A lithium battery digital twin online state estimation method and system

Abstract

The present application relates to a kind of lithium battery digital twin online state estimation method and system, belong to lithium battery state monitoring technical field.It includes: training TP-FNO model, and the working condition parameter and space variable are mapped into positive and negative active particle lithium ion solid phase concentration distribution;The model is embedded in nonlinear state space equation, combined with the system state posterior estimation of previous time and current input, obtain system state prior estimation and covariance prior;Through observation equation, the voltage prediction value is calculated, and the observation residual is obtained by comparing with real-time measurement value;Using state estimation algorithm, the observation residual is used to update system state prior estimation and covariance prior, and the system state posterior estimation and covariance posterior are obtained;Feedback posterior estimation result, construct the model input feature of next time, realize closed-loop iteration.The present application fuses physical mechanism and data driving, can be accurately estimated in line the microstate in lithium battery, provides support for lithium risk assessment and battery safety management.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of lithium battery state monitoring, in particular to a lithium battery digital twin online state estimation method and system. BACKGROUND

[0002] With the rapid development of new energy vehicles, power storage and other fields, lithium ion battery packs are increasing in capacity and are being used in increasingly complex environments, which puts higher requirements on the safety, reliability and fine management level of battery management systems (BMS). Accurate monitoring of battery internal microstate (such as positive and negative electrode particle concentration distribution) and macrostate of charge (SOC) is the key to ensuring safe operation and prolonging the service life of the battery. Existing lithium battery state estimation techniques are mainly divided into three categories, each of which has significant defects:

[0003] The first category is a filtering estimation method based on an equivalent circuit model (ECM) or a strongly simplified electrochemical model. This type of method uses extended Kalman filter (EKF), unscented Kalman filter (UKF) and other algorithms to estimate the battery SOC online, but is limited by the simplified nature of the model itself, which simplifies the internal state of the battery to only two low-dimensional variables: "average concentration" and "surface concentration". This has obvious hysteresis and memory effects, and cannot capture the complete solid-phase concentration field distribution. This simplification results in significant hysteresis and memory effects in state estimation, leading to SOC prediction bias and difficulty in warning of lithium precipitation and other safety risks;

[0004] The second category is a numerical solution scheme based on a complete electrochemical model. To improve estimation accuracy, the academic and industrial communities have proposed single particle model (SPM), improved single particle model (SPMe), Doyle-Fuller-Newman model (DFN) and other schemes. These models can theoretically accurately describe the physical mechanisms of lithium ion diffusion, transport and reaction through partial differential equations (PDE). However, due to the high computational complexity and tedious iteration steps of PDE numerical solution, real-time performance is extremely poor, and even after simplification, it is still difficult to directly embed into resource-constrained vehicle BMS or embedded systems, making it impossible to meet the real-time requirements of online monitoring.

[0005] The third category is a black box model method based on machine learning. With the development of deep learning, there have been schemes that use neural networks to directly fit the terminal voltage-current relationship. This type of method can achieve good fitting accuracy within a specific data range, but lacks clear physical mechanism constraints, has poor interpretability, and has insufficient generalization ability, making it difficult to adapt to the aging process and complex and variable working conditions throughout the battery's life cycle. At the same time, this type of black box model cannot be naturally combined with state space-based filtering algorithms, which is not conducive to the construction of a battery digital twin system that can be physically explained and corrected in real time.

[0006] In recent years, unlike the traditional neural network modeling approach of directly mapping input and output, operator learning methods represented by Fourier Neural Operator (FNO) have emerged. It approximates the solution operator of PDE by learning integral operators in the frequency domain, realizing the mapping from function space to function space. Compared with methods based on discrete numerical solution or neural network point value regression, FNO can directly output high-fidelity physical fields at a speed of several orders of magnitude faster, and has resolution independence. However, as an open-loop predictor, the solving ability of the pure FNO model cannot perfectly adapt to the solution of the battery solid-phase diffusion equation, and it also faces the problems of model bias accumulation and initial state uncertainty, making it difficult to independently cope with battery aging and working condition changes throughout the life cycle. Therefore, how to combine the high-efficiency physical field derivation capability of FNO with the closed-loop correction capability of the state observer to construct a battery digital twin system with physical interpretation and real-time correction is a technical problem that needs to be solved at present. SUMMARY

[0007] To achieve the above object, the present application provides the following scheme:

[0008] In a first aspect, the present application provides a lithium battery digital twin online state estimation method, comprising the following steps:

[0009] Training a TP-FNO model based on a sample set, the TP-FNO model being used to map lithium battery working condition parameters and spatiotemporal variables to positive and negative active particle lithium ion solid-phase concentration distribution, wherein the solid-phase concentration distribution at least includes particle surface concentration and particle center concentration;

[0010] Embedding the trained TP-FNO model into a nonlinear state space equation, and based on the system state posterior estimation at the previous time and the input at the current time, calculating the system state prior estimation and covariance prior;

[0011] According to the system state prior estimation, calculating the voltage prediction value through the observation equation, and obtaining the corresponding real-time measurement value, calculating the difference between the two as the observation residual;

[0012] Using a state estimation algorithm, updating the system state prior estimation and covariance prior based on the observation residual, to obtain the system state posterior estimation and covariance posterior;

[0013] Taking the system state posterior estimation and covariance posterior result as new system state information, used to construct the input features of the TP-FNO model at the next time and perform recursive prediction, forming a closed loop of model prediction and posterior correction.

[0014] Preferably, the TP-FNO model comprises an input dimension increasing layer, at least one physically enhanced three-parallel-operators layer and an output feature reconstruction layer connected in sequence, wherein:

[0015] The input dimension increasing layer is configured to map the input feature to a high-dimensional feature space through linear transformation;

[0016] The physically enhanced three-parallel-operators layer is integrated with a globally spectral convolution operator, an explicit diffusion differential operator and a residual enhancement operator connected in parallel, and the three-parallel-operators layer adds the outputs of the three operators element by element and then processes the sum through the same nonlinear activation function to obtain the output of the layer;

[0017] The output feature reconstruction layer is configured to map the output of the physically enhanced three-parallel-operators layer to the solid-phase lithium ion concentration distribution in the positive and negative active particles.

[0018] Preferably, the globally spectral convolution operator is configured to perform Fourier transform on the input feature, multiply the input feature with a learnable complex weight point by point in the frequency domain, and then inverse transform back to the spatial domain to complete the global operator mapping;

[0019] The explicit diffusion differential operator is configured to perform differential operation on the input feature according to a learnable diffusion coefficient weight within a predefined local receptive field to complete ion diffusion flux simulation;

[0020] The residual enhancement operator mixes the input feature through a standard convolution layer, and adds the mixed feature and the input feature in short circuit.

[0021] Preferably, the TP-FNO model is trained by a weighted loss function, and the weighted loss function at least includes: a mean square error main loss term for evaluating the accuracy of the overall concentration field, a surface special loss term for strengthening the prediction accuracy of the surface concentration of the constrained particles, and a regularization loss term for controlling the complexity of the model.

[0022] Preferably, the calculation of the system state prior estimate includes: constructing a system state vector containing the state of charge of the lithium battery and the finite-dimensional concentration of lithium ions in the positive and negative active particles; combining the trained TP-FNO model with the ampere-hour integral method for updating the state of charge to construct a state transition function; based on the state transition function, substituting the system state posterior estimate at the previous time and the input at the current time to calculate the system state prior estimate at the current time;

[0023] The calculation of the covariance prior includes: calculating the partial derivative of the state transition function with respect to the system state vector to obtain a state transition Jacobian matrix; and calculating the covariance prior at the current time according to the state transition Jacobian matrix, the covariance posterior at the previous time and a process noise matrix.

[0024] Preferably, the observation equation is composed of four parts: open circuit voltage curve, reaction overpotential, ohmic voltage drop and observation noise, wherein the open circuit voltage curve is determined by the test after the battery is shipped, the reaction overpotential is calculated by the electrochemical Butler-Volmer formula, and its value is determined by at least the finite dimensional concentration of lithium ions in the positive and negative active particles, the ohmic voltage drop is determined by the product of the ohmic internal resistance of the battery and the real-time working current, and the observation noise is used to represent the uncertainty interference in the observation process.

[0025] Preferably, the state estimation algorithm is used to update the prior estimation and covariance of the system state based on the observation residual, and obtain the posterior estimation and covariance of the system state, including:

[0026] The partial derivative of the observation equation with respect to the system state vector is calculated to obtain the observation Jacobian matrix;

[0027] Based on the covariance prior, the innovation covariance is calculated by combining the observation Jacobian matrix and the preset observation noise covariance matrix, and the observation noise covariance matrix is determined according to the measurement accuracy of the voltage sensor of the battery management system;

[0028] Based on the innovation covariance, the observation Jacobian matrix and the covariance prior, the Kalman gain is further calculated;

[0029] Based on the observation residual and the Kalman gain, the prior estimation of the system state is corrected to obtain the posterior estimation of the system state at the current time;

[0030] Based on the covariance prior, the observation Jacobian matrix and the Kalman gain, the covariance posterior is calculated.

[0031] Preferably, after forming the closed loop of model prediction and posterior correction, the digital twin safety evaluation step is further included: based on the posterior estimation of the system state, at least one micro-safety evaluation index is calculated to quantify the lithium precipitation risk of the lithium battery, and the micro-safety evaluation index is fed back to the battery management system to dynamically adjust the battery charging and discharging strategy, and the micro-safety evaluation index at least includes one of the following: surface concentration margin, concentration gradient, potential margin, and comprehensive risk index obtained by weighted combination of the above three.

[0032] Preferably, the surface concentration margin is the difference between the surface concentration of the negative electrode particles extracted based on the posterior estimation of the system state and the maximum allowable concentration of the negative electrode material;

[0033] The concentration gradient is the difference between the surface concentration of the negative electrode particles and the central concentration; the potential margin is the difference between the negative electrode potential determined based on the surface concentration of the negative electrode and the real-time current and the preset critical potential; and the comprehensive risk index is the weighted sum of the surface concentration margin, the concentration gradient, and the potential margin.

[0034] In a second aspect, the present application also provides a lithium battery digital twin online state estimation system, which comprises a memory and a processor, the memory stores a computer program, and the processor executes the steps of the lithium battery digital twin online state estimation method of the first aspect.

[0035] The lithium battery digital twin online state estimation method provided by the present application has the following beneficial effects: (1) high fidelity and real-time performance: the pre-trained TP-FNO model can approximately solve high-dimensional PDEs such as solid-phase diffusion, convert complex electrochemical processes into a single forward inference, greatly reduce the computational load, and accurately restore the concentration field distribution of positive and negative electrode particles, which is suitable for real-time online application of embedded systems such as BMS. (2) Macro-micro full-dimensional joint estimation: the state vector synchronously contains SOC and the concentration field distribution of positive and negative electrode particles, and the state transfer function is constructed by TP-FNO (responsible for concentration field state transfer prediction) and ampere-hour integration method (responsible for SOC update) in cooperation, realizing full-dimensional internal state joint estimation of the battery and improving the fitting degree of the digital twin model to the real battery behavior. (3) Explainable and easy to land: the TP-FNO model retains the physical structure information of the electrochemical process, and forms a "physical constraint + closed-loop correction" dynamic model with the state estimation algorithm, which has stronger explainability than pure black box data-driven methods, is easy to verify and safety certified, and reduces the landing threshold. (4) Precise early warning of safety risks: based on the micro information of the concentration field, the safety evaluation index related to lithium precipitation is calculated, the potential risks are quantified accurately, high-value feedback is provided for BMS or control strategy, and safety hazards are avoided in advance. (5) Strong cross-platform adaptability: the TP-FNO model has resolution independence, and can adapt to different resolutions or non-uniform grid inferences without retraining, which can flexibly match BMS hardware with different computing power and sampling accuracy, reducing the cost of algorithm transplantation and calibration. BRIEF DESCRIPTION OF DRAWINGS

[0036] Figure 1 A flowchart of the lithium battery digital twin online state estimation method according to the present application;

[0037] Figure 2 A concentration prediction error diagram of the TP-FNO model under a specific test condition;

[0038] Figure 3 A structural diagram of the lithium battery digital twin online state estimation system according to the present application. DETAILED DESCRIPTION

[0039] In order to make the objects, technical solutions and advantages of the present application clearer, the present application will be specifically described below in conjunction with embodiments and drawings, but the protection scope of the present application is not limited thereto.

[0040] Referring to the drawings Figure 1 The present application relates to a lithium battery digital twin online state estimation method, which comprises the following steps:

[0041] Step 1. Training a TP-FNO model based on a sample set, the TP-FNO model being used to map lithium battery operating condition parameters and spatiotemporal variables to positive and negative active particle internal lithium ion solid phase concentration distribution without solving partial differential equations, wherein the solid phase concentration distribution at least includes particle surface concentration and particle center concentration;

[0042] In one embodiment, training the TP-FNO model comprises:

[0043] Step 1.1. Constructing a sample set, the core requirement of the sample set being: containing lithium battery operating condition parameters, spatiotemporal variable related input features, and corresponding solid phase concentration field distribution output data, and the input features need to cover the operating condition diversity and data effectiveness required for model training, and the output data need to accurately reflect the concentration distribution law from the center to the surface of the positive and negative electrode particles (including particle surface concentration and center concentration). The specific construction method of the sample set is not limited, as long as the above data matching and effectiveness requirements are met, it can be used for TP-FNO model training. In one embodiment, the construction process of the sample set is: using a finite difference method (FDM) high-fidelity numerical solver, for randomly generated multi-current operating conditions (including constant current, step and dynamic current modes) and random initial electrode concentration, the battery solid phase diffusion partial differential equation is adaptively stepped numerically solved. This solving process can accurately capture the spatiotemporal coupled solid phase concentration field evolution law in the battery particles, and finally generate 10000 effective samples, each sample containing 4-channel input features (current, initial concentration, normalized radius, and normalized time), and the corresponding N-dimensional solid phase concentration field output at the next time (N-dimensional discrete points from the center to the surface of the particle, the default value is 64). The sample generation process uses multi-process parallel computing to improve efficiency, and introduces mass conservation physical constraints to screen out invalid samples, ensuring data effectiveness, and providing high-quality data support for stable training of the TP-FNO model.

[0044] In one embodiment, the solid phase partial differential equation is represented by the spherical coordinate form of the second Fick's law, and in order to obtain a unique solution of the partial differential equation, two physical boundary conditions are applied in this embodiment: a spherical symmetry boundary condition at the center of the particle, which assumes that the lithium ion distribution inside the particle is radially symmetric, and the concentration gradient at the center of the sphere is zero, and a flux boundary condition at the surface of the particle, which establishes a physical coupling relationship between the macroscopic input current and the microcosmic concentration field evolution, and is also the physical basis for taking the current as a key input feature when constructing the TP-FNO model later.

[0045] Step 1.2. Constructing a TP-FNO model comprising an input upsampling layer, at least one physical enhanced three-way parallel operator layer and an output downsampling layer connected in sequence, wherein:

[0046] In one embodiment, the input upsampling layer is used to map the input features to a high-dimensional feature space through linear transformation; in one embodiment, the input tensor of the TP-FNO is consistent with the input features of the sample set constructed in step 1.1, which is composed of four channel features: real-time current, solid phase concentration field distributed along the radial direction at the current time, spatial coordinate feature and time step. Subsequently, the four-channel input is sent to the input upsampling layer for processing, and the upsampling operation can be realized by basic operators such as linear mapping, and the specific implementation manner is not limited in the present scheme.

[0047] In one embodiment, the physical enhanced three-way parallel operator layer integrates a globally spectral convolution operator, an explicit diffusion differential operator and a residual enhancement operator connected in parallel, and the output of the three operators is added element by element, and then processed by the same nonlinear activation function to obtain the output of the layer;

[0048] Wherein, the global spectral convolution operator is used to perform Fourier transform on the upsampled input features, and after point-by-point complex multiplication operation with learnable complex weights in the frequency domain, it is inversely transformed back to the spatial domain to complete the global operator mapping and realize accurate capture of the long-range dependence relationship and overall distribution trend of the electrochemical concentration field;

[0049] The explicit diffusion differential operator is consistent with the form of the solid phase diffusion partial differential equation of the battery, and is used to perform differential operation on the input features according to the learnable diffusion coefficient weight within the predefined local receptive field, complete the ion diffusion flux simulation, and efficiently restore the local diffusion / gradient propagation process of lithium ions inside the solid phase particle; in one embodiment, the predefined local receptive field is 3x3, and the learnable diffusion coefficient weight is constructed by discrete difference form;

[0050] The residual enhancement operator is used for efficient channel mixing of the input features through a 1x1 standard convolution layer, improving the cross-feature interaction capability, and then adding the mixed features and the input features in a short circuit to ensure effective transmission of feature information and stable training of the deep network.

[0051] Through the scheme, compared with the traditional FNO network using spectral convolution, the parallel fusion structure realizes the organic combination of global spectral operator and local diffusion prior, which can capture the long-range coupling of the electrochemical concentration field (global effect) through the global spectral convolution operator, and can efficiently simulate the local diffusion / gradient propagation (local effect) through the explicit diffusion differential operator, while the residual enhancement operator strengthens the cross-feature interaction capability, and finally completes the approximate replacement of the concentration field evolution with one forward propagation, significantly reduces the calculation cost, and meets the real-time deployment requirements of edge devices.

[0052] In one embodiment, the output dimension reduction layer is used to map the output of the physical enhancement three-way parallel operator layer back to the target physical space. As the terminal mapping module of the TP-FNO model, the output dimension reduction layer receives the high-dimensional features processed by the physical enhancement three-way parallel operator layer, and accurately maps the high-dimensional abstract features back to the target physical space through linear transformation and feature compression operation, and finally outputs the prediction results corresponding to the actual physical meaning, that is, the feature matrix containing the concentration of the positive and negative electrode particles on the surface of the lithium battery, the central concentration and the global solid concentration field distribution. The core role of the output dimension reduction layer is to strip the high-dimensional feature redundancy introduced in the model training process, retain the key information directly related to the electrochemical concentration field, and ensure that the output results not only conform to the dimensional constraints of physical quantities, but also can directly provide accurate microstate inputs for subsequent system state vector construction and state estimation steps, realizing the closed-loop conversion from feature learning to physical quantity output.

[0053] Step 1.3. Model training, in one embodiment, the model training process is as follows: input the training data set constructed by step 1.1 into the TP-FNO network built in step 1.2, and use an adaptive optimizer to iteratively optimize the model parameters, wherein the training batch size is set to 64, the total training rounds are set to 100 rounds, and the initial learning rate is configured to 0.002; in order to improve the stability and convergence effect of model training, the cosine annealing learning rate scheduling strategy is introduced at the same time, and the learning rate is dynamically adjusted according to the training rounds, so that the model can quickly explore the parameter space in the early stage of training and accurately converge to the optimal solution in the later stage; at the same time, the gradient clipping strategy is adopted, and the gradient clipping threshold is set to 1.0, which limits the gradient generated in the training process to avoid model training shock or non-convergence caused by gradient explosion, and finally the parameter optimization of the TP-FNO network is completed through the above training strategies, and a trained model with concentration field prediction capability is obtained.

[0054] In one embodiment, the training of the TP-FNO model employs a weighted loss function for optimization, which at least includes: a mean square error main loss term for evaluating the overall concentration field accuracy, a surface special loss term for strengthening the prediction accuracy of the constrained particle surface concentration, and a regularization loss term for controlling the model complexity. In one embodiment, the total loss function is composed of three parts, each part is adjusted by a preset weighting coefficient to adjust the weight proportion, and the sum of all weighting coefficients is 1, and the exemplary values are: the weight a of the mean square error main loss term is 0.5, the weight b of the particle surface concentration special loss term is 0.4, and the weight c of the regularization loss term is 0.1. Among them, the mean square error main loss term is used to evaluate the overall fitting accuracy of the global solid phase concentration field predicted by the model and the true concentration field, to ensure the global prediction reliability of the concentration field distribution; the particle surface concentration loss is specially calculated for the mean square error of the positive and negative electrode particle surface concentration, which can improve the weight proportion of this loss term to force the model to focus on optimizing the prediction effect of the surface high gradient area in the training process, and reduce the estimation error of the key area; the regularization loss term is used to constrain the square sum of all learnable parameters of the model, effectively inhibiting model overfitting, controlling network complexity, and ensuring the stable generalization ability of the model under different working conditions. Accordingly, the estimation accuracy of the digital twin system for the surface state of the lithium battery electrode can be effectively improved, and the technical problem of high prediction error prone to occur in the particle surface concentration gradient of the battery is solved.

[0055] According to the TP-FNO model trained according to the above steps, the solid phase concentration field distribution can be deduced according to the current time lithium battery working condition parameters and space-time variables. To verify its prediction accuracy, Figure 2 The concentration prediction error of the model under a specific test working condition is exemplarily shown.

[0056] In one embodiment, the TP-FNO works in a self-recurrent manner, and the prediction at each time strictly depends on the state input at the previous time. If the initial state is not clear or accurate, it will cause the recursive process to fail to start or make the prediction error continuously accumulate and spread in the time dimension. To start the recursive prediction of the TP-FNO model and ensure the accuracy of its time recursion, the complete initial state of the system at zero time must be established, which specifically includes:

[0057] Collecting measured current and terminal voltage data of the battery at an initial moment, and preprocessing the data; determining the initial state of charge of the battery based on the preprocessed initial terminal voltage and the pre-stored empirical curve of open-circuit voltage of the battery; and calculating the initial average lithium ion concentration of the positive and negative electrode particles according to the initial state of charge, the pre-defined maximum lithium ion concentration of the positive and negative active materials, and the pre-stored empirical curve of open-circuit voltage of the positive and negative electrodes through electrochemical equilibrium relationship; wherein the determined initial state of charge and the calculated initial average lithium ion concentration jointly constitute the complete initial state of the system at zero moment, which is used to initialize the autoregressive recursive prediction process of the TP-FNO model.

[0058] Step 2. Embed the trained TP-FNO model in a nonlinear state space equation, and calculate the system state prior estimation and covariance prior based on the system state posterior estimation at the previous moment and the input at the current moment.

[0059] In one embodiment, calculating the system state prior estimation comprises: constructing a system state vector containing the state of charge of the lithium battery and the finite-dimensional concentration of lithium ions in the positive and negative active particles, it is noted that the system state vector of the finite-dimensional concentration of lithium ions in the positive and negative active particles is obtained from the solid-phase concentration distribution of lithium ions in the positive and negative active particles, the present application uses the finite-dimensional concentration of lithium ions in the positive and negative active particles instead of the solid-phase concentration of lithium ions in the positive and negative active particles for constructing the system state vector, mainly to reduce the cost and facilitate system landing; combining the trained TP-FNO model with the ampere-hour integral method for updating the state of charge to construct a state transition function, the formula of the state transition function is:

[0060]

[0061] In the formula, k represents the moment, represents the system state vector at k moment, represents the system state vector at k+1 moment, represents the input, i.e. the input current , is the process noise, represents calling the trained TP-FNO model, and respectively represent the negative electrode particle concentration distribution and the positive electrode particle concentration distribution at k moment, represents the state of charge at k+1 moment.

[0062] Based on the state transition function, substituting the system state posterior estimation at the previous moment and the input at the current moment, the system state prior estimation at the current moment is calculated.

[0063] In one embodiment, the calculating the covariance prior includes: calculating partial derivatives of the state transition function with respect to the system state vector to obtain a state transition Jacobian matrix, it is to be noted that the partial derivatives of the state transition function with respect to the system state vector can be calculated by an automatic differentiation method, a numerical difference method or a combination thereof, which is not limited here; calculating the covariance prior at the current time according to the state transition Jacobian matrix, the covariance posterior at the previous time and a process noise matrix, in one embodiment, the process noise matrix is constructed based on the prediction error characteristics of the TP-FNO model and the cumulative error characteristics of the integral method, and a diagonal matrix form is used to achieve accurate quantization.

[0064] Step 3. According to the system state prior estimate, the voltage prediction value is calculated by the observation equation, and the corresponding real-time measurement value is obtained, and the difference between the two is calculated as the observation residual.

[0065] In one embodiment, the observation equation is composed of four parts: open circuit voltage curve, reaction overpotential, ohmic voltage drop and observation noise. The open circuit voltage curve is determined by the test after the battery is shipped, which represents the inherent mapping relationship between the state of charge of the lithium battery and the open circuit voltage, and provides a basic reference benchmark for voltage prediction. The reaction overpotential is calculated by the electrochemical Butler-Volmer formula and its value is determined by at least the finite concentration of lithium ions in the positive and negative active particles. By affecting the electrode reaction kinetics process to change the overpotential value, the calculation of the overpotential is accurately associated with the micro-reaction state of the battery. The ohmic voltage drop is determined by the product of the ohmic internal resistance of the battery and the real-time working current, wherein the ohmic internal resistance is the inherent resistance of the battery internal electrolyte, electrode current collector and other components, which can be obtained by factory test or online identification, and the real-time working current is the working condition input parameter at the current time, which ensures that the calculation of the ohmic voltage drop reflects the real-time working state. The observation noise is used to represent the uncertainty interference in the observation process, including the random deviation caused by the measurement error of the voltage sensor, environmental electromagnetic interference and other factors, which can be used to ensure the modeling integrity of the observation equation. After the voltage prediction value is calculated by the above observation equation, the real-time voltage measurement value of the lithium battery at the current time is collected by the voltage sensor carried by the battery management system, and then the difference between the voltage prediction value and the real-time measurement value is calculated, which is the observation residual. The observation residual directly reflects the deviation between the system state prior estimate and the actual battery running state, which provides a core basis for subsequent system state posterior correction based on the state estimation algorithm.

[0066] Step 4. The state estimation algorithm is used to update the system state prior estimate and the covariance prior based on the observation residual to obtain the system state posterior estimate and the covariance posterior. It is to be noted that the state estimation algorithm can be extended Kalman filter, unscented Kalman filter, cubature Kalman filter or particle filter, which is not limited here.

[0067] In one embodiment, the state estimation algorithm is an extended Kalman filter algorithm, which takes the observation residual as the core correction basis, iteratively updates the prior estimation of system state and the prior covariance, and finally obtains the posterior estimation of system state and the posterior covariance with high precision. The specific steps include:

[0068] Step 4.1. Calculate the partial derivative of the observation equation with respect to the system state vector to obtain the observation Jacobian matrix;

[0069] Step 4.2. Based on the prior covariance, the observation Jacobian matrix and the preset observation noise covariance matrix, the innovation covariance is calculated. The observation noise covariance matrix is determined according to the measurement accuracy of the battery management system voltage sensor;

[0070] Step 4.3. Based on the innovation covariance, the observation Jacobian matrix and the prior covariance, the Kalman gain is further calculated;

[0071] Step 4.4. Based on the observation residual and the Kalman gain, the prior estimation of system state is corrected to obtain the posterior estimation of system state at the current time;

[0072] Step 4.5. Based on the prior covariance, the observation Jacobian matrix and the Kalman gain, the posterior covariance is calculated.

[0073] Step 5. The posterior estimation of system state and the posterior covariance result are used as new system state information to construct the input features of the next time of the TP-FNO model and perform recursive prediction, forming a closed loop of model prediction and posterior correction.

[0074] In one embodiment, after the closed loop of model prediction and posterior correction, a digital twin safety evaluation step is further included: based on the posterior estimation of system state, at least one micro-safety evaluation index is calculated to quantify the lithium precipitation risk of the lithium battery, and the micro-safety evaluation index is fed back to the battery management system to dynamically adjust the battery charging and discharging strategy. The micro-safety evaluation index includes at least one of the following: surface concentration margin, concentration gradient, potential margin, and comprehensive risk index obtained by weighted combination of the above three, wherein:

[0075] The surface concentration margin is the difference between the surface concentration of the negative electrode particles extracted based on the posterior estimation of system state and the maximum allowed concentration of the negative electrode material. This index directly reflects the distance between the surface concentration of the negative electrode particles and the lithium precipitation critical concentration. The smaller the difference, the higher the risk of lithium precipitation.

[0076] The concentration gradient is the difference between the surface concentration of the negative electrode particles and the central concentration, and its value represents the balance of ion diffusion in the negative electrode particles. The larger the gradient, the greater the ion diffusion resistance, and the more likely it is to cause lithium ion accumulation on the negative electrode surface, thereby triggering lithium precipitation risk.

[0077] The potential margin is the difference between the negative electrode potential determined based on the negative electrode surface concentration and the real-time current and the preset critical potential. This indicator directly determines the risk of lithium precipitation from the perspective of electrochemical potential. When the difference is less than or equal to 0, it indicates that lithium precipitation has occurred. The smaller the difference, the more serious the lithium precipitation.

[0078] The comprehensive risk index is the weighted sum of the surface concentration margin, the concentration gradient, and the potential margin. By presetting the weight coefficients of each indicator (calibrated according to different battery types and application scenarios), multiple dimensions of lithium precipitation influencing factors are comprehensively considered to form a single quantitative indicator, which facilitates the battery management system to quickly determine the overall lithium precipitation risk level. Exemplary weight coefficients are: surface concentration margin weight a = 0.4, concentration gradient weight b = 0.3, and potential margin weight c = 0.3, satisfying a + b + c = 1 (which can be adjusted according to the battery type, such as increasing the potential margin weight to 0.5 under low-temperature conditions); At the same time, the risk level threshold is preset: comprehensive risk index RI ≥ 0.8 is low risk (normal charging and discharging), 0.3 ≤ RI < 0.8 is medium risk (reduce the charging and discharging rate to 1C or less), and RI < 0.3 is high risk (stop charging and discharging). The battery management system dynamically adjusts the charging and discharging strategy according to the risk level to avoid lithium precipitation hazards in advance.

[0079] Through the above closed-loop iteration and safety evaluation steps, the lithium precipitation-related safety evaluation indicators are calculated based on the concentration field micro information, the potential risk is accurately quantified, and high-value feedback is provided for the BMS or control strategy to avoid safety hazards in advance.

[0080] Figure 3 The application provides a structure diagram of a lithium battery digital twin online state estimation system, as shown in Figure 3 The system includes:

[0081] A model training module is configured to train a TP-FNO model based on a sample set, and the TP-FNO model is used to map lithium battery operating parameters and spatiotemporal variables to a solid-phase concentration field distribution containing particle surface concentration and central concentration.

[0082] A prediction module is configured to embed the trained TP-FNO model into a nonlinear state space equation, and based on the system state posterior estimation at the previous time and the input at the current time, calculate the system state prior estimation and covariance prior.

[0083] An observation residual calculation module is configured to calculate a voltage prediction value according to the system state prior estimation through an observation equation, obtain a real-time measurement value, and calculate a difference between the two values as an observation residual;

[0084] A state correction module is configured to update the system state prior estimation and covariance prior based on the observation residual by using a state estimation algorithm, and obtain a system state posterior estimation and covariance posterior.

[0085] A closed-loop iteration module is configured to use the system state posterior estimation and covariance posterior as new system state information to construct an input feature of the TP-FNO model at a next time and perform recursive prediction, thereby forming a closed loop of model prediction and posterior correction.

[0086] The above modules are used to execute the method provided in the foregoing embodiments, and have similar implementation principles and technical effects, which will not be described here. The above modules can be one or more integrated circuits configured to implement the above method, for example, one or more application specific integrated circuits (ASICs), or one or more digital signal processors (DSPs), or one or more field programmable gate arrays (FPGAs), etc. For another example, when the above module is implemented in the form of a processing element scheduling code, the processing element can be a general-purpose processor, such as a central processing unit (CPU) or other processor that can call code. For another example, the modules can be integrated together to implement a system-on-a-chip (SOC).

[0087] Optionally, the embodiments of the present application also provide a lithium battery digital twin online state estimation system, which comprises a processor and a storage medium, and the storage medium stores machine readable instructions executable by the processor. When the electronic device is running, the processor executes the machine readable instructions to perform the steps of the above method embodiments. The specific implementation and technical effects are similar, which will not be described here.

[0088] In several embodiments provided in the present application, it should be understood that the disclosed system and method can be implemented in other manners. For example, the division of the above-described apparatus embodiments is merely an example, and there can be other division manners. For example, the units or components can be combined or integrated into another system, or some features can be ignored or not executed. In addition, the displayed or discussed mutual couplings or direct couplings or communication connections can be indirect couplings or communication connections through some interfaces, devices or units, and can be in electrical, mechanical or other forms.

[0089] The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, i.e., they can be located in one place or distributed on multiple network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the embodiment.

[0090] In addition, the functional units in each embodiment of the present application can be integrated into a processing unit, or each unit can be physically present separately, or two or more units can be integrated into one unit. The integrated unit can be realized in the form of hardware or in the form of hardware plus software functional units.

[0091] The integrated unit realized in the form of software functional units can be stored in a computer readable storage medium. The software functional units stored in the storage medium include a plurality of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) or a processor (English: processor) to execute part of the steps of the method described in each embodiment of the present application. The foregoing storage medium includes a U disk, a mobile hard disk, a read-only memory (English: Read-Only Memory, abbreviated as: ROM), a random access memory (English: Random Access Memory, abbreviated as: RAM), a magnetic disk or an optical disk, and various program code storage media.

[0092] The above is only a preferred embodiment of the present application and is not intended to limit the present application. For those skilled in the art, the present application can have various modifications and changes. Any modification, equivalent replacement, improvement, etc. within the spirit and principles of the present application shall be included in the protection scope of the present application.

Claims

1. A method for online state estimation of lithium battery digital twin, characterized in that, The method comprises: training a TP-FNO model based on a sample set, the TP-FNO model being used for mapping lithium battery operating condition parameters and spatiotemporal variables to a lithium ion solid-phase concentration distribution in positive and negative active particles, wherein the solid-phase concentration distribution at least includes a particle surface concentration and a particle center concentration; the TP-FNO model comprises an input dimension increasing layer, at least one physical enhanced three-way parallel operator layer and an output feature reconstruction layer connected in sequence, wherein: the input dimension increasing layer is used for mapping input features to a high-dimensional feature space through linear transformation; the physical enhanced three-way parallel operator layer integrates a globally spectral convolution operator, an explicit diffusion differential operator and a residual enhancement operator connected in parallel, the three-way parallel operator layer elementwisely adds outputs of the three operators and processes the added outputs through a same nonlinear activation function to obtain an output of the layer; the output feature reconstruction layer is used for mapping an output of the physical enhanced three-way parallel operator layer to the lithium ion solid-phase concentration distribution in the positive and negative active particles; embedding the trained TP-FNO model into a nonlinear state space equation and calculating a system state prior estimation and a covariance prior based on a system state posterior estimation at a previous moment and an input at a current moment; calculating a voltage prediction value through an observation equation according to the system state prior estimation, obtaining a corresponding real-time measurement value and calculating a difference between the two values as an observation residual; updating the system state prior estimation and the covariance prior based on the observation residual by using a state estimation algorithm to obtain a system state posterior estimation and a covariance posterior; taking the system state posterior estimation and the covariance posterior result as new system state information for constructing an input feature of the TP-FNO model at a next moment and performing recursive prediction to form a closed loop of model prediction and posterior correction.

2. The lithium battery digital twin online state estimation method according to claim 1, wherein: the globally spectral convolution operator is used for performing Fourier transform on the input features, performing point-by-point complex multiplication operation with learnable complex weights in the frequency domain and inversely transforming back to the spatial domain to complete global operator mapping; the explicit diffusion differential operator is used for performing differential operation on the input features according to a learnable diffusion coefficient weight within a predefined local receptive field to complete ion diffusion flux simulation; the residual enhancement operator performs channel mixing on the input features through a standard convolution layer and adds the mixed features and the input features in short circuit. 3.The lithium battery digital twin online state estimation method of claim 1, wherein, The TP-FNO model is trained through a weighted loss function, and the weighted loss function at least includes: a mean square error main loss term for evaluating the accuracy of the overall concentration field, a surface special loss term for strengthening the prediction accuracy of the particle surface concentration and a regularization loss term for controlling the model complexity. 4.The lithium battery digital twin online state estimation method of claim 1, wherein, The calculation of the system state prior estimation comprises: constructing a system state vector comprising the state of charge of the lithium battery, the finite-dimensional concentration of lithium ions in the positive and negative active particles; combining the trained TP-FNO model with the ampere-hour integral method for updating the state of charge to construct a state transition function; based on the state transition function, substituting the system state posterior estimation at the previous time and the input at the current time to calculate the system state prior estimation at the current time; The calculation of the covariance prior comprises: calculating the partial derivative of the state transition function with respect to the system state vector to obtain a state transition Jacobian matrix; and calculating the covariance prior at the current time according to the state transition Jacobian matrix, the covariance posterior at the previous time, and a process noise matrix.

5. The lithium battery digital twin online state estimation method of claim 4, wherein, The observation equation is composed of four parts: an open-circuit voltage curve, a reaction overpotential, an ohmic voltage drop, and an observation noise, wherein the open-circuit voltage curve is determined by testing after the battery is manufactured, the reaction overpotential is calculated by the electrochemical Butler-Volmer formula and its value is determined by at least the finite-dimensional concentration of lithium ions in the positive and negative active particles, the ohmic voltage drop is determined by the product of the ohmic internal resistance of the battery and the real-time working current, and the observation noise is used to represent the uncertainty interference in the observation process.

6. The lithium battery digital twin online state estimation method of claim 5, wherein, The state estimation algorithm is used to update the system state prior estimation and the covariance prior based on the observation residual to obtain the system state posterior estimation and the covariance posterior, comprising: calculating the partial derivative of the observation equation with respect to the system state vector to obtain an observation Jacobian matrix; based on the covariance prior, combining the observation Jacobian matrix with a preset observation noise covariance matrix to calculate an innovation covariance, wherein the observation noise covariance matrix is determined according to the measurement accuracy of the voltage sensor of the battery management system; further calculating a Kalman gain based on the innovation covariance, the observation Jacobian matrix, and the covariance prior; based on the observation residual and the Kalman gain, correcting the system state prior estimation to obtain the system state posterior estimation at the current time; based on the covariance prior, the observation Jacobian matrix, and the Kalman gain, calculating the covariance posterior.

7. The lithium battery digital twin online state estimation method of claim 1, wherein, After forming the closed loop of model prediction and posterior correction, the method further comprises a digital twin safety evaluation step: based on the system state posterior estimation value, calculating at least one micro-safety evaluation index to quantify the lithium precipitation risk of the lithium battery, and feeding back the micro-safety evaluation index to the battery management system for dynamically adjusting the battery charging and discharging strategy, wherein the micro-safety evaluation index at least comprises one of the following: a surface concentration margin, a concentration gradient, a potential margin, and a comprehensive risk index obtained by weighted combination of the above three.

8. The lithium battery digital twin online state estimation method of claim 7, wherein, The surface concentration margin is the difference between the surface concentration of the negative electrode particles and the maximum allowable concentration of the negative electrode material based on the system state posterior estimation value; the concentration gradient is the difference between the surface concentration of the negative electrode particles and the central concentration; the potential margin is the difference between the negative electrode potential and the preset critical potential determined based on the surface concentration of the negative electrode particles and the real-time current; and the comprehensive risk index is the weighted sum of the surface concentration margin, the concentration gradient, and the potential margin. 9.A lithium battery digital twin online state estimation system, comprising a memory and a processor, the memory storing a computer program, characterized in that: The processor implements the steps of the lithium battery digital twin online state estimation method according to any one of claims 1-8 when executing the computer program.

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