Lithium battery digital twin model updating method based on multi-physics field simulation

Abstract

The invention relates to a lithium battery digital twin model updating method based on multi-physics field simulation, which comprises the following steps: determining basic information of a battery, establishing a lithium battery multi-physics field simulation model, screening physical parameters through sensitivity analysis, and constructing an agent model. And performing online sequence model updating on the multi-physical field simulation model and the physical parameter random degradation model based on regular routine detection data, and predicting related physical characteristic output of the lithium battery by using an updated digital twin model. The method not only considers the coupling influence of multiple physical fields, but also considers the uncertainty and random degradation characteristics of physical parameters, realizes the online updating of the physics-based digital twinborn model, can enable the digital twinborn model to maintain high simulation degree, and can reliably predict the future state of a physical entity.

Description

Technical Field

[0001] The present invention relates to the field of digital twins of lithium batteries, and in particular to a method for updating a digital twin model of a lithium battery based on multi-physics field simulation. Background Art

[0002] After decades of in-depth research, lithium batteries are widely used as energy sources for electric vehicles, energy storage systems, etc., and their importance need not be repeated too much. However, due to the diverse application scenarios and complex degradation mechanisms of lithium batteries, there are still obstacles and challenges in aspects such as state estimation, design optimization, temperature management, and degradation prediction of lithium batteries. To address the above challenges, it is necessary to establish a highly realistic digital twin model that can be updated online to reflect the physical information of the lithium battery entity in real time, so as to accurately estimate the internal state of the battery that cannot be directly measured, comprehensively judge the battery safety status, and accurately predict the remaining life.

[0003] Existing digital twin models can be divided into two categories: physics-driven models and data-driven models. The data-driven model regards the battery as a black box and captures system characteristics to the greatest extent from available data. This characteristic also determines that the model lacks physical meaning and ignores the fundamental physical reasons for battery degradation at the material level. At the same time, for machine learning methods, sufficient training data is necessary, but this is not available in many actual usage scenarios. And physics-based models, such as lithium battery electrochemical models and three-dimensional heat transfer models, can realize the simulation from the mechanism level to measurable physical quantities, and can be especially used for some battery systems that do not have available historical data at all, which gives them great research value.

[0004] However, when the physics-based digital twin model of lithium batteries is applied in practice, there are inevitably some technical problems. First, the physical model of lithium batteries is highly complex. Although there are simplified models such as single particle (SP) and pseudo-two-dimensional (P2D), the simulation time cost is still unacceptable in many applications. Second, there are a large number of physical parameters with uncertainties in the physical model, and their values greatly affect the accuracy of the simulation. Especially after coupling multiple physical fields such as heat, force, and flow, it is more difficult to ensure high-fidelity simulation. Third, lithium batteries have a degradation phenomenon, and the digital twin model should be able to dynamically adjust according to new observation data to maintain high-precision simulation and prediction. Many studies have been devoted to solving the first problem. A typical method is to use the surrogate model method to reduce the computational cost. The second problem widely exists in physical modeling, and the simulation results are always inevitably different from the actual measured values. Therefore, a model correction process is needed to identify the uncertain model parameters based on actual experimental data to improve the simulation accuracy. Currently, it is rarely applied in the multi-physical field model of lithium batteries. For the problem of battery degradation in the third point, the existing mainstream model correction methods cannot capture the dynamic changes of uncertain physical parameters in real time, which makes the current physics-based digital twin model of lithium batteries often difficult to meet the actual engineering needs.

[0005] In view of this, on the basis of considering the uncertainty and stochastic degradation of physical parameters, in order to keep the digital twin model of lithium batteries consistent with the actual state in real time, it is necessary to propose a method for updating the digital twin model of lithium batteries based on multi-physical field simulation. Summary of the Invention

[0006] The purpose of the present invention is to solve the problems existing in the digital twin technology of lithium batteries, and propose a method for updating the digital twin model of lithium batteries based on multi-physical field simulation. This method is based on the multi-physical field simulation of lithium batteries, considering the uncertainty of physical parameters, and carrying out sequential stochastic model correction according to regularly measured data, realizing the online update of the digital twin model of lithium batteries. It mainly includes the following steps:

[0007] Step 1: Determine the basic information of the lithium battery. Analyze the size and structure of the lithium battery, establish a three-dimensional CAD model, and at the same time confirm the physical parameters related to the material system, working conditions and working environment of the lithium battery to support subsequent multi-physical field modeling.

[0008] Step 2: Establish a multi-physics simulation model for lithium batteries; starting from the single-cell level, considering the coupled effects of the electric field, thermal field, and flow field, establish an electrical model and a thermal-fluid coupling model for lithium batteries; the electrical model includes an electrochemical model, an equivalent circuit model, and an empirical model; according to the given lithium battery parameters and heat dissipation conditions, construct a three-dimensional thermal model of the lithium battery, including the Bernardi heat generation model, the solid heat transfer model, and the non-isothermal flow model based on laminar flow, k-ε, and k-ω turbulence; the multi-physics coupling simulation model is solved using the finite element method to obtain the change curves of the terminal voltage of the lithium battery and the temperature at the concerned characteristic points with time during a single discharge process under given conditions.

[0009] Step 3: Screen the input parameters of the simulation model to identify the parameters that have a significant impact on the selected output characteristics for dimensionality reduction; according to the complexity of the selected simulation model, consider different combinations of input parameters, including the electrical model parameters of the lithium battery, material thermodynamics parameters, environmental parameters, and the maximum capacity of the battery's current cycle state, and determine the initial value ranges of these parameters according to the corresponding materials; perform Latin hypercube sampling and use the PAWN global sensitivity analysis algorithm to calculate the sensitivity index of each parameter, and screen out the parameters with high enough sensitivity based on the Kolmogorov-Smirnov two-sample critical value. Conduct uncertainty modeling for the screened parameters, considering both random and epistemic uncertainties. Regard the electrical model parameters and material parameters that reflect the individual differences of the battery as random uncertain parameters and characterize the uncertainty with a Gaussian distribution; regard the other parameters as epistemic uncertain parameters and characterize the uncertainty with a value interval.

[0010] Step 4: Sample according to the uncertainty model of the screened parameters, conduct multi-physics simulation based on the samples to obtain the change curves of the terminal voltage and temperature, equally spaced points are taken on them as output characteristics, and use the Gaussian process regression method to establish a surrogate model from the screened parameters to the output characteristics.

[0011] Step 5: Collect the conventional detection data of the lithium battery, including the terminal voltage of the lithium battery and the temperature data of the surface characteristic points. During the charge and discharge cycle degradation process of the lithium battery, collect data at fixed time intervals.

[0012] Step 6: Based on the early measurement data Y obs (t k ), k = 0,..., m and the surrogate model, initially correct the multi-physics simulation model; adopt the Bayesian correction framework, where the likelihood function uses the approximate Bayesian computation method, and embed statistical distances to measure the differences between the simulation values and the measurement values, including the Euclidean distance and the Bhattacharyya distance; at the same time, use the Markov chain Monte Carlo algorithm to achieve sampling from the posterior distribution; further use X(t obtained from the initial correction k), where \(k = 0,\cdots,m\) are used as observed values to correct the undetermined coefficients in the nonlinear Wiener process and establish a parametric stochastic degradation model.

[0013] Step 7: Perform sequential Bayesian correction; for cycle rounds \(n>m\), regularly collect new lithium battery test data \(Y\) obs (t n ), and use the initial parametric degradation model to predict the model's uncertain input parameters for this round and use this as prior information for the correction in this round; use the model correction method in Step 6 to correct and obtain the parameters \(X(t\) n ) of round \(n\); using all previous time instants \(X(t\) i ), \(i = 0,1,\cdots,n\) as observed values, update the coefficient \(\lambda\) in the parametric degradation model to predict the input parameters for the next round

[0014] Step 8: Repeat Step 7, regularly collect test data, perform sequential Bayesian correction according to the method in Step 7, and update the simulation model and parametric stochastic degradation model in real time until there is no new measurement data, and obtain the digital twin model in the latest state.

[0015] Step 9: Based on the latest input parameter uncertainty model and stochastic degradation model obtained in Step 8, predict the input parameters at future time instants and perform multi-physics field simulation to obtain the predicted physical field information.

[0016] Through the above steps, a method for updating the digital twin model of a lithium battery based on multi-physics field simulation is presented.

[0017] The excellent effects of the present invention are as follows: in the field of digital twins of lithium batteries, by organically combining technologies such as multi-physics coupling simulation methods, hybrid uncertainty modeling methods, Bayesian stochastic model correction methods, and nonlinear Wiener processes, a method for updating the digital twin model of a lithium battery based on multi-physics field simulation is proposed. The method not only considers the coupling effects of multi-physics fields, but also takes into account the uncertainty and stochastic degradation characteristics of physical parameters, realizes the online update of the physics-based digital twin model, enables the digital twin to maintain a high degree of fidelity, and can reliably predict the future state of the physical entity. Description of the Drawings

[0018] Figure 1 Flowchart of the method for updating the digital twin model of a lithium battery based on multi-physics field simulation

[0019] Figure 2 Flowchart of the sequential stochastic model update algorithm

[0020] Figure 3 Structure of the lithium battery and diagram of the simulation geometric model

[0021] Figure 4 Sensitivity analysis result diagram

[0022] Figure 5 Initial correction result diagram of physical parameters

[0023] Figure 6 Correction and prediction result diagram of physical parameter degradation model

[0024] Figure 7 Comparison diagram of simulation output prediction results Specific implementation manner

[0025] To make the features and advantages of the present invention clearer, the following takes a typical commercial lithium battery as an example and makes a detailed description in conjunction with the accompanying drawings as follows:

[0026] Step 1: Determine the basic information of the lithium battery. Take the lithium iron phosphate / graphite battery of A123's APR18650M1A model. The rated voltage and capacity of the battery cell are 3.6V and 1.1Ah respectively. The lithium battery undergoes charge and discharge cycles in a constant temperature air-cooled heat dissipation environment at 30°C. The discharge condition is 4C, the cut-off voltage is 2V, and the charging condition is randomly selected from different fast charging strategies, with a charging rate from 3.6V to 6V. The structure and geometric simulation model of the lithium battery are shown in Figure 3 .

[0027] Step 2: Establish a multi-physical field simulation model of the lithium battery. Starting from the single-cell level, considering the coupled effects of the electric field, thermal field, and flow field, establish the electrical model and the thermal-fluid coupling model of the lithium battery. The electrical model is described by the pseudo-two-dimensional (P2D) electrochemical model. The P2D electrochemical model mainly describes the mass transfer and charge migration during the charge and discharge process of the lithium battery, and is mainly described by the charge conservation, mass conservation, and electrochemical kinetics equations. Each equation is summarized in Table 1.

[0028] Summary of electrochemical physical equations in Table 1

[0029]

[0030]

[0031] The charge conservation at the electrode and electrolyte is described by Faraday's law and Ohm's law respectively, as shown in equations (T1)-(T5); the diffusion of lithium ions in the solid and liquid phases is expressed by the mass conservation equation, as shown in equations (T6)-(T8); the electrochemical reaction on the surface of the active particles is described by the Butler-Volmer equation, as shown in equations (T10) and (T11); finally, the maximum battery capacity of the current cycle is calculated by formula (T12).

[0032] According to the given parameters of the lithium battery and the heat dissipation conditions, a three-dimensional thermal model of the lithium battery is constructed, including the Bernardi heat generation model, the solid heat transfer model, and the non-isothermal flow model based on k-ε turbulence. The above heat-fluid models have mature theoretical methods, and the detailed descriptions of the model mathematical equations are omitted. The multi-physics field coupling simulation model is solved using the finite element method to obtain the variation curves of the terminal voltage of the lithium battery and the temperature of the concerned characteristic points with time during a single discharge process under the given conditions.

[0033] Step 3: Screen the input parameters of the simulation model to identify the parameters that have a significant impact on the selected output characteristics for dimensionality reduction. According to the established simulation model, considering the input parameters including 17 parameters of the lithium battery electrical model, material thermodynamics parameters, and environmental parameters, the parameter names and value ranges are shown in Table 2.

[0034] Table 2 Input Parameters of the Multi-Physics Field Simulation Model

[0035]

[0036] Perform Latin hypercube sampling on the above 17 parameters, use the PAWN global sensitivity analysis algorithm to calculate the sensitivity index of each parameter, and screen out the parameters with a high enough sensitivity according to the following formula:

[0037]

[0038] Among them, is the Kolmogorov-Smirnov statistic, that is, the PAWN sensitivity index; N u is taken as the total number of sampling samples, which is taken as 500 here; N c is the total amount divided by the number of input intervals of the PAWN method, taken as 50; c(α) is the Kolmogorov-Smirnov two-sample critical value at the confidence level α, here c(0.1) = 1.22, and the calculated threshold is 0.18.

[0039] There are three main types of output characteristics to be investigated. The first characteristic is the time t it takes for the lithium battery to discharge to the cut-off voltage of 2V end ; The second part comes from the terminal voltage change curve during the discharge process, where the terminal voltage values at equally spaced times t s = k·t end , k = 0.1, 0.2,..., 0.9 are taken as output characteristics; The third part of the output characteristics is the temperature value of the battery characteristic point at time t s , and the characteristic point is selected as the center point of the battery outer surface. The calculation results of the sensitivity indices of each parameter corresponding to different output characteristics and whether they exceed the threshold are shown in Figure 4 , and 6 parameters with sensitivity indices exceeding the threshold are screened out, including: h conv , Q, and R film .

[0040] Perform uncertainty modeling on the selected parameters, Q and R film The four parameters have physical practical significance and vary due to individual battery differences. Therefore, they are considered as random uncertainty parameters, following a normal distribution, to describe the inconsistency of batteries of the same model. They are the parameters that have been simplified / equivalent in the P2D model. Since the prior knowledge is insufficient to determine their values, they are considered as epistemic uncertainty parameters, which are fixed values within a certain interval. h conv It is related to the external environment and is also considered to have uncertainty due to insufficient knowledge. Therefore, it is also regarded as an epistemic uncertainty parameter. The finally established parameter uncertainty model is shown in Table 3.

[0041] Table 3 Parameter Uncertainty Model

[0042]

[0043] Step 4: Sample the selected uncertainty parameters according to the uncertainty model. Use each group of samples as input to conduct multi-physics field simulations, and extract output features from the output physical information to obtain samples for constructing the surrogate model. The output features refer to those examined in Step 3. Take k = 0.1, 0.5, 0.9, and the total number of three types of output features is 7. A total of 250 groups are sampled, of which 200 groups are used to train the Gaussian regression process surrogate model, and 50 groups are used to verify the accuracy of the surrogate model. The finally obtained mean squared error (MSE) of the surrogate model for the verification samples is shown in Table 4.

[0044] Table 4 Surrogate Model Verification Group MSE

[0045] Output feature 1 2 3 4 5 6 7 MSE 0.0024 0.0025 0.0007 0.0007 0.0064 0.0108 0.0122

[0046] Step 5: Collect the conventional detection data of lithium batteries, including the terminal voltage and temperature data of the surface characteristic points of the lithium batteries. In this example, a set of input parameters is constructed using the nonlinear Wiener process, and the observed data is generated through simulation. The parameter degradation model of the nonlinear Wiener process is expressed as:

[0047]

[0048] In the formula, is the predicted value of the parameter degraded to time t k , which is calculated through the standard Brownian motion B(t) and the nonlinear drift function μ(τ; λ); the form of the drift function is set as μ(τ; λ) = abt b-1 , and thus the undetermined coefficients λ = {a, b, σ B}. The design input parameter degradation model parameters are shown in Table 5. According to this parameter degradation model, 50 samples are sampled, 15 rounds of input parameter degradation processes are constructed, and multi-physics field simulations are carried out accordingly to obtain an observation sample set.

[0049] Table 5 Design values of the parameter degradation process

[0050]

[0051] Step 6: Based on the early measurement data Y obs (t k ), k = 0,..., 5 and the surrogate model, the multi-physics field simulation model is initially corrected. The Bayesian correction framework is adopted, where the likelihood function uses the approximate Bayesian computation method, and the Bhattacharyya distance is embedded to measure the difference between the simulation value and the measurement value. The Bhattacharyya distance is expressed as:

[0052]

[0053] In the formula, represents the PMF value in the interval . There are n subscripts in the interval symbol, indicating that the calculated PMF is the joint probability mass function in the n-dimensional space. Therefore, the approximate likelihood function constructed using the Gaussian kernel and the Bhattacharyya distance is defined as follows:

[0054]

[0055] In the formula, d B (Y exp , Y sim ) is the Bhattacharyya distance; σ is called the width coefficient, which can control the shape of the posterior distribution obtained by correction and the number of iterations. The Markov chain Monte Carlo algorithm is used to generate a series of intermediate distributions, continuously approaching the final target distribution, and realizing sampling from the posterior distribution. Further, the X(t k ), k = 0,..., m obtained by the initial correction is used as the observation value, and a parameter stochastic degradation model is established through the nonlinear Wiener process. The undetermined coefficients are also realized using the Bayesian correction method in this step. The physical parameter correction results of the initial 3rd round are shown in Figure 5 . Note that for the random uncertain parameters, what is corrected here is the distribution characteristics, that is, the mean and variance.

[0056] Step 7: Carry out sequential Bayesian correction. The observation samples of the 4th to 10th rounds are used for the sequential correction process, and the parameter degradation model is used to predict the input parameter characteristics of the next round When predicting, the epistemic uncertainty parameter directly uses the posterior of θ epis (t k ) to predict the prior distribution of the next round of correction through the following formula

[0057]

[0058] For random uncertainty parameters, θ is used. alea (t k ) The posterior mean and variance are used to predict the prior distribution for the next round of correction through the following formula

[0059]

[0060] Based on the regular detection data and the predicted prior information, perform random Bayesian correction to obtain the corrected θ(t k+1 ) and X(t k+1 ). Then, taking X(t i ), i = 0, 1,..., k + 1 as the observation samples, use the same method to update the undetermined coefficients in the parameter degradation model.

[0061] Step 8: Repeat Step 7 until the 10th round is reached. Subsequently, use the parameter degradation model corrected by the sequence to predict the future change trend of the physical parameters. The correction and prediction results at each stage are shown in Figure 6 . The absolute percentage errors between the predicted values and the true values of the 6 physical parameters in the 15th round are summarized in Table 6, and the maximum does not exceed 5%.

[0062] Table 6 Prediction Errors of Physical Parameters

[0063]

[0064] Step 9: Based on the latest input parameter uncertainty model and the random degradation model obtained in Step 8, predict the input parameters at future times. According to the physical parameter uncertainty model predicted in the 15th round, perform sampling and carry out multi-physics field simulation to calculate the change curves of the terminal voltage and the characteristic point temperature. The comparison with the observed output characteristic samples is shown in Figure 7 .

[0065] The method provided by the present invention not only considers the coupling effects of multiple physical fields, but also considers the uncertainty and random degradation characteristics of physical parameters, realizes the online update of the physics-based digital twin model, enables the digital twin to maintain a high degree of fidelity, and can reliably predict the future state of the physical entity.

[0066] The above is the preferred solution of the present invention. For those skilled in the art, without departing from the overall concept of the present invention, modifications or equivalent replacements can be made to the specific implementation manners of the present invention, and these should also be regarded as the protection scope of the present invention.

Claims

1. A method for updating a digital twin model of a lithium battery based on multi-physics field simulation, characterized in that: It includes the following steps: Step 1: Determine the basic information of the lithium battery, analyze the size and structure of the lithium battery, establish a 3D CAD model, and at the same time confirm the material system, working conditions and physical parameters related to the working environment of the lithium battery to support subsequent multi-physics field modeling; Step 2: Establish a multi-physics field simulation model of the lithium battery; Starting from the single-cell level, considering the coupling effects of the electric field, thermal field, and flow field, establish an electrical model and a thermal-fluid coupling model of the lithium battery; the electrical model includes an electrochemical model, an equivalent circuit model, and an empirical model; according to the given lithium battery parameters and heat dissipation conditions, construct a three-dimensional thermal model of the lithium battery, including the Bernardi heat generation model, the solid heat transfer model, and the non-isothermal flow model based on laminar flow, k-ε, and k-ω turbulence; the multi-physics field coupling simulation model is solved using the finite element method to obtain the change curves of the terminal voltage of the lithium battery and the temperature of the concerned characteristic points over time during a single discharge process under given conditions; Step 4: Screen the input parameters of the simulation model to identify the parameters that have a great impact on the selected output characteristics to achieve dimensionality reduction; According to the complexity of the selected simulation model, consider different combinations of input parameters, including three categories of lithium battery electrical model parameters, material thermodynamics parameters, and environmental parameters, as well as the maximum capacity Q0 of the battery's current cycle state, and determine the initial value ranges of these parameters according to the corresponding materials; perform Latin hypercube sampling, use the PAWN global sensitivity analysis algorithm to calculate the sensitivity index of each parameter, and screen out the parameters with high enough sensitivity according to the following formula: Among them, is the Kolmogorov-Smirnov statistic, that is, the PAWN sensitivity index, N u is taken as the total sampling sample size, N c is the total amount divided by the number of input intervals of the PAWN method, and is the Kolmogorov-Smirnov two-sample critical value under the confidence level α, obtained by looking up the table; uncertainty modeling is carried out on the selected parameters, considering two kinds of uncertainties, random and epistemic; the electrical model parameters and material parameters reflecting the individual differences of the batteries are regarded as random uncertain parameters, and the uncertainty is characterized by a Gaussian distribution; the other parameters are regarded as epistemic uncertain parameters, and the uncertainty is characterized by a value interval; Step 6: Sample the screened uncertain parameters, conduct multi-physics field simulations, and use the Gaussian process regression method to establish a surrogate model; Step 7: Collect regular routine detection data of the lithium battery; Step 6: Based on the early measurement data Y obs (t k ), k = 0, ..., m and the surrogate model, perform an initial correction on the multi-physics simulation model; adopt the Bayesian correction framework, where the likelihood function uses the approximate Bayesian computation method, and embed the statistical distance to measure the difference between the simulation value and the measurement value, including the Euclidean distance and the Bhattacharyya distance; at the same time, use the Markov chain Monte Carlo algorithm to achieve sampling from the posterior distribution; further use the X(t k ), k = 0, ..., m obtained from the initial correction as the observed values, and establish a parameter stochastic degradation model through the nonlinear Wiener process. The degradation model of each parameter is expressed as: wherein, is the predicted value when the parameter degenerates to t k which is obtained by calculating through the standard Brownian motion B(t) and the nonlinear drift function μ(τ; λ); the form of the drift function is set as μ(τ; λ) = abt b-1 , from which the undetermined coefficients λ = {a, b, σ B} are determined by Bayesian correction or optimization algorithm; Step 7: Conduct sequential Bayesian correction; for cycle rounds n > m, periodically collect new lithium battery test data Y obs (t n ). Use the initial parameter degradation model to predict the model's uncertain input parameters for this round and use this as prior information for the correction in this round; use the model correction method in Step 6 to correct and obtain the parameters X(t n ) for round n; use all previous moments X(t i ), i = 0, 1,..., n as observations to update the coefficient λ in the parameter degradation model to predict the input parameters for the next round Step 8: Repeat Step 7 until there is no new measurement data; regularly collect detection data, perform sequential Bayesian correction according to the method in Step 7, and update the simulation model and the parameter random degradation model in real time to obtain a digital twin model in the latest state; Step 9: Predict the uncertain parameters at future times and further calculate the physical field information; based on the latest input parameter uncertainty model and random degradation model obtained in Step 8, predict the input parameters at future times and conduct multi-physics field simulations to obtain the predicted physical field information.

2. The method for updating a digital twin model of a lithium battery based on multi-physics field simulation according to claim 1, characterized in that: In Step 4, sample according to the uncertainty model of the parameters screened in Step 3, conduct multi-physics field simulations based on the samples to output the change curves of the terminal voltage and temperature, equally spaced points are taken on them as output characteristics, and the Gaussian process regression method is used to establish a surrogate model from the screened parameters to the output characteristics.

3. The method for updating a digital twin model of a lithium battery based on multi-physics field simulation according to claim 1, characterized in that: In Step 5, during the charge and discharge cycle degradation process of the lithium battery, regularly collect routine detection data, including the terminal voltage of the lithium battery under a single constant current discharge condition and the temperature data of the surface characteristic points.

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