A method for estimating the internal state of a lithium battery based on a physical information neural network

Abstract

This invention relates to the field of battery health state management technology and discloses a lithium battery internal state estimation method based on a physical information neural network. It utilizes an e-SPM model to obtain a loss function for optimizing the internal parameters of the neural network model. The neural network model is then trained using this loss function to optimize its internal parameters, thereby achieving lithium battery internal state estimation. This invention directly maps lithium battery current, voltage, and temperature to the internal electrochemical state of the lithium battery, making the output of the physical neural network more interpretable, easier to understand and analyze. Furthermore, it employs an unsupervised learning approach, substituting the output state variables into a simplified physical model of voltage, embedding them as constraints into the neural network's loss function. This training process does not require a large amount of labeled data, reducing the difficulty of obtaining experimental data.

Description

Technical Field

[0001] This invention relates to the field of battery health status management technology, specifically to a method for estimating the internal state of a lithium battery based on a physical information neural network. Background Technology

[0002] Electric vehicles (EVs) are widely regarded as an effective way to address the challenges of excessive carbon emissions and the gradual depletion of fossil fuels. Among them, energy storage systems, as the core components of electric vehicles, largely determine their performance and commercial potential. Due to their advantages such as high energy density and long lifespan, lithium-ion batteries (LIBs) dominate the energy storage field of electric vehicles. In order to meet the high voltage and high capacity requirements of electric vehicles, multiple individual cells are usually used to form a battery system. Therefore, a battery management system (BMS) is needed to monitor and control these battery cells to maintain the safe and efficient operation of the entire system. State estimation is the key to obtaining dynamic information inside the battery and is also a prerequisite for the efficient realization of other BMS functions.

[0003] The prior art proposes an RNN for online SOC and SOH estimation of electric vehicle batteries, which shows better performance than the traditional multilayer perceptron; the prior art proposes an LSTM network for SOC and SOH estimation under different ambient temperatures, where LSTM shows better performance than the standard RNN; the prior art proposes a combined convolutional neural network (CNN)-LSTM for SOC estimation of lithium-ion batteries, which can extract spatial and temporal features from the input data and outperforms CNN and LSTM itself.

[0004] While these data-driven methods have achieved satisfactory results in SOC or SOH estimation, no data-driven approach based on physical models has yet been proposed to track the dynamic changes of the unmeasurable electrochemical states inside lithium-ion batteries. Furthermore, they require a large amount of training data to optimize the loss function and network parameters, and cannot accurately estimate the internal states of batteries that are difficult to obtain experimentally. Summary of the Invention

[0005] (a) Technical problems to be solved

[0006] To address the shortcomings of existing technologies, this invention provides a method for estimating the internal state of lithium batteries based on physical information neural networks. This method has advantages such as simplified data labeling and solves the problem that the difficulty in obtaining the internal state of lithium batteries affects their internal state estimation.

[0007] (II) Technical Solution

[0008] To achieve the above objectives, the present invention provides the following technical solution: a method for estimating the internal state of a lithium battery based on a physical information neural network, comprising the following steps:

[0009] S1. Simplify the P2D model into the e-SPM model to obtain a simplified physical model in which the voltage is represented by the concentration of lithium ions in the solid phase and the concentration of lithium ions in the liquid phase.

[0010] S2. Input the actual detected voltage U, current I, and temperature T into the neural network model to obtain the output state variables;

[0011] S3. Substitute the output state variables into the simplified physical model of the voltage to obtain the estimated terminal voltage value, and then substitute this value into the SOC calculation formula to obtain the estimated terminal voltage value of the battery body. The loss function is obtained by calculating the mean square error between the actual detected voltage value and the actual SOC at the detection terminal.

[0012] S4. The neural network model optimizes its internal parameters through a loss function to achieve internal state estimation of the lithium battery.

[0013] Preferably, the simplified physical model of the voltage is obtained by:

[0014] Assume that the solid phase concentration is in the two electrodes. Since the x-dimensional value remains constant, the liquid-phase lithium-ion concentration model is as follows:

[0015] ;

[0016] The solid-phase lithium-ion concentration model is as follows:

[0017] ;

[0018] Among them, the solid phase concentration in both electrodes It remains constant in the x-dimensional dimension. This indicates the initial lithium ion concentration in the electrolyte. , and These represent the electrolyte volume fractions at the negative electrode, membrane, and positive electrode, respectively. , and These represent the lengths of the negative electrode, separator, and positive electrode, respectively, and S represents the cross-sectional area of ​​the battery cell. and These represent the initial lithium-ion concentrations of the negative and positive electrodes, respectively. and These represent the volume fractions of the negative and positive electrodes, respectively.

[0019] When the battery temperature When the changes in the x-dimensional dimension are small and only follow time t, inputting the solid-phase lithium-ion concentration model and the liquid-phase lithium-ion concentration model into the e-SPM model yields four voltage term models:

[0020] ,

[0021] ,

[0022] ,

[0023] ,

[0024] Therefore, the simplified physical model of voltage is:

[0025] ,

[0026] in, This represents the estimated equilibrium potential. The first part is the ohmic potential drop caused by the electrolyte conductivity, and the second part is the estimated overpotential of the electrolyte concentration. This represents the voltage across the thin-film resistor. Indicates overpotential. and This represents the equilibrium potential between the positive and negative electrodes. and These represent the surface lithium ion concentrations of the negative and positive electrodes, respectively. , as well as Represent the effective reaction rate constants of the negative electrode, the separator, and the positive electrode, respectively; I represents the charging and discharging current; R represents the universal gas constant; and F represents the Faraday constant. Represents the lithium-ion transference number. and These represent the positive and negative thin-film resistors, respectively. and Let represent the interfacial areas of the positive and negative electrode spherical particles, respectively, and α represent the charge transfer coefficient of the electrode. and These represent the exchange current densities of the positive and negative terminals, respectively.

[0027] Preferably, the method for obtaining the loss function is as follows:

[0028] Voltage U, current I, and temperature T are input into the neural network model, which outputs three output state variables. , and These are the electrode surface concentration, the average electrode concentration, and the electrolyte concentration, respectively. Substituting these three output state variables into the estimated terminal voltage model yields a simplified voltage term model:

[0029]

[0030]

[0031]

[0032]

[0033] Therefore, the estimated terminal voltage value can be calculated:

[0034] ,

[0035] in, , , and These are the four voltage term model equations, where G is the simplified physical model equation for voltage. This represents a simplified equilibrium potential estimate. The first part is the simplified ohmic potential drop caused by the electrolyte conductivity, and the second part is the oversimplified potential estimate of the electrolyte concentration. This represents the simplified voltage across the thin-film resistor. This represents a simplified overpotential;

[0036] The battery body estimation end was calculated. :

[0037] ,

[0038] in, This indicates the average concentration at the anode electrode. and These represent the maximum and minimum lithium insertion capacity of the anode within the operating voltage range, respectively. This indicates the maximum lithium-ion concentration at the anode.

[0039] Estimating end and estimated voltage value Compared with the actual SOC and actual detection voltage value at the detection terminal The loss function is obtained by calculating the mean squared error:

[0040] ,

[0041] in, Represents time samples, This represents the actual detected voltage value at time t. This represents the estimated terminal voltage value at time t. This indicates the estimation at time t. , This represents the SOC at the actual detection end at time t.

[0042] (III) Beneficial Effects

[0043] Compared with existing technologies, this invention provides a method for estimating the internal state of a lithium battery based on a physical information neural network, which has the following advantages:

[0044] 1. This paper proposes a method for estimating the internal state of lithium batteries based on physical information neural networks. It utilizes the e-SPM model to obtain a loss function for optimizing the internal parameters of the neural network model, directly mapping the lithium battery current, voltage, and temperature to the internal electrochemical state of the lithium battery. This makes the output results of the physical neural network (PINNs) more interpretable, easier to understand, and easier to analyze.

[0045] 2. This method for estimating the internal state of lithium batteries based on physical information neural networks differs from traditional data-driven methods that require a large amount of known data for training. This method adopts an unsupervised learning approach, substituting the output state variables into a simplified physical model of voltage and embedding them as constraints into the loss function of the neural network. This training process does not require a large amount of labeled data, reducing the difficulty of obtaining experimental data. Attached Figure Description

[0046] Figure 1 This is a schematic diagram of the process of the present invention;

[0047] Figure 2 This is a diagram of the e-SPM model of the present invention;

[0048] Figure 3 This is a P2D model diagram of the present invention;

[0049] Figure 4 This is a block diagram of the physical neural network (PINNs) structure of the present invention. Detailed Implementation

[0050] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0051] like Figure 1-4 As shown, a method for estimating the internal state of a lithium battery based on a physical information neural network includes the following steps:

[0052] S1. Simplify the P2D model into the e-SPM model to obtain a simplified physical model in which the voltage is represented by the concentration of lithium ions in the solid phase and the concentration of lithium ions in the liquid phase.

[0053] S2. Input the actual detected voltage U, current I, and temperature T into the neural network model to obtain the output state variables;

[0054] S3. Substitute the output state variables into the simplified physical model of the voltage to obtain the estimated terminal voltage value, and then substitute this value into the SOC calculation formula to obtain the estimated terminal voltage value of the battery body. The loss function is obtained by calculating the mean square error between the actual detected voltage value and the actual SOC at the detection terminal.

[0055] S4. The neural network model optimizes its internal parameters through a loss function to achieve internal state estimation of the lithium battery.

[0056] In this embodiment, such as Figure 1 As shown, the solid phase in the anode and cathode consists of two electrodes with radii of... and The particle representation, hence the simplified physical model of voltage is obtained as follows:

[0057] Assume that the solid phase concentration is in the two electrodes. Since the x-dimensional value remains constant, the liquid-phase lithium-ion concentration model is as follows:

[0058] ;

[0059] The solid-phase lithium-ion concentration model is as follows:

[0060] ;

[0061] Among them, the solid phase concentration in both electrodes It remains constant in the x-dimensional dimension. This indicates the initial lithium ion concentration in the electrolyte. , and These represent the electrolyte volume fractions at the negative electrode, membrane, and positive electrode, respectively. , and These represent the lengths of the negative electrode, separator, and positive electrode, respectively, and S represents the cross-sectional area of ​​the battery cell. and These represent the initial lithium-ion concentrations of the negative and positive electrodes, respectively. and These represent the volume fractions of the negative and positive electrodes, respectively.

[0062] When the battery temperature When the changes in the x-dimensional dimension are small and only follow time t, inputting the solid-phase lithium-ion concentration model and the liquid-phase lithium-ion concentration model into the e-SPM model yields four voltage term models:

[0063] ,

[0064] ,

[0065] ,

[0066] ,

[0067] Therefore, the simplified physical model of voltage is:

[0068] ,

[0069] in, This represents the estimated equilibrium potential. The first part is the ohmic potential drop caused by the electrolyte conductivity, and the second part is the estimated overpotential of the electrolyte concentration. This represents the voltage across the thin-film resistor. Indicates overpotential. and This represents the equilibrium potential between the positive and negative electrodes. and These represent the surface lithium ion concentrations of the negative and positive electrodes, respectively. , as well as Represent the effective reaction rate constants of the negative electrode, the separator, and the positive electrode, respectively; I represents the charging and discharging current; R represents the universal gas constant; and F represents the Faraday constant. Represents the lithium-ion transference number. and These represent the positive and negative thin-film resistors, respectively. and Let represent the interfacial areas of the positive and negative electrode spherical particles, respectively, and α represent the charge transfer coefficient of the electrode. and These represent the exchange current densities of the positive and negative terminals, respectively.

[0070] In this embodiment, the loss function is obtained as follows:

[0071] Voltage U, current I, and temperature T are input into the neural network model, which outputs three output state variables. , and These are the electrode surface concentration, the average electrode concentration, and the electrolyte concentration, respectively. Substituting these three output state variables into the estimated terminal voltage model yields a simplified voltage term model:

[0072]

[0073]

[0074]

[0075]

[0076] Therefore, the estimated terminal voltage value can be calculated:

[0077] ,

[0078] in, , , and These are the four voltage term model equations, where G is the simplified physical model equation for voltage. This represents a simplified equilibrium potential estimate. The first part is the simplified ohmic potential drop caused by the electrolyte conductivity, and the second part is the oversimplified potential estimate of the electrolyte concentration. This represents the simplified voltage across the thin-film resistor. This represents a simplified overpotential;

[0079] The battery body estimation end was calculated. :

[0080] ,

[0081] in, This indicates the average concentration at the anode electrode. and These represent the maximum and minimum lithium insertion capacity of the anode within the operating voltage range, respectively. This indicates the maximum lithium-ion concentration at the anode.

[0082] Estimating end and estimated voltage value Compared with the actual SOC and actual detection voltage value at the detection terminal The loss function is obtained by calculating the mean squared error:

[0083] ,

[0084] in, Represents time samples, This represents the actual detected voltage value at time t. This represents the estimated terminal voltage value at time t. This indicates the estimation at time t. , This represents the SOC at the actual detection end at time t.

[0085] It should be noted that the Adam algorithm is used in this method to optimize the loss function and update parameters. Due to the use of momentum term and adaptive learning rate, it has the advantage of high computational efficiency and is suitable for solving optimization problems with large amounts of data and parameters. The loss function can converge quickly with the Adam optimization algorithm.

[0086] The specific optimization parameters within the neural network model in S4 are as follows:

[0087] The loss function is embedded as a constraint in the neural network model, thereby updating the neural network parameters as follows:

[0088] ,

[0089] ,

[0090] ,

[0091] ,

[0092] ,

[0093] ,

[0094] in, It's the learning rate. and These are the two exponential decay rates from the estimate. For parameters loss function, and These are the biased first-order moment estimate and the biased second-order moment estimate, respectively. For the update parameters at time step t, , and The initial values ​​were set to 0.001, 0.9, and 0.999 respectively, to avoid the denominator being 0. .

[0095] In addition, to better estimate the internal state of lithium batteries, the side reaction overpotential is also an important monitoring value. If it is less than zero, a series of reactions such as lithium plating may occur inside the battery. Therefore, the side reaction overpotential... The definition is as follows:

[0096] ,

[0097] in, This represents the equilibrium potential of the side reaction, and it is assumed that it is known. The most critical value occurs at the interface between the anode and the diaphragm; assuming Based on the simplified e-SPM equation, the estimated value of the side reaction overpotential is... It can be described by the following formula:

[0098] .

[0099] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for estimating the internal state of a lithium battery based on a physical information neural network, characterized in that, Includes the following steps: S1. Simplify the P2D model into the e-SPM model to obtain a simplified physical model in which the voltage is represented by the concentration of lithium ions in the solid phase and the concentration of lithium ions in the liquid phase. S2. Input the actual detected voltage U, current I, and temperature T into the neural network model to obtain the output state variables; S3. Substitute the output state variables into the simplified physical model of the voltage to obtain the estimated terminal voltage value, and then substitute this value into the SOC calculation formula to obtain the estimated terminal voltage value of the battery body. The loss function is obtained by calculating the mean square error between the actual detected voltage value and the actual SOC at the detection terminal. S4. The neural network model optimizes its internal parameters through a loss function to achieve internal state estimation of lithium batteries. The method for obtaining the simplified physical model: Assume that the solid phase concentration is in the two electrodes. Since the x-dimensional value remains constant, the liquid-phase lithium-ion concentration model is as follows: ； The solid-phase lithium-ion concentration model is as follows: ； Among them, the solid phase concentration in both electrodes It remains constant in the x-dimensional dimension. This indicates the initial lithium ion concentration in the electrolyte. , and These represent the electrolyte volume fractions at the negative electrode, membrane, and positive electrode, respectively. , and These represent the lengths of the negative electrode, separator, and positive electrode, respectively, and S represents the cross-sectional area of ​​the battery cell. and These represent the initial lithium-ion concentrations of the negative and positive electrodes, respectively. and These represent the volume fractions of the negative and positive electrodes, respectively. When the battery temperature When the changes in the x-dimensional dimension are small and only follow time t, inputting the solid-phase lithium-ion concentration model and the liquid-phase lithium-ion concentration model into the e-SPM model yields four voltage term models: ， ， ， ， Therefore, the simplified physical model of voltage is: ， in, This represents the estimated equilibrium potential. The first part is the ohmic potential drop caused by the electrolyte conductivity, and the second part is the estimated overpotential of the electrolyte concentration. This represents the voltage across the thin-film resistor. Indicates overpotential. and This represents the equilibrium potential between the positive and negative electrodes. and These represent the surface lithium ion concentrations of the negative and positive electrodes, respectively. , as well as Represent the effective reaction rate constants of the negative electrode, the separator, and the positive electrode, respectively; I represents the charging and discharging current; R represents the universal gas constant; and F represents the Faraday constant. Represents the lithium-ion transference number. and These represent the positive and negative thin-film resistors, respectively. and Let represent the interfacial areas of the positive and negative electrode spherical particles, respectively, and α represent the charge transfer coefficient of the electrode. and These represent the exchange current densities of the positive and negative terminals, respectively. The method for obtaining the loss function is as follows: Voltage U, current I, and temperature T are input into the neural network model, which outputs three output state variables. , and These are the electrode surface concentration, the average electrode concentration, and the electrolyte concentration, respectively. Substituting these three output state variables into the estimated terminal voltage model yields a simplified voltage term model: Therefore, the estimated terminal voltage value can be calculated: ， in, , , and These are the four voltage term model equations, where G is the simplified physical model equation for voltage. This represents a simplified equilibrium potential estimate. The first part is the simplified ohmic potential drop caused by the electrolyte conductivity, and the second part is the oversimplified potential estimate of the electrolyte concentration. This represents the simplified voltage across the thin-film resistor. This represents a simplified overpotential; The battery body estimation end was calculated. : ， in, This indicates the average concentration at the anode electrode. and These represent the maximum and minimum lithium insertion capacity of the anode within the operating voltage range, respectively. Indicates the maximum lithium-ion concentration at the anode; The estimation end and estimated voltage value Compared with the actual SOC and actual detection voltage value at the detection terminal The loss function is obtained by calculating the mean squared error: , in, Represents time samples, This represents the actual detected voltage value at time t. This represents the estimated terminal voltage value at time t. This indicates the estimation at time t. , This represents the SOC at the actual detection end at time t.

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