Mechanism-data fusion lithium-ion battery state-of-charge estimation method and system

Abstract

The present application relates to a lithium ion battery state of charge estimation method and system based on mechanism-data fusion, which builds a state space equation by fusing a double-particle electrochemical model and a first-order RC equivalent circuit, taking into account the battery micro solid-phase diffusion kinetics mechanism and the macro electrical external characteristics; and builds a parameter identification framework based on a physical information neural network, realizes high-precision synchronous iterative updating of parameters through a multi-class residual adaptive weighted loss function and an automatic differentiation gradient solving mechanism, and completes online identification of the state space equation in combination with a fourth-order Runge-Kutta discrete iteration and a closed-loop residual updating mechanism; finally, the state space equation after convergence optimization is used to realize high-precision online estimation of the state of charge, polarization voltage and cell temperature of the lithium ion battery, which can effectively improve the stability and generalization ability of the lithium ion battery state estimation under complex working conditions, reduce the algorithm consumption of online iterative updating, and realize high-precision, strong robustness and low algorithm consumption of the battery state continuous estimation.

Description

Technical Field

[0001] This invention relates to the field of power battery management system technology, and in particular to a mechanism-data fusion method and system for estimating the state of charge of lithium-ion batteries. Background Technology

[0002] The state of charge (SOC) of a lithium-ion battery is a core parameter of the battery management system (BMS). Accurately estimating the SOC is crucial for ensuring battery safety, optimizing energy control, preventing overcharging and over-discharging, and extending battery life.

[0003] Currently, mainstream SOC estimation methods can be divided into two categories: mechanism-driven and data-driven. Mechanism-driven methods rely on the accuracy of the model, and their parameters are easily affected by battery aging, temperature, and changes in operating conditions, resulting in insufficient robustness. Although data-driven methods can directly learn complex mapping relationships from data, they usually lack the embedding of the battery's intrinsic physical laws, resulting in poor model interpretability and limited generalization ability under operating conditions not covered by the training data.

[0004] Developing a method that can embed mechanistic models into neural network frameworks in a learnable and optimizable manner to achieve a fusion of online parameter identification and state co-estimation is urgently needed to improve the accuracy, adaptability, and engineering practicality of SOC estimation. Summary of the Invention

[0005] This invention addresses the technical problems of existing lithium-ion battery state-of-charge (SOC) estimation methods, such as insufficient robustness of pure mechanistic models, weak generalization ability of pure data-driven models, high computational cost for online parameter identification, and limited adaptability to operating conditions. It proposes a mechanism-data fusion method for SOC estimation of lithium-ion batteries. This method constructs a state-space equation that integrates a two-particle electrochemical model with a first-order RC equivalent circuit, taking into account both the microscopic solid-phase diffusion dynamics and macroscopic electrical characteristics of the battery. A parameter identification framework is built based on a physical information neural network. High-precision synchronous iterative updates of parameters are achieved through multi-class residual adaptive weighted loss functions and automatic differential gradient solving mechanisms. Online identification of the state-space equation is completed by combining a fourth-order Runge-Kutta discrete iteration and closed-loop residual update mechanism. Finally, the converged and optimized state-space equation is used to achieve high-precision online estimation of the lithium-ion battery's SOC, polarization voltage, and cell temperature. This method effectively improves the stability and generalization ability of lithium-ion battery SOC estimation under complex operating conditions, reduces the computational cost of online iterative updates, and achieves high-precision, robust, and low-computational-cost continuous estimation of the battery SOC. This invention also relates to a mechanism-data fusion-based lithium-ion battery state of charge estimation system.

[0006] The technical solution of the present invention is as follows:

[0007] A mechanism-data fusion method for estimating the state of charge of lithium-ion batteries, characterized by the following steps:

[0008] S1. Taking lithium-ion batteries as the object, single-particle models are established for both the positive and negative electrodes, and combined to form a two-particle electrochemical model. The Arrhenius equation is embedded into the two sets of solid-phase diffusion partial differential equations corresponding to the positive and negative electrodes in the two-particle electrochemical model to characterize the coupling relationship between temperature and solid-phase diffusion kinetics. Boundary conditions are configured for both sets of solid-phase diffusion partial differential equations, where the lithium-ion flux at the particle center is zero and the lithium-ion flux on the particle surface is coupled with the battery charge / discharge current. The two sets of solid-phase diffusion partial differential equations are transformed into a set of ordinary differential equations using numerical discretization. The real-time collected battery charge / discharge current and cell temperature are substituted into these ordinary differential equations to solve the set of ordinary differential equations, obtaining the discrete solid-phase lithium-ion concentration. The lithium filling ratio is then calculated from the discrete solid-phase lithium-ion concentration. A first-order RC equivalent circuit is introduced to construct a parameter mapping relationship with lithium filling ratio and real-time acquired cell temperature as inputs, and ohmic internal resistance, polarization internal resistance, and polarization capacitance as outputs. This parameter mapping relationship realizes the mechanistic fusion of the two-particle electrochemical model and the first-order RC equivalent circuit. Based on the mapped ohmic internal resistance, polarization internal resistance, and polarization capacitance, a dynamic differential equation for polarization voltage corresponding to the first-order RC equivalent circuit is established to characterize the time-domain variation characteristics of polarization voltage. This is combined with the temperature energy conservation dynamic equation to characterize the dynamic evolution of cell temperature. The three state variables of discrete solid-phase lithium ion concentration, polarization voltage, and cell temperature are integrated to form a unified state vector, and a state-space equation that simultaneously includes the microscopic solid-phase diffusion mechanism and macroscopic electrical external characteristics is constructed.

[0009] S2. Construct a parameter identification framework based on a physical information neural network, and within the parameter identification framework, construct an adaptive weighted total penalty loss function that simultaneously includes the residuals of the solid-phase diffusion partial differential equation, initialization residuals, boundary condition residuals, and the observation residuals of the first-order RC equivalent circuit model under the operating conditions. The adaptive weighted total penalty loss function assigns corresponding weights according to the magnitude of the residuals, with larger residuals receiving higher weights. The lithium-ion solid-phase diffusion coefficient, ohmic internal resistance, polarization internal resistance, and polarization capacitance corresponding to the state-space equation, as well as the weight parameters and bias parameters corresponding to the physical information neural network, are set together as the parameters to be updated for synchronous iterative optimization. A gradient solution channel for all parameters to be updated is established using the adaptive weighted total penalty loss function based on an automatic differentiation mechanism, and all parameters to be updated constitute a joint optimization parameter set.

[0010] S3. The state-space equations are discretized in the time domain using a fourth-order Runge-Kutta numerical discretization algorithm. Utilizing the constructed adaptive weighted total penalty loss function, the established gradient solution channel, and the established joint optimization parameter set, a gradient-based backpropagation optimization algorithm is used to synchronously iteratively update each parameter to be updated, completing the online parameter identification of the state-space equations. The predicted terminal voltage and predicted cell temperature obtained through the discretization and recursive calculation of the state-space equations are fed back to step S2 to recalculate the residuals of the first-order RC equivalent circuit model under operating conditions, thereby updating the adaptive weighted total penalty loss function for iterative optimization of each parameter to be updated. After the iterative optimization of each parameter to be updated meets the preset convergence condition, the process proceeds to step S4.

[0011] S4. Using the state-space equations that have been converged through parameter iteration in step S3, the real-time charge and discharge current of the lithium-ion battery is used as the input quantity of the state-space equations for solving. The online estimation results of the state of charge, polarization voltage, and cell temperature of the lithium-ion battery are obtained from the solved state vectors.

[0012] Preferably, in step S1, the two sets of solid-phase diffusion partial differential equations are transformed into a set of ordinary differential equations using the finite difference method or spherical harmonic functions; the lithium filling ratio and average lithium filling ratio on the positive and negative electrode surfaces are calculated from the discrete solid-phase lithium ion concentration; the ohmic internal resistance and polarization internal resistance are obtained through parameter mapping based on the surface lithium filling ratio and the real-time collected cell temperature; the open-circuit voltage and polarization capacitance are obtained through parameter mapping based on the average lithium filling ratio and the real-time collected cell temperature; the mechanism of the two-particle electrochemical model and the first-order RC equivalent circuit is integrated through this parameter mapping relationship to form a wide-temperature-range electrochemical-equivalent circuit fusion model of lithium-ion battery; the three state variables of discrete solid-phase lithium ion concentration, polarization voltage, and cell temperature are integrated to form a unified state vector, and the constructed state-space equation is the state-space equation corresponding to the wide-temperature-range electrochemical-equivalent circuit fusion model of lithium-ion battery.

[0013] Preferably, in step S2, when constructing the adaptive weighted total penalty loss function, physical equation residuals are constructed for the solid-phase diffusion partial differential equation of the two-particle electrochemical model, initialization residuals are constructed for the initial state, boundary condition residuals are constructed for the particle boundary constraints, and operating condition fitting simulation observation residuals are constructed for the predicted terminal voltage and measured terminal voltage of the first-order RC equivalent circuit model. Adaptive weighted combination is achieved by configuring independent weight coefficients for the four types of residuals. The gradient of the adaptive weighted total penalty loss function is obtained by relying on automatic differentiation technology to build a gradient solution channel. Through the backpropagation gradient descent optimization strategy, the physical parameters corresponding to the state space equation and the weight parameters and bias parameters corresponding to the physical information neural network are synchronously and jointly iteratively optimized.

[0014] Preferably, in step S3, a fourth-order Runge-Kutta numerical discretization algorithm is used to discretize the continuous-time state-space equation in the time dimension. The discretization process uses differentiable operators to construct recursive formulas so that the gradient of the parameters to be updated can be obtained by automatic differentiation within the physical information neural network framework. The gradient-based backpropagation optimization algorithm uses gradient descent, Adam optimizer, or Runge-Kutta optimization algorithm to perform synchronous backpropagation iterative updates on each parameter to be updated. The state variables are solved recursively step by step according to the set sampling time step to obtain the predicted terminal voltage and predicted cell temperature at the corresponding time and feed them back to step S2 to update the observation residuals. After multiple iterations until the parameters to be updated meet the preset convergence conditions, the process jumps to step S4 to complete the joint identification and solution of the parameters of the state-space equation.

[0015] Preferably, in step S4, when performing state of charge estimation, a bidirectional gated recurrent unit is embedded inside the physical information neural network to construct a state of charge estimation model. The bidirectional gated recurrent unit is composed of two independent gated recurrent units stacked together, which respectively perform forward sequence feature extraction and reverse sequence feature extraction on the battery time-series operating data, fuse the hidden states output by the two branches, and capture the bidirectional dependency relationship of the time-series data. The predicted terminal voltage and predicted cell temperature obtained by discrete recursive calculation through state-space equations, the real-time collected battery terminal voltage and cell temperature, the state of charge calculated by ampere-hour integration, and the real-time collected battery charging and discharging current are used as the network input parameters of the state of charge estimation model, and the actual state of charge of the battery is used as the output label of the state of charge estimation model. The adaptive weighted total penalty loss function is used as a constraint to train the state of charge estimation model, and the online estimation of the state of charge of lithium-ion batteries is realized based on the trained state of charge estimation model.

[0016] Preferably, in step S4, each group of gated loop units in the bidirectional gated loop unit is independently configured with two types of gated structures: update gate and reset gate. Each group of gated loop units uses the Sigmoid activation function to calculate the update gate weight coefficient and the reset gate weight coefficient respectively. After filtering the historical hidden state at the previous time step using the reset gate weight, candidate hidden states are generated by calculating the Tanh activation function. The original hidden state and candidate hidden state at the historical time step are weighted and fused element-wise according to the update gate weight to obtain the final hidden state of a single branch. The final hidden states obtained by solving the forward and reverse branches of the bidirectional gated loop unit are fused element-wise to complete the feature capture of the bidirectional dependency relationship of the battery time series data.

[0017] Preferably, in step S4, an event-triggered scheduling mechanism is configured to dynamically schedule the iterative identification process of the joint optimization parameter set. Specifically, this includes: calculating the voltage residual by comparing the predicted terminal voltage obtained from the state space equation through discrete recursive calculation with the real-time battery acquisition terminal voltage; calculating the temperature residual by comparing the predicted cell temperature obtained from the state space equation through discrete recursive calculation with the real-time battery acquisition cell temperature; accumulating the voltage residual and temperature residual; and when the accumulated total residual exceeds a preset threshold, returning to steps S2 and S3 to re-execute parameter identification and iterative optimization. A minimum trigger interval is set based on the event trigger judgment condition, and a forgetting factor is introduced to attenuate and weight the historical residuals to reduce the frequency of invalid retraining triggers caused by historical residuals.

[0018] A mechanism-data fusion lithium-ion battery state-of-charge estimation system is characterized by comprising, in sequence, a coupled state-space equation construction module, an adaptive weighted physical information network identification framework construction module, a Runge-Kutta discrete iterative parameter identification and convergence calculation module, and a battery multi-parameter joint estimation module, wherein...

[0019] The coupled state-space equation construction module, taking lithium-ion batteries as the object, establishes single-particle models at both the positive and negative electrodes, combining them to form a two-particle electrochemical model. The Arrhenius equation is embedded within the two sets of solid-phase diffusion partial differential equations corresponding to the positive and negative electrodes in the two-particle electrochemical model to characterize the coupling relationship between temperature and solid-phase diffusion kinetics. Boundary conditions are configured for both sets of solid-phase diffusion partial differential equations, where the lithium-ion flux at the particle center is zero and the lithium-ion flux at the particle surface is coupled with the battery charge / discharge current. The two sets of solid-phase diffusion partial differential equations are transformed into a set of ordinary differential equations using numerical discretization. The ordinary differential equations are then solved by substituting the real-time collected battery charge / discharge current and cell temperature to obtain the discrete solid-phase lithium-ion concentration. The lithium filling ratio is calculated. A first-order RC equivalent circuit is introduced to construct a parameter mapping relationship with lithium filling ratio and real-time acquired cell temperature as inputs, and ohmic internal resistance, polarization internal resistance, and polarization capacitance as outputs. This parameter mapping relationship realizes the mechanism fusion of the two-particle electrochemical model and the first-order RC equivalent circuit. Based on the mapped ohmic internal resistance, polarization internal resistance, and polarization capacitance, a dynamic differential equation for polarization voltage corresponding to the first-order RC equivalent circuit is established to characterize the time-domain variation characteristics of polarization voltage. The dynamic equation of temperature energy conservation is combined to characterize the dynamic evolution of cell temperature. The three state variables of discrete solid-phase lithium ion concentration, polarization voltage, and cell temperature are integrated to form a unified state vector, and a state-space equation that simultaneously includes the microscopic solid-phase diffusion mechanism and macroscopic electrical external characteristics is constructed.

[0020] The adaptive weighted physical information network identification framework construction module constructs a parameter identification framework based on a physical information neural network. Within this framework, an adaptive weighted total penalty loss function is built that simultaneously includes the residuals of the solid-phase diffusion partial differential equation, initialization residuals, boundary condition residuals, and the simulation observation residuals of the first-order RC equivalent circuit model under operating conditions corresponding to the two-particle electrochemical model. The adaptive weighted total penalty loss function assigns corresponding weights according to the magnitude of the residuals, with larger residuals receiving higher weights. The lithium-ion solid-phase diffusion coefficient, ohmic internal resistance, polarization internal resistance, and polarization capacitance corresponding to the state-space equation, as well as the weight parameters and bias parameters corresponding to the physical information neural network, are collectively set as parameters to be updated through synchronous iterative optimization. A gradient solution channel for all parameters to be updated is established using the adaptive weighted total penalty loss function based on an automatic differentiation mechanism, and all parameters to be updated constitute a joint optimization parameter set.

[0021] The Runge-Kutta discrete iterative parameter identification and convergence module employs a fourth-order Runge-Kutta numerical discretization algorithm to discretize the state-space equations in the time domain. Utilizing a constructed adaptive weighted total penalty loss function, an established gradient solution channel, and a set of joint optimization parameters, it performs synchronous iterative updates on each parameter using a gradient-based backpropagation optimization algorithm, thus completing the online parameter identification of the state-space equations. The predicted terminal voltage and predicted cell temperature obtained through the discrete recursive operation of the state-space equations are fed back to the adaptive weighted physical information network identification framework construction module. This is used to recalculate the residuals from the simulation observation of the first-order RC equivalent circuit model under operating conditions, updating the adaptive weighted total penalty loss function for iterative optimization of each parameter. After the iterative optimization of each parameter meets the preset convergence conditions, the module proceeds to the battery multi-parameter joint estimation module.

[0022] The battery multi-parameter joint estimation module uses the state-space equation after parameter iteration convergence completed by the Runge-Kutta discrete iterative parameter identification and convergence calculation module. The real-time charging and discharging current of the lithium-ion battery is used as the input quantity of the state-space equation for solving. The online estimation results of the lithium-ion battery state of charge, polarization voltage and cell temperature are obtained from the obtained state vector.

[0023] Preferably, in the coupled state-space equation construction module, two sets of solid-phase diffusion partial differential equations are transformed into a set of ordinary differential equations using the finite difference method or spherical harmonic functions; the lithium filling ratio and average lithium filling ratio on the positive and negative electrode surfaces are calculated from the discrete solid-phase lithium ion concentration; the ohmic internal resistance and polarization internal resistance are obtained through parameter mapping based on the surface lithium filling ratio and the real-time acquired cell temperature; the open-circuit voltage and polarization capacitance are obtained through parameter mapping based on the average lithium filling ratio and the real-time acquired cell temperature; the mechanism of the two-particle electrochemical model and the first-order RC equivalent circuit is integrated through this parameter mapping relationship to form a wide-temperature-range electrochemical-equivalent circuit fusion model of lithium-ion battery; the three state variables of discrete solid-phase lithium ion concentration, polarization voltage, and cell temperature are integrated to form a unified state vector, and the constructed state-space equation is the state-space equation corresponding to the wide-temperature-range electrochemical-equivalent circuit fusion model of lithium-ion battery.

[0024] Preferably, in the battery multi-parameter joint estimation module, when performing state of charge estimation, a bidirectional gated recurrent unit is embedded inside the physical information neural network to construct a state of charge estimation model. The bidirectional gated recurrent unit is composed of two independent gated recurrent units stacked together, which respectively perform forward sequence feature extraction and reverse sequence feature extraction on the battery time-series operating data, fuse the hidden states output by the two branches, and capture the bidirectional dependency relationship of the time-series data. The predicted terminal voltage and predicted cell temperature obtained by discrete recursive calculation through state-space equations, the real-time collected battery terminal voltage and cell temperature, the state of charge calculated by ampere-hour integration, and the real-time collected battery charging and discharging current are used as the network input parameters of the state of charge estimation model, and the actual state of charge of the battery is used as the output label of the state of charge estimation model. The adaptive weighted total penalty loss function is used as a constraint to train the state of charge estimation model, and the online estimation of the state of charge of lithium-ion batteries is realized based on the trained state of charge estimation model.

[0025] The technical effects of this invention are as follows:

[0026] This invention relates to a mechanism-data fusion method for estimating the state of charge (SOC) of lithium-ion batteries. Its S1 step accurately characterizes the microscopic dynamics of lithium-ion solid-phase diffusion using a two-particle electrochemical model of the positive and negative electrodes. It incorporates the Arrhenius equation to achieve temperature-dependent correction of the solid-phase diffusion rate. Combined with physical boundary conditions of zero flux at the particle center and surface current coupling, this significantly improves the realism of the description of internal ion evolution under low-temperature and high-temperature wide-temperature conditions. It solves the problems of pure equivalent circuit models failing to reflect temperature effects and lacking microscopic mechanisms, leading to poor adaptability under various operating conditions. The method numerically discretizes the partial differential equations of solid-phase diffusion into a system of ordinary differential equations, which can be directly obtained through measured current... Numerical solutions for cell temperature were obtained, enabling the engineering application of the mechanistic equations and avoiding the limitation of high-order partial differential equations that cannot be calculated online in real time. A parameter mapping relationship was established between lithium filling ratio, cell temperature, and the internal resistance and capacitance of the RC circuit, achieving deep coupling between the microscopic electrochemical mechanism and the macroscopic first-order RC equivalent circuit. This retains the high accuracy advantage of the electrochemical model while simplifying the calculation complexity of external characteristics by relying on the equivalent circuit, balancing model accuracy and online computing power. A unified state-space equation was constructed by integrating solid-phase lithium-ion concentration, polarization voltage, and cell temperature, realizing a unified temporal evolution description of multiple physical quantities and providing a standardized mathematical carrier for subsequent synchronous parameter identification and joint estimation of multiple state quantities. Its S2 step is based on a physical information neural network to build an identification framework. It incorporates electrochemical equation residuals, initial value residuals, boundary residuals, and circuit observation residuals into the loss function. It uses physical equations to constrain the neural network training process, overcoming the shortcomings of pure data-driven models that rely on a large amount of calibration data and have weak extrapolation and generalization capabilities. It can still ensure identification reliability under small sample conditions. It adopts a residual numerical adaptive weighting mechanism, assigning higher penalty weights to residual terms with larger deviations, automatically correcting the problem of unbalanced fitting deviations of various equations under different conditions, and improving the balance and accuracy of parameter identification under complex dynamic conditions. It packages electrochemical mechanism parameters with neural network weights and bias parameters into a joint optimization parameter set, and relies on automatic differentiation to open up the gradient solution channel for all parameters. It realizes synchronous iterative updates of physical parameters of the mechanism model and data-driven network parameters, avoiding the problems of parameter coupling mismatch and large cumulative error caused by step-by-step identification, and improving the consistency of parameters of the entire model.Its S3 step uses a fourth-order Runge-Kutta algorithm to perform high-precision time-domain discretization of the state-space equations. Compared with low-order discretization methods such as the Euler method, the numerical truncation error is smaller, and the drift of state variables is significantly reduced under long-term iteration, ensuring the stability of online parameter identification. A closed-loop iterative link is constructed, which consists of "parameter iterative update - discrete recursive output of predicted voltage / cell temperature - back transmission of S2 step to update observation residuals". Each round of parameter update is based on the latest operating condition observation deviation correction loss function, forming a closed-loop self-correction mechanism to continuously offset the model drift caused by sensor noise and aging attenuation. A parameter convergence judgment condition is set to terminate the iteration process to avoid unlimited iteration and computational redundancy. Under the premise of ensuring the identification accuracy meets the standard, the online computing power consumption of the vehicle embedded terminal is effectively reduced, solving the pain point of excessive computing power consumption in traditional online identification. Its S4 step directly calls the coupled state-space equations that have been converged and optimized. Only the real-time charge and discharge current needs to be input to solve the state vector at once. It simultaneously outputs three key state variables: state of charge, polarization voltage, and cell temperature, realizing integrated online estimation of multiple parameters. Based on the state-space equations that have been optimized by mechanism coupling and parameter convergence in the previous steps, the estimation results are less affected by disturbances such as dynamic large current, temperature fluctuations, and battery aging. This effectively improves the robustness of state of charge estimation and avoids the problem of estimation jumps and error deviations caused by a single model under harsh operating conditions.

[0027] This invention presents a mechanism-data fusion-based method for estimating the state of charge (SOC) of lithium-ion batteries, which improves both accuracy and robustness. By coupling the mechanism of two-particle electrochemistry with a first-order RC equivalent circuit, and superimposing a physical information neural network with multi-residual adaptive weighted constraints, it overcomes the shortcomings of insufficient robustness of pure mechanism models and weak generalization ability of pure data models. Under complex vehicle operating conditions such as wide temperature range, dynamic power variation, and slight battery aging, the estimation errors of SOC, polarization voltage, and cell temperature are smaller, and the long-term operational stability is stronger. The method also boasts high parameter identification accuracy and good consistency: it achieves joint synchronous gradient optimization of electrochemical physical parameters and neural network weight parameters, coupled with a fourth-order Runge-Kutta (RK4) high-precision discretization and residual closed-loop self-correction iterative mechanism, significantly improving the online identification accuracy of the state-space equation and effectively suppressing model drift. Finally, the computational cost is reasonable and controllable: through convergence condition truncation iteration, engineering-based discretization transformation of partial differential equations, and a closed-loop on-demand update mechanism, the computational load of online iteration is reduced, making it compatible with vehicle-mounted BMS. The embedded chip low-computing-power operating environment solves the problem of excessive computing power and difficulty in engineering implementation of traditional high-precision online identification algorithms; multi-state quantity integrated output: a fusion model can simultaneously complete the real-time estimation of three core state quantities: SOC, polarization voltage, and cell temperature; a single algorithm realizes multi-target state perception, simplifies the algorithm architecture of the battery management system, and reduces program deployment and maintenance costs; strong temperature condition adaptability: the temperature coupling mechanism of the Arrhenius equation runs through the entire solid-phase diffusion calculation process, and the model can automatically adapt to the changes in ion diffusion rate under high and low temperature environments, greatly expanding the temperature range in which the algorithm can reliably operate.

[0028] Furthermore, by using the finite difference method or spherical harmonic functions to transform the solid-phase diffusion partial differential equations into a system of ordinary differential equations, the numerical stability and computational accuracy of the discrete solution of the electrochemical mechanism equations can be guaranteed. By mapping the differences in lithium filling ratios on the positive and negative electrode surfaces and the average lithium filling ratio to different parameters of the equivalent circuit, the coupling logic between the electrochemical micro-concentration characteristics and macro-electrical parameters can be made more consistent with the actual physicochemical laws of the battery. This allows for the accurate construction of a wide-temperature-range electrochemical-equivalent circuit fusion model, further enhancing the ability of the final state-space equations to characterize the internal evolution characteristics of the battery under high and low temperature conditions. This strengthens the wide-temperature-range adaptability of the entire method from the modeling source.

[0029] Furthermore, by clarifying the independent weighting configuration of four types of residuals, the gradient solution implementation method, and the joint optimization strategy, independent weight coefficients are set for the physical equation residuals, initialization residuals, boundary condition residuals, and observation residuals. The penalty intensity can be adaptively allocated according to the fitting deviation of various constraint terms under different working conditions, avoiding the problem of fitting failure of a certain type of mechanism constraint caused by a single weight. A complete gradient solution channel is built based on automatic differentiation technology, and a backpropagation strategy is adopted to simultaneously optimize the mechanism physical parameters and neural network hyperparameters. This eliminates the defects of parameter coupling mismatch and cumulative error amplification caused by step-by-step parameter identification, greatly improves the identification consistency and global optimality of the joint optimization parameter set, and enhances the balance and reliability of parameter identification under complex dynamic working conditions.

[0030] Furthermore, in the discretization process of the fourth-order Runge-Kutta numerical discretization algorithm (RK4), a differentiable operator is used to construct the recursive formula, ensuring that the discretization operation link can be connected to the PINN automatic differentiation framework (physical information neural network framework) to complete gradient backpropagation, thus solving the pain point that traditional numerical discretization cannot participate in the backpropagation of neural networks. Multiple high-precision optimization algorithms such as Adam are limited to be selected, which improves the convergence speed of multi-parameter joint optimization and the ability to escape local optima. The prediction value is recursively backpropagated according to the time step and the observation residual is updated in a closed loop, forming an iterative self-correcting closed loop. At the same time, the iteration is terminated by the convergence condition, which reduces the consumption of ineffective iteration computing power while ensuring that the parameter identification accuracy meets the standard, and further reduces the computational overhead of online identification on the embedded end.

[0031] Furthermore, a bidirectional gated recurrent unit (Bi-GRU) time-series network embedding optimization scheme is added on top of the basic estimation function in step S4. By using bidirectional stacked independent GRUs to extract forward and reverse time-series features respectively, the long-term dependency relationship between battery historical operating data and future operating conditions is fully explored, making up for the shortcomings of the basic state-space equation relying only on instantaneous input quantity estimation and insufficient capture of time-series dynamic changes. The combination of multi-dimensional and multi-source input features and the real state of charge label supervised training mode, combined with the preceding adaptive weighted loss function for mechanistic constraints, allows the estimation model to have both electrochemical and physical rule constraints and learn the implicit laws of massive time-series operating conditions, effectively improving the anti-disturbance capability and long-term generalization performance of SOC estimation under variable current and dynamic impact conditions.

[0032] Furthermore, each independent GRU in the Bi-GRU is equipped with two types of gating structures: update gates and reset gates. The Sigmoid activation function controls the gating switch, and the Tanh activation function completes the nonlinear mapping of candidate hidden states. The final hidden state within the branch is solved through element-wise weighted fusion rules. Then, the outputs of the positive and negative branches are fused element-wise to achieve full reuse of bidirectional temporal information. The standardized gating operation rules can stably filter out historical invalid temporal information and retain long-period deep correlation features, making the feature extraction of bidirectional temporal dependencies more accurate. This further enhances the ability of the state of charge estimation model to perceive the long-term operating condition fluctuations of the battery and reduces the estimation error caused by temporal lag.

[0033] Furthermore, an event-triggered closed-loop dynamic scheduling mechanism is added to dynamically schedule the iterative identification process of the joint optimization parameter set. The predicted terminal voltage obtained by discrete recursive operation of the state space equation is compared with the real-time battery acquisition terminal voltage to calculate the voltage residual. The predicted cell temperature obtained by discrete recursive operation of the state space equation is compared with the real-time battery acquisition cell temperature to calculate the temperature residual. That is, the judgment rule of calculating the residuals separately and then accumulating them completely eliminates the ambiguity of the judgment logic caused by subtracting across physical quantities. Only when the total residual exceeds the limit is the S2 and S3 re-identification triggered retrospectively, replacing the continuous cyclic iteration mode, which significantly saves the continuous computing power occupation under normal stable working conditions. The minimum trigger interval limit is superimposed to avoid frequent repeated triggering of iteration in a short period of time. At the same time, a forgetting factor is introduced to attenuate and weight the superposition of historical residuals, weakening the interference of old working condition residuals on the current judgment, greatly reducing the frequency of invalid retraining caused by small noise fluctuations in the battery. While maintaining the closed-loop self-correction capability of the model, the identification computing power is allocated on demand, further optimizing the power consumption and computing efficiency of algorithm engineering implementation.

[0034] This invention also relates to a mechanism-data fusion lithium-ion battery state-of-charge estimation system, corresponding to the mechanism-data fusion lithium-ion battery state-of-charge estimation method described above. It can be understood as a system that implements the aforementioned mechanism-data fusion lithium-ion battery state-of-charge estimation method. This system includes a coupled state-space equation construction module, an adaptive weighted physical information network identification framework construction module, a Runge-Kutta discrete iterative parameter identification and convergence calculation module, and a battery multi-parameter joint estimation module, connected sequentially. These modules work collaboratively to construct a state-space equation that integrates a two-particle electrochemical model and a first-order RC equivalent circuit, taking into account the battery's microstructure. This study investigates the phase diffusion dynamics mechanism and macroscopic electrical external characteristics. A parameter identification framework is built based on a physical information neural network. High-precision synchronous iterative updates of parameters are achieved through multi-class residual adaptive weighted loss functions and automatic differential gradient solving mechanisms. Online identification of the state-space equation is completed by combining fourth-order Runge-Kutta discrete iteration and closed-loop residual update mechanisms. Finally, the convergent and optimized state-space equations are used to achieve high-precision online estimation of battery state of charge, polarization voltage, and cell temperature. This effectively improves the stability and generalization ability of battery state estimation under complex operating conditions, reduces the computational cost of online iterative updates, and achieves high-precision, robust, and low-computational-cost continuous estimation of battery state. Attached Figure Description

[0035] Figure 1 This is a flowchart of the mechanism-data fusion method for estimating the state of charge of lithium-ion batteries according to the present invention. Detailed Implementation

[0036] The present invention will now be described with reference to the accompanying drawings.

[0037] This invention provides a mechanism-data fusion method for estimating the state of charge (SOC) of lithium-ion batteries. First, it constructs a state-space equation integrating a two-particle electrochemical model and a first-order RC equivalent circuit, completing the mechanism coupling modeling of the battery's microscopic solid-phase diffusion dynamics and the external characteristics of the macroscopic equivalent circuit. Then, based on a physical information neural network architecture, it builds a joint parameter identification framework, constructing an adaptive weighted penalty loss function from the solid-phase diffusion equation residuals, boundary condition residuals, and equivalent circuit observation simulation residuals. Furthermore, it uses electrochemical mechanism physical parameters, neural network weights, and bias parameters as jointly optimized parameters that can be synchronously iteratively updated. Finally, it employs... The fourth-order Runge-Kuttako differentiable discrete algorithm, combined with optimizers such as Adam and gradient descent, synchronously backpropagates and iteratively updates all joint parameters. Relying on the predicted voltage and temperature closed-loop backpropagation to update the loss function, it completes online identification and parameter convergence solution of the state-space equation. Then, a bidirectional gated recurrent unit network is embedded to extract the battery's time-series bidirectional dependency features to optimize the state-of-charge estimation effect. Finally, an event-triggered scheduling mechanism dynamically schedules the parameter re-identification process based on the cumulative threshold of the partial residuals, and utilizes a forgetting factor to decay historical residuals and reduce invalid triggers, ultimately achieving high-precision, low-computational-cost online estimation of the battery's state of charge for lithium-ion batteries. Figure 1 The flowchart shown includes the following steps:

[0038] S1. Steps for constructing coupled state-space equations

[0039] Taking lithium-ion batteries as the object, single-particle models are established for both the positive and negative electrodes, and combined to form a two-particle electrochemical model. The Arrhenius equation is embedded into the two sets of solid-phase diffusion partial differential equations corresponding to the positive and negative electrodes in the two-particle electrochemical model to characterize the coupling relationship between temperature and solid-phase diffusion kinetics. Boundary conditions are configured for both sets of solid-phase diffusion partial differential equations, where the lithium-ion flux at the particle center is zero and the lithium-ion flux on the particle surface is coupled with the battery charge / discharge current. The two sets of solid-phase diffusion partial differential equations are transformed into a set of ordinary differential equations using numerical discretization. The ordinary differential equations are solved by substituting the real-time acquired battery charge / discharge current and cell temperature to obtain the discrete solid-phase lithium-ion concentration. The lithium filling ratio is then calculated from the discrete solid-phase lithium-ion concentration. A first-order RC equivalent circuit is introduced to construct a system based on the lithium filling ratio and real-time... The collected cell temperature is used as input, and a parameter mapping relationship is established with ohmic internal resistance, polarization internal resistance, and polarization capacitance as outputs. This parameter mapping relationship is used to achieve the fusion of the mechanism of the two-particle electrochemical model and the first-order RC equivalent circuit. Based on the ohmic internal resistance, polarization internal resistance, and polarization capacitance obtained by mapping, a dynamic differential equation of polarization voltage corresponding to the first-order RC equivalent circuit is established to characterize the time-domain variation characteristics of polarization voltage. A dynamic equation of temperature energy conservation is introduced to characterize the dynamic evolution of cell temperature. The three state variables of discrete solid-phase lithium-ion concentration, polarization voltage, and cell temperature are integrated to form a unified state vector. A state-space equation that simultaneously includes the microscopic solid-phase diffusion mechanism and macroscopic electrical external characteristics is constructed. The constructed state-space equation is the state-space equation corresponding to the wide-temperature-range electrochemical-equivalent circuit fusion model of lithium-ion battery.

[0040] In other words, step S1 involves establishing a wide-temperature-range electrochemical-equivalent circuit fusion model for lithium-ion batteries and constructing the corresponding state-space equations based on this fusion model. The wide-temperature-range electrochemical-equivalent circuit fusion model of lithium-ion batteries described here is obtained by coupling a two-particle electrochemical mechanism model with a first-order RC equivalent circuit mechanism. The two-particle electrochemical model uses one particle to simulate the solid-phase lithium-ion diffusion process at the positive electrode and another particle to simulate the solid-phase lithium-ion diffusion process at the negative electrode. This model uses the battery charge / discharge current and cell temperature as inputs to solve for the lithium-ion solid-phase concentration distribution inside the positive and negative electrodes. Then, using the solved lithium-ion solid-phase concentration distributions at the positive and negative electrodes, the surface lithium filling ratio of the positive electrode, the surface lithium filling ratio of the negative electrode, and the average lithium filling ratio of both electrodes are calculated. Based on the surface lithium filling ratio and real-time cell temperature, the ohmic internal resistance and polarization internal resistance parameters are obtained through parameter mapping. Based on the average lithium filling ratio and real-time cell temperature, the open-circuit voltage and polarization capacitance parameters are obtained through parameter mapping. Through the above parameter mapping, the mechanism fusion of the two-particle electrochemical model and the first-order RC equivalent circuit is completed, ultimately forming the wide-temperature-range electrochemical-equivalent circuit fusion model of lithium-ion batteries.

[0041] S11. Establish a wide-temperature-range two-particle electrochemical model.

[0042] First, taking a single lithium-ion battery as the object, single-particle models are established for both the positive and negative electrodes to form a two-particle electrochemical model. Let the radii of the active particles in the positive and negative electrodes be... , Then at any temperature Below, the radial distribution of lithium-ion concentration in the solid phase at both electrodes is described by the Fick diffusion equation:

[0043] (1)

[0044] (2)

[0045] In the formula, , These represent the lithium-ion concentrations in the positive and negative electrode solid phases, respectively. The radius of the radial distance from any point inside the spherical active particle to the center of the particle, with a range of values. (Positive electrode particles) (Negative electrode particles) are the spatial independent variables in the Fick diffusion equation; , The solid-phase diffusion coefficient, which varies with temperature, can be described using the Arrhenius form:

[0046] , (3)

[0047] In the formula, It is the universal gas constant, a fixed physical constant; The reference temperature for the solid-phase diffusion coefficient is used as the reference quantity for temperature offset in the Arrhenius equation. , These are the activation energies for lithium-ion solid-phase diffusion at the positive and negative electrodes, respectively. , Reference temperature Benchmark values ​​for the diffusion coefficient of lithium ions in the solid phase of the lower positive and negative electrodes.

[0048] The boundary conditions are that the flux at the center of the sphere is zero, and the surface flux is proportional to the battery current.

[0049] (4)

[0050] (5)

[0051] In the formula, This represents the battery current (positive during discharge). , The specific surface area of ​​the positive and negative electrode active particles. , The volume of the positive and negative electrode plates. It is Faraday's constant. and These represent the lithium ion concentration distribution inside the positive and negative electrode particles at any given time.

[0052] Equations (1) to (2) can be discretized radially using methods such as finite difference or spherical harmonic function expansion. With nodes, the PDE can be discretized into a system of ordinary differential equations:

[0053] (6)

[0054] S12. Calculate the surface and average state of charge from the concentration distribution.

[0055] The surface concentrations of the positive and negative electrodes and the average concentration can be directly calculated from the discretized concentration vectors.

[0056] (7)

[0057] Further define the surface and average lithium filling ratios of the positive and negative electrodes (i.e., the surface state of charge and average state of charge at the electrode layer):

[0058] (8)

[0059] In the formula, , This represents the maximum lithium concentration of the material. The overall average SOC of the battery can be obtained by weighting the average fill ratios of the positive and negative electrodes by capacity:

[0060] (9)

[0061] S13. Construct a parameter mapping from the state of charge to the equivalent circuit model.

[0062] In the electrochemical-equivalent circuit fusion model, the average state of charge given by the two-particle model is used to drive the changes of various parameters in the equivalent circuit with SOC and temperature.

[0063] (1) Open circuit voltage:

[0064] (10)

[0065] In the formula, , The equilibrium potential of the positive and negative electrodes can be obtained through polynomial fitting or table lookup. , It represents the average state of charge of both the positive and negative poles. This is a correction for the entropy variable.

[0066] (2) Ohmic resistance and polarization resistance:

[0067] Based on the state of charge on the positive and negative electrode surfaces , and temperature Constructing Ohmic internal resistance With polarization internal resistance Mapping relationship:

[0068] (11)

[0069] (3) Polarization capacitor:

[0070] Polarized capacitor It is mainly related to the active area and concentration gradient of the electrode surface, and can be determined by the average state of charge and temperature.

[0071] (12)

[0072] S14. Equivalent Circuit Structure and Wide Temperature Range State-Space Equation

[0073] Based on the above parameter mapping, a first-order RC equivalent circuit model is constructed, with the following terminal voltage:

[0074] (13)

[0075] in, The voltage on the polarized RC branch has the following dynamic equation:

[0076] (14)

[0077] To unify the writing in state-space form, we introduce state vectors:

[0078] (15)

[0079] Therefore, over a wide temperature range, the state-space equation of the electrochemical-equivalent circuit fusion model can be written as:

[0080] (16)

[0081] In the formula, The temperature dynamic equation (e.g., established from the energy conservation equation). , Calculated from equations (7) to (8), and then mapped from equations (10) to (13). .

[0082] S2. Steps for building an adaptive weighted physical information network identification framework

[0083] A parameter identification framework is constructed based on a physical information neural network. Within this framework, an adaptive weighted total penalty loss function is built that simultaneously includes the residuals of the solid-phase diffusion partial differential equation, initialization residuals, boundary condition residuals, and the residuals of the first-order RC equivalent circuit model (referred to as the equivalent circuit model) under operating conditions. The adaptive weighted total penalty loss function assigns corresponding weights according to the magnitude of the residuals, with larger residuals receiving higher weights. The lithium-ion solid-phase diffusion coefficient, ohmic internal resistance, polarization internal resistance, and polarization capacitance corresponding to the state-space equation, as well as the weight parameters and bias parameters corresponding to the physical information neural network, are collectively set as the parameters to be updated in synchronous iterative optimization. A gradient solution channel for all parameters to be updated is established using the adaptive weighted total penalty loss function based on an automatic differentiation mechanism. All parameters to be updated constitute a joint optimization parameter set.

[0084] This step establishes a battery model parameter identification framework based on a physical information neural network architecture. The simulation error of fitting the equivalent circuit model under operating conditions is introduced into the penalty function of the neural network, while the model parameters are used as learnable parameters of the neural network. Introducing the simulation error of fitting the equivalent circuit model under operating conditions into the penalty function of the neural network means calculating the prediction error based on the battery terminal voltage, temperature, and other parameters predicted by the equivalent circuit model over a future period or after a period of time, comparing it with real data, and incorporating this prediction error into the neural network's penalty function. The final penalty function of the neural network includes four parts: the output prediction error of the equivalent circuit model, the initialization residual, the boundary condition residual, and the neural network prediction residual, which are iteratively combined using a weighted method. Further, when constructing the adaptive weighted total penalty loss function, physical equation residuals are constructed for the solid-phase diffusion partial differential equation of the two-particle electrochemical model, initialization residuals are constructed for the initial state, boundary condition residuals are constructed for particle boundary constraints, and operating condition fitting simulation observation residuals are constructed for the predicted and measured terminal voltages of the first-order RC equivalent circuit model. Adaptive weighted combination is achieved by assigning independent weight coefficients to each of the four types of residuals. When the residual of the battery model prediction increases, it is given a larger weight value; otherwise, it is given a smaller weight value.

[0085] By relying on automatic differentiation technology to obtain the gradient of the adaptive weighted total penalty loss function to build a gradient solution channel, and through the backpropagation gradient descent optimization strategy, the physical parameters corresponding to the state space equation and the weight parameters and bias parameters corresponding to the physical information neural network are simultaneously and jointly iteratively optimized.

[0086] Using model parameters as learnable parameters of a neural network means incorporating the model's identifying parameters into the neural network weights and iteratively calculating the model parameters during backpropagation training. Therefore, the model parameters themselves are not only used to predict the output of the equation, but also serve as network parameters.

[0087] S21. Constructing constraints for partial differential equations

[0088] For the two-particle model with positive and negative poles, the constraint can be abstracted as follows:

[0089] (17)

[0090] (18)

[0091] (19)

[0092] In the formula, Represents the independent variable in the radial space inside the particle. For time, Find the solution domain in the equation space. To solve for the domain boundary, Define the domain at the initial time. To solve the interval in full time, The physical field quantity to be determined is the concentration of lithium ions in the solid phase. For the first-order gradient operator, For the second-order Laplace differential operator, For the governing equation operator; For boundary operators, Let be the initial concentration distribution function. Let the boundary flux constraint function be... The set of parameters to be identified includes mechanistic parameters such as the solid-phase diffusion coefficient of the two-particle model, the Arrhenius activation energy, the ohmic internal resistance of the equivalent circuit, the polarization internal resistance, and the polarization capacitance.

[0093] Based on the two-particle-equivalent circuit fusion model given in step S1, it is possible to... Specifically, it is expressed as a solid-phase diffusion equation, a temperature equation, and a terminal voltage constraint determined by concentration, but under the PINN framework, it is uniformly written in the form of equation (17), which facilitates automatic differentiation and loss construction.

[0094] S22, PINN structure and physical residual construction

[0095] Construct a multilayer perceptron neural network ,in These are the network weights and bias parameters. For a given space-time sampling point... The network output approximates the physical quantity:

[0096] (20)

[0097] Using automatic differentiation (Auto-Diff) technology, for about Differentiation yields spatial and temporal derivatives of arbitrary order. Substituting these derivatives into the governing equation operators allows us to construct the physical residuals:

[0098] (twenty one)

[0099] Similarly, for the initial and boundary conditions, corresponding residuals can be constructed:

[0100] (twenty two)

[0101] (twenty three)

[0102] In battery parameter identification scenarios, it is also necessary to consider the observation residuals between measurable terminal voltage, surface temperature, and other data and the model output. Let the first... The time for each measurement point is Corresponding current and measured terminal voltage The terminal voltage estimate calculated based on the fusion model is:

[0103] (twenty four)

[0104] In the formula, This is a mapping operator used to calculate the equivalent circuit terminal voltage by mapping solid phase concentration state variables to the fusion model.

[0105] The corresponding observation residuals are:

[0106] (25)

[0107] In the formula, To predict the terminal voltage for the model, This is the measured terminal voltage of the battery.

[0108] S23. Comprehensive Loss Function and Parameter-Network Joint Optimization

[0109] Taking into account the residuals of the physical control equations, the residuals of the initial / boundary conditions, and the residuals of the observed data, the total loss function of PINN is constructed as follows:

[0110] (26)

[0111] In the formula, These represent the number of sampling points for the physical equations, the number of initial value sampling points, the number of boundary sampling points, and the number of observation points, respectively. For the physical equation residuals, For the initial condition residual, For boundary condition residuals, The residuals are the fitting values ​​for the terminal voltage observations; These are the weights for each loss term, used to balance the importance of different residuals.

[0112] Unlike traditional PINN, which only uses network parameters Unlike trainable variables, physical parameters are used in model parameter identification scenarios. It is also considered as a variable to be optimized, that is:

[0113] (27)

[0114] Using gradient descent, Adam optimizer, or Runge-Kutta adaptive optimization algorithms, for and Synchronized Updates:

[0115] (28)

[0116] In the formula, The learning rate can be obtained simultaneously through backpropagation and automatic differentiation. and This ensures that the network weights and electrochemical and equivalent circuit parameters satisfy physical constraints.

[0117] S3. Runge-Kutta Discrete Iteration Parameter Identification and Convergence Calculation Steps

[0118] The state-space equations are discretized in the time domain using a fourth-order Runge-Kutta numerical discretization algorithm. A constructed adaptive weighted total penalty loss function, an established gradient solution channel, and a set of joint optimization parameters are used. A gradient-based backpropagation optimization algorithm is employed to synchronously iteratively update each parameter, completing the online parameter identification of the state-space equations. The predicted terminal voltage and predicted cell temperature obtained from the discretized recursive calculation of the state-space equations are fed back to step S2 to recalculate the residuals from the simulation observations of the first-order RC equivalent circuit model under operating conditions, thus updating the adaptive weighted total penalty loss function for iterative optimization of each parameter. After the iterative optimization of each parameter meets the preset convergence condition, the process proceeds to step S4.

[0119] This step is based on the discretization and differentiability of the state equation using the Runge-Kutta method. Specifically, it uses gradient descent, Runge-Kutta, and other methods to simultaneously update the network weights and the parameters to be identified in the state equation, thereby achieving system identification and parameter optimization of the equivalent circuit model of the power battery based on a physical information neural network.

[0120] Furthermore, a fourth-order Runge-Kutta numerical discretization algorithm is used to discretize the continuous-time state-space equation in the time dimension. The discretization process uses differentiable operators to construct recursive formulas so that the gradient of the parameters to be updated can be obtained by automatic differentiation within the physical information neural network framework. The gradient-based backpropagation optimization algorithm can use gradient descent algorithm, Adam optimizer or Runge-Kutta optimization algorithm to perform synchronous backpropagation iterative update of each parameter to be updated. The state variables are solved recursively step by step according to the set sampling time step to obtain the predicted terminal voltage and predicted cell temperature at the corresponding time and feed them back to step S2 to update the observation residual. Multiple iterations are performed until the parameters to be updated meet the preset convergence conditions, and then the process jumps to step S4 to complete the joint identification and solution of the parameters of the state-space equation.

[0121] To facilitate end-to-end training in the Physical Information Neural Network (PINN), the continuous-time fusion state-space equations after convergence in step S2 are solved discretely and recursively using a fourth-order Runge-Kutta (RK4) numerical algorithm in the time dimension. A fixed-time discrete sampling step size is set as... , No. The discrete time intervals are Then we have:

[0122] (29)

[0123] In the formula, , , , For the slope increment of the state change predicted in four steps within a single step of the fourth-order Runge-Kutta algorithm; For the derivative mapping function of the continuous state differential equation of the fusion model; For the first The internal state vector of the system at any given moment; , , The charging and discharging current is used as the excitation at the corresponding time. This is the set of battery physical parameters after joint optimization and convergence.

[0124] The state update formula is:

[0125] (30)

[0126] The above equation is implemented entirely by differentiable operators, and therefore can be solved within the PINN framework through automatic differentiation pairs. Find the gradient. Therefore, given a current excitation... and initial state Then, the entire time domain can be obtained recursively using equation (29). And calculate the corresponding terminal voltage prediction. , .

[0127] S4, Battery Multi-parameter Joint Estimation Steps

[0128] The state-space equations, which are obtained after parameter iteration convergence through step S3, are solved by using the real-time charge and discharge current of the lithium-ion battery as the input quantity. The online estimation results of the state of charge, polarization voltage, and cell temperature of the lithium-ion battery are obtained from the solved state vectors.

[0129] In this embodiment, the step is to estimate the state of the physical information neural network structure of the Bi-GRU (Bi-Gated Recurrent Unit). Specifically, by introducing a bi-directional temporal feature extraction structure, a neural network of the Bi-GRU is established. The operation and scheduling of the model parameter identification algorithm are optimized using an event triggering mechanism, thereby realizing the estimation of the battery state of charge.

[0130] Specifically, during state of charge (SOC) estimation, a bidirectional gated recurrent unit is embedded within the physical information neural network to construct the SOC estimation model. This bidirectional gated recurrent unit consists of two independent stacked gated recurrent units, introducing a bidirectional structure on top of the gated recurrent units. It performs forward and reverse sequence feature extraction on the battery time-series data, respectively, fusing the hidden states output from the two branches, while considering the bidirectional dependency between the current time step and historical and future time series. The predicted terminal voltage and predicted cell temperature obtained through discrete recursive calculations of the state-space equations, the real-time acquired battery terminal voltage and cell temperature, the SOC calculated by ampere-hour integration, and the real-time acquired battery charging and discharging current are used as the network input parameters of the SOC estimation model. The actual battery SOC is used as the output label of the SOC estimation model. The adaptive weighted total penalty loss function is used as a constraint to train the SOC estimation model, and the trained SOC estimation model enables online estimation of the lithium-ion battery's SOC.

[0131] Furthermore, each group of gated loop units in the bidirectional gated loop unit is independently configured with two types of gate structures: update gate and reset gate. Each group of gated loop units uses the Sigmoid activation function to calculate the update gate weight coefficient and the reset gate weight coefficient respectively. After filtering the historical hidden state at the previous time step using the reset gate weight, candidate hidden states are generated by calculating the Tanh activation function. The original hidden state and candidate hidden state at the previous time step are weighted and fused element-wise according to the update gate weight to obtain the final hidden state of a single branch. The final hidden states obtained by solving the forward and reverse branches of the bidirectional gated loop unit are fused element-wise to complete the feature capture of the bidirectional dependency relationship of the battery time series data.

[0132] Furthermore, as a preferred embodiment, an event-triggered scheduling mechanism can be configured to dynamically schedule the iterative identification process of the joint optimization parameter set. This event-triggered mechanism adopts a scheduling logic based on threshold-based event-driven parameter re-identification: when the predicted terminal voltage and predicted cell temperature obtained by the discrete recursive operation of the state space equation of the mechanism-data fusion in this application deviate too much from the actual terminal voltage and actual cell temperature collected in real time by the battery, a parameter re-identification event is triggered. Specifically, the determination method is as follows: calculate the voltage residual by comparing the predicted terminal voltage obtained by the discrete recursive operation of the state space equation with the actual terminal voltage collected in real time by the battery, and calculate the temperature residual by comparing the predicted cell temperature obtained by the discrete recursive operation of the state space equation with the actual cell temperature collected in real time by the battery. The voltage residual and temperature residual are accumulated. When the total accumulated residual exceeds a preset threshold, the process jumps back to steps S2 and S3 to re-execute parameter identification and iterative optimization.

[0133] To improve the stability and estimation accuracy of parameter identification during long-term continuous battery operation, a minimum trigger interval is forcibly set based on the event trigger judgment conditions to avoid frequent repeated iterations caused by small residual oscillations in a short period of time. At the same time, an improved event trigger rule with the introduction of a forgetting factor is adopted. The forgetting factor is used to attenuate and weight the historical residuals, weakening the interference of residuals from early historical operating conditions on the current trigger judgment, thereby reducing the frequency of invalid retraining triggers caused by historical residuals and reducing unnecessary computational power consumption of the algorithm.

[0134] Furthermore, based on the basic state vector analytical estimation in step S4, this embodiment can embed a bidirectional gated recurrent neural network to construct a state of charge (SOC) estimation model to further improve the estimation accuracy. The training method for this SOC estimation model is as follows: the predicted terminal voltage and predicted cell temperature obtained through discrete recursive calculations of the state-space equations, the real-time collected battery terminal voltage and real cell temperature, the SOC calculated using the ampere-hour integral method, and the real-time battery charging and discharging current are used as network input parameters. The actual SOC of the battery is used as the model's supervised output label. The training process uses the adaptive weighted total penalty loss function constructed in step S2 as a constraint term, and follows the parameter iteration update strategy of step S3 to complete the synchronous training of network weights and model physical parameters. The network model after training convergence can achieve accurate online estimation of the SOC of lithium-ion batteries.

[0135] S41. Optimization of the physical information neural network structure integrating Bi-GRU

[0136] A bidirectional gated recurrent unit (Bi-GRU) is employed to capture temporal information. One set performs forward temporal feature learning, while the other performs inverse temporal feature learning. The states from both sets are then fused to fully utilize the complete temporal information across all dimensions. For time step t, assuming the input vector of the current time step is x, and the hidden state of the previous time step is h...t-1 Then the calculation formula for the update gate is:

[0137] (31)

[0138] In the formula, Mapping the input vector to the weights of the update gate, The weights of the update gate are mapped to the hidden state of the previous time step. To update the gate, calculate the bias coefficient. This is the activation function, typically the Sigmoid function.

[0139] The formula for resetting the door is:

[0140] (32)

[0141] In the formula, The input vector is mapped to the weights of the reset gate. The weights of the hidden state from the previous time step mapped to the reset gate. Calculate the offset coefficient for the reset door.

[0142] Then, calculate the candidate hidden states:

[0143] (33)

[0144] In the formula, , Calculate the weights corresponding to the candidate hidden states. Calculate the bias coefficients for the candidate hidden states. The Hadamard product represents the element-wise multiplication of vectors.

[0145] Ultimately, the updated hidden state output by GRU is:

[0146] (34)

[0147] When the update gate output weight is close to 1, the model will almost maintain the original state without change (approximately retaining the original hidden state from the previous time step), weakening the impact of newly added input information. However, when the update gate output weight is close to 0, the new hidden state is strongly correlated with the candidate state, and can capture deep temporal relationships of sequences spanning long time steps.

[0148] The Bi-GRU model used in this embodiment adds a bidirectional parallel architecture to the basic GRU unit, consisting of two independent GRU layers: one for forward sequence deduction and the other for backward sequence backtracking. This associates the inherent coupling relationship between the current time step and historical and future time series data, and mines the bidirectional dependency features of the time series samples. After solving the hidden states of the forward and backward branches respectively, the two sets of state variables are fused through element-wise operations to obtain the final output feature state variables of the bidirectional gated recurrent unit. The specific calculation expression is as follows:

[0149] (35)

[0150] In the formula, To output the hidden state for the positive GRU branch, To output the hidden state of the reverse GRU branch, , These represent the historical hidden states of the corresponding branch at the previous time step, and the final output is... It is the temporal feature vector of the hidden states of the bidirectional branches after element-wise fusion of the Hadamard product.

[0151] S42. Neural Network Scheduling Optimization Based on Event-Triggered Mechanism

[0152] Considering that the aging of power batteries is a long-term process, it is generally sufficient to identify and update the model once every 5-10 cycles to meet the requirements of the entire life cycle operation. Therefore, it is necessary to optimize the operating mechanism of the physical information neural network. This scheme adopts a joint triggering strategy of time hard constraint minimum interval + residual event threshold. Based on the residual judgment triggering condition, a minimum triggering interval is forcibly limited to ensure the stability of the algorithm and reduce unnecessary computing power overhead. The basic event triggering mechanism for model updates is as follows:

[0153] (36)

[0154] In the formula, For the first Event triggering flag factor at the sampling time, This indicates that parameter re-identification will not be triggered. This indicates that the model is being backtracked and re-optimized. This represents the number of residual sampling points within the sliding statistical window. For the first The actual observations measured by the point sensor include the measured terminal voltage and the measured cell temperature. The model recursively predicts the terminal voltage and cell temperature at the corresponding time points. For a single observation residual; The threshold for determining the total residual accumulation is set in advance.

[0155] Specifically, considering that the triggering factor will remain within the allowable error range of the residuals, and to avoid unnecessary repeated model updates caused by small fluctuations in the residuals, this embodiment introduces a forgetting factor. By attenuating and superimposing historical residuals, an optimized event triggering mechanism is obtained:

[0156] (37)

[0157] The forgetting decay weighting coefficient is defined as follows: , b>1.

[0158] In the formula, For the first The forgetting weight corresponding to the historical residual decreases exponentially as the order of time i increases; b is the base of the forgetting factor, which satisfies the constraint b>1. The larger the base value, the faster the historical residual decays.

[0159] This invention also relates to a mechanism-data fusion lithium-ion battery state-of-charge estimation system, corresponding to the mechanism-data fusion lithium-ion battery state-of-charge estimation method described above. It can be understood as a system that implements the aforementioned mechanism-data fusion lithium-ion battery state-of-charge estimation method. This system includes a coupled state-space equation construction module, an adaptive weighted physical information network identification framework construction module, a Runge-Kutta discrete iterative parameter identification and convergence calculation module, and a battery multi-parameter joint estimation module, connected sequentially.

[0160] The coupled state-space equation construction module, taking lithium-ion batteries as the object, establishes single-particle models at both the positive and negative electrodes, combining them to form a two-particle electrochemical model. The Arrhenius equation is embedded within the two sets of solid-phase diffusion partial differential equations corresponding to the positive and negative electrodes in the two-particle electrochemical model to characterize the coupling relationship between temperature and solid-phase diffusion kinetics. Boundary conditions are configured for both sets of solid-phase diffusion partial differential equations, where the lithium-ion flux at the particle center is zero and the lithium-ion flux at the particle surface is coupled with the battery charge / discharge current. The two sets of solid-phase diffusion partial differential equations are transformed into a set of ordinary differential equations using numerical discretization. The ordinary differential equations are then solved by substituting the real-time collected battery charge / discharge current and cell temperature to obtain the discrete solid-phase lithium-ion concentration. The lithium filling ratio is calculated. A first-order RC equivalent circuit is introduced to construct a parameter mapping relationship with lithium filling ratio and real-time acquired cell temperature as inputs, and ohmic internal resistance, polarization internal resistance, and polarization capacitance as outputs. This parameter mapping relationship realizes the mechanism fusion of the two-particle electrochemical model and the first-order RC equivalent circuit. Based on the mapped ohmic internal resistance, polarization internal resistance, and polarization capacitance, a dynamic differential equation for polarization voltage corresponding to the first-order RC equivalent circuit is established to characterize the time-domain variation characteristics of polarization voltage. The dynamic equation of temperature energy conservation is combined to characterize the dynamic evolution of cell temperature. The three state variables of discrete solid-phase lithium ion concentration, polarization voltage, and cell temperature are integrated to form a unified state vector, and a state-space equation that simultaneously includes the microscopic solid-phase diffusion mechanism and macroscopic electrical external characteristics is constructed.

[0161] The adaptive weighted physical information network identification framework construction module constructs a parameter identification framework based on a physical information neural network. Within this framework, an adaptive weighted total penalty loss function is built that simultaneously includes the residuals of the solid-phase diffusion partial differential equation, initialization residuals, boundary condition residuals, and the simulation observation residuals of the first-order RC equivalent circuit model under operating conditions corresponding to the two-particle electrochemical model. The adaptive weighted total penalty loss function assigns corresponding weights according to the magnitude of the residuals, with larger residuals receiving higher weights. The lithium-ion solid-phase diffusion coefficient, ohmic internal resistance, polarization internal resistance, and polarization capacitance corresponding to the state-space equation, as well as the weight parameters and bias parameters corresponding to the physical information neural network, are collectively set as parameters to be updated through synchronous iterative optimization. A gradient solution channel for all parameters to be updated is established using the adaptive weighted total penalty loss function based on an automatic differentiation mechanism, and all parameters to be updated constitute a joint optimization parameter set.

[0162] The Runge-Kutta discrete iterative parameter identification and convergence module employs a fourth-order Runge-Kutta numerical discretization algorithm to discretize the state-space equations in the time domain. Utilizing a constructed adaptive weighted total penalty loss function, an established gradient solution channel, and a set of joint optimization parameters, it performs synchronous iterative updates on each parameter using a gradient-based backpropagation optimization algorithm, thus completing the online parameter identification of the state-space equations. The predicted terminal voltage and predicted cell temperature obtained through the discrete recursive operation of the state-space equations are fed back to the adaptive weighted physical information network identification framework construction module. This is used to recalculate the residuals from the simulation observation of the first-order RC equivalent circuit model under operating conditions, updating the adaptive weighted total penalty loss function for iterative optimization of each parameter. After the iterative optimization of each parameter meets the preset convergence conditions, the module proceeds to the battery multi-parameter joint estimation module.

[0163] The battery multi-parameter joint estimation module uses the state-space equation after parameter iteration convergence completed by the Runge-Kutta discrete iterative parameter identification and convergence calculation module. The real-time charging and discharging current of the lithium-ion battery is used as the input quantity of the state-space equation for solving. The online estimation results of the lithium-ion battery state of charge, polarization voltage and cell temperature are obtained from the obtained state vector.

[0164] Furthermore, in the coupled state-space equation construction module, the two sets of solid-phase diffusion partial differential equations are transformed into a set of ordinary differential equations using the finite difference method or spherical harmonic functions. The lithium filling ratio and average lithium filling ratio on the positive and negative electrode surfaces are calculated from the discrete solid-phase lithium ion concentration. Based on the surface lithium filling ratio and the real-time acquired cell temperature, the ohmic internal resistance and polarization internal resistance are obtained through parameter mapping. Based on the average lithium filling ratio and the real-time acquired cell temperature, the open-circuit voltage and polarization capacitance are obtained through parameter mapping. Through this parameter mapping, the mechanism of the two-particle electrochemical model and the first-order RC equivalent circuit are integrated to form a wide-temperature-range electrochemical-equivalent circuit fusion model of lithium-ion battery. The three state variables of discrete solid-phase lithium ion concentration, polarization voltage, and cell temperature are integrated to form a unified state vector. The constructed state-space equation is the state-space equation corresponding to the wide-temperature-range electrochemical-equivalent circuit fusion model of lithium-ion battery.

[0165] Furthermore, in the battery multi-parameter joint estimation module, when performing state of charge estimation, a bidirectional gated recurrent unit is embedded inside the physical information neural network to construct a state of charge estimation model. The bidirectional gated recurrent unit is composed of two independent gated recurrent units stacked together, which respectively perform forward sequence feature extraction and reverse sequence feature extraction on the battery time-series operating data, fuse the hidden states output by the two branches, and capture the bidirectional dependency relationship of the time-series data. The predicted terminal voltage and predicted cell temperature obtained by discrete recursive calculation through state-space equations, the real-time collected battery terminal voltage and cell temperature, the state of charge calculated by ampere-hour integration, and the real-time collected battery charging and discharging current are used as the network input parameters of the state of charge estimation model, and the actual state of charge of the battery is used as the output label of the state of charge estimation model. The adaptive weighted total penalty loss function is used as a constraint to train the state of charge estimation model, and the online estimation of the state of charge of lithium-ion batteries is realized based on the trained state of charge estimation model.

[0166] It should be noted that the specific embodiments described above enable those skilled in the art to more fully understand the present invention, but do not limit the present invention in any way. Therefore, although the present invention has been described in detail with reference to the accompanying drawings and embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the present invention. In short, all technical solutions and improvements that do not depart from the spirit and scope of the present invention should be covered within the protection scope of the present invention patent.

Claims

1. A mechanism-data fusion method for estimating the state of charge of a lithium-ion battery, characterized in that, Includes the following steps: S1. Taking lithium-ion batteries as the object, single-particle models are established for both the positive and negative electrodes, and combined to form a two-particle electrochemical model. The Arrhenius equation is embedded into the two sets of solid-phase diffusion partial differential equations corresponding to the positive and negative electrodes in the two-particle electrochemical model to characterize the coupling relationship between temperature and solid-phase diffusion kinetics. Boundary conditions are configured for both sets of solid-phase diffusion partial differential equations, where the lithium-ion flux at the particle center is zero and the lithium-ion flux on the particle surface is coupled with the battery charge / discharge current. The two sets of solid-phase diffusion partial differential equations are transformed into a set of ordinary differential equations using numerical discretization. The real-time collected battery charge / discharge current and cell temperature are substituted into these ordinary differential equations to solve the set of ordinary differential equations, obtaining the discrete solid-phase lithium-ion concentration. The lithium filling ratio is then calculated from the discrete solid-phase lithium-ion concentration. A first-order RC equivalent circuit is introduced to construct a parameter mapping relationship with lithium filling ratio and real-time acquired cell temperature as inputs, and ohmic internal resistance, polarization internal resistance, and polarization capacitance as outputs. This parameter mapping relationship realizes the mechanistic fusion of the two-particle electrochemical model and the first-order RC equivalent circuit. Based on the mapped ohmic internal resistance, polarization internal resistance, and polarization capacitance, a dynamic differential equation for polarization voltage corresponding to the first-order RC equivalent circuit is established to characterize the time-domain variation characteristics of polarization voltage. This is combined with the temperature energy conservation dynamic equation to characterize the dynamic evolution of cell temperature. The three state variables of discrete solid-phase lithium ion concentration, polarization voltage, and cell temperature are integrated to form a unified state vector, and a state-space equation that simultaneously includes the microscopic solid-phase diffusion mechanism and macroscopic electrical external characteristics is constructed. S2. Construct a parameter identification framework based on a physical information neural network, and within the parameter identification framework, construct an adaptive weighted total penalty loss function that simultaneously includes the residuals of the solid-phase diffusion partial differential equation, initialization residuals, boundary condition residuals, and the observation residuals of the first-order RC equivalent circuit model under the operating conditions fitting simulation corresponding to the two-particle electrochemical model; the adaptive weighted total penalty loss function assigns corresponding weights according to the magnitude of the residual values, with larger residual values ​​receiving higher weights. The lithium-ion solid-phase diffusion coefficient, ohmic internal resistance, polarization internal resistance, and polarization capacitance corresponding to the state-space equation, as well as the weight parameters and bias parameters corresponding to the physical information neural network, are set together as the parameters to be updated for synchronous iterative optimization. The gradient solution channel of the adaptive weighted total penalty loss function for all parameters to be updated is established based on the automatic differentiation mechanism, and all parameters to be updated constitute a joint optimization parameter set. S3. The state space equation is discretized in the time domain using the fourth-order Runge-Kutta numerical discretization algorithm. The constructed adaptive weighted total penalty loss function, the established gradient solution channel, and the constructed joint optimization parameter set are used to perform synchronous iterative updates on each parameter to be updated through a gradient-based backpropagation optimization algorithm to complete the online parameter identification of the state space equation. The predicted terminal voltage and predicted cell temperature obtained by the discrete recursive calculation of the state-space equation are fed back to step S2 to recalculate the observation residual of the first-order RC equivalent circuit model under the operating condition fitting simulation, so as to realize the update of the adaptive weighted total penalty loss function for the iterative optimization of each parameter to be updated; after the iterative optimization of each parameter to be updated meets the preset convergence condition, the process proceeds to step S4. S4. Using the state-space equations that have been converged through parameter iteration in step S3, the real-time charge and discharge current of the lithium-ion battery is used as the input quantity of the state-space equations for solving. The online estimation results of the state of charge, polarization voltage, and cell temperature of the lithium-ion battery are obtained from the solved state vectors.

2. The mechanism-data fusion method for estimating the state of charge of a lithium-ion battery according to claim 1, characterized in that, In step S1, the two sets of solid-phase diffusion partial differential equations are transformed into a set of ordinary differential equations by using the finite difference method or spherical harmonic functions. The lithium filling ratio and average lithium filling ratio on the positive and negative electrode surfaces are calculated from the discrete solid-phase lithium ion concentration. Based on the surface lithium filling ratio and the real-time acquired cell temperature, the ohmic internal resistance and polarization internal resistance are obtained through parameter mapping. Based on the average lithium filling ratio and the real-time acquired cell temperature, the open-circuit voltage and polarization capacitance are obtained through parameter mapping. Through this parameter mapping, the mechanism of the two-particle electrochemical model and the first-order RC equivalent circuit are integrated to form a wide-temperature-range electrochemical-equivalent circuit fusion model of lithium-ion battery. The three state variables of discrete solid-phase lithium ion concentration, polarization voltage and cell temperature are integrated to form a unified state vector. The constructed state-space equation is the state-space equation corresponding to the wide-temperature-range electrochemical-equivalent circuit fusion model of lithium-ion battery.

3. The mechanism-data fusion method for estimating the state of charge of a lithium-ion battery according to claim 1, characterized in that, In step S2, when constructing the adaptive weighted total penalty loss function, physical equation residuals are constructed for the solid-phase diffusion partial differential equation of the two-particle electrochemical model, initialization residuals are constructed for the initial state, boundary condition residuals are constructed for the particle boundary constraints, and operating condition fitting simulation observation residuals are constructed for the predicted terminal voltage and measured terminal voltage of the first-order RC equivalent circuit model. Adaptive weighted combination is achieved by configuring independent weight coefficients for the four types of residuals. The gradient of the adaptive weighted total penalty loss function is obtained by relying on automatic differentiation technology to build a gradient solution channel. Through the backpropagation gradient descent optimization strategy, the physical parameters corresponding to the state space equation and the weight parameters and bias parameters corresponding to the physical information neural network are synchronously and jointly iteratively optimized.

4. The mechanism-data fusion method for estimating the state of charge of a lithium-ion battery according to claim 1, characterized in that, In step S3, a fourth-order Runge-Kutta numerical discretization algorithm is used to discretize the continuous-time state-space equation in the time dimension. The discretization process uses differentiable operators to construct recursive formulas so that the gradient of the parameters to be updated can be obtained by automatic differentiation within the physical information neural network framework. The gradient-based backpropagation optimization algorithm uses gradient descent, Adam optimizer, or Runge-Kutta optimization algorithm to perform synchronous backpropagation iterative updates on each parameter to be updated. The state variables are solved recursively step by step according to the set sampling time step to obtain the predicted terminal voltage and predicted cell temperature at the corresponding time and feed them back to step S2 to update the observation residuals. After multiple iterations, the parameters to be updated meet the preset convergence conditions and then jump to step S4 to complete the joint identification and solution of the parameters of the state-space equation.

5. The mechanism-data fusion method for estimating the state of charge of a lithium-ion battery according to any one of claims 1 to 4, characterized in that, In step S4, during the state of charge (SOC) estimation, a bidirectional gated recurrent unit is embedded within the physical information neural network to construct the SOC estimation model. This bidirectional gated recurrent unit consists of two stacked independent gated recurrent units, which respectively perform forward and reverse sequence feature extraction on the battery time-series data, fusing the hidden states of the two branches to capture the bidirectional dependencies of the time-series data. The predicted terminal voltage and predicted cell temperature obtained through discrete recursive calculations of the state-space equations, the real-time acquired battery terminal voltage and cell temperature, the SOC calculated by ampere-hour integration, and the real-time acquired battery charging and discharging current are used as the network input parameters of the SOC estimation model. The actual battery SOC is used as the output label of the SOC estimation model. The adaptive weighted total penalty loss function is used as a constraint to train the SOC estimation model, and the trained SOC estimation model enables online estimation of the lithium-ion battery's SOC.

6. The mechanism-data fusion method for estimating the state of charge of a lithium-ion battery according to claim 5, characterized in that, In step S4, each group of gated loop units in the bidirectional gated loop unit is independently configured with two types of gated structures: update gate and reset gate. Each group of gated loop units uses the Sigmoid activation function to calculate the update gate weight coefficient and the reset gate weight coefficient respectively. After filtering the historical hidden state at the previous time step using the reset gate weight, the candidate hidden state is generated by calculating the Tanh activation function. The original hidden state and the candidate hidden state at the previous time step are weighted and fused element by element according to the update gate weight to obtain the final hidden state of a single branch. The final hidden states obtained by solving the forward and reverse branches of the bidirectional gated loop unit are fused element by element to complete the feature capture of the bidirectional dependency relationship of battery time series data.

7. The mechanism-data fusion method for estimating the state of charge of a lithium-ion battery according to any one of claims 1 to 4, characterized in that, In step S4, an event-triggered scheduling mechanism is configured to dynamically schedule the iterative identification process of the joint optimization parameter set. Specifically, this includes: calculating the voltage residual by comparing the predicted terminal voltage obtained from the state space equation through discrete recursive calculation with the real-time battery acquisition terminal voltage; calculating the temperature residual by comparing the predicted cell temperature obtained from the state space equation through discrete recursive calculation with the real-time battery acquisition cell temperature; accumulating the voltage residual and temperature residual; and returning to steps S2 and S3 to re-execute parameter identification and iterative optimization when the total accumulated residual exceeds a preset threshold. A minimum trigger interval is set based on the event trigger judgment condition, and a forgetting factor is introduced to attenuate and weight the historical residuals to reduce the frequency of invalid retraining triggers caused by historical residuals.

8. A mechanism-data fusion-based lithium-ion battery state-of-charge estimation system, characterized in that, The module includes a coupled state-space equation construction module, an adaptive weighted physical information network identification framework construction module, a Runge-Kutta discrete iterative parameter identification and convergence calculation module, and a battery multi-parameter joint estimation module, which are connected in sequence. The coupled state-space equation construction module, taking lithium-ion batteries as the object, establishes single-particle models at both the positive and negative electrodes, combining them to form a two-particle electrochemical model. The Arrhenius equation is embedded within the two sets of solid-phase diffusion partial differential equations corresponding to the positive and negative electrodes in the two-particle electrochemical model to characterize the coupling relationship between temperature and solid-phase diffusion kinetics. Boundary conditions are configured for both sets of solid-phase diffusion partial differential equations, where the lithium-ion flux at the particle center is zero and the lithium-ion flux at the particle surface is coupled with the battery charge / discharge current. The two sets of solid-phase diffusion partial differential equations are transformed into a set of ordinary differential equations using numerical discretization. The ordinary differential equations are then solved by substituting the real-time collected battery charge / discharge current and cell temperature to obtain the discrete solid-phase lithium-ion concentration. The lithium filling ratio is calculated. A first-order RC equivalent circuit is introduced to construct a parameter mapping relationship with lithium filling ratio and real-time acquired cell temperature as inputs, and ohmic internal resistance, polarization internal resistance, and polarization capacitance as outputs. This parameter mapping relationship realizes the mechanism fusion of the two-particle electrochemical model and the first-order RC equivalent circuit. Based on the mapped ohmic internal resistance, polarization internal resistance, and polarization capacitance, a dynamic differential equation for polarization voltage corresponding to the first-order RC equivalent circuit is established to characterize the time-domain variation characteristics of polarization voltage. The dynamic equation of temperature energy conservation is combined to characterize the dynamic evolution of cell temperature. The three state variables of discrete solid-phase lithium ion concentration, polarization voltage, and cell temperature are integrated to form a unified state vector, and a state-space equation that simultaneously includes the microscopic solid-phase diffusion mechanism and macroscopic electrical external characteristics is constructed. The adaptive weighted physical information network identification framework construction module constructs a parameter identification framework based on a physical information neural network. Within this framework, an adaptive weighted total penalty loss function is built that simultaneously includes the residuals of the solid-phase diffusion partial differential equation, initialization residuals, boundary condition residuals, and the simulation observation residuals of the first-order RC equivalent circuit model under operating conditions corresponding to the two-particle electrochemical model. The adaptive weighted total penalty loss function assigns corresponding weights according to the magnitude of the residuals, with larger residuals receiving higher weights. The lithium-ion solid-phase diffusion coefficient, ohmic internal resistance, polarization internal resistance, and polarization capacitance corresponding to the state-space equation, as well as the weight parameters and bias parameters corresponding to the physical information neural network, are collectively set as parameters to be updated through synchronous iterative optimization. A gradient solution channel for all parameters to be updated is established using the adaptive weighted total penalty loss function based on an automatic differentiation mechanism, and all parameters to be updated constitute a joint optimization parameter set. The Runge-Kutta discrete iterative parameter identification and convergence module employs a fourth-order Runge-Kutta numerical discretization algorithm to discretize the state-space equations in the time domain. Utilizing a constructed adaptive weighted total penalty loss function, an established gradient solution channel, and a set of joint optimization parameters, it performs synchronous iterative updates on each parameter using a gradient-based backpropagation optimization algorithm, thus completing the online parameter identification of the state-space equations. The predicted terminal voltage and predicted cell temperature obtained through the discrete recursive operation of the state-space equations are fed back to the adaptive weighted physical information network identification framework construction module. This is used to recalculate the residuals from the simulation observation of the first-order RC equivalent circuit model under operating conditions, updating the adaptive weighted total penalty loss function for iterative optimization of each parameter. After the iterative optimization of each parameter meets the preset convergence conditions, the module proceeds to the battery multi-parameter joint estimation module. The battery multi-parameter joint estimation module uses the state-space equation after parameter iteration convergence completed by the Runge-Kutta discrete iterative parameter identification and convergence calculation module. The real-time charging and discharging current of the lithium-ion battery is used as the input quantity of the state-space equation for solving. The online estimation results of the lithium-ion battery state of charge, polarization voltage and cell temperature are obtained from the obtained state vector.

9. The mechanism-data fusion lithium-ion battery state-of-charge estimation system according to claim 8, characterized in that, In the coupled state-space equation construction module, two sets of solid-phase diffusion partial differential equations are transformed into a set of ordinary differential equations by using the finite difference method or spherical harmonic functions. The lithium filling ratio and average lithium filling ratio on the positive and negative electrode surfaces are calculated from the discrete solid-phase lithium ion concentration. Based on the surface lithium filling ratio and the real-time acquired cell temperature, the ohmic internal resistance and polarization internal resistance are obtained through parameter mapping. Based on the average lithium filling ratio and the real-time acquired cell temperature, the open-circuit voltage and polarization capacitance are obtained through parameter mapping. Through this parameter mapping, the mechanism of the two-particle electrochemical model and the first-order RC equivalent circuit are integrated to form a wide-temperature-range electrochemical-equivalent circuit fusion model of lithium-ion battery. The three state variables of discrete solid-phase lithium ion concentration, polarization voltage and cell temperature are integrated to form a unified state vector. The constructed state-space equation is the state-space equation corresponding to the wide-temperature-range electrochemical-equivalent circuit fusion model of lithium-ion battery.

10. The mechanism-data fusion lithium-ion battery state-of-charge estimation system according to claim 8 or 9, characterized in that, In the battery multi-parameter joint estimation module, when performing state of charge (SOC) estimation, a bidirectional gated recurrent unit is embedded within the physical information neural network to construct the SOC estimation model. The bidirectional gated recurrent unit consists of two independent sets of gated recurrent units stacked together, which respectively perform forward sequence feature extraction and reverse sequence feature extraction on the battery time-series operating data, fuse the hidden states output by the two branches, and capture the bidirectional dependency relationship of the time-series data. The predicted terminal voltage and predicted cell temperature obtained by discrete recursive calculation through state-space equations, the real-time acquired battery terminal voltage and cell temperature, the SOC calculated by ampere-hour integration, and the real-time acquired battery charging and discharging current are used as the network input parameters of the SOC estimation model, and the actual battery SOC is used as the output label of the SOC estimation model. The adaptive weighted total penalty loss function is used as a constraint to train the SOC estimation model, and the trained SOC estimation model is used to realize online estimation of the lithium-ion battery SOC.

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