A method for joint prediction of battery state parameters and remaining lifetime

Abstract

This invention discloses a method for jointly predicting battery state parameters and remaining lifespan, relating to the field of state perception and lifespan management technology for electrochemical energy storage systems. The method includes the following steps: Step 1, acquiring multi-source monitoring data during the operation of a lithium-ion battery, where the multi-source monitoring data characterizes the battery's dynamic behavior and aging process; Step 2, constructing a physical mechanism guiding layer; Step 3, constructing a data-driven correction layer: a data-driven correction layer is constructed to characterize the deviation relationship between actual operating behavior and physical prediction results; Step 4, constructing a time-series state correction layer and outputting the prediction results. This invention can balance physical consistency and data adaptability, focusing on solving the problem of continuously and accurately reflecting the internal state evolution and lifespan changes of batteries under conditions of multiple operating conditions, significant individual battery differences, and limited sample conditions.

Description

Technical Field

[0001] This invention relates to the field of state sensing and lifetime management technology for electrochemical energy storage systems, and particularly to a method for jointly predicting battery state parameters and remaining lifetime. Background Technology

[0002] With the widespread application of electrochemical energy storage systems in new energy generation, grid, and user sectors, lithium-ion batteries, as their core energy storage units, face increasingly prominent issues regarding safety, reliability, and economy under long-term charge-discharge cycles and complex operating conditions. During actual operation, the battery's internal state parameters (such as state of charge, state of health, and internal resistance) and remaining lifespan continuously change with operating conditions, environmental factors, and aging. If these states cannot be accurately perceived and effectively predicted, it can easily lead to accelerated capacity decay, performance imbalance, and even safety accidents. This has become a significant technical problem restricting the efficient operation and lifespan management of energy storage systems. Currently, traditional solutions for estimating lithium-ion battery state parameters and predicting lifespan typically employ model-based or filter-based estimation methods to calculate the battery's state of charge or state of health. These methods rely on simplified equivalent battery models and pre-set parameters. The modeling process usually requires extensive experimental calibration, and the model structure is insufficient to fully characterize the complex electrochemical reactions and thermal behavior within the battery. For example, in applications such as grid-side energy storage or power-side peak shaving, lithium-ion batteries need to frequently participate in charge and discharge regulation. During operation, charge and discharge switching is frequent and load fluctuations are significant. At the same time, under certain environmental conditions, the ambient temperature of the battery may also vary greatly. When there is a deviation between the operating conditions and the assumptions made during the model establishment phase, or when the battery enters different aging stages as it is used, the model parameters are prone to mismatch, resulting in cumulative deviations in the state estimation results, which in turn affects the stability and reliability of lifetime prediction.

[0003] Data-driven state estimation and lifetime prediction methods offer a viable solution to engineering mismatch. These methods typically utilize historical operational data, employing statistical analysis or machine learning models to establish a mapping between measurable external signals and internal state parameters of the battery, thus reducing reliance on precise physical models to some extent. However, these methods are highly dependent on data quality and scale. Furthermore, due to the lack of effective constraints on the battery's internal electrochemical mechanisms and aging evolution, data-driven models struggle to maintain long-term reliability under small sample sizes or online application conditions. To overcome the shortcomings of both traditional model-based and purely data-driven methods, fusion methods combining physical models and data-driven models have gained significant attention in recent years. By incorporating battery physical mechanism information, the training and prediction processes of data-driven models can be constrained, improving the rationality of state estimation and lifetime prediction. However, existing methods often employ simplified physical models or introduce physical constraints as additional conditions, resulting in a relatively coarse characterization of the multiple physical processes within the battery, making it difficult to accurately reflect the true state evolution under complex operating conditions and long-term aging. Meanwhile, in practical applications, there are objective differences in manufacturing, operating environment, and aging path among different individual batteries. Existing conventional digital-analog fusion methods are still prone to insufficient generalization ability or decreased model stability when faced with changes in operating conditions or limited sample size. They are still difficult to meet the comprehensive requirements for state perception accuracy, stability, and engineering usability under the operating conditions of the entire battery life cycle.

[0004] In summary, existing technologies for battery state parameter estimation and lifetime prediction generally suffer from insufficient model adaptability, limited predictive stability, and limited generalization ability under complex operating conditions, long-term aging evolution, and significant individual battery variations. These limitations make it difficult to provide reliable state awareness and lifetime assessment results continuously over the long term. Therefore, there is an urgent need for a method for predicting state parameters and remaining lifetime throughout the entire battery lifecycle. This method should be able to accurately estimate the internal state of the battery and stably predict its lifetime evolution under various operating conditions and limited sample conditions, thereby providing effective technical support for the safe operation, performance optimization, and lifetime management of battery systems. Summary of the Invention

[0005] To address the above shortcomings, this invention provides a method for jointly predicting battery state parameters and remaining lifespan, which can balance physical consistency and data adaptability. It focuses on solving the problem of continuously and accurately reflecting the internal state evolution and lifespan changes of batteries under various operating conditions, significant individual differences in batteries, and limited sample conditions.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: A method for jointly predicting battery state parameters and remaining lifetime includes the following steps: Step 1: Data Acquisition and Preprocessing: Acquire multi-source monitoring data during the operation of the lithium-ion battery. The multi-source monitoring data characterizes the dynamic behavior and aging process of the battery. Construct an improved physical simulation model based on the coupling of the electro-thermal-mechanical three fields to generate simulation data for multiple operating conditions and multiple indicators. The collected data needs to be time-aligned and preprocessed to form input sequence data for subsequent state estimation and lifetime prediction. Step 2: Construct a physical mechanism guidance layer: Based on the physical constraints of battery state evolution, construct a physical mechanism guidance layer to characterize the basic evolution law of battery internal state parameters changing over time. It also receives the input sequence data formed in Step 1 and outputs battery state parameters and their evolution trend prediction results that conform to physical consistency, serving as the physical baseline for the subsequent prediction process of the system and constraining the rationality of the overall prediction results. Step 3: Construct a data-driven correction layer: Construct a data-driven correction layer to characterize the deviation relationship between actual operating behavior and physical prediction results. At the same time, take the collected measured operating data and the physical prediction results output by the physical mechanism guidance layer as input to learn and correct systematic deviations, and output adaptively adjusted battery state parameters and remaining life prediction results to improve the system's adaptability to complex operating conditions and individual battery differences. Step 4: Construct a timing state correction layer and output prediction results: Construct a timing state correction layer for timing consistency correction and dynamic updating of prediction results. Continuously track and correct the prediction results output by the data-driven correction layer to generate continuous and stable battery state parameters and remaining life prediction results. Output the final prediction information for battery state monitoring and life management to achieve reliable state perception and life assessment of the entire battery life cycle operation process.

[0007] Preferably, the multi-source monitoring data includes current, voltage, power, temperature, operating conditions, cycle stages, and time information. Specifically, the operating condition data mainly includes charging conditions, discharging conditions, resting conditions, and rate conditions; the cycle stage data includes the number of cycles, charging stage identifier, discharging stage identifier, and depth of charge / discharge; and the time information includes the sampling time, sampling interval, and cumulative operating time.

[0008] Preferably, step 1 includes the following steps: Step 1.1 Obtain multi-source monitoring data during the operation of the lithium-ion battery. The multi-source monitoring data characterizes the dynamic behavior and aging process of the battery. Step 1.2 Constructing an improved physical simulation model: Constructing an improved P2D model that couples classical electrochemical and electrothermal models with mechanical effects; Step 1.3 Perform unified time alignment, standardization, and basic denoising on the acquired simulation data and measured data to form complete time series data with multiple operating conditions and multiple indicators. This time series data is the input sequence data.

[0009] Preferably, in step 1.2, the classical electrochemical kinetic equations include the solid-phase diffusion equation, the electrolyte transport equation, the charge conservation equation, and the electrode reaction kinetic equation. The classical electrochemical kinetic equations introduce temperature-dependent solid-phase diffusivity and conductivity, enabling the P2D model to simulate the effects of ambient temperature fluctuations and changes in heat dissipation conditions on battery kinetics. At the same time, the electrode reaction kinetic parameters are set as temperature-related parameters to reflect the effects of temperature changes on the interfacial reaction rate and electrochemical kinetic behavior.

[0010] Preferably, in step 1.2, the mechanical theory is based on linear elasticity theory, introducing electrode volume expansion or compression through stress-strain relationship, and through contact resistance. Coupling maps the change in impedance due to deformation during cyclic aging to the electrochemical response.

[0011] Preferably, the basic denoising process in step 1.3 is achieved through wavelet decomposition: ; in These are the wavelet decomposition coefficients. The wavelet decomposition level is typically determined by a preset decomposition level threshold. Divide the wavelet decomposition coefficients when When the wavelet decomposition coefficients are used, they characterize high-frequency detail components and are used to characterize noise, transient fluctuations, and local abrupt changes. At that time, the corresponding wavelet decomposition coefficients characterize the low-frequency trend components, which are used to characterize the overall change trend and slow evolution characteristics of the signal; Indicates the first Each feature at time The time series signal after wavelet decomposition and denoising reconstruction is used to distinguish it from the original acquired signal. The symbol "^" above the variable indicates the estimated or reconstructed value after model processing, and the same applies to subsequent values.

[0012] Preferably, step 2 includes the following steps: Step 2.1 Construct a structured physical information neural network based on PINN-surrogate. The input of this structured physical information neural network is time-series multi-source data. The outputs are SOC, particle concentration gradient, temperature rise, and internal resistance; its core principle is through the residual function. Electrochemical, thermodynamic, and mechanical coupled equations are embedded in a network for forward propagation: ; in Represents the residuals of solid-state diffusion, charge conservation, interfacial reaction, thermal equilibrium, and strain-impedance coupling, with weights. Control all contributions; The PINN-surrogate mapping network, representing the embedded electro-thermal-mechanical coupling mechanism constraint, is used to establish external observations. The nonlinear mapping relationship between the system and its internal state variables.

[0013] Step 2.2 Introduce learnable physical parameters to achieve three-field coupling of electricity, heat and force; set the key parameters in the P2D model as learnable physical parameters, embed them into the computation graph to participate in forward propagation, the parameters are dynamically adjusted according to the running state, and backpropagation is carried out through physical residuals; Step 2.3 uses a recursive residual iteration method to perform time expansion on the PINN-surrogate network, so that it can simulate the physical evolution of the battery state between adjacent time steps. The time update form is as follows: ; in, This represents a state evolution operator composed of multi-physics coupling mechanisms. Through this recursive structure, the structured physical information neural network can approximate the rapid inference of the time evolution process of the P2D multi-physics model without relying on an explicit numerical solver. Step 2.4: Using the high-fidelity simulation data generated by the improved P2D multi-field coupled physics simulation model constructed in the above steps, pre-train the PINN-surrogate physics mechanism guiding layer; during the training process, both the physical residuals and the simulation data fitting error need to be constrained simultaneously, and its loss function... It can be defined as: ; As the physical prediction baseline of the system, its output format is: ; in Indicates at time External observations collected, Indicates the state of charge of the battery. Indicates the radial position inside the solid particles ,time The ion concentration distribution is used to characterize the diffusion state within the electrode particles. Indicates temperature; Indicates internal resistance; The PINN-surrogate mapping network represents the embedded electro-thermal-mechanical coupling mechanism, while Indicates the physical layer at time The output state vector.

[0014] Preferably, in step 2.2, the learnable physical parameters are expressed as a set of learnable physical parameters. ; in, This represents the temperature-dependent solid-phase diffusivity. Indicates the effective conductivity of the electrode and the electrolyte. Indicates the interfacial reaction kinetic coefficient. This represents the coupling coefficient between electrode volume expansion / compression and contact resistance change.

[0015] Preferably, step 3 includes the following steps: Step 3.1 employs a residual learning architecture, constructing a correction layer based on two inputs: measured data and the physical baseline output from the physical mechanism guidance layer. The core function of this layer is to learn the residual term between the true state and the physical baseline prediction. ; in, The parameter is Residual learning mapping network, Input the actual operating data. The prediction results are output by the physical mechanism guidance layer; Battery state prediction results after data-driven correction layer Then it is obtained by superimposing the physical baseline and the residual term: ; Step 3.2 The internal physical state variables output by the physical mechanism guidance layer will be used as soft labels to constrain the training process of the data-driven correction layer; Its downward distillation loss function It can be represented as: ; in, This represents the battery state prediction result after correction by the data-driven correction layer. This represents the physical baseline prediction results output by the physical mechanism guidance layer at the same time. It is a physical feature mapping operator used to extract physical features reflecting the battery state evolution trend from the state prediction results. By minimizing the consistency constraint loss, the data-driven correction prediction results are kept consistent with the physical baseline prediction at the physical feature level, thereby ensuring that the residual correction does not destroy the physical rationality of the battery state evolution over time. Step 3.3 Establish an upward distillation parameter correction mechanism based on residual feedback. Stable deviation information is applied inversely to the learnable parameters of the physical mechanism guidance layer. Through reverse gradient propagation, the internal parameters of the physical layer gradually approximate the equivalent physical characteristics of the real battery. ; in, This represents the up-distillation loss function. Indicates the physical baseline prediction results. This represents the final prediction result after correction by the data-driven layer. This represents the residual term learned by the data-driven correction layer; During joint training, through the overall loss function This allows for comprehensive optimization of prediction errors and distillation constraints, which can be simply expressed as: ; and These are the weighting coefficients for the distillation loss term, used to balance the contributions of the downflow distillation constraint and the upflow distillation constraint to the overall optimization objective; Through bidirectional distillation, the physical layer and the correction layer form a closed-loop synergy: the physical layer provides structured physical constraints to guide the correction layer in learning reasonable residuals; the correction layer provides feedback on stable bias information to optimize the parameters of the physical layer, so that the two enhance each other in prediction accuracy and physical consistency.

[0016] Preferably, step 4 includes the following specific steps: Step 4.1 Based on the output of the correction layer, a learning filter module is constructed to perform continuous time series correction on the battery state parameters and remaining lifetime prediction results. This filter module mainly handles the dynamic continuity and smoothness of the corrected prediction results, while providing uncertainty assessment. The input is the residual correction prediction of the data-driven correction layer output. The filter automatically adapts to different individual batteries and operating conditions through learnable noise covariance and state transition matrix. Its basic principle can be expressed as: ; ; in, The internal state variables of the filter at time t include SOC, internal resistance, temperature rise, and health status indicators. For input operation signals; Indicates at time The system state in the state transition matrix The natural evolution results under the influence of the environment are used to characterize the dynamic changes of the internal state of the battery without external control input. This characterizes the control effect of external inputs on the system state, mapping charging and discharging conditions and environmental disturbances as driving forces for state changes; For the observed variable, the output of the data-driven correction layer is used here. As observed values; Represents state variables After observation matrix The mapped theoretical observations are used to establish the correspondence between the hidden states inside the filter and the actual observations; and These are state and observation noise, respectively, and can be dynamically adjusted via network-learnable parameters. Step 4.2 After the filter completes its iterations, these states are mapped to the final battery health status indicators and remaining lifespan, generating smooth and continuous prediction results. The final prediction information output will be set as follows: ; ; in, This represents the continuous state prediction results after time-correction, including the battery's state of charge. Internal resistance ,temperature Health status and remaining lifespan ; This is the covariance matrix, used to quantify the uncertainty of prediction results.

[0017] Preferably, the battery management system can obtain the probability distribution characteristics of battery state parameters and lifespan through the final prediction information.

[0018] The working principle and beneficial effects of this invention: The core objective of this invention is to establish a joint prediction system for battery state parameters and remaining life based on a physical mechanism layer guidance, a data-driven layer correction, a time-series state layer correction, and multi-level synergistic effects. This system aims to achieve accurate estimation of state parameters and stable prediction of remaining life for lithium-ion batteries throughout their entire lifecycle. Specifically, the physical mechanism guidance layer characterizes the fundamental physical constraints governing the evolution of the battery's internal state over time, generating a physically consistent state prediction baseline. The data-driven correction layer learns the systematic deviations between the physical prediction results and actual operating data to adapt to different operating conditions and individual battery variations. The time-series state correction layer dynamically tracks and corrects the prediction results, improving the continuity and stability of state estimation and life prediction. While maintaining the physical rationality of the battery state evolution process, this system achieves stable prediction of battery state parameters and life changes under complex operating conditions through adaptive correction of non-ideal behaviors in the operating data, thus balancing the generalization ability of the prediction results with the feasibility of engineering applications. Attached Figure Description

[0019] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below.

[0020] Figure 1 This is a flowchart illustrating the overall technical process of a method for jointly predicting battery state parameters and remaining life according to the present invention. Detailed Implementation

[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0022] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances. Furthermore, the technical features involved in the different embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0023] like Figure 1 As shown, a method for jointly predicting battery state parameters and remaining lifetime includes the following steps: Step 1: Data Acquisition and Preprocessing. A comprehensive data acquisition and preprocessing system for the entire lifecycle of lithium-ion batteries is constructed to provide high-quality, structured input information for downstream processes. Multiple signals, including current, voltage, power, temperature, and cycle status, are collected during battery operation. Charge-discharge cycle and time-series characteristics under various operating conditions are recorded. Time alignment, outlier removal, and basic cleaning are performed to ensure data quality and consistency. Furthermore, to enhance feature coverage under small sample conditions, an improved electro-thermal-mechanical three-field coupled P2D simulation model is introduced to generate multi-index simulation data at different rates, temperatures, and cycle stages, covering key physical quantities such as SOC, particle concentration gradient, temperature rise, and internal resistance. Through the fusion and serialization of measured and simulated data, a continuous and unified input sequence is formed, providing complete and reliable basic data for battery state characterization and aging trend analysis.

[0024] Step 1 includes the following specific steps: Step 1.1: High-precision current and voltage sensors are placed at the electrode ports of the lithium-ion battery, while temperature sensors are placed on the battery surface and at key internal locations to collect real-time data on current, voltage, power, and temperature changes during the charging and discharging process. The collected data is time-synchronized at a fixed sampling frequency to ensure that all signals correspond under the same time reference, forming a complete multivariate time series. Cycling stage information is recorded by the charge / discharge controller, including charge / discharge depth, number of cycles, and operating mode, to characterize the battery's response differences under different operating conditions. The collected electrochemical signals reflect the battery's internal state of charge, voltage curve, and transient response, while the temperature signal captures the battery's thermal behavior under different rates, environmental conditions, and internal chemical reactions.

[0025] Step 1.2 Based on the improved P2D model, the classical electrochemical kinetic equations, thermal equilibrium equations, and mechanical coupling effects are modeled in a unified manner to realize the interaction of the three fields of electricity, heat, and force. The electrochemical part is based on the solid-state diffusion equation: Describe the lithium-ion diffusion process in solid-phase particles, where It is a temperature-dependent diffusion coefficient that can characterize the effect of ambient temperature and heat dissipation conditions on the diffusion rate. The lithium-ion concentration in the solid particles reflects the distribution of lithium ions within the electrode material and its evolution over time; electrolyte transport equation. Describe the changes in ion concentration in the electrolyte to ensure mass conservation; among which, This indicates the lithium ion concentration in the electrolyte; The electrolyte diffusion coefficient; Lithium-ion transference number (LTF) represents the proportion of current carried by lithium ions. It is Faraday's constant; This represents the reaction current density at the electrode interface. The charge conservation equation is then applied... , Describe the potential distribution of the solid phase and electrolyte, where conductivity and The effect of temperature on conductivity is shown by the change in temperature. This represents the distribution of electron potential in the solid phase of the electrode. The distribution of ion potentials in the electrolyte is represented; the electrode reaction kinetics are given by the Butler–Volmer equation: ; in Represents the hyperbolic sine function. The reaction rate constant is temperature-dependent. , , Characterizing the reaction rate sensitivity under varying expansion rates; specifically... This indicates the maximum concentration of lithium ions in the solid particles. This term represents the effect of the current solid-phase lithium concentration on the reaction rate. This is a dimensionless overpotential term that reflects the driving force of the electrode reaction. Its magnitude reflects the sensitivity of the reaction rate to changes under different rate conditions.

[0026] The mechanical part is based on linear elasticity theory, introducing electrode volume expansion / compression through stress-strain relationship, and relating it to contact resistance. Coupling maps the change in impedance due to deformation during cyclic aging to the electrochemical response. The thermal equilibrium equation... Describe the heat of electrochemical reaction With Ohm The contribution to temperature distribution ensures thermal-electric coupling. Among these, This term represents the heat accumulation per unit volume and is used to describe the dynamic process of temperature change over time. Thermal conductivity is the material's ability to conduct heat within the battery. This is the pyrogen term of the electrochemical reaction, originating from the energy release or absorption during the electrode reaction process; while This is the Ohmic heating term, which is the Joule heating generated by the current passing through the internal resistance of the electrodes, electrolyte, etc.

[0027] By iteratively solving the above three-field coupling equations of electricity, heat, and force, the model can generate high-fidelity simulation data with multiple indicators at different magnification, temperature, and cycling stages, including SOC, particle concentration gradient, temperature rise, and internal resistance change data. This data can be used to supplement the measured data and provide a physical consistency baseline for subsequent physical layer networks.

[0028] Step 1.3 unifies the processing of high-fidelity simulation data generated by the improved P2D model with the measured operational data. A time alignment method is used to map data from different sources and with different sampling rates to a unified time scale. Subsequently, the data is standardized to normalize various indicators to a uniform numerical range, reducing the impact of deviations between different units on subsequent model training. Noise suppression is achieved through wavelet decomposition. ; in These are the wavelet decomposition coefficients. Let i be the time series signal of the i-th feature at time t. This represents the wavelet decomposition level.

[0029] This processing removes high-frequency noise while preserving the main trends of the signal. Ultimately, the processed multi-condition, multi-index data will form a continuous and unified sequence, providing stable and structured input for downstream levels.

[0030] Step 2 Specific Implementation Method: A physical mechanism guiding layer is constructed, embedding the internal electrochemical, thermodynamic, and mechanical coupling relationships of the battery into a trainable network to achieve physically constrained predictions of the battery's state parameter evolution. This layer uses the PINN-surrogate model as its core structure. By embedding temperature-dependent solid-phase diffusivity, conductivity, electrode reaction kinetics parameters, and electrode volume expansion / compression and contact resistance coupling terms based on linear elasticity theory, the predictions of physical quantities such as SOC, particle concentration gradient, temperature rise, and internal resistance are subject to the interactive constraints of electrical, thermal, and mechanical fields. During forward propagation, the network simulates the evolution of the battery's internal state over time through residual iteration, achieving a physically consistent baseline output. This provides reliable guidance for downstream bias learning while maintaining interpretability and high-speed inference capabilities.

[0031] Step 2 includes the following specific steps: Step 2.1 Constructs a structured physical information neural network based on PINN-surrogate to map time-series multi-source operational data into an approximation of the battery's internal state field that satisfies physical constraints. Unlike traditional methods that only predict state scalars, this network is designed to directly output continuous state field functions with explicit physical meaning, embedding a unified representation of electrochemical, thermodynamic, and mechanical states at the network structure level.

[0032] Specifically, the network receives operational data and physical variables as input in a continuous-time manner, and performs parameterized mapping. The output is a set of state field variables that change continuously with time and space. These outputs are not regarded as independent predictions, but as functional approximations of the real physical state field. Their form can directly participate in the construction and calculation of physical equations, thus limiting the expression space of the neural network to the function space defined by physical laws.

[0033] During forward propagation, the network output state field calculates its temporal derivative and spatial gradient through an automatic differentiation mechanism to characterize the dynamic characteristics of the state's evolution under varying operating conditions. The time derivative of the state is implicitly given by the chain relationship between the network mapping and the input time series, and its calculation form is as follows: ; in, Indicates the network at time The predicted output state; Indicates by parameters The neural network mapping function representing the representation; This represents the input feature vector that changes over time. This represents the gradient of the network output with respect to the input; This represents the rate of change of the input features over time, used to characterize the temporal dynamics of external operating conditions. It can be obtained directly by automatic differentiation, enabling state evolution to be expressed in continuous form without explicit time discretization.

[0034] For spatially relevant physical quantities, such as the lithium-ion concentration distribution inside electrode particles, its spatial gradient is also naturally given by the differentiability of the network output with respect to spatial variables, expressed as: ; Where ∇ represents the gradient operator, which is used to characterize the rate of change of a physical quantity in spatial coordinates; This indicates the radial position inside the solid particles predicted by the network. ,time Lithium ion concentration distribution; Let represent the neural network mapping function used to characterize the concentration field, with parameters as follows: ; For a moment The input feature vector; The radial spatial coordinates inside the particle; Represents spatial variables The gradient operator is used to characterize the rate of change of concentration in space. Ultimately, a continuous approximate representation of the diffusion process is formed within the neural network.

[0035] Based on the aforementioned state field and its derivatives, multiple physical processes, including electrochemical diffusion, interfacial reaction kinetics, and thermal equilibrium, are uniformly represented as a set of parallel-computable physical equation residual terms. These residuals are explicitly constructed during the network's forward propagation and introduced into the loss function as physical consistency constraints, directly participating in the network parameter update process through the backpropagation mechanism. ; in, This represents the set of residuals consisting of multiple physical processes, including diffusion residuals. Reaction kinetic residuals Thermal equilibrium residual wait; Indicates the first The residual terms corresponding to physical processes; Construct a function for the residuals of the corresponding physical equations; Represents the state field variables predicted by the network; and Let represent the derivatives of the state field with respect to time and space, respectively, obtained by automatic differentiation calculation; and These are neural network parameters used to characterize the mapping relationship between the state field and its derivatives in the physical equations.

[0036] Therefore, any state field function shape that leads to an increase in the residual of the physical equation will be subject to gradient penalty during training, thereby restricting the network's learning process to a function space that approximately satisfies the constraints of multiple physical mechanisms of electro-thermal-mechanical systems, rather than relying solely on data-driven empirical fitting.

[0037] Step 2.2 In the structured physical information neural network, key physical parameters that were originally considered constants or empirical scalars in the improved P2D model will be explicitly introduced as a set of learnable physical parameters: ; in, This represents the temperature-dependent solid-phase diffusivity. Indicates the effective conductivity of the electrode and the electrolyte. Indicates the interfacial reaction kinetic coefficient. This represents the coupling coefficient between electrode volume expansion / compression and contact resistance change. These parameters are not directly output by the network, but rather serve as intermediate variables controlling the behavior of the physical channels, embedded in the network's computational graph and participating in the forward propagation process.

[0038] During the forward computation, the network first generates corresponding parameter estimates based on the implicit representation of the input time series states. This data is then incorporated into electrochemical, thermodynamic, and mechanically related physical constraints to dynamically adjust the diffusion rate, potential distribution, reaction intensity, and impedance changes according to the operating conditions. Temperature prediction results are used in the modulation process. , and This reflects the feedback effect of the thermal field on the electrochemical process; simultaneously, the volumetric strain caused by changes in particle concentration is reflected through... The mapping is represented as an increase in contact resistance, which in turn affects the equivalent internal resistance and the Joule heat source term, thus realizing the coupling feedback of mechanical effects on the electro-thermal process.

[0039] The aforementioned learnable physical parameters do not alter the basic structural form of the physical residuals. Instead, they serve as state-dependent representations of key physical coefficients in the residuals, participating in forward computation. Their gradients are also backpropagated through the physical residuals during training. Through this parameterization method, the interactions between the electrical, thermal, and mechanical fields no longer rely on fixed empirical models. Instead, they form dynamic coupling pathways within the network through learnable physical parameters. This allows the network to adaptively characterize the multi-physics field co-evolution characteristics under different operating conditions and aging stages while maintaining the unchanged physical constraint structure.

[0040] Step 2.3 Through the above two steps, in the prediction phase, the PINN-surrogate network will recursively extrapolate the time-series input based on the embedded physical residual structure and learnable physical parameters. For the input information at each time step, the network first internally generates a set of physical state representations that satisfy electrochemical, thermal, and mechanical consistency constraints. The formation process of this state is simultaneously influenced by the residual constraint structure and the set of learnable physical parameters. The combined control of these factors ensures that the prediction results always remain within the physically feasible solution space.

[0041] Based on this, the network will perform a time-varying expansion of the state sequence using a recursive structure, taking the predicted state from the previous time step as prior input to guide the current state update, thus achieving continuous modeling of the multi-physics coupled evolution process inside the battery. Its prediction process can be uniformly represented as: ,in, When indicating Predicted physical state When indicating +1 predicts the physical state. Input the corresponding operating conditions. The set of physical parameters that have been learned. This represents the physical residual constraint structure embedded within the network. This is a recursive prediction mapping operator that integrates multiphysics consistency and data-driven capabilities. Through this recursive deduction method, the network can achieve efficient approximate prediction of the temporal evolution behavior of high-dimensional P2D multiphysics models without relying on explicit numerical solvers.

[0042] Step 2.4 Finally, during network training, parameter updates are implemented using a joint optimization mechanism prioritizing physical consistency. Specifically, in each iteration, the network's forward propagation induces two types of error information simultaneously, one of which is generated by the multi-physics coupled residuals. Another type of characterization is the deviation between the predicted state and the high-fidelity simulated trajectory. The two characteristics together constitute the error information for a single iteration. Specifically, the total error information is expressed as follows: ,in: ; ; in Indicates the first The residual function corresponding to the physical constraint equation is used to measure the degree to which the current network output satisfies physical constraints such as electrochemical equation, thermal balance equation and mechanical coupling equation. This indicates that the reference state trajectory generated by the high-fidelity multiphysics simulation model is used as a supervision target during the network training process.

[0043] These two types of errors work together in the gradient space to influence the parameter update direction, so that the network is always subject to explicit constraints of the electro-thermal-mechanical coupling mechanism during the learning process.

[0044] During the backpropagation phase, the total error information is mapped to the parameter space via gradients, resulting in a unified update of the network parameters. The parameter update is no longer dominated by the single data fitting error, but rather determined jointly by the physical residual gradient and the data error gradient within the same parameter space. This update can be expressed as: ; in, During parameter updates, constraints are imposed on update directions that do not satisfy the electro-thermal-mechanical coupling mechanism, thus limiting the gradient descent path to the physically feasible solution space. This drives the network to converge toward a high-fidelity simulated trajectory; furthermore, Indicates the first Network parameters at the next iteration This represents the learning rate, which controls the step size for each parameter update.

[0045] Through this joint optimization mechanism, the network will gradually develop a data representation capability dominated by physical consistency during the training process, so that its internal state mapping can not only approximate the simulation data distribution, but also maintain a structured characterization of electrochemical dynamics, heat conduction and mechanical coupling relationships.

[0046] Step 3: Specific implementation method: A residual learning and state correction mechanism based on real operating data is introduced to specifically compensate for the physical consistency prediction results output by the physical mechanism guidance layer. The data-driven correction layer uses the prediction results obtained from the physical layer as a priori reference. Through downspinning constraints, it maintains the consistency between the prediction results and the physical evolution trend in the feature space, ensuring that residual compensation only proceeds in the physically permissible direction and avoiding the introduction of correction components that contradict the electro-thermal-mechanical laws. At the same time, the upspinning mechanism backmaps the stable systematic deviations learned by the data-driven correction layer to the learnable parameters of the physical layer, adjusting the physical layer parameters so that the physical mechanism guidance layer gradually approximates the equivalent physical characteristics of the real battery.

[0047] Step 3.1 In the calculation process of the correction layer, the physical mechanism guiding layer at time... The output physically consistent state vector is treated as a deterministic physical prior trajectory and input into the residual learning network along with the measured operational data collected at the same time. To avoid the correction layer disrupting the long-term evolution trend depicted by the physical layer, the output of the residual network is explicitly constrained to a zero-mean perturbation form, with its time expectation satisfying: This ensures that the correction term only compensates for local deviations, without reshaping the overall state evolution.

[0048] Furthermore, during the training phase, the correction layer does not directly use the absolute state error as the optimization target, but rather uses the residual consistency error as the core driver. This approach forces the deviation between the network output and the "real-physical baseline" to be structurally consistent, allowing the residual learning network to focus on absorbing non-ideal factors that the physical model cannot explicitly characterize.

[0049] To further suppress the oscillations of the residuals over time, this layer also introduces residual smoothing constraints, which limit the changes in the correction terms at adjacent time points and constrain their continuity. It can be written as: This constraint makes the correction process a slow, evolving systematic shift rather than an instantaneous jump, thus better reflecting the physical characteristics of real aging and operating condition disturbances.

[0050] Through the above mechanism, the correction layer forms a working mode of "physical baseline dominance, limited residual correction, and continuous time constraint" during the implementation process, so that the final state prediction is close to the measured data while maintaining consistency with the physical mechanism guidance layer in terms of trend and structure.

[0051] Step 3.2 During the training of the data-driven correction layer, the internal state of the physical mechanism guidance layer needs to be introduced as a soft label; this is the downlink distillation constraint. Specifically, the physical representation extracted from the feature space by the physical baseline prediction is first considered as the reference direction: ; in, This represents the physical representation of the physical mechanism guidance layer in the feature space. This represents the feature mapping function, used to map physical state quantities to a higher-level feature space; Indicates the physical baseline at time... The predicted state vector.

[0052] The state prediction result of the data-driven correction layer after residual superposition is also mapped to this physical feature space: ; ; in, This represents the state prediction result after data-driven correction; For physical baseline prediction results; The residual term is obtained from the data-driven correction layer learning; This represents the modified prediction result in the feature space. Similarly, this is the feature mapping function.

[0053] Ultimately, by making: ; This creates an alignable physical description, ensuring that the correction results maintain an evolutionary trend consistent with the physical baseline at the physical feature level. Furthermore, to prevent the data-driven correction layer from deviating from the physical evolution during training, directional constraints are introduced in the feature space, ensuring that the gradient updates of the residual network follow physically permissible directions, i.e.: ; Among them, the physical projection constraint term represents the constraint loss term used to measure the consistency between the current parameter update direction and the physical mechanism evolution direction. This represents the residual loss function with respect to the parameters of the correction layer. The gradient; This indicates the physical projection constraint terms with respect to the correction layer parameters. The gradient; This represents the vector inner product operation. This constraint requires that the two gradient directions maintain a non-negative angle, thereby ensuring that the parameter update direction is consistent with the physical evolution direction and preventing the optimization process from deviating from the physical mechanism constraint.

[0054] This constraint ensures that data-driven residuals are compensated only in physically permissible directions, without introducing correction components that contradict the electrothermal-mechanical evolution of the battery.

[0055] Furthermore, at the implementation level, by weighting and combining gradients during the backpropagation phase, the physical consistency constraint has a "priority pruning" effect in parameter updates, and its update form can be written as: ; in, This represents the projection operator along the direction consistent with physical characteristics. This is the consistency adjustment coefficient, used to control the strength of the influence of physical distillation constraints on residual learning. Represents the total loss function Relative to the correction layer parameters The gradient.

[0056] By introducing the aforementioned downward distillation mechanism, a clear hierarchical relationship of "physical dominance - data compensation" is formed between the physical mechanism guidance layer and the data-driven correction layer. This significantly improves the physical reliability and long-term stability of the correction layer's prediction results under complex operating conditions, small sample sizes, and significant individual differences in batteries.

[0057] Step 3.3 Downward distillation ensures that the data-driven correction layer can learn systematic biases. Similarly, to enable the physical mechanism guidance layer to gradually adapt to the operating characteristics of the real battery, this stable bias information needs to be applied back to the learnable parameters of the physical layer through an upward distillation mechanism. In practical implementation, firstly, feature extraction is performed on the residual network output at each time step to obtain a long-term stable bias signal, which is then mapped to the gradient space of the physical layer parameters. Subsequently, a gradient correction operator is constructed. The deviation signal and the physical layer learnable parameters Coupled updates are performed so that the parameters within the physical layer are adjusted in directions that reduce long-term residuals, rather than directly constraining the predicted values ​​themselves. This includes the gradient correction operator. Specifically: ; Indicates the physical layer output for parameters The Jacobian matrix represents the sensitivity of the physical layer parameters to the prediction results, while That is, its transpose; This is the up-distillation weight matrix, used to control the contribution of the residuals of different state variables to the update of physical layer parameters. For data-driven correction layers in time The learned residual signal. Finally, the update of the physical layer parameters can be expressed as: ; in Let t be the learning rate and t be the time. The physical layer parameters are corrected by gradient descent by accumulating the residual signals at each time step, so that the physical layer gradually adapts to the characteristics of the real battery.

[0058] In the final implementation, updistillation and downdistillation are combined into the overall loss function to achieve bidirectional closed-loop collaborative optimization: + ; in, This represents the prediction loss of the data-driven layer. This is an upward distillation constraint term. This is a downward distillation constraint term, and and Then these are the weight coefficients of the corresponding constraint terms mentioned above.

[0059] This joint optimization ensures that the data-driven correction layer can learn non-ideal behaviors, while the physical mechanism-guided layer continuously and adaptively corrects parameters through residual feedback, enabling the entire system to maintain high-fidelity, physically consistent state prediction and remaining lifetime estimation under complex operating conditions and small sample scenarios.

[0060] Step 4: Specific implementation method: Based on the physical consistency state and data-driven residuals of the first two layers of output, a time-series state estimation framework is constructed. Through iterative smoothing and dynamic adjustment of adaptive filters, the reliability of the system output is further optimized, so that the predicted values ​​of output such as SOC, internal resistance, temperature rise, SOH and RUL not only conform to the historical evolution trend, but also reflect the changes in real battery data, thereby generating high-fidelity state and lifetime information that can be directly used in the battery management system.

[0061] Step 4.1 Correcting the prediction of the input residuals This is mapped onto the state space of the filter to construct a state vector that includes parameters such as SOC and internal resistance. The filter then updates the state at each time step recursively, ensuring the prediction results remain smooth and continuous over time. Specifically, the filter first uses a state transition function to advance the state from the previous time step and introduces state noise. To reflect random disturbances present in battery operation, thereby obtaining a predicted state. , This is the state transition function inside the filter.

[0062] Then based on The projection in the filter space is obtained by observing the mapping function. Calculate the observation residuals : ; Utilizing residuals and the state covariance matrix The estimate can be used to calculate the time-adaptive gain. The predicted state is then corrected to obtain the filtered state vector: And gain , Represents the observation mapping matrix, This represents the observation noise covariance matrix; through this gain, the filter can adaptively project the observation residuals into the state space, ensuring the stability of state updates under different operating conditions and individual battery differences.

[0063] The entire process is iterative in time, with each step passing the state prediction, residual correction, and covariance information from the previous moment to the next, achieving smooth correction of the continuous time series. State vector After the iteration, it includes both the deviation compensation information provided by the residual correction layer and maintains temporal continuity.

[0064] Step 4.2 After the filter completes iterative correction and generates a continuous state vector Finally, these states need to be mapped to the final battery health status indicators and remaining lifespan. To this end, a set of learnable mapping functions is introduced. and The key physical quantities in the filter output state vector, such as the state of charge SOC(t) and internal resistance, are... Parameters such as temperature T(t) and cumulative cycle count are mapped to health status and remaining lifespan: ; in, The relationship between battery capacity degradation and characteristics such as SOC, internal resistance, and cycle count and the battery's health status can be fitted using historical cycle degradation curves, reflecting the degree of battery capacity degradation. Based on the current State of Health (SOH) and state evolution rate, the remaining available cycles or time are predicted. Through this mapping, the output at each time step not only retains the smooth continuity provided by the filter but also provides a direct prediction of key battery parameters.

[0065] Meanwhile, the covariance matrix of the filter output This will also be mapped to the uncertainty in health status and life expectancy prediction, providing confidence estimates for SOH and RUL at each time point: ; in For mapping functions and For the state vector The Jacobian matrix represents the sensitivity of small changes in state variables to SOH and RUL. By applying time-correlation regularization and covariance updates to the entire time series, smooth and well-defined SOH and RUL prediction sequences can be obtained, forming the final output vector. ; The corresponding uncertainty covariance matrix can be expressed as: ; in These are the weighting coefficients. This is the uncertainty covariance matrix of the model's prediction results for time series, used to characterize the prediction variance and correlation of each state variable in the time dimension; This indicates that the modified covariance matrix after introducing time-correlation regularization improves the stability and interpretability of uncertainty estimation by diagonalizing the original covariance matrix and superimposing regularization terms. This is a time-dependent regularization term used to constrain the smoothness of changes in prediction results between adjacent time points, suppress unreasonable abrupt changes, and enhance time consistency. This output can be directly used by the battery management system to achieve continuous monitoring and safety assessment of battery status, performance degradation, and remaining life.

[0066] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for jointly predicting battery state parameters and remaining lifetime, characterized in that, Includes the following steps: Step 1: Data Acquisition and Preprocessing: Acquire multi-source monitoring data during the operation of the lithium-ion battery. The multi-source monitoring data characterizes the dynamic behavior and aging process of the battery. An improved physical simulation model based on the coupling of electric, thermal, and mechanical fields was constructed to generate simulation data with multiple operating conditions and multiple indicators. The collected data needs to be time-aligned and preprocessed to form input sequence data for subsequent state estimation and lifetime prediction. Step 2: Construct a physical mechanism guidance layer: Based on the physical constraints of battery state evolution, construct a physical mechanism guidance layer to characterize the basic evolution law of battery internal state parameters changing over time. It also receives the input sequence data formed in Step 1 and outputs battery state parameters and their evolution trend prediction results that conform to physical consistency, serving as the physical baseline for the subsequent prediction process of the system and constraining the rationality of the overall prediction results. Step 3: Construct a data-driven correction layer: Construct a data-driven correction layer to characterize the deviation relationship between actual operating behavior and physical prediction results. At the same time, take the collected measured operating data and the physical prediction results output by the physical mechanism guidance layer as input to learn and correct systematic deviations, and output adaptively adjusted battery state parameters and remaining life prediction results to improve the system's adaptability to complex operating conditions and individual battery differences. Step 4: Construct a timing state correction layer and output prediction results: Construct a timing state correction layer for timing consistency correction and dynamic updating of prediction results. Continuously track and correct the prediction results output by the data-driven correction layer to generate continuous and stable battery state parameters and remaining life prediction results. Output the final prediction information for battery state monitoring and life management to achieve reliable state perception and life assessment of the entire battery life cycle operation process.

2. The method for jointly predicting battery state parameters and remaining life according to claim 1, characterized in that: The multi-source monitoring data includes current, voltage, power, temperature, operating conditions, cycle stage, and time information.

3. The method for jointly predicting battery state parameters and remaining life according to claim 1, characterized in that: Step 1 includes the following specific steps: Step 1.1 Obtain multi-source monitoring data during the operation of the lithium-ion battery. The multi-source monitoring data characterizes the dynamic behavior and aging process of the battery. Step 1.2 Constructing an improved physical simulation model: Constructing an improved P2D model that couples classical electrochemical and electrothermal models with mechanical effects; Step 1.3 Perform unified time alignment, standardization, and basic denoising on the acquired simulation data and measured data to form complete time series data with multiple operating conditions and multiple indicators. This time series data is the input sequence data.

4. The method for jointly predicting battery state parameters and remaining life according to claim 3, characterized in that: In step 1.2, the classical electrochemical kinetic equations include the solid-phase diffusion equation, the electrolyte transport equation, the charge conservation equation, and the electrode reaction kinetic equation. The classical electrochemical kinetic equations introduce temperature-dependent solid-phase diffusivity and conductivity, enabling the P2D model to simulate the effects of ambient temperature fluctuations and changes in heat dissipation conditions on battery kinetics. At the same time, the electrode reaction kinetic parameters are set as temperature-related parameters to reflect the influence of temperature changes on the interfacial reaction rate and electrochemical kinetic behavior.

5. The method for jointly predicting battery state parameters and remaining life according to claim 3, characterized in that: In step 1.2, the mechanical theory is based on linear elasticity, introducing electrode volume expansion or compression through stress-strain relationship, and then relating it to contact resistance. Coupling maps the change in impedance due to deformation during cyclic aging to the electrochemical response.

6. The method for jointly predicting battery state parameters and remaining life according to claim 3, characterized in that: The basic denoising process in step 1.3 is achieved through wavelet decomposition: ； in These are the wavelet decomposition coefficients. The wavelet decomposition level index is typically based on a preset decomposition level threshold. Divide the wavelet decomposition coefficients when When the wavelet decomposition coefficients are used, they characterize high-frequency detail components and are used to characterize noise, transient fluctuations, and local abrupt changes. At that time, the corresponding wavelet decomposition coefficients characterize the low-frequency trend components, which are used to characterize the overall change trend and slow evolution characteristics of the signal; Indicates the first Each feature at time The time series signal after wavelet decomposition and denoising reconstruction is used to distinguish it from the original acquired signal.

7. The method for jointly predicting battery state parameters and remaining life according to claim 1, characterized in that: Step 2 includes the following specific steps: Step 2.1 Construct a structured physical information neural network based on PINN-surrogate. The input of this structured physical information neural network is time-series multi-source data. The outputs are SOC, particle concentration gradient, temperature rise, and internal resistance; its core principle is through the residual function. Electrochemical, thermodynamic, and mechanical coupled equations are embedded in a network for forward propagation: ； in Represents the residuals of solid-state diffusion, charge conservation, interfacial reaction, thermal equilibrium, and strain-impedance coupling, with weights. Control all contributions; The PINN-surrogate mapping network, representing the embedded electro-thermal-mechanical coupling mechanism constraint, is used to establish external observations. The nonlinear mapping relationship between the system and its internal state variables; Step 2.2 Introduce learnable physical parameters to achieve three-field coupling of electricity, heat and force; set the key parameters in the P2D model as learnable physical parameters, embed them into the computation graph to participate in forward propagation, the parameters are dynamically adjusted according to the running state, and backpropagation is carried out through physical residuals; Step 2.3 uses a recursive residual iteration method to perform time expansion on the PINN-surrogate network, so that it can simulate the physical evolution of the battery state between adjacent time steps. The time update form is as follows: ； in, This represents a state evolution operator composed of multiple physical coupling mechanisms; Step 2.4 uses the data generated in Step 2.3 to pre-train the PINN-surrogate physical mechanism guidance layer; during training, both the physical residuals and the simulation data fitting error need to be constrained simultaneously, and its loss function... It can be defined as: ； As the physical prediction baseline of the system, its output format is: ； in Indicates at time The external observations collected, among which, Indicates the state of charge of the battery. Indicates the radial position inside the solid particles ,time The ion concentration distribution is used to characterize the diffusion state within the electrode particles. Indicates temperature; Indicates internal resistance; This represents a PINN-surrogate mapping network that incorporates constraints related to the embedded electro-thermal-mechanical coupling mechanism. This indicates that the PINN-surrogate physical layer is at time [time missing]. The output is a state vector that satisfies the physical constraints.

8. The method for jointly predicting battery state parameters and remaining life according to claim 7, characterized in that: In step 2.2, the learnable physical parameters are expressed as a set of learnable physical parameters. ; in, This represents the temperature-dependent solid-phase diffusivity. Indicates the effective conductivity of the electrode and the electrolyte. Indicates the interfacial reaction kinetic coefficient. This represents the coupling coefficient between electrode volume expansion / compression and contact resistance change.

9. The method for jointly predicting battery state parameters and remaining life according to claim 1, characterized in that: Step 3 includes the following specific steps: Step 3.1 employs a residual learning architecture, constructing a correction layer based on two inputs: measured data and the physical baseline output from the physical mechanism guidance layer. The core function of this correction layer is to learn the residual term between the true state and the physical baseline prediction. ； in, The parameter is Residual learning network, Input the actual operating data. The PINN-surrogate physical mechanism guiding layer at time The output is a state vector that satisfies the physical constraints. Battery state prediction results after data-driven correction layer Then it is obtained by superimposing the physical baseline and the residual term: ； Step 3.2 The internal physical state variables output by the physical mechanism guidance layer will be used as soft labels to constrain the training process of the data-driven correction layer; Its downward distillation loss function It can be represented as: ； in, This represents the battery state prediction result after correction by the data-driven correction layer. This represents the physical baseline prediction results output by the physical mechanism guidance layer at the same time. It is a physical feature mapping operator used to extract physical features reflecting the battery state evolution trend from the state prediction results. By minimizing the consistency constraint loss, the data-driven correction prediction results are kept consistent with the physical baseline prediction at the physical feature level, thereby ensuring that the residual correction does not destroy the physical rationality of the battery state evolution over time. Step 3.3 Establish an upward distillation parameter correction mechanism based on residual feedback. Stable deviation information is applied inversely to the learnable parameters of the physical mechanism guidance layer. Through reverse gradient propagation, the internal parameters of the physical layer gradually approximate the equivalent physical characteristics of the real battery. ； in, This represents the up-distillation loss function. Indicates the physical baseline prediction results. This represents the final prediction result after correction by the data-driven layer. This represents the residual term learned by the data-driven correction layer; During joint training, through the overall loss function This allows for comprehensive optimization of prediction errors and distillation constraints, which can be simply expressed as: ; and These are the weighting coefficients for the distillation loss term, used to balance the contributions of the downflow distillation constraint and the upflow distillation constraint to the overall optimization objective; Through bidirectional distillation, the physical layer and the correction layer form a closed-loop synergy: the physical layer provides structured physical constraints to guide the correction layer in learning reasonable residuals; the correction layer provides feedback on stable bias information to optimize the parameters of the physical layer, so that the two enhance each other in prediction accuracy and physical consistency.

10. The method for jointly predicting battery state parameters and remaining life according to claim 1, characterized in that: Step 4 includes the following specific steps: Step 4.1 Based on the output of the correction layer, a learning-based filter module is constructed to perform continuous time series correction on the battery state parameters and remaining lifetime prediction results. This filter module handles the dynamic continuity and smoothness of the corrected prediction results, while providing uncertainty assessment. The input is the residual correction prediction of the data-driven correction layer output. The filter automatically adapts to different individual batteries and operating conditions through learnable noise covariance and state transition matrix, as shown below: ； ； in, These represent the filter's internal state variables, including SOC, internal resistance, temperature rise, and health status indicators. For input operation signals; Indicates at time The system state in the state transition matrix The natural evolution results under the influence of the environment are used to characterize the dynamic changes of the internal state of the battery without external control input. This characterizes the control effect of external inputs on the system state, mapping charging and discharging conditions and environmental disturbances as driving forces for state changes; For the observed variable, the output of the data-driven correction layer is used here. As observed values; Represents state variables After observation matrix The mapped theoretical observations are used to establish the correspondence between the hidden states inside the filter and the actual observations; and These are state and observation noise, respectively, and can be dynamically adjusted via network-learnable parameters. Step 4.2 After the filter completes its iterations, these states are mapped to the final battery health status indicators and remaining lifespan, generating smooth and continuous prediction results. The final prediction information output will be set as follows: ； ； in, This represents the continuous state prediction results after time-correction, including the battery's state of charge. Internal resistance ,temperature Health status and remaining lifespan ; This is the covariance matrix, used to quantify the uncertainty of prediction results.

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