Valve regulated lead acid storage battery cross-scale joint estimation method and system

Abstract

The invention relates to a valve-regulated lead-acid storage battery cross-scale joint estimation method and system, and the method comprises the steps: synchronously collecting voltage, current, temperature and ultrasonic signals, generating a high-dimensional feature tensor through space-time alignment and feature construction, and dividing the high-dimensional feature tensor into a physical mechanism channel and a data driving channel; the standardized features are input into a Group-Radial KAN network, orthogonal grouping modeling is carried out according to physical attributes, and nonlinear mapping is carried out by adopting a rational fraction; generating a physical prior weight based on equivalent circuit parameters of physical mechanism channel identification, and dynamically fusing the physical prior weight with a data-driven attention weight to realize feature weighting of physical guidance; sOC and SOH are jointly estimated through double-branch output, and the physical constraint weight and the capacity regeneration suppression coefficient are dynamically adjusted by a degradation stage self-adaptive module according to the cycle index and the SOH. The method significantly improves the estimation robustness of extreme working conditions and aging stages, effectively inhibits the capacity regeneration interference, has the full-life-cycle adaptive capability and the edge deployment feasibility, and greatly improves the estimation efficiency on the premise of not increasing the reasoning time consumption. The problem of estimation distortion caused by poor robustness of a data-driven model and capacity regeneration in the later stage of aging under extreme working conditions is solved.

Description

Technical Field

[0001] This invention belongs to the field of battery state monitoring technology, specifically relating to a cross-scale joint estimation method and system for the state of charge (SOC) and state of health (SOH) of valve-regulated lead-acid batteries based on the physically informed Group-Rational KAN (Kolmogorov-Arnold Network). Background Technology

[0002] Valve-regulated lead-acid (VRLA) batteries are widely used in power distribution terminals, communication base stations, and uninterruptible power supplies (UPS) due to their compact structure, good sealing, and maintenance-free operation. Accurate estimation of their State of Charge (SOC) and State of Harm (SOH) is crucial for ensuring reliable system operation.

[0003] Currently, lead-acid battery state estimation techniques are mainly divided into three categories: 1) Data-driven methods, such as models based on Kolmogorov-Arnold representation theory, have strong nonlinear fitting capabilities, but suffer from problems such as large number of parameters, low computational efficiency, insufficient robustness under extreme conditions, and lack of physical prior guidance; 2) Filtering algorithms, such as extended Kalman filtering (EKF), have acceptable accuracy under normal conditions, but in the later stages of battery aging or under extreme conditions, the fixed noise covariance is difficult to adapt to sudden changes in state, leading to increased estimation bias; 3) Physical mechanism models, such as Thevenin equivalent circuit model, although interpretable, are difficult to accurately describe complex electrochemical degradation processes and have limited accuracy under dynamic conditions.

[0004] Furthermore, existing technologies focus primarily on individual cells, lacking effective modeling of battery pack inconsistencies, and complex models are difficult to deploy on resource-constrained edge devices, thus limiting their engineering practicality. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a cross-scale joint estimation method and system for lead-acid batteries with high estimation accuracy, strong robustness, and adaptability to the entire battery life cycle and extreme operating conditions. This invention solves the contradiction between the lack of physical interpretability of data-driven models and the poor dynamic adaptability of physical models, and effectively suppresses the estimation bias caused by capacity regeneration during the aging stage.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: a cross-scale joint estimation method for valve-regulated lead-acid batteries, comprising the following steps:

[0007] S1. Multimodal data acquisition and preprocessing: Simultaneously acquire voltage, current, temperature and ultrasonic signals during the operation of lead-acid batteries; perform spatiotemporal alignment and reconstruction on signals with different sampling frequencies to construct a high-dimensional feature tensor containing electrothermal time-series features and acoustic statistical features; standardize the high-dimensional feature tensor to obtain the data-driven channel input, and use the aligned original voltage and current signals as the physical mechanism channel input;

[0008] S2. Physically Informed Feature Extraction: The standardized high-dimensional feature tensor is input into the Group-Rational KAN network; the Group-Rational KAN network divides the input features into at least three orthogonal feature groups based on electrical, thermal, and structural evolution physical properties, and performs nonlinear mapping within each group using learnable rational fractions; physical prior weights are calculated based on the equivalent circuit model parameters identified from the physical mechanism channels; the features extracted by the Group-Rational KAN network are dynamically weighted and fused by combining the physical prior weights and data-driven weights to obtain weighted features;

[0009] S3. Dual-branch joint output and adaptive adjustment: Weighted features are input to the SOC estimation branch and the SOH estimation branch respectively, and the SOC and SOH estimates are jointly output. Based on the battery's cumulative cycle count and SOH, the physical constraint weights and capacity regeneration suppression coefficient are dynamically adjusted through the degradation stage adaptive switching module. The physical constraint weights are used to balance the proportion of physical constraint terms and data-driven terms in the loss function, and the capacity regeneration suppression coefficient is used to control the penalty strength of the mutual information constraint terms on the correlation between the SOC and SOH estimates.

[0010] Furthermore, in step S1, the spatiotemporal alignment and reconstruction specifically include:

[0011] The sampling time of the voltage signal is used as a unified time reference;

[0012] For current signals with the same frequency as the voltage, direct mapping is used;

[0013] The temperature signal is reconstructed using linear interpolation.

[0014] The ultrasound signal is reconstructed using a zero-order preservation strategy.

[0015] Further, in step S1, constructing the high-dimensional feature tensor specifically involves: using time-aligned voltage, current, and temperature signals, along with their derived power, impedance, and differential components, to form an electrothermal time-series feature subspace; dividing the ultrasonic signal into frequency domain sub-bands and extracting the statistical features of each sub-band to form an acoustic statistical feature subspace; and concatenating the electrothermal time-series feature subspace with the acoustic statistical feature subspace to obtain the high-dimensional feature tensor.

[0016] Further, in step S2, in the Group-Rational KAN network, the nonlinear mapping within each feature group is implemented through rational fraction nodes, and the calculation formula for the rational fraction nodes is:

[0017]

[0018] In the formula, k is the physical group index; i is the neuron index within the group; M represents the input features; M is the dimension of the input features for the k-th group. For the nonlinear gain sum used to fit the features, For group-specific learnable coefficients; Overfitting is avoided by introducing pole constraints. Learnable coefficients specific to a group.

[0019] Furthermore, in the Group-Rational KAN network, within the characteristic group corresponding to the temperature field, the denominator polynomial coefficients of all rational fraction nodes are constrained to be shared.

[0020] Further, in step S2, the calculation of the physical prior weights specifically includes:

[0021] Based on the voltage and current signals input through the physical mechanism channel, the ohmic internal resistance R0, polarization resistance R1, and polarization capacitance C1 are identified through the equivalent circuit model.

[0022] Calculate the sensitivity of each circuit parameter to the open-circuit voltage OCV;

[0023] The sensitivity is extended to a high-dimensional feature dimension and normalized to obtain the physical prior weights.

[0024] Furthermore, in step S2, the dynamic weighted fusion is achieved through the following formula:

[0025]

[0026] Based on weight Element-wise weighting is applied to the output features of Group-Rational KAN:

[0027]

[0028] in, For physical prior weights, For data-driven weights generated through a data-driven attention mechanism, For physical constraint weights, Features extracted for the Group-Rational KAN network, ⊗ represents element-wise multiplication, are weighted features.

[0029] Furthermore, in step S3, the total loss function of model training is:

[0030]

[0031] where is the mean square error loss of the SOC and SOH estimation values, is the physical constraint loss based on the terminal voltage equation of the equivalent circuit model, [[ID=IS=18]] is the mutual information between the SOC and SOH estimation values, is the capacity regeneration suppression coefficient.

[0032] Furthermore, in step S3, the degradation stage adaptive switching module dynamically adjusts the physical constraint weight and the capacity regeneration suppression coefficient according to the following rules:

[0033] When the cumulative cycle number N ≤ 500 and SOH ≥ 90%, it is determined as the new battery stage, and set = 0.2, [[ID=3I=34]] = 0;

[0034] When 500 < N ≤ 1500 and 70% ≤ SOH < 90%, it is determined as the transition stage, and set = 👉0.2+(N - 500) / 1000×0.5, = 0;

[0035] When N > 1500 or SOH < 70%, it is determined as the aging stage, and set = 0.7, = 0.2.

[0036] The present invention also provides a valve-regulated lead-acid battery cross-scale joint estimation system, including a memory, a processor, and computer program instructions stored on the memory and capable of being run by the processor. When the processor runs the computer program instructions, the above method can be implemented.

[0037] Compared with the prior art, the present invention has achieved remarkable technical effects in terms of feature modeling method, state estimation robustness, and full-life cycle adaptability by structurally integrating the battery electrochemical physical mechanism and the deep learning model, which are specifically reflected in the following aspects:

[0038] 1. Solve the problems of dimensionality disaster and feature drowning in multi-source heterogeneous feature fusion from the structural level

[0039] Traditional state estimation methods based on KANs or fully connected networks typically input low-dimensional electrical signals such as voltage and current directly into the model along with high-dimensional signals such as temperature fields and ultrasound. This often leads to key electrochemical features being masked by high-dimensional noise in the high-dimensional space, resulting in a significant "feature submersion" phenomenon. Furthermore, the parameter redundancy introduced by the fully connected structure increases computational complexity and reduces inference efficiency, hindering engineering deployment. This invention constructs a Group-Rational KAN architecture based on orthogonal decoupling of physical properties. This architecture forces grouping of electrical, thermal, and structural evolution features at the network structure level, enabling nonlinear mapping of different physical field features within independent subspaces and preventing aliasing of heterogeneous information in the early stages of fusion. Furthermore, by introducing a parameter-sharing rational basis function mapping mechanism, the invention significantly reduces parameter size and computational complexity while effectively preserving subtle but crucial electrochemical dynamic features such as voltage fluctuations and current change rates. This significantly improves the purity and discriminative power of feature representation while maintaining inference efficiency.

[0040] 2. Overcoming the "black box" and failure problems of pure data-driven models under extreme conditions.

[0041] Existing data-driven models based on attention mechanisms primarily rely on statistical correlations in training samples. Under extreme conditions such as low temperatures and high magnification, attention weights are prone to mismatch due to sample distribution shifts or data scarcity, leading to a significant decrease in state estimation accuracy and robustness, exhibiting a clear "black box failure" characteristic. This invention introduces a physically informed attention module, utilizing the sensitivity information of parameters such as ohmic internal resistance, polarization resistance, and polarization capacitance in the Thevenin equivalent circuit model to SOC, to physically guide and constrain network feature weights. Even in extreme low-temperature environments such as -25℃, the model can still adaptively focus on feature channels highly correlated with changes in internal resistance based on electrochemical mechanisms, avoiding complete reliance on statistical data distribution for attention weights and achieving collaborative decision-making between data-driven and physical mechanisms. Experimental results show that this invention can stably control the SOC estimation error within 1% even under extreme conditions, significantly improving the model's environmental adaptability and engineering reliability.

[0042] 3. Effectively overcomes the estimation distortion problem caused by the "capacity regeneration" phenomenon in the later stages of battery aging.

[0043] Existing joint SOC and SOH estimation methods mostly employ simple multi-task learning frameworks, neglecting the dynamic impact of SOH degradation on SOC evolution. In the later stages of battery aging, these methods are susceptible to interference from "capacity regeneration," leading to spurious SOC rebounds and significant deviations between estimated and actual values. This invention establishes a cross-scale coupling mechanism based on mutual information constraints and adaptive switching of degradation stages. When the battery enters the aging stage, the model automatically increases the weight of physical constraints in the loss function and simultaneously activates a capacity regeneration suppression strategy, thus limiting the SOC response to spurious capacity regeneration signals at the mechanism level. Attached Figure Description

[0044] Figure 1 The flowchart shows the implementation of the physically informed Group-Rational KAN model architecture and the cross-scale joint estimation method for valve-regulated lead-acid batteries provided in the embodiments of the present invention; wherein, (a) is the multimodal input and preprocessing layer and its processing flow, (b) is the multi-feature fusion and physically informed processing layer and its processing flow, and (c) is the dual-branch joint output layer and its processing flow.

[0045] Figure 2 This is a flowchart of the adaptive switching strategy during the degradation phase in an embodiment of the present invention.

[0046] Figure 3 This is a visualization distribution of the physical awareness attention weights under different aging stages in an embodiment of the present invention.

[0047] Figure 4 The diagram shows a comparison of the estimation errors of the embodiments of the present invention and the prior art (EKF, original KAN) under different operating conditions; where (a) is the -25℃ low temperature 1C discharge condition, (b) is the 5C high rate charging condition, and (c) is the SOH=65% aging stage NEDC condition. Detailed Implementation

[0048] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0049] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0050] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0051] like Figure 1 As shown, this embodiment provides a cross-scale joint estimation method for valve-regulated lead-acid batteries, including the following steps:

[0052] S1. Multimodal data acquisition and preprocessing: Simultaneously acquire voltage, current, temperature and ultrasonic signals during the operation of lead-acid batteries; perform spatiotemporal alignment and reconstruction on signals with different sampling frequencies to construct a high-dimensional feature tensor containing electrothermal time-series features and acoustic statistical features; standardize the high-dimensional feature tensor to obtain the data-driven channel input, and use the aligned original voltage and current signals as the physical mechanism channel input;

[0053] S2. Physically Informed Feature Extraction: The standardized high-dimensional feature tensor is input into the Group-Rational KAN network; the Group-Rational KAN network divides the input features into at least three orthogonal feature groups based on electrical, thermal, and structural evolution physical properties, and performs nonlinear mapping within each group using learnable rational fractions; physical prior weights are calculated based on the equivalent circuit model parameters identified from the physical mechanism channels; the features extracted by the Group-Rational KAN network are dynamically weighted and fused by combining the physical prior weights and data-driven weights to obtain weighted features;

[0054] S3. Dual-branch joint output and adaptive adjustment: Weighted features are input to the SOC estimation branch and the SOH estimation branch respectively, and the SOC and SOH estimates are jointly output. Based on the battery's cumulative cycle count and SOH, the physical constraint weights and capacity regeneration suppression coefficient are dynamically adjusted through the degradation stage adaptive switching module. The physical constraint weights are used to balance the proportion of physical constraint terms and data-driven terms in the loss function, and the capacity regeneration suppression coefficient is used to control the penalty strength of the mutual information constraint terms on the correlation between the SOC and SOH estimates.

[0055] This invention embeds the electrochemical physical mechanisms of batteries into the data flow and decision-making process of deep learning in the form of explicit constraints, thereby achieving a unity of data-driven modeling capabilities and physical interpretability. Based on the engineering characteristics of lead-acid batteries, such as multi-physics coupling, significant differences in state evolution timescales, and complex dynamic characteristics during aging, this invention divides the overall processing flow into the following three mutually synergistic core stages:

[0056] 1. Multimodal input and preprocessing stage ( Figure 1 (a)

[0057] This stage serves as the system's data sensing and unified modeling entry point, responsible for the synchronous acquisition, anomaly removal, and spatiotemporal alignment of multi-source heterogeneous signals such as voltage, current, temperature, and ultrasound. By constructing a unified time base and reconstructing multi-rate signals, the system outputs two data streams:

[0058] One path is time-series data that maintains the original scale of physical quantities, used for subsequent offline or quasi-online identification of Thevenin equivalent circuit model parameters, in order to ensure the authenticity and interpretability of physical parameters;

[0059] The other approach uses a standardized multidimensional feature tensor as input to a deep learning model, providing a high-quality data foundation for cross-scale state estimation.

[0060] 2. Physical awareness feature extraction stage ( Figure 1 (b)

[0061] In this stage, a Group-Rational KAN structure is introduced to perform physical attribute-based grouping modeling of high-dimensional features, avoiding the information overload problem caused by direct aliasing of multi-source features. Simultaneously, by constructing a physically informed attention module and combining it with equivalent circuit parameter sensitivity analysis, physically guided weights are applied to different feature channels, enabling the network to adaptively focus on key physical information highly correlated with battery state evolution during feature extraction.

[0062] 3. Dual-branch joint output stage ( Figure 1 (c)

[0063] Based on feature fusion, the system adopts a dual-branch output structure to jointly estimate the state of charge (SOC) and the state of health (SOH). By introducing mutual information constraints and an adaptive physical weight adjustment mechanism in the output layer, the cross-scale coupling relationship between SOC and SOH is explicitly characterized, thereby effectively suppressing the interference of non-ideal phenomena such as capacity regeneration during the aging stage on the estimation results while ensuring estimation accuracy.

[0064] The specific implementation scheme of the present invention is as follows.

[0065] I. Input Layer: Spatiotemporal Alignment and Dual-Channel Splitting Mechanism for Multimodal Heterogeneous Data

[0066] like Figure 1 As shown in (a), this layer serves as the sensing front end of the system, responsible for high-precision acquisition and unified modeling of four types of multimodal heterogeneous signals: voltage (V), current (I), temperature (T), and ultrasound (T). By constructing a multi-rate signal temporal reconstruction and physical-data dual-channel decoupling mechanism, a temporally consistent, physically reliable, and structurally standardized data input foundation is provided for subsequent cross-scale joint estimation.

[0067] (1) Definition and sampling strategy of multi-rate signal

[0068] To address the significant differences in the response timescales of different physical quantities during lead-acid battery operation, and to reduce data storage and computational overhead while ensuring the integrity of critical dynamic information, the system adopts a hierarchical multi-rate sampling strategy:

[0069] High-frequency electrical signals (voltage V(t) and current I(t)): Setting the sampling frequency Sampling period T s =0.1s, to accurately capture millisecond-level electrochemical polarization transient responses.

[0070] Medium frequency thermal signal (temperature T) raw (t): Set the sampling frequency It adapts to the hysteresis characteristics of battery thermal conduction;

[0071] Low-frequency acoustic signals (ultrasound U) raw (t): Set the signal sampling frequency It is used to monitor slow-changing physical processes such as changes in the electrode structure.

[0072] (2) Spatiotemporal alignment reconstruction algorithm based on benchmark unification

[0073] To address the issue of misaligned sampling frequencies from multiple data sources, a unified time reference axis is constructed. A time window length of L=100 is set, and sampling times are based on high-frequency voltage. Using the master clock reference, time-series reconstruction is performed on heterogeneous data:

[0074] Electrical signal synchronization mapping:

[0075] Since the current and voltage are triggered synchronously at the same frequency, the direct mapping method is used:

[0076]

[0077] Linear reconstruction of thermal signals:

[0078] For mid-frequency temperature data, a linear interpolation algorithm is used to fill in time gaps and ensure the smoothness of thermal field changes.

[0079]

[0080] In the formula, m is the original temperature sampling index, ensuring that in Temperature continuity within the interval.

[0081] Zero-order (ZOH) preservation of acoustic signal:

[0082] For low-frequency ultrasound data, a zero-order hold (ZOH) strategy is employed to maintain the state unchanged within the low-frequency sampling period, preventing the introduction of spurious high-frequency structural noise due to over-interpolation. Keep the value from the previous moment:

[0083]

[0084] (3) Construction of 780-dimensional feature tensor

[0085] Based on the aligned data, a high-dimensional feature vector containing physical time series and waveform statistics is constructed. It is composed of the following two parts.

[0086] Electrothermal temporal characteristic subspace (700 dimensions):

[0087] Integrating voltage, current, temperature, and their higher-order physical quantities (power P=VI, impedance R=V / I) with dynamic differential components ( These constitute a 100×7 time series matrix, used to fully characterize the dynamic evolution of the battery's operating state.

[0088] Acoustic statistical feature subspace (80 dimensions):

[0089] The ultrasonic echo signal was decomposed into 10 sub-bands in the frequency domain, and 8 statistical features (mean, variance, kurtosis, skewness, energy, information entropy, etc.) were extracted from each band to characterize the micro-porosity change and structural degradation trend of the electrode plate with low-dimensional statistics.

[0090] (4) Physical-Data Dual-Channel Data Splitting Mechanism

[0091] To simultaneously satisfy the physical model's dependence on real-dimensional data and the deep learning model's requirement for numerical stability, this invention designs a physical-data dual-channel off-path architecture at the input layer (e.g., Figure 1 As shown in (a):

[0092] Physical mechanism channel (output A, dashed path)

[0093] Output the original physical quantity matrix The channel data is input directly into the Thevenin equivalent circuit model module without any standardization, and the circuit parameters are periodically identified using the recursive least squares (RLS) method. This is to ensure that the physical parameters have clear electrochemical and physical significance.

[0094] The identification objective function is defined as follows:

[0095]

[0096] In the formula, To measure voltage, This is the estimated SOC value at the previous sampling time. This is the polarization voltage term (based on the zero-state response assumption). This represents the sampling time point. This formula ensures that the identified parameters have genuine electrochemical and physical significance.

[0097] Data-driven channel (output B, solid line path)

[0098] After Z-score normalization of the feature tensor X, it is input into the Group-Rational KAN network. By eliminating the problems of dimensional differences and numerical scale inconsistencies, the model convergence is accelerated and the feature extraction efficiency is improved.

[0099] II. Feature Layer (Structure): Group-Rational KAN with Parameter Sharing Based on Physical Attribute Decoupling

[0100] like Figure 1 As shown in (b), in view of the characteristics of lead-acid batteries with multi-physical field coupling and huge differences in response time scale (electrochemical reaction is on the order of milliseconds, and thermal conduction is on the order of minutes), this layer abandons the black box mapping paradigm of traditional fully connected networks and innovatively constructs a rational function mapping mechanism with physical attribute-oriented orthogonal grouping topology and parameter sharing.

[0101] (1) Orthogonal decoupling grouping strategy for multiphysics features

[0102] To address the "feature overload" problem caused by direct aliasing of heterogeneous data, the preprocessed 780-dimensional high-dimensional feature tensor is projected onto three physically independent sub-feature spaces:

[0103] Fast response electronic eigenspace (Group 1): Focuses on voltage V, current I and their higher-order difference components to capture transient high-frequency fluctuations of electrochemical polarization and ohmic voltage drop.

[0104] Slow-response thermal characteristic subspace (Group 2): Focuses on the spatiotemporal distribution of the temperature field T, adapting to the low-frequency hysteresis characteristics caused by the battery's thermal capacity.

[0105] Structural evolution feature subspace (Group 3, ultrasound / fusion): Focusing on ultrasound spectrum statistics and cross-modal cross terms, it characterizes long-period structural degradation behaviors such as plate corrosion and porosity changes.

[0106] (2) Rational KAN node design based on rational approximation

[0107] Unlike traditional MLPs that use a fixed activation function, this architecture constructs a nonlinear mapping basis within each physical group through a learnable rational function, thereby approximating the complex electrochemical nonlinear curves of the battery (such as the OCV-SOC hysteresis curve) with higher parameter efficiency.

[0108] The formula for calculating Rational KAN nodes is defined as follows:

[0109]

[0110] In the formula, k is the physical grouping index (k=1,2,3 correspond to the electrical characteristic group, temperature field group, and ultrasound / fusion group, respectively); i is the neuron index within the group; Let M be the input feature and M be the dimension of the input feature for the k-th group. For the nonlinear gain sum used to fit the features, For group-specific learnable coefficients; Overfitting is avoided by introducing pole constraints. For group-specific learnable coefficients;

[0111] Compared to the traditional ReLU activation function (piecewise linear), the rational fractional structure can more accurately fit the nonlinear electrochemical characteristics of the battery, and ensures that the characteristic mapping of different physical fields is adapted to its own laws by using a set of specific polynomials.

[0112] (3) Parameter sharing mechanism guided by physical priors

[0113] To address the computational redundancy caused by high-dimensional data and prevent model overfitting, a parameter sharing strategy based on physical properties was designed for the temperature field group:

[0114] Sharing rule: Given the low-frequency smoothness of temperature field changes, all neurons in this group are forced to share the denominator polynomial coefficients. (i.e., sharing the system's pole distribution), only the numerator coefficients are retained. The independence of the fit is used to fit local differences.

[0115] Mathematical expression: .

[0116] Complexity optimization: This mechanism reduces the parameter space complexity of the feature mapping layer from... Reduce to (Where N is the hidden layer width and G=3 is the number of groups), which not only improves the model inference speed by more than 3 times, but also effectively suppresses the interference of high-frequency measurement noise on SOH estimation through physical-level low-pass filtering constraints.

[0117] (4) Tensor Reorganization of Grouped Feature Flows

[0118] Each physical group, after being computed through the aforementioned Rational KAN nodes, outputs its high-dimensional nonlinear eigenvector. (K is the number of neurons in the group), the three sets of feature vectors are concatenated to form As input to the subsequent physically informed attention module, the effectiveness and robustness of features are further improved through a weighted fusion of physical priors and data-driven approaches.

[0119] III. Feature Layer (Mechanism): Mathematical Implementation of the Physically Aware Attention Module

[0120] like Figure 1 (b) and Figure 3 As shown, this invention constructs a physically informed attention mechanism in the feature layer to achieve dynamic fusion of physical prior information and data-driven feature weights. This module explicitly calculates the physical weights. With data weight The dynamic combination enables adaptive switching of the focus of feature attention in different operation and aging stages.

[0121] (1) Physical prior weights

[0122] The physical prior weights are based on the Thevenin equivalent circuit model. By characterizing the sensitivity of changes in key circuit parameters to the state of charge (SOC), the importance of different physical factors in the current operating state is quantified.

[0123] First, calculate the sensitivity S of the ohmic internal resistance R0, polarization resistance R1, and polarization capacitance C1 to the state of charge (SOC). R0 , S R1 , S C1 .

[0124]

[0125] Through the mapping matrix Extend the scalar sensitivity to the feature dimension and normalize it:

[0126]

[0127] This weight reflects the strength of the physical correlation between different characteristic channels and key parameters of the battery equivalent circuit under the current operating conditions.

[0128] (2) Data-driven weights

[0129] To supplement the ability of pure physical modeling to express high-dimensional nonlinear features under complex conditions, this invention simultaneously introduces a data-driven attention branch based on the Squeeze-and-Excitation (SE) structure, which is used to adaptively learn feature weights from the statistical properties of the data.

[0130] Activation function definition: Choose ReLU activation function To increase nonlinearity; The Sigmoid activation function is selected to constrain the output weights to the interval [0, 1].

[0131] Calculation formula:

[0132]

[0133] in For a dimension reduction matrix, It is an upgraded matrix.

[0134] (3) Dynamic weighting mechanism for physical-data fusion

[0135] To achieve adaptive switching between physical constraints and data-driven approaches at different operational stages, this invention introduces a physical confidence coefficient. Used to adjust the proportion of the two types of weights in the final attention allocation.

[0136] The final feature weight calculation formula is defined as follows:

[0137]

[0138] Based on this weight, the output features of Group-Rational KAN are weighted element-wise:

[0139]

[0140] In the formula, This indicates element-wise multiplication. Through this mechanism, when the battery enters the aging stage or physical uncertainties increase, Automatically increase the physical prior weights This forces the model to focus on characteristic channels that are highly correlated with changes in internal resistance, thus suppressing the interference of data noise on the estimation results.

[0141] 1. Output layer and total loss function

[0142] like Figure 1 As shown in (c), the output layer contains two fully connected branches, which output... and .

[0143] SOC branch output formula: ,in This is the weight matrix of the fully connected layer. For bias terms;

[0144] SOH branch output formula: ,in This is the weight matrix of the fully connected layer. This is a bias term.

[0145] Total loss function during model training The definition is as follows:

[0146]

[0147] Note: That is, the mutual information coefficient and the regeneration inhibition coefficient are the same hyperparameter, which is dynamically adjusted by the degradation stage adaptive switching module.

[0148] estimation error It is clearly divided into two parts:

[0149]

[0150] Physical constraint loss Based on the second-order RC model, the terminal voltage constraint is:

[0151]

[0152] Mutual information constraints: The variational lower bound method is used for approximate calculation. , This is the regeneration inhibition coefficient.

[0153] In the formula, The mean square error loss is for SOC and SOH; Loss due to physical constraints; As a mutual information term, by maximizing the mutual information between SOC and SOH, SOC is forced to estimate the aging information of the implicit SOH; and These are the physical constraint weights and mutual information coefficients, respectively, which are dynamically adjusted by the following adaptive module.

[0154] 2. Adaptive switching module during degradation phase

[0155] like Figure 2As shown, this module is the core adaptive adjustment unit for achieving high-precision joint estimation of the entire battery life cycle in this invention. It is used to dynamically adjust key hyperparameters according to the actual aging state of the battery during the model training and online inference stages, thereby overcoming the technical defects of traditional models that use fixed parameters and are difficult to adapt to different aging stages.

[0156] This module uses a two-dimensional collaborative discrimination mechanism of charge / discharge cycle count R and health status K to output physical constraint weights in real time. With capacity regeneration inhibition coefficient This ensures that the model achieves the optimal balance between physical mechanism constraints and data-driven modeling in the three typical stages of new battery, transition, and aging.

[0157] (1) Core input and judgment mechanism of the module

[0158] Core input parameters:

[0159] Charge-discharge cycle number N: refers to the total number of complete charge-discharge cycles completed by the battery. It is a macroscopic quantitative indicator that characterizes the degree of battery aging and directly reflects long-term degradation effects such as plate sulfation and electrolyte loss.

[0160] State of Health (SOH): Defined as the ratio of the current actual maximum usable capacity of the battery to its rated capacity. It is a direct reflection of the battery's degradation state and is used to correct indirect estimation biases in the number of cycles N.

[0161] Auxiliary verification parameters: Real-time collected voltage V and current I time series data are used to back-infer the consistency between SOC and SOH through the Thevenin model, avoiding misjudgment of stages caused by abnormal data.

[0162] Two-dimensional judgment logic:

[0163] This module employs a priority judgment strategy of "N as the primary step and SOH as the secondary step." It first divides the aging interval into N steps, and then uses SOH to fine-tune the boundary conditions, thereby improving the stability and reliability of the stage judgment. The specific rules are as follows:

[0164] If SOH < 70%, regardless of whether N reaches 1500, it is directly judged as the aging stage (covering the scenario of premature battery degradation).

[0165] If N > 1500, even if SOH ≥ 70%, it is still judged as the aging stage to cover the slow decay scenario caused by cycle accumulation;

[0166] The transition phase and the new battery phase must simultaneously meet the dual threshold conditions of N and SOH to avoid erroneous switching caused by fluctuations in a single parameter.

[0167] (2) Three-stage parameter adaptive adjustment rules

[0168]

[0169] The parameter settings, physical meanings, and adjustment logic for each stage are as follows:

[0170] New battery mode (N≤500 AND SOH≥90%):

[0171] Key characteristics of this stage: The internal electrochemical system of the battery is stable, the fluctuation range of physical parameters such as ohmic internal resistance R0, polarization resistance R1, and polarization capacitance C1 is ≤5%, the polarization effect is highly reversible, there is no capacity regeneration phenomenon, and the statistical regularity of multimodal data is highly consistent.

[0172] Parameter setting logic:

[0173] Physical prior weights account for a low percentage (only 20%), while data-driven weights (β) are dominant. data Dominated (80%), fully leveraging the Group-Rational KAN network's feature mining capabilities for high-dimensional data, capturing subtle data correlations such as voltage fluctuations and current change rates, and achieving high-precision SOC estimation;

[0174] : Disable capacity regeneration suppression function, because there is no false capacity recovery phenomenon in the new battery stage, and avoid unnecessary constraints that will reduce the generalization ability of the model.

[0175] Parameter update mechanism: The parameters are fixed during this stage and do not need to be dynamically adjusted until N > 500 or SOH < 90%, which triggers the first switch to ensure the stability of the new battery stage estimate.

[0176] Transition mode (500 < N ≤ 1500 AND 70% ≤ SOH < 90%)

[0177] Key characteristics of the stage: The battery gradually enters the degradation period, slight sulfation begins to appear on the surface of the plates, the internal resistance slowly increases (R0 increases by about 5%-20%), the thermal hysteresis effect is enhanced, and the stability of data statistical regularity decreases, but the physical mechanism still maintains a strong consistency. It is a key transition period from data-driven dominance to physical-data fusion dominance.

[0178] Parameter setting logic: λ phy =0.2+(N−500) / 1000×0.5, .

[0179] λ phyLinear increment: The weight is gradually and smoothly increased from 0.2 to 0.7, and the proportion of physical prior weights transitions from 20% to 70%. Guided by the sensitivity of Thevenin model parameters, the weights of core physical features such as internal resistance and polarization capacitance are gradually strengthened to offset the estimation bias caused by the degradation of data regularity; at the same time, linear adjustment avoids model oscillation caused by sudden parameter changes.

[0180] The regeneration suppression function remains off because the rate of capacity regeneration at this stage is less than 5% and the magnitude is slight. Excessive constraints will affect the model's ability to adapt to normal capacity fluctuations.

[0181] Parameter update mechanism: λ is recalculated every 10 charge-discharge cycles based on the latest N and SOH values. phy This ensures that parameter adjustments are synchronized with the aging process.

[0182] Aging mode (N>1500 OR SOH<70%):

[0183] Key characteristics of the stage: The battery enters a deep degradation period, the plates are severely sulfated, the internal resistance increases significantly (R0 increase > 20%), the electrolyte concentration is uneven, capacity regeneration occurs frequently (capacity recovery in a single cycle can reach 5%-10%), physical parameters change frequently, and the pure data-driven model is susceptible to noise and false capacity signals, resulting in a significant increase in estimation bias.

[0184] Parameter setting logic: =0.7, .

[0185] =0.7: Physical prior weights dominate (70%), forcing the model to focus on physical characteristics strongly related to aging, such as ohmic internal resistance R0 and polarization resistance R1. The estimation results are stabilized by the terminal voltage constraint of the Thevenin model, avoiding the blind fitting of the black box model to false capacity signals and ensuring the physical rationality of the estimation.

[0186] : The capacity regeneration suppression function is activated, which punishes abnormal capacity recovery by using the mutual information correction term in the loss function, forces the aging trend of the implicit SOH in the SOC estimation, and corrects the SOC drift caused by capacity regeneration.

[0187] Parameter update mechanism: The parameters are fixed at (0.7, 0.2), but every 50 charge-discharge cycles, the Thevenin model parameters (R0, R1, C1) are fine-tuned based on the latest V / I static data (resting period), thereby updating the physical prior weights. This ensures the real-time effectiveness of physical constraints.

[0188] (3) Interaction logic between the module and other core modules

[0189] Interaction with the Physically Aware Attention Module: Dynamic Output Directly used as physical prior weights With data-driven weights β nata The fusion coefficient is used in the final feature weighting calculation. This allows for the switching of focus in feature extraction at different stages;

[0190] Interaction with the loss function: The weights, as mutual information constraint terms, are used in the total loss function. It acts on the model training process, and strengthens the inhibition of capacity regeneration during the aging phase;

[0191] Interaction with the online estimation module: During online inference, N and SOH are updated synchronously after each SOC / SOH estimation is completed, and stage discrimination and parameter calibration are triggered in real time to ensure that the model always maintains a dynamic match with the actual state of the battery.

[0192] The method provided by this invention is implemented according to the following steps to achieve a high-precision joint estimation of the state of charge (SOC) and state of health (SOH) of a lead-acid battery throughout its entire life cycle:

[0193] Step 1: Multimodal data acquisition and preprocessing

[0194] A battery testing and data acquisition platform was established to simultaneously collect the following multimodal signal data during battery charging and discharging operations:

[0195] Voltage and current signals, with a sampling frequency of 10Hz;

[0196] Battery surface temperature signal, sampled at a frequency of 5Hz;

[0197] Ultrasonic echo signal, with a sampling frequency of 1Hz.

[0198] The collected multi-source heterogeneous data undergoes temporal alignment and feature construction to generate a 780-dimensional feature matrix X. Subsequently, the feature matrix is ​​subjected to Z-score normalization, specifically as follows:

[0199]

[0200] In the formula, These are the mean vector and standard deviation vector of the features in the training set, respectively.

[0201] Step 2: Model Initialization and Configuration

[0202] A Group-Rational KAN network structure was constructed and divided into three physical groups according to physical properties: electrical feature group, thermal feature group, and ultrasonic / fusion feature group.

[0203] During the initial training phase, when the battery cycle count R=0, the physical constraint weights and regeneration inhibition coefficient are initialized according to the degradation phase adaptive switching rule. Regeneration inhibition coefficient .

[0204] Simultaneously, using the original physical quantity matrix (output A) output from the preprocessing stage, the parameters of the Thevenin equivalent circuit model are determined through offline parameter identification methods. This serves as the initial input to the physical awareness attention module.

[0205] Step 3: Model Training and Adaptive Optimization

[0206] The standardized feature data is input into the Group-Rational KAN network, and the following training process is performed.

[0207] 1. Input the preprocessed data into the network and perform forward propagation calculations. and .

[0208] 2. Calculate dynamic weights: using the attention module formula Calculate feature weighting

[0209] 3. Calculate the total loss: Update the total loss based on the current iteration count N using the segmentation rule. and Substitute into the formula Calculate the loss.

[0210] 4. Update network parameters (including KAN coefficients) using backpropagation with the Adam optimizer. (Generate the network weights) until the validation set error converges. Training stops if and only if the following two conditions are met:

[0211]

[0212] Step 4: Online estimation and parameter fine-tuning

[0213] During the model deployment phase, the battery management system (BMS) collects operational data in real time, which is then time-aligned and feature-built before being input into the trained model, outputting online estimation results of SOC and SOH in real time.

[0214] At the same time, a parameter fine-tuning mechanism is introduced to adapt to parameter drift during long-term battery operation, specifically:

[0215] Fine-tune the trigger conditions:

[0216] A parameter fine-tuning is triggered every 100 charge-discharge cycles completed, or when the cumulative energy throughput reaches a preset threshold.

[0217] Fine-tuning methods:

[0218] Using recently stored static operating condition data (resting phase), the Thevenin model parameters (R0, R1, C1) are updated using recursive least squares (RLS) with an introduced forgetting factor, and the physical sensitivity vector is recalculated accordingly. To ensure the timeliness and accuracy of physical prior constraints.

[0219] Example

[0220] (I) Example 1: Cross-scale joint estimation experiment of a lead-acid battery

[0221] 1. Experimental Platform and Testing Conditions

[0222] Experimental equipment: Ambient temperature control: A constant temperature chamber is used to control the ambient temperature (-25℃, 0℃, 25℃, 45℃, 55℃).

[0223] Charge / discharge equipment can be set to charge / discharge rates: 0.5C, 1C, 2C, 3C, 5C;

[0224] Sensor configuration: The sensors include a voltage sensor (accuracy ±0.1%FS), a current sensor (accuracy ±0.2%FS), an infrared thermal imager (temperature measurement accuracy ±0.5℃), and an ultrasonic probe (center frequency 5MHz).

[0225] 2. Data Acquisition and Sample Construction

[0226] Data acquisition: Cyclic aging tests were conducted on the batteries, and full-condition data were collected every 100 cycles until the SOH dropped to 60%; a total of 2000 valid samples were collected and divided into training and validation sets in a 7:3 ratio.

[0227] 3. Model Training and Parameter Setting

[0228] Model training: The proposed Group-Rational KAN network structure is used for training, with the following specific settings:

[0229] The Group-Rational KAN model is configured with 3 groups (G=3), 3 rational basis functions, and 256-dimensional feature layer output; initial physical constraint weights λ. phy =0.2, regeneration inhibition coefficient γ reg=0; Adam optimizer is used with a learning rate of 1e-4, batch size of 32, and 500 training epochs. During training, the degradation phase adaptive switching module dynamically adjusts the physical constraint weights of each batch in real time based on the number of iterations N of the input samples. and regeneration inhibition coefficient To adapt to the data characteristics at different aging stages, the validation set SOC error decreased to 1.2% at 100th epoch, to 0.9% at 200th epoch, and stabilized at 0.72% (SOC-MAE) and 1.85% (SOH-MAE) after 350th epoch, satisfying the convergence condition, and training stopped. The learning rate decayed to 5e-5 at 250th epoch and to 2.5e-5 at 400th epoch.

[0230] 4. Verification of experimental results

[0231] (1) Validation of the effectiveness of the physical cognitive attention mechanism

[0232] To verify whether the physically-informed attention module proposed in this invention truly learns electrochemical laws, we conducted a visual analysis of the attention weights at different aging stages, such as... Figure 3 As shown:

[0233] New battery stage ( Figure 3 (Left bar chart): The model pays less attention to the ohmic internal resistance R0 (about 20%), and at this time it mainly relies on data-driven features.

[0234] During the aging stage ( Figure 3 (Right-side bar chart): As SOH decreases, the model automatically adjusts its strategy, significantly increasing the weight of the ohmic internal resistance R0 to 45%, while the weight of the polarization capacitor C1 remains at a high level.

[0235] Analysis conclusion: Figure 3 This intuitively demonstrates that the model is not a "black box," but rather can automatically focus on the characteristic channels related to internal resistance based on physical mechanisms (aging leads to increased internal resistance). This is the core reason why the present invention can still maintain high accuracy in the SOH<70% stage.

[0236] (2) Error analysis under extreme working conditions and aging stage

[0237] The model of this invention is compared with the traditional Extended Kalman Filter (EKF) and the original KAN model. The experimental results are as follows: Figure 4 As shown:

[0238] Low temperature and high rate operation (such as) Figure 4 (a) and Figure 4 (as shown in (b))

[0239] Under the low temperature of -25℃ and 1C discharge conditions ( Figure 4 In (a), the traditional EKF model, due to its fixed parameters, cannot adapt to low-temperature characteristics, resulting in a MAE error as high as 5.2%; while the model of this invention, guided by physical parameters, stably controls the error at 0.98%.

[0240] Under 5C high-rate charging conditions ( Figure 4 In (b), the model of this invention also exhibits excellent robustness, with a MAE of only 2.3%, which is significantly better than the original KAN model's 3.5%.

[0241] Capacity regeneration inhibition during aging (e.g.) Figure 4 As shown in (c):

[0242] During the aging stage with SOH=65% ( Figure 4 In the middle (c), the traditional model is greatly affected by the "capacity regeneration" phenomenon, and the prediction curve shows a false capacity rebound, resulting in a bias of up to 4.2%.

[0243] The model of this invention benefits from the adaptive switching module of the degradation stage, which automatically activates regeneration suppression when an anomaly is detected, resulting in a smooth prediction curve that closely matches the true value, and reducing the SOH estimation error to 1.9%.

[0244] Figure 4 The comparison curves fully demonstrate that the adaptability of the present invention throughout the entire life cycle and in extreme environments is significantly better than that of the prior art.

[0245] As can be seen from the above embodiments, the cross-scale joint estimation method proposed in this invention has good stability and robustness under different environmental conditions and battery aging stages. It can effectively overcome the impact of extreme conditions and capacity regeneration on the accuracy of state estimation, and its implementation effect is significantly better than the existing technology.

[0246] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0247] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0248] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0249] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0250] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A method of cross-scale joint estimation of a valve regulated lead acid battery, characterized by, Comprising the following steps: S1, multi-modal data acquisition and preprocessing: synchronously acquiring voltage, current, temperature and ultrasonic signals during the operation of the lead-acid battery; performing time-space alignment and reconstruction on signals of different sampling frequencies to construct a high-dimensional feature tensor containing electrical and thermal time sequence characteristics and acoustic statistical characteristics; standardizing the high-dimensional feature tensor to obtain data-driven channel input, and taking the aligned original voltage and current signals as physical mechanism channel input; S2, physical informed feature extraction: inputting the standardized high-dimensional feature tensor into the Group-Rational KAN network; the Group-Rational KAN network divides the input features into three orthogonal feature groups according to electrical, thermal and structural evolution physical properties, and uses learnable rational fractions for non-linear mapping within each group; Based on the equivalent circuit model parameters identified from the physical mechanism channel, the physical prior weight is calculated; the features extracted by the Group-Rational KAN network are dynamically weighted and fused by combining the physical prior weight and the data-driven weight, and the weighted features are obtained; S3, dual-branch joint output and adaptive adjustment: inputting the weighted features into the SOC estimation branch and the SOH estimation branch respectively, and jointly outputting the state of charge (SOC) estimation value and the state of health (SOH) estimation value; based on the cumulative cycle number and the state of health (SOH) of the battery, the physical constraint weight and the capacity regeneration inhibition coefficient are dynamically adjusted through the degradation stage adaptive switching module; the physical constraint weight is used to balance the proportion of the physical constraint term and the data-driven term in the loss function, and the capacity regeneration inhibition coefficient is used to control the punishment intensity of the mutual information constraint term on the correlation between the SOC and SOH estimation values.

2. A method of cross-scale joint estimation of a valve regulated lead acid battery according to claim 1, wherein, In step S1, the time-space alignment and reconstruction specifically includes: Taking the sampling time of the voltage signal as the unified time reference; For the current signal with the same frequency as the voltage, direct mapping is used; The temperature signal is reconstructed by linear interpolation; The ultrasonic signal is reconstructed by the zero-order hold strategy.

3. A method of cross-scale joint estimation of a valve regulated lead acid battery according to claim 1, wherein In step S1, the high-dimensional feature tensor is constructed as follows: the voltage, current and temperature signals after time sequence alignment and their derived power, impedance and differential quantities form the electrical and thermal time sequence characteristic subspace; The ultrasonic signal is divided into subbands in the frequency domain, and the statistical characteristics of each subband are extracted to form the acoustic statistical characteristic subspace; the electrical and thermal time sequence characteristic subspace and the acoustic statistical characteristic subspace are spliced to obtain the high-dimensional feature tensor.

4. The method of claim 1, wherein, In step S2, the non-linear mapping in each feature group in the Group-Rational KAN network is realized by rational fraction nodes, and the calculation formula of the rational fraction node is: In the formula, k is a physical grouping index; i is a neuron index within a grouping; is an input feature; M is the input feature dimension of the k-th group; is a non-linear gain for fitting the feature, is a group-specific learnable coefficient; overfitting is avoided by introducing pole constraints, is a group-specific learnable coefficient.

5. A method of cross-scale joint estimation of a valve regulated lead acid battery according to claim 4, wherein, In the Group-Rational KAN network, the denominator polynomial coefficients of all rational fraction nodes in the feature group corresponding to the temperature field are constrained to be shared.

6. The method of claim 1, wherein, In step S2, the calculation of the physical prior weight specifically includes: Based on the voltage and current signals input from the physical mechanism channel, the ohmic resistance R0, the polarization resistance R1 and the polarization capacitance C1 are identified by the equivalent circuit model; Sensitivities of each circuit parameter to open circuit voltage (OCV) are calculated; The sensitivities are extended to high dimensional feature space and normalized to obtain physical prior weights.

7. The method of claim 1, wherein, In step S2, the dynamic weighted fusion is realized by the following formula: Based on weights Element-wise weighting of Group-Rational KAN output features: wherein, is a physical prior weight, is a data-driven weight generated by a data-driven attention mechanism, is a physical constraint weight, is a feature extracted by a Group-Rational KAN network, denotes element-wise multiplication, is a weighted feature.

8. The method of claim 1, wherein, In step S3, the total loss function of the model training is L = L1 + L2 + L3 wherein, is a mean square error loss for SOC and SOH estimates, is a physical constraint loss based on an equivalent circuit model terminal voltage equation, is a mutual information between SOC and SOH estimates, is a capacity regeneration suppression coefficient.

9. The method of claim 1, wherein, In step S3, the degradation stage adaptive switching module dynamically adjusts the physical constraint weight according to the following rule and the capacity regeneration inhibition coefficient : When the cumulative cycle number N is ≤ 500 and the SOH is ≥ 90%, it is determined that it is a new battery stage, and the following is set = 0.2, = 0; When 500 < N ≤ 1500 and 70% ≤ SOH < 90%, it is determined to be a transition stage, and the setting is = 0.2 + (N - 500) / 1000 x 0.5, = 0; When N > 1500 or SOH < 70%, it is determined that the aging stage, set = 0.7, = 0.

2.

10. A system for cross-scale joint estimation of a valve regulated lead acid battery, comprising: The computer program instructions can be executed by the processor to implement the method according to any one of claims 1-9. The computer program instructions can be executed by the processor to implement the method according to any one of claims 1-9.

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