Sodium-ion battery state joint estimation method based on aging coupling and physical constraint

Abstract

The present application relates to the technical field of electrochemical energy storage, and particularly relates to a sodium-ion battery state joint estimation method based on aging coupling and physical constraints, comprising: S1: constructing a time sequence sliding window sequence; S2: inputting the time sequence sliding window sequence into an aging feature decoupling model, extracting hidden variable features representing the current aging stage of the battery, and outputting an initial SOH estimation value; S3: inputting the time sequence sliding window sequence and the hidden variable features into a time sequence prediction model, dynamically generating a compensation factor by using the hidden variable features to adaptively correct the aging information, and outputting an initial SOC estimation value; S4: training the aging feature decoupling model and the time sequence prediction model in combination with a two-stage fine-tuning training strategy; S5: constructing a real-time sliding window sequence; S6: outputting SOH prediction values and SOC prediction values through the trained aging feature decoupling model and the time sequence prediction model. The present application realizes accurate joint estimation of the SOC and SOH of a sodium-ion battery.

Description

Technical Field

[0001] This invention relates to the field of electrochemical energy storage technology, specifically to a method for joint estimation of the state of sodium-ion batteries based on aging coupling and physical constraints. Background Technology

[0002] As the global energy structure transitions towards green and low-carbon practices, electrochemical energy storage technology plays a crucial role in mitigating grid fluctuations and facilitating the integration and consumption of new energy sources. Among these technologies, sodium-ion batteries (SIBs) demonstrate significant application potential in large-scale energy storage due to their abundant resources, low cost, and excellent low-temperature performance. However, in real-world operating conditions, energy storage batteries frequently encounter high-frequency random power fluctuations and complex dynamic operating conditions, facing the challenge of long-term safe and stable operation. This severely impacts battery lifespan and health status assessment, placing higher demands on battery management systems (BMS). Therefore, real-time and accurate joint estimation of the state of charge (SOC) and state of health (SOH) of sodium-ion batteries is not only fundamental to optimizing energy dispatch and extending system lifespan but also a key technology for preventing battery overcharging and over-discharging, and avoiding safety accidents such as thermal runaway.

[0003] Currently, battery state estimation methods are mainly divided into two types: mechanistic model-based and data-driven methods. Mechanism-based models (such as equivalent circuit models and electrochemical models) mainly infer battery state by establishing analytical relationships between voltage and internal state variables, which has strong physical interpretability. However, during the long-term aging process of sodium-ion batteries, the complex electrochemical side reactions and phase transition characteristics lead to highly nonlinear model parameters, and the parameters drift drastically with battery aging, resulting in insufficient model robustness. In contrast, data-driven methods based on deep learning show significant advantages in handling nonlinear fitting problems by mining feature mapping relationships in historical operating data. However, when pure data-driven methods are applied to full life cycle state estimation, their problems are becoming increasingly apparent: model performance is highly dependent on the quality of the training dataset. When there is a deviation between actual operating conditions and the training distribution, the model often exhibits prediction drift; in addition, as a "black box" model, its prediction logic relies entirely on statistical regularities and ignores the underlying electrochemical mechanisms.

[0004] Existing joint estimation frameworks for SOC and SOH mostly employ a "decoupled" or "serialized" approach, where SOH is estimated independently first and then used as a fixed parameter input into the SOC model. However, battery SOC estimation and SOH evolution are deeply coupled processes: as SOH decreases, the battery's polarization response, internal resistance evolution, and the mapping relationship between SOC and terminal voltage all dynamically drift. Simple parameter transfer is insufficient to characterize the impact of the aging process on the SOC voltage characteristic curve, leading to a gradual decrease in the model's prediction accuracy with increasing cycle count during long-term operation.

[0005] In summary, how to construct a joint estimation method for SOC and SOH that can reflect the aging coupling mechanism and take into account physical consistency constraints has become a key technical challenge that urgently needs to be overcome in the field of battery management systems. Summary of the Invention

[0006] To address the shortcomings of the existing technologies, the technical problem to be solved by this invention is: how to provide a joint estimation method for the state of sodium-ion batteries based on aging coupling and physical constraints, which can accurately capture the nonlinear aging of the battery through feature decoupling and adaptive modulation mechanism, and ensure that the prediction results conform to the real dynamic electrochemical laws inside the battery while ensuring the estimation accuracy, thereby achieving accurate joint estimation of the SOC and SOH of sodium-ion batteries.

[0007] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0008] A joint state estimation method for sodium-ion batteries based on aging coupling and physical constraints includes:

[0009] S1: Construct a time-series sliding window sequence based on multi-dimensional operational data of sodium-ion batteries during charge-discharge cycles;

[0010] S2: Input the time-series sliding window sequence into the aging feature decoupling model, extract the latent variable features that characterize the current aging stage of the battery, and output the initial SOH estimate based on the latent variable features;

[0011] S3: Input the time-series sliding window sequence and latent variable features into the time-series prediction model, use the latent variable features to dynamically and adaptively correct the aging information, and output the initial SOC estimate.

[0012] S4: Calculate the joint training total loss based on the initial estimates of SOH and SOC, combined with the corresponding SOH and SOC true value labels, and train the aging feature decoupling model and time series prediction model using a two-stage fine-tuning training strategy;

[0013] S5: Construct a real-time sliding window sequence based on the multi-dimensional operational data of the sodium-ion battery to be processed;

[0014] S6: Input the real-time sliding window sequence of the sodium-ion battery to be processed into the trained aging feature decoupling model and time series prediction model respectively, and output the corresponding SOH prediction value and SOC prediction value.

[0015] Preferably, step S1 specifically includes the following processing steps:

[0016] S101: Obtain a multidimensional operational dataset of a sodium-ion battery during charge-discharge cycles;

[0017] S102: Preprocess the data in the multidimensional running dataset to obtain preprocessed running feature data;

[0018] S103: Use the sliding operator to slice the preprocessed running feature data to obtain a time-series sliding window sequence.

[0019] Preferably, in step S2, the processing steps of the aging feature decoupling model include:

[0020] S201: Extraction of health feature factors related to capacity decay based on time-series sliding window sequences;

[0021] S202: Input the health feature factors into the first hidden layer, and map the health feature factors to a high-dimensional space through nonlinear transformation to obtain high-dimensional features;

[0022] The formula for calculating the first hidden layer is:

[0023] ;

[0024] In the formula: The high-dimensional features output by the first hidden layer; As a health characteristic factor; , These are the weight matrix and bias vector of the first hidden layer, respectively; For activation functions;

[0025] S203: Input the high-dimensional features output from the first hidden layer into the second hidden layer, compress the aging information and decouple the features by reducing the number of neurons, and obtain the latent variable features that characterize the current aging stage of the battery.

[0026] The formula for calculating the second hidden layer is:

[0027] ;

[0028] In the formula: To characterize the latent variable features of the current aging stage of the battery; , These are the weight matrix and bias vector of the second hidden layer, respectively;

[0029] S204: Input the latent variable features into the output layer, and map the latent variable features to the health status through the weight matrix to obtain the initial estimate of SOH;

[0030] The formula for calculating the output layer is:

[0031] ;

[0032] In the formula: This is the initial estimate of SOH; , These are the weight matrix and bias vector of the output layer, respectively.

[0033] Preferably, step S201 specifically includes the following processing steps:

[0034] S2011: Extracting initial health feature factors from a time-series sliding window sequence;

[0035] S2012: Calculate the correlation coefficients of each initial health characteristic factor;

[0036] S2013: Select initial health characteristic factors with correlation coefficients greater than a preset threshold as health characteristic factors related to capacity decay.

[0037] Preferably, in step S3, the processing steps of the time series prediction model include:

[0038] S301: Input the temporal sliding window sequence into the LSTM network to obtain the hidden state vector;

[0039] S302: The hidden state vector output by the LSTM network is modified in real time by using the latent variable features through the feature linear modulation layer to obtain the reconstructed feature vector after adaptive correction of aging information.

[0040] S303: Input the reconstructed feature vector into the output head composed of fully connected layers, and obtain the initial estimate of SOC at the current time through nonlinear activation calculation;

[0041] The formula for calculating the output head is:

[0042] ;

[0043] In the formula: This is the initial estimate of SOC; For activation functions; , These are the weight matrix and bias vector of the output head, respectively; To reconstruct the feature vector.

[0044] Preferably, in step S302, the processing steps of the characteristic linear modulation layer include:

[0045] S3021: Using a modulation parameter generator composed of multiple fully connected layers, with latent variable features As input, scaling factors with the same dimension as the hidden state vector are generated through a nonlinear mapping layer. Translation factor ;

[0046] The formula is expressed as:

[0047] ;

[0048] ;

[0049] In the formula: , These are the weight matrix and bias vector for generating the scaling factor, respectively; , These are the weight matrix and bias vector for generating the translation factor, respectively;

[0050] S3022: Using scaling factors through affine transformation Translation factor The hidden state vector output by the LSTM network is reconstructed to obtain the reconstructed feature vector injected with aging physical information;

[0051] The formula is expressed as:

[0052] ;

[0053] In the formula: To reconstruct the feature vector; The Hadamard product represents element-wise multiplication. Sampling time The hidden state vector output by the LSTM network.

[0054] Preferably, in step S4, the two-stage fine-tuning training strategy includes:

[0055] Phase 1: Freeze the backbone weight parameters of the aging feature decoupling model and the time series prediction model, and optimize the output layer parameters of the aging feature decoupling model and the characteristic linear modulation layer and output head parameters of the time series prediction model only under the physical constraint loss constraint, until the aging feature decoupling model and the time series prediction model converge.

[0056] The second stage involves decoupling the backbone weight parameters of the aging feature decoupling model and the time series prediction model, and jointly optimizing the parameters of the aging feature decoupling model and the time series prediction model through joint training total loss until the aging feature decoupling model and the time series prediction model converge.

[0057] Preferably, physical constraint loss The calculation formula is:

[0058] ;

[0059] In the formula: Loss due to physical constraints; This represents the quantity of the current batch. , The first Each window sample corresponds to an initial estimate of SOH and an initial estimate of SOC; For charge and discharge efficiency; Indicates current; This refers to the battery's nominal capacity.

[0060] Preferably, in step S4, the formula for calculating the total loss of joint training is:

[0061] ;

[0062] ;

[0063] ;

[0064] In the formula: Total losses in joint training; This represents the mean square error loss of SOH. This is the mean square error loss of SOC; Loss due to physical constraints; For physical constraint weights; This represents the quantity of the current batch. , The first Each window sample corresponds to an initial estimate of SOH and an initial estimate of SOC; , The first Each window sample corresponds to a true SOH value label and a true SOC value label.

[0065] Preferably, in step S4, an annealing strategy algorithm is introduced into the two-stage fine-tuning training strategy to update the physical constraint weights with each training round. ;

[0066] The calculation formula for the annealing strategy algorithm is as follows:

[0067] ;

[0068] In the formula: For the current training round Physical constraint weights; This is the initial round in which physical constraints are introduced; The final round when the physical constraints reach their maximum strength; This is the preset maximum physical constraint weight.

[0069] Compared with existing technologies, the sodium-ion battery state joint estimation method based on aging coupling and physical constraints in this invention has the following advantages:

[0070] (1) Compared with conventional preprocessing methods that only scale for a single cycle or a local window, this invention uses global statistics covering the entire process of the battery from the initial state (BOL) to the end of life (EOL) for mapping. This feature can completely preserve key physical information such as the absolute drop in voltage plateau and the increase in internal resistance polarization as the battery evolves with the aging process, providing the model with input features that have a "physical reference system", thereby suppressing the benchmark drift of the estimation results in long-term operation.

[0071] (2) This invention achieves a deep separation of degradation mechanism and dynamic characteristics through an aging feature decoupling network architecture. By mapping the health factors extracted from the charge / discharge curves to a high-dimensional feature space, and then extracting low-dimensional latent variable features characterizing the current aging stage of the battery, an indirect mapping of internal degradation processes such as loss of active material (LAM) and loss of sodium ions (LLI) is achieved. The latent variable features act as a dynamic "fingerprint" of battery aging, which can accurately capture nonlinear degradation inflection points. This not only preserves the physical interpretability of the features, but also provides aging criteria for subsequent state estimation, effectively alleviating the parameter confusion problem when the model deals with multi-process coupled aging behavior.

[0072] (3) This invention introduces a joint loss function with physical consistency constraints. By transforming the conservation law of ampere-hour integral into a physical constraint loss and incorporating it into a multi-objective loss function, it achieves a deep integration of the data-driven model and the battery electrochemical physical criteria. Through a two-stage fine-tuning strategy, the optimization search space of the model is constrained, forcing a strict algebraic relationship between the change in SOC, the current SOH value, and the actual charge. This method of incorporating physical information eliminates the phenomenon that the estimation results violate physical laws, achieving deep coupling and closed-loop consistency of the two independent tasks of SOC and SOH at the physical level, ensuring high mathematical convergence and high physical reliability of the estimation results. Attached Figure Description

[0073] To make the objectives, technical solutions, and advantages of the invention clearer, the invention will now be described in further detail with reference to the accompanying drawings, wherein:

[0074] Figure 1This is a logic block diagram of a joint state estimation method for sodium-ion batteries based on aging coupling and physical constraints.

[0075] Figure 2 This is a flowchart of a method for joint state estimation of sodium-ion batteries based on aging coupling and physical constraints.

[0076] Figure 3 This is a comparison chart showing the estimation results of the state of health (SOH) of sodium-ion batteries in the embodiments of the present invention.

[0077] Figure 4 Plot the absolute error of SOH estimation.

[0078] Figure 5 This is a time-series evolution feature map of the latent variable z.

[0079] Figure 6 Comparison of state of charge (SOH) estimation results for sodium-ion batteries at different cycle numbers: Figure 6 (a) is the estimated result with 14 iterations; Figure 6 (b) is the estimated result for 168 iterations; Figure 6 (c) shows the estimated results for 348 iterations; Figure 6 (d) is the estimated result with 520 iterations.

[0080] Figure 7 This is a comparison chart of SOC estimation errors on the test set. Detailed Implementation

[0081] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but only to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0082] The following detailed explanation illustrates the specific implementation methods:

[0083] Example:

[0084] Electrochemical energy storage systems have become core supporting units in dynamic power scenarios such as grid frequency regulation and wind and solar power integration. Among them, sodium-ion batteries (SIBs) have shown significant application potential in large-scale energy storage due to their abundant resources and excellent low-temperature performance. However, the safety issues of energy storage systems under complex environmental conditions are becoming increasingly prominent. Accurately assessing the battery state is crucial for ensuring the safety of energy storage systems and optimizing energy management. Existing state estimation techniques mostly focus on a single dimension and do not fully consider the dynamic modulation effect of the battery's internal aging mechanism on the external voltage response characteristics. In actual operation, the internal electrochemical state of the battery and its external electrical characteristics exhibit highly nonlinear coupling characteristics, while purely data-driven models often lack physical consistency constraints. This leads to prediction accuracy drift in the battery's life cycle state estimation, which in turn causes safety hazards such as overcharging and over-discharging, thus restricting the safe operation of energy storage systems.

[0085] To address the aforementioned problems, this embodiment discloses the following: Figure 1 and Figure 2 The method for joint state estimation of sodium-ion batteries based on aging coupling and physical constraints, as shown, includes:

[0086] S1: Construct a time-series sliding window sequence based on multidimensional operating data of sodium-ion batteries during charge-discharge cycles, and determine the true SOH and true SOC labels of the time-series sliding window sequence.

[0087] S2: Input the time-series sliding window sequence into the aging feature decoupling model, extract the latent variable features that characterize the current aging stage of the battery, and output the initial SOH estimate based on the latent variable features;

[0088] S3: Input the time-series sliding window sequence and latent variable features into the time-series prediction model, use the latent variable features to dynamically generate compensation factors for adaptive correction of aging information, and output the initial SOC estimate.

[0089] S4: Calculate the joint training total loss based on the initial estimates of SOH and SOC, combined with the corresponding SOH and SOC true value labels, and train the aging feature decoupling model and time series prediction model using a two-stage fine-tuning training strategy;

[0090] S5: Construct a real-time sliding window sequence based on the multi-dimensional operational data of the sodium-ion battery to be processed;

[0091] S6: Input the real-time sliding window sequence of the sodium-ion battery to be processed into the trained aging feature decoupling model and time series prediction model respectively, and output the corresponding SOH prediction value and SOC prediction value. Figure 3 A comparison chart of SOH estimation results. Figure 4The corresponding error distribution diagram is shown. It can be seen that the network model of this invention can accurately capture the nonlinear capacity decay trend of sodium-ion batteries during long-term operation.

[0092] To better illustrate the technical solution of the present invention, this embodiment will be described in more detail through the following parts.

[0093] I. Time-series sliding window sequence

[0094] In the specific implementation process, the steps for constructing the time-series sliding window sequence include:

[0095] S101: Obtain a multidimensional operational dataset of a sodium-ion battery during charge-discharge cycles;

[0096] In this embodiment, the battery capacity was calibrated using a 1 C constant current-constant voltage (CC-CV) method under a constant temperature environment of 25°C. During the charging phase, constant current charging was used to 4.0 V, followed by constant voltage charging until the current dropped below 0.05 C. During the discharging phase, 1 C constant current discharging was used to 1.5 V to the cutoff voltage. Throughout the experiment, data such as voltage, current, discharge capacity, time, and cycle count were collected in real time. The experiment was terminated when the battery capacity decayed to 60% of its initial nominal capacity (i.e., end-of-life state), ultimately obtaining a multi-dimensional time-series dataset of the battery's entire lifespan.

[0097] S102: Because traditional normalization methods often process data independently for a single cycle, the absolute voltage plateau characteristic caused by battery aging is masked. Therefore, this invention uses the Z-score normalization algorithm to preprocess the data in the multidimensional running dataset to obtain preprocessed running feature data;

[0098] The formula for calculating the Z-score normalization algorithm is:

[0099] ;

[0100] In the formula: The data has been standardized. The original data before standardization processing; and This represents the global mean and global standard deviation of the corresponding data. Global statistics are used to ensure that voltage platforms at different aging stages can be compared across the same physical benchmark.

[0101] S103: Use a sliding operator to slice the preprocessed running feature data to obtain a time-series sliding window sequence;

[0102] No. A time-series sliding window sequence of windows The formula is:

[0103] ;

[0104] In the formula: For the first The starting sampling time index of each window satisfies ; Set the length of the window (to 20); Step size; For characteristic dimensions (such as voltage, current, temperature, etc.); Sampling time The preprocessed runtime characteristic data.

[0105] Synchronously associate the corresponding SOC true value label with the SOH true value label of the cycle to provide a data foundation for subsequent joint estimation.

[0106] This invention employs a global Z-Score algorithm for data standardization preprocessing. Compared to traditional local standardization, this invention retains the voltage plateau sinking characteristics of the battery as it evolves with cycles by fixing a physical benchmark. This enables real-time capture of battery aging information without increasing sensor complexity, significantly improving the model's recognition frequency and timeliness of long-cycle aging trends, and providing a feasible path for rapid online status updates.

[0107] II. Aging Feature Decoupling Model

[0108] In specific implementation, the processing steps of the aging characteristic decoupling model include:

[0109] S201: Since battery aging is a complex process involving loss of active material (LAM) and loss of available sodium ions (LLI), these processes are mapped onto the evolution of external characteristics. Therefore, health characteristic factors related to capacity decay are extracted based on a time-series sliding window sequence.

[0110] S202: Input the health feature factors into the first hidden layer, and map the health feature factors to a high-dimensional space through nonlinear transformation to obtain high-dimensional features;

[0111] The formula for calculating the first hidden layer is:

[0112] ;

[0113] In the formula: The high-dimensional features output by the first hidden layer; As a health characteristic factor; , These are the weight matrix and bias vector of the first hidden layer, respectively; For activation functions;

[0114] S203: Input the high-dimensional features output from the first hidden layer into the second hidden layer, compress the aging information and decouple the features by reducing the number of neurons, and obtain the latent variable features that characterize the current aging stage of the battery.

[0115] The formula for calculating the second hidden layer is:

[0116] ;

[0117] In the formula: To characterize the latent variable features of the current aging stage of the battery; , These are the weight matrix and bias vector of the second hidden layer, respectively;

[0118] S204: Input the latent variable features into the output layer, and map the latent variable features to the health status through the weight matrix to obtain the initial estimate of SOH;

[0119] The formula for calculating the output layer is:

[0120] ;

[0121] In the formula: This is the initial estimate of SOH; , These are the weight matrix and bias vector of the output layer, respectively.

[0122] Specifically, the processing steps for extracting health characteristic factors include:

[0123] S2011: Extracting initial health feature factors from a time-series sliding window sequence;

[0124] In this embodiment, the initial health characteristic factors include time-domain related health characteristic factors (HIs) such as constant voltage charge-discharge time and constant current charge-discharge time, as well as characteristic factors such as peak position, peak height, and peak area within a specific voltage range extracted based on incremental capacity analysis (ICA) curves.

[0125] S2012: The correlation coefficients of each initial health characteristic factor were calculated using the Pearson correlation coefficient method;

[0126] The formula for calculating the Pearson correlation coefficient is as follows:

[0127] ;

[0128] In the formula: Initial health characteristic factors Labels with actual SOH values The correlation coefficient between them; The number of samples; and These are the mean values ​​of the initial health characteristic factors and the true SOH values, respectively.

[0129] S2013: Selecting the correlation coefficient Initial health characteristic factors exceeding a preset threshold are considered as health characteristic factors strongly correlated with capacity decay.

[0130] This invention extracts low-dimensional latent variable features through an aging feature decoupling network, which can separate macroscopic voltage features into those reflecting internal aging information, thereby achieving accurate mapping and providing accurate aging fingerprints for subsequent state prediction. At the same time, the introduction of a feature linear modulation mechanism enables online adaptive reconstruction of the model, effectively alleviating parameter drift caused by aging due to a single data-driven path, and solving the "model mismatch" problem that traditional models encounter when facing batteries at different aging stages, significantly reducing the estimation error at the end of aging.

[0131] III. Time Series Forecasting Model

[0132] In practice, the processing steps of the time series forecasting model include:

[0133] S301: Input the time-series sliding window sequence into the LSTM network, and capture the nonlinear dynamic evolution of voltage and current over time through the gating mechanism to obtain the hidden state vector;

[0134] The calculation formula for LSTM networks is as follows:

[0135] ;

[0136] In the formula: Sampling time The hidden state vector output by the LSTM network. is the dimension of the hidden layer neurons in the LSTM network; For the state transition function of the LSTM network; The time-series sliding window sequence is the input to the LSTM network; Sampling time The hidden state vector output by the LSTM network;

[0137] S302: The hidden state vector output by the LSTM network is modified in real time by using the latent variable features through the Feature Linear Modulation (FiLM) layer to obtain the reconstructed feature vector after adaptive correction with aging information.

[0138] S303: Input the reconstructed feature vector into the output head composed of fully connected layers, and obtain the initial estimate of SOC at the current time through nonlinear activation calculation;

[0139] The formula for calculating the output head is:

[0140] ;

[0141] In the formula: This is the initial estimate of SOC; For activation functions; , These are the weight matrix and bias vector of the output head, respectively; To reconstruct the feature vector.

[0142] Specifically, the processing steps of the characteristic linear modulation layer include:

[0143] S3021: Using a modulation parameter generator composed of multiple fully connected layers, with latent variable features As input, scaling factors with the same dimension as the hidden state vector are generated through a nonlinear mapping layer. Translation factor ;

[0144] The formula is expressed as:

[0145] ;

[0146] ;

[0147] In the formula: , These are the weight matrix and bias vector for generating the scaling factor, respectively; , These are the weight matrix and bias vector for generating the translation factor, respectively;

[0148] S3022: Using scaling factors through affine transformation Translation factor The hidden state vector output by the LSTM network is reconstructed to obtain the reconstructed feature vector injected with aging physical information;

[0149] The formula is expressed as:

[0150] ;

[0151] In the formula: To reconstruct the feature vector; The Hadamard product represents element-wise multiplication. Sampling time The hidden state vector output by the LSTM network.

[0152] In practical implementation, to address the problem of "the model being difficult to adapt to different aging stages," this invention introduces an aging feature adaptive mechanism, based on the current latent variable characteristics of the battery. The activation intensity of neurons in the time-series prediction model is dynamically adjusted to compensate for the estimation bias caused by increased internal resistance and voltage drop. For example... Figure 5 Latent variable features shown Temporal evolution feature map, and 16-dimensional latent variable features extracted. The battery exhibits a highly heterogeneous aging evolution trajectory throughout its entire lifecycle. With increasing cycle count, the feature distribution within the embedding space shows a clear evolutionary trend, especially in the later stages of cycling. Multiple dimensions show strong feature mappings corresponding to intensified internal polarization and abrupt changes in physical properties, accurately capturing the key inflection point of sodium-ion batteries entering the accelerated aging stage. Furthermore, Figure 5 The differential evolution distribution of monotonic and non-monotonic features demonstrates that the aging feature decoupling model in this invention can automatically separate the capacity degradation trend of battery decay from the nonlinear internal resistance polarization evolution, successfully achieving effective decoupling between the aging mechanism and operational dynamics. Finally, through the characteristic linear modulation (FiLM) modulation mechanism, the complex nonlinear aging information of the battery in the middle and later stages is mapped into the time-series prediction model, thereby realizing closed-loop adaptive correction of state estimation.

[0153] IV. Two-stage fine-tuning training strategy

[0154] In practice, the two-stage fine-tuning training strategy includes:

[0155] Phase 1: Freeze the backbone weight parameters of the aging feature decoupling model and the time series prediction model, and optimize the output layer parameters of the aging feature decoupling model and the characteristic linear modulation layer and output head parameters of the time series prediction model only under the physical constraint loss constraint, until the aging feature decoupling model and the time series prediction model converge.

[0156] The second stage involves decoupling the core weight parameters of the aging feature decoupling model and the time series prediction model, achieving deep coupling of the parameter space under the constraint of the physical loss function, and jointly optimizing the parameters of the aging feature decoupling model and the time series prediction model through joint training of the total loss until the aging feature decoupling model and the time series prediction model converge.

[0157] Specifically, physical constraint loss The calculation formula is:

[0158] ;

[0159] In the formula: Loss due to physical constraints; This represents the quantity of the current batch. , The first Each window sample corresponds to an initial estimate of SOH and an initial estimate of SOC; For charge and discharge efficiency; Indicates current; This refers to the battery's nominal capacity.

[0160] This invention introduces physical constraint loss of ampere-hour integration. Through a two-stage fine-tuning strategy, it forces the change in SOC to be consistent with the current SOH estimate at the physical level, eliminates the logical bias of the black-box model, and achieves accurate joint estimation of SOC and SOH.

[0161] Specifically, the formula for calculating the total loss during joint training is as follows:

[0162] ;

[0163] ;

[0164] ;

[0165] In the formula: Total losses in joint training; This represents the mean square error loss of SOH. This is the mean square error loss of SOC; Loss due to physical constraints; For physical constraint weights; This represents the quantity of the current batch. , The first Each window sample corresponds to an initial estimate of SOH and an initial estimate of SOC; , The first Each window sample corresponds to a true SOH value label and a true SOC value label.

[0166] V. Annealing Strategy Algorithm

[0167] An annealing algorithm is introduced into the two-stage fine-tuning training strategy to update the physical constraint weights with each training epoch. ;

[0168] The calculation formula for the annealing strategy algorithm is as follows:

[0169] ;

[0170] In the formula: For the current training round Physical constraint weights; This is the initial round in which physical constraints are introduced; The final round when the physical constraints reach their maximum strength; This is the preset maximum physical constraint weight, used to balance the order of magnitude of data error and physical residual.

[0171] Phase 1 (Initial Training): Setup ,at this time The model prioritizes learning the nonlinear mapping characteristics between features such as voltage and current and SOC, constructing the basic statistical logic. The decoupled network and the prediction network are trained solely on the total loss from joint training. Update the parameters to ensure that the initial predicted values ​​of SOH and SOC conform to the evolution of the true value curves;

[0172] In the second phase (mid-training): when At that time, the annealing algorithm is started, and after each epoch, the current annealing algorithm is calculated according to the formula. . As the value gradually increases, the physical loss term generates a gradient, correcting the predicted trajectory that violates the ampere-hour integral law;

[0173] In gradient adjustment (late training stage): Reaching the preset maximum penalty coefficient The gradient generated by the physics term gradually increases in proportion during backpropagation, enabling the model to maintain a high degree of physical consistency even in the later stages of aging.

[0174] As the number of training epochs increases, The slope increases linearly from 0 to the maximum penalty coefficient according to a preset slope, thereby achieving a smooth transition from pure data-driven to physical information-guided, and finally enabling the model to output a physically consistent joint estimation result of battery SOC and SOH.

[0175] The three-stage collaborative training strategy employed in this invention achieves a progressive evolution from feature perception and feature modulation to global stability fine-tuning in terms of technical logic. By balancing the weight relationships between SOC, SOH, and physical loss through stepwise gradient freezing and multi-objective joint optimization, the accuracy of each state parameter estimation is ensured while achieving decoupling and collaboration among prediction modules. This prevents the model from solely relying on local statistical regularities and effectively suppresses the accumulation of random errors during state estimation, providing solid technical support for accurate state estimation of sodium-ion batteries.

[0176] When applying this embodiment in a specific way, Figure 6 This is a comparison chart of SOC estimation results for different number of iterations. Figure 6 (a) is the estimated result with 14 iterations; Figure 6 (b) is the estimated result for 168 iterations; Figure 6 (c) shows the estimated results for 348 iterations; Figure 6 (d) shows the estimated results with 520 iterations. For example... Figure 6 As shown, by introducing features based on latent variables... With its adaptive modulation mechanism for aging characteristics, the model proposed in this invention exhibits extremely high estimation accuracy throughout the entire battery lifecycle. Figure 7 This is a graph showing the SOC estimation error on the test set in an embodiment of the present invention. From... Figure 7 Analysis shows that the model proposed in this invention maintains low mean absolute error (MAE) and root mean square error (RMSE) of SOC estimation throughout the entire life cycle, which fully demonstrates that the model of this invention can achieve accurate joint estimation of SOC-SOH and has excellent robustness when dealing with the complex aging mechanism of sodium-ion batteries.

[0177] In summary, this embodiment proposes a joint estimation method for sodium-ion battery state based on aging coupling and physical constraints to achieve long-term, high-precision joint estimation of sodium-ion battery state. This method forms a complete chain from "global feature extraction - aging latent variable decoupling - feature adaptive modulation - physical consistency constraints" through the construction of a global physical benchmark and the extraction of aging latent variables. This innovative physical information integration architecture and model adaptive reconstruction method significantly improve the prediction accuracy of sodium-ion battery state of charge and health throughout its entire life cycle. Therefore, it can provide effective support for safety early warning, life management, and maintenance planning of sodium-ion battery energy storage power stations, and has good engineering application value.

[0178] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit the technical solutions. Those skilled in the art should understand that any modifications or equivalent substitutions to the technical solutions of the present invention without departing from the spirit and scope of the present invention should be covered within the scope of the claims of the present invention.

Claims

1. A joint estimation method for the state of sodium-ion batteries based on aging coupling and physical constraints, characterized in that, include: S1: Construct a time-series sliding window sequence based on multi-dimensional operational data of sodium-ion batteries during charge-discharge cycles; S2: Input the time-series sliding window sequence into the aging feature decoupling model, extract the latent variable features that characterize the current aging stage of the battery, and output the initial SOH estimate based on the latent variable features; S3: Input the time-series sliding window sequence and latent variable features into the time-series prediction model, use the latent variable features to dynamically and adaptively correct the aging information, and output the initial SOC estimate. S4: Calculate the joint training total loss based on the initial estimates of SOH and SOC, combined with the corresponding SOH and SOC true value labels, and train the aging feature decoupling model and time series prediction model using a two-stage fine-tuning training strategy; S5: Construct a real-time sliding window sequence based on the multi-dimensional operational data of the sodium-ion battery to be processed; S6: Input the real-time sliding window sequence of the sodium-ion battery to be processed into the trained aging feature decoupling model and time series prediction model respectively, and output the corresponding SOH prediction value and SOC prediction value.

2. The method for joint estimation of the state of sodium-ion batteries based on aging coupling and physical constraints as described in claim 1, characterized in that: Step S1 specifically includes the following processing steps: S101: Obtain a multidimensional operational dataset of a sodium-ion battery during charge-discharge cycles; S102: Preprocess the data in the multidimensional running dataset to obtain preprocessed running feature data; S103: Use the sliding operator to slice the preprocessed running feature data to obtain a time-series sliding window sequence.

3. The method for joint estimation of the state of sodium-ion batteries based on aging coupling and physical constraints as described in claim 1, characterized in that: In step S2, the processing steps of the aging feature decoupling model include: S201: Extraction of health feature factors related to capacity decay based on time-series sliding window sequences; S202: Input the health feature factors into the first hidden layer, and map the health feature factors to a high-dimensional space through nonlinear transformation to obtain high-dimensional features; The formula for calculating the first hidden layer is: ； In the formula: The high-dimensional features output by the first hidden layer; As a health characteristic factor; , These are the weight matrix and bias vector of the first hidden layer, respectively; For activation functions; S203: Input the high-dimensional features output from the first hidden layer into the second hidden layer, compress the aging information and decouple the features by reducing the number of neurons, and obtain the latent variable features that characterize the current aging stage of the battery. The formula for calculating the second hidden layer is: ； In the formula: To characterize the latent variable features of the current aging stage of the battery; , These are the weight matrix and bias vector of the second hidden layer, respectively; S204: Input the latent variable features into the output layer, and map the latent variable features to the health status through the weight matrix to obtain the initial estimate of SOH; The formula for calculating the output layer is: ； In the formula: This is the initial estimate of SOH; , These are the weight matrix and bias vector of the output layer, respectively.

4. The method for joint estimation of the state of sodium-ion batteries based on aging coupling and physical constraints as described in claim 3, characterized in that: Step S201 specifically includes the following processing steps: S2011: Extracting initial health feature factors from a time-series sliding window sequence; S2012: Calculate the correlation coefficients of each initial health characteristic factor; S2013: Select initial health characteristic factors with correlation coefficients greater than a preset threshold as health characteristic factors related to capacity decay.

5. The method for joint estimation of the state of sodium-ion batteries based on aging coupling and physical constraints as described in claim 3, characterized in that: In step S3, the processing steps of the time series prediction model include: S301: Input the temporal sliding window sequence into the LSTM network to obtain the hidden state vector; S302: The hidden state vector output by the LSTM network is modified in real time by using the latent variable features through the feature linear modulation layer to obtain the reconstructed feature vector after adaptive correction of aging information. S303: Input the reconstructed feature vector into the output head composed of fully connected layers, and obtain the initial estimate of SOC at the current time through nonlinear activation calculation; The formula for calculating the output head is: ； In the formula: This is the initial estimate of SOC; For activation functions; , These are the weight matrix and bias vector of the output head, respectively; To reconstruct the feature vector.

6. The method for joint estimation of the state of sodium-ion batteries based on aging coupling and physical constraints as described in claim 5, characterized in that: In step S302, the processing steps of the characteristic linear modulation layer include: S3021: Using a modulation parameter generator composed of multiple fully connected layers, with latent variable features As input, scaling factors with the same dimension as the hidden state vector are generated through a nonlinear mapping layer. Translation factor ; The formula is expressed as: ； ； In the formula: , These are the weight matrix and bias vector for generating the scaling factor, respectively; , These are the weight matrix and bias vector for generating the translation factor, respectively; S3022: Using scaling factors through affine transformation Translation factor The hidden state vector output by the LSTM network is reconstructed to obtain the reconstructed feature vector injected with aging physical information; The formula is expressed as: ； In the formula: To reconstruct the feature vector; The Hadamard product represents element-wise multiplication. Sampling time The hidden state vector output by the LSTM network.

7. The method for joint estimation of the state of sodium-ion batteries based on aging coupling and physical constraints as described in claim 5, characterized in that: In step S4, the two-stage fine-tuning training strategy includes: Phase 1: Freeze the backbone weight parameters of the aging feature decoupling model and the time series prediction model, and optimize the output layer parameters of the aging feature decoupling model and the characteristic linear modulation layer and output head parameters of the time series prediction model only under the physical constraint loss constraint, until the aging feature decoupling model and the time series prediction model converge. The second stage involves decoupling the backbone weight parameters of the aging feature decoupling model and the time series prediction model, and jointly optimizing the parameters of the aging feature decoupling model and the time series prediction model through joint training total loss until the aging feature decoupling model and the time series prediction model converge.

8. The method for joint estimation of the state of sodium-ion batteries based on aging coupling and physical constraints as described in claim 7, characterized in that: Physical constraint loss The calculation formula is: ； In the formula: Loss due to physical constraints; This represents the quantity of the current batch. , The first Each window sample corresponds to an initial estimate of SOH and an initial estimate of SOC; For charge and discharge efficiency; Indicates current; This refers to the battery's nominal capacity.

9. The method for joint estimation of the state of sodium-ion batteries based on aging coupling and physical constraints as described in claim 8, characterized in that: In step S4, the formula for calculating the total loss of joint training is: ； ； ； In the formula: Total losses in joint training; This represents the mean square error loss of SOH. This is the mean square error loss of SOC; Loss due to physical constraints; For physical constraint weights; This represents the quantity of the current batch. , The first Each window sample corresponds to an initial estimate of SOH and an initial estimate of SOC; , The first Each window sample corresponds to a true SOH value label and a true SOC value label.

10. The method for joint estimation of the state of sodium-ion batteries based on aging coupling and physical constraints as described in claim 9, characterized in that: In step S4, an annealing algorithm is introduced into the two-stage fine-tuning training strategy to update the physical constraint weights with each training round. ; The calculation formula for the annealing strategy algorithm is as follows: ； In the formula: For the current training round Physical constraint weights; This is the initial round in which physical constraints are introduced; The final round when the physical constraints reach their maximum strength; This is the preset maximum physical constraint weight.

Images