model by adopting a gradient descent algorithm until a preset third maximum iteration number is reached or the total loss function is stably converged, and completing third training of the network prediction model;
and predicting the parameters of the lithium ion battery through the network prediction model after three times of training.
Compared with the prior art, the first aspect of the invention has the following beneficial effects:
in order to improve the prediction accuracy of the network prediction model and reduce the calculated amount of the network prediction model, the partial differential equation of the lithium ion battery is obtained according to the charge conservation law and the ohm law, and the boundary condition and the initial condition are defined according to the partial differential equation; constructing a network prediction model based on a physical information neural network, wherein the network prediction model comprises a positive electrode network, a DOD network, a flux network and a negative electrode network; constructing a first loss function of the anode network, the DOD network, the flux network and the cathode network according to data driving, and iteratively updating parameters of the network prediction model by adopting a gradient descent algorithm until a preset first maximum iteration number is reached or the first loss function is stably converged, thereby completing first training of the network prediction model; constructing second loss functions of the positive electrode network, the DOD network, the flux network and the negative electrode network according to the data drive, the boundary condition and the initial condition, and iteratively updating parameters of the network prediction model by adopting a gradient descent algorithm until a preset second maximum iteration number or second loss function is stably converged, thereby completing second training of the network prediction model; constructing a third loss function of the anode network, the DOD network, the flux network and the cathode network according to the data drive, the partial differential equation, the boundary condition and the initial condition, and constructing a total loss function according to the third loss function of the anode network, the DOD network, the flux network and the cathode network; iteratively updating the parameters of the network prediction model by adopting a gradient descent algorithm until a preset third maximum iteration number or a total loss function is stably converged, and completing third training of the network prediction model; and predicting parameters of the lithium ion battery through the network prediction model after three times of training. The method comprises the steps that a network prediction model is trained for the first time, and first loss functions of a positive pole network, a DOD network, a flux network and a negative pole network are constructed through data driving; the network prediction model is trained for the second time to construct a second loss function of the anode network, the DOD network, the flux network and the cathode network according to the data drive, the boundary condition and the initial condition; the third training of the network prediction model is carried out according to data drive, partial differential equations, boundary conditions and initial conditions to construct a third loss function of the positive electrode network, the DOD network, the flux network and the negative electrode network, and a total loss function is constructed according to the third loss function of the positive electrode network DOD network, the flux network and the negative electrode network; the prediction accuracy of the network prediction model is improved through three times of training. According to the method, the network prediction model is constructed based on the physical information neural network, the physical information is used, the data use amount is greatly reduced, and the training of the network prediction model can be completed only by a small amount of data, so that the calculation amount of the network prediction model is reduced.
According to some embodiments of the invention, the obtaining partial differential equations for lithium ion batteries according to the law of conservation of charge and ohm's law comprises:
according to the charge conservation law and the ohm law, the partial differential equation of the positive electrode potential and the negative electrode potential of the lithium ion battery is obtained by adopting a Poisson equation:
Figure DEST_PATH_IMAGE001
wherein the content of the first and second substances,
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the expression of the laplacian operator is shown,
Figure DEST_PATH_IMAGE003
represents the potential of the positive electrode of the lithium ion battery,
Figure 42005DEST_PATH_IMAGE004
represents the negative electrode potential of the lithium ion battery,
Figure DEST_PATH_IMAGE005
represents the resistance of the positive electrode of the lithium ion battery,
Figure 270861DEST_PATH_IMAGE006
represents the resistance of the negative electrode of the lithium ion battery,
Figure DEST_PATH_IMAGE007
represents the spatial domain of the positive electrode of the lithium ion battery,
Figure 754932DEST_PATH_IMAGE008
represents the spatial domain of the negative electrode of the lithium ion battery,
Figure DEST_PATH_IMAGE009
represents the current density between the positive electrode and the negative electrode of the lithium ion battery
Figure 614304DEST_PATH_IMAGE009
Is expressed as
Figure 816615DEST_PATH_IMAGE010
Y and U represent fitting parameters;
by the said
Figure 458949DEST_PATH_IMAGE009
Obtaining a partial differential equation of the current density;
by integral term
Figure DEST_PATH_IMAGE011
And converting the auxiliary depth of discharge to obtain a partial differential equation of the depth of discharge, wherein the expression for converting is as follows:
Figure 266368DEST_PATH_IMAGE012
where D represents depth of discharge, t represents time,
Figure DEST_PATH_IMAGE013
representing the theoretical capacity of the electrode per unit area.
According to some embodiments of the invention, the defining boundary conditions and initial conditions according to the partial differential equation comprises:
according to the partial differential equation of the anode potential, defining the boundary condition of the anode potential:
Figure 296641DEST_PATH_IMAGE014
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE015
representing the gradient in the normal direction outside the boundary,
Figure 455090DEST_PATH_IMAGE016
showing the regions of the positive electrode other than the tabs,
Figure DEST_PATH_IMAGE017
a tab of the positive electrode is shown,
Figure 25748DEST_PATH_IMAGE018
which is representative of the current flowing through it,
Figure DEST_PATH_IMAGE019
represents a length;
defining initial conditions for the anode potential:
Figure 687674DEST_PATH_IMAGE020
wherein, the first and the second end of the pipe are connected with each other,
Figure DEST_PATH_IMAGE021
which represents the initial value of the potential of the positive electrode,
Figure 560952DEST_PATH_IMAGE022
represents the above
Figure 737855DEST_PATH_IMAGE009
An initial value of (1);
defining the boundary condition of the cathode potential according to the partial differential equation of the cathode potential:
Figure DEST_PATH_IMAGE023
wherein the content of the first and second substances,
Figure 784309DEST_PATH_IMAGE024
showing the negative electrode region other than the tab,
Figure DEST_PATH_IMAGE025
a tab representing a negative electrode;
defining initial conditions for the cathode potential:
Figure 504003DEST_PATH_IMAGE026
Figure DEST_PATH_IMAGE027
represents the above
Figure 616359DEST_PATH_IMAGE004
Is started.
According to some embodiments of the invention, a loss function of the network prediction model is constructed, the loss function comprising a data-driven part and a physical information part, wherein:
constructing loss functions for data-driven parts
Figure 280558DEST_PATH_IMAGE028
：
Figure DEST_PATH_IMAGE029
Wherein the content of the first and second substances,
Figure 68386DEST_PATH_IMAGE030
representing the results of the prediction by the network prediction model,
Figure DEST_PATH_IMAGE031
representing spatial position, i representing the current of the lithium ion battery, t representing time,
Figure 970483DEST_PATH_IMAGE032
which is indicative of the measured data and,
Figure DEST_PATH_IMAGE033
indicating the amount of said measured data,
Figure 513460DEST_PATH_IMAGE034
representing a mean square error between a result of the network prediction model prediction and the measured data;
constructing a loss function of the physical information part, the loss function of the physical information part comprising a loss function of a partial differential equation, a loss function of an initial condition, and a loss function of a boundary condition, wherein:
constructing a loss function of the partial differential equation
Figure DEST_PATH_IMAGE035
：
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Wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE037
the equation of control is expressed in terms of,
Figure 318790DEST_PATH_IMAGE038
which represents the number of sample points,
Figure DEST_PATH_IMAGE039
to represent
Figure 809815DEST_PATH_IMAGE040
Substituting the result predicted by the network prediction model into the mean square error of the residual error generated in the control equation at each sampling point;
constructing a loss function for the initial conditions
Figure DEST_PATH_IMAGE041
：
Figure 523693DEST_PATH_IMAGE042
Wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE043
representing the result of the initial moment predicted by the network prediction model,
Figure 303430DEST_PATH_IMAGE044
a value representing a known initial time instant,
Figure DEST_PATH_IMAGE045
representing the number of initial sampling points;
constructing a loss function for the boundary condition
Figure 495377DEST_PATH_IMAGE046
：
Figure DEST_PATH_IMAGE047
Wherein, the first and the second end of the pipe are connected with each other,
Figure 903224DEST_PATH_IMAGE048
expressing the result predicted by the network prediction model is brought into a boundary condition equation and calculated
Figure DEST_PATH_IMAGE049
The sum of the residuals of the boundary condition equations at the boundary sample points;
constructing a loss function of the network prediction model according to the loss function of the data driving part and the loss function of the physical information part:
Figure 53583DEST_PATH_IMAGE050
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE051
representing a set of weights and bias parameters in the network,
Figure 117354DEST_PATH_IMAGE052
representing the total loss function value of the currently trained network prediction model,
Figure DEST_PATH_IMAGE053
a weight of a loss function representing the data portion,
Figure 50675DEST_PATH_IMAGE054
weights representing loss functions of the partial differential equations,
Figure DEST_PATH_IMAGE055
a weight of a loss function representing the initial condition,
Figure 250712DEST_PATH_IMAGE056
a weight of a loss function representing the boundary condition.
According to some embodiments of the invention, the constructing a first loss function of the positive network, the DOD network, the flux network, and the negative network comprises:
constructing a first loss function of the positive network
Figure DEST_PATH_IMAGE057
：
Figure 571972DEST_PATH_IMAGE058
Wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE059
representing a loss function of a data driven portion of the positive network,
Figure 185356DEST_PATH_IMAGE060
represents the result of the prediction of the positive network,
Figure DEST_PATH_IMAGE061
represents measured data corresponding to the positive network,
Figure 719105DEST_PATH_IMAGE062
representing a mean square error between a result of the positive network prediction and measured data corresponding to the positive network;
constructing a first loss function for the DOD network
Figure DEST_PATH_IMAGE063
：
Figure 976911DEST_PATH_IMAGE064
Wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE065
a loss function representing a data-driven portion of the DOD network,
Figure 463213DEST_PATH_IMAGE066
representing the result of the DOD network prediction,
Figure DEST_PATH_IMAGE067
representing measured data corresponding to the DOD network,
Figure 235997DEST_PATH_IMAGE068
representing a mean square error between a result of the DOD network prediction and measured data corresponding to the DOD network;
constructing a first loss function of the flux network
Figure DEST_PATH_IMAGE069
：
Figure 635755DEST_PATH_IMAGE070
Wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE071
a loss function representing a data driven portion of the flux network,
Figure 75963DEST_PATH_IMAGE072
represents the result of the flux network prediction,
Figure DEST_PATH_IMAGE073
representing measured data corresponding to the flux network,
Figure 739026DEST_PATH_IMAGE074
representing a mean square error between a result of the flux network prediction and measured data corresponding to the flux network;
constructing a first loss function of the negative network
Figure DEST_PATH_IMAGE075
：
Figure 530264DEST_PATH_IMAGE076
Wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE077
a loss function representing a data driven portion of the negative network,
Figure 405816DEST_PATH_IMAGE078
representing the result of the negative network prediction,
Figure DEST_PATH_IMAGE079
representing measured data corresponding to the negative pole network,
Figure 638215DEST_PATH_IMAGE080
and the mean square error between the result of the negative pole network prediction and the measured data corresponding to the negative pole network is represented.
According to some embodiments of the invention, the constructing a second loss function for the positive network, the DOD network, the flux network, and the negative network comprises:
constructing a second loss function of the positive network
Figure DEST_PATH_IMAGE081
：
Figure 941020DEST_PATH_IMAGE082
Wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE083
representing a loss function of a data driven portion of the positive network,
Figure 219554DEST_PATH_IMAGE084
weights representing loss functions of a data driven portion of the positive network,
Figure DEST_PATH_IMAGE085
a loss function representing an initial condition of the positive network,
Figure 164377DEST_PATH_IMAGE086
a weight of a loss function representing an initial condition of the positive network,
Figure DEST_PATH_IMAGE087
a loss function representing a boundary condition of the positive network,
Figure 579178DEST_PATH_IMAGE088
a weight of a loss function representing a boundary condition of the positive network;
constructing a second loss function for the DOD network
Figure DEST_PATH_IMAGE089
：
Figure 380780DEST_PATH_IMAGE090
Wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE091
a loss function representing a data-driven portion of the DOD network,
Figure 881032DEST_PATH_IMAGE092
weights representing a loss function of a data-driven portion of the DOD network,
Figure DEST_PATH_IMAGE093
a loss function representing an initial condition of the DOD network,
Figure 98387DEST_PATH_IMAGE094
a weight of a loss function representing an initial condition of the DOD network,
Figure DEST_PATH_IMAGE095
a loss function representing a boundary condition of the DOD network,
Figure 633273DEST_PATH_IMAGE096
a weight of a loss function representing a boundary condition of the DOD network;
constructing a second loss function of the flux network
Figure DEST_PATH_IMAGE097
：
Figure 215564DEST_PATH_IMAGE098
Wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE099
a loss function representing a data driven portion of the flux network,
Figure 937532DEST_PATH_IMAGE100
weights representing loss functions of data-driven portions of the flux networkThe weight of the steel is heavy,
Figure DEST_PATH_IMAGE101
a loss function representing an initial condition of the flux network,
Figure 230017DEST_PATH_IMAGE102
a weight of a loss function representing an initial condition of the flux network,
Figure DEST_PATH_IMAGE103
a loss function representing a boundary condition of the flux network,
Figure 212885DEST_PATH_IMAGE104
a weight of a loss function representing a boundary condition of the flux network;
constructing a second loss function for the negative network
Figure DEST_PATH_IMAGE105
：
Figure 231657DEST_PATH_IMAGE106
Wherein, the first and the second end of the pipe are connected with each other,
Figure DEST_PATH_IMAGE107
a loss function representing a data driven portion of the negative network,
Figure 440921DEST_PATH_IMAGE108
weights representing loss functions of a data driven portion of the negative network,
Figure DEST_PATH_IMAGE109
a loss function representing an initial condition of the negative network,
Figure 62395DEST_PATH_IMAGE110
a weight of a loss function representing an initial condition of the negative network,
Figure DEST_PATH_IMAGE111
a loss function representing a boundary condition of the negative network,
Figure 40716DEST_PATH_IMAGE112
a weight of a loss function representing a boundary condition of the negative network.
According to some embodiments of the invention, the constructing a third loss function for the positive network, the DOD network, the flux network, and the negative network comprises:
constructing a third loss function of the positive network
Figure DEST_PATH_IMAGE113
：
Figure 558285DEST_PATH_IMAGE114
Wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE115
a loss function representing a partial differential equation of the positive network,
Figure 192528DEST_PATH_IMAGE116
weights representing loss functions of partial differential equations of the positive network;
constructing a third loss function for the DOD network
Figure DEST_PATH_IMAGE117
：
Figure 555377DEST_PATH_IMAGE118
Wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE119
a loss function representing a partial differential equation of the DOD network,
Figure 653783DEST_PATH_IMAGE120
weights representing loss functions of partial differential equations of the DOD network;
constructing a third loss function of the flux network
Figure DEST_PATH_IMAGE121
：
Figure 138991DEST_PATH_IMAGE122
Wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE123
a loss function representing a partial differential equation of the flux network,
Figure 588426DEST_PATH_IMAGE124
weights representing loss functions of partial differential equations of the flux network;
constructing a third loss function for the negative network
Figure DEST_PATH_IMAGE125
：
Figure 489386DEST_PATH_IMAGE126
Wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE127
a loss function representing a partial differential equation of the negative network,
Figure 707878DEST_PATH_IMAGE128
weights representing loss functions of partial differential equations of the negative network.
In a second aspect, an embodiment of the present invention further provides a lithium ion battery modeling system, where the lithium ion battery modeling system includes:
the equation acquisition unit is used for acquiring a partial differential equation of the lithium ion battery according to the charge conservation law and the ohm law, and defining boundary conditions and initial conditions according to the partial differential equation;
the model building unit is used for building a network prediction model based on the physical information neural network, and the network prediction model comprises a positive electrode network, a DOD network, a flux network and a negative electrode network;
the first training unit is used for constructing first loss functions of the positive electrode network, the DOD network, the flux network and the negative electrode network according to data driving, iteratively updating parameters of the network prediction model by adopting a gradient descent algorithm until a preset first maximum iteration time is reached or the first loss functions are stably converged, and completing first training of the network prediction model;
the second training unit is used for constructing second loss functions of the anode network, the DOD network, the flux network and the cathode network according to the data drive, the boundary condition and the initial condition, iteratively updating parameters of the network prediction model by adopting a gradient descent algorithm until a preset second maximum iteration time is reached or the second loss functions are stably converged, and completing second training of the network prediction model;
a third training unit, configured to construct a third loss function of the positive electrode network, the DOD network, the flux network, and the negative electrode network according to the data drive, the partial differential equation, the boundary condition, and the initial condition, and construct a total loss function according to the third loss function of the positive electrode network, the DOD network, the flux network, and the negative electrode network; iteratively updating the parameters of the network prediction model by adopting a gradient descent algorithm until a preset third maximum iteration number is reached or the total loss function is stably converged, and completing third training of the network prediction model;
and the parameter prediction unit is used for predicting the parameters of the lithium ion battery through the network prediction model which completes three times of training.
In a third aspect, an embodiment of the present invention further provides a lithium ion battery modeling apparatus, including at least one control processor and a memory, where the memory is used for being connected to the at least one control processor in a communication manner; the memory stores instructions executable by the at least one control processor to enable the at least one control processor to perform a lithium ion battery modeling method as described above.
In a fourth aspect, the embodiment of the present invention further provides a computer-readable storage medium, where computer-executable instructions are stored, and the computer-executable instructions are configured to cause a computer to execute a lithium ion battery modeling method as described above.
It is to be understood that the advantageous effects of the second aspect to the fourth aspect in comparison with the related art are the same as the advantageous effects of the first aspect in comparison with the related art, and reference may be made to the related description in the first aspect, and details are not repeated here.
Drawings
The above and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
fig. 1 is a flow chart of a lithium ion battery modeling method according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of the flow of current in parallel plate electrodes of a lithium ion battery in accordance with an embodiment of the present invention;
FIG. 3 is a schematic diagram of the positive electrode space domain of a lithium ion battery according to an embodiment of the present invention;
fig. 4 is a schematic diagram of a negative electrode space domain of a lithium ion battery according to an embodiment of the invention;
FIG. 5 is a schematic diagram of a network prediction model according to an embodiment of the present invention;
fig. 6 is a structural diagram of a lithium ion battery modeling system according to an embodiment of the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
In the description of the present invention, if there are first, second, etc. described, it is only for the purpose of distinguishing technical features, and it is not understood that relative importance is indicated or implied or that the number of indicated technical features is implicitly indicated or that the precedence of the indicated technical features is implicitly indicated.
In the description of the present invention, it should be understood that the orientation or positional relationship referred to, for example, the upper, lower, etc., is indicated based on the orientation or positional relationship shown in the drawings, and is only for convenience of description and simplification of description, but does not indicate or imply that the device or element referred to must have a specific orientation, be constructed in a specific orientation, and be operated, and thus should not be construed as limiting the present invention.
In the description of the present invention, it should be noted that unless otherwise explicitly defined, terms such as arrangement, installation, connection and the like should be broadly understood, and those skilled in the art can reasonably determine the specific meanings of the above terms in the present invention in combination with the specific contents of the technical solutions.
First, several terms referred to in the present application are resolved:
lithium ion battery two-dimensional model: the current flows between the parallel plate electrodes of the battery and among the parallel plate electrodes in the process of charging and discharging the battery. The one-dimensional model assumes that the gradient of the variable employed in modeling is negligible in both directions parallel to the current collector, which assumption is valid for small-scale batteries. However, for large scale batteries, a two-dimensional model is used because there may be a significant potential drop along the current collector due to ohmic drop, which affects the current distribution.
Physical information: refers to the prior knowledge of the physics governing the physical process in the actual process, including the principle laws of physics, and the partial differential equations describing various physical processes. Physical information is valuable a priori knowledge in the modeling process.
Deep neural network: the neural network is an operational model and is formed by connecting a large number of nodes, or neurons. A particular output function, called the stimulus function, is represented by each node. Every connection between two nodes represents a weighted value, called weight, for the signal passing through the connection, which is equivalent to the memory of an artificial neural network. The output of the network is different according to the connection mode of the network, the weight value and the excitation function. The network itself is usually an approximation to some algorithm or function in nature, and may be an expression of a logic strategy.
Latin Hypercube Sampling (LHS): the method is hierarchical random sampling, and can perform efficient sampling from the distribution interval of variables.
In the existing battery modeling technology, a modeling method based on traditional numerical calculation, such as a finite element method or a finite difference method, solves a partial differential equation, and a large amount of computing resources and computing time are consumed. And the machine learning modeling method based on data driving regards the electrode reaction of the battery as a black box model, only concerns the relation between the input and the output of the model, and the training of the model is completed by updating network parameters by using input and output data obtained by actual testing. Although this method no longer requires complete equation information and a large amount of calculation, the accuracy depends on the accuracy and scale of the sampled data, and the cost of obtaining enough high-precision test data is also very large.
In order to solve the problems, in order to improve the prediction accuracy of a network prediction model and reduce the calculated amount of the network prediction model, a partial differential equation of a lithium ion battery is obtained according to a charge conservation law and an ohm law, and boundary conditions and initial conditions are defined according to the partial differential equation; constructing a network prediction model based on a physical information neural network, wherein the network prediction model comprises a positive electrode network, a DOD network, a flux network and a negative electrode network; according to data driving, constructing a first loss function of a positive electrode network, a DOD network, a flux network and a negative electrode network, and iteratively updating parameters of a network prediction model by adopting a gradient descent algorithm until a preset first maximum iteration time is reached or the first loss function is stably converged, thereby completing first training of the network prediction model; constructing second loss functions of the positive electrode network, the DOD network, the flux network and the negative electrode network according to the data drive, the boundary condition and the initial condition, and iteratively updating parameters of the network prediction model by adopting a gradient descent algorithm until a preset second maximum iteration number or second loss function is stably converged, thereby completing second training of the network prediction model; constructing a third loss function of the anode network, the DOD network, the flux network and the cathode network according to the data drive, the partial differential equation, the boundary condition and the initial condition, and constructing a total loss function according to the third loss function of the anode network, the DOD network, the flux network and the cathode network; iteratively updating the parameters of the network prediction model by adopting a gradient descent algorithm until a preset third maximum iteration number or a total loss function is stably converged, and completing third training of the network prediction model; and predicting parameters of the lithium ion battery through the network prediction model after three times of training. The network prediction model is trained for the first time, and a first loss function of a positive electrode network, a DOD network, a flux network and a negative electrode network is constructed through data driving; the network prediction model is trained for the second time to construct a second loss function of the anode network, the DOD network, the flux network and the cathode network according to the data drive, the boundary condition and the initial condition; the third training of the network prediction model constructs a third loss function of the anode network, the DOD network, the flux network and the cathode network according to the data drive, the partial differential equation, the boundary condition and the initial condition, and constructs a total loss function according to the third loss function of the DOD network, the flux network and the cathode network of the anode network; the prediction accuracy of the network prediction model is improved through three times of training. According to the invention, the network prediction model is constructed based on the physical information neural network, the physical information is used, the data usage amount is greatly reduced, and the training of the network prediction model can be completed only by a small amount of data, so that the calculation amount of the network prediction model is reduced.
Referring to fig. 1, an embodiment of the present invention provides a lithium ion battery modeling method, where the lithium ion battery modeling method includes:
and S100, obtaining a partial differential equation of the lithium ion battery according to the charge conservation law and the ohm law, and defining boundary conditions and initial conditions according to the partial differential equation.
Specifically, referring to fig. 2, according to the law of conservation of charge and the ohm law, the poisson equation is used to obtain the partial differential equation of the positive electrode potential and the negative electrode potential of the lithium ion battery:
Figure DEST_PATH_IMAGE129
wherein, the first and the second end of the pipe are connected with each other,
Figure 239354DEST_PATH_IMAGE002
the expression of the laplacian operator is shown,
Figure 441665DEST_PATH_IMAGE003
represents the potential of the positive electrode of the lithium ion battery,
Figure 83999DEST_PATH_IMAGE004
represents the negative electrode potential of the lithium ion battery,
Figure 422576DEST_PATH_IMAGE005
represents the resistance of the positive electrode of the lithium ion battery,
Figure 859374DEST_PATH_IMAGE006
represents the resistance of the negative electrode of the lithium ion battery,
Figure 221085DEST_PATH_IMAGE007
represents the spatial domain of the positive electrode of the lithium ion battery,
Figure 260585DEST_PATH_IMAGE008
representing the spatial domain of the negative electrode of a lithium ion battery,
Figure 860194DEST_PATH_IMAGE009
represents the current density between the positive and negative electrodes of a lithium ion battery as a function of the potential difference between the positive and negative electrodes,
Figure 78946DEST_PATH_IMAGE009
the expression of (a) is:
Figure 255849DEST_PATH_IMAGE010
by passing
Figure 974407DEST_PATH_IMAGE009
The partial differential equation of the current density is obtained. Where Y and U represent fitting parameters that are functions of depth of discharge, the expressions for Y and U are as follows:
Figure 287576DEST_PATH_IMAGE130
wherein, the first and the second end of the pipe are connected with each other,
Figure DEST_PATH_IMAGE131
to
Figure 659652DEST_PATH_IMAGE132
Is a constant determined by experiment, and can obtain the current density on the electrode
Figure 199218DEST_PATH_IMAGE009
Is a function of position and time on the electrode. An expression for depth of discharge can thus be obtained:
Figure DEST_PATH_IMAGE133
where t is the time of the discharge and,
Figure 111679DEST_PATH_IMAGE134
is the theoretical capacity of the electrode per unit area.
By integral term
Figure 420300DEST_PATH_IMAGE011
And converting the auxiliary depth of discharge to obtain a partial differential equation of the depth of discharge, wherein the expression for converting is as follows:
Figure 228856DEST_PATH_IMAGE012
where D represents depth of discharge, t represents time,
Figure 990139DEST_PATH_IMAGE013
representing the theoretical capacity per unit area of the electrode.
According to the partial differential equation of the anode potential, the boundary condition of the anode potential is defined:
Figure 112816DEST_PATH_IMAGE014
spatial domain
Figure DEST_PATH_IMAGE135
、
Figure 603840DEST_PATH_IMAGE136
And
Figure DEST_PATH_IMAGE137
referring to fig. 3, wherein a in fig. 3 represents a schematic diagram of a positive electrode of a lithium ion battery, and b in fig. 3 represents a spatial domain
Figure 317718DEST_PATH_IMAGE135
A diagram c in fig. 3 shows a schematic diagram of a positive electrode region except for a tab, and a diagram d in fig. 3 shows a schematic diagram of a tab of a positive electrode; wherein, the first and the second end of the pipe are connected with each other,
Figure 628614DEST_PATH_IMAGE015
representing the gradient in the normal direction outside the boundary,
Figure 617298DEST_PATH_IMAGE016
showing the region of the positive electrode other than the tabs,
Figure 369354DEST_PATH_IMAGE017
a tab of the positive electrode is shown,
Figure 50871DEST_PATH_IMAGE018
which is representative of the current flowing through it,
Figure 786746DEST_PATH_IMAGE019
indicating the length. Boundary condition
Figure 579121DEST_PATH_IMAGE138
Meaning the electrode area other than the tab
Figure 716841DEST_PATH_IMAGE136
No current flows; boundary condition
Figure DEST_PATH_IMAGE139
Means a pass length of
Figure 772522DEST_PATH_IMAGE019
Ear tab
Figure 917064DEST_PATH_IMAGE017
Has a linear current density of
Figure 388497DEST_PATH_IMAGE140
。
According to the partial differential equation of the anode potential, the initial condition of the anode potential is defined as follows:
Figure 505358DEST_PATH_IMAGE020
wherein the content of the first and second substances,
Figure 138464DEST_PATH_IMAGE021
which represents the initial value of the potential of the positive electrode,
Figure 645669DEST_PATH_IMAGE022
represent
Figure 779847DEST_PATH_IMAGE009
The initial value of (1);
defining the boundary condition of the cathode potential according to the partial differential equation of the cathode potential:
Figure 626580DEST_PATH_IMAGE023
spatial domain
Figure DEST_PATH_IMAGE141
、
Figure 357819DEST_PATH_IMAGE024
And
Figure 414637DEST_PATH_IMAGE025
referring to fig. 4, wherein a in fig. 4 represents a schematic diagram of a lithium ion battery cathode, and b in fig. 4 represents a spatial domain
Figure 227872DEST_PATH_IMAGE141
A schematic diagram, wherein a diagram c in fig. 4 shows a schematic diagram of a negative electrode region except a tab, and a diagram d in fig. 4 shows a tab schematic diagram of a negative electrode; wherein, the first and the second end of the pipe are connected with each other,
Figure 319325DEST_PATH_IMAGE024
showing the negative electrode area other than the tab,
Figure 294234DEST_PATH_IMAGE025
a tab of the negative electrode is shown. Boundary condition
Figure 307190DEST_PATH_IMAGE142
Meaning the area of the electrode other than the tab
Figure 783170DEST_PATH_IMAGE024
No current flows; boundary condition
Figure DEST_PATH_IMAGE143
Meaning the tab at the negative electrode
Figure 463550DEST_PATH_IMAGE025
The potential at (b) is fixed to zero as a reference potential.
According to the partial differential equation of the cathode potential, the initial condition of the cathode potential is defined:
Figure 343782DEST_PATH_IMAGE026
Figure 375192DEST_PATH_IMAGE027
represent
Figure 326967DEST_PATH_IMAGE004
Of (4) is calculated.
In the above-mentioned equation, the first and second equations,
Figure 2799DEST_PATH_IMAGE005
、
Figure 709724DEST_PATH_IMAGE006
、
Figure 838217DEST_PATH_IMAGE019
and
Figure 656000DEST_PATH_IMAGE013
are known battery related parameters.
Step S200, constructing a network prediction model based on the physical information neural network, wherein the network prediction model comprises a positive electrode network, a DOD network, a flux network and a negative electrode network.
Specifically, referring to fig. 5, a network prediction model is constructed based on the physical information neural network, and the network prediction model includes a positive electrode network for predicting the positive electrode potential of the battery, a DOD network for predicting the depth of discharge on the battery electrodes, a flux network for predicting the current density between the battery electrodes, and a negative electrode network for predicting the negative electrode potential of the battery. Constructing a loss function of the network prediction model, wherein the loss function comprises a data driving part and a physical information part, and the loss function comprises the following steps:
constructing loss functions for data driven parts
Figure 248655DEST_PATH_IMAGE028
：
Figure 1848DEST_PATH_IMAGE029
Wherein the content of the first and second substances,
Figure 476692DEST_PATH_IMAGE030
representing the results of the prediction by the network prediction model,
Figure 973532DEST_PATH_IMAGE031
representing a spatial position, wherein the spatial position is a coordinate point randomly selected in space and time by adopting a Latin Hypercube Sampling (LHS) method, i represents the current of the lithium ion battery, t represents time,
Figure 748590DEST_PATH_IMAGE144
as an input to the network prediction model,
Figure 469421DEST_PATH_IMAGE032
the measured data is represented by a representation of,
Figure 838086DEST_PATH_IMAGE033
which is indicative of the amount of the measured data,
Figure 997672DEST_PATH_IMAGE034
representing the mean square error between the result predicted by the network prediction model and the measured data;
constructing a loss function of the physical information part, the loss function of the physical information part comprising a loss function of a partial differential equation, a loss function of an initial condition and a loss function of a boundary condition, wherein:
constructing loss functions of partial differential equations
Figure 237023DEST_PATH_IMAGE035
：
Figure 456652DEST_PATH_IMAGE036
Wherein, the first and the second end of the pipe are connected with each other,
Figure 843771DEST_PATH_IMAGE037
the equation of control is expressed in terms of,
Figure 682414DEST_PATH_IMAGE038
which represents the number of sample points,
Figure 166485DEST_PATH_IMAGE039
to represent
Figure 432381DEST_PATH_IMAGE040
Substituting the result predicted by the network prediction model into the mean square error of residual errors generated in a control equation at each sampling point;
constructing a loss function for initial conditions
Figure 634692DEST_PATH_IMAGE041
：
Figure 808185DEST_PATH_IMAGE042
Wherein the content of the first and second substances,
Figure 287708DEST_PATH_IMAGE043
representing the results of the initial moments predicted by the network prediction model,
Figure 577700DEST_PATH_IMAGE044
a value representing a known initial time instant,
Figure 142674DEST_PATH_IMAGE045
representing the number of initial sampling points;
constructing a loss function of boundary conditions
Figure 119857DEST_PATH_IMAGE046
：
Figure 844099DEST_PATH_IMAGE047
Wherein the content of the first and second substances,
Figure 186219DEST_PATH_IMAGE048
expressing the result predicted by the network prediction model is brought into the boundary condition equation and calculated
Figure 97543DEST_PATH_IMAGE049
The sum of the residuals of the boundary condition equations at the boundary sample points;
the goal of the training of the network prediction model is to find suitable network parameters that minimize the loss function, and therefore, the present embodiment considers introducing physical information into the loss function so that the training of the network prediction model can better converge on the true solution of the partial differential equation. Therefore, the present embodiment constructs a loss function of the network prediction model according to the loss function of the data driving part and the loss function of the physical information part:
Figure 878417DEST_PATH_IMAGE050
wherein the content of the first and second substances,
Figure 332533DEST_PATH_IMAGE051
representing a set of weights and bias parameters in the network,
Figure 235767DEST_PATH_IMAGE052
representing the total loss function value of the currently trained network prediction model,
Figure 244174DEST_PATH_IMAGE053
the weight of the loss function representing the data portion,
Figure 891056DEST_PATH_IMAGE054
the weight of the loss function representing the partial differential equation,
Figure 996415DEST_PATH_IMAGE055
the weight of the loss function representing the initial conditions,
Figure 945917DEST_PATH_IMAGE056
the weight of the loss function representing the boundary condition.
Note that, in the DOD network of the present embodiment, the integral term thereof
Figure 831833DEST_PATH_IMAGE011
Conversion by auxiliary output variables, i.e.
Figure DEST_PATH_IMAGE145
. The calculation of the partial derivative term is realized by automatic differentiation of the neural network.
In this embodiment, the network structure used by the physical information neural network is a fully connected network structure, and the fully connected network has the advantages of high network throughput, high reliability and low delay. The embodiment utilizes the knowledge of the auxiliary physical information neural network, and the model converts the integral term by defining the auxiliary output variable, thereby facilitating the calculation of the network.
Step S300, a first loss function of the anode network, the DOD network, the flux network and the cathode network is constructed according to data driving, iterative updating is carried out on parameters of the network prediction model by adopting a gradient descent algorithm until a preset first maximum iteration frequency is reached or the first loss function is stably converged, and first training of the network prediction model is completed.
Specifically, according to data driving, a first loss function of the anode network, the DOD network, the flux network and the cathode network is constructed, iterative updating is carried out on parameters of the network prediction model through a gradient descent algorithm, the first loss function is descended until a preset first maximum iteration number is reached or the first loss function is stably converged, and first training of the network prediction model is completed. Wherein:
constructing a first loss function of the anode network
Figure 485668DEST_PATH_IMAGE057
：
Figure 914375DEST_PATH_IMAGE146
Wherein, the first and the second end of the pipe are connected with each other,
Figure 159412DEST_PATH_IMAGE059
representing the loss function of the data-driven part of the positive network,
Figure 204728DEST_PATH_IMAGE060
the results of the positive network prediction are shown,
Figure 68779DEST_PATH_IMAGE061
represents the measured data corresponding to the positive network,
Figure 476627DEST_PATH_IMAGE062
the mean square error between the result of the anode network prediction and the measured data corresponding to the anode network is represented;
constructing a first loss function for a DOD network
Figure 502352DEST_PATH_IMAGE063
：
Figure 362860DEST_PATH_IMAGE064
Wherein the content of the first and second substances,
Figure 827340DEST_PATH_IMAGE065
representing the loss function of the data-driven part of the DOD network,
Figure 965060DEST_PATH_IMAGE066
representing the result of the DOD network prediction,
Figure 286320DEST_PATH_IMAGE067
represents the measured data corresponding to the DOD network,
Figure 509491DEST_PATH_IMAGE068
representing the mean square error between the result of the DOD network prediction and the measured data corresponding to the DOD network;
constructing a first loss function of a flux network
Figure 105557DEST_PATH_IMAGE069
：
Figure 894522DEST_PATH_IMAGE070
Wherein the content of the first and second substances,
Figure 527628DEST_PATH_IMAGE071
representing the loss function of the data driven part of the flux network,
Figure 97150DEST_PATH_IMAGE072
the results of the flux network prediction are shown,
Figure 106694DEST_PATH_IMAGE073
represents the measured data corresponding to the flux network,
Figure 750165DEST_PATH_IMAGE074
representing a mean square error between a result of the flux network prediction and measured data corresponding to the flux network;
constructing a first loss function of the negative network
Figure 944386DEST_PATH_IMAGE075
：
Figure 876570DEST_PATH_IMAGE076
Wherein the content of the first and second substances,
Figure 548860DEST_PATH_IMAGE077
representing the loss function of the data driven part of the negative network,
Figure 250100DEST_PATH_IMAGE078
the result of the negative network prediction is shown,
Figure 287326DEST_PATH_IMAGE079
indicating the measured data corresponding to the negative network,
Figure 831440DEST_PATH_IMAGE080
and the mean square error between the result of the negative electrode network prediction and the measured data corresponding to the negative electrode network is shown.
After first loss functions of the positive electrode network, the DOD network, the flux network and the negative electrode network are constructed, parameters of four networks in the network prediction model are respectively updated in an iterative mode through a gradient descent algorithm, the first loss function corresponding to each network is descended until a preset first maximum iteration time is reached or the first loss function is stably converged, and first training of the network prediction model is completed.
It should be noted that the actual measurement data in this embodiment is low-frequency data, and the low-frequency data is obtained by sampling, and fine sampling is not performed, so that the information amount of the data is relatively small.
And S400, constructing second loss functions of the anode network, the DOD network, the flux network and the cathode network according to the data drive, the boundary condition and the initial condition, and iteratively updating parameters of the network prediction model by adopting a gradient descent algorithm until a preset second maximum iteration time is reached or the second loss function is stably converged, so as to complete second training of the network prediction model.
Specifically, second loss functions of the positive electrode network, the DOD network, the flux network and the negative electrode network are constructed according to the data drive, the boundary conditions and the initial conditions, and parameters of the network prediction model are iteratively updated by adopting a gradient descent algorithm, so that the second loss functions are descended until a preset second maximum iteration number is reached or the second loss functions are stably converged, and second training of the network prediction model is completed. Wherein:
second loss function for constructing positive pole network
Figure 917207DEST_PATH_IMAGE081
：
Figure 869026DEST_PATH_IMAGE082
Wherein the content of the first and second substances,
Figure 280416DEST_PATH_IMAGE083
representing the loss function of the data-driven part of the positive network,
Figure 983929DEST_PATH_IMAGE084
weights representing loss functions of the data-driven part of the positive network,
Figure 263601DEST_PATH_IMAGE085
a loss function representing the initial conditions of the positive network,
Figure 673854DEST_PATH_IMAGE086
the weight of the loss function representing the initial conditions of the positive network,
Figure 380779DEST_PATH_IMAGE087
a loss function representing the boundary conditions of the positive network,
Figure 571589DEST_PATH_IMAGE088
weights of loss functions representing boundary conditions of the positive network;
second loss function for constructing DOD network
Figure 264738DEST_PATH_IMAGE089
：
Figure 185290DEST_PATH_IMAGE090
Wherein the content of the first and second substances,
Figure 407323DEST_PATH_IMAGE091
representing the loss function of the data-driven part of the DOD network,
Figure 413326DEST_PATH_IMAGE092
weights representing loss functions of the data-driven portion of the DOD network,
Figure 910166DEST_PATH_IMAGE093
a loss function representing initial conditions of the DOD network,
Figure 357328DEST_PATH_IMAGE094
weights of the loss functions representing initial conditions of the DOD network,
Figure 406055DEST_PATH_IMAGE095
a loss function representing the boundary conditions of the DOD network,
Figure 509141DEST_PATH_IMAGE096
weights of loss functions representing boundary conditions of the DOD network;
second loss function for constructing flux network
Figure 403147DEST_PATH_IMAGE097
：
Figure 173657DEST_PATH_IMAGE098
Wherein the content of the first and second substances,
Figure 393286DEST_PATH_IMAGE099
representing the loss function of the data driven part of the flux network,
Figure 780405DEST_PATH_IMAGE100
weights representing loss functions of data-driven portions of the flux network,
Figure 619048DEST_PATH_IMAGE101
a loss function representing the initial conditions of the flux network,
Figure 368698DEST_PATH_IMAGE102
the weight of the loss function representing the initial conditions of the flux network,
Figure 634594DEST_PATH_IMAGE103
a loss function representing the boundary conditions of the flux network,
Figure 836906DEST_PATH_IMAGE104
weights of loss functions representing boundary conditions of the flux network;
second loss function for constructing negative electrode network
Figure 948081DEST_PATH_IMAGE105
：
Figure 552238DEST_PATH_IMAGE106
Wherein the content of the first and second substances,
Figure 989035DEST_PATH_IMAGE107
representing the loss function of the data driven part of the negative network,
Figure 350746DEST_PATH_IMAGE108
weights representing loss functions of the data-driven part of the negative network,
Figure 655826DEST_PATH_IMAGE109
a loss function representing the initial conditions of the negative network,
Figure 989855DEST_PATH_IMAGE110
the weight of the loss function representing the initial conditions of the negative network,
Figure 722188DEST_PATH_IMAGE111
a loss function representing the boundary conditions of the negative network,
Figure 508878DEST_PATH_IMAGE112
a weight of a loss function representing a boundary condition of the negative network.
After second loss functions of the positive electrode network, the DOD network, the flux network and the negative electrode network are constructed, iterative updating is carried out on parameters of each network in the network prediction model by adopting a gradient descent algorithm, so that the second loss function corresponding to each network is descended until a preset second maximum iteration number is reached or the second loss function is stably converged, and second training of the network prediction model is completed.
It should be noted that, in the loss function of the data driving portion of this embodiment, the measured data is used, and the used measured data is high frequency data, and the high frequency data is obtained by sampling and performing fine sampling, so that the information amount of the data is relatively large.
Step S500, constructing third loss functions of the positive electrode network, the DOD network, the flux network and the negative electrode network according to the data drive, the partial differential equation, the boundary condition and the initial condition, and constructing a total loss function according to the third loss functions of the positive electrode network, the DOD network, the flux network and the negative electrode network; and (3) iteratively updating the parameters of the network prediction model by adopting a gradient descent algorithm until a preset third maximum iteration number or a total loss function is stably converged, and finishing third training of the network prediction model.
Specifically, a third loss function of the positive electrode network, the DOD network, the flux network and the negative electrode network is constructed according to the data drive, the partial differential equation, the boundary condition and the initial condition, and a total loss function is constructed according to the third loss functions of the positive electrode network, the DOD network, the flux network and the negative electrode network; and (3) iteratively updating the parameters of the network prediction model by adopting a gradient descent algorithm, so that the total loss function descends until a preset third maximum iteration number is reached or the total loss function is stably converged, and finishing the third training of the network prediction model. Wherein:
constructing a third loss function for the anode network
Figure 617649DEST_PATH_IMAGE113
：
Figure 806184DEST_PATH_IMAGE114
Wherein, the first and the second end of the pipe are connected with each other,
Figure 709418DEST_PATH_IMAGE115
a loss function representing a partial differential equation of the positive network,
Figure 45722DEST_PATH_IMAGE116
weights representing loss functions of partial differential equations of the positive network;
constructing a third loss function for a DOD network
Figure 567970DEST_PATH_IMAGE117
：
Figure 1225DEST_PATH_IMAGE118
Wherein the content of the first and second substances,
Figure 950727DEST_PATH_IMAGE119
a loss function representing a partial differential equation of the DOD network,
Figure 119801DEST_PATH_IMAGE120
weights representing loss functions of partial differential equations of the DOD network;
third loss function for constructing flux network
Figure 180161DEST_PATH_IMAGE121
：
Figure 467922DEST_PATH_IMAGE122
Wherein, the first and the second end of the pipe are connected with each other,
Figure 447380DEST_PATH_IMAGE123
a loss function representing a partial differential equation of the flux network,
Figure 695958DEST_PATH_IMAGE124
weights representing loss functions of partial differential equations of the flux network;
third loss function for constructing negative electrode network
Figure 684643DEST_PATH_IMAGE125
：
Figure 702278DEST_PATH_IMAGE126
Wherein the content of the first and second substances,
Figure 118215DEST_PATH_IMAGE127
a loss function representing a partial differential equation of the negative network,
Figure 854090DEST_PATH_IMAGE128
representing the weight of the loss function of the partial differential equation of the negative network.
After the third loss functions of the anode network, the DOD network, the flux network and the cathode network are constructed, the total loss function of the network prediction model is constructed according to the third loss functions of the anode network, the DOD network, the flux network and the cathode network
Figure DEST_PATH_IMAGE147
Comprises the following steps:
Figure 115307DEST_PATH_IMAGE148
。
and after a total loss function of the network prediction model is constructed, simultaneously training a positive electrode network, a DOD network, a flux network and a negative electrode network, and iteratively updating parameters of the network prediction model by adopting a gradient descent algorithm until a preset third maximum iteration time or the total loss function is stably converged, thereby completing the third training of the network prediction model.
It should be noted that, in the loss function of the data driving portion of this embodiment, the measured data is used, and the used measured data is high frequency data, and the high frequency data is obtained by sampling and performing fine sampling, so that the information amount of the data is relatively large.
And S600, predicting parameters of the lithium ion battery through the network prediction model after three times of training.
Specifically, parameters of the lithium ion battery are predicted through a network prediction model which completes three times of training, and the parameters of the lithium ion battery comprise the positive electrode potential of the lithium ion battery, the negative electrode potential of the lithium ion battery, the current density distribution between electrodes of the lithium ion battery and the discharge depth on the electrodes of the lithium ion battery.
It should be noted that, in the present embodiment, the network prediction models trained for the first time and the second time are obtained by respectively training four networks in the network prediction models to complete the training of the network prediction models, and the network prediction model trained for the third time is obtained by simultaneously training four networks in the network prediction models to complete the training of the network prediction models.
In the present embodiment, the purpose of modeling the lithium ion battery electrodes is to predict the positive electrode potential of the lithium ion battery, the negative electrode potential of the lithium ion battery, the current density distribution between the electrodes of the lithium ion battery, and the depth of discharge on the electrodes of the lithium ion battery. The embodiment simultaneously utilizes physical information and data drive, uses the physical information, greatly reduces the data use amount, and can complete the training of the network prediction model by only a small amount of data, so that the established model is more accurate and efficient. Therefore, parameters such as the positive electrode potential of the lithium ion battery, the negative electrode potential of the lithium ion battery, the current density distribution between the electrodes of the lithium ion battery and the discharge depth on the electrodes of the lithium ion battery can be accurately obtained through the constructed network prediction model, so that the characteristics of the battery can be better mastered and reasonable electrode design can be carried out. In the embodiment, low-frequency information is used for pre-training in model training, and high-frequency information is used for training in two stages to finish loss function convergence, so that the training precision and efficiency are enhanced. The present embodiment also introduces battery current as a control input to help the network predictive model better identify and predict.
Referring to fig. 6, an embodiment of the present invention further provides a lithium ion battery modeling system, where the lithium ion battery modeling system includes an equation obtaining unit 100, a model building unit 200, a first training unit 300, a second training unit 400, a third training unit 500, and a parameter prediction unit 600, where:
the equation obtaining unit 100 is configured to obtain a partial differential equation of the lithium ion battery according to the charge conservation law and the ohm law, and define a boundary condition and an initial condition according to the partial differential equation;
the model building unit 200 is used for building a network prediction model based on a physical information neural network, wherein the network prediction model comprises a positive electrode network, a DOD network, a flux network and a negative electrode network;
the first training unit 300 is configured to construct a first loss function of the positive electrode network, the DOD network, the flux network and the negative electrode network according to data driving, and iteratively update parameters of the network prediction model by using a gradient descent algorithm until a preset first maximum iteration number or a first loss function is stably converged, thereby completing first training of the network prediction model;
the second training unit 400 is configured to construct second loss functions of the positive electrode network, the DOD network, the flux network and the negative electrode network according to the data driving, the boundary condition and the initial condition, and iteratively update parameters of the network prediction model by using a gradient descent algorithm until a preset second maximum iteration number is reached or the second loss function is stably converged, so as to complete second training of the network prediction model;
a third training unit 500, configured to construct a third loss function of the positive electrode network, the DOD network, the flux network, and the negative electrode network according to the data driver, the partial differential equation, the boundary condition, and the initial condition, construct a total loss function according to the third loss function of the positive electrode network, the DOD network, the flux network, and the negative electrode network, iteratively update parameters of the network prediction model by using a gradient descent algorithm until a preset third maximum iteration number is reached or the total loss function is stably converged, and complete third training of the network prediction model;
and the parameter prediction unit 600 is configured to predict parameters of the lithium ion battery through the network prediction model after the three times of training.
It should be noted that, since the lithium ion battery modeling system in the embodiment is based on the same inventive concept as the lithium ion battery modeling method, the corresponding contents in the method embodiment are also applicable to the embodiment of the system, and detailed descriptions thereof are omitted here.
The embodiment of the invention also provides a lithium ion battery modeling device, which comprises: at least one control processor and a memory for communicative connection with the at least one control processor.
The memory, which is a non-transitory computer readable storage medium, may be used to store non-transitory software programs as well as non-transitory computer executable programs. Further, the memory may include high speed random access memory, and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid state storage device. In some embodiments, the memory optionally includes memory located remotely from the processor, and these remote memories may be connected to the processor through a network. Examples of such networks include, but are not limited to, the internet, intranets, local area networks, mobile communication networks, and combinations thereof.
The non-transitory software programs and instructions required to implement a lithium ion battery modeling method of the above-described embodiments are stored in a memory, and when executed by a processor, perform a lithium ion battery modeling method of the above-described embodiments, for example, perform the above-described method steps S100 to S600 in fig. 1.
The above described system embodiments are merely illustrative, wherein the units illustrated as separate components may or may not be physically separate, i.e. may be located in one place, or may also be distributed over a plurality of network elements. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of the embodiment.
Embodiments of the present invention also provide a computer-readable storage medium storing computer-executable instructions, which, when executed by one or more control processors, may cause the one or more control processors to perform a lithium ion battery modeling method in the above method embodiments, for example, to perform the functions of the method steps S100 to S600 in fig. 1 described above.
It will be understood by those of ordinary skill in the art that all or some of the steps, systems, and methods disclosed above may be implemented as software, firmware, hardware, or suitable combinations thereof. Some or all of the physical components may be implemented as software executed by a processor, such as a central processing unit, digital signal processor, or microprocessor, or as hardware, or as an integrated circuit, such as an application specific integrated circuit. Such software may be distributed on computer readable media, which may include computer storage media (or non-transitory media) and communication media (or transitory media). The term computer storage media includes volatile and nonvolatile, removable and non-removable media implemented in any method or technology for storage of information such as computer readable instructions, data structures, program modules or other data, as is well known to those of ordinary skill in the art. Computer storage media includes, but is not limited to, RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, digital Versatile Disks (DVD) or other optical disk storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to store the desired information and which can accessed by a computer. In addition, communication media typically embodies computer readable instructions, data structures, program modules or other data in a modulated data signal such as a carrier wave or other transport mechanism and includes any information delivery media as known to those skilled in the art.
The embodiments of the present invention have been described in detail with reference to the accompanying drawings, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge of those skilled in the art without departing from the gist of the present invention.

Claims (10)

1. A lithium ion battery modeling method is characterized by comprising the following steps:
according to the law of conservation of charge and the ohm law, obtaining a partial differential equation of the lithium ion battery, and defining a boundary condition and an initial condition according to the partial differential equation;
constructing a network prediction model based on a physical information neural network, wherein the network prediction model comprises a positive electrode network, a DOD network, a flux network and a negative electrode network;
constructing a first loss function of the anode network, the DOD network, the flux network and the cathode network according to data driving, and iteratively updating parameters of the network prediction model by adopting a gradient descent algorithm until a preset first maximum iteration frequency is reached or the first loss function is stably converged, thereby completing first training of the network prediction model;
constructing second loss functions of the anode network, the DOD network, the flux network and the cathode network according to the data drive, the boundary condition and the initial condition, and iteratively updating parameters of the network prediction model by adopting a gradient descent algorithm until a preset second maximum iteration time is reached or the second loss functions are stably converged, thereby completing second training of the network prediction model;
constructing a third loss function of the positive pole network, the DOD network, the flux network and the negative pole network according to the data drive, the partial differential equation, the boundary condition and the initial condition, and constructing a total loss function according to the third loss function of the positive pole network, the DOD network, the flux network and the negative pole network; iteratively updating the parameters of the network prediction model by adopting a gradient descent algorithm until a preset third maximum iteration number is reached or the total loss function is stably converged, and completing third training of the network prediction model;
and predicting the parameters of the lithium ion battery through the network prediction model after three times of training.
2. The lithium ion battery modeling method of claim 1, wherein obtaining a partial differential equation for a lithium ion battery according to conservation of charge law and ohm law comprises:
according to the law of conservation of charge and the ohm law, the Poisson equation is adopted to obtain partial differential equations of the positive electrode potential and the negative electrode potential of the lithium ion battery:
Figure 80420DEST_PATH_IMAGE002
wherein the content of the first and second substances,
Figure 542626DEST_PATH_IMAGE004
the expression of the laplacian operator is shown,
Figure 562534DEST_PATH_IMAGE006
represents the potential of the positive electrode of the lithium ion battery,
Figure 893021DEST_PATH_IMAGE008
represents the negative electrode potential of the lithium ion battery,
Figure 619669DEST_PATH_IMAGE010
represents the resistance of the positive electrode of the lithium ion battery,
Figure 315092DEST_PATH_IMAGE012
represents the lithium ion batteryThe resistance of the negative electrode is set to be,
Figure 150193DEST_PATH_IMAGE014
represents the spatial domain of the positive electrode of the lithium ion battery,
Figure 628579DEST_PATH_IMAGE016
represents the spatial domain of the negative electrode of the lithium ion battery,
Figure 599946DEST_PATH_IMAGE018
represents the current density between the positive electrode and the negative electrode of the lithium ion battery
Figure 263009DEST_PATH_IMAGE018
Is expressed as
Figure 460772DEST_PATH_IMAGE020
Y and U represent fitting parameters;
by the said
Figure 133062DEST_PATH_IMAGE018
Obtaining a partial differential equation of the current density;
by integral term
Figure 99881DEST_PATH_IMAGE022
And converting the auxiliary depth of discharge to obtain a partial differential equation of the depth of discharge, wherein the expression for converting is as follows:
Figure 137107DEST_PATH_IMAGE024
where D represents depth of discharge, t represents time,
Figure 681221DEST_PATH_IMAGE026
representing the theoretical capacity of the electrode per unit area.
3. The lithium ion battery modeling method of claim 2, wherein said defining boundary conditions and initial conditions according to said partial differential equation comprises:
defining the boundary condition of the anode potential according to the partial differential equation of the anode potential:
Figure 32568DEST_PATH_IMAGE028
wherein, the first and the second end of the pipe are connected with each other,
Figure 712948DEST_PATH_IMAGE030
representing the gradient in the normal direction outside the boundary,
Figure 124337DEST_PATH_IMAGE032
showing the region of the positive electrode other than the tabs,
Figure 161607DEST_PATH_IMAGE034
a tab of the positive electrode is shown,
Figure 51065DEST_PATH_IMAGE036
which is representative of the current flowing through it,
Figure 117110DEST_PATH_IMAGE038
represents a length;
defining initial conditions of the anode potential:
Figure 699401DEST_PATH_IMAGE040
wherein, the first and the second end of the pipe are connected with each other,
Figure 218107DEST_PATH_IMAGE042
which represents the initial value of the potential of the positive electrode,
Figure 707994DEST_PATH_IMAGE044
represents the above
Figure 238333DEST_PATH_IMAGE018
The initial value of (1);
defining the boundary condition of the cathode potential according to the partial differential equation of the cathode potential:
Figure 116159DEST_PATH_IMAGE046
wherein the content of the first and second substances,
Figure 997527DEST_PATH_IMAGE048
showing the negative electrode region other than the tab,
Figure 353422DEST_PATH_IMAGE050
a tab representing a negative electrode;
defining initial conditions for the cathode potential:
Figure 3847DEST_PATH_IMAGE052
Figure 786995DEST_PATH_IMAGE054
represents the above
Figure 155659DEST_PATH_IMAGE008
Is started.
4. The lithium ion battery modeling method of claim 1, wherein a loss function of the network prediction model is constructed, the loss function comprising a data-driven part and a physical information part, wherein:
constructing loss functions for data-driven parts
Figure 987349DEST_PATH_IMAGE056
：
Figure 882493DEST_PATH_IMAGE058
Wherein, the first and the second end of the pipe are connected with each other,
Figure 711908DEST_PATH_IMAGE060
representing the results of the prediction by the network prediction model,
Figure 692503DEST_PATH_IMAGE062
representing spatial position, i representing the current of the lithium ion battery, t representing time,
Figure 265567DEST_PATH_IMAGE064
which is indicative of the measured data and,
Figure 749638DEST_PATH_IMAGE066
indicating the amount of said measured data,
Figure 15534DEST_PATH_IMAGE068
representing a mean square error between results of the network prediction model prediction and the measured data;
constructing a loss function of the physical information part, the loss function of the physical information part comprising a loss function of a partial differential equation, a loss function of an initial condition, and a loss function of a boundary condition, wherein:
constructing a loss function of the partial differential equation
Figure 217845DEST_PATH_IMAGE070
：
Figure 656917DEST_PATH_IMAGE072
Wherein, the first and the second end of the pipe are connected with each other,
Figure 136440DEST_PATH_IMAGE074
the equation of control is expressed in terms of,
Figure 697871DEST_PATH_IMAGE076
which represents the number of sample points,
Figure 997265DEST_PATH_IMAGE078
represent
Figure 302345DEST_PATH_IMAGE080
Substituting the result predicted by the network prediction model into the mean square error of the residual error generated in the control equation at each sampling point;
constructing a loss function for the initial conditions
Figure 636374DEST_PATH_IMAGE082
：
Figure 40810DEST_PATH_IMAGE084
Wherein, the first and the second end of the pipe are connected with each other,
Figure 217714DEST_PATH_IMAGE086
representing the results of the initial moments predicted by the network prediction model,
Figure 936271DEST_PATH_IMAGE088
a value representing a known initial time instant,
Figure 249441DEST_PATH_IMAGE090
representing the number of initial sampling points;
constructing a loss function for the boundary condition
Figure 28041DEST_PATH_IMAGE092
：
Figure 364344DEST_PATH_IMAGE094
Wherein, the first and the second end of the pipe are connected with each other,
Figure 11226DEST_PATH_IMAGE096
expressing the result predicted by the network prediction model is brought into a boundary condition equation and calculated
Figure 319848DEST_PATH_IMAGE098
The sum of the residuals of the boundary condition equations at the boundary sample points;
constructing a loss function of the network prediction model according to the loss function of the data driving part and the loss function of the physical information part:
Figure 128404DEST_PATH_IMAGE100
wherein, the first and the second end of the pipe are connected with each other,
Figure 889687DEST_PATH_IMAGE102
representing a set of weights and bias parameters in the network,
Figure 12363DEST_PATH_IMAGE104
representing the total loss function value of the currently trained network prediction model,
Figure 294266DEST_PATH_IMAGE106
a weight of a loss function representing the data portion,
Figure 414669DEST_PATH_IMAGE108
weights representing loss functions of the partial differential equations,
Figure 53460DEST_PATH_IMAGE110
a weight of a loss function representing the initial condition,
Figure 917511DEST_PATH_IMAGE112
a weight of a loss function representing the boundary condition.
5. The lithium ion battery modeling method of claim 4, wherein the constructing a first loss function for the positive network, the DOD network, the flux network, and the negative network comprises:
constructing a first loss function of the positive network
Figure 59780DEST_PATH_IMAGE114
：
Figure 616663DEST_PATH_IMAGE116
Wherein, the first and the second end of the pipe are connected with each other,
Figure 477171DEST_PATH_IMAGE118
representing a loss function of a data driving portion of the positive network,
Figure 879334DEST_PATH_IMAGE120
represents the result of the positive network prediction,
Figure 876109DEST_PATH_IMAGE122
represents measured data corresponding to the positive electrode network,
Figure 603893DEST_PATH_IMAGE124
representing a mean square error between a result of the positive network prediction and measured data corresponding to the positive network;
constructing a first loss function for the DOD network
Figure 951698DEST_PATH_IMAGE126
：
Figure 157552DEST_PATH_IMAGE128
Wherein, the first and the second end of the pipe are connected with each other,
Figure 274412DEST_PATH_IMAGE130
a loss function representing a data driven portion of the DOD network,
Figure 173098DEST_PATH_IMAGE132
representing the result of the DOD network prediction,
Figure 414723DEST_PATH_IMAGE134
representing measured data corresponding to the DOD network,
Figure 548902DEST_PATH_IMAGE136
representing a mean square error between a result of the DOD network prediction and measured data corresponding to the DOD network;
constructing a first loss function of the flux network
Figure 661214DEST_PATH_IMAGE138
：
Figure 589856DEST_PATH_IMAGE140
Wherein the content of the first and second substances,
Figure 787619DEST_PATH_IMAGE142
a loss function representing a data driven portion of the flux network,
Figure 459909DEST_PATH_IMAGE144
representing the result of the flux network prediction,
Figure 161148DEST_PATH_IMAGE146
representing measured data corresponding to the flux network,
Figure 260692DEST_PATH_IMAGE148
representing a mean square error between a result of the flux network prediction and measured data corresponding to the flux network;
constructing a first loss function of the negative network
Figure 945751DEST_PATH_IMAGE150
：
Figure 687311DEST_PATH_IMAGE152
Wherein the content of the first and second substances,
Figure 508636DEST_PATH_IMAGE154
a loss function representing a data driven portion of the negative network,
Figure 44660DEST_PATH_IMAGE156
representing the result of the negative network prediction,
Figure 685857DEST_PATH_IMAGE158
representing measured data corresponding to the negative pole network,
Figure 699949DEST_PATH_IMAGE160
and the mean square error between the result of the negative electrode network prediction and the measured data corresponding to the negative electrode network is represented.
6. The lithium ion battery modeling method of claim 4, wherein the constructing a second loss function for the positive network, the DOD network, the flux network, and the negative network comprises:
constructing a second loss function of the positive network
Figure 438098DEST_PATH_IMAGE162
：
Figure 754810DEST_PATH_IMAGE164
Wherein the content of the first and second substances,
Figure 7937DEST_PATH_IMAGE166
representing a loss function of a data driving portion of the positive network,
Figure 701086DEST_PATH_IMAGE168
weights representing loss functions of a data driven portion of the positive network,
Figure 293741DEST_PATH_IMAGE170
a loss function representing an initial condition of the positive network,
Figure 171568DEST_PATH_IMAGE172
a weight of a loss function representing an initial condition of the positive network,
Figure 52936DEST_PATH_IMAGE174
a loss function representing a boundary condition of the positive network,
Figure 414690DEST_PATH_IMAGE176
a weight of a loss function representing a boundary condition of the positive network;
constructing a second loss function for the DOD network
Figure 65114DEST_PATH_IMAGE178
：
Figure 848263DEST_PATH_IMAGE180
Wherein, the first and the second end of the pipe are connected with each other,
Figure 216927DEST_PATH_IMAGE182
a loss function representing a data driven portion of the DOD network,
Figure 376513DEST_PATH_IMAGE184
weights representing loss functions of a data driven portion of the DOD network,
Figure 881444DEST_PATH_IMAGE186
a loss function representing an initial condition of the DOD network,
Figure 101072DEST_PATH_IMAGE188
a weight of a loss function representing an initial condition of the DOD network,
Figure 957033DEST_PATH_IMAGE190
a loss function representing a boundary condition of the DOD network,
Figure 326834DEST_PATH_IMAGE192
a weight of a loss function representing a boundary condition of the DOD network;
constructing a second loss function of the flux network
Figure 76485DEST_PATH_IMAGE194
：
Figure 342381DEST_PATH_IMAGE196
Wherein the content of the first and second substances,
Figure 279113DEST_PATH_IMAGE198
a loss function representing a data driven portion of the flux network,
Figure 921447DEST_PATH_IMAGE200
weights representing loss functions of a data driven portion of the flux network,
Figure 525603DEST_PATH_IMAGE202
a loss function representing an initial condition of the flux network,
Figure 759139DEST_PATH_IMAGE204
a weight of a loss function representing an initial condition of the flux network,
Figure 324112DEST_PATH_IMAGE206
a loss function representing a boundary condition of the flux network,
Figure 98033DEST_PATH_IMAGE208
a weight of a loss function representing a boundary condition of the flux network;
constructing a second loss function of the negative network
Figure 697642DEST_PATH_IMAGE210
：
Figure 102078DEST_PATH_IMAGE212
Wherein, the first and the second end of the pipe are connected with each other,
Figure 278982DEST_PATH_IMAGE214
a loss function representing a data driven portion of the negative network,
Figure 997539DEST_PATH_IMAGE216
weights representing loss functions of a data driven portion of the negative network,
Figure 310709DEST_PATH_IMAGE218
is shown inThe loss function of the initial condition of the negative network,
Figure 89309DEST_PATH_IMAGE220
a weight of a loss function representing an initial condition of the negative network,
Figure 425612DEST_PATH_IMAGE222
a loss function representing a boundary condition of the negative network,
Figure 72494DEST_PATH_IMAGE224
a weight of a loss function representing a boundary condition of the negative network.
7. The lithium ion battery modeling method of claim 6, wherein the constructing a third loss function for the positive network, the DOD network, the flux network, and the negative network comprises:
constructing a third loss function of the positive network
Figure 381116DEST_PATH_IMAGE226
：
Figure 455251DEST_PATH_IMAGE228
Wherein the content of the first and second substances,
Figure 950954DEST_PATH_IMAGE230
a loss function representing a partial differential equation of the positive network,
Figure 401527DEST_PATH_IMAGE232
weights representing loss functions of partial differential equations of the positive network;
constructing a third loss function for the DOD network
Figure 361393DEST_PATH_IMAGE234
：
Figure 481796DEST_PATH_IMAGE236
Wherein, the first and the second end of the pipe are connected with each other,
Figure 120588DEST_PATH_IMAGE238
a loss function representing a partial differential equation of the DOD network,
Figure 984638DEST_PATH_IMAGE240
weights representing loss functions of partial differential equations of the DOD network;
constructing a third loss function of the flux network
Figure 861328DEST_PATH_IMAGE242
：
Figure 418211DEST_PATH_IMAGE244
Wherein, the first and the second end of the pipe are connected with each other,
Figure 950823DEST_PATH_IMAGE246
a loss function representing a partial differential equation of the flux network,
Figure 477620DEST_PATH_IMAGE248
weights representing loss functions of partial differential equations of the flux network;
constructing a third loss function for the negative network
Figure 615340DEST_PATH_IMAGE250
：
Figure 485336DEST_PATH_IMAGE252
Wherein the content of the first and second substances,
Figure 177349DEST_PATH_IMAGE254
a loss function representing a partial differential equation of the negative network,
Figure 773415DEST_PATH_IMAGE256
a weight representing a loss function of a partial differential equation of the negative network.
8. A lithium ion battery modeling system, comprising:
the equation acquisition unit is used for acquiring a partial differential equation of the lithium ion battery according to the charge conservation law and the ohm law and defining a boundary condition and an initial condition according to the partial differential equation;
the model building unit is used for building a network prediction model based on a physical information neural network, and the network prediction model comprises a positive electrode network, a DOD network, a flux network and a negative electrode network;
the first training unit is used for constructing first loss functions of the positive electrode network, the DOD network, the flux network and the negative electrode network according to data driving, iteratively updating parameters of the network prediction model by adopting a gradient descent algorithm until a preset first maximum iteration time is reached or the first loss functions are stably converged, and completing first training of the network prediction model;
the second training unit is used for constructing second loss functions of the anode network, the DOD network, the flux network and the cathode network according to the data drive, the boundary condition and the initial condition, and performing iterative updating on parameters of the network prediction model by adopting a gradient descent algorithm until a preset second maximum iteration number is reached or the second loss function is stably converged, so as to complete second training of the network prediction model;
a third training unit, configured to construct a third loss function of the positive electrode network, the DOD network, the flux network, and the negative electrode network according to the data drive, the partial differential equation, the boundary condition, and the initial condition, and construct a total loss function according to the third loss function of the positive electrode network, the DOD network, the flux network, and the negative electrode network; iteratively updating the parameters of the network prediction model by adopting a gradient descent algorithm until a preset third maximum iteration number is reached or the total loss function is stably converged, and completing third training of the network prediction model;
and the parameter prediction unit is used for predicting the parameters of the lithium ion battery through the network prediction model which completes three times of training.
9. A lithium ion battery modeling apparatus comprising at least one control processor and a memory for communicative connection with the at least one control processor; the memory stores instructions executable by the at least one control processor to enable the at least one control processor to perform the lithium ion battery modeling method of any of claims 1-7.
10. A computer-readable storage medium having stored thereon computer-executable instructions for causing a computer to perform the lithium ion battery modeling method of any of claims 1-7.
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