Lithium ion battery health state assessment method based on physical information and data driving

Abstract

The invention provides a lithium ion battery health state assessment method based on physical information and data driving, and belongs to the technical field of lithium ion battery health state assessment, and the method comprises the steps: constructing a physical model for describing a lithium ion battery capacity attenuation rule according to empirical model constraints and physical rule constraints; a physical information neural network model is built, the physical information neural network model comprises an attention-based cross-modal fusion estimation network and a loss function embedded into a physical model, and optimization strategies such as adaptive weight equalization, time-frequency domain equalization and boundary hard constraint are introduced; training the physical information neural network model by using the battery aging data; and estimating the health state of the lithium ion battery by using the trained physical information neural network model. According to the method, under the condition that only a small amount of training data is used, the estimation precision and stability of the battery health state under the scenes of interpolation and extrapolation are remarkably improved, and the problem of small-sample battery SOH prediction is solved.

Description

Technical Field

[0001] This invention belongs to the field of lithium-ion battery health status assessment technology, and particularly relates to a lithium-ion battery health status assessment method based on physical information and data-driven approach. Background Technology

[0002] With the rapid development of new energy vehicles, the state of health (SOH) assessment of lithium-ion batteries has become a key technology for ensuring battery safety and reliability. Traditional model-based methods are often limited by problems such as modeling difficulties and insufficient generalization. While emerging data-driven methods have overcome these problems to some extent, their inherent lack of interpretability and dependence on large amounts of data also bring new challenges.

[0003] Current methods for estimating the state of energy (SOH) of lithium-ion batteries are mainly divided into two categories: model-driven and data-driven. While model-driven methods can deeply analyze battery aging at the mechanistic level, their complex modeling process, high parameter identification costs, and insufficient generalization ability in dynamic environments limit their practical application. Data-driven methods, on the other hand, overcome these challenges to some extent by not requiring complex mechanistic modeling, demonstrating good nonlinear fitting capabilities. However, their strong dependence on massive amounts of high-quality data, the inherent black-box nature of the models leading to insufficient interpretability, and poor robustness in small sample sizes or when data distribution changes remain insurmountable obstacles. Especially in the field of lithium-ion battery state monitoring, existing methods face significant contradictions: on the one hand, aging mechanism-based models have stringent requirements for the completeness and accuracy of experimental data, making parameter identification extremely difficult; on the other hand, the long-term data acquisition process for batteries is challenging, and the long testing period and potential instability factors can easily lead to incomplete battery aging trajectories or sparse data in the experimental dataset, directly constituting the small sample problem and severely restricting the performance of data-driven models. Although some studies have begun to explore hybrid-driven methods that combine the advantages of both, how to effectively integrate heterogeneous multimodal information (such as ultrasound signals and electrical parameters) and maintain high accuracy and robustness in real-world applications with sparse data remains a key challenge that urgently needs to be addressed in the field of SOH assessment. Summary of the Invention

[0004] The purpose of this invention is to provide a method for assessing the health status of lithium-ion batteries based on physical information and data-driven approaches. This is achieved by constructing a physical information neural network model, which includes a cross-modal fusion estimation network and a composite loss function. The cross-modal fusion estimation network utilizes modules such as feature dimension alignment, stochastic Fourier feature frequency domain equalization, attention mechanisms, and hard boundary layers to achieve efficient and robust fusion of multimodal features (including ultrasonic features). The loss function incorporates physical model residuals, adaptive weighting, and gradient residual constraints to embed prior physical knowledge describing battery aging mechanisms into the network training, balancing data fitting with adherence to physical laws. Through the synergistic effect of the cross-modal fusion estimation network and the composite loss function, the model can still achieve high-precision and robust health status estimation and prediction even under conditions of sparse training data.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: A physical information and data-driven method for assessing the health status of lithium-ion batteries includes: S1: Construct a physical model describing the capacity decay law of lithium-ion batteries based on empirical model constraints and physical law constraints; S2: Construct a physical information neural network model, which includes an attention-based cross-modal fusion estimation network and a loss function embedded in the physical model; the attention-based cross-modal fusion estimation network integrates a feature dimension alignment module and an attention feature fusion module, adds random Fourier features between the feature dimension alignment module and the attention feature fusion module, and introduces a hard boundary coding layer in the attention feature fusion module; S3: Use battery aging data to train the physical information neural network model; S4: Use a trained physical information neural network model to estimate the health status of lithium-ion batteries.

[0006] Furthermore, the construction of the physical model in step S1 is specifically as follows: S101: Establish empirical model constraints, introducing upper limit K for battery capacity loss, initial capacity loss C, and health characteristics based on the Verhulst model. A partial differential equation is established, and the degradation rate constant r is constructed as a learnable parameter related to the ultrasonic signal amplitude Pt, resulting in the empirical model constraint formula: ; In the formula, The percentage of capacity loss. As a scaling factor to enhance the response to battery heterogeneity, For time; S102, Physical laws constrain, IC characteristics It is positively correlated with the SOH of the battery, which is constrained by physical laws: ; In the formula, For the battery's health status, For incremental capacity; S103. Obtain the physical model based on empirical model constraints and physical law constraints: .

[0007] Furthermore, the attention-based cross-modal fusion estimation network in step S2 is specifically as follows: The feature dimension alignment module maps the multimodal input features to a unified feature space to achieve feature dimension alignment. The aligned features are mapped to a high-dimensional frequency domain space using the random Fourier feature method to achieve frequency domain equalization; Eight attention heads are constructed to compute feature representations of different subspaces in parallel. Each attention head takes the frequency domain equalization as input. The fused features are obtained by concatenating and linearly transforming the outputs of multiple attention heads. The fused features are input into the hard-boundary coding layer to correct the initial state of the network; The corrected output in the hard-boundary coding layer is used as the prediction value to calculate the loss function.

[0008] Furthermore, the stochastic Fourier feature method specifically includes: The random Fourier feature method uses an encoder Frequency domain equalization is achieved by encoding the aligned features and mapping them to a high-dimensional frequency domain space; the encoding formula is as follows: ; in Satisfies a random normal distribution This is used to map features to a high-dimensional space; It is an adjustable parameter. For the aligned low-dimensional features, It represents high-dimensional frequency domain features.

[0009] Furthermore, the formula for the hard constraint mechanism of the hard boundary coding layer is as follows: ; In the formula, It is the raw output of the physical neural network. This is the final network output after applying hard boundary constraints. This represents the initial health state of the battery. It is the initial time; using the double tangent function tanh, the time is... When approaching 0, The value approaches 0.

[0010] Furthermore, the loss function in step S2 is specifically as follows: (1) Loss of observation data Physical model constraint loss loss with initial boundary conditions Construct the initial loss function: ; in For the network weights of the neural network, These are unknown parameters in the physical model; (2) Introduce adaptive weights and gradient residual constraints into the initial loss function to construct the loss function.

[0011] Furthermore, adaptive weights and gradient residual constraints are introduced into the initial loss function as follows: Assuming that the noise from the data loss and the physical model constraint loss follows a Gaussian distribution, a learnable noise parameter is introduced into the initial loss function. and The noise levels of the observed data and physical model constraints during the training phase are respectively characterized; the weights of the loss terms are inversely proportional to the noise parameters, and the weights of the observed data loss term and the physical model constraint loss term are respectively... and Furthermore, a regularization term is introduced. Thus, the loss function for adaptive weights is expressed as: ; Calculate physical residuals Sampling points relative to physical model constraints Differential The derivative result is added as an additional constraint to the loss function of the adaptive weights. After gradient boosting, the model's loss function is: .

[0012] Furthermore, the components of the loss function are defined as follows: ; in, The residual between the neural network model and the physical model. Used to constrain the monotonic relationship between IC characteristics and battery health status; For the sampling points of the observation data, Sampling points constrained by the physical model; This refers to the total number of sampling points, including the number of observed data points. and the number of constraint points in the physical model , This is the sample's index number. It is the first The sampling time points of each observation data point The time point for collecting the initial sample observation data. It is the first Sampling time points constrained by a physical model The SOH value predicted by the neural network model. For the first The health characteristics of each sample are input.

[0013] Furthermore, step S3 specifically involves training the physical information neural network model constructed in step S2 using the first 50% of the data from the battery aging process, and artificially increasing the experimental scenario of data sparsity by expanding the sampling interval so that the physical information neural network model can only utilize 10% of the original data.

[0014] The beneficial effects of this invention are as follows: 1. This application effectively addresses the limitations of model-driven and data-driven methods, achieving complementary advantages. It constructs a physical model (PDE model) that integrates battery health characteristics and embeds this model as a constraint in the loss function of a neural network, thus building a physical information neural network. This hybrid-driven architecture leverages the profound descriptive ability of the physical model to describe battery capacity decay patterns, ensuring model interpretability and physical consistency, while also utilizing the powerful nonlinear fitting capabilities of data-driven methods, reducing reliance on precise mechanistic models. This allows for high-precision SOH assessment without excessive dependence on massive amounts of data.

[0015] 2. Significantly improves the model's robustness and generalization ability in sparse data scenarios. By introducing a series of network training strategies, including frequency domain equalization based on stochastic Fourier features, hard boundary constraints, adaptive weight equalization, and temporal equalization based on gradient reinforcement learning, this method can effectively train under small sample conditions. It solves the problems of difficult long-term battery data collection and the small sample size caused by data sparsity.

[0016] 3. By integrating ultrasonic non-destructive testing signals, this application achieves sensitive capture of early battery aging characteristics and prediction of potential degradation paths. The ultrasonic signal amplitude (Pt) is introduced into the physical model as a key health feature, thus correlating the attenuation coefficient with the ultrasonic characteristics. This ultrasonic-based physical information fusion enables the assessment method to identify battery heterogeneity and potential faults earlier and more accurately, providing a new technical approach for early warning and accurate prediction of battery health status.

[0017] 4. An improved physical information neural network training mechanism effectively overcomes the training challenges of traditional PINN, enhancing model convergence speed and prediction accuracy. Hard boundary constraints, directly satisfying initial conditions through network structure design, avoid convergence difficulties that may arise from soft constraints, thus improving training efficiency. An adaptive weight balancing strategy dynamically adjusts the contributions of different loss terms, alleviating gradient imbalance in multi-task learning and ensuring training stability. Gradient-enhanced temporal balancing, by constraining the smoothness of physical residuals, ensures the model uniformly satisfies physical laws throughout the entire time domain, improving long-term prediction accuracy. Attached Figure Description

[0018] Figure 1 This is an ultrasonic signal diagram of each battery after 50 cycles, provided by the present invention. Figure 2 This is a basic framework diagram of PINN provided by the present invention; Figure 3 This is a graph of the improved physical information neural network loss function provided by the present invention; Figure 4 This is a diagram of the improved physical information neural network prediction model provided by the present invention; Figure 5 This is a comparison chart of the estimation results of the data-driven model and the PINN model provided by this invention; Figure 6 This is the training loss value of the basic framework provided by this invention; Figure 7 This is a graph showing the estimation results of the PINN model with multidimensional balanced training provided by this invention; Figure 8 This is the weighted training loss value for multidimensional balanced training provided by the present invention; Figure 9 This is a comparison chart of battery aging trends provided by the present invention; Figure 10 This is a comparison chart of the convergence speeds of the soft and hard boundary constraints provided by this invention; Figure 11 This is a graph showing the estimation results of the PINN model with hard boundary constraints provided by this invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0020] The application principle of the present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0021] Example 1: A physical information and data-driven method for assessing the health status of lithium-ion batteries includes: S1: A physical model (improved PDE model) describing the capacity decay of lithium-ion batteries is constructed based on empirical model constraints and physical law constraints. The capacity decay process of lithium-ion batteries exhibits nonlinear characteristics, necessitating the establishment of a dynamic physical model (improved PDE model) capable of describing its degradation kinetics. Based on the classic Verhulst model, an improved PDE model is proposed as physical information to integrate the physical mechanism of battery degradation with data-driven methods. The specific physical model construction method is as follows:

[0022] S101, Empirical Model Constraints Based on the classic Verhulst model, partial differential equations are established by integrating the upper limit of capacity loss, initial capacity loss, and battery health characteristics, thereby constructing empirical model constraints, as follows: The original Verhulst model formula is as follows: ; The Verhuls model assumes that the degradation rate is proportional to the current capacity loss and its remaining loss, whereby... This represents the percentage of capacity loss (PCL = 1 - SOH). The degradation rate constant is given, and considering that the growth of the SEI (Solid Electrolyte Interphase) is finite, an upper limit for the capacity loss of the battery is introduced. In this application, it is set to 25%, and the improved model is as follows: ; In addition, the new batteries already have initial capacity loss due to SEI formation when they leave the factory. And satisfy , This represents the maximum initial loss value; the improved model starts from... The degradation process is now described to better reflect the initial state of the battery, avoiding the idealized assumptions about initial conditions made by the traditional Verhuls model. The corrected model is as follows: ; in This represents the number of loops (time). The percentage of capacity loss over time Changes. Meanwhile, considering the heterogeneity of batteries, health characteristics... It was used for modeling battery aging. for The real number vector yields the improved capacity loss percentage. The improved form also changes over time. and health characteristics By relating the change to capacity loss and establishing a partial differential equation, we obtain: ; After 50 charge-discharge cycles, although the state of harmonics (SOH) of different batteries did not show significant differences in capacity characterization for the time being, Figure 1 The ultrasonic testing results showed significant differences in the amplitude of the ultrasonic signals echoed from the bottom surfaces of different batteries. Notably, the differential attenuation of the ultrasonic signals exhibited a clear positive correlation with the subsequent capacity degradation trend of the batteries. This indicates that even before significant capacity degradation occurs, ultrasonic technology can sensitively capture the early evolution characteristics of the battery's internal structure, providing experimental evidence for predicting potential battery degradation paths using non-destructive ultrasonic signals. Therefore, the attenuation coefficient... It can be further changed from a constant to a learnable parameter related to the ultrasonic amplitude Pt. , Introduction As a scaling factor to enhance the handling of battery heterogeneity, the empirical model constraint formula is obtained: ; S102, Physical Law Constraints To standardize the learning paradigm of neural network models, physical laws are introduced, namely, the IC feature. (Incremental capacity) is positively correlated with battery state of harmonics (SOH), which can be constrained by physical laws: ; S103. Obtain the physical model based on empirical model constraints and physical law constraints: ; S2: Build a physical information neural network model. For example... Figure 2 As shown, a physical information neural network model (improved PINN) is constructed based on PINN. The improved PINN consists of two parts: an attention-based cross-modal fusion estimation network and a loss function embedded in the physical model. Details are as follows:

[0023] S201, Attention-based cross-modal fusion estimation network The attention-based cross-modal fusion estimation network consists of a feature dimension alignment module and an attention feature fusion module. Random Fourier features are added between these two modules as input to the attention feature fusion module, which incorporates a hard-boundary coding layer. This attention-based cross-modal fusion estimation network is used to process the multimodal input features of lithium-ion batteries. Through feature dimension alignment, frequency domain equalization, attention fusion, and hard-boundary constraints, it achieves effective fusion of heterogeneous features, providing a high-quality feature foundation for subsequent SOH estimation. Details are as follows:

[0024] (1) Feature dimension alignment: The feature dimension alignment module maps the multimodal input features to a unified feature space to achieve feature dimension alignment.

[0025] (2) Frequency domain equalization based on random Fourier features To overcome the "spectral bias" problem of neural networks (i.e., prioritizing the learning of low-frequency components and making it difficult to capture high-frequency dynamics), this application proposes to combine Fourier features with a physical information neural network model as the input of the attention feature fusion module, and map the aligned features to a high-dimensional frequency domain space, aiming to enhance the model's ability to model complex dynamics.

[0026] A random Fourier feature mapping method is used to map the aligned features to a high-dimensional frequency domain space. An encoder is then used. Encode using aligned features. For the aligned low-dimensional features, For high-dimensional frequency domain features, the aligned features are mapped to a high-dimensional frequency domain space to achieve frequency domain equalization. The encoding formula is as follows: ; in Satisfies a random normal distribution This is used to map features to a high-dimensional space; It is an adjustable parameter. The essence of frequency domain mapping is to transform the model's training mode from directly performing differentiation operations in the time domain to analyzing the signal components in the frequency domain. Its implementation in the network structure is as follows: Figure 4 As shown, by introducing random Fourier features, the physical information neural network model can simultaneously focus on the high-frequency and low-frequency components in the input signal, thereby effectively mitigating the spectral bias problem of the neural network.

[0027] (3) Attention fusion Eight attention heads are constructed to compute feature representations for different subspaces in parallel. Each attention head may focus on different levels of information from different modalities. Each attention head takes frequency-equalized data as input. By concatenating and linearly transforming the outputs of multiple attention heads, the fused features are obtained. The model can fuse feature information from different subspaces, thereby capturing deep correlations across modal data and achieving a more comprehensive feature understanding. Finally, the concatenated features from the eight attention heads (the fused features) are input into the hard-boundary coding layer to correct the network's initial state.

[0028] (4) Hard boundary constraints In basic physical information neural network frameworks, boundary conditions are typically imposed using soft constraints, which transform the boundary conditions into penalty terms in the loss function. This is achieved by minimizing a composite loss function that includes the residuals of the governing equations and the residuals of the boundary conditions. However, this approach has some limitations. First, the indirect optimization method may lead to the physical field values ​​at the boundaries failing to converge precisely to the expected values. Second, treating the boundary conditions as additional loss terms increases the complexity of the neural network training process and may slow down or even prevent convergence. This application proposes to transform traditional soft constraints into hard constraints, such as... Figure 4 As shown, the hard constraint is applied as a hard-boundary encoding layer after the attention feature fusion module. The corrected output of the hard-boundary encoding layer is used as the predicted value to calculate the total loss function. The initial conditions are explicitly encoded directly in the output layer, avoiding the convergence difficulty of soft-boundary constraints. The specific hard constraint mechanism is shown in the formula: ; In the formula, It is the raw output of the physical neural network. This is the final network output after applying hard boundary constraints. This represents the initial health state of the battery. This is the initial time. Using the double tangent function... This makes time When approaching 0, The value approaches 0.

[0029] S202, Loss Function Construction (1) The main goal of PINN is to embed physical information into the loss function. Its core is to standardize the training process of the neural network by constructing a composite loss function that includes data loss terms, initial boundary condition loss terms, and empirical model constraint and physical law constraint loss terms. The loss is determined by the observed data. Physical model constraint loss loss with initial boundary conditions The constructed initial loss function: ; in For the network weights of the neural network, These are unknown parameters in the physical model. The observed data loss represents the difference between the predicted value and the actual battery SOH value of the cross-modal attention feature fusion model, and is obtained by calculating the residual between the observed value and the model output; Initial boundary condition loss is essentially a type of data constraint. Since the initial state of harmonics (SOH) of a battery is always 100%, the initial boundary condition is used to ensure that the model's prediction at the initial moment matches the known initial state of the battery, thus guiding the model's learning in the initial stage. As a constraint loss for the physical model, and as an unsupervised constraint, a custom timestamp is defined within the domain, and the first-order partial derivative in the PDE model is calculated through automatic differentiation. Then calculate its relationship with the physical model. The residuals allow the neural network to satisfy the constraints of the physical model, thus limiting the solution space to a range consistent with physical laws and enabling prior physical knowledge to guide model training. The components of the loss function are defined as follows: ; in, The residual between the neural network model and the physical model. Used to constrain the monotonic relationship between IC characteristics and battery health status. For the sampling points of the observation data, the corresponding The sampling points constrained by the physical model are derived from the timestamps set within the parameter domain. This refers to the total number of sampling points, including the number of observed data points. and the number of constraint points in the physical model , This is the sample's index number. It is the first The sampling time points of each observation data point The time point for collecting the initial sample observation data. It is the first Sampling time points constrained by a physical model The SOH value predicted by the neural network model. For the first The health characteristics of each sample are input.

[0030] (2) Introduce adaptive weight balancing into the initial loss function To address the imbalance between data fitting loss and physical model constraint loss during PINN training, an adaptive weight balancing strategy is adopted. By dynamically adjusting the weights of different loss terms, the model can simultaneously consider both data fitting and physical model constraints.

[0031] Assuming that the noise from the observed data loss and the physical model constraint loss follows a Gaussian distribution, a learnable noise parameter is introduced into the initial loss function. and These represent the noise levels of the observed data and the physical model constraints, respectively, during the training phase. The weights of the loss terms are inversely proportional to the noise parameters. The weights of the observed data loss term and the physical model constraint loss term are defined as follows: and When the noise in a certain type of loss is high, it can be considered that this part has high uncertainty and should be given a smaller weight in the overall loss function. It is important to note that the noise parameter is not a fixed value, but is automatically optimized through backpropagation during training, thus achieving dynamic adjustment.

[0032] In addition, to prevent the weight parameters from exploding during training, a regularization term is introduced. This regularization term ensures that a larger penalty is imposed when the weights are too large, thus maintaining the stability of the training process. Finally, the loss function of the model after adaptive weight balancing is expressed as: ; Through this adaptive weighting mechanism, the PINN model can dynamically adjust the importance of observation data fitting and physical model constraints during training, thereby learning complex battery degradation behaviors more effectively.

[0033] (3) Introduce a gradient residual constraint term into the initial loss function with adaptive weights to construct the loss function.

[0034] To address the issue that when applying PINN to solve the injected battery degradation problem, gradient imbalance occurs due to the conflict between temporal dynamic non-uniformity and the global nature of the optimization objective. This imbalance leads to the inability of traditional PINN to balance the training intensity across time stamps, resulting in insufficient optimization of the physical residual in some time periods. This application proposes an improved gradient boosting method, aiming to ensure the smooth evolution of the physical residual over time by balancing the training intensity across time stamps in the temporal domain. Specifically:

[0035] Calculate physical residuals Sampling points relative to physical model constraints Differential (Gradient residual constraint term), and add the derivative result as an additional constraint to the loss function that introduces adaptive weights. The derivative... It is added to the loss function as a gradient residual constraint to ensure that the model improves as it trains. This effectively ensures the smoothness of the physical residuals over the time domain, avoiding drastic local oscillations. It means the model can adjust parameters relatively evenly across different time points, thus more effectively meeting the constraints of the physical model. The loss function of the model after gradient boosting is: ; like Figure 3 As shown, the optimized loss function incorporates an adaptive weighting mechanism and a gradient residual constraint term on top of the original data loss, initial boundary condition loss, and physical model constraint loss, enabling it to better follow physical laws while meeting data fitting requirements.

[0036] S3: Use battery aging data to train the physical information neural network model. Train the physical information neural network model built in step S2 using the first 50% of the data in the battery aging process. Further increase the experimental scenario of data sparsity by expanding the sampling interval so that the physical information neural network model can only use about 10% of the original data.

[0037] S4: Use a trained physical information neural network model to estimate the health status of lithium-ion batteries.

[0038] Example 2: (1) PINN model estimation results combined with physical model In a few-shot learning scenario, the leave-one-out cross-validation method (Example 1) is used to compare and analyze the performance differences between physical information machine learning and traditional data-driven methods, systematically evaluating the performance of physical information constraints under few-shot conditions. Taking battery 1 as an example, the model's training data comes from sparse sampling of the first half of the aging process of batteries 2 and 3, used to construct the model's data constraints. Regarding the physical model constraints, to ensure the model follows the physical laws of the battery aging process, the sampling comprehensively covers the complete aging trajectory of the three batteries. This ensures that the established physical model constraints can effectively cover the entire battery aging process, not only uncovering potential dynamic patterns in the sample domain not covered by the data sampling but also ensuring that the model still follows the physical mechanism of battery aging outside the sample domain. The predictive performance of the model is then systematically evaluated using the root mean square error (RMSE).

[0039] like Figure 5As shown, the comparison results clearly demonstrate the difference in predictive performance between the PINN model, which combines a data-driven model with physical information machine learning, under small sample conditions. For batteries 1 and 3, in the mid-to-late aging stages (cycle count > 100) beyond the training data range, while the pure data-driven method can capture short-term fluctuations in the capacity decay curve by learning local features, its extrapolation ability is significantly insufficient due to a lack of understanding of the physical laws governing the global aging trend of the battery. This results in a sharp increase in RMSE outside the sample domain to 2.70% and 3.51%, respectively. In contrast, PINN, by introducing additional physical information to supplement the aging pattern of the battery, achieves RMSEs of 1.36% and 1.38% on the test set with the same sample size. It not only maintains accurate capture of the initial aging stage but also demonstrates extrapolation ability outside the sample domain. The PINN model, by introducing additional physical information to constrain the battery aging process, achieves RMSEs of only 1.36% and 1.38% on the test set with the same small sample size. This not only demonstrates that PINN can maintain high prediction accuracy in the initial aging stage, but more importantly, it shows that physical information has the ability to be effectively extrapolated beyond the training data range. The paradigm learned within the sample domain can guide the model to learn patterns that conform to the inherent laws of battery aging.

[0040] However, the estimation results in battery 2 show that PINN is not effective in some cases, as it fails to obtain the correct aging trend (R0) in the extrapolation interval. 2 <0), and its accuracy in the interpolation interval is also lower than that of the data-driven method. Figure 6 The reasons for the failure of the estimation method were analyzed from the loss values ​​during the training process.

[0041] Regarding the differences in magnitude between different loss terms, it can be observed that the loss value for data fitting of all batteries can stably converge to 10. -5 The magnitude is different, but the PDE residual loss value remains at 10. -3 Particularly in Battery 2, the physical model constraints for the training and testing batteries differ significantly in magnitude. This difference in convergence magnitude, as well as the differences between individual batteries, suggests that the basic PINN framework may not effectively balance data matching and physical constraints during optimization. The high PDE residual loss indicates that the model still falls short in satisfying physical laws, while the differences in physical model constraint losses between different batteries suggest potential issues with the model's adaptability to the characteristics of different individual batteries. This optimization imbalance may prevent the physical model constraints from fully playing their role in actual predictions, ultimately affecting the overall solution performance of the model.

[0042] (2) Model estimation results of multidimensional training equilibrium optimization To address the optimization imbalance problem in PINN, this paper proposes a three-pronged approach to balance PINN training, resulting in the optimized PINN termed B-PINN. First, the optimization imbalance during PINN training is often due to spectral bias, where the network tends to approximate measurement data with low-frequency basis functions, failing to meet the PDE constraint on high-frequency derivatives. To address this, Fourier features are used to map the input vector to a high-dimensional space for frequency domain enhancement, enabling the model to learn both high-frequency and low-frequency features in a balanced manner. Second, considering the inherent magnitude differences between different loss terms, adaptive weights are implemented based on the loss gradient to balance the optimization contributions of data-driven terms and PDE residual terms, thus preventing a single loss term from dominating the update direction. Finally, to avoid temporal causality issues caused by the model's late-stage aging during priority training and to ensure the optimization balance of the physical model constraints in the temporal domain, additional constraints are applied to the loss term of the physical residuals in the temporal domain, guaranteeing balanced learning of the model in the temporal domain.

[0043] like Figure 7 As shown, the B-PINN framework, after multidimensional balance optimization, demonstrates improved performance across all batteries, particularly in the aging prediction task of battery 2. Its health state estimation curve shows significantly improved alignment with the true values, and the interpolation and extrapolation predictions are smoother and more stable, exhibiting performance largely consistent with batteries 1 and 3, fully demonstrating the broad applicability of this optimization method. Compared to the original framework, multidimensional balance optimization for training effectively addresses the optimization imbalance problem across different batteries, enabling the model to make more balanced and accurate predictions for batteries with varying characteristics.

[0044] Figure 8 This demonstrates the dynamic changes in the weighted loss of B-PINN during training. (Compared to...) Figure 6 Compared to the loss curve of the basic framework, the loss curve of B-PINN is smoother and decreases faster overall. Furthermore, the loss values ​​of the physical model constraints for different batteries are more similar, demonstrating the effectiveness of the multidimensional equilibrium optimization strategy. Adaptive weight processing significantly reduces the order-of-magnitude difference between the data loss and the physical model constraints, helping the model better balance the two during training. Simultaneously, gradient-based loss constraints ensure a balanced loss value in the time domain, avoiding causal violations that might result from the model prioritizing later data during training.

[0045] To quantify the oscillation of the loss value during model training, the study introduced the coefficient of variation (CV) to measure the oscillation of the loss value during model training, which is calculated as follows: ; in and These represent the variance and mean of the loss curve, respectively. The coefficient of variation is calculated after normalizing the loss curve, as shown in Table 1.

[0046] Table 1 Comparison of coefficients of variation of loss curves

[0047] As shown in Table 1, the coefficient of variation of the B-PINN model after multidimensional equilibrium optimization is significantly lower than that of the basic PINN model on all loss components, with an overall reduction of 19.71%. This indicates that multidimensional equilibrium optimization can effectively improve the stability of model training, reduce loss fluctuations, and make the PINN model more stable during convergence.

[0048] Furthermore, Fourier features and the gradient-enhanced PINN method exhibit a good synergistic effect. Fourier features optimize the model's representation of the signal from a frequency domain perspective, making the model more stable when learning physical laws and avoiding gradient oscillations caused by drastic signal changes. This, combined with gradient-enhanced PINN, results in a smoother loss curve. Fourier features significantly improve the model's ability to capture high-frequency information in the dynamics of battery aging, especially under certain special conditions, such as the capacity recovery phase, where the battery's state of harmonics (SOH) may experience a brief increase, manifesting as a rapid abrupt change in the time domain, which is a high-frequency signal. Figure 9 Furthermore, it is demonstrated that even in the extrapolated region outside the training data range, the B-PINN method can still capture this non-monotonic aging trend relatively accurately, fully demonstrating the superior ability of Fourier features in extracting and modeling such high-frequency dynamic information.

[0049] (3) Estimation results of the improved model with hard boundary constraints (physical information neural network model) Comparative analysis of the training process demonstrates the significant advantages of the hard-constraint method. For example... Figure 10 As shown, the loss curve of the hard-boundary-constrained model reaches a stable plateau after approximately 500 iterations, while the model without hard-coded constraints requires approximately 800 iterations to reach a similar convergence state, resulting in a 38% improvement in training efficiency. This demonstrates that directly embedding physical boundary conditions into the network architecture forces the model to strictly adhere to physical laws from the early stages of training, effectively guiding the optimization direction during network training and significantly improving training efficiency. It also greatly enhances the stability and convergence speed of the optimization process. Notably, the hard-constraint scheme maintains more stable convergence characteristics in the later stages of training, indicating that this method has stronger robustness to hyperparameter selection.

[0050] This paper compares and analyzes the performance of the basic PINN framework, the B-PINN framework optimized through multidimensional training equilibrium, and the HB-PINN (Physical Information Neural Network Model) framework improved by introducing hard boundary constraints in a few-shot learning scenario. Through comprehensive analysis... Figure 11 The HB-PINN estimation results shown, along with the RMSE indices of the three models in the interpolation and extrapolation stages in Table 2, allow for an in-depth comparison of the specific performance improvements of each optimization strategy.

[0051] Table 2 Comparison of PINN estimation errors

[0052] In the table, BT1 represents battery 1; BT2 represents battery 2; BT3 represents battery 3; Mean represents the average value of the three batteries; Data-Driven is a purely data-driven model, a cross-modal attention fusion model without any physical model constraints; PINN is a physically-informed neural network, containing only basic data loss, boundary loss, and physical loss terms, without applying subsequent equalization and hard constraint optimization measures; B-PINN is a PINN optimized through multi-dimensional training equalization, with added optimization strategies to address imbalance issues during training; HB-PINN is a B-PINN with added hard boundary constraints.

[0053] The HB-PINN model demonstrated superior SOH estimation performance across all three cells. Figure 11 As shown, the model can not only generate a smooth decay curve, but also accurately track the decay trajectory of SOH. Even in the extrapolation stage, it exhibits reliable prediction stability, which fully demonstrates that the HB-PINN method, which integrates multidimensional training equilibrium and hard boundary constraints, can effectively solve the problem of few-shot learning.

[0054] Table 2 shows that during the interpolation prediction stage, the average RMSE of B-PINN and HB-PINN reached 0.37% and 0.39%, respectively, which are significantly improved compared to the 0.48% of the basic PINN. The multi-dimensional training balancing strategy enhances the model's ability to learn from physical model constraints, and the synergistic effect of hard boundary constraints in strictly guaranteeing initial boundary conditions provides crucial support for accurate estimation under sparse data conditions.

[0055] The improved performance of the PINN model is particularly evident in the extrapolation prediction stage. Compared to the traditional PINN method, B-PINN, based on multidimensional training equilibrium, effectively addresses the problem of training failure for some battery samples, controlling the average RMSE to 1.12%. Furthermore, HB-PINN, which introduces hard boundary constraints, further improves the prediction accuracy to 1.08%, with the most significant performance improvement on battery 2, reducing the relative error by 0.32%. Experimental results demonstrate that the proposed optimization strategy based on multidimensional training equilibrium and hard boundary constraints can significantly enhance the model's generalization performance in unknown data regions, providing a more reliable solution for battery SOH estimation in small sample scenarios.

[0056] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for assessing the health status of lithium-ion batteries based on physical information and data-driven approaches, characterized in that, include: S1: Construct a physical model describing the capacity decay law of lithium-ion batteries based on empirical model constraints and physical law constraints; S2: Construct a physical information neural network model, which includes an attention-based cross-modal fusion estimation network and a loss function embedded in the physical model; the attention-based cross-modal fusion estimation network integrates a feature dimension alignment module and an attention feature fusion module, adds random Fourier features between the feature dimension alignment module and the attention feature fusion module, and introduces a hard boundary coding layer in the attention feature fusion module; S3: Use battery aging data to train the physical information neural network model; S4: Use a trained physical information neural network model to estimate the health status of lithium-ion batteries.

2. The lithium-ion battery health status assessment method based on physical information and data-driven approach according to claim 1, characterized in that, The construction of the physical model in step S1 is specifically as follows: S101: Establish empirical model constraints, introducing upper limit K for battery capacity loss, initial capacity loss C, and health characteristics based on the Verhulst model. A partial differential equation is established, and the degradation rate constant r is constructed as a learnable parameter related to the ultrasonic signal amplitude Pt, resulting in the empirical model constraint formula: In the formula, The percentage of capacity loss. As a scaling factor to enhance the response to battery heterogeneity, For time; S102, Physical laws constrain, IC characteristics It is positively correlated with the SOH of the battery, which is constrained by physical laws: In the formula, For the battery's health status, For incremental capacity; S103. Obtain the physical model based on empirical model constraints and physical law constraints: 。 3. The lithium-ion battery health status assessment method based on physical information and data-driven approach according to claim 1, characterized in that, The attention-based cross-modal fusion estimation network in step S2 is specifically as follows: The feature dimension alignment module maps the multimodal input features to a unified feature space to achieve feature dimension alignment. The aligned features are mapped to a high-dimensional frequency domain space using the random Fourier feature method to achieve frequency domain equalization; Eight attention heads are constructed to compute feature representations of different subspaces in parallel. Each attention head takes the frequency domain equalization as input. The fused features are obtained by concatenating and linearly transforming the outputs of multiple attention heads. The fused features are input into the hard-boundary coding layer to correct the initial state of the network; The corrected output in the hard-boundary coding layer is used as the prediction value to calculate the loss function.

4. The lithium-ion battery health status assessment method based on physical information and data-driven approach according to claim 3, characterized in that, The random Fourier feature method is as follows: The random Fourier feature method uses an encoder Frequency domain equalization is achieved by encoding the aligned features and mapping them to a high-dimensional frequency domain space; the encoding formula is as follows: in Satisfies a random normal distribution This is used to map features to a high-dimensional space; It is an adjustable parameter. For the aligned low-dimensional features, It represents high-dimensional frequency domain features.

5. The lithium-ion battery health status assessment method based on physical information and data-driven approach according to claim 3, characterized in that, The formula for the hard constraint mechanism of the hard boundary coding layer is: In the formula, It is the raw output of the physical neural network. This is the final network output after applying hard boundary constraints. This represents the initial health state of the battery. It is the initial time; Using the double tangent function tanh, the time... When approaching 0, The value approaches 0.

6. The lithium-ion battery health status assessment method based on physical information and data-driven approach according to claim 1, characterized in that, The loss function in step S2 is as follows: (1) Loss of observation data Physical model constraint loss loss with initial boundary conditions Construct the initial loss function: in For the network weights of the neural network, These are unknown parameters in the physical model; (2) Introduce adaptive weights and gradient residual constraints into the initial loss function to construct the loss function.

7. The lithium-ion battery health status assessment method based on physical information and data-driven approach according to claim 6, characterized in that, The initial loss function incorporates adaptive weights and gradient residual constraints as follows: Assuming that the noise from the data loss and the physical model constraint loss follows a Gaussian distribution, a learnable noise parameter is introduced into the initial loss function. and The noise levels of the observed data and physical model constraints during the training phase are respectively characterized; the weights of the loss terms are inversely proportional to the noise parameters, and the weights of the observed data loss term and the physical model constraint loss term are respectively... and Furthermore, a regularization term is introduced. Thus, the loss function for adaptive weights is expressed as: ； Calculate physical residuals Sampling points relative to physical model constraints Differential The derivative result is added as a gradient residual constraint term to the loss function of the adaptive weights. After gradient enhancement, the model's loss function is: 。 8. The lithium-ion battery health status assessment method based on physical information and data-driven approach according to claim 7, characterized in that, The loss function is defined as follows: in, The residual between the neural network model and the physical model. Used to constrain the monotonic relationship between IC characteristics and battery health status; For the sampling points of the observation data, Sampling points constrained by the physical model; This refers to the total number of sampling points, including the number of observed data points. and the number of constraint points in the physical model , This is the sample's index number. It is the first The sampling time points of each observation data point The time point for collecting the initial sample observation data. It is the first Sampling time points constrained by a physical model The SOH value predicted by the neural network model. For the first Input the health characteristics of each sample.

9. The lithium-ion battery health status assessment method based on physical information and data-driven approach according to claim 1, characterized in that, In step S3, the physical information neural network model constructed in step S2 is trained using the first 50% of the data from the battery aging process. The experimental scenario of data sparsity is artificially increased and the sampling interval is expanded so that the physical information neural network model can only utilize 10% of the original data.

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