Energy storage battery health state monitoring management method and system

Abstract

The invention relates to an energy storage battery health state monitoring management method and system. The method comprises the following steps: constructing a multi-dimensional physical characteristic tensor according to charging and discharging data of a battery; establishing a KAN network fused with a physical model, inputting the multi-dimensional physical feature tensor into the KAN network for joint pre-training, and updating spline coefficients in the KAN network and physical parameters in the physical model; performing first-order Taylor expansion on the spline coefficient based on a total loss function of joint pre-training, and calculating the physical sensitivity of each connection in the KAN; performing structure pruning on the KAN network according to the physical sensitivity, and screening effective input features in the multi-dimensional physical feature tensor according to a structure pruning result; subspace fine tuning is carried out on the KAN network after structure pruning, a sparse neural network model used for battery health state estimation is obtained, and the neural network model training method and the battery management system achieve deployment of the neural network model containing physical constraints in a BMS hardware resource limited scene.

Description

Technical Field

[0001] This application relates to the field of battery monitoring technology, specifically to a method and system for monitoring and managing the state of energy storage batteries. Background Technology

[0002] Lithium-ion batteries, due to their high energy density and long cycle life, are widely used in electric vehicles, energy storage power stations, and portable electronic devices. During long-term use, factors such as temperature fluctuations, changes in charge / discharge rates, and electrochemical side reactions cause irreversible capacity decay and impedance growth within the battery, leading to a gradual reduction in usable capacity. Accurately estimating the battery's State of Health (SOH) is crucial for ensuring the safe operation of the power system and for developing reasonable maintenance strategies. Currently, battery health estimation methods can be broadly categorized into two types: methods based on equivalent circuit models or electrochemical mechanism models, and data-driven methods based on machine learning. While mechanism-based methods possess clear physical interpretation capabilities, the online identification of model parameters is computationally complex and lacks real-time performance. Data-driven methods achieve good prediction accuracy due to their ability to fit high-dimensional nonlinear relationships; however, these methods lack explicit constraints on the physical laws of battery degradation during training, making them prone to producing predictions that violate electrochemical principles when faced with noise interference or biased training data distribution.

[0003] To balance physical interpretability and data fitting capabilities, researchers have recently attempted to incorporate growth models describing the saturation characteristics of population growth into battery degradation analysis. These models characterize the S-shaped saturation decay trend of battery capacity with cycle count, and the model equations are used as soft constraints in the training process of neural networks, constructing a hybrid prediction framework that combines physical meaning with nonlinear modeling capabilities. Furthermore, novel neural network structures based on the Kolmogorov-Arnold representation theorem, by configuring learnable spline functions at the network edges instead of traditional fixed activation functions, have demonstrated higher function approximation efficiency, providing a new network carrier for the aforementioned hybrid framework. However, these physically constrained network models typically maintain a fully connected, dense topology during construction, with the number of parameters often reaching tens of thousands or even higher. For embedded battery management system (BMS) chips with extremely limited computing power and storage resources, directly deploying such dense models presents practical difficulties.

[0004] To address the conflict between model size and hardware resources, an intuitive approach is to prune the trained network structure to reduce the number of parameters. However, existing network pruning methods still face several practical difficulties when applied to hybrid prediction models with physical constraints. Firstly, after significant parameter pruning, the model's prediction curve often exhibits abnormal fluctuations inconsistent with the battery's electrochemical aging trend. For example, it may show non-physical phenomena such as capacity recovery in the later stages of degradation, violating the monotonic decay law. This problem becomes more pronounced with increasing compression ratio, severely weakening the reliability of the model's output. Secondly, even after simplifying the internal network structure, existing solutions still perform complete acquisition, transmission, and preprocessing of data from all original sensor channels during system operation. This results in unnecessary computational and storage overhead for the BMS front-end hardware in data throughput, analog-to-digital conversion, and feature calculation, hindering the transfer of the benefits of lightweight design to the overall system level. These shortcomings make the engineering deployment of physically constrained neural network models on resource-limited embedded battery management platforms still challenging. Summary of the Invention

[0005] In view of this, embodiments of this application provide a neural network model training method and a battery management system for monitoring battery health status, aiming to solve the problems that neural network models with physical constraints are difficult to deploy in BMS hardware resource-constrained scenarios due to their large model size, and that conventional pruning strategies easily destroy the physical consistency of prediction curves.

[0006] This application proposes a method for monitoring and managing the state of energy storage batteries, characterized by the following steps: S1: Construct a multidimensional physical feature tensor based on the battery's charge and discharge data; S2: Establish a KAN network that integrates the physical model, input the multidimensional physical feature tensor into the KAN network for joint pre-training, and synchronously update the spline coefficients in the KAN network and the physical parameters in the physical model; the physical model is a Verhulst model used to describe the battery capacity decay characteristics, and its expression is: ; in, t This refers to the number of charge / discharge cycles. u ( t )for t Battery capacity loss rate at any given time For capacity loss rate, k The decay rate constant is M For the maximum theoretical capacity loss, k and M Embedded in the network as learnable physical parameters.

[0007] S3: Perform a first-order Taylor expansion on the spline coefficients based on the total loss function of joint pre-training, and calculate the physical sensitivity of each connection in the KAN network; S4: Perform structural pruning on the KAN network based on the physical sensitivity, and filter the effective input features in the multidimensional physical feature tensor based on the structural pruning results; S5: Subspace fine-tuning is performed on the KAN network after structural pruning to obtain a sparse neural network model for battery health state estimation. The model outputs a high-precision SOH estimate, and simultaneously outputs the aging rate constant and maximum capacity loss parameter, providing additional physical diagnostic basis for the quality analysis of the battery's entire life cycle.

[0008] The total loss function includes data fitting loss and physical residual loss. The data fitting loss is the mean square error between the predicted value of the KAN network and the actual battery health state value. The physical residual loss is constructed based on the deviation between the Verhulst model and the predicted output of the KAN network. The total loss function L for: ; in, L For the total loss function, The mean square error between the network-predicted value and the actual SOH value. For physical residual loss, The weighting coefficient for the physical residual loss. D The sample batch size for the training data. m For the index of sample data, For the first m The true volume loss rate of each sample Let m be the capacity loss rate predicted by the network for the m-th sample. This is the physical residual function.

[0009] Furthermore, the construction of a multidimensional physical feature tensor based on the battery's charge and discharge data includes: extracting at least two of the following from the charge and discharge data: number of cycles, ohmic internal resistance, constant current charging time, constant voltage charging time, maximum temperature during discharge, and average voltage during discharge; and normalizing the extracted features to form the multidimensional physical feature tensor.

[0010] Furthermore, the connections between adjacent layer nodes in the KAN network employ parameterized B-spline basis functions; the KAN network's... l The first layer j The node is passed to the first node via the join function. l +1 floor i The output of each node is represented as: ; in, For the first l The first layer j The node and the first l+ 1st floor i The connection function between nodes For the first l The first layer j The output value of each node, N This represents the total number of spline basis functions in the connection function. n For the index of the B-spline basis functions, B n For the first in the join function n basis functions For the first in the join function n Learnable spline coefficients of each basis function.

[0011] Furthermore, the physical sensitivity is calculated as follows: ; in, For the first in the join function n The learnable spline coefficients of the basis functions, For the total loss function, This represents the gradient of the total loss function with respect to the spline coefficients. For the first l Layer j The node and the first l +1 floor i Physical sensitivity score of connections between nodes.

[0012] Furthermore, the structural pruning of the KAN network based on the physical sensitivity includes: Calculate the mean of the physical sensitivity scores for all connections in the current layer; The pruning threshold is determined by multiplying the mean value by the pruning intensity adjustment parameter; Generate a binary mask matrix, set the mask corresponding to the connection whose physical sensitivity score is lower than the pruning threshold to zero, and cut off the corresponding signal transmission path.

[0013] Furthermore, the step of filtering the effective input features in the multidimensional physical feature tensor based on the structural pruning results includes: checking the output connection status of each feature node in the input layer of the KAN network; in response to detecting that all output connections of any feature node have been pruned, determining the input feature corresponding to any feature node as a physically irrelevant feature and removing it.

[0014] Furthermore, the subspace fine-tuning of the structurally pruned KAN network includes: freezing the binary mask matrix generated by structural pruning, and fine-tuning the retained spline coefficients and physical parameters in the physical model under a fixed sparse topology.

[0015] A battery management system was also proposed, including a data acquisition module, a central processing module, and a storage module; The data acquisition module is used to collect battery voltage, current and temperature data; The storage module contains a neural network model trained using the above method. The central processing module is used to construct a multidimensional physical feature tensor based on the data collected by the data acquisition module, and to call the neural network model to monitor the battery health status.

[0016] Compared with the prior art, the present invention has the following beneficial effects: 1) This invention employs physical sensitivity pruning based on the first-order Taylor expansion of total loss. This mechanism effectively smooths measurement noise, ensures that the SOH prediction curve strictly follows the monotonic decay trend of electrochemical aging, avoids non-physical phenomena such as capacity recovery, significantly improves the reliability of the model, thereby eliminating non-physical prediction trajectories and enhancing robustness.

[0017] 2) This invention utilizes pruning results to filter input features in reverse. By automatically identifying nodes in the network input layer where all output connections have been pruned, redundant feature channels that do not contribute to physical laws are determined and shut down. This filtering mechanism reduces the computational load and storage consumption of the BMS hardware data acquisition and preprocessing stages, thereby achieving physical-oriented automatic feature filtering and reducing hardware computing power overhead.

[0018] 3) Through physical-guided sparsification, this invention can compress the number of parameters of the original KAN network by 70%~80% while maintaining stable prediction accuracy, significantly reducing the hardware cost of BMS, thereby achieving lightweight implementation and adapting to BMS hardware resource constraints.

[0019] 4) Unlike the "black box" prediction of traditional neural networks, this invention deeply integrates the Verhulst model with the KAN network. The trained model can not only output high-precision SOH estimates, but also simultaneously output aging rate constants and maximum capacity loss parameters with clear physical meanings, providing additional physical diagnostic basis for the quality analysis of the entire battery life cycle, thereby achieving strong interpretability and physical parameter identification capabilities. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1 This is a schematic flowchart of a neural network model training method for battery health status monitoring provided in an embodiment of this application; Figure 2 This is a flowchart illustrating a neural network model training method for battery health status monitoring, provided in another embodiment of this application. Figure 3 This is a schematic diagram of the PINN-KAN network model architecture and joint pre-training principle provided in an embodiment of this application; Figure 4 This is a comparison chart of the lightweighting effect of a network model provided in one embodiment of this application; Figure 5 This is a comparison chart of battery SOH prediction results provided in an embodiment of this application; Figure 6 This is a dynamic identification diagram of physical parameters provided in an embodiment of this application; Figure 7 This is a comparison chart of MAE under different pruning rates provided in an embodiment of this application; Figure 8 This is a schematic diagram of the hardware architecture of a battery management system provided in an embodiment of this application. Detailed Implementation

[0022] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of this application with unnecessary detail.

[0023] like Figure 1 As shown, the neural network model training method for battery health status monitoring provided in this application includes the following steps S101 to S106: Step S101: Construct a multidimensional physical feature tensor based on the battery's charge and discharge data; Step S102: Establish a KAN network that integrates the physical model, input the multidimensional physical feature tensor into the KAN network for joint pre-training, and synchronously update the spline coefficients in the KAN network and the physical parameters in the physical model. Step S103: Perform a first-order Taylor expansion on the spline coefficients based on the total loss function of the joint pre-training, and calculate the physical sensitivity of each connection in the KAN network; Step S104: Perform structural pruning on the KAN network based on the physical sensitivity, and filter the effective input features in the multidimensional physical feature tensor based on the structural pruning results; Step S105: Subspace fine-tuning is performed on the KAN network after structural pruning to obtain a sparse neural network model for battery health state estimation.

[0024] In applications, constructing a multidimensional physical feature tensor based on battery charge and discharge data involves the processor segmenting and cleaning historical charge and discharge curves recorded by the battery management system, removing abnormal data points caused by sensor malfunctions or communication interruptions. Then, physical quantities reflecting the battery's internal electrochemical aging state are extracted from the charge and discharge curves of each complete cycle, such as ohmic internal resistance, constant current charging time, constant voltage charging time, peak temperature during discharge, and average voltage. These features encompass battery degradation information in different dimensions: increased internal resistance reflects thickening of the solid electrolyte interface film and loss of active materials; changes in charging time reflect reduction in usable capacity; and temperature characteristics indirectly reflect the activity level of internal side reactions. After normalizing each feature, a multidimensional vector is formed, which is then stacked row by row to form a feature tensor, serving as the signal source for each node in the subsequent KAN network input layer.

[0025] In applications, establishing a KAN network that integrates the physical model and performing joint pre-training refers to initializing a Kolmogorov-Arnold (KAN) network in the processor's memory. The key difference between this network and the traditional Multilayer Perceptron (MLP) lies in the fact that the connections between layers are not simply scalar weights multiplied by a fixed activation function, but rather learnable connection functions composed of parameterized B-spline basis functions. The output of each connection equals a weighted sum of a set of B-spline basis functions, and the learnable spline coefficients determine the shape of the connection function. The physical model is embedded in the network training process by incorporating the differential equation describing the battery capacity decay dynamics as an additional constraint into the loss function. This ensures that the network, while fitting experimental data, also satisfies the pre-defined physical evolution equations. During joint pre-training, the backpropagation algorithm simultaneously calculates the gradient of the loss function with respect to the spline coefficients and physical parameters in each iteration, and updates both synchronously using gradient descent. This allows the network to both initially fit the data distribution and identify a set of model parameter values ​​that conform to physical laws after the first stage of training.

[0026] In application, calculating the physical sensitivity by performing a first-order Taylor expansion of the spline coefficients based on the total loss function of joint pre-training refers to using the first-order Taylor approximation principle from calculus to measure the impact of removing each spline connection in the network on the total loss function. The total loss function includes both data fitting error and physical residual terms; therefore, the calculated sensitivity score comprehensively reflects the contribution of the connection to maintaining prediction accuracy and satisfying physical constraints. Specifically, treating the spline coefficients as variables to be evaluated, when they change from their current value to zero (i.e., the connection is cut), the change in the loss function can be approximated by a first-order Taylor expansion as the product of the coefficient magnitude and the corresponding gradient. This calculation can be completed by performing one forward and backward propagation after pre-training and when the network parameters have converged, resulting in low computational overhead. A higher sensitivity score indicates that the connection is more important for maintaining the physical consistency of the model and the accuracy of data fitting.

[0027] In application, structural pruning and effective input feature selection of the KAN network based on physical sensitivity involves setting a dynamic threshold related to the current network layer's sensitivity statistical distribution, based on the sensitivity score calculated in the previous step. Spline connections with sensitivity scores below this threshold are removed from the network topology. This removal is achieved by setting the weight matrix of the corresponding connection to zero and generating a binary mask. Connections marked as zero by the mask are no longer involved in forward computation during subsequent inference, thus reducing the number of multiply-accumulate operations and parameter storage. After pruning the internal connections of the network, the output connection status of each feature node in the input layer is further checked: if all output connections of a feature node have been pruned, it means that the signal of that feature cannot be transmitted to subsequent layers of the network, i.e., the feature does not significantly contribute to SOH prediction in a physical sense. It can be identified as a redundant feature and removed. In actual deployment, the corresponding sensor acquisition channel is shut down or the calculation process for that feature is skipped.

[0028] In applications, subspace fine-tuning of the pruned KAN network involves freezing the binary mask matrix generated in the previous step, ensuring that the pruned connections remain zero throughout the fine-tuning phase. Gradient updates are only performed on the active spline coefficients and physical model parameters retained in the network. The purpose of this operation is to allow the sparsified network to readjust to the data distribution within a fixed topology, compensating for potential accuracy loss due to the removal of numerous connections. After fine-tuning, the resulting sparse neural network model has a significantly smaller parameter size and lower computational cost compared to the original dense model. It can be directly converted into lookup table or sparse matrix instruction formats and burned into the embedded storage unit of the BMS controller for online inference.

[0029] Specifically, such as Figure 2 As shown, the complete workflow of this solution is as follows: First, the BMS data acquisition module acquires raw data on battery charge / discharge voltage, current, and temperature under multiple cycles. The central processing module then segments, cleans, and extracts features from the data to obtain candidate feature tensors containing several physical quantity dimensions. Next, the processor initializes the KAN network and embeds the physical model equations as residual constraints into the loss function, performing a joint pre-training phase to ensure synchronous convergence of the network spline coefficients and physical parameters. After pre-training, a first-order Taylor expansion is performed on all spline coefficients using the total loss function to calculate the physical sensitivity score for each connection. A binary mask is generated based on the comparison between this score and a dynamic threshold, pruning low-sensitivity connections and identifying redundant feature channels at the input. Finally, under the constraint of a fixed mask, the remaining parameters are fine-tuned in the subspace, outputting a sparse network model deployable to an embedded platform. The entire process forms a closed loop from data input to model output. The training phase is completed on a host computer or workstation, and the inference phase after deployment only requires sparse matrix operations on the BMS controller to achieve real-time estimation of SOH.

[0030] Feature extraction from the multidimensional physical feature tensor can employ charging curve fitting to extract internal resistance and charging time features during constant current-constant voltage charging, or incremental capacity analysis (ICA) to extract degradation features from the peak displacement of the dQ / dV curve. The B-spline basis functions in the KAN network can use cubic uniform B-splines or non-uniform rational B-splines (NURBS) to achieve more flexible fitting capabilities for complex functions. The optimizer in the joint pre-training can use the Adam optimizer to balance convergence speed and stability, or an SGD optimizer with cosine annealing to obtain a flatter loss surface convergence region.

[0031] This embodiment embeds the physical model into the loss function and uses the sensitivity of the first-order Taylor expansion as the pruning criterion. This allows the network to strictly adhere to the monotonic decay law of electrochemical aging even after large-scale parameter compression, eliminating non-physical prediction phenomena such as capacity recovery and significantly improving the model's robustness and reliability in noisy environments. Through a physical sensitivity-driven automatic input feature filtering mechanism, redundant features that do not contribute to prediction can be identified and eliminated at the model level, reducing the data acquisition and preprocessing burden on the BMS front-end data link. This reduces the system's hardware cost and power consumption across the entire link from the sensor end to the algorithm end. Furthermore, the physical parameters (such as the decay rate constant and maximum capacity loss) identified synchronously during joint pre-training endow the model with additional physical diagnostic capabilities, which can be used to analyze the differences in aging rates between different batches of batteries, providing quantitative basis for the full lifecycle management of battery manufacturers and operators.

[0032] In one embodiment, constructing a multidimensional physical feature tensor based on the battery's charge and discharge data includes: extracting at least two of the following from the charge and discharge data: number of cycles, ohmic internal resistance, constant current charging time, constant voltage charging time, maximum temperature during discharge, and average voltage during discharge; and normalizing the extracted features to form the multidimensional physical feature tensor.

[0033] In applications, the above six feature dimensions are extracted from charge / discharge data. Among them, the number of cycles is... t Normalized current charge / discharge cycle count of the battery; Ohmic internal resistance. R s Ohmic internal resistance value extracted based on current pulse response method or charging curve fitting; constant current charging time. I t The duration of constant current charging; the duration of constant voltage charging. V t The duration of constant voltage charging; maximum temperature. T Peak battery surface temperature during a single discharge cycle; average voltage. V The average voltage during a single discharge process. These characteristics, after normalization, are used as the original node signals for the input layer of the KAN network.

[0034] Specifically, in the actual operation of this solution, the processor reads the voltage-current-temperature time series of each complete charge-discharge cycle from the BMS data memory according to the cycle index. First, it divides the data into constant current charging, constant voltage charging, and discharging segments according to preset cutoff conditions (such as current dropping to a set threshold, voltage reaching an upper or lower limit). Then, it calculates the corresponding characteristic values ​​in each segment. Taking ohmic internal resistance as an example, the ratio of the voltage change to the current change at the moment of discharge start can be obtained. Taking constant current charging duration as an example, the time difference between the start and end of the CC stage can be recorded. Among the six characteristic dimensions, at least two can be selected and combined according to the monitored battery type and available sensor configuration in actual use. For example, for a lightweight BMS equipped only with voltage and current sensors but lacking a temperature sensor, only the four-dimensional features of cycle number, ohmic internal resistance, constant current charging duration, and constant voltage charging duration can be selected to construct a tensor.

[0035] This embodiment, by clearly defining six candidate physical features and their extraction methods, ensures that the input data comprehensively covers the electrochemical, thermal, and kinetic degradation information of the battery from different dimensions, providing rich physical prior knowledge for the subsequent multi-angle nonlinear fitting of the KAN network. Simultaneously, normalization eliminates the differences in the dimensions and orders of magnitude of different features, effectively improving the uniformity of parameter updates during gradient descent, accelerating the convergence speed of the joint pre-training stage, and reducing the risk of training instability.

[0036] In one embodiment, the connections between adjacent layer nodes in the KAN network employ parameterized B-spline basis functions; the KAN network's... l The first layer j The node is passed to the first node via the join function. l +1 floor i The output of each node is represented as: ; in, For the first l The first layer j The node and the first l+ 1st floor i The connection function between nodes For the first l The first layer j The output value of each node, N This represents the total number of spline basis functions in the connection function. n For the index of the B-spline basis functions, B n For the first in the join function n basis functions For the first in the join function n Learnable spline coefficients of each basis function.

[0037] In the application, a PINN-KAN network is initialized in memory. The network adopts the KAN architecture, and the connections between layers do not use scalar weights, but rather parameterized B-spline basis functions. The essence of using B-spline basis functions as inter-layer connections in the KAN network is that, in traditional neural networks, information transfer between adjacent nodes is accomplished by multiplying a scalar weight by the input value and then mapping it through a fixed-shape activation function. The KAN network replaces this process with a single, learnable spline curve. B-spline basis functions are piecewise polynomial functions defined on equally or non-equally spaced node vectors in numerical analysis, possessing favorable mathematical properties such as local support, non-negativity, and unity factorization. N B-spline basis functions are configured on each connection in the KAN network, and each basis function is multiplied by its corresponding learnable coefficient. The summation then constitutes the output value of the connection. The learning process of spline coefficients is equivalent to searching for an optimal nonlinear mapping curve in the function space, which fits the training data as closely as possible to the physical constraints. Compared to the fixed ReLU or Sigmoid activation functions of traditional MLPs, B-spline functions can approximate the target function with the same accuracy with less network depth. This is the theoretical basis for the superior function approximation efficiency of the KAN architecture compared to MLPs.

[0038] Specifically, such as Figure 3As shown, in this scheme, a three-layer KAN network (input layer - hidden layer - output layer) is used as an example. The input layer contains d nodes corresponding to d-dimensional physical features, the hidden layer contains h nodes, and the output layer contains one node that outputs the predicted value of SOH. There are d×h connections between the input layer and the hidden layer, and N cubic B-spline basis functions are placed on each connection, corresponding to N learnable coefficients. l Output value of the j-th node in layer The values ​​are fed into these N basis functions for evaluation. Each basis function value is multiplied by its corresponding coefficient and then summed to obtain the value passed to the Nth basis function. l +1 floor i The contribution of each node. All nodes in this layer. j The contributions from each node are summed, and after possible biasing or normalization, the result is the sum of the contributions from the first node. l +1 floor i Activation value of each node During network training, all spline coefficients on all connections together constitute the set of parameters to be optimized. These parameters are updated step by step through the backpropagation gradient of the loss function until the entire network converges.

[0039] This embodiment replaces the traditional combination of scalar weights and fixed activation functions with B-spline basis functions, enabling each connection in the network to possess flexible nonlinear mapping capabilities, achieving higher-precision function approximation at the same network depth. Furthermore, since the behavior of each connection is entirely determined by its spline coefficients, subsequent physical sensitivity calculations can be performed directly on the spline coefficients, resulting in finer granularity and more accurate evaluation. This provides a naturally suited network infrastructure for achieving efficient and physically consistent structural pruning.

[0040] In one embodiment, the physical model is the Verhulst model used to describe the battery capacity degradation characteristics, and its expression is: ; in, t This refers to the number of charge / discharge cycles. u ( t )for t Battery capacity loss rate at any given time For capacity loss rate, k The decay rate constant is M For the maximum theoretical capacity loss, k and M Embedded in the network as learnable physical parameters.

[0041] In applications, parameters k Controlling the rate of decay, M The upper bound of the controlled capacity loss, along with the other factor, jointly determines the shape of the decay curve. In this scheme, k andM Instead of being a pre-given constant, it is embedded in the network as a learnable parameter. During training, its optimal value is automatically identified through gradient descent, enabling the model to adaptively fit the specific degradation dynamics of batteries of different models and operating conditions.

[0042] Specifically, the Verhulst model is introduced into the KAN network training process by: defining u(t) as... u ( t )=1-SOH( t Substituting this into the Verhulst equation, where SOH( t The result is given by the forward output of the KAN network. This is obtained by automatically differentiating the network output with respect to the input variable t. Thus, in each training iteration, the network's forward propagation simultaneously generates the SOH prediction and the corresponding capacity loss rate prediction. Substituting these two into the Verhulst equation and calculating the residual gives the physical residual term. The smaller this residual term, the better the network prediction conforms to the decay dynamics described by the Verhulst model. Physical parameters k and M During training, these parameters participate in gradient calculation. As the iteration progresses, their values ​​gradually converge from random initial values ​​to stable values ​​that reflect the true aging characteristics of the battery. After training is completed, these two parameters have clear physical interpretation meaning.

[0043] This embodiment uses the Verhulst model as a physical constraint, which provides the network with prior knowledge reflecting the S-shaped saturation characteristics of battery aging without excessively restricting the network's fitting degrees of freedom. The Verhulst equation only constrains the macroscopic decay trend of the output curve, while the microscopic data fitting is still undertaken by the spline function of the KAN network. k and M Embedded into the network as learnable parameters, the model generates aging kinetic parameters with physical interpretations while performing SOH prediction. These parameters can serve as auxiliary diagnostic indicators for judging batch quality differences and estimating remaining lifespan in battery health management.

[0044] In one embodiment, the total loss function includes a data fitting loss and a physical residual loss. The data fitting loss is the mean squared error between the predicted values ​​of the KAN network and the actual battery health state values. The physical residual loss is constructed based on the deviation between the Verhulst model and the predicted output of the KAN network. The total loss function L for: ; in, L For the total loss function, The mean square error between the network-predicted value and the actual SOH value. For physical residual loss, The weighting coefficient for the physical residual loss. D The sample batch size for the training data. m For the index of sample data, For the first m The true volume loss rate of each sample For the network to the first m The predicted capacity loss rate for each sample. This is the physical residual function.

[0045] In the application, each training batch contains D There are 1 sampling point, and each sampling point corresponds to one loop number. t and its actual capacity loss rate During forward propagation, the network receives feature tensors as input and outputs... D Predicted capacity loss rate At the same time, the automatic differential pair is used to output about t Differentiation yields D Each predicted capacity loss rate. Then, calculate... and Multiply the latter by the weighting factor Later and Add them together to get the total loss L The optimizer is based on L For all learnable parameters (including spline coefficients and physical parameters) k and M The gradient is calculated and parameters are updated. This process is repeated across multiple training epochs until the total loss converges to a preset threshold or the maximum number of training epochs is reached. The total loss function includes gradient information for both data and physics terms, which forms the basis for subsequent physics sensitivity calculations to comprehensively evaluate the contribution of data fit and physics consistency.

[0046] This embodiment injects prior physical knowledge of battery degradation into the network training process by explicitly introducing Verhulst model constraint terms into the total loss function. This effectively avoids the risk of non-physical predictions in sparse data regions caused by the lack of physical constraints in purely data-driven methods. The dual-objective loss structure provides a gradient field containing both data fitting and physical consistency information for subsequent physical sensitivity calculations, enabling pruning operations to accurately distinguish between critical connections that contribute significantly to the physical boundary and redundant connections that only serve noise fitting.

[0047] In one embodiment, the physical sensitivity is calculated as follows: ; in, For the first in the join function n The learnable spline coefficients of the basis functions, For the total loss function, This represents the gradient of the total loss function with respect to the spline coefficients. For the first l Layer j The node and the first l +1 floor i Physical sensitivity score of connections between nodes.

[0048] In applications, physical sensitivity The computation essentially uses the first-order Taylor approximation to evaluate whether a certain connection can be completely removed (i.e., all connections on it are removed). N How much will the total loss function increase after setting all spline coefficients to zero? N The physical sensitivity score of the connection is obtained by summing the contributions of each basis function. The sensitivity score incorporates additional gradient information: even if the absolute value of a coefficient is small, if its corresponding gradient is large (i.e., the loss function is extremely sensitive in that direction), its sensitivity score will still be high, and the connection will be preserved. This mechanism effectively avoids the accidental deletion of key small coefficients that maintain the physical boundary conditions of the Verhulst model, ensuring the physical consistency of the network's prediction curves after pruning.

[0049] Specifically, after pre-training converges, the processor performs a complete forward and backward propagation on the entire training set and records the total loss function. L For each spline coefficient in the network gradient value For the connection of the first l Layer j The node and the first l +1 floor i The connection function of each node has a total of N Each spline coefficient is calculated individually. And on n From 1 to N Summing yields the physical sensitivity of the connection. After traversing all connections in all layers of the network, a complete sensitivity score table is obtained, which will serve as the sole quantitative basis for the next step of structural pruning. Since gradient calculation is a standard operation in neural network frameworks, the additional computational cost of this step is equivalent to only one regular training iteration and will not significantly increase the overall training time.

[0050] This embodiment's physical sensitivity calculation method integrates information from two dimensions—coefficient magnitude and loss gradient—into a single scalar score. This overcomes the inherent flaw of traditional magnitude pruning, which only focuses on parameter magnitude while ignoring the direction and intensity of their impact on the global loss. Since the total loss function includes physical residual terms, the gradient information naturally carries information about the direction of physical consistency. This allows the sensitivity score to accurately identify spline coefficients with small absolute values ​​that are crucial for maintaining the Verhulst decay pattern. Consequently, these critical paths are protected from pruning during subsequent large-scale compression, effectively eliminating non-physical prediction phenomena caused by pruning.

[0051] In one embodiment, the structural pruning of the KAN network based on the physical sensitivity includes: Calculate the mean of the physical sensitivity scores for all connections in the current layer; The pruning threshold is determined by multiplying the mean value by the pruning intensity adjustment parameter; Generate a binary mask matrix, set the mask corresponding to the connection whose physical sensitivity score is lower than the pruning threshold to zero, and cut off the corresponding signal transmission path.

[0052] In the application, the mean physical sensitivity score of all connections in the current layer is calculated. μ l This is a process of statistically summarizing the sensitivity of all connections in the current layer. The mean reflects the overall average importance level of the connections in the current layer, providing a benchmark for subsequently determining the pruning threshold. Based on the mean... μ l With pruning intensity adjustment parameters α The product determines the pruning threshold. T l = μ l × α It is achieved through an adjustable hyperparameter. α To control the degree of aggressiveness in pruning. α The larger the value, the higher the threshold, the greater the proportion of connections pruned, and the deeper the model compression. α The smaller the value, the lower the threshold, the more connections are retained, and the shallower the compression.

[0053] In applications, generating a binary mask matrix and setting the mask corresponding to low-sensitivity connections to zero is the operation of structural pruning. For the first... l Layer and First l For the connection matrix between +1 layers, create a binary matrix Mask of the same dimension, initially with all elements set to 1. Iterate through each connection of this layer ( i , j If its physical sensitivity score is less than the threshold Tl If the mask value is 0, then the mask value at the corresponding position is changed from 1 to 0. In subsequent forward inference, the spline coefficients of a connection with a mask value of 0 are effectively multiplied by the mask, resulting in a zero output. This is physically equivalent to cutting off the signal transmission path, retaining only the critical connections sensitive to the evolution of the Verhulst model. After performing the above operation layer by layer in the network, the sparsity of the entire network structure is completed.

[0054] Inspect each feature node in the input layer of the KAN network. If all connections originating from a certain feature node are pruned, the feature is determined to be physically independent. In subsequent model deployment configurations, the data acquisition channel for this physical feature is disabled, thereby reducing the computing power and storage overhead of the BMS front-end.

[0055] This embodiment introduces a dynamic threshold mechanism linked to hierarchical sensitivity statistics, enabling the pruning boundary of each layer to adaptively reflect the importance distribution of connections within that layer. This avoids over-pruning or under-pruning issues caused by fixed thresholds across different layers. The binary mask matrix, serving as the carrier of the pruning results, can apply structural constraints at zero cost during subsequent fine-tuning and inference stages, without requiring intrusive modifications to the network code. Simultaneously, the pruning intensity adjustment parameter α provides system engineers with an intuitive knob, allowing for flexible configuration of the compression level based on the hardware budget of different BMS platforms.

[0056] In one embodiment, the step of filtering the effective input features in the multidimensional physical feature tensor based on the results of structural pruning includes: checking the output connection status of each feature node in the input layer of the KAN network; in response to detecting that all output connections of any feature node have been pruned, determining the input feature corresponding to any feature node as a physically irrelevant feature and removing it.

[0057] In applications, checking the output connection status of input layer feature nodes refers to examining the mask values ​​of all connections from each input layer node to the first hidden layer after structural pruning. Each node in the input layer of a KAN network corresponds to one dimension of a multidimensional physical feature tensor. If all connections from a certain input node to the first hidden layer are masked to zero during pruning, it means that no matter how the value of that feature changes, it will not affect the calculation of subsequent layers of the network or the final SOH output. In this case, the feature is determined to be a physically independent feature, meaning that in the SOH prediction task under the constraints of the Verhulst model, there is no significant causal relationship between the change of this physical quantity and the capacity decay. After the determination is completed, the feature is marked as disabled in the model's deployment configuration file. The BMS can then skip the data reading and preprocessing operations for that sensor channel during actual runtime, or directly omit the sensor during the hardware design phase, thereby saving resources.

[0058] The feature selection mechanism in this embodiment transmits the structural pruning results within the network back to the input, achieving collaborative optimization from the model level to the data link level. Unlike traditional feature selection methods (such as mutual information or Pearson correlation coefficient), which only evaluate feature correlation at the data statistical level, this scheme's selection is based on the gradient information of the loss function containing physical constraints. Therefore, the identified redundant features are dimensions that do not affect the predicted output under specific physical constraints, making the selection results more physically interpretable. Simultaneously, by shutting down redundant sensor channels at the hardware level, redundant sensor channels are directly reduced, lowering the power consumption, storage, and communication bandwidth requirements of the BMS front end. This has practical engineering value for cost control in automotive-grade and energy storage-grade BMS.

[0059] In one embodiment, the subspace fine-tuning of the structurally pruned KAN network includes: freezing the binary mask matrix generated by structural pruning, and fine-tuning the retained spline coefficients and physical parameters in the physical model under a fixed sparse topology.

[0060] In the application, during subspace fine-tuning, the processor loads the mask matrix into memory as a constant tensor. During each forward propagation step, the spline coefficient matrix is ​​element-wise multiplied by the mask matrix before computation, thus automatically masking pruned connections. During backpropagation, although the gradients corresponding to the masked coefficients are calculated, they are also multiplied by the mask to zero during the parameter update step, ensuring these coefficient values ​​remain constant and are not recovered. The learning rate during fine-tuning is typically set to one-tenth to one-hundredth of the pre-training rate to avoid excessive parameter jumps in the sparse subspace. After fine-tuning, the final sparse coefficient matrix, the node vector parameters of the B-spline basis functions, and the physical parameters are... k and M The data is exported in a unified manner and converted into a data format suitable for embedded platform execution (such as fixed-point lookup table or compressed sparse row format), and then burned into the Flash memory of the BMS controller.

[0061] In the application, the comparison of the lightweight effect of the experimental network model in the example is shown in the figure below. Figure 4 As shown, through physical-guided sparsity processing, this invention can compress the number of parameters in the original KAN network by 70%~80%, while maintaining almost no decrease in accuracy or even slightly improving it, significantly reducing the hardware cost of BMS. Figure 4 Experimental data shows that the original dense KAN network has as many as 32,592 parameters, while the model processed by this invention has 7,504 parameters, achieving a parameter compression rate of 77.0%. This 77.0% parameter reduction not only occurs within the network but is also directly reflected in the sparsity of the input layer connections. This is achieved by automatically identifying and disabling redundant input feature channels whose connection weights have been completely pruned. A comparison of the experimental battery SOH prediction results is shown in the example. Figure 5 As shown, even with a significant 77% reduction in the number of parameters, the root mean square error (RMSE) of the predicted trajectory (red dashed line) of this invention is 0.0026, the mean absolute error (MAE) is 0.0018, the relative error is 0.29%, and the coefficient of determination (R²) is [missing information]. 2 =0.9973 and training time = 24.1s. All indicators show that the predicted trajectory of this invention (red dashed line) closely matches the actual value (black solid line), and maintains a good monotonic decay trend even in the later stages of battery aging. It can achieve online high-precision prediction and has good noise resistance and robustness. The dynamic identification diagram of experimental physical parameters in the example is as follows. Figure 6 As shown, the physical parameters gradually tend towards fixed values ​​with the increase of training rounds. The trained model can not only output SOH, but also aging parameters with clear physical meaning, providing battery manufacturers with additional diagnostic basis for analyzing batch quality differences in batteries. The comparison of MAE under different pruning rates for SOH prediction after conventional pruning and pruning according to this invention is shown in the example. Figure 7 As shown, with the increase of pruning rate, the prediction error of the prior art (blue dashed line) is relatively large; while the error of the present invention (red solid line) remains stable and low.

[0062] like Figure 8 As shown in the figure, this application embodiment also provides a battery management system, including a data acquisition module, a central processing module, and a storage module; The data acquisition module is used to collect battery voltage, current and temperature data; The storage module is pre-loaded with a neural network model trained using the method described in any of the above embodiments. The central processing module is used to construct a multidimensional physical feature tensor based on the data collected by the data acquisition module, and to call the neural network model to monitor the battery health status.

[0063] In applications, the data acquisition module is the front-end component that directly interacts with the battery cells in the BMS hardware system. Its responsibility is to acquire key electrical and thermal parameters during battery operation in real time. Voltage acquisition is typically accomplished through a high-precision differential analog-to-digital converter (ADC), converting the analog terminal voltage signal of the battery cell into a digital quantity. Current acquisition is usually achieved through Hall effect sensors or shunt resistors in conjunction with amplifier circuits, converting the charging and discharging current through the battery into a quantifiable electrical signal. Temperature acquisition is typically accomplished through an NTC thermistor attached to the battery surface, converting temperature changes into resistance changes, which are then sampled by the ADC and converted into digital temperature values. The acquired data is low-pass filtered and outlier removed before being transmitted to the central processing module. The number of data acquisition channels and the sampling frequency are configured according to actual needs. Guided by feature filtering results, sensor acquisition channels corresponding to features determined to be physically irrelevant can be shut down to reduce data throughput.

[0064] In applications, the storage module is a non-volatile storage device in the BMS control unit used to persistently store model parameters and configuration data, typically Flash memory or EEPROM. The pre-installed neural network model is the final product after training and sparsification using the complete process described above. It includes the sparsified B-spline coefficient matrix, the corresponding binary mask matrix or equivalent sparse index table, the node vector parameters of the B-spline basis functions, and the identified physical parameters k and M. These parameters are written to the storage module before leaving the factory or during online updates, and are read into the running memory by the central processing module for inference calculations after the system powers on. Because the model undergoes 70% to 80% parameter compression, its storage footprint is significantly lower than the original dense model, making it suitable for embedded chips with limited storage capacity.

[0065] In application, the central processing module is the core computing component of the BMS, responsible for executing all computational tasks from data preprocessing to SOH inference output. Its workflow is as follows: First, it receives digitized voltage, current, and temperature data sequences from the data acquisition module, calculates physical features such as ohmic resistance and charging time according to preset feature extraction logic (only calculating the effective dimensions retained after feature filtering), and assembles them into a multi-dimensional physical feature tensor after normalization. Then, it loads sparse model parameters from the storage module, performs forward inference operations in the form of sparse matrix multiplication, and outputs the SOH estimate for the current loop. Finally, it sends the SOH value to the upper-level control system or display terminal via the CAN bus or UART interface, and optionally outputs the identified physical parameters k and M for in-depth diagnostic analysis by the upper-level system.

[0066] Specifically, the complete data processing chain of the battery management system described in this solution during actual operation is as follows: The data acquisition module triggers a data report at a fixed period (e.g., after each charge-discharge cycle), packaging and transmitting the voltage-current-temperature sampling data of the current cycle to the central processing module. The central processing module performs segmentation and feature extraction on the received data to obtain the physical feature vector corresponding to the current cycle. After normalization, this vector is fed into the forward inference process of the sparse PINN-KAN network, which outputs the current capacity loss rate prediction. u ( t ), from which SOH( t )=1- u ( t After the central processing module reports the SOH value and physical parameters through the communication interface, it completes one monitoring cycle and waits for the next data trigger. The physical parameters k and M have converged to stable values ​​during the training phase, and can be directly output after deployment to provide aging diagnosis information to the upper-level system.

[0067] The central processing module can utilize a microcontroller based on the ARM Cortex-M series (such as the STM32F4 series) to meet the embedded requirements of automotive-grade BMS with its low power consumption and cost. Alternatively, it can employ a high-performance DSP chip with a hardware floating-point unit (such as the TI C2000 series) to provide sufficient computing power for scenarios requiring higher inference speeds. The communication interface can adopt the CAN bus protocol to comply with industry-standard communication specifications for automotive electronics, or it can use UART or SPI interfaces to achieve flexible data transmission in non-automotive applications such as energy storage systems.

[0068] This embodiment deeply integrates the sparse model trained in the above method embodiments with the BMS hardware architecture, forming an end-to-end closed-loop system from sensor acquisition, feature extraction, sparse inference to result output. The low parameter count and low computational cost of the sparse model enable it to run in real time on cost-sensitive embedded processors without relying on external cloud servers or high-performance computing units, meeting the stringent latency and reliability requirements of automotive and energy storage scenarios. The feature selection results directly guide the configuration of the data acquisition channels, realizing collaborative optimization between the model and hardware, further reducing the overall system cost and power consumption.

[0069] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A method for monitoring and managing the state of energy storage batteries, characterized in that, Including the following steps: S1: Construct a multidimensional physical feature tensor based on the battery's charge and discharge data; S2: Establish a KAN network that integrates the physical model, input the multidimensional physical feature tensor into the KAN network for joint pre-training, and synchronously update the spline coefficients in the KAN network and the physical parameters in the physical model; the physical model is a Verhulst model used to describe the battery capacity decay characteristics, and its expression is: ； in, t This refers to the number of charge-discharge cycles. u ( t )for t Battery capacity loss rate at any given time For capacity loss rate, k The decay rate constant is M For the maximum theoretical capacity loss, k and M Embedded into the network as learnable physical parameters; S3: Perform a first-order Taylor expansion on the spline coefficients based on the total loss function of joint pre-training, and calculate the physical sensitivity of each connection in the KAN network; S4: Perform structural pruning on the KAN network based on the physical sensitivity, and filter the effective input features in the multidimensional physical feature tensor based on the structural pruning results; S5: Subspace fine-tuning is performed on the KAN network after structural pruning to obtain a sparse neural network model for battery health state estimation. The model outputs a high-precision SOH estimate, and simultaneously outputs the aging rate constant and maximum capacity loss parameter, providing additional physical diagnostic basis for the quality analysis of the battery's entire life cycle. The total loss function includes data fitting loss and physical residual loss. The data fitting loss is the mean square error between the predicted value of the KAN network and the actual battery health state value. The physical residual loss is constructed based on the deviation between the Verhulst model and the predicted output of the KAN network. The total loss function L for: ； in, L For the total loss function, The mean squared error between the network-predicted value and the actual SOH value. For physical residual loss, The weighting coefficient for the physical residual loss. D The sample batch size for the training data. m For the index of sample data, For the first m The true volume loss rate of each sample Let m be the capacity loss rate predicted by the network for the m-th sample. This is the physical residual function.

2. The method as described in claim 1, characterized in that, The construction of a multidimensional physical feature tensor based on the battery's charge and discharge data includes: extracting at least two of the following from the charge and discharge data: number of cycles, ohmic internal resistance, constant current charging time, constant voltage charging time, maximum temperature during discharge, and average voltage during discharge; and normalizing the extracted features to form the multidimensional physical feature tensor.

3. The method as described in claim 1, characterized in that, The connections between adjacent layer nodes in the KAN network employ parameterized B-spline basis functions; the KAN network's... l The first layer j The node is passed to the first node via the join function. l +1 floor i The output of each node is represented as: ； in, For the first l The first layer j The node and the first l+ 1st floor i The connection function between nodes For the first l The first layer j The output value of each node, N This represents the total number of spline basis functions in the connection function. n For the index of the B-spline basis functions, B n For the first in the join function n basis functions For the first in the join function n Learnable spline coefficients of each basis function.

4. The method as described in claim 1, characterized in that, The physical sensitivity is calculated as follows: ； in, For the first in the join function n The learnable spline coefficients of the basis functions, For the total loss function, This represents the gradient of the total loss function with respect to the spline coefficients. For the first l Layer j The node and the first l +1 floor i Physical sensitivity score of connections between nodes.

5. The method as described in claim 4, characterized in that, The structural pruning of the KAN network based on the physical sensitivity includes: Calculate the mean of the physical sensitivity scores for all connections in the current layer; The pruning threshold is determined by multiplying the mean value by the pruning intensity adjustment parameter; Generate a binary mask matrix, set the mask corresponding to the connection whose physical sensitivity score is lower than the pruning threshold to zero, and cut off the corresponding signal transmission path.

6. The method as described in claim 5, characterized in that, The step of filtering the effective input features in the multidimensional physical feature tensor based on the structural pruning results includes: checking the output connection status of each feature node in the input layer of the KAN network; in response to detecting that all output connections of any feature node have been pruned, determining the input feature corresponding to any feature node as a physically irrelevant feature and removing it.

7. The method as described in claim 1, characterized in that, The subspace fine-tuning of the KAN network after structural pruning includes: freezing the binary mask matrix generated by structural pruning, and fine-tuning the retained spline coefficients and physical parameters in the physical model under a fixed sparse topology.

8. A battery management system, characterized in that, It includes a data acquisition module, a central processing module, and a storage module; The data acquisition module is used to collect battery voltage, current and temperature data; The storage module is pre-loaded with a neural network model trained using the method described in any one of claims 1 to 7; The central processing module is used to construct a multidimensional physical feature tensor based on the data collected by the data acquisition module, and to call the neural network model to monitor the battery health status.

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