A joint method and device for battery state of health estimation and remaining life prediction

Abstract

The application discloses a kind of battery health degree estimation and residual life prediction combined method and device, belong to battery management technical field.The parameter identification framework based on electrochemical model is established, the model is solved using whale optimization algorithm, and the multi-dimensional mechanism characteristic parameters related to aging are extracted;Based on the extracted characteristic parameters, a single hidden layer feedforward neural network with an adaptive forgetting factor is constructed to estimate the current health of the battery online with the characteristic parameters as input, wherein the adaptive forgetting factor is adjusted in real time according to the output estimation error;Based on the health estimation result, a double exponential function decay model is constructed to predict the number of cycles when the health decays to the end-of-life threshold by extrapolation, and the residual life of the battery is output.The application realizes end-to-end collaborative modeling from mechanism feature extraction to health estimation to life prediction, improving the accuracy and robustness of the prediction results.

Description

Technical Field

[0001] This invention relates to the field of battery management technology, and in particular to a combined method, apparatus, device, and storage medium for estimating battery health and predicting remaining life. Background Technology

[0002] Batteries, with their core advantages such as high energy density and rechargeability, have been widely used in the energy storage field. However, during long-term use, battery performance gradually declines over time and with increasing cycle count. Therefore, accurate estimation of battery health (SOH) and prediction of remaining life (RUL) are crucial for ensuring the safe and stable operation of energy storage systems. SOH estimation focuses on assessing the current health status of the battery, with the core objective of determining the degree of capacity and power degradation; RUL prediction aims to predict the future duration of the battery's sustainable service life.

[0003] Currently, relevant estimation and forecasting methods have formed a diversified system, but there are still many areas for improvement under actual working conditions, specifically in the following three aspects:

[0004] Firstly, short-hair optimization still suffers from significant drawbacks such as slow convergence speed and insufficient optimization accuracy, making it difficult to meet the parameter tuning requirements of complex models.

[0005] Secondly, some methods extract highly correlated features from the IC curve and use data fitting to estimate the battery's SOH. However, such methods require obtaining prediction label data in advance to determine the optimal fitting parameters. Furthermore, when there are differences in battery charging and discharging strategies, the fitting parameters identified from one battery are difficult to transfer to the SOH estimation scenario of other batteries, resulting in poor versatility. Although the Single Hidden Layer Feedforward Neural Network (SLFN) can achieve cross-sample training and estimation of SOH for different batteries and has strong robustness and universality, this algorithm does not distinguish the differential impact of new samples and old samples on the model's predictive performance, resulting in weak adaptability to complex time-varying systems and difficulty in adapting to dynamic performance changes during battery aging. Summary of the Invention

[0006] The present invention aims to at least partially solve one of the technical problems in the related art.

[0007] To address this, this invention proposes a joint method for battery health estimation and remaining life prediction. By establishing a parameter identification framework based on an electrochemical model, and using the whale optimization algorithm to solve the model, multi-dimensional mechanistic feature parameters related to battery aging are extracted. Based on these feature parameters, a single-hidden-layer feedforward neural network with an adaptive forgetting factor is constructed to estimate the current battery health online using the feature parameters as input. The adaptive forgetting factor is adjusted in real-time according to the output estimation error. Based on the health estimation results, a double exponential function decay model is constructed. By extrapolating, the number of cycles required for the health to decay to the lifespan termination threshold is predicted, and the remaining battery life is output. This achieves coordinated and accurate prediction of both health and remaining life, effectively improving the accuracy and reliability of the prediction results.

[0008] Another object of the present invention is to provide a combined device for battery health estimation and remaining life prediction.

[0009] The third objective of this invention is to provide a computer device.

[0010] A fourth objective of this invention is to provide a non-transitory computer-readable storage medium.

[0011] To achieve the above objectives, this invention proposes a combined method for battery health estimation and remaining life prediction, comprising: A parameter identification framework based on an electrochemical model was established, and the electrochemical model was solved using the whale optimization algorithm to extract multi-dimensional mechanism characteristic parameters related to battery aging. Based on the multidimensional mechanism feature parameters, a single hidden layer feedforward neural network with an adaptive forgetting factor is constructed. The multidimensional mechanism feature parameters are used as input to estimate the current health of the battery online. The adaptive forgetting factor is adjusted in real time according to the model's output estimation error. Based on the estimated health status, a double exponential function decay model is constructed, and the number of cycles when the health status decays to the end-of-life threshold is predicted by extrapolation to output the remaining lifespan of the battery.

[0012] The combined method for battery health estimation and remaining life prediction according to an embodiment of the present invention may also have the following additional technical features: In one embodiment of the present invention, the establishment of a parameter identification framework based on an electrochemical model, and the solution of the electrochemical model using the whale optimization algorithm to extract multidimensional mechanism feature parameters related to battery aging, includes: A DFN model describing the internal electrochemical processes of a lithium-ion battery is constructed. The DFN model includes a solid-phase diffusion equation, an electrolyte mass conservation equation, a charge conservation equation, and a Butler-Volmer kinetic equation. The electrochemical parameters to be identified are set as the position vectors of individual whales, and a fitness function is constructed with the goal of minimizing the error between the simulated terminal voltage output by the DFN model and the measured terminal voltage. The whale optimization algorithm is used for iterative optimization. In each iteration, the position of the individual whale is updated through random search and prey encirclement mechanism, and local optimization is performed through spiral trajectory update mechanism until the convergence condition is met. The electrochemical parameters corresponding to the optimal position of the individual whale are output as multi-dimensional mechanism feature parameters related to battery aging. The multi-dimensional mechanism feature parameters include at least one of the following: maximum lithium ion concentration, solid diffusion coefficient and electrode specific surface area.

[0013] In one embodiment of the present invention, a single-hidden-layer feedforward neural network with an adaptive forgetting factor is constructed based on the multidimensional mechanistic feature parameters. Using the multidimensional mechanistic feature parameters as input, the current health of the battery is estimated online, including: A single hidden layer feedforward neural network is constructed, with the multidimensional mechanism feature parameters as input layer nodes and battery health as output layer nodes, and the number of hidden layer nodes and activation function are set. During the offline initialization phase, the initial output weights of the single hidden layer feedforward neural network are calculated using historical datasets. In the online recursive update phase, whenever new running data is acquired, an adaptive forgetting factor is calculated based on the current model's output estimation error, and the initial output weights are recursively updated according to the adaptive forgetting factor. The updated network is then used to estimate the battery health at the current moment. The adaptive forgetting factor is constructed from the inverse cotangent function, and its value is negatively correlated with the model's root mean square error. When the estimation error increases, the adaptive forgetting factor decreases to reduce the impact of historical data on the current weight update.

[0014] In one embodiment of the present invention, the step of constructing a double exponential function decay model based on the health level estimation result, and extrapolating to predict the number of cycles when the health level decays to the end-of-life threshold, to output the remaining battery life, includes: A double exponential function model is constructed to describe the long-term degradation trend of battery health. The double exponential function model uses the number of cycles to be predicted as the independent variable and battery health as the dependent variable. The double exponential function model is converted into a state-space equation form, which includes a state equation and a measurement equation, and the estimated current health is used as the initial value for state updates. Based on the outward extrapolation of the state-space equation, the health value corresponding to the number of future cycles is predicted. When the predicted health value first decays to the preset lifespan termination threshold, the difference between the current number of cycles and the number of cycles already run is recorded as the remaining lifespan of the battery.

[0015] In one embodiment of the present invention, before establishing the parameter identification framework based on the electrochemical model, the method further includes: Historical battery operation data, including voltage, current, and temperature, is collected. The historical operation data is then preprocessed to remove outliers and missing values, forming a standardized training dataset for subsequent parameter identification of electrochemical models and training of neural network models.

[0016] In one embodiment of the present invention, calculating the adaptive forgetting factor based on the output estimation error of the current model further includes: During the online recursive update phase, the residual sequence between the output value of the single hidden layer feedforward neural network and the measured health status is monitored in real time. When the residual sequence increases continuously and exceeds the preset fluctuation range, the dynamic adjustment mechanism of the adaptive forgetting factor is triggered to accelerate the model's response speed to new features of battery aging.

[0017] To achieve the above objectives, another aspect of the present invention provides a combined device for battery health estimation and remaining life prediction, comprising: The electrochemical model feature extraction module is used to establish a parameter identification framework based on the electrochemical model and solve the electrochemical model using the whale optimization algorithm to extract multi-dimensional mechanism feature parameters related to battery aging. An adaptive health estimation module is used to construct a single hidden layer feedforward neural network with an adaptive forgetting factor based on the multidimensional mechanism feature parameters. The module uses the multidimensional mechanism feature parameters as input to estimate the current health of the battery online. The adaptive forgetting factor is adjusted in real time according to the model's output estimation error. The dual-exponential lifespan prediction module is used to construct a dual-exponential function decay model based on the estimated health status, and extrapolate to predict the number of cycles when the health status decays to the lifespan termination threshold, so as to output the remaining lifespan of the battery.

[0018] This invention discloses a combined method and apparatus for battery health estimation and remaining life prediction. It establishes a parameter identification framework based on an electrochemical model and solves it using a whale optimization algorithm to extract multi-dimensional mechanistic feature parameters related to aging. Based on the extracted features, a single-hidden-layer feedforward neural network with an adaptive forgetting factor is constructed. The current battery health is estimated online using the feature parameters as input, where the adaptive forgetting factor is adjusted in real-time according to the output estimation error. Based on the health estimation results, a double exponential function decay model is constructed. The remaining life is output by extrapolating and predicting the number of cycles when the health decays to the life termination threshold. This effectively solves the problems of insufficient prediction accuracy and weak robustness caused by insufficient feature extraction, poor model dynamic adaptability, and separate modeling in existing technologies. This invention achieves integrated modeling from mechanistic feature extraction and online health estimation to remaining life extrapolation prediction, significantly improving the accuracy and reliability of the prediction results and enhancing the model's adaptability and engineering applicability in the dynamic process of battery aging.

[0019] To achieve the above objectives, a third aspect of this application provides a computer device comprising a processor and a memory; wherein the processor runs a program corresponding to the executable program code by reading executable program code stored in the memory, for implementing a combined method for battery health estimation and remaining life prediction as described in the first aspect embodiment.

[0020] To achieve the above objectives, a fourth aspect of this application provides a non-transitory computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements a combined method for battery health estimation and remaining life prediction as described in the first aspect embodiment.

[0021] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0022] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein: Figure 1 This is a flowchart of a combined method for battery health estimation and remaining life prediction according to an embodiment of the present invention; Figure 2 This is a framework diagram of SOH estimation and RUL prediction for another combined method of battery health estimation and remaining life prediction according to an embodiment of the present invention. Figure 3 This is a structural diagram of a single hidden layer feedforward neural network (SLFN) for another joint method of battery health estimation and remaining life prediction according to an embodiment of the present invention; Figure 4 This is a diagram illustrating the training process of a single hidden layer feedforward neural network (SLFN) for another joint method of battery health estimation and remaining life prediction according to an embodiment of the present invention. Figure 5 This is a schematic diagram of the structure of a combined device for battery health estimation and remaining life prediction according to an embodiment of the present invention; Figure 6 It is a computer device according to an embodiment of the present invention. Detailed Implementation

[0023] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0024] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0025] The following description, with reference to the accompanying drawings, describes a combined method, apparatus, device, and storage medium for battery health estimation and remaining life prediction according to embodiments of the present invention.

[0026] The core idea of ​​this invention is to establish a parameter identification framework based on an electrochemical model and solve it using the whale optimization algorithm to extract multi-dimensional mechanistic feature parameters strongly correlated with the battery aging process, providing a physically interpretable feature foundation for subsequent state assessment. Based on this, a single-hidden-layer feedforward neural network with an adaptive forgetting factor is constructed. Using the extracted multi-dimensional mechanistic feature parameters as input, the current battery health is estimated online. The adaptive forgetting factor is dynamically adjusted in real time according to the estimation error of the model output, enabling the estimation model to adaptively track the time-varying characteristics of the battery aging process and effectively suppress feature shifts between historical data and current operating conditions. Furthermore, a double exponential function decay model is constructed based on the health estimation results. By extrapolating and predicting the number of cycles when the health decays to a preset lifespan threshold, the remaining battery lifespan is output. This transforms the traditional separate tasks of feature extraction, health estimation, and lifespan prediction into an integrated intelligent assessment system driven by electrochemical mechanisms, centered on adaptive learning, and aimed at collaborative prediction. This invention significantly improves the accuracy, robustness, and engineering applicability of battery health and remaining life prediction by deeply coupling mechanism-guided feature extraction, dynamic adaptive online estimation, and long-term extrapolation lifetime prediction.

[0027] Example 1 To achieve the above invention, embodiments of the present invention provide a combined method for battery health estimation and remaining life prediction, such as... Figure 1 As shown, it includes: S1. A parameter identification framework based on an electrochemical model was established, and the electrochemical model was solved using the whale optimization algorithm to extract multi-dimensional mechanism characteristic parameters related to battery aging.

[0028] Specifically, firstly, a quasi-two-dimensional (P2D) model describing the internal physicochemical processes of lithium-ion batteries is established to construct a nonlinear mapping relationship between battery terminal voltage and internal state variables. This model is based on porous electrode theory and concentrated solution theory, utilizing solid-phase diffusion equations, liquid-phase mass conservation equations, charge conservation equations, and Butler equations. The Volmer electrochemical kinetic equations comprehensively characterize the insertion, extraction, and migration processes of lithium ions in solid and liquid phases. Based on this, the mechanistic changes during battery aging, such as electrode material degradation, loss of active material, and increased internal resistance, are mapped to changes in key parameters within the electrochemical model. By transforming the parameter identification problem into a high-dimensional nonlinear optimization problem, and utilizing the global search capability and fast convergence characteristics of the whale optimization algorithm, an error objective function is constructed between the measured terminal voltage and the model output voltage. Through iterative optimization, electrochemical parameters strongly correlated with the aging state are identified, thus achieving reverse analysis from macroscopic electrical signals to microscopic mechanistic characteristics.

[0029] Specifically, a DFN electrochemical model for lithium-ion batteries is first constructed, and a set of parameters to be identified is determined, including mechanistic parameters with clear physical significance such as the maximum lithium-ion concentration of the positive and negative electrodes, the solid-phase diffusion coefficient, and the electrode specific surface area. These parameters are encoded as position vectors of individual whales in a whale optimization algorithm, with each individual representing a set of candidate solutions. The root mean square error between the simulated terminal voltage output by the DFN model under the same current excitation and the measured terminal voltage of the battery is used as the fitness function; the smaller the error, the better the set of parameters reflects the current true aging state of the battery. The whale optimization algorithm iteratively optimizes by simulating the predatory behavior of a whale group: in the global exploration phase, a random search mechanism traverses the solution space; in the local development phase, a prey-encircling mechanism narrows the search range; simultaneously, a spiral update mechanism is introduced to simulate the predatory behavior of whale bubble nets, enhancing the algorithm's local fine-grained search capability. When the maximum number of iterations is reached or the fitness function meets the convergence threshold, the electrochemical parameters corresponding to the optimal individual are output as multi-dimensional mechanistic features characterizing the current aging state of the battery.

[0030] Furthermore, the multidimensional mechanistic characteristic parameters extracted in this invention include, but are not limited to, the following indicators with clear physical meaning: maximum lithium-ion concentration, which reflects the degree of loss of active material in the electrode material; as battery cycling intensifies, the total amount of lithium ions that can be inserted and extracted gradually decreases; solid diffusion coefficient, which characterizes the diffusion rate of lithium ions within the active material particles; electrode structure degradation during aging leads to a decrease in the diffusion coefficient; and electrode specific surface area, which reflects the effective reaction interface between the electrode and the electrolyte; accumulation of by-reaction products reduces the specific surface area. All of the above parameters have a clear mechanistic correlation with the battery aging process, and their changing trends can explain the intrinsic reasons for capacity decay and power reduction from an electrochemical perspective. Compared with the statistical features extracted by traditional data-driven methods, the mechanistic parameters extracted by this method have good cross-condition generalization ability and physical interpretability, providing a solid characteristic foundation for subsequent health estimation and lifetime prediction.

[0031] Specifically, in electric vehicle applications, this method can utilize real-time voltage and current data collected by the vehicle's battery management system to extract electrochemical mechanism parameters online, providing OEMs with a quantitative assessment basis for battery degradation and supporting residual value evaluation and cascade utilization decisions. In power storage power station scenarios, this method can periodically or trigger-based parameter identification of hundreds or thousands of battery cells, identifying consistent degradation trends within the battery pack, providing early warnings of abnormal cells, and ensuring the safe and stable operation of the energy storage system. In battery R&D and testing scenarios, this method can serve as an analysis tool for accelerated aging test data, assisting in optimizing battery material formulations and manufacturing processes by comparing the evolution patterns of mechanism parameters under different aging paths. The mechanism parameters extracted by this invention can also serve as the underlying input for battery digital twin models, supporting full lifecycle state tracking from the cell level to the system level.

[0032] Specifically, compared to methods based solely on incremental capacity curves or statistical features, the mechanistic parameters extracted in this invention exhibit excellent cross-condition generalization ability, stably characterizing aging states under different charge / discharge rates and temperatures. The introduction of the whale optimization algorithm effectively overcomes the shortcomings of traditional optimization algorithms that easily get trapped in local optima when dealing with strongly nonlinear, multi-peak electrochemical models, significantly improving computational efficiency while maintaining identification accuracy. The electrochemical mechanistic parameters obtained through reverse identification not only intuitively reflect the degree of degradation of internal battery materials but also provide high-quality feature inputs for subsequently constructing adaptive health estimation models, ensuring the overall accuracy and reliability of battery state assessment and lifetime prediction from the source.

[0033] Furthermore, S1 includes: S11. Construct a DFN model describing the internal electrochemical processes of a lithium-ion battery. The DFN model includes a solid-phase diffusion equation, an electrolyte mass conservation equation, a charge conservation equation, and a Butler-Volmer kinetic equation. Set the position vector of the individual whale as the electrochemical parameters to be identified, and construct a fitness function with the goal of minimizing the error between the simulated terminal voltage and the measured terminal voltage output by the DFN model.

[0034] Specifically, firstly, by establishing a DFN model describing the internal physicochemical processes of a lithium-ion battery, the nonlinear mapping relationship between the external electrical response and internal state variables of the battery is formalized. This model, based on porous electrode theory and concentrated solution theory, uses a solid-phase diffusion equation to characterize the concentration distribution and diffusion behavior of lithium ions within the active material particles, an electrolyte mass conservation equation to describe the transport and accumulation of lithium ions in the liquid phase, a charge conservation equation to characterize the potential distribution in the solid and liquid phases, and a Butler equation... The Volmer kinetic equations establish the constitutive relationship between electrode reaction rate and overpotential. These equations, when combined, form a complete set of electrochemical governing equations, capable of reproducing the battery's terminal voltage response under different operating conditions at the mechanistic level. Based on this, the parameter identification problem is transformed into an optimization problem. The electrochemical parameters to be identified are used as optimization variables, and the deviation between the simulated terminal voltage output by the DFN model and the measured terminal voltage is used as the optimization objective. By minimizing this deviation, the goal of inferring internal mechanistic parameters from the external response is achieved.

[0035] Specifically, firstly, based on the positive and negative electrode material systems and geometric structures of the battery, a set of governing equations for the DFN model is established, along with corresponding boundary and initial conditions. The electrochemical parameters to be identified, including the maximum lithium-ion concentration at the positive and negative electrodes, solid-phase diffusion coefficient, and electrode specific surface area, are encoded as position vectors of individual whales in the whale optimization algorithm, with each individual representing a set of candidate solutions. The measured operating current is used as the input excitation for the DFN model, driving the model to obtain the simulated terminal voltage curve. A fitness function is constructed, typically using the root mean square error or mean absolute error between the simulated and measured terminal voltages as a quantification index; a smaller error indicates that the set of parameters more accurately reflects the current true state of the battery. After generating an initial population in the solution space, the whale optimization algorithm iteratively searches by simulating whale-like behaviors such as surrounding prey and bubble-net attacks, continuously updating individual positions to reduce the fitness function value. In each iteration, the parameters corresponding to the current optimal individual are substituted into the DFN model to recalculate the fitness until the preset convergence condition is met, ultimately outputting the optimal parameter combination that minimizes the fitness function.

[0036] Furthermore, the solid-state diffusion coefficient characterizes the migration rate of lithium ions within the active material particles of both the positive and negative electrodes. Its magnitude directly determines the relaxation characteristics of the lithium concentration gradient distribution, affecting the battery's rate performance and polarization behavior. The maximum lithium-ion concentration reflects the limit capacity that the electrode material can accommodate lithium ions; as the battery cycles and ages, the loss of active material and structural degradation cause this parameter to gradually decrease. The electrode specific surface area is defined as the effective contact area between the electrode active material and the electrolyte; its changes are closely related to aging mechanisms such as the growth of side reaction films and the cracking of active particles. These parameters collectively constitute a multi-dimensional mechanistic feature space describing the battery's aging state. Compared to equivalent circuit model parameters that rely solely on externally measurable signals such as terminal voltage and current, the DFN model parameters extracted in this step have a direct correspondence with the internal physicochemical processes of the battery, enabling a deeper understanding of the intrinsic mechanisms of aging.

[0037] Specifically, during the battery R&D phase, parameter identification under different aging states and temperatures establishes a mapping relationship between mechanistic parameters and aging paths, providing a quantitative basis for material formulation optimization and manufacturing process improvement. In battery pack applications, this step can be used to periodically identify parameters of individual cells within the battery pack, identify trends in parameter consistency degradation, promptly detect abnormal cells, and provide early warnings of potential safety risks. In vehicle battery management systems or energy management systems for energy storage power stations, this step can be embedded as a core algorithm module, using high-quality data collected during vehicle charging or rest periods to trigger parameter identification, providing underlying input for subsequent health assessments and lifespan predictions. Furthermore, the mechanistic parameters extracted in this step can also serve as a calibration basis for the battery digital twin model, achieving state synchronization between the virtual model and the physical entity.

[0038] Specifically, compared to parameter identification methods based on equivalent circuit models, the parameters extracted in this step have clear physical meanings, revealing the intrinsic mechanism of battery aging and exhibiting good generalization ability across different operating conditions and aging stages. By constructing a fitness function that minimizes the error between simulated and measured terminal voltages, the accuracy and reliability of the identification results are ensured. The parameters to be identified are encoded as position vectors of individual whales, and the global search capability and fast convergence characteristics of the whale optimization algorithm are utilized to effectively overcome the shortcomings of traditional gradient descent methods, which are prone to getting trapped in local optima when dealing with strongly nonlinear, multi-peak electrochemical models. This step provides high-quality feature inputs for subsequent online health estimation and remaining life prediction, fundamentally guaranteeing the overall accuracy and robustness of battery state assessment.

[0039] S12, iterative optimization is performed using the whale optimization algorithm. In each iteration, the position of the individual whale is updated through random search and prey encirclement mechanism, and local optimization is performed through spiral trajectory update mechanism until the convergence condition is met. The electrochemical parameters corresponding to the optimal position of the individual whale are output as multi-dimensional mechanism feature parameters related to battery aging. The multi-dimensional mechanism feature parameters include at least one of the following: maximum lithium ion concentration, solid diffusion coefficient and electrode specific surface area.

[0040] Specifically, the core principles of the algorithm include three position update strategies: a random search mechanism simulates a whale randomly wandering in unknown waters to explore prey, corresponding to the global exploration phase, which guides the search direction by randomly selecting individuals and avoids the algorithm getting stuck in local optima; an encirclement mechanism simulates a whale shrinking its encirclement after identifying the prey's location, corresponding to the local development phase, which achieves a refined search of the solution space by converging towards the current best individual; and a spiral trajectory update mechanism simulates a whale attacking prey with spiral motion and blowing bubbles, further enhancing the local optimization ability, updating the individual's position through a spiral equation, balancing development accuracy and convergence speed. These three strategies dynamically switch based on probability during iteration, achieving efficient traversal of the high-dimensional nonlinear fitness function space and approximation of the optimal solution. By mapping the electrochemical parameters to be identified to the position vectors of individual whales, and using the minimization of the error between the simulated and measured terminal voltages as the fitness guide, the algorithm ultimately outputs the parameter combination corresponding to the globally optimal individual, revealing the battery aging state from a mechanistic perspective.

[0041] Specifically, the whale population is first initialized, with each individual's position vector corresponding to a set of electrochemical parameters to be identified, randomly assigned within the physical constraints of these parameters. A maximum number of iterations and a fitness convergence threshold are set. Upon entering the iteration loop, the fitness value of each individual is calculated, marking the current optimal individual. In each iteration, an update strategy is selected based on a random probability p: if p is less than the threshold, a prey-surrounding mechanism is used, with the individual shrinking towards the current optimal position; if p is greater than or equal to the threshold, a spiral trajectory update mechanism is used, with the individual swimming towards the optimal position along a spiral path. Simultaneously, a random search mechanism is introduced: when the coefficient vector magnitude is greater than 1, the individual randomly selects a reference position for global exploration. After each position update, the fitness is recalculated and the global optimum is updated. Iteration continues until the maximum number of iterations is reached or the fitness change is less than the set threshold. After convergence, the optimal individual's position vector is decoded into actual physical parameters, outputting multi-dimensional mechanistic characteristic parameters including maximum lithium-ion concentration, solid diffusion coefficient, and electrode specific surface area, used to characterize the current aging state of the battery.

[0042] Furthermore, the maximum lithium-ion concentration reflects the limit of lithium-ion capacity that the positive and negative electrode active materials can accommodate. With cycle aging, the loss of active material, structural collapse, or the formation of lithium plating will cause this parameter to gradually decrease, directly characterizing the degree of capacity decay. The solid diffusion coefficient characterizes the migration rate of lithium ions within the active material particles. During aging, the degradation of the electrode material's crystal structure and the thickening of the surface film hinder lithium-ion diffusion, causing a decrease in the diffusion coefficient, which in turn affects the battery's rate performance and polarization characteristics. The electrode specific surface area reflects the effective contact interface between the electrode active material and the electrolyte. The accumulation of by-reaction products (such as solid electrolyte interfacial films) will reduce the specific surface area, leading to increased reactive polarization. These parameters quantify the degradation of internal battery materials and kinetic performance from different dimensions, providing mechanistically supported characteristic inputs for subsequent health estimation.

[0043] Specifically, in electric vehicle battery management systems, high-quality voltage and current data collected during vehicle charging or rest periods can be used to trigger the Whale Optimization Algorithm for parameter identification, real-time extraction of battery aging characteristics, and provision of battery health status assessment data for OEMs. In energy storage power station scenarios, individual cells within battery clusters can be periodically identified to detect parameter consistency drift, providing early warnings of abnormal batteries and ensuring safe system operation. In battery R&D testing laboratories, this step can serve as an analysis tool for accelerated aging test data, guiding material system optimization and manufacturing process improvement by comparing the evolution patterns of mechanistic parameters under different aging paths. Furthermore, the identified mechanistic parameters can serve as the underlying input for battery digital twin models, supporting full lifecycle state tracking and simulation calibration from the cell level to the system level.

[0044] Specifically, compared to traditional gradient descent or particle swarm optimization, the whale algorithm exhibits stronger ability to escape local optima in a multi-peak, strongly nonlinear fitness function space, ensuring that the identification results closely approximate the true physical parameters. The extracted multi-dimensional mechanistic feature parameters possess clear physical interpretability, overcoming the weak feature generalization ability of purely data-driven methods, and can stably characterize the aging state under different charge / discharge rates and temperature conditions. This step provides high-quality feature input for the subsequent construction of an adaptive health estimation model, ensuring the accuracy of battery state assessment from the source. Furthermore, by correlating the physical meaning of the parameters, it helps to analyze the battery aging mechanism, providing a scientific basis for battery system safety early warning and tiered utilization decisions.

[0045] S2, a single hidden layer feedforward neural network with an adaptive forgetting factor is constructed based on the multidimensional mechanism feature parameters. The current health of the battery is estimated online using the multidimensional mechanism feature parameters as input. The adaptive forgetting factor is adjusted in real time according to the output estimation error of the model.

[0046] Specifically, traditional single-hidden-layer feedforward neural networks, employing a batch learning model, struggle to adapt to the time-varying parameters during battery aging. This invention introduces an adaptive forgetting factor. Its core principle lies in establishing a dynamic mapping relationship between the forgetting factor and the model's output estimation error, enabling the network to distinguish the differences in the contribution of historical and current data to the model. When the estimation error increases, it indicates a significant change in battery aging characteristics. In this case, the adaptive forgetting factor decreases, reducing the influence of historical data in weight updates and allowing the model to quickly adapt to new operating conditions. Conversely, when the estimation error is small, it indicates a stable battery state, and the forgetting factor increases, fully utilizing historical information to stabilize the estimation results. This mechanism borrows the idea of ​​a variable forgetting factor from adaptive signal processing. By constructing a nonlinear negative correlation between the forgetting factor and the root mean square error through the inverse cotangent function, it achieves an adaptive balance between model memory depth and tracking speed, enabling the neural network to continuously track the dynamic evolution of the battery aging process.

[0047] Specifically, a single-hidden-layer feedforward neural network structure is first constructed, using the multi-dimensional mechanistic feature parameters extracted in step one as input layer nodes and battery health as output layer nodes. The number of hidden layer nodes is determined based on empirical formulas or cross-validation, and the Sigmoid function is selected as the hidden layer activation function. Network training is divided into two stages: offline initialization and online update. In the offline initialization stage, using historical aging test datasets, the initial output weights are calculated once using the generalized inverse matrix solution method to establish a basic estimation model. In the online recursive update stage, whenever the battery management system collects new operating data and extracts the corresponding mechanistic feature parameters, these are input into the network to obtain an estimate of the current battery health. Simultaneously, the output estimation error between the estimated value and subsequent measured or reference values ​​is calculated, typically using the root mean square error as a quantification indicator. Based on this error, an adaptive forgetting factor is constructed using the inverse cotangent function; the larger the error, the smaller the forgetting factor. The forgetting factor is substituted into the recursive least squares form of the update formula to adjust the network output weights online. The updated weights are then used to recalculate the current battery health estimate, achieving real-time tracking of the battery aging state.

[0048] Furthermore, the neural network structure parameters include the number of nodes in the input layer, which is equal to the dimension of the multidimensional mechanistic feature parameters extracted in step one; the number of nodes in the hidden layer needs to be balanced between model complexity and generalization ability; too few nodes make it difficult to fit nonlinear relationships, while too many nodes easily lead to overfitting; the number of nodes in the output layer is a single health value. The activation function used is the Sigmoid function, whose continuous differentiability is suitable for gradient calculation and weight updates. The parameters related to the adaptive forgetting factor include the minimum forgetting factor preset value and the root mean square error threshold. The minimum forgetting factor ensures that the model retains its basic memory ability during drastic changes, avoiding complete reset; the root mean square error threshold is used to normalize the error magnitude, so that the forgetting factor adjustment range matches the error dynamics. These parameters together determine the model's tracking sensitivity and estimation stability for the battery aging process, and need to be calibrated and optimized according to the battery type and application conditions.

[0049] Specifically, in the electric vehicle sector, this step can serve as a core algorithm module for the vehicle battery management system. Utilizing real-time data collected during vehicle operation or charging, it continuously updates the neural network weights and outputs the current battery health online, providing OEMs with data support for residual value assessment, warranty strategy formulation, and alleviating user range anxiety. In energy storage power station scenarios, this step can perform parallel health estimation for each individual cell or battery cluster within the battery pack, identifying battery consistency degradation trends and assisting maintenance personnel in developing balanced maintenance plans to extend the overall lifespan of the energy storage system. In secondary utilization screening scenarios, this step can quickly assess the residual health of retired batteries, providing a quantitative basis for battery grading and reconfiguration. On cloud-based battery management platforms, this step can serve as a remote health monitoring tool, aggregating operational data from multiple vehicles and power stations to achieve cloud-based synchronization and big data analysis of battery status.

[0050] Specifically, compared to traditional neural networks with fixed forgetting factors or batch learning, this method can adjust the model's memory depth of historical data in real time based on the estimation error. It maintains estimation stability when the battery state is stable and responds quickly to accelerated aging or sudden changes in operating conditions, effectively resolving the contradiction between "memory inertia" and "rapid tracking." The forgetting factor adjustment mechanism constructed through the inverse cotangent function achieves error-driven adaptive adjustment, avoiding the tedious process of manual parameter tuning and improving the model's engineering applicability. Using multidimensional mechanistic feature parameters as input, combined with adaptive online updates, the health estimation results possess both physical interpretability and good dynamic accuracy, providing a reliable state benchmark for subsequent remaining life prediction. Overall, this step represents a technological leap from static modeling to dynamic tracking, significantly enhancing the real-time performance and robustness of battery health estimation.

[0051] Furthermore, S2 includes: S21, construct a single hidden layer feedforward neural network, using the multidimensional mechanism feature parameters as input layer nodes and battery health as output layer nodes, and set the number of hidden layer nodes and activation function.

[0052] Specifically, according to neural network theory, a single-hidden-layer feedforward neural network with a sufficient number of hidden layer nodes can approximate any continuous nonlinear function with arbitrary precision. This invention utilizes this principle to learn and express the complex nonlinear relationship between the multidimensional mechanistic feature parameters extracted in step one and battery health through a neural network. Input layer nodes correspond to the multidimensional mechanistic features characterizing the battery aging state, output layer nodes correspond to the battery health to be estimated, and the hidden layer, as the core of feature transformation and nonlinear mapping, introduces nonlinear processing capabilities through activation functions. The construction of this network structure provides a basic framework for the subsequent introduction of adaptive forgetting factors and online weight updates, enabling the model to not only possess static fitting capabilities but also the potential to dynamically track the battery aging process. The determination of the network topology directly determines the model's expressive power and generalization performance, and is a technical prerequisite for achieving online estimation.

[0053] Specifically, the number of input layer nodes is first determined based on the dimensions of the multidimensional mechanistic feature parameters extracted in Step 1. If the extracted features include the maximum lithium-ion concentration, solid diffusion coefficient, and electrode specific surface area, then the number of input layer nodes is set to three. The number of output layer nodes is fixed at one, corresponding to the single-value output of battery health. The setting of the number of hidden layer nodes needs to comprehensively consider model complexity and generalization ability. It is usually determined by combining empirical formulas with cross-validation. The empirical formula can be expressed as the number of hidden layer nodes equals the square root of the sum of the number of input layer nodes and the number of output layer nodes multiplied by an adjustment coefficient, or by searching for the optimal value within a preset range through trial and error. The sigmoid function is selected as the activation function for the hidden layer. Its mathematical expression is f=1 / f. This function has the characteristics of being continuous, differentiable, nonlinear, and having an output value range between zero and one, which matches the value range of health. At the same time, its derivative is easy to calculate, which facilitates gradient propagation in the subsequent weight update process. After the network structure is determined, the connection weights between the input layer and the hidden layer, as well as the connection weights between the hidden layer and the output layer, are initialized. Small random numbers are usually used for initialization to avoid symmetry violation. This completes the construction of the neural network infrastructure, laying the foundation for subsequent offline initialization training and online recursive updates.

[0054] Furthermore, the number of input layer nodes is directly equal to the dimension of the multidimensional mechanistic feature parameters extracted in step one. This value determines the richness of the model's input information; a higher dimension contains more comprehensive aging information, but it also increases model complexity and the risk of overfitting. The number of hidden layer nodes is a core control parameter for model capacity. Too few nodes lead to underfitting, failing to capture the complex nonlinear relationship between input and output; too many nodes easily lead to overfitting, reducing the model's generalization ability on unseen data. Typically, a value between five and twenty is chosen based on the data scale and problem complexity in the actual application. The number of output layer nodes is always one, corresponding to battery health. The activation function used is the Sigmoid function, whose saturation region characteristic ensures that the output changes smoothly when the input is too large or too small, helping to stabilize the training process, but it also brings the potential risk of gradient vanishing. Weight initialization typically uses normally distributed random numbers with a mean of zero and a small standard deviation to ensure that the initial state of each neuron is in the non-saturation region of the activation function, providing a starting point for subsequent effective learning.

[0055] Specifically, in the embedded environment of an onboard battery management system, the network structure determined in this step needs to consider computational resource limitations. The number of hidden layer nodes should be as small as possible while ensuring estimation accuracy to meet real-time requirements. In the centralized monitoring system of energy storage power stations, a slightly larger network structure can be adopted, utilizing cloud computing resources to achieve higher accuracy in health estimation. In battery cascade utilization screening scenarios, the network constructed in this step can serve as an offline evaluation tool to quickly calibrate the health of retired batteries, providing a basis for battery grading and reorganization. During the battery R&D and testing phase, the network structure in this step can serve as a core component of an aging data analysis platform. By adjusting the number of hidden layer nodes and the type of activation function, the impact of different network configurations on the ability to fit aging trends can be explored, guiding improvements in battery material systems and manufacturing processes. Furthermore, this network structure has good portability and can be adapted to batteries of different models and chemical systems; only the number of input layer nodes needs to be adjusted according to the corresponding feature dimensions.

[0056] Specifically, the one-to-one correspondence between input layer nodes and multidimensional mechanistic feature parameters ensures that the network can fully utilize physically meaningful feature information, avoiding feature redundancy or information loss problems in traditional methods. The introduction of the Sigmoid activation function enables the network to handle nonlinear aging patterns and effectively fit the complex curve of health decay with the number of iterations. A reasonable setting of the number of hidden layer nodes strikes a balance between model complexity and generalization ability, avoiding estimation bias caused by underfitting and preventing a decrease in generalization ability due to overfitting. Compared to arbitrarily set network structures without validation, this step, through parameterized design and initialization, gives the network good convergence potential from the start of training, providing structural support for subsequent offline initialization calculation of initial weights and rapid adaptation in the online recursive update stage, ultimately resulting in improved accuracy and stability of health estimation results.

[0057] S22, In the offline initialization phase, the initial output weights of the single hidden layer feedforward neural network are calculated using historical datasets.

[0058] Specifically, traditional neural network training typically employs backpropagation to iteratively adjust all weights, which suffers from slow convergence, susceptibility to local optima, and sensitivity to the learning rate. This invention draws upon the core idea of ​​Extreme Learning Machines (ELM), fixing the connection weights between the input and hidden layers and the hidden layer biases during offline initialization. This transforms the network training problem into solving a minimum-norm least-squares solution for a linear system. Specifically, when the input weights and biases are randomly generated and remain unchanged, the hidden layer output matrix is ​​determined accordingly, exhibiting a linear relationship between the network output and the hidden layer output. By solving the generalized inverse matrix of this linear system, the analytical solution for the output weights that minimizes the training error can be calculated in one step, without iterative optimization. This principle ensures that the initial output weights are optimal in the minimum-norm sense, while significantly improving computational efficiency and providing a stable and reliable initial state for subsequent online recursive updates.

[0059] Specifically, a historical dataset is first constructed. This dataset contains the multi-dimensional mechanistic feature parameters extracted in step one as input samples, and the measured battery health values ​​at corresponding times as the target output. The input weights and hidden layer biases set in the offline initialization phase are substituted into the activation function to calculate the output responses of all historical samples in the hidden layer, forming the hidden layer output matrix. The number of rows in this matrix equals the number of training samples, and the number of columns equals the number of hidden layer nodes. According to the mathematical model of a single-hidden-layer feedforward neural network, the network output equals the hidden layer output matrix multiplied by the output weight matrix. With the goal of minimizing the training error, the optimization problem of the output weight matrix can be transformed into solving a system of linear equations using least-squares solutions. Moore's algorithm is employed. The Penrose generalized inverse matrix method directly calculates the generalized inverse of the hidden layer output matrix and multiplies it by the target output matrix to obtain an analytical expression for the output weights. This calculation process is completed in one step without iteration, and the result is the optimal output weight that minimizes the sum of squared training errors and the norm. After calculation, the output weights are stored for later use as initial values ​​in the online recursive update phase.

[0060] Specifically, the number of training samples determines the amount of information in the historical dataset. Too few samples may lead to underfitting of the initial model, while too many samples require a trade-off between computational efficiency and storage resources. Typically, representative samples covering different aging stages are selected based on the volume of data from the entire battery lifecycle aging process. The number of hidden layer nodes is determined during network construction and directly affects the dimension and rank of the hidden layer output matrix during offline initialization, thus impacting the numerical stability of the generalized inverse computation and the generalization performance of the output weights. The condition number of the hidden layer output matrix reflects the ill-conditioned nature of the matrix. An excessively large condition number may make the generalized inverse computation sensitive to noise, affecting the reliability of the initial weights. This can be adjusted by using an appropriate input weight initialization range. The norm of the output weights measures the model complexity. Extreme learning machine theory guarantees that the obtained solution has a minimum norm, which helps improve the model's generalization ability and avoid overfitting. These parameters collectively determine the accuracy and robustness of the offline initialized model.

[0061] Specifically, when new battery models are put into production or existing battery systems are replaced, this step can be performed using historical aging test datasets to quickly establish a basic health estimation model without spending a lot of time on iterative training. For electric vehicle manufacturers, accelerated aging data from laboratories or early road-collected data can be used to pre-set initial output weights for the vehicle battery management system through this step, enabling vehicles to have basic estimation capabilities from the factory. Before the commissioning of energy storage power stations, consistent test data of battery cells in the same batch can be used to establish a basic model applicable to that batch of batteries through this step, laying the foundation for subsequent online monitoring. In the scenario of cascade utilization, when establishing a health assessment model for retired batteries, a small amount of calibration data can be used to quickly initialize the model through this step, supporting large-scale screening efficiency improvements. On cloud-based battery management platforms, this step can serve as the underlying tool for automatic model updates. When new battery family data is collected, the basic model can be rebuilt offline through initialization, supporting model version iteration.

[0062] Specifically, the properties of solving for the least-norm least-squares solution ensure the statistical optimality of the initial output weights, enabling the base model to achieve good fitting accuracy on historical datasets. Simultaneously, minimizing the weight norm enhances the model's generalization ability and avoids overfitting to the training data. The strategy of randomly generating and fixing input weights and biases effectively avoids the convergence instability problem caused by initial value sensitivity in traditional neural network training. The initial output weights output in this step serve as the starting point for the online recursive update phase. Since they are already in a region close to the optimal solution, subsequent online updates only require fine-tuning based on the initial values, rather than learning from scratch, thus significantly improving the convergence speed and estimation stability in the online phase. Overall, this step lays a reliable foundation for the subsequent introduction of the adaptive forgetting factor and online weight updates, ensuring the real-time performance and accuracy of health estimation.

[0063] S23, enter the online recursive update stage. Whenever new running data is acquired, the adaptive forgetting factor is calculated based on the current model's output estimation error, and the initial output weights are recursively updated according to the adaptive forgetting factor. The updated network is then used to estimate the battery health at the current moment. The adaptive forgetting factor is constructed by the inverse cotangent function, and its value is negatively correlated with the model's root mean square error. When the estimation error increases, the adaptive forgetting factor decreases to reduce the impact of historical data on the current weight update.

[0064] Specifically, battery aging is a typical time-varying process, and the mapping relationship between its health and mechanistic characteristics gradually drifts with the number of cycles, making it difficult for offline initialization models to maintain optimal performance over the long term. This invention introduces an adaptive forgetting factor, the core principle of which is to dynamically adjust the contribution weights of historical and current data in weight updates by establishing a negative correlation between the forgetting factor and the model's output estimation error. When the battery's operating state is stable and the estimation error is small, the forgetting factor is larger, allowing the model to fully utilize historical information to maintain estimation stability. When battery aging accelerates or sudden changes in operating conditions lead to an increase in estimation error, the forgetting factor adaptively decreases, reducing the weight of old data and enabling the model to quickly track new features. The forgetting factor is constructed using the inverse cotangent function, utilizing its monotonically decreasing characteristic to achieve error-driven smooth adjustment, avoiding the shortcomings of a fixed forgetting factor in rapidly changing scenarios with lag or noise amplification in stable scenarios. This mechanism enables the neural network to possess both memory decay and rapid adaptation capabilities, fundamentally aligning with the time-varying characteristics of the battery aging process.

[0065] Specifically, the online recursive update phase begins with the output weights obtained from offline initialization. Whenever the battery management system collects new operational data and extracts the multidimensional mechanistic feature parameters for the current moment through step one, it first inputs these parameters into the current network to obtain an estimate of the health status. Subsequently, when the actual or reference health status for that moment is obtained through other means, the output estimation error between the estimated value and the actual value is calculated, typically using the root mean square error within a sliding window as the quantification metric. Based on this error, an adaptive forgetting factor is calculated using the inverse cotangent function: λ = λ_min + (1-λ_min)·arccot(RMSE / RMSE_th) / (π / 2), where λ_min is the preset minimum forgetting factor and RMSE_th is the error threshold. Substituting the forgetting factor into the recursive least squares form of the weight update formula: first, the gain vector is calculated, then the output weights are updated, and simultaneously, the covariance matrix is ​​updated. Using the updated output weights, combined with the current input features, the health status estimate is recalculated as the final output for that moment. This process is executed cyclically each time new data arrives, achieving online adaptation of the model parameters.

[0066] Furthermore, the minimum forgetting factor λ_min typically ranges from 0.95 to 0.99, determining the basic memory length retained by the model during the most drastic changes. A value that is too small will make the model overly sensitive to noise, while a value that is too large will reduce tracking speed. The root mean square error threshold RMSE_th is used to normalize the error magnitude. Its setting needs to match the expected accuracy of battery health estimation and is usually determined through historical data statistics or cross-validation. The introduction of the inverse cotangent function causes the forgetting factor to decrease rapidly after the error exceeds the threshold and tend to one when the error is below the threshold, achieving smooth nonlinear adjustment. The covariance matrix in the recursive algorithm reflects the uncertainty of the current parameter estimation. Its initial value is usually set as the identity matrix multiplied by a large constant, gradually converging during the update process. The update of the covariance matrix is ​​also affected by the forgetting factor; the smaller the forgetting factor, the faster the covariance matrix increases, allowing subsequent updates to adjust weights with larger step sizes. These parameters collectively determine the convergence speed, steady-state accuracy, and robustness of the online update process.

[0067] Specifically, in the electric vehicle sector, this step serves as the core online algorithm of the vehicle battery management system. It continuously updates the model using data from each charging or driving cycle, outputting the current health status in real time. This provides OEMs with accurate residual value assessments and user range predictions. In energy storage power station scenarios, this step can perform parallel online updates for hundreds or thousands of individual battery cells, promptly identifying trends in health differentiation among cells. This assists maintenance personnel in implementing precise balancing and maintenance, extending the overall lifespan of the power station. In secondary utilization scenarios, this step can be deployed in the monitoring system after battery refitting, continuously tracking the health evolution of retired batteries during secondary use, providing dynamic support for safety warnings and lifespan management. On cloud-based battery management platforms, this step can aggregate multi-source data, performing distributed online learning on battery groups under different regions and operating conditions, continuously optimizing model parameters, and improving the accuracy of the platform's predictive services.

[0068] Specifically, compared to the fixed forgetting factor method, this step can adjust the model's dependence on historical data in real time based on the estimation error, maintaining the smoothness and stability of the estimation when the battery state is stable, and responding quickly to accelerated aging or sudden changes in operating conditions. This effectively solves the trade-off between tracking speed and noise suppression in traditional online learning algorithms. The forgetting factor adjustment mechanism constructed by the inverse cotangent function achieves error-driven adaptive smooth adjustment, avoiding update oscillations caused by step changes. Based on offline initialization of weights, only fine-tuning is required in the online stage instead of retraining, significantly reducing computational overhead and meeting the real-time requirements of embedded systems. By continuously tracking battery aging characteristics, the accuracy of the health estimation results is maintained throughout the entire lifespan, providing a reliable state benchmark for subsequent remaining lifespan prediction. Overall, this represents a technological leap from static calibration to dynamic tracking.

[0069] Furthermore, S23 includes: S231, during the online recursive update phase, monitors the residual sequence between the output value of the single hidden layer feedforward neural network and the measured health status in real time. When the residual sequence increases continuously and exceeds the preset fluctuation range, the dynamic adjustment mechanism of the adaptive forgetting factor is triggered to accelerate the model's response speed to new features of battery aging.

[0070] Specifically, the battery aging process is not always a smooth evolution. At certain stages, sudden degradation such as internal short circuits, lithium plating, and electrolyte drying may cause state jumps. In such cases, conventional continuous adaptive updates may have a response lag. This step constructs statistical features of the residuals, such as moving mean, moving variance, or cumulative sum, by monitoring the residual sequence between the neural network output value and the measured health status in real time. When the residual sequence shows a continuous increase or exceeds the preset fluctuation range, it indicates that the current model can no longer accurately describe the battery state, and there may be a sudden change in the aging mode. At this time, the dynamic adjustment mechanism of the adaptive forgetting factor is triggered to further reduce the forgetting factor, so that the model can reduce the weight of historical data and amplify the contribution of new data to a greater extent in the short term, thereby accelerating the capture of new aging features. This principle upgrades conventional error-driven adaptation to event-driven enhanced adaptation, improving the model's ability to track non-stationary processes.

[0071] Specifically, a sliding window storage mechanism for the residual sequence is first established. The window length can be set according to the battery aging rate and sampling frequency, typically covering several to dozens of charge-discharge cycles. In each online update cycle, the estimated residual at the current moment is calculated and stored in the window. Simultaneously, the statistical characteristics of the residuals within the window are updated, including the moving mean, moving standard deviation, or cumulative residual sum. Criteria for continuous increase in residuals are set, such as three or more consecutive residual values ​​being greater than the residual at the previous moment, or the cumulative residual sum exceeding a preset threshold. A quantitative indicator for the fluctuation range is set, typically using the residual standard deviation during the offline initialization phase or stable operation phase as a benchmark, defining the fluctuation range as a multiple of the benchmark standard deviation, such as the three-standard-deviation principle. When the residual sequence meets the trigger condition, the forgetting factor is dynamically adjusted: further reducing it from the original adaptive forgetting factor, or directly resetting it to the preset minimum forgetting factor, and gradually restoring it to the normal adjustment range over several subsequent update cycles. The adjusted forgetting factor is substituted into the weight update formula to accelerate weight changes in the current and subsequent iterations. Once the residual sequence has returned to normal, the forgetting factor is restored to the conventional adaptive calculation value.

[0072] Furthermore, the length of the residual monitoring window needs to be balanced between response sensitivity and statistical stability. A window that is too short is susceptible to false triggering due to single-shot noise interference, while a window that is too long delays anomaly detection. A length of five to twenty is typically used. The threshold for continuous increase is usually set to increase at three or four consecutive points, drawing on the runs rule in statistical process control. The fluctuation range factor is based on the residual standard deviation, typically ranging from two to three, corresponding to a confidence interval of approximately 95% to 99.7% under a normal distribution. The adjustment range of the forgetting factor can be set according to the severity of the anomaly. For mild anomalies, the original adaptive value is multiplied by a decay coefficient; for severe anomalies, it is directly set to the preset minimum forgetting factor. The recovery rate control parameter determines the speed at which the forgetting factor returns to normal after an anomaly. An exponential decay or linear increase method can be used to ensure a smooth model transition. The above parameters need to be calibrated in conjunction with the specific battery type and application conditions to achieve the optimal balance between sensitivity and robustness.

[0073] Specifically, in the electric vehicle sector, when vehicles encounter harsh operating conditions, excessive fast charging, or collisions, batteries may experience sudden accelerated aging. This step can quickly identify anomalies through residual monitoring, adjust the estimation model in a timely manner, and provide OEMs with accurate health status assessments, supporting safety warnings and maintenance decisions. In energy storage power station scenarios, long-term battery operation may lead to cell consistency drift or precursors to thermal runaway. This step, through real-time monitoring of residual sequences, can identify abnormal cells early, trigger maintenance alarms in advance, and prevent the fault from escalating. In secondary use scenarios, retired batteries may experience rapid performance degradation in the early stages of reuse. This step can quickly capture this characteristic, providing timely status updates to the battery management system and ensuring safe secondary use. On cloud-based battery management platforms, this step can serve as an anomaly detection algorithm, monitoring massive amounts of battery operating data in real time, identifying clustered anomaly trends, and supporting battery model iteration and quality improvement.

[0074] Specifically, compared to continuous adaptive updates that rely solely on error-driven mechanisms, this step can proactively accelerate model adjustments by identifying abnormal trends through statistical monitoring before regular adjustments have fully responded, effectively shortening the time delay between state abrupt changes and model adaptation. The combined use of continuously increasing criteria and fluctuation range thresholds can capture systematic drift while filtering out random noise interference, avoiding false triggers caused by single fluctuations. The event-driven enhanced adaptive mechanism complements the original continuous adaptive mechanism, enabling the model to maintain estimation stability during stable operation and possess rapid tracking capabilities during abnormal phases, achieving a balance between dynamic performance and steady-state accuracy. Overall, this step provides a higher level of safety and reliability support for online battery health estimation, making it particularly suitable for applications with stringent safety margin requirements.

[0075] S3. Based on the estimated health status, a double exponential function decay model is constructed, and the number of cycles when the health status decays to the end-of-life threshold is predicted by extrapolation to output the remaining lifespan of the battery.

[0076] Specifically, the degradation of battery health over cycle count typically exhibits a non-linear characteristic of initial slow decline followed by accelerated degradation. The double exponential function is widely used because it can characterize two degradation mechanisms at different time scales. This invention uses the health sequence estimated in real-time in step two as model input to construct a double exponential function model describing the long-term evolution of battery health. This model consists of two superimposed exponential terms, corresponding to the dominant stages of different degradation mechanisms during battery aging, such as initial reversible capacity loss and later irreversible material degradation. By coupling the health estimation results with the double exponential model, the short-term accuracy of online health estimation is combined with the long-term trend characterization capability of the double exponential model, enabling extrapolation from the current state to the future state. When the health predicted by the model first degrades to a preset lifespan threshold, the difference between the corresponding number of cycles and the currently completed number of cycles represents the remaining lifespan. This principle realizes a mathematical mapping from real-time monitoring data to future lifespan prediction, providing a quantitative basis for battery lifecycle management.

[0077] Specifically, based on the battery health estimation results output in step two, a historical health sequence is first constructed, spanning all available data from the battery's initial use to the current moment. A double exponential function model is then constructed, typically expressed as SOH = a·exp(b·k) + c·exp(d·k), where k is the cycle number, and a, b, c, and d are undetermined model parameters. A nonlinear least squares fitting method is used, employing the historical health sequence as observations, to estimate the optimal parameter combination of the double exponential function. A weighted strategy can be used during parameter fitting, assigning higher weights to recent data to reflect the dominant role of the current aging trend. Once the model parameters are determined, the health value corresponding to future cycle numbers is extrapolated from the current moment, with the step size set to a single cycle or a fixed interval depending on the prediction requirements. During the extrapolation process, it is monitored in real-time whether the predicted health has reached a preset lifespan termination threshold. This threshold is typically set based on battery specifications or application requirements, such as when the health decays to 80% of its initial value. When the decay condition is met for the first time, record the corresponding number of future cycles, subtract the number of cycles already run, and obtain the remaining lifetime prediction value and output it.

[0078] Furthermore, the exponential coefficients b and d in the double exponential function determine the curvature and inflection point of the decay curve; positive values ​​indicate growth, but negative values ​​are typically used to describe decay, and their absolute values ​​reflect the decay rate. Coefficients a and c are amplitude parameters, determining the contribution weight of each exponential term to the overall health. The estimation accuracy of these parameters directly affects the accuracy of extrapolation predictions, requiring sufficient length and signal-to-noise ratio in the historical health sequence. The lifespan termination threshold is the baseline value for defining remaining lifespan; it is typically set at 80% for electric vehicle power batteries and 70% or lower for energy storage batteries, with the specific value determined based on the application scenario. Quality control parameters during the fitting process include goodness of fit, residual standard deviation, and confidence intervals for parameter estimation, used to evaluate the model's fit quality to historical data and warn of potential prediction biases. The extrapolation step size and maximum prediction horizon during the prediction process determine the temporal resolution and confidence range of the prediction.

[0079] Specifically, in the electric vehicle sector, remaining life prediction results can serve as a core basis for assessing the residual value of batteries in used car transactions, providing OEMs, financial insurance companies, and consumers with a transparent and reliable reference for battery value; it can also be used to predict battery replacement timelines and optimize vehicle maintenance plans. In energy storage power station scenarios, this step can predict the remaining life of each individual cell within a battery cluster, identify cells with low lifespans, guide balanced maintenance and replacement strategies for the battery pack, and extend the overall service life of the energy storage system. In secondary utilization scenarios, this step can serve as a key tool for screening and classifying retired batteries, categorizing them into different application levels based on their predicted secondary lifespan to maximize resource utilization. In grid-side energy storage applications such as frequency regulation and peak shaving, remaining life prediction results can be used to optimize charging and discharging strategies, slowing down the aging rate while meeting grid dispatch requirements and improving the economic efficiency of the energy storage system.

[0080] Specifically, compared to linear extrapolation methods based solely on current battery health, the dual-exponential model can characterize the nonlinear features and inflection point behavior during the health degradation process, significantly improving the accuracy of long-term predictions. Using the real-time health estimate from step two as model input ensures that the prediction starting point reflects the battery's current true state, avoiding prediction bias caused by baseline health errors. By fitting historical data using nonlinear least squares, the model parameters can adapt to the differentiated characteristics of different individual batteries and different aging paths, exhibiting good generalization ability. The remaining life prediction results are output in the form of cycle count, which is intuitive and easy to integrate with the battery management system's maintenance plan. Overall, this step organically unifies short-term estimation and long-term prediction, forming a complete technical chain from real-time monitoring to future projections, providing reliable technical support for battery lifecycle value assessment and proactive maintenance decisions.

[0081] Furthermore, S3 includes: S31, Construct a double exponential function model to describe the long-term degradation trend of battery health, wherein the double exponential function model uses the number of cycles to be predicted as the independent variable and battery health as the dependent variable.

[0082] Specifically, the decline in battery health with increasing cycle count is not a simple linear or single-exponential process, but rather the result of multiple degradation mechanisms. In the early stages of aging, the decline rate is relatively slow, primarily influenced by factors such as the reversible growth of the solid electrolyte interfacial film and surface modification of active materials. As cycling progresses, irreversible active material loss, lithium plating formation, and electrode structure degradation gradually dominate, accelerating the decline rate. The double-exponential function, composed of two superimposed exponential terms, can characterize these two different time-scale decline components: the first exponential term corresponds to the rapid initial reversible decline, while the second exponential term corresponds to the slow later irreversible decline, or vice versa, depending on the parameter settings. By constructing a double-exponential model with the number of cycles to be predicted as the independent variable and battery health as the dependent variable, a mathematical mapping from the time dimension to the state dimension is established, providing a physically interpretable trend description tool for subsequent extrapolation predictions.

[0083] Specifically, the mathematical expression of the double exponential function model is first determined, typically in the form: SOH = a·exp(b·k) + c·exp(d·k), where SOH represents battery health, k represents the number of cycles, and a, b, c, and d are the model parameters to be fitted. In practical applications, considering the characteristic that health decays with the number of cycles, parameters b and d are usually negative, causing the exponential term to decrease as k increases; the signs of parameters a and c may be positive or negative, depending on the direction of contribution of each exponential term to the total health, and are usually set to be positive and summed to around one. After the model is built, the health sequence obtained in real-time estimation in step two is used as the observation data, and the number of cycles from when the battery was put into use to the current time and the corresponding health values ​​are selected to form the training dataset. A nonlinear least squares algorithm is used to fit the model parameters. The algorithm minimizes the sum of squared residuals between the model output and the historical health sequence through iterative optimization. During the fitting process, a reasonable range of parameter values ​​needs to be set to ensure that the exponential term does not diverge or produce non-physical numerical results. Once the model parameters are determined, the double exponential function model is constructed and can be used for subsequent extrapolation and prediction.

[0084] Furthermore, parameters a and c are amplitude coefficients, representing the contribution weights of the two exponential terms to the initial health value, respectively. Their magnitudes reflect the proportion of different degradation mechanisms in the total degradation, and the sum of a and c should be close to the initial battery health value. Parameters b and d are degradation rate coefficients, which are negative. Their absolute values ​​determine the degradation rate; a larger absolute value of b corresponds to a rapid degradation component, and a smaller absolute value of d corresponds to a slow degradation component. The relative magnitudes of b and d determine the inflection point and curvature change of the health degradation curve. Fit quality indices include goodness of fit, used to evaluate the model's interpretability of historical data; residual standard deviation, reflecting the average deviation between model predictions and historical observations; and confidence intervals for parameter estimates, used to evaluate the reliability of parameter identification. These parameter indices collectively determine the accuracy and predictive reliability of the dual-exponential model in describing battery aging trends.

[0085] Specifically, in the electric vehicle sector, this model can be built based on historical vehicle operating data, providing OEMs with a mathematical expression of the battery's full life-cycle degradation curve, supporting warranty strategy formulation and used vehicle residual value assessment. In energy storage power station scenarios, the model can be built separately for different battery cells or battery clusters, identifying the differences in degradation characteristics of each unit and providing a quantitative basis for balanced maintenance and replacement plans for battery packs. In secondary utilization scenarios, the model can be built using short-term test data of retired batteries, quickly predicting their degradation trends during secondary use, assisting in battery grading and application matching. During the battery R&D and testing phase, the model can serve as an analysis tool for accelerated aging test data, guiding battery performance optimization by comparing differences in model parameters under different material systems and manufacturing processes. On cloud-based battery management platforms, the model can be applied in batches to massive amounts of battery data to achieve statistical analysis of group aging trends.

[0086] Specifically, compared to the single-exponential model, the double-exponential model can characterize the inflection points and curvature changes during the health degradation process, more accurately reflecting the transition characteristics of the battery from initial reversible loss to later irreversible degradation, and significantly improving the fitting ability to complex aging paths. Compared to high-order polynomial or non-parametric models, the double-exponential model has fewer parameters and clear physical meanings, avoiding the risk of overfitting, and is less prone to non-physical behaviors such as divergence or oscillation during extrapolation. Using the health sequence estimated in real time in step two as the data foundation for model construction ensures that the model can reflect the current true state of the battery and avoids model distortion caused by baseline data deviation. This step provides a mathematical framework with good extrapolation performance for subsequent remaining lifetime prediction, serving as a key bridge connecting short-term online estimation and long-term trend prediction, fundamentally guaranteeing the accuracy and reliability of remaining lifetime prediction.

[0087] S32, the double exponential function model is converted into a state-space equation form, which includes a state equation and a measurement equation, and the estimated current health is used as the initial value for state update.

[0088] Specifically, while the double exponential function model can characterize the long-term decline trend of battery health, it is essentially a deterministic mathematical expression and cannot account for the influence of random disturbances and uncertainties during future operation. By converting the double exponential model into a state-space equation, and defining the model parameters or health itself as the system state evolving over time, a state equation is established to describe the dynamic evolution of state variables, and a measurement equation is established to describe the mapping relationship between state variables and observable health. The state-space model provides a mathematical framework for subsequent recursive prediction using filtering algorithms, enabling the integration of the latest health observation information during the prediction process, continuously refining the state estimate, and achieving dynamic updates to the prediction results. Using the current health obtained from the online estimation in step two as the initial value for the state update ensures a high degree of consistency between the prediction starting point and the actual battery state, fundamentally improving the accuracy of long-term prediction.

[0089] Specifically, the first step is to determine the composition of the state vector. Based on the mathematical form of the double exponential function model SOH = a·exp(b·k) + c·exp(d·k), two state definition strategies can be adopted: one is to use the four parameters a, b, c, and d in the double exponential function as state variables, in which case the state vector is four-dimensional, and the state equation describes the evolution of these parameters with the number of cycles, typically modeled as a random walk process or a first-order Markov process; the other is to use the current health level and its related auxiliary variables as state variables, and to transform the double exponential function into a recursive form by introducing a difference equation. After determining the state vector, the state equation is established, generally in the form x_{k+1} = f(x_k) + w_k, where f is the state transition function and w_k is the process noise. The measurement equation is established in the form z_k = h(x_k) + v_k, where h is the observation function, mapping the state to the observed health level, and v_k is the measurement noise. The health level estimated in step two at the current time is used as the initial state x_0, and the initial state covariance matrix is ​​set. Thus, the double exponential function model was successfully transformed into state-space equation form, laying the foundation for subsequent filtering and recursive prediction.

[0090] Furthermore, the dimension of the state vector depends on the state definition strategy. If parameters are used as states, the dimension is four; if health and related variables are used, the dimension may be lower. Dimension selection requires a trade-off between model expressiveness and computational complexity. The process noise covariance matrix reflects the random fluctuation amplitude of state variables over time. Its value determines the filter's adaptability to model uncertainty. Too small a value will cause the filter to over-rely on the model and ignore new data, while too large a value may introduce excessive noise. The measurement noise covariance matrix reflects the uncertainty of health observations and can usually be calibrated based on the error statistics of the estimation results in step two. The initial state covariance matrix characterizes the uncertainty of the initial state estimation. The initial value setting needs to reflect the confidence level of the current health estimation in step two. These parameters collectively determine the accuracy of the state-space model in describing the battery aging process and the convergence performance of the filter.

[0091] Specifically, in the electric vehicle sector, this model can be embedded in onboard battery management systems. Starting with the current battery health, it dynamically predicts remaining lifespan by combining statistical characteristics of future vehicle usage conditions, providing OEMs with real-time updated battery status information. In energy storage power station scenarios, the model can construct state-space representations for each individual cell within a battery cluster. Combining power station operation plans and load forecasts, it dynamically updates the predicted remaining lifespan of each cell, supporting refined operation and maintenance decisions. In secondary utilization scenarios, the model can use the current health of retired batteries as an initial value to predict their lifespan trajectory in secondary use scenarios, assisting in battery grading and application matching. On cloud-based battery management platforms, the model can serve as a core prediction engine, performing parallel state-space modeling on massive amounts of battery data to achieve group lifespan prediction and anomaly identification. During the battery R&D and testing phase, the model can be used as an aging test data analysis tool to assess the impact of different operating conditions on battery lifespan.

[0092] Specifically, the introduction of the state-space model transforms remaining lifetime prediction from a fixed extrapolation after a one-time fitting into a dynamic adjustment of the state estimate based on the latest health observation information in each prediction cycle. This significantly improves the ability of the prediction results to track the actual aging trajectory of the battery. Using the current health level estimated in real time in step two as the initial value for state updates ensures high accuracy at the prediction starting point and avoids systematic prediction errors caused by initial value deviations. The combination of the state-space model and subsequent filtering algorithms quantifies the uncertainty of the prediction results, outputting a probability distribution of remaining lifetime rather than a single numerical value, providing richer information for risk decision-making. Overall, this step injects dynamic updating capabilities and uncertainty quantification capabilities into remaining lifetime prediction, serving as a crucial bridge connecting deterministic models and adaptive prediction, fundamentally improving the accuracy and reliability of long-term predictions.

[0093] S33, based on the state-space equation, extrapolates outward to predict the health value corresponding to the number of future cycles. When the predicted health value first decays to the preset lifespan termination threshold, it records the difference between the current cycle number and the number of cycles already run, as the remaining lifespan of the battery.

[0094] Specifically, within the state-space model framework, the future evolution of battery health is viewed as a stochastic process starting from the current state. By iterating forward through the state equations, a predicted trajectory of health over future cycles can be generated. Since the process noise introduced into the state equations reflects the random fluctuations of the aging process, the prediction results present a probability distribution rather than a single deterministic value. A lifespan termination threshold, as a pre-defined failure criterion, defines the lower limit of unacceptable battery health. When the predicted health trajectory first crosses this threshold, the corresponding cycle number is the lifespan termination moment. Remaining lifespan is defined as the difference between this moment and the current number of cycles already run. This principle transforms the battery remaining lifespan problem into a first-arrival time problem of a stochastic process, not only providing a point estimate of the remaining lifespan but also offering a theoretical basis for subsequent uncertainty quantification. Through multiple Monte Carlo simulations, the probability density function of the remaining lifespan can be obtained, providing richer information for risk decision-making.

[0095] Specifically, the system first obtains the current state estimate and its covariance matrix as the starting point for extrapolation prediction. A maximum horizon for the prediction is set, i.e., the maximum number of extrapolation iterations allowed, to avoid infinite computation. The system then enters a recursive prediction loop: for each future iteration step, the predicted state value for the next moment is calculated based on the state equation, and random perturbations are added based on the process noise covariance matrix to generate Monte Carlo sample trajectories; the state prediction is converted into a health prediction value based on the measurement equation. At each prediction step, the health prediction value is compared with a preset lifespan termination threshold. If the health prediction value is lower than or equal to the threshold for the first time, the number of future iterations corresponding to that step is recorded, and the prediction for that sample trajectory is stopped. This process is repeated for a large number of Monte Carlo sample trajectories, and the distribution of lifespan termination times for each trajectory is statistically analyzed. Finally, the median or mean of the lifespan termination times for all sample trajectories is calculated as a point estimate of the remaining lifespan; the number of iterations already run is subtracted to obtain the remaining lifespan output. A prediction interval, such as the 5% to 95% quantile, can also be calculated to characterize the uncertainty range of the prediction result. The output results may include the point estimate of the remaining lifespan, probability distribution, and confidence interval.

[0096] Furthermore, the end-of-life threshold is typically determined based on battery specifications, application requirements, or safety standards. For electric vehicle power batteries, the industry standard is 80% of the initial capacity; for energy storage batteries, it may be set to 70% or lower depending on grid dispatch requirements. The selection of this threshold directly affects the magnitude of the remaining life prediction and battery replacement decisions. The maximum prediction horizon needs to cover the possible remaining life range of the battery, typically set at 120% of the battery's rated cycle life, ensuring that all possible failure moments are captured. The Monte Carlo sample size determines the statistical stability of the prediction results. Too small a sample size leads to large fluctuations in quantile estimates, while too large a sample size increases the computational burden; a balance is usually struck between 1,000 and 10,000. The statistics output for remaining life include the mean, median, standard deviation, and quantiles at a specified confidence level, used to meet the risk tolerance requirements of different decision-making scenarios.

[0097] Specifically, in the electric vehicle sector, remaining life prediction can serve as range maintenance information displayed on the vehicle's dashboard, reminding users of upcoming battery replacement needs. It also acts as a core basis for assessing battery residual value in used car transactions, providing OEMs, financial insurance companies, and consumers with a transparent and reliable value reference. In energy storage power station scenarios, remaining life prediction can be used to formulate battery pack replacement plans, identify low-life cells, and optimize spare parts procurement and maintenance resource allocation. Combined with time-of-use pricing and grid dispatch requirements, charging and discharging strategies can be dynamically adjusted to extend the overall system life. In secondary utilization scenarios, remaining life prediction can serve as a key basis for screening and grading retired batteries. Based on the predicted secondary lifespan, batteries can be categorized into different application levels, such as grid frequency regulation, industrial and commercial energy storage, or residential energy storage, maximizing resource utilization. On cloud-based battery management platforms, this step can be applied in batches to massive amounts of battery data to achieve group life prediction and health profiling, supporting battery model iteration and quality improvement.

[0098] Specifically, compared to traditional methods based on empirical formulas or single-model extrapolation, this step fully considers the random fluctuations and uncertainties during the aging process. It generates a probability distribution of remaining lifespan through Monte Carlo simulation, providing decision-makers with more comprehensive risk information. Using the current health level estimated online in step two as the starting point for prediction ensures the real-time nature and accuracy of the prediction benchmark. Combined with the dynamic updating capability of the state-space model, the prediction results can be continuously corrected according to the actual operating trajectory of the battery, avoiding the error accumulation of fixed models in long-term predictions. The remaining lifespan is output in the form of cycle count, which is intuitive and easy to integrate with the battery management system's maintenance plan. The calculation of the prediction interval quantifies the reliability of the prediction results, providing a risk warning basis for high-safety-level applications. Overall, this step organically connects short-term health estimation with long-term lifespan prediction, forming a complete closed loop from real-time monitoring to future projection, providing reliable technical support for battery lifecycle value assessment and proactive operation and maintenance decisions.

[0099] S4 collects historical battery operating data, including voltage, current, and temperature; and preprocesses the historical operating data to remove outliers and missing values, forming a standardized training dataset for subsequent parameter identification of electrochemical models and training of neural network models.

[0100] Specifically, during battery operation, physical quantities such as voltage, current, and temperature are continuously collected by sensors at a certain sampling frequency, forming a raw time series reflecting the battery's dynamic behavior and external characteristics. However, in actual operating environments, factors such as sensor noise, communication interference, measurement anomalies, or missing records can lead to outliers, missing segments, or non-steady-state fluctuations in the raw data. If these are used directly for modeling without processing, they will introduce errors and may even cause the model to fail. Therefore, this step involves data cleaning and standardization to remove outliers and fill in missing values, ensuring the data meets statistical consistency requirements. Simultaneously, standardization transformations eliminate the influence of different dimensions and magnitudes, allowing multi-source data to participate in modeling at a unified scale. This processing provides a clean and standardized data foundation for subsequent electrochemical model parameter identification and neural network training, ensuring that the model learns the battery's true physicochemical behavior rather than data noise.

[0101] Specifically, the first step is to deploy a battery management system or data acquisition platform to continuously record the terminal voltage, load current, and surface temperature of the battery during operation at a fixed sampling frequency (usually 1Hz to 10Hz). Simultaneously, it records the cumulative cycle count at corresponding times and health reference values ​​calibrated through other methods (such as laboratory capacity test values). The collected data is stored in time-series format, forming the raw dataset. The preprocessing stage begins with outlier removal. Statistical methods, such as box plot criteria or the three-standard-deviation principle, are used to identify and remove data points in voltage, current, and temperature that deviate from the normal range, while also removing obviously invalid data caused by sensor malfunctions or communication errors. The second step is missing value handling. For short, consecutive missing segments, linear interpolation or nearest-neighbor mean filling can be used; for long-term missing segments, the data is directly removed to avoid introducing false information. The third step is data standardization. Z-score normalization or Min-Max scaling is used to transform each physical quantity to a standard normal distribution with a mean of 0 and a variance of 1, or a unified interval [0,1], eliminating the influence of dimensions. After preprocessing, the dataset is divided into training, validation and test sets, and the health values ​​at corresponding times are labeled to form a standardized training dataset for subsequent parameter identification and neural network training.

[0102] Furthermore, the sampling frequency determines the temporal resolution of the data. For dynamic operating conditions, a sufficiently high sampling rate is required to capture transient changes. Typically, the sampling frequency for a battery management system is set to 1Hz, but for mixed pulse operating conditions, it may need to be increased to 10Hz or higher. Outlier thresholds often employ statistical control limits, such as calculating the mean and standard deviation based on historical data, and defining data points exceeding the mean ± 3 times the standard deviation as outliers. Alternatively, methods based on physical constraints can be used, directly discarding data with voltages exceeding the electrochemical window (e.g., 2.5V~4.2V) or currents exceeding hardware current limits. In handling missing values, linear interpolation is used when the number of consecutive missing points is less than or equal to 3; otherwise, the segment is discarded. Standardization parameters include the mean and standard deviation (Z-score) or minimum and maximum values ​​(Min-Max) of each feature column. These need to be calculated and saved based on the training set so that the same transformation can be applied to the validation and test sets later. The proper setting of these parameters directly affects data quality and the stability of model training.

[0103] Specifically, in the actual operation of electric vehicles, the on-board battery management system records voltage, current, and temperature data in real time and uploads them to the cloud via a remote information processing unit. This step can be executed in the cloud or on-vehicle edge computing unit, cleaning up voltage jumps during charging gun insertion and removal, abnormal spikes caused by occasional temperature sensor failures, etc., providing clean data for subsequent health assessments. In energy storage power stations, data from hundreds of cells within a battery cluster are aggregated through a centralized monitoring system. This step can batch process multi-channel data, eliminating outliers caused by communication delays or acquisition board failures, ensuring the consistency of power station-level state estimation. In laboratory testing, high-precision data collected by charging and discharging equipment also needs to be preprocessed to eliminate power frequency interference or equipment switching noise, providing reliable input for electrochemical model parameter identification. Furthermore, in the rapid sorting of batteries for secondary use, this step can be used as part of an automated data cleaning process to standardize short-term test data, supporting rapid modeling.

[0104] Specifically, outlier removal effectively avoids the misleading influence of sensor noise or occasional interference on parameter identification, preventing the model from learning unrealistic physical behaviors. Missing value handling ensures the continuity of the time series, enabling time-dependent models (such as state-space models) to operate stably. Standardization eliminates the impact of differences in the dimensions of different physical quantities on neural network training, accelerates gradient descent convergence, and improves the model's generalization ability to data under different operating conditions. The preprocessed dataset allows electrochemical model parameter identification to converge more accurately to the true parameters, resulting in a smoother neural network training loss curve and higher final accuracy. Overall, this step lays a solid data foundation for the entire battery health estimation and lifetime prediction method, serving as the first hurdle to ensure the effectiveness of subsequent steps and directly affecting the accuracy and reliability of the final prediction results.

[0105] This invention discloses a joint method for battery health estimation and remaining life prediction. By establishing a parameter identification framework based on an electrochemical model and utilizing the whale optimization algorithm to extract multi-dimensional mechanistic feature parameters, a single-hidden-layer feedforward neural network with an adaptive forgetting factor is constructed to achieve online health estimation. Based on the estimation results, a double exponential function decay model is built to extrapolate the remaining life. This effectively solves the problems of insufficient prediction accuracy and weak robustness caused by insufficient feature extraction, poor model dynamic adaptability, and separate modeling in existing technologies. It achieves integrated modeling from mechanistic feature extraction and online health estimation to remaining life extrapolation prediction, significantly improving the accuracy and reliability of battery state assessment and enhancing the generalization ability and engineering applicability of the prediction model under complex operating conditions.

[0106] Example 2 To achieve the above invention, embodiments of the present invention also provide another combined method for battery health estimation and remaining life prediction, including: The experimental subject of this invention is a catl280Ah lithium iron phosphate battery. First, battery parameter features related to battery aging are extracted through parameter identification based on a battery model; then, a single hidden layer feedforward neural network (SLFN) algorithm with an adaptive forgetting factor is used; finally, an improved whale optimization algorithm is employed to improve optimization accuracy and the accuracy of battery SOH estimation and RUL prediction. Specifically, this includes: Step 1: Collect battery data.

[0107] The battery's historical operating voltage, current, temperature, and battery health were collected as a test set.

[0108] Step 2: Extract battery characteristic parameters.

[0109] Specifically, the electrochemical model includes: first, establishing the governing equations of the DFN model to describe mass transfer, charge conservation, and lithium flux density in the solid and electrolyte. The DFN model simulates the solid-state and electrolyte kinetics of lithium-ion batteries based on porous electrode theory. For example... Figure 2 As shown, the radius is R s,k Within the domain of the spherical electrode particles, where k∈{n=negative, p=positive}, the electrolyte passes through two porous electrodes and a diaphragm (0≤x≤L). The negative electrode region is... The diaphragm is The region corresponding to the positive electrode is "n", "m", and "p" represent the variables in the negative electrode, membrane, and positive electrode, respectively. The corresponding governing equations and boundary conditions are as follows: Li + Diffusion in the solid phase is as follows:

[0110] In the formula, Indicates solid concentration. This represents the reaction flux across the solid-phase boundary. Represents the diffusion coefficient of a solid. It is the specific surface area. Indicates particle radius, Let Faraday's constant be denoted as . The lithium concentration on the particle surface is expressed as . .

[0111] The change in the potential of a solid electrode is expressed as:

[0112] In the formula For effective electrode conductivity, is the electrode specific surface area.

[0113] Mass conservation in electrolytes:

[0114] Boundary conditions:

[0115] In the formula, It refers to the electrolyte concentration. It is the effective electrolyte diffusion coefficient. . It is the volume fraction of the electrolyte. is the lithium transfer number, typically taken as 0.363. The Bruggeman coefficient, denoted as brug, is typically taken as 1.5. Internal boundary conditions are applied at the junctions of the three regions of the cell to achieve continuity.

[0116] Charge conservation in electrolyte:

[0117] In the formula, It is the electrolyte phase potential. Effective ionic conductivity , yes A concise expression, Specific surface area It is Faraday's constant.

[0118] Boundary conditions for the two current collectors:

[0119] Lithium flux through the solid electrolyte interface:

[0120] In the formula, It is an overpotential, which is the additional force required to overcome the surface reaction. It is the open-circuit potential of the electrode, and the lithium surface concentration. The function. It is a solid potential. It is the electrolyte potential.

[0121] Battery voltage:

[0122] In the formula Let I be the DC resistance of the membrane, and I be the input current. Solving the system of equations yields the final expression for the terminal voltage:

[0123] In the formula, It is the open-circuit potential of the electrode, and is a function of the lithium surface concentration cs,e. That is the maximum lithium-ion concentration. It is an overpotential. It is the electrolyte potential. It is a membrane DC resistor. .

[0124] Furthermore, battery electrochemical parameters are extracted using the whale algorithm parameter identification.

[0125] The parameters are Maximum lithium-ion concentration Solid diffusion coefficient Electrode specific surface area. Compared to particle swarm optimization and genetic algorithms, the whale optimization algorithm has the advantages of fast computation speed, high search accuracy, and fewer adjustable parameters. The calculation steps of the whale algorithm are as follows: (1) Initialization: First, at the start of the algorithm, an initial location needs to be set for each whale and an initial population needs to be generated.

[0126] (2) Search: Each whale explores the space according to certain rules. This process can simulate the process of whales surrounding, chasing and attacking prey.

[0127] This process can be expressed as follows: (12) (13) in, This is the current iteration number. It is the current optimal solution. It is a position vector. and It is a variable coefficient. and The mathematical expression is as follows: (14) (15) (16) in, It is a random vector in [0,1]; This is the maximum number of iterations. When... At that time, the whale optimization algorithm selects a random search agent to search for prey from the whale population. At that time, the WOA algorithm selects the best solution to update the location of the search agent.

[0128] (3) Evaluation: Whenever a whale moves, the fitness value of the current whale population is calculated. If the current fitness value is better than the previous fitness value, the current fitness value is set as the optimal solution.

[0129] Whales swim towards their prey in a spiral trajectory. Local optimization is achieved by shrinking the surrounding area and updating the position of the spiral.

[0130] (17) in, It is a constant. . yes A random number. yes Random numbers in the array.

[0131] (4) Update: Once all whales have completed their movement and evaluation, the algorithm will update the positions of all whales and repeat the above steps.

[0132] (5) Iteration: The whale optimization algorithm can be iterated multiple times until the optimal solution is found. When whales determine the location of their prey, they will gather in groups around the prey.

[0133] Step 3: Input the features from Step 2 (the battery electrochemical parameter features from Step 2) into a single hidden layer feedforward neural network (SLFN) based on an adaptive forgetting factor, and train the single hidden layer feedforward neural network (SLFN) model.

[0134] The mathematical expression of a single hidden layer feedforward neural network (SLFN) is as follows: (18) in, It is the Sigmoid activation function; and They are the first The input weights and bias coefficients of each hidden layer node; These are the output weights of the i-th hidden layer and the output layer; and These are the network's input and output values, respectively. The goal of a single hidden layer feedforward neural network (SLFN) is to minimize the output error; its minimum loss function can be expressed as: (19) A single hidden layer feedforward neural network (SLFN) can transform the problem into the following matrix form: (20)

[0135] (twenty one) in, It is the output matrix of the hidden layer.

[0136] The training objective of the Single Hidden Layer Feedforward Neural Network (SLFN) algorithm is to solve linear systems. The minimum norm solution. The calculation formula is as follows: (twenty two) in, It is a matrix The generalized inverse matrix.

[0137] This invention proposes a single hidden layer feedforward neural network (SLFN) with an adaptive forgetting factor.

[0138] Phase 1: Assumptions , This refers to the size of the training set. Initial output weights. The expression is as follows: (twenty three) in, ;

[0139] ;

[0140] Online training phase: Using a set of k+1 elements, the weights are calculated using a loop method, as shown in the following expression: (twenty four) Adaptive forgetting factor The formula is as follows: (25) in, It is the inverse cotangent function; It is an adaptive forgetting factor; It is the smallest forgetting factor; It is the root mean square error of the model. It is the root mean square error threshold. An adaptive forgetting factor is introduced. The output weights can be expressed as: (26) Step 4: Predict SOH and RUL using actual operational characteristic data.

[0141] The method proposed in this invention can simultaneously perform battery SOH estimation and RUL prediction. When estimating battery SOH, features extracted from the measurement signal are used as input to the single hidden layer feedforward neural network (SLFN) trained in step 4 based on an adaptive forgetting factor to estimate battery SOH. The expression of the estimation model is as follows: (27) in, These are the extracted features; It is the number of selected features; The SOH is estimated by the model; It represents the number of charge-discharge cycles.

[0142] For long-term battery RUL prediction, a double exponential function model is mainly established using the battery SOH estimation results. The double exponential function state equation and measurement equation are as follows: (28)

[0143] (29) in, It is a state vector; , , and These are the coefficients of the equation to be identified; , , , and It is noise with an average value of 0; , , , and It is the variance of the noise; It is the predicted value of the exponential function model.

[0144] During the extrapolation prediction process, when the battery's State of Health (SOH) predicted by the exponential function model decays to a certain value, the battery can be considered to have reached the End-of-Life (EOL) threshold. The RUL (Rating Limit Up) is then obtained from the prediction.

[0145] Another method for jointly estimating battery health and predicting remaining life in this invention establishes a parameter identification framework based on an electrochemical model and uses the whale optimization algorithm to extract multi-dimensional mechanistic feature parameters. It then constructs a single-hidden-layer feedforward neural network with an adaptive forgetting factor to achieve online health estimation. Based on the estimation results, a double-exponential function decay model is constructed to extrapolate the remaining life. This effectively solves the problems of insufficient prediction accuracy and weak robustness caused by insufficient feature extraction, poor model dynamic adaptability, and separate modeling in existing technologies. It achieves integrated modeling from mechanistic feature extraction and online health estimation to remaining life extrapolation prediction, significantly improving the accuracy and reliability of battery state assessment and enhancing the generalization ability and engineering applicability of the prediction model under complex operating conditions.

[0146] Example 3 To achieve the above invention, such as Figure 5As shown, this embodiment also provides a combined device 10 for battery health estimation and remaining life prediction, the device 10 comprising: The electrochemical model feature extraction module 100 is used to establish a parameter identification framework based on the electrochemical model and solve the electrochemical model through the whale optimization algorithm to extract multi-dimensional mechanism feature parameters related to battery aging.

[0147] The adaptive health estimation module 200 is used to construct a single hidden layer feedforward neural network with an adaptive forgetting factor based on the multidimensional mechanism feature parameters. The multidimensional mechanism feature parameters are used as input to estimate the current health of the battery online. The adaptive forgetting factor is adjusted in real time according to the output estimation error of the model.

[0148] The dual-exponential lifespan prediction module 300 is used to construct a dual-exponential function decay model based on the health estimation results, and extrapolate to predict the number of cycles when the health decays to the lifespan termination threshold, so as to output the remaining lifespan of the battery.

[0149] This invention discloses a combined device for battery health estimation and remaining life prediction. It establishes a parameter identification framework based on an electrochemical model through an electrochemical model feature extraction module and extracts multi-dimensional mechanistic feature parameters using a whale optimization algorithm. An adaptive health estimation module constructs a single-hidden-layer feedforward neural network with an adaptive forgetting factor to achieve online health estimation. A double-exponential life prediction module constructs a double-exponential function decay model based on the health estimation results to extrapolate the remaining life. This effectively solves the problems of insufficient prediction accuracy and weak robustness caused by insufficient feature extraction, poor model dynamic adaptability, and separate modeling in existing technologies. It achieves integrated modeling from mechanistic feature extraction and online health estimation to remaining life extrapolation prediction, significantly improving the accuracy and reliability of battery state assessment and enhancing the generalization ability and engineering applicability of the prediction model under complex operating conditions.

[0150] To implement the methods of the above embodiments, the present invention also provides a computer device, such as... Figure 6 As shown, the computer device 600 includes a memory 601 and a processor 602; wherein, the processor 602 reads executable program code stored in the memory 601 to run a program corresponding to the executable program code, so as to implement the various steps of the combined method for battery health estimation and remaining life prediction described above.

[0151] To implement the above embodiments, this application also proposes a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements a combined method for battery health estimation and remaining life prediction as described in the foregoing embodiments.

[0152] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0153] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.

Claims

1. A combined method for battery health estimation and remaining life prediction, characterized in that, include: A parameter identification framework based on an electrochemical model was established, and the electrochemical model was solved using the whale optimization algorithm to extract multi-dimensional mechanism characteristic parameters related to battery aging. Based on the multidimensional mechanism feature parameters, a single hidden layer feedforward neural network with an adaptive forgetting factor is constructed. The multidimensional mechanism feature parameters are used as input to estimate the current health of the battery online. The adaptive forgetting factor is adjusted in real time according to the model's output estimation error. Based on the estimated health status, a double exponential function decay model is constructed, and the number of cycles when the health status decays to the end-of-life threshold is predicted by extrapolation to output the remaining lifespan of the battery.

2. The method as described in claim 1, characterized in that, The established parameter identification framework based on the electrochemical model, and the solution of the electrochemical model using the whale optimization algorithm, extract multi-dimensional mechanism feature parameters related to battery aging, including: A DFN model describing the internal electrochemical processes of a lithium-ion battery is constructed. The DFN model includes a solid-phase diffusion equation, an electrolyte mass conservation equation, a charge conservation equation, and a Butler-Volmer kinetic equation. The electrochemical parameters to be identified are set as the position vectors of individual whales, and a fitness function is constructed with the goal of minimizing the error between the simulated terminal voltage output by the DFN model and the measured terminal voltage. The whale optimization algorithm is used for iterative optimization. In each iteration, the position of the individual whale is updated through random search and prey encirclement mechanism, and local optimization is performed through spiral trajectory update mechanism until the convergence condition is met. The electrochemical parameters corresponding to the optimal position of the individual whale are output as multi-dimensional mechanism feature parameters related to battery aging. The multi-dimensional mechanism feature parameters include at least one of the following: maximum lithium ion concentration, solid diffusion coefficient and electrode specific surface area.

3. The method as described in claim 1, characterized in that, Based on the aforementioned multidimensional mechanistic feature parameters, a single-hidden-layer feedforward neural network with an adaptive forgetting factor is constructed. Using the aforementioned multidimensional mechanistic feature parameters as input, the current health of the battery is estimated online, including: A single hidden layer feedforward neural network is constructed, with the multidimensional mechanism feature parameters as input layer nodes and battery health as output layer nodes, and the number of hidden layer nodes and activation function are set. During the offline initialization phase, the initial output weights of the single hidden layer feedforward neural network are calculated using historical datasets. In the online recursive update phase, whenever new running data is acquired, an adaptive forgetting factor is calculated based on the current model's output estimation error, and the initial output weights are recursively updated according to the adaptive forgetting factor. The updated network is then used to estimate the battery health at the current moment. The adaptive forgetting factor is constructed from the inverse cotangent function, and its value is negatively correlated with the model's root mean square error. When the estimation error increases, the adaptive forgetting factor decreases to reduce the impact of historical data on the current weight update.

4. The method as described in claim 1, characterized in that, The method involves constructing a double exponential function decay model based on the health level estimation results, and extrapolating to predict the number of cycles when the health level decays to the end-of-life threshold, in order to output the remaining battery life, including: A double exponential function model is constructed to describe the long-term degradation trend of battery health. The double exponential function model uses the number of cycles to be predicted as the independent variable and battery health as the dependent variable. The double exponential function model is converted into a state-space equation form, which includes a state equation and a measurement equation, and the estimated current health is used as the initial value for state updates. Based on the outward extrapolation of the state-space equation, the health value corresponding to the number of future cycles is predicted. When the predicted health value first decays to the preset lifespan termination threshold, the difference between the current number of cycles and the number of cycles already run is recorded as the remaining lifespan of the battery.

5. The method as described in claim 1, characterized in that, Before establishing a parameter identification framework based on electrochemical models, the following steps are also required: Historical battery operation data, including voltage, current, and temperature, is collected. The historical operation data is then preprocessed to remove outliers and missing values, forming a standardized training dataset for subsequent parameter identification of electrochemical models and training of neural network models.

6. The method as described in claim 3, characterized in that, The adaptive forgetting factor is calculated based on the output estimation error of the current model, and also includes: During the online recursive update phase, the residual sequence between the output value of the single hidden layer feedforward neural network and the measured health status is monitored in real time. When the residual sequence increases continuously and exceeds the preset fluctuation range, the dynamic adjustment mechanism of the adaptive forgetting factor is triggered to accelerate the model's response speed to new features of battery aging.

7. A combined device for battery health estimation and remaining life prediction, characterized in that, include: The electrochemical model feature extraction module is used to establish a parameter identification framework based on the electrochemical model and solve the electrochemical model using the whale optimization algorithm to extract multi-dimensional mechanism feature parameters related to battery aging. An adaptive health estimation module is used to construct a single hidden layer feedforward neural network with an adaptive forgetting factor based on the multidimensional mechanism feature parameters. The module uses the multidimensional mechanism feature parameters as input to estimate the current health of the battery online. The adaptive forgetting factor is adjusted in real time according to the model's output estimation error. The dual-exponential lifespan prediction module is used to construct a dual-exponential function decay model based on the estimated health status, and extrapolate to predict the number of cycles when the health status decays to the lifespan termination threshold, so as to output the remaining lifespan of the battery.

8. An electronic device, comprising: processor; The memory stores executable instructions; when the processor executes the instructions, it implements a combined method for battery health estimation and remaining life prediction as described in any one of claims 1-6.

9. A computer-readable storage medium storing a computer program, which, when executed by a processor, implements a combined method for battery health estimation and remaining life prediction as claimed in any one of claims 1-6.

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