A battery fast charging dynamic security boundary identification method based on a physical information network

Abstract

The application discloses a battery fast charging dynamic safety boundary identification method based on a physical information network and belongs to the technical field of battery management. The method comprises the following steps: S1, constructing a lithium ion battery fast charging lithium precipitation model based on reaction data of the lithium ion battery during operation, and obtaining time sequence data of a lithium precipitation reaction current inside the battery based on the lithium ion battery fast charging lithium precipitation model; S2, constructing a TCN-FCNN-SG neural network, and obtaining a lithium precipitation current prediction value based on the time sequence data; and S3, judging a safety boundary during battery fast charging based on the lithium precipitation current prediction value. The application provides a PINN model using a TCN-FCNN-SG architecture, and realizes online detection of vehicle lithium precipitation under complex working conditions.

Description

Technical Field

[0001] This invention belongs to the field of battery management technology, specifically relating to a method for identifying dynamic safety boundaries for fast-charging batteries based on physical information networks. Background Technology

[0002] With the booming development of the new energy vehicle industry, ultra-fast charging technology has become a core solution to alleviate users' "range anxiety." However, high-rate charging can easily disrupt the internal kinetic balance of the battery, inducing a side reaction that causes lithium metal deposition on the negative electrode. This not only leads to accelerated battery capacity degradation but also creates safety hazards such as internal short circuits and thermal runaway. Therefore, accurately identifying lithium deposition behavior inside the battery and overcoming the technical bottleneck of lossless fast charging has become a key scientific issue for ensuring the ultimate safety of on-board energy storage systems.

[0003] Lithium metal deposition, as a hidden side reaction highly dependent on operating conditions, makes its microscopic evolution difficult to capture directly through macroscopic signals from the battery's external environment. Traditional disassembly analysis methods (such as scanning electron microscopy (SEM) and X-ray diffraction (XRD)) can visually confirm the morphology and phase of lithium deposition, but these are irreversible and destructive detection methods, completely lacking the ability to provide early warning of lithium deposition. On the other hand, although advanced in-situ characterization techniques such as neutron diffraction (ND) and nuclear magnetic resonance (NMR) demonstrate extremely high precision in non-destructive quantification, they are heavily reliant on large and expensive laboratory equipment, still unable to meet the online deployment requirements of vehicle battery management systems (BMS).

[0004] To meet the requirements of non-destructive, online lithium plating identification in automotive applications, existing methods largely rely on electrical signal analysis. For example, they extract the "voltage relaxation plateau" induced by secondary lithium intercalation during the resting period, or track the characteristic peak shift in the capacity increment (ICA) curve caused by dead lithium stripping. However, actual automotive operating conditions are complex and variable, and external electrical signals are highly susceptible to strong coupling interference from dynamic loads and ambient temperature, resulting in poor adaptability and insufficient robustness of pure signal analysis methods. Therefore, overcoming these limitations and exploring an online lithium plating identification scheme adaptable to complex operating conditions has become an urgent problem to be solved.

[0005] Novel detection technologies based on mechanics (thickness / expansion stress) and frequency domain electronics (electrochemical impedance spectroscopy, EIS) have attracted much attention in recent years. Normal lithium intercalation only causes limited volume expansion of the graphite lattice in the battery negative electrode, while lithium deposition, due to its lower bulk density and irreversible deposition, can cause an abnormal surge in the battery's macroscopic thickness or internal constraint stress. Based on the stress-strain characteristics of the negative electrode, thickness / expansion stress detection technology can identify lithium deposition behavior inside the battery. On the other hand, EIS technology analyzes the internal interface polarization characteristics through AC perturbation. Given the kinetic differences between lithium reduction and lithium intercalation processes, it uses relaxation time distribution (DRT) to extract lithium deposition characteristic peaks from complex spectra. However, the above methods are still limited by severe physical bottlenecks in practical applications. Mechanical monitoring is easily affected by thermal expansion caused by heat generated during charging and discharging, and the complex mechanical structure of the module makes the nonlinear decoupling of the "force-thermal" signal extremely difficult. Meanwhile, EIS measurement demands a "quasi-steady state" premise from the system. Not only is full-frequency sweep time long, but its spectrum is also prone to severe non-stationary distortion under dynamic high magnification conditions, making it difficult to balance anti-interference capability and real-time early warning requirements.

[0006] Besides mining physical feature signals, pure data-driven methods, as another major technical approach in the field of state estimation, have demonstrated powerful nonlinear mapping and feature extraction capabilities in recent years. However, these methods are essentially "black box" models, heavily reliant on massive amounts of labeled data to fit the mapping relationship between input and output. Due to the lack of underlying electrochemical mechanism constraints, they often exhibit limitations such as limited generalization ability and prediction results that violate physical laws when facing complex and variable boundary conditions. To address this, Physical Information Neural Networks (PINNs) have emerged. As a new paradigm of machine learning that deeply integrates prior physical knowledge into the network training process, PINNs cleverly transform electrochemical mechanism equations into soft constraint terms embedded in the loss function, effectively breaking down the "black box" barrier. Summary of the Invention

[0007] Addressing the urgent need for online lithium plating detection under complex operating conditions in vehicle battery management systems (BMS), and inspired by the successful application of PINN in state estimation, this invention provides a non-destructive early identification framework for lithium plating based on a TCN-FCNN fusion architecture. First, a fast-charging dataset containing high-fidelity internal lithium plating features is generated using a calibrated pseudo-two-dimensional (P2D) electrochemical model. In terms of network architecture, this invention uses a temporal convolutional network (TCN) as the backbone to extract temporal features and innovatively integrates a fully connected neural network (FCNN) branch. The physical constraint error is constructed by predicting local virtual overpotentials using FCNN and deeply coupled with the data-driven error. Furthermore, a soft-gate component (SG) is introduced into the model to effectively suppress numerical artifacts in lithium plating prediction and reduce the false positive rate. In scenarios with limited test data, this model significantly reduces its dependence on internal implicit physical labels without adding any hardware sensors, accurately capturing the lithium plating initiation and termination boundaries in bench tests.

[0008] To achieve the above objectives, the present invention provides the following solution: a method for identifying dynamic safety boundaries for fast-charging batteries based on physical information networks, comprising the following steps: S1: Based on the reaction data of lithium-ion battery during operation, a lithium-ion battery fast-charging lithium deposition model is constructed, and the time-series data of the lithium metal deposition reaction current inside the battery is obtained based on the lithium-ion battery fast-charging lithium deposition model. S2: Construct a TCN-FCNN-SG neural network to obtain the predicted value of lithium metal deposition current based on the time series data; S3: Determine the safety boundary for fast charging of the battery based on the predicted value of lithium metal deposition current.

[0009] More preferably, the lithium-ion battery fast-charging lithium plating model includes: an electrochemical reaction model on the surface of electrode active particles, a lithium-ion motion equation, a temperature model during battery charging and discharging, and a current density model.

[0010] More preferably, the current density model includes: ; in, ; ; In the formula, This represents the total current density passing through the solid-liquid interface; This represents the lithium-ion flux density generated by the electrochemical reaction on the surface of the active particles. This represents the local current density of the lithium metal deposition side reaction; Indicates the number of charges carried by lithium ions; Denotes Faraday's constant; Indicates the lithium metal deposition reaction rate; This indicates the lithium-ion concentration on the surface of solid particles; Indicates the anode / cathode transfer coefficient; Represents the universal gas constant; This indicates the overpotential at which lithium metal deposition occurs; , These represent the solid-phase potential and the liquid-phase potential, respectively. This represents the equilibrium potential of the lithium metal deposition reaction. Represents solid-state current density; This represents the resistance generated by the solid electrolyte passivation film on the particle surface.

[0011] More preferably, the TCN-FCNN-SG neural network includes: a TCN convolutional module, a TCN main branch, a physical branch, and a soft-gate component; The TCN convolution module is used to perform convolution processing on the input tensor to obtain the latent feature vector; The main branch of the TCN is used to perform nonlinear mapping on the latent feature vector to obtain electrochemical features; The physical branch takes the potential feature vector as input to obtain the predicted value of the negative electrode overpotential; Based on the electrochemical characteristics and the negative electrode overpotential, the predicted value of lithium metal deposition current is obtained. The predicted value of lithium metal deposition current is introduced into the soft gate assembly to obtain the final predicted value of lithium metal deposition current.

[0012] More preferably, the method for obtaining the negative electrode overpotential includes: ; ; In the formula, Indicates the process The final output of the physical branch after layer transformation; For the first Layer weight matrix; For the first The activation output vector of the layer; For the first Layer bias vector; It is a linear activation function.

[0013] More preferably, the total loss function of the TCN-FCNN-SG neural network include: ; in, ; In the formula, The mean squared error loss function represents the data-driven term. This represents the weighting coefficient of the physical constraint term. Represents the loss function for physical constraint terms; This indicates a constraint that the deposition current is nonnegative; This indicates a potential-current consistency constraint; This represents the predicted value of lithium metal deposition current; This represents the predicted overpotential value of the negative electrode.

[0014] More preferably, the method for processing the predicted value of the lithium metal deposition current by the soft-gate assembly includes: ; In the formula, This represents the final predicted lithium plating current; Indicates the activation function; This indicates the gain value, used to amplify overpotential; This represents the overpotential predicted by the physics branch.

[0015] More preferably, the method for determining the safety boundary of the battery during fast charging based on the predicted value of the lithium metal deposition current includes: Based on the predicted lithium deposition current, transient external characteristics at the occurrence and termination of the lithium deposition reaction are obtained; the transient external characteristics include: state of charge, current, and temperature; A three-dimensional lithium-free fast charging boundary surface is constructed based on the state of charge, charging current, and real-time battery temperature. Based on the three-dimensional lithium-free fast charging boundary surface, a table showing the relationship between charging current and state of charge at different temperatures is determined, thereby determining the dynamic safety boundary for fast charging of the battery.

[0016] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention proposes a physical information neural network architecture based on the deep fusion of temporal convolution and fully connected networks (TCN-FCNN), which significantly reduces the reliance on implicit information tags inside the battery and achieves non-intrusive estimation of lithium plating state without adding new sensors. Based on the architecture's high-speed inference capability that avoids complex numerical calculations and its accurate identification of lithium plating start and end points, a three-dimensional fast-charging lithium plating-free boundary surface covering "temperature-SOC-charging rate" is quantitatively constructed under the computing power limitations of automotive-grade computing chips. Furthermore, through dimensionality-reduced projection along the temperature plane, the "SOC-current" safety tolerance threshold is accurately extracted for each temperature zone. With extremely low computational overhead, this provides direct quantitative physical criteria for developing dynamic and adaptive safe fast-charging strategies for automotive BMS. Attached Figure Description

[0017] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a schematic diagram of a method for identifying dynamic safety boundaries for fast-charging batteries based on physical information networks, provided in an embodiment of the present invention. Figure 2 This is a comparison chart of experimental simulation results provided in the embodiments of the present invention; wherein, Figure 2 (a) is the voltage test simulation curve; Figure 2 (b) shows the temperature simulation curve; Figure 2 (c) shows the lithium plating current curve; Figure 3 The structure diagram of the lithium plating prediction model based on the TCN-FCNN-SG neural network provided in the embodiments of the present invention is shown. Figure 4 This is a schematic diagram illustrating the predicted results of lithium metal deposition during fast charging of batteries, provided in an embodiment of the present invention; wherein, Figure 4 (a) is a schematic diagram of lithium plating prediction at -20°C; Figure 4 (b) is a schematic diagram of lithium plating prediction at 5C@20°C; Figure 4 (c) is a schematic diagram of lithium plating prediction at 1C@-20°C; Figure 4 (d) is a schematic diagram of lithium plating prediction at 1C@20°C; Figure 4 (e) is a schematic diagram of lithium plating prediction at 3C@0°C; Figure 4 (f) is a schematic diagram of the test condition error; Figure 5 This is a schematic diagram of the lithium plating prediction curve inside the bench experiment provided in an embodiment of the present invention; Figure 6 This is a schematic diagram of the fast-charging lithium-free boundary surface of the experimental battery provided in an embodiment of the present invention; Figure 6 (a) is a three-dimensional boundary surface diagram of lithium-free fast charging safety; Figure 6 (b) is a dimensionality-reduced interpolation through an isothermal cross section; a schematic diagram of the two-dimensional boundary curve at any temperature node on the "current-SOC" plane; Figure 7 This is a schematic diagram of the lithium-free boundary of "SOC-charging current" at 15°C, provided in an embodiment of the present invention. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0021] Example 1: like Figure 1 As shown, this embodiment provides a method for identifying the dynamic safety boundary of battery fast charging based on a physical information network, including the following steps: S1: Based on the reaction data of the lithium-ion battery during operation, a lithium-ion battery fast charging lithium deposition model is constructed, and time-series data of the lithium metal deposition reaction current inside the battery is obtained based on the lithium-ion battery fast charging lithium deposition model; the lithium-ion battery fast charging lithium deposition model includes: an electrochemical reaction model on the surface of electrode active particles, a lithium-ion motion equation, a temperature model during battery charging and discharging, and a current density model. S2: A TCN-FCNN-SG neural network is constructed, and a predicted value of the lithium metal deposition current is obtained based on the time-series data; S3: The safety boundary during battery fast charging is determined based on the predicted value of the lithium metal deposition current. The method for determining the safety boundary of battery fast charging based on the predicted value of lithium metal deposition current includes: obtaining transient external features when lithium deposition reaction occurs and terminates based on the predicted value of lithium metal deposition current; the transient external features include: state of charge, current and temperature; constructing a three-dimensional lithium-free fast charging safety boundary surface based on the state of charge, charging current and real-time battery temperature; determining the relationship table between charging current and state of charge at different temperatures based on the three-dimensional lithium-free fast charging safety boundary surface, and then determining the dynamic safety boundary of battery fast charging.

[0022] Since the lithium plating side reaction is an internal process of the battery, traditional battery operation datasets do not include internal signals of the battery. Therefore, this embodiment uses a high-precision electrochemical model to generate a battery operation dataset (external current, voltage, temperature, and internal lithium plating current) that includes the internal lithium plating current of the battery, for training and testing of the TCN-FCNN-SG neural network.

[0023] In this embodiment, the lithium-ion battery fast-charging lithium deposition model is based on the electrochemical-thermal coupled multiphysics model of a pseudo-two-dimensional (P2D) power battery and integrates the lithium metal deposition side reaction to provide time-series data including the lithium metal deposition reaction current inside the battery. This model considers the active material along the electrode thickness direction (…). ) and within solid particles ( Charge and species transport. Control. and The equations for the direction of the reaction describe the electrochemical reaction coupling on the surface of active material particles through the Butler-Volmer relation.

[0024] The electrochemical reactions that occur on the surface of electrode active particles during lithium-ion battery operation are described by the Butler-Volmer kinetic equations. ; in, ; ; In the formula, Represents solid-state current density; Indicates the number of charges carried by lithium ions; Denotes Faraday's constant; Indicates lithium-ion flux density; Indicates the exchange current density; These are the anode transfer coefficient and the cathode transfer coefficient; Represents the universal gas constant; Indicates battery temperature; Indicates the negative electrode overpotential; A constant representing an electrochemical reaction; , These represent the lithium-ion concentration in the negative electrode solid phase and the lithium-ion concentration in the positive electrode solid phase, respectively. Indicates the maximum lithium intercalation concentration of the electrode active material; , These represent the solid-phase potential and the liquid-phase potential, respectively. It represents the open-circuit potential, which is determined by the lithium-ion concentration ratio on the surface of the electrode active material particles. It is a quantity that is only related to the characteristics of the electrode active material itself. This represents the resistance generated by the solid electrolyte passivation film on the particle surface.

[0025] The diffusion process of lithium ions in electrode active material particles can be described by Fick's law. ,in, , representing the inner radius of the solid particle Gradient of direction; Indicates the solid-phase diffusion coefficient; Indicates the concentration of lithium ions in the solid phase; This represents the distance along the radius of the solid particles; This indicates the time required for the diffusion process.

[0026] In the electrolyte, lithium ions undergo both diffusion and migration processes, and their motion equations can be obtained from the concentrated solution theory. In this embodiment, the lithium ion motion equations include: ; In the formula, It represents the liquid phase volume fraction (i.e., the porosity of solid particles). Indicates the concentration of lithium ions in the liquid phase; , indicating along the electrode thickness direction The gradient; , representing the effective diffusion coefficient of the liquid phase in a lithium-ion battery; Indicates the liquid phase diffusion coefficient; Indicates the specific surface area of ​​the particles; This represents the lithium-ion transfer coefficient.

[0027] A zero-dimensional thermal model was coupled into the P2D electrochemical model to simulate the battery's self-heating and heat dissipation phenomena. The Arrhenius equation was used to correct the internal electrochemical reaction rate of the battery based on the real-time battery temperature. The formula for the heat convection dissipation from the battery surface to the environment is as follows: ; In the formula, This represents the amount of heat dissipation due to convection. Indicates the surface area of ​​the battery; Indicates the convective heat transfer coefficient; The ambient temperature.

[0028] Considering the ohmic heat, reaction heat, polarization heat of the battery, and the battery's heat dissipation process to the external environment, the temperature model for battery charging and discharging is as follows: ; In the formula, These represent the battery's mass and specific heat capacity, respectively. Indicates the thickness of a single-layer battery material; Indicates an ohmic heat source. Indicates the heat source of the reaction. This indicates a polarized heat source.

[0029] To determine the relationship between lithium battery operating conditions and lithium metal deposition, a correction term for side reactions is introduced into the lithium-ion battery fast-charging lithium deposition model. This side reaction competes with the normal lithium-ion intercalation reaction during battery charging and discharging, consuming recyclable lithium ions in the electrolyte and causing a decrease in usable battery capacity. To simplify the model, this invention primarily considers the lithium metal deposition side reaction, neglecting the solid electrolyte layer growth and aging reactions related to long-term battery cycling. The complete current density model considering the competition from side reactions is as follows: ; in, ; ; In the formula, This represents the total current density passing through the solid-liquid interface; This represents the lithium-ion flux density generated by the electrochemical reaction on the surface of the active particles. This represents the local current density of the lithium metal deposition side reaction; Indicates the lithium metal deposition reaction rate; This indicates the lithium-ion concentration on the surface of solid particles; Indicates the anode / cathode transfer coefficient; This indicates the overpotential at which lithium metal deposition occurs; This represents the equilibrium potential of the lithium metal deposition reaction.

[0030] After lithium metal is deposited, some of the lithium ions that have been converted into lithium metal no longer participate in the lithium ion cycle, resulting in a reduction in the cyclic lithium in the battery.

[0031] Corresponding to the real-world bench test of fast battery charging, the simulation results were compared with the experimental results at -10°C, 0°C, and 25°C. Figure 2 (a) and Figure 2 As shown in (b). Figure 2 (a) is a comparison of battery voltage curves from bench tests and simulation experiments. The solid line in the figure represents the experimental measurement value, and the dotted line with triangles represents the simulation result. It can be found that at low temperatures, the constant current charging range of the battery is shorter, and the two voltage curves have a higher degree of overlap. Figure 2 (b) is a comparison of the battery temperature curves from bench tests and simulation tests. Figure 2 In the table, solid lines represent experimental measurements, and dotted lines represent simulation results. Table 1 shows the errors between the simulation results and experimental results of the lithium-ion battery fast-charging lithium deposition model. Overall, the simulation results given by the lithium-ion battery fast-charging lithium deposition model are close to the real data from bench experiments and can be used to construct battery datasets that include the current of the lithium metal deposition reaction.

[0032] Table 1

[0033] Figure 2(c) presents some simulation results of lithium plating current, with the solid line representing 20°C, the circular solid line representing 0°C, and the triangular solid line representing -20°C. It can be observed that at an ambient temperature of 20°C, no lithium metal plating occurs during fast charging. At an ambient temperature of -20°C, significant lithium metal plating occurs during fast charging, primarily at the beginning of the charging process. At -20°C, the lithium plating current decreases with increasing battery temperature for 3C and 5C charging. For batteries charged at 1C, the lithium plating current only decreases after the charging current decreases during the constant voltage charging stage. The lithium plating situation is more complex for batteries fast-charging at 0°C. At 0°C, the internal lithium plating current of a battery charged at 5C is close to that of a battery charged at the same rate at -20°C, and the lithium plating current decreases rapidly with increasing battery temperature. Batteries charged at 3C do not experience lithium plating at the beginning of charging, and batteries charged at 1C only experience lithium plating during the constant voltage charging stage in the later stages of charging. It is evident that the lithium plating reaction during fast charging is coupled with multiple factors such as battery SOC, battery temperature, and charging current, making accurate prediction of it extremely challenging.

[0034] The simulation datasets for 25 operating conditions were divided into a training set: validation set: test set ratio of 16:4:5, as shown in Table 2. In the table, "●" indicates that lithium metal deposition occurred during the corresponding fast charging condition, and "○" indicates that lithium metal deposition did not occur during the corresponding fast charging condition. The training set data is uniformly underlined and covers ambient temperatures from -20°C to 20°C and charging rates from 1C to 5C to ensure the generalization ability of the TCN-FCNN-SG neural network model and avoid local overfitting. Meanwhile, the operating conditions involved in the validation and test sets are as dispersed as possible, and include fast charging conditions where lithium deposition did not occur, thereby verifying the model's predictive effectiveness.

[0035] Table 2

[0036] In this embodiment, the TCN-FCNN-SG neural network integrates TCN and a fully connected neural network (FCNN). TCN serves as the main neural network body, learning the battery time-series signal. FCNN is used to generate the overpotential inside the battery and serves as the physical constraint loss function and soft-gate component to predict the lithium plating reaction current. Its structure is as follows: Figure 3 As shown, after processing through multiple layers of residual dilated convolutional blocks, the network extracts a latent feature vector containing temporal information. This vector is then split into two paths, flowing to the physical branch and the subsequent TCN main branch, respectively.

[0037] Specifically, the TCN-FCNN-SG neural network includes: a TCN convolutional module, a TCN main branch, a physical branch, and a soft-gate component; the TCN convolutional module and the TCN main branch are respectively the first and second parts of the TCN network (for specific division, please refer to...). Figure 3 The TCN convolution module is used to perform convolution processing on the input tensor to obtain a latent feature vector; the TCN main branch is used to perform nonlinear mapping on the latent feature vector to obtain electrochemical features; the physical branch uses the latent feature vector as input to obtain a predicted value of the negative electrode overpotential; based on the electrochemical features and the negative electrode overpotential, a predicted value of the lithium metal deposition current is obtained; the predicted value of the lithium metal deposition current is introduced into the soft gate component to obtain the final predicted value of the lithium metal deposition current.

[0038] In the task of lithium-ion battery state estimation, a system is established based on observable measurements (battery voltage). Battery current Battery temperature A mapping model from the local current density of lithium metal deposition side reactions to the internal unobservable state (lithium metal deposition inside the battery) is crucial. While traditional RNNs / LSTMs can handle time-series data, they suffer from training time consumption and gradient vanishing problems when dealing with high-frequency sampled battery data (long sequences). TCNs, through causal convolution and dilation mechanisms, can effectively capture long-range dependencies in battery voltage curves, and their parallel computing characteristics are more conducive to deployment in battery management systems (BMS).

[0039] This embodiment treats battery state estimation as a sequence modeling problem. Let the input sequence of voltage, current, etc., be... ,in, express A multidimensional vector at time. express A real-dimensional space. The goal is to learn a nonlinear mapping. ,predict The current of lithium metal deposition inside the battery at any given time : ; In the formula, Represents a nonlinear mapping; Indicates the length of the historical window for review.

[0040] The nonlinear mapping comprises a series of dilated convolutional layers, weight normalization layers, and random forgetting layers. This is particularly important for estimating the lithium metal deposition current inside the battery, as battery side reactions involve complex nonlinear aging feature extraction. To extract features from the battery's historical data, TCN employs dilated causal convolution. Causality is guaranteed. The estimation result of lithium deposition current at time t depends only on time t. Including previous data, preventing future information leakage. Expansion is used to capture the long-term dynamics of the battery by introducing an expansion coefficient. This allows the network to have a sufficiently large receptive field to cover the complex dynamic changes of the battery without significantly increasing the computational burden. For the input sequence... and convolution kernel At any moment The operation is as follows: ; in, This represents the output feature of the dilated convolutional layer at time t, i.e., the latent feature vector; Indicate to For interval pair sequences Perform convolution operations; Indicates the size of the convolution kernel; This represents the index variable inside the convolution kernel. Indicates the convolution kernel at the th... The weight coefficient of each position, Indicates the input sequence at historical moments Element.

[0041] To extract deeper electrochemical features while preventing degradation caused by deep networks, TCN introduces residual learning and normalizes the weights. Output Defined as: ; In the formula, It is the input vector. This represents a linear activation function.

[0042] Furthermore, to further improve the stability of internal covariate shifts and accelerate model convergence, weight normalization is introduced into the convolutional layers within the residual blocks. Unlike batch normalization, weight normalization normalizes the weight matrix of the convolutional kernel by... Direction vector With amplitude scalar Decouple the computation: ; In the formula, The direction vector representing the weights, The magnitude scalar representing the weight.

[0043] In the physical modeling of lithium-ion batteries, the evolution of the battery's internal state is typically described by a complex set of partial differential equations and algebraic equations. According to the general approximation theorem, an FCNN with at least one hidden layer and a nonlinear activation function can approximate any continuous function defined on a compact set with arbitrary precision. Therefore, this invention utilizes FCNN as a data-driven surrogate model to construct a nonlinear mapping from externally observable electrical characteristics (voltage, current, temperature) to the internal electrochemical state (negative electrode overpotential), thereby avoiding the direct numerical solution of complex PDEs.

[0044] The input vector of the FCNN network is ,in, Represents the dimension of real space; the output vector (negative overpotential) is . No. The propagation formula for hidden layers is: ; In the formula, Indicates the first The activation output vector of the layer; The input vector; Indicates the first Layer weight matrix; Indicates the first The bias vector of the layer.

[0045] go through After the layer transformation, the final output is: .

[0046] To ensure that the predictions of the TCN neural network conform to the electrochemical mechanism of lithium-ion batteries, this invention introduces a loss function based on physical knowledge. A fully connected FCNN layer is used to approximate the solution of the complex differential equations controlling the lithium plating reaction kinetics of the battery, thereby obtaining the predicted overpotential of the negative electrode. and will The loss function module passed to the main branch of TCN. The total loss function of the TCN-FCNN-SG neural network. It consists of data-driven terms and physical constraint terms: ; In the formula, The mean squared error loss function represents the data-driven term; Indicates the weighting coefficient of the physical constraint term; This represents the loss function of the physical constraint term, which is constrained by the non-negativity of the extracted current. and potential-current consistency constraints constitute.

[0047] in, ; In the formula, This represents the predicted lithium deposition current value from the model. A penalty is applied when the predicted current is negative, and the penalty is zero when the predicted current is positive. For logic switch items, when When this condition is met, the term is positive; if at this time... The product will produce a huge loss, forcing the network to push the current prediction down to 0. When When this value is 0, the physical constraint is "loosened," allowing the network to freely predict non-zero extraction currents based on the data.

[0048] Although it allows the model to learn the physical mechanisms, at the boundaries ( It's never clean enough; there will be residual false positive noise. Therefore, in The soft gate component (SG) was then introduced to structurally ensure the physical rationality of the output, and its expression is as follows: ; In the formula, This represents the final predicted lithium plating current; Indicates the activation function; This indicates the gain value, used to amplify overpotential; This represents the overpotential predicted by the physics branch.

[0049] when At that time, the Sigmoid approaches 0, even if If the prediction is wrong and noise occurs, as long as That's right, the soft-control door can force it back to 0. Because Through It was calculated, so Errors can be propagated back through the chain rule. This means that in order to make current predictions more accurate, the model will automatically optimize. The prediction.

[0050] The essence of model training is to find a high-dimensional parameter space. The nonconvex optimization process for finding the minimum. During the backpropagation phase, the network iterates over all trainable parameters according to the total loss function. Calculate the gradient and iteratively update using the Adaptive Moment Estimator (Adam) optimizer. Assume we are currently at the... The update rule for the network parameters in each training iteration can be expressed as follows: ; In the formula, Indicates the first The set of optimization parameters for the next iteration; Indicates the learning rate; This represents the gradient operator.

[0051] Expanding to the specific gradient chain derivative, for the TCN residual block, a weight-normalized convolutional layer is introduced, whose core parameters... and The iterative update formula is: ; ; In the formula, , They represent the first The direction vector of the weight in the next iteration, the first iteration weight The magnitude scalar of the weights in the next iteration. This is achieved through the total loss. Injection The physical mechanism information is obtained, and the descent direction of the gradient is restricted to a feasible region that conforms to the internal electrochemical reaction kinetics of the battery, thereby avoiding the overfitting and physical failure problems that are prone to occur in pure data-driven models under small sample or unknown operating conditions.

[0052] The training of the TCN-FCNN-SG neural network includes the following steps: hyperparameter optimization; model training; and lithium plating prediction. In the hyperparameter optimization stage, this embodiment employs a Bayesian optimization strategy. Specifically, within the Sequential Model Basis Optimization (SMBO) framework, a tree-based Parzen estimator is used as a surrogate model to perform automatic search. Iterative search of the hyperparameter space is guided by updating network weights on the training set and evaluating the model's generalization performance on the validation set. Specifically, this embodiment focuses on optimizing hyperparameters across three core dimensions: first, training control parameters, including the initial learning rate and batch size; second, network structure parameters, including the number of TCN channels and the cardinality of the inflation rate, and the number of hidden layer nodes and the random forgetting ratio in the FCNN branches; and finally, physical information fusion parameters, encompassing the weight coefficients balancing the data-driven loss and the physical penalty term, and the scaling factor controlling the activation steepness of the soft-gating function. The optimized model's determined hyperparameters are shown in Table 3.

[0053] Table 3

[0054] During the model training phase, this invention employs an adaptive moment estimation (Adam) optimizer combined with a backpropagation algorithm to drive network weight updates. The training process overcomes the limitations of purely data-driven approaches by constructing a composite loss function that includes mean squared error (MSE) and a physical penalty term. When the network output violates electrochemical laws, the physical loss term imposes a strong penalty, thereby forcing the model to deeply internalize the physical boundaries of lithium deposition while fitting time-series features.

[0055] Example 2: During the testing and evaluation phase of lithium plating prediction, the model's weights are frozen, and end-to-end inference is performed using the forward propagation algorithm. To eliminate floating-point noise and false positive predictions common in deep learning, a hard truncation filtering mechanism is introduced at the output. The model uses physical branches to calculate the gated confidence score; if this value is lower than a preset safety threshold, the indicator function will forcibly flatten the original predicted current. This algorithm accurately cuts off non-physical noise, ensuring that the model's output is absolutely zero within the safe potential range, significantly improving the physical reliability of the model in applications.

[0056] The final model can accurately reconstruct the internal overpotential of the battery based on measurable signals from the external environment, thereby quantitatively predicting the lithium plating side reaction current and identifying the onset and dynamic intensity of lithium deposition. Furthermore, the model possesses deep aging mode identification capabilities, able to decouple and distinguish between a single solid electrolyte membrane growth mode and a mixed aging mode accompanied by lithium plating. Based on the identified critical conditions for lithium plating, the model can further construct a dynamic lithium-free safe charging boundary, providing a physical basis for the formulation of long-life fast-charging strategies.

[0057] Figure 4 The model's lithium plating current estimation results are presented under various typical temperature and rate conditions. This is achieved thanks to the improved mechanistic loss function (based on...). With the introduction of physical constraints, the model not only exhibits extremely high tracking accuracy during the intense lithium plating stage, but also strictly adheres to the electrochemical physical boundary conditions.

[0058] Figure 4 (a) Figure 4 (c) and Figure 4 (e) Three typical lithium deposition evolution scenarios with distinctly different mechanisms are depicted: initial lithium deposition at high rates in extremely cold conditions ( Figure 4 (a), 5C@-20°C: Under this extreme condition, the low temperature leads to a sharp increase in the solid electrolyte interphase (SEI) and charge transfer impedance at the negative electrode, resulting in a severe lithium plating reaction in the early stages of charging. Subsequently, due to the significant Joule heating effect inside the battery, the local temperature gradually increases, the lithium-ion insertion / extraction kinetics improve, and the lithium plating current shows a monotonically decreasing trend. The TCN-FCNN-SG model accurately tracks this nonlinear dynamic mitigation process.

[0059] SOC-dependent progressive lithium plating Figure 4(c), 1C@-20°C: Unlike extremely high rates, lithium plating is relatively weak in the initial stage of 1C charging. However, as the state of charge (SOC) continues to increase, the lithium-ion concentration on the surface of the negative electrode particles becomes saturated, and the limited solid-phase diffusion leads to increasingly severe lithium plating. It is not until the middle of the constant voltage (CV) charging stage that the step decay of the total charging current forces the lithium plating side reaction to weaken rapidly. The model accurately captures this aging path that deteriorates with increasing SOC.

[0060] Dynamic lithium plating at transition boundaries ( Figure 4 (e), 3C@0°C): This scenario reflects more complex dynamic boundary characteristics. The lithium plating reaction only occurs in the early to mid-stages. As the charging process progresses, the kinetic gains from the battery temperature rise outweigh the diffusion resistance caused by the increase in SOC. Coupled with the decrease in current at the end of the charging process, the lithium plating reaction eventually stops completely. The model accurately identifies this physical critical point of "lithium plating disappearance," demonstrating a very strong state awareness capability.

[0061] It is worth emphasizing that, Figure 4 (b) and Figure 4 (d) demonstrates the prediction performance under normal temperature (20°C) conditions without lithium plating. In traditional pure data-driven networks, such zero-boundary states are highly susceptible to interference from input feature noise, resulting in non-physical "false positive" predictions, i.e., ghost currents. However, this embodiment guides the model to learn the internal overpotential (as shown by the green dashed line) through an improved mechanistic loss function. As shown in the figure, combined with the SG gating mechanism, the predicted output is forcibly clamped to 0A within the region where the overpotential is positive. This perfectly verifies the decisive role of introducing prior physical knowledge in ensuring the robustness and physical consistency of the model.

[0062] Figure 4 (f) The quantitative error indices under various typical lithium plating conditions were further summarized. The results show that the lightweight network based on TCN-FCNN-SG maintains excellent and stable prediction accuracy under different combinations of conditions. In all test scenarios, the maximum root mean square error (RMSE) is only 0.096A, and the normalized root mean square error (nRMSE) and normalized mean absolute error (nMAE) are strictly controlled below 3.9% and 3.0%, respectively.

[0063] By leveraging electrochemical models to provide prior knowledge of internal aging and combining a lightweight TCN-FCNN-SG network optimized with a physical mechanism loss function, the engineering bottleneck of directly measuring the lithium plating side reaction current was successfully overcome. While ensuring low computational overhead, the precise definition of the lithium plating boundary and dynamic quantification of reaction intensity under complex operating conditions were achieved, providing reliable data support and theoretical basis for subsequently establishing a safe fast-charging boundary without lithium plating.

[0064] To simulate real-world battery management system (BMS) application scenarios and verify the model's generalization and diagnostic capabilities, this embodiment further conducted extensive bench tests covering critical lithium plating conditions, in addition to the simulation dataset. A high-density, multi-dimensional test matrix was set up: the charging rate range was set to 2.5A~25A (gradient of 2.5A), and the ambient temperature range was set to 0°C~20°C (gradient of 5°C). A total of 50 sets of real-world multi-condition feature sequences, including transient voltage, current, and surface temperature, were collected.

[0065] The aforementioned sensor feature data (without internal lithium plating signals) were input into a pre-trained TCN-FCNN-SG model for end-to-end inference to quickly identify hidden internal lithium plating side reaction currents. In 50 bench tests, the model successfully captured 34 scenarios where significant lithium metal deposition occurred (defined as local lithium plating current density exceeding 0.01 A / m). 2 (Safety threshold). The dynamic lithium plating current curves reconstructed from the model under various operating conditions are shown below. Figure 5 As shown.

[0066] Depend on Figure 5 The coupled influence of ambient temperature and charging rate on the kinetics of side reactions can be intuitively observed: the peak value and envelope area of ​​the curves directly reflect the severity of the lithium plating reaction and the accumulated capacity loss. As the ambient temperature decreases, the critical current threshold for lithium metal deposition shifts significantly earlier. Specifically, at a normal temperature of 20°C (red curves), a charging current of 17.5A (approximately 3.5C) is required to trigger a weak lithium plating signal; however, at a low temperature of 0°C (blue curves), a low charging rate of only 5A (approximately 1C) has already crossed the physical safety boundary, generating a visible lithium plating side reaction current. Furthermore, the time integral area of ​​each curve indicates that the extreme combination of "low temperature + high charging rate" will induce exponentially deteriorating lithium deposition, leading to extremely high risks of early capacity drops and thermal runaway. Based on the dynamic lithium plating spectrum generated by this model, combinations of physical boundary parameters highly correlated with lithium metal deposition (such as critical SOC, charging rate, and temperature) can be quickly extracted, providing high-fidelity data support for the lossless fast-charging management of power batteries.

[0067] To further transform diagnostic results into control target curves and support the implementation of optimal control strategies, this invention... Figure 5 Feature extraction was performed on the lithium plating current time-series curve to accurately pinpoint the transient external characteristics (SOC, current, and temperature) at the onset and termination of the lithium plating reaction. Table 4 provides a detailed statistical summary of the actual start and end times predicted by the model.

[0068] Table 4

[0069] Based on the data in Table 4, a three-dimensional "lithium-free safe fast-charging boundary" surface for the experimental battery was further constructed, as shown below. Figure 6 As shown. In Figure 6 In the three-dimensional coordinate system, the X and Y axes represent the battery's state of charge (SOC) and charging current, respectively, while the Z axis represents the real-time battery temperature. This spatial surface rigorously delineates the critical envelope surface for "lithium-free" charging under thermodynamic and kinetic equilibrium conditions: the space behind the surface (high SOC, high current, low temperature region) is the dangerous lithium deposition domain, while the space in front of the surface is the absolutely safe fast-charging operation domain. Typically, vehicle BMS limits the battery's fast-charging current based on the current battery temperature and SOC using a lookup table method. Therefore, based on the three-dimensional "lithium-free safe fast-charging boundary" surface, further dimensionality reduction interpolation using isothermal cross-sections can generate two-dimensional boundary curves at arbitrary temperature nodes on the lower "current-SOC" plane, such as... Figure 6 As shown in (b).

[0070] In practical BMS applications, there are tables showing the relationship between charging current and state of charge (SOC) at various temperatures (e.g., 10°C, 11°C, 12°C, ..., 25°C) to limit the charging current. Here, we take 15°C as an example. Figure 7 A lithium-free boundary for the "SOC-charging current" curve at 15°C was plotted. This curve clearly defines the maximum safe current and matching SOC range that the battery can withstand during fast charging, with the lower side of the curve representing the safe lithium-free region. The projection of the three-dimensional "lithium-free safe fast charging boundary" at the specified target temperature provides a direct reference for designing stepped or pulsed fast charging curves.

[0071] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for identifying dynamic safety boundaries for fast-charging batteries based on physical information networks, characterized in that, Includes the following steps: S1: Based on the reaction data of lithium-ion battery during operation, a lithium-ion battery fast-charging lithium deposition model is constructed, and the time-series data of the lithium metal deposition reaction current inside the battery is obtained based on the lithium-ion battery fast-charging lithium deposition model. S2: Construct a TCN-FCNN-SG neural network to obtain the predicted value of lithium metal deposition current based on the time series data; S3: Determine the safety boundary for fast charging of the battery based on the predicted value of lithium metal deposition current.

2. The method for identifying dynamic safety boundaries for fast-charging batteries based on physical information networks according to claim 1, characterized in that, The lithium-ion battery fast-charging lithium plating model includes: an electrochemical reaction model on the surface of electrode active particles, a lithium-ion motion equation, a temperature model during battery charging and discharging, and a current density model.

3. The method for identifying dynamic safety boundaries for fast-charging batteries based on physical information networks according to claim 2, characterized in that, The current density model includes: ； in, ； ； In the formula, This represents the total current density passing through the solid-liquid interface; This represents the lithium-ion flux density generated by the electrochemical reaction on the surface of the active particles. This represents the local current density of the lithium metal deposition side reaction; Indicates the number of charges carried by lithium ions; Denotes Faraday's constant; Indicates the lithium metal deposition reaction rate; This indicates the lithium-ion concentration on the surface of solid particles; Indicates the anode / cathode transfer coefficient; Represents the universal gas constant; This indicates the overpotential at which lithium metal deposition occurs; , These represent the solid-phase potential and the liquid-phase potential, respectively. This represents the equilibrium potential of the lithium metal deposition reaction. Represents solid-state current density; This represents the resistance generated by the solid electrolyte passivation film on the particle surface.

4. The method for identifying dynamic safety boundaries for fast-charging batteries based on physical information networks according to claim 1, characterized in that, The TCN-FCNN-SG neural network includes: a TCN convolutional module, a TCN main branch, a physical branch, and a soft-gate component; The TCN convolution module is used to perform convolution processing on the input tensor to obtain the latent feature vector; The main branch of the TCN is used to perform nonlinear mapping on the latent feature vector to obtain electrochemical features; The physical branch takes the potential feature vector as input to obtain the predicted value of the negative electrode overpotential; Based on the electrochemical characteristics and the negative electrode overpotential, the predicted value of lithium metal deposition current is obtained. The predicted value of lithium metal deposition current is introduced into the soft gate assembly to obtain the final predicted value of lithium metal deposition current.

5. The method for identifying dynamic safety boundaries for fast-charging batteries based on physical information networks according to claim 4, characterized in that, The methods for obtaining the negative electrode overpotential include: ； ； In the formula, Indicates the process The final output of the physical branch after layer transformation; For the first Layer weight matrix; For the first The activation output vector of the layer; For the first Layer bias vector; It is a linear activation function.

6. The method for identifying dynamic safety boundaries for fast-charging batteries based on physical information networks according to claim 5, characterized in that, The total loss function of the TCN-FCNN-SG neural network include: ； in, ； In the formula, The mean squared error loss function represents the data-driven term. This represents the weighting coefficient of the physical constraint term. Represents the loss function for physical constraint terms; This indicates a constraint that the deposition current is nonnegative; This indicates a potential-current consistency constraint. This represents the predicted value of lithium metal deposition current; This represents the predicted overpotential value of the negative electrode.

7. The method for identifying dynamic safety boundaries for fast-charging batteries based on physical information networks according to claim 6, characterized in that, The method for processing the predicted value of lithium metal deposition current by the soft-gate component includes: ； In the formula, This represents the final predicted lithium plating current; Indicates the activation function; Indicates the gain; This represents the overpotential predicted by the physics branch.

8. The method for identifying dynamic safety boundaries for fast-charging batteries based on physical information networks according to claim 1, characterized in that, The method for determining the safety boundary of a battery during fast charging based on the predicted value of lithium metal deposition current includes: Based on the predicted lithium deposition current, transient external characteristics at the occurrence and termination of the lithium deposition reaction are obtained; the transient external characteristics include: state of charge, current, and temperature; A three-dimensional lithium-free fast charging boundary surface is constructed based on the state of charge, charging current, and real-time battery temperature. Based on the three-dimensional lithium-free fast charging boundary surface, a table showing the relationship between charging current and state of charge at different temperatures is determined, thereby determining the dynamic safety boundary for fast charging of the battery.

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