Lithium battery digital twin online state estimation method and system

Abstract

The invention relates to a lithium battery digital twin online state estimation method and system, and belongs to the technical field of lithium battery state monitoring. Comprising the following steps: training a TP-FNO model, and mapping working condition parameters and time-space variables into lithium ion solid phase concentration distribution in positive and negative active particles; the model is embedded into a nonlinear state-space equation, and system state priori estimation and covariance priori are obtained in combination with system state posteriori estimation at the previous moment and current input; calculating a voltage prediction value through an observation equation, and comparing the voltage prediction value with a real-time measurement value to obtain an observation residual error; updating the system state prior estimation and the covariance prior by using the observation residual by adopting a state estimation algorithm to obtain system state posteriori estimation and covariance posteriori; and feeding back a posteriori estimation result, and constructing a model input feature at the next moment to realize closed-loop iteration. According to the method, a physical mechanism and data driving are fused, the internal microscopic state of the lithium battery can be accurately estimated on line, and support is provided for lithium precipitation risk assessment and battery safety management.

Description

Technical Field

[0001] This invention relates to the field of lithium battery state monitoring technology, specifically to an online state estimation method and system for lithium battery digital twins. Background Technology

[0002] With the rapid development of new energy vehicles and energy storage, lithium-ion battery packs are experiencing increasingly larger capacities and more complex operating environments, placing higher demands on the safety, reliability, and sophisticated management capabilities of battery management systems (BMS). Accurate monitoring of the battery's internal microstate (such as the concentration distribution of positive and negative electrode particles) and macroscopic state of charge (SOC) is crucial for ensuring safe battery operation and extending its lifespan. Existing lithium battery state estimation technologies are mainly divided into three categories, all of which have significant shortcomings:

[0003] The first category is filtering estimation methods based on equivalent circuit models (ECM) or strongly simplified electrochemical models. These methods often employ algorithms such as extended Kalman filtering (EKF) and unscented Kalman filtering (UKF) to estimate the battery's state of charge (SOC) online. However, limited by the simplification inherent in the models themselves, they reduce the battery's internal state to only two low-dimensional variables: "average concentration" and "surface concentration." This results in significant hysteresis and memory effects, failing to capture the complete solid-phase concentration field distribution. This simplification leads to significant hysteresis and memory effects in state estimation, causing SOC prediction errors and making it difficult to predict safety risks such as lithium plating.

[0004] The second category is numerical solution schemes based on complete electrochemical models. To improve estimation accuracy, academia and industry have proposed schemes such as the single-particle model (SPM), the improved single-particle model (SPMe), and the Doyle–Fuller–Newman model (DFN). These models can theoretically accurately describe the physical mechanisms of lithium-ion diffusion, transport, and reaction through partial differential equations (PDEs). However, due to the high computational complexity and cumbersome iterative steps of the PDE numerical solution process, its real-time performance is extremely poor. Even after simplification, it is still difficult to directly embed it into resource-constrained vehicle BMS or embedded systems, and thus cannot meet the real-time requirements of online monitoring.

[0005] The third category is black-box model methods based on machine learning. With the development of deep learning, schemes have emerged that directly fit the voltage-current relationship using neural networks. These methods can achieve good fitting accuracy within a specific data range, but they lack clear physical mechanism constraints, have poor interpretability, insufficient generalization ability, and are difficult to adapt to the aging process and complex and changing operating conditions throughout the battery's entire life cycle. At the same time, these black-box models cannot be naturally combined with state-space based filtering algorithms, which is not conducive to building a physically interpretable and real-time correctable battery digital twin system.

[0006] In recent years, unlike the traditional neural network modeling approach that directly maps input to output, operator learning methods, represented by the Fourier Neural Operator (FNO), have emerged. These methods approximate the solution operator of a PDE by learning an integral operator in the frequency domain, achieving a mapping from function space to function space. Compared to methods based on discrete numerical solutions or neural network point-value regression, FNO can directly output high-fidelity physical fields at speeds several orders of magnitude faster and is resolution-independent. However, a simple FNO model, as an open-loop predictor, cannot perfectly adapt to solving the battery solid-state diffusion equation and faces problems of model bias accumulation and initial state uncertainty, making it difficult to independently cope with battery aging and operating condition changes throughout its entire lifecycle. Therefore, how to combine the efficient physical field deduction 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 capabilities is a pressing technical problem that needs to be solved. Summary of the Invention

[0007] To achieve the above objectives, the present invention provides the following solution:

[0008] In a first aspect, the present invention provides an online state estimation method for lithium battery digital twins, the method comprising the following steps:

[0009] The TP-FNO model is trained based on the sample set. The TP-FNO model is used to map lithium battery operating parameters and spatiotemporal variables to the lithium ion solid phase concentration distribution in the positive and negative electrode active particles. The solid phase concentration distribution includes at least the particle surface concentration and the particle center concentration.

[0010] The trained TP-FNO model is embedded into a nonlinear state-space equation, and the system state prior estimate and covariance prior are calculated based on the system state posterior estimate of the previous time step and the input of the current time step.

[0011] Based on the prior estimation of the system state, the voltage prediction value is calculated through the observation equation, and the corresponding real-time measurement value is obtained. The difference between the two is calculated as the observation residual.

[0012] A state estimation algorithm is used to update the prior estimate of the system state and the prior covariance based on the observed residuals, so as to obtain the posterior estimate of the system state and the posterior covariance.

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

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

[0015] The input upscaling layer is used to map the input features to a high-dimensional feature space through a linear transformation.

[0016] The physical enhancement three-way parallel operator layer integrates a parallel-connected global spectral convolution operator, an explicit diffusion differential operator, and a residual enhancement operator. The three-way parallel operator layer adds the outputs of the three operators element by element and then processes them through the same nonlinear activation function to obtain the output of the layer.

[0017] The output feature reconstruction layer is used to map the output of the physically enhanced three-way parallel operator layer to the lithium ion solid phase concentration distribution within the positive and negative electrode active particles.

[0018] Preferably, the global spectral convolution operator is used to perform a Fourier transform on the input features, perform point-by-point complex multiplication with learnable complex weights in the frequency domain, and then inversely transform back to the spatial domain to complete the global operator mapping.

[0019] The explicit diffusion differential operator is used to perform differential operations on the input features within a predefined local receptive field based on learnable diffusion coefficient weights to complete the simulation of ion diffusion flux.

[0020] The residual enhancement operator performs channel mixing on the input features through a standard convolutional layer and then adds the mixed features to the input features via a short-circuit method.

[0021] Preferably, the TP-FNO model is trained using a weighted loss function, which includes at least: a mean squared error main loss term for evaluating the overall concentration field accuracy, a surface-specific loss term for enhancing the accuracy of particle surface concentration prediction, and a regularization loss term for controlling model complexity.

[0022] Preferably, the calculation of the prior estimate of the system state 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 electrode active particles; combining the trained TP-FNO model with the ampere-hour integral method used to update the state of charge to construct a state transition function; and based on the state transition function, substituting the posterior estimate of the system state at the previous moment and the input at the current moment to calculate the prior estimate of the system state at the current moment.

[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 the state transition Jacobian matrix; and calculating the covariance prior at the current time based on the state transition Jacobian matrix, the covariance posterior of the previous time step, and the process noise matrix.

[0024] Preferably, the observation equation consists of four parts: open-circuit voltage curve, reaction overpotential, ohmic voltage drop, and observation noise. The open-circuit voltage curve is determined by testing after the battery leaves the factory. The reaction overpotential is calculated using the electrochemical Butler-Volmer formula, and its value is determined at least by the finite-dimensional concentration of lithium ions in the positive and negative electrode active particles. The ohmic voltage drop is determined by the product of the battery's ohmic internal resistance and the real-time operating current. The observation noise is used to characterize the uncertainty interference during the observation process.

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

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

[0027] Based on the covariance prior, and combined with the observation Jacobian matrix and the preset observation noise covariance matrix, the innovative covariance is calculated. 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 aforementioned innovative covariance, observation Jacobian matrix, and covariance prior, the Kalman gain is further calculated.

[0029] Based on the observation residuals and Kalman gain, the prior estimate of the system state is corrected to obtain the posterior estimate of the system state at the current moment.

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

[0031] Preferably, after the closed loop of the formation model prediction and posterior correction, a digital twin safety assessment step is further included: based on the posterior estimate of the system state, at least one microscopic safety assessment index is calculated to quantify the lithium battery lithium plating risk, and the microscopic safety assessment index is fed back to the battery management system for dynamically adjusting the battery charging and discharging strategy. The microscopic safety assessment index includes at least one of the following: surface concentration margin, concentration gradient, potential margin, and a comprehensive risk index obtained by weighted combination of the first three.

[0032] Preferably, the surface concentration margin is the difference between the surface concentration of the negative electrode particles extracted based on the posterior estimate 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 and the center concentration of the negative electrode particles; 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; 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 invention also provides an online state estimation system for a lithium battery digital twin, the system comprising: a memory and a processor, the memory storing a computer program, and the processor executing the steps of the online state estimation method for a lithium battery digital twin described in the first aspect.

[0035] The online state estimation method for lithium battery digital twins provided in this application has the following beneficial effects: (1) High fidelity and real-time performance are combined: The pre-trained TP-FNO model can approximate the solution of high-dimensional PDEs such as solid-phase diffusion, transforming complex electrochemical processes into single forward inference, greatly reducing the amount of computation, and accurately restoring the concentration field distribution of positive and negative electrode particles, which is suitable for real-time online applications of embedded systems such as BMS. (2) Macro-micro joint estimation: The state vector synchronously includes SOC and the concentration field distribution of positive and negative electrode particles. The state transition function is constructed by TP-FNO (responsible for concentration field state transition prediction) and ampere-hour integral method (responsible for SOC update) to realize joint estimation of the internal state of the battery in all dimensions, and improve the fit of the digital twin model to the behavior of real batteries. (3) Interpretable and easy to implement: The TP-FNO model retains the physical structure information of the electrochemical process and forms a dynamic model of "physical constraint + closed-loop correction" with the state estimation algorithm. Compared with the pure black box data-driven method, it has stronger interpretability, is easier to verify in engineering and safety certification, and lowers the threshold for implementation. (4) Precise early warning of safety risks: Based on the microscopic information of the concentration field, the safety assessment indicators related to lithium plating are calculated, and potential risks are accurately quantified, providing high-value feedback for BMS or control strategies and avoiding safety hazards in advance. (5) Strong cross-platform adaptability: The TP-FNO model is resolution independent and can be adapted to inference with different resolutions or non-uniform grids without retraining. It can flexibly match BMS hardware with different computing power and sampling accuracy, reducing the cost of algorithm porting and calibration. Attached Figure Description

[0036] Figure 1 The flowchart is shown below for the online state estimation method for lithium battery digital twins involved in this invention.

[0037] Figure 2 This is a schematic diagram illustrating the concentration prediction error of the TP-FNO model under specific test conditions.

[0038] Figure 3 The present invention relates to a schematic diagram of an online state estimation system for a lithium battery digital twin. Detailed Implementation

[0039] To make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be specifically described below in conjunction with the embodiments and accompanying drawings, but the scope of protection of the present invention is not limited thereto.

[0040] See attached document Figure 1 As shown, this invention relates to an online state estimation method for lithium battery digital twins, the method comprising:

[0041] Step 1. Train the TP-FNO model based on the sample set. The TP-FNO model is used to map the operating parameters of the lithium battery and spatiotemporal variables to the solid phase concentration distribution of lithium ions in the positive and negative electrode active particles without solving partial differential equations. The solid phase concentration distribution includes at least the particle surface concentration and the particle center concentration.

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

[0043] Step 1.1. Construct a sample set. The core requirements for the sample set are: it must include lithium battery operating parameters, spatiotemporal variable-related input features, and corresponding solid-phase concentration field distribution output data. The input features must cover the diversity of operating conditions and data validity required for model training, and the output data must accurately reflect the concentration distribution from the center to the surface within the positive and negative electrode particles (including particle surface concentration and center concentration). The specific method of constructing the sample set is not limited; as long as the above data matching and validity requirements are met, it can be used for TP-FNO model training. In one embodiment, the sample set construction process is as follows: using a finite difference method (FDM) high-fidelity numerical solver, an adaptive step-size numerical solution is performed on the battery solid-phase diffusion partial differential equation for randomly generated multivariate current conditions (including constant current, step current, and dynamic current modes) and random initial electrode concentrations. This solution process accurately captures the spatiotemporal coupling evolution of the solid-phase concentration field within battery particles, ultimately generating 10,000 valid samples. Each sample contains four input features (current, initial concentration, normalized radius, and normalized time), and the corresponding N-dimensional solid-phase concentration field output at the next time step (N-dimensional number of discrete points from the particle center to the surface, default value 64). The sample generation process employs multi-process parallel computation to improve efficiency, while introducing mass conservation physical constraints to filter invalid samples, ensuring data validity and providing high-quality data support for the stable training of the TP-FNO model.

[0044] In one embodiment, the solid-state partial differential equation is represented in spherical coordinates by Fick's second law. To obtain a unique solution to this partial differential equation, this embodiment applies two physical boundary conditions: a spherical symmetry boundary condition at the particle center, assuming that the lithium ion distribution inside the particle is radially symmetric and the concentration gradient at the center is zero, and a flux boundary condition at the particle surface. This boundary condition establishes a physical coupling relationship between the macroscopic input current and the microscopic concentration field evolution, and is also the physical basis for using current as a key input feature when constructing the TP-FNO model.

[0045] Step 1.2. Construct the TP-FNO model, which includes an input dimensionality increase layer, at least one physically enhanced three-way parallel operator layer, and an output dimensionality reduction layer connected in sequence, wherein:

[0046] In one embodiment, the input upscaling layer is used to map the input features to a high-dimensional feature space through a linear transformation. In another embodiment, the input tensor of the TP-FNO is consistent with the input features of the sample set constructed in step 1.1, consisting of four-channel features: real-time current, the radially distributed solid phase concentration field at the current moment, spatial coordinate features, and time step. Subsequently, this four-channel input is fed into the input upscaling layer for processing. The upscaling operation can be implemented through basic operators such as linear mapping, and the specific implementation method is not limited in this scheme.

[0047] In one embodiment, the physically 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 physically enhanced three-way parallel operator layer adds the outputs of the three operators element by element and then processes them through the same nonlinear activation function to obtain the output of the layer.

[0048] Among them, the global spectral convolution operator is used to perform Fourier transform on the input features after dimensionality increase. After performing point-by-point complex multiplication with the learnable complex weights in the frequency domain, it is inversely transformed back to the spatial domain to complete the global operator mapping, thereby achieving accurate capture of the long-range dependence and overall distribution trend of the electrochemical concentration field.

[0049] An explicit diffusion differential operator, consistent with the form of the partial differential equation for solid-phase diffusion in a battery, is used to perform differential operations on the input features within a predefined local receptive field based on learnable diffusion coefficient weights, thereby simulating ion diffusion flux and efficiently reproducing the local diffusion / gradient propagation process of lithium ions within solid-phase particles. In one embodiment, the predefined local receptive field is 3×3, and the learnable diffusion coefficient weights are constructed through discrete difference.

[0050] The residual enhancement operator performs efficient channel mixing on the input features through a 1×1 standard convolutional layer, improving cross-feature interaction capabilities. The mixed features are then short-circuited and added to the input features, ensuring effective transmission of feature information and stable training of deep networks.

[0051] Compared to traditional FNO networks using spectral convolution, this parallel fusion structure achieves an organic combination of global spectral operators and local diffusion priors. It can capture the long-range coupling (global effect) of the electrochemical concentration field through global spectral convolution operators, and efficiently simulate local diffusion / gradient propagation (local effect) through explicit diffusion differential operators. At the same time, it strengthens cross-feature interaction capabilities with residual enhancement operators, and finally completes an approximate substitution of the concentration field evolution with a single forward propagation, significantly reducing computational costs and meeting the real-time deployment requirements of edge devices.

[0052] In one embodiment, the output dimensionality reduction layer is used to map the output of the physically enhanced three-way parallel operator layer back to the target physical space. As the final mapping module of the TP-FNO model, the output dimensionality reduction layer receives the high-dimensional features processed by the physically enhanced three-way parallel operator layer. Through linear transformation and feature compression operations, it accurately maps the high-dimensional abstract features back to the target physical space, ultimately outputting a prediction result whose dimension corresponds to its actual physical meaning. This is a feature matrix containing the surface concentration, center concentration, and global solid phase concentration field distribution of lithium battery positive and negative electrode particles. The core function of this output dimensionality reduction layer is to remove the high-dimensional feature redundancy introduced during model training, retaining key information directly related to the electrochemical concentration field. This ensures that the output result not only conforms to physical dimension constraints but also provides accurate microscopic state input for subsequent steps such as system state vector construction and state estimation, achieving a closed-loop transformation from feature learning to physical quantity output.

[0053] Step 1.3. Model Training. In one embodiment, the model training process is as follows: The training dataset constructed in Step 1.1 is input into the TP-FNO network built in Step 1.2. An adaptive optimizer is used to iteratively optimize the model parameters. The training batch size is set to 64, the total number of training rounds is set to 100, and the initial learning rate is configured to 0.002. To improve the stability and convergence effect of model training, a cosine annealing learning rate scheduling strategy is introduced simultaneously. 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, a gradient pruning strategy is adopted, and the gradient pruning threshold is set to 1.0 to limit the gradient generated during training and avoid model training oscillation or non-convergence due to gradient explosion. Finally, the parameters of the TP-FNO network are optimized through the above training strategies to obtain a trained model with concentration field prediction capability.

[0054] In one embodiment, the training of the TP-FNO model is optimized using a weighted loss function, which includes at least: a mean squared error main loss term for evaluating the overall concentration field accuracy, a surface-specific loss term for enhancing the accuracy of particle surface concentration prediction, and a regularization loss term for controlling model complexity. In one embodiment, the total loss function consists of three weighted components, each with a weight ratio adjusted by a preset weighting coefficient, and the sum of all weighting coefficients is 1. An exemplary value is: mean squared error main loss term weight a = 0.5, particle surface concentration specific loss term weight b = 0.4, and regularization loss term weight c = 0.1. The main loss term, the mean squared error (MSE), is used to evaluate the overall fitting accuracy between the model's predicted global solid-phase concentration field and the actual concentration field, ensuring the reliability of the global concentration field prediction. The particle surface concentration loss term specifically calculates the MSE of the surface concentrations of both positive and negative electrode particles. By increasing the weight of this loss term, the model is forced to prioritize optimizing the prediction performance in high-gradient regions during training, reducing estimation errors in critical areas. The regularization loss term constrains the sum of squares of all learnable parameters, effectively suppressing overfitting, controlling network complexity, and ensuring stable generalization ability under different operating conditions. Therefore, the estimation accuracy of the digital twin system for the surface state of lithium battery electrodes can be effectively improved, specifically addressing the technical problem of large concentration gradients on battery particle surfaces leading to high prediction errors.

[0055] The TP-FNO model trained using the above steps can infer the solid phase concentration field distribution based on the current lithium battery operating parameters and spatiotemporal variables. To verify its prediction accuracy, Figure 2 The concentration prediction error of the model under specific test conditions is illustrated by example.

[0056] In one embodiment, TP-FNO operates in an autoregressive manner, where the prediction at each time step strictly depends on the state input at the previous time step. If the initial state is unclear or inaccurate, the recursive process will fail to start, or the prediction error will accumulate and spread over time. To initiate the recursive prediction of the TP-FNO model and ensure the accuracy of its time recursion, the complete initial state of the system at time zero must first be established, specifically including:

[0057] The measured current and terminal voltage data of the battery at the initial moment are collected and preprocessed. Based on the preprocessed initial terminal voltage and the pre-stored empirical curve of the battery open-circuit voltage, the initial state of charge of the battery is determined. According to the initial state of charge, the predefined maximum lithium-ion concentration of the positive and negative electrode active materials, and the pre-stored empirical curve of the positive and negative electrode open-circuit voltage, the initial average lithium-ion concentration of the positive and negative electrode particles is calculated through the electrochemical equilibrium relationship. The determined initial state of charge and the calculated initial average lithium-ion concentration together constitute the complete initial state of the system at time zero, which is used to initialize the autoregressive recursive prediction process of the TP-FNO model.

[0058] Step 2. Embed the trained TP-FNO model into the nonlinear state-space equation, and calculate the system state prior estimate and covariance prior based on the system state posterior estimate of the previous time step and the input of the current time step.

[0059] In one embodiment, calculating the prior estimate of the system state includes: constructing a system state vector containing the state of charge of the lithium battery and the finite-dimensional concentration of lithium ions within the positive and negative electrode active particles. It should be noted that the system state vector containing the finite-dimensional concentration of lithium ions within the positive and negative electrode active particles is extracted from the lithium ion solid-phase concentration distribution within the positive and negative electrode active particles. This invention uses the finite-dimensional concentration of lithium ions within the positive and negative electrode active particles, rather than the lithium ion solid-phase concentration, to construct the system state vector, mainly to reduce costs and facilitate system deployment; combining the trained TP-FNO model with the ampere-hour integral method used to update the state of charge to construct a state transition function. The formula for the state transition function is:

[0060]

[0061] In the formula, k represents time. Let k represent the system state vector at time k. This represents the system state vector at time k+1. Describe the input, that is, the input current. , For process noise, This indicates that the trained TP-FNO model has been invoked. and Let K represent the concentration distribution of negative electrode particles and positive electrode particles at time k, respectively. This represents the state of charge at time k+1.

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

[0063] In one embodiment, calculating the covariance prior includes: calculating the partial derivative of the state transition function with respect to the system state vector to obtain the state transition Jacobian matrix. It should be noted that the partial derivative of the state transition function with respect to the system state vector can be calculated using automatic differentiation methods, numerical difference methods, or a combination thereof, and is not limited here. Based on the state transition Jacobian matrix, the covariance posterior of the previous time step, and the process noise matrix, the covariance prior of the current time step is calculated. 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 ampere-hour integral method, and is accurately quantified using a diagonal matrix form.

[0064] Step 3. Based on the prior estimation of the system state, calculate the predicted voltage value through the observation equation, obtain the corresponding real-time measurement value, and calculate the difference between the two as the observation residual;

[0065] In one embodiment, the observation equation consists of four parts: open-circuit voltage curve, reaction overpotential, ohmic voltage drop, and observation noise. The open-circuit voltage curve is determined by post-factory testing and characterizes the inherent mapping relationship between the lithium battery's state of charge and open-circuit voltage, providing a basic reference for voltage prediction. The reaction overpotential is calculated using the electrochemical Butler-Volmer formula, and its value is determined at least by the finite-dimensional concentration of lithium ions within the positive and negative electrode active particles. By influencing the electrode reaction kinetics, the overpotential value is altered, ensuring an accurate correlation between the overpotential calculation and the battery's microscopic reaction state. The ohmic voltage drop is determined by the product of the battery's internal ohmic resistance and the real-time operating current. The internal ohmic resistance is the inherent resistance of components such as the electrolyte and electrode current collectors within the battery, which can be obtained through factory testing or online identification. The real-time operating current is the current operating condition input parameter, ensuring that the ohmic voltage drop calculation reflects the real-time operating state. Observation noise characterizes uncertainties and interferences during the observation process, including measurement errors of the voltage sensor and random deviations caused by environmental electromagnetic interference, ensuring the integrity of the observation equation modeling. After calculating the predicted voltage value using the aforementioned observation equation, the real-time voltage measurement of the lithium battery is acquired by the voltage sensor mounted on the battery management system. The difference between the predicted voltage value and the real-time measurement value is then calculated; this difference is the observation residual. This observation residual directly reflects the deviation between the prior estimation of the system state and the actual battery operating state, providing a core basis for subsequent posterior correction of the system state based on the state estimation algorithm.

[0066] Step 4. Using a state estimation algorithm, update the prior estimate of the system state and the prior covariance based on the observed residuals to obtain the posterior estimate of the system state and the posterior covariance. It should be noted that the state estimation algorithm can be extended Kalman filtering, unscented Kalman filtering, commensurate Kalman filtering, or particle filtering, etc., and is not limited here.

[0067] In one embodiment, the state estimation algorithm is an extended Kalman filter algorithm, which uses the observation residuals as the core correction basis to iteratively update the prior estimation of the system state and the prior covariance, and finally obtains a high-precision posterior estimation of the system state and the posterior covariance. 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 covariance prior, and combining the observation Jacobian matrix with the preset observation noise covariance matrix, the innovative 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 innovative covariance, the observation Jacobian matrix, and the covariance prior, the Kalman gain is further calculated;

[0071] Step 4.4. Based on the observation residuals and Kalman gain, correct the prior estimate of the system state to obtain the posterior estimate of the system state at the current time.

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

[0073] Step 5. Use the posterior estimate of the system state and the posterior result of the covariance as new system state information to construct the input features of the TP-FNO model at the next time step 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 assessment step is further included: based on the posterior estimate of the system state, at least one microscopic safety assessment index is calculated to quantify the lithium battery lithium plating risk, and the microscopic safety assessment index is fed back to the battery management system for dynamically adjusting the battery charging and discharging strategy. The microscopic safety assessment index includes at least one of the following: surface concentration margin, concentration gradient, potential margin, and a comprehensive risk index obtained by weighted combination of the first three, wherein:

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

[0076] The concentration gradient is the difference between the concentration on the surface of the negative electrode particle and the concentration at the center. Its magnitude characterizes the uniformity of ion diffusion inside the negative electrode particle. The larger the gradient, the greater the resistance to ion diffusion, and the easier it is for lithium ions to accumulate on the negative electrode surface, thereby triggering the risk of lithium plating.

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

[0078] The comprehensive risk index is a weighted sum of surface concentration margin, concentration gradient, and potential margin. By pre-setting weighting coefficients for each indicator (calibrated according to different battery types and application scenarios), it comprehensively considers multiple dimensions of lithium plating influencing factors to form a single quantitative index, facilitating the battery management system's rapid assessment of the overall lithium plating risk level. An example weighting coefficient is: 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 (this can be adjusted according to battery type; for example, the potential margin weight can be increased to 0.5 under low-temperature conditions). Simultaneously, risk level thresholds are preset: a comprehensive risk index RI ≥ 0.8 indicates low risk (normal charging and discharging), 0.3 ≤ RI < 0.8 indicates medium risk (reducing the charge / discharge rate to below 1C), and RI < 0.3 indicates high risk (stopping charging and discharging). The battery management system dynamically adjusts the charging and discharging strategy based on the risk level to proactively avoid potential lithium plating risks.

[0079] Through the above closed-loop iteration and safety assessment steps, lithium-related safety assessment indicators are calculated based on the microscopic information of the concentration field, accurately quantifying potential risks and providing high-value feedback for BMS or control strategies to avoid safety hazards in advance.

[0080] Figure 3 This application provides a schematic diagram of the structure of an online state estimation system for a lithium battery digital twin, as shown below. Figure 3 The system shown includes:

[0081] Model training module: used to train the TP-FNO model based on the sample set. The TP-FNO model is used to map lithium battery operating parameters and spatiotemporal variables into a solid phase concentration field distribution that includes particle surface concentration and center concentration.

[0082] Prediction module: used to embed the trained TP-FNO model into the nonlinear state-space equation, and calculate the system state prior estimate and covariance prior based on the system state posterior estimate of the previous time step and the input of the current time step;

[0083] The observation residual calculation module is used to calculate the voltage prediction value based on the prior estimation of the system state through the observation equation, obtain the corresponding real-time measurement value, and calculate the difference between the two as the observation residual.

[0084] State correction module: used to update the prior estimate of the system state and the prior covariance based on the observed residuals using a state estimation algorithm, so as to obtain the posterior estimate of the system state and the posterior covariance.

[0085] Closed-loop iteration module: Used to take the posterior estimate of the system state and the posterior result of the covariance as new system state information, to construct the input features of the TP-FNO model at the next time step and to perform recursive prediction, forming a closed loop of model prediction and posterior correction.

[0086] The modules described above are used to execute the methods provided in the foregoing embodiments, and their implementation principles and technical effects are similar, so they will not be repeated here. These modules can be one or more integrated circuits configured to implement the above methods, such as one or more Application Specific Integrated Circuits (ASICs), one or more Digital Signal Processors (DSPs), or one or more Field Programmable Gate Arrays (FPGAs), etc. Furthermore, when a module is implemented through processing element scheduler code, the processing element can be a general-purpose processor, such as a Central Processing Unit (CPU) or other processor capable of calling program code. Alternatively, these modules can be integrated together to form a system-on-a-chip (SOC).

[0087] Optionally, embodiments of this application also provide an online state estimation system for a lithium battery digital twin. This system includes a processor and a storage medium. 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-described method embodiments. The specific implementation and technical effects are similar and will not be repeated here.

[0088] In the several embodiments provided in this application, it should be understood that the disclosed systems and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

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

[0090] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or in a combination of hardware and software functional units.

[0091] The integrated units implemented as software functional units described above can be stored in a computer-readable storage medium. These software functional units, stored in a storage medium, include several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) or processor to execute some steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0092] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this 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 to map lithium battery operating condition parameters and spatiotemporal variables to a lithium ion solid-phase concentration distribution within positive and negative active particles, wherein the solid-phase concentration distribution at least includes a particle surface concentration and a particle center concentration; embedding the trained TP-FNO model into a nonlinear state space equation, and based on a system state posterior estimation at a previous moment and an input at a current moment, calculating a system state prior estimation and a covariance prior; according to the system state prior estimation, calculating a voltage prediction value through an observation equation, and obtaining a corresponding real-time measurement value, and calculating a difference between the two 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; using the system state posterior estimation and the covariance posterior result as new system state information to construct an input feature of the TP-FNO model at a next moment and perform recursive prediction, forming a closed loop of model prediction and posterior correction. 2.The lithium battery digital twin online state estimation method of claim 1, wherein, 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 to map the input feature 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 adds the outputs of the three operators element by element, and then processes the output of the layer through the same nonlinear activation function to obtain the output of the layer; the output feature reconstruction layer is used to map the output of the physical enhanced three-way parallel operator layer to the lithium ion solid-phase concentration distribution within the positive and negative active particles.

3. The lithium battery digital twin online state estimation method according to claim 2, wherein: the globally spectral convolution operator is used to perform Fourier transform on the input feature, perform point-by-point complex multiplication operation with a learnable complex weight in the frequency domain, and then inverse transform back to the spatial domain to complete global operator mapping; the explicit diffusion differential operator is used 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; the residual enhancement operator performs channel mixing on the input feature through a standard convolution layer, and adds the mixed feature and the input feature in short circuit. 4.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.

5. 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, 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 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.

6. The lithium battery digital twin online state estimation method of claim 5, wherein, The observation equation is composed of four parts: an open-circuit voltage curve, a reaction overpotential, an ohmic voltage drop, and 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.

7. The lithium battery digital twin online state estimation method of claim 6, 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; based on the innovation covariance, the observation Jacobian matrix, and the covariance prior, further calculating a Kalman gain; 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.

8. 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.

9. The lithium battery digital twin online state estimation method of claim 8, wherein, The surface concentration margin is the difference between the negative electrode particle surface concentration extracted based on the system state posterior estimation value and the maximum allowable concentration of the negative electrode material; the concentration gradient is the difference between the negative electrode particle surface concentration and the central concentration; 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; and the comprehensive risk index is the weighted sum of the surface concentration margin, the concentration gradient, and the potential margin. 10.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 1-9 when executing the computer program.

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