Battery state prediction method based on fusion of time sequence neural network and physical information neural network

Abstract

This invention discloses a battery state prediction method based on the fusion of temporal neural networks and physical information neural networks. The method mainly includes a fusion framework of temporal neural networks and physical information neural networks. First, the temporal neural network is used to mine hidden temporal features of each time-series state and predict the battery's state of health (SOH) and relative uptime (RUL). Then, the mined hidden temporal features of each time-series state are used as prior knowledge and input into TNPINN's DeepHTPM (Deep Hidden Time Series Physical Model) module to guide its learning process. DeepHTPM also receives battery capacity data for each time series and the predicted values ​​from the temporal neural network as input. Based on these inputs, the DeepHTPM module jointly establishes an implicit physical model for battery health prediction and effectively combines the RUL or SOH prediction loss from the temporal neural network with the loss obtained from the implicit physical model as the final loss to constrain the model. This invention's method can be used to predict the SOH and RUL of lithium-ion battery datasets with various negative electrode materials.

Description

Technical Field

[0001] This invention relates to the field of deep learning technology, particularly battery management and life prediction technology, and is especially applicable to the fields of battery state monitoring and battery health management systems. Specifically, it relates to a battery state prediction method based on the fusion of temporal neural networks and physical information neural networks. Background Technology

[0002] Lithium-ion batteries are the most common type of rechargeable battery, widely used in various portable electronic devices, aerospace, and electric vehicles. The rapid development of the electric vehicle market has further increased the demand for lithium-ion batteries. As the primary energy source for electric vehicles, lithium-ion batteries have become one of the most important industrial consumer products. Due to the high cost of battery replacement after degradation and the serious impact of battery degradation on the safety and performance of electric vehicles, Battery Management Systems (BMS) are now widely developed for electric vehicles. The main tasks of a BMS are to estimate the State of Health (SOH) and predict the Remaining Useful Life (RUL). Accurate SOH and RUL estimates help to obtain relevant information about the battery's condition in advance, allowing for timely battery replacement before the battery capacity degrades to a safe threshold, thus ensuring the safe operating environment of the electric vehicle's power system.

[0003] Research on the prediction of SOH and RUL of lithium-ion batteries has received widespread attention, with many researchers proposing various prediction methods. These methods can be categorized into three types: physics-based, experience-based, and data-driven. Among them, data-driven methods have gained significant attention in recent years because they do not require consideration of the complex physical and electrochemical reactions within lithium-ion batteries. They can predict the state of lithium-ion batteries by directly mining the implicit battery degradation patterns from historical battery data. Furthermore, with the in-depth development of artificial intelligence technology, an increasing number of deep neural networks, including Long Short-Term Memory (LSTM), Convolutional Neural Networks (CNN), and Recurrent Neural Networks (RNN), are being used for SOH and RUL prediction.

[0004] Despite some progress in predicting battery state of health (SOH) and relative uptime (RUL), a careful review of existing work reveals the following challenges: 1) Lithium-ion batteries experience long degradation cycles and numerous cycles, requiring a significant time to test a complete battery degradation process. Data acquisition difficulties result in a limited number of battery data samples. Using traditional deep learning methods on small datasets for battery state prediction leads to severe overfitting, poor generalization ability, and low prediction accuracy. 2) Transfer learning is a feasible method for addressing small sample problems. However, the electrochemical characteristics and battery features of batteries using different anode materials vary significantly. Pre-training transfer learning on a relatively abundant dataset of lithium-ion batteries using a specific anode material and then applying the learned knowledge to datasets of other materials is difficult to guarantee effective results.

[0005] Physics-Informed Neural Networks (PINNs) overcome the limitations of insufficient data samples by using physical laws as priors to guide various models during the learning process, thus becoming an effective method for predicting small datasets. For example, the paper [HYSun, LSPeng, SLHuang, SSLi, Y.Long, S.Wang, and W.Zhao, "Development of a physics-informed doubly fedcross-residual deep neural network for high-precision magnetic flux leakage defect size estimation," IEEE Trans.Ind.Informat., vol.18, no.3, pp.1629–1640, 2022.] proposed a battery state prediction method based on PINNs. The authors integrated known physical laws and equations into the neural network model to combine the advantages of traditional physical models with the flexibility of data-driven models. However, many physical laws and equations in this study require a large amount of accurate experimental measurement data, and many physical properties are difficult to obtain.The literature [M. Raissi, "Deep hidden physics models: Deep learning of nonlinear partial differential equations," J. Mach. Learn. Res., vol. 19, pp. 932–955, 2018.] and [S. Cofre-Martel, ELDroguett, and M. Modarres, "Remaining useful life estimation through deep learning partial differential equation models: A framework for degradation dynamics interpretation using latent variables," Shock Vib., vol. 2021, p. 9937846, 2021.] further proposes the Deep Hidden Physics Model (DeepHPM), which uses the method of establishing semi-empirical semi-physical partial differential equations (PDEs) to simulate the degradation kinetics of lithium-ion batteries, thereby further enhancing the model's predictive performance. The literature [Wang F, Zhai Z, Zhao Z, et al. Physics-informed neural network for lithium-ion battery degradation stable modeling and prognosis[J]. Nature communications, 2024, 15(1): 4332.] proposes a dynamic prediction and modeling method for battery state of equilibrium (SOH) based on PINN. However, this study only integrates linear neural networks with the dynamic model for battery state prediction, without fully exploring the potential temporal characteristics of battery data. This results in model instability when processing time series data, and the model's prediction performance is not ideal.

[0006] To address the aforementioned issues and accurately predict the State of Health (SOH) and Rullow Usage (RUL) of small-sample silicon-based batteries, this invention proposes an integrated framework of Temporal Neural Network and Physics-Informed Neural Network (TNPINN). This architecture first utilizes a temporal series neural network to mine hidden temporal features of each time-series state and predict the battery's SOH and RUL. Then, the mined hidden temporal features are used as prior knowledge and input into TNPINN's Deep Hidden Time Series Physical Model (DeepHTPM) module to guide its learning process. DeepHTPM also receives battery capacity data from each time series and the predicted values ​​from the temporal series neural network as input. Based on these inputs, the DeepHTPM module jointly establishes an implicit physical model for predicting the battery's state of health. Finally, the prediction loss of RUL or SOH from the temporal series neural network is effectively combined with the loss obtained from the implicit physical model, serving as the final loss to constrain the model. Summary of the Invention

[0007] The purpose of this invention is to address the shortcomings of existing technologies by providing a battery state prediction method based on the fusion of temporal neural networks and physical information neural networks. By combining the advantages of physical information neural networks in guiding the network model using physical laws with the ability of temporal neural networks to uncover hidden temporal features, this method enhances the accuracy of RUL and SOH predictions on small-sample lithium battery datasets, and improves the model's generalization ability and stability. This provides a practical solution for predicting the health status of lithium batteries. This solution can significantly reduce the testing time for the cycle life of new material batteries, thus promoting the industrialization of new battery materials.

[0008] To achieve the above objectives, this invention provides a battery state prediction method based on the fusion of temporal neural networks and physical information neural networks, comprising the following steps:

[0009] (1) Obtain the lithium battery capacity degradation dataset;

[0010] (2) Construct a fusion model of time series neural network and physical information neural network for lithium battery prediction;

[0011] (3) The time series data of lithium batteries in the dataset are processed by the time series neural network, and the hidden time series features of each time series state are mined by the time series neural network. The mined hidden time series features of each time series state are used as prior knowledge and input into the deep hidden time series physical module of the fusion model to guide the learning process of the deep hidden time series physical module.

[0012] (4) The deep hidden time series physical model simultaneously receives battery capacity data from each time series, SOH or RUL prediction values ​​from the time series neural network, and hidden time series features mined by the time series neural network as input information; the deep hidden time series physical model constructs an implicit physical model for predicting battery health status based on the input information; the prediction loss of RUL or SOH, the loss obtained from the implicit PDE, and the gradient loss of the implicit PDE are used together as the final loss to constrain and optimize the fusion model.

[0013] (5) Introduce the Bayesian optimization algorithm to automatically adjust the initial hyperparameters of the fusion model in order to optimize the overall prediction performance of the fusion model and improve the convergence speed of the model;

[0014] (6) The optimized fusion model is used to predict the SOH and RUL of lithium batteries.

[0015] Furthermore, before constructing a fusion model of time series neural networks and physical information neural networks, the feasibility of predicting using a combined data-driven and temporal feature-based implicit dynamic model is analyzed through mathematical formulas.

[0016] Furthermore, the expression for the deep hidden temporal physics module is:

[0017]

[0018] in, x represents the remaining battery capacity after the k-th cycle. k For the remaining capacity u n The rate of change, DeepHTPM represents the deep hidden temporal physics module. Represents the predicted values ​​of a temporal neural network; h′1,…,h′ k-1 ,h′ k+1 ,…,h′ n-1 They represent and Φ is the trainable network parameter of the temporal neural network.

[0019] Furthermore, the temporal neural network receives time series variables X. n Using the initial hidden state h0 as input, the input sequence is processed step by step according to time steps; at each time step, the input x of the current time step is received. iThe hidden state h of the previous time step i-1 Then, the hidden state h for the next time step is generated using a temporal neural network. i Then h i This process continues, using the new input as a reference, until the final predicted value is obtained. Represented as:

[0020]

[0021] In the formula, θ is a nonlinear function;

[0022] The loss function of a temporal neural network is used to minimize the predicted value. and the actual remaining battery capacity value u n The difference between them, the loss function L u Represented as:

[0023]

[0024] Furthermore, let H x =[h′1,…,h′ k-1 ,h′ k+1 ,…,h′ n-1 ] T The parameters of DeepHTPM are minimized. The training is based on the mean squared error loss between the predicted and actual values, expressed as:

[0025]

[0026] In addition, define the function f(X) n ;θ,Φ):

[0027]

[0028] in Let u be the first partial derivative of x; let the gradient of the PDE residual be used as a loss to constrain DeepHTPM; let X represents n For f(X) n The derivatives of θ and Φ; the gradient loss of the PDE residual is expressed as:

[0029]

[0030] L fx The extreme value of f should approach 0, while when f X The closer L is to 0 fx The closer to the extreme value; the more comprehensive the three losses L u L f and The total loss function of the fusion model is:

[0031]

[0032] Where λ u , λ f and Represents the weight of different losses in the total loss, and

[0033] Furthermore, the training process of the fusion model is as follows: First, initialize the hyperparameters, including the neural network hyperparameters θ, Φ, and λ. u , λ f , Then, a cyclical training process begins, in which each round of training first uses a time-series neural network to calculate the predicted values ​​of the state of health (SOH) or remaining useful life (RUL). Next, the input data X is calculated using an automatic differentiation tool. n For predicted values The partial derivatives are obtained. Then X is further calculated. k right The partial derivatives are obtained. After obtaining these derivatives, the dynamic model G is used in conjunction with the input data, predicted values, and partial derivatives to calculate the predicted output of the dynamic model. Then, a new function f is constructed, whose value is and The difference is calculated again using automatic differentiation. About X k The partial derivatives are obtained. During the loss calculation phase, the predicted values ​​are calculated separately. The mean square error between the true value u and the actual value u is the loss. Calculation function The error from zero is obtained calculate The error from zero is obtained Finally, the total loss is calculated by combining these loss values; then, the hyperparameters of the neural network are updated based on the loss values, and the regularization coefficient λ is updated using a Bayesian optimization algorithm. u , λ f , λ fn The entire training process is repeated continuously until the preset convergence condition is met or the maximum number of training rounds is reached.

[0034] The beneficial effects of this invention are as follows: This invention proposes a fusion architecture for predicting the battery health status of small-sample lithium battery datasets. This architecture is a novel scheme that seamlessly integrates prior information from physical or empirical models with monitoring data in the dataset. This scheme utilizes hidden temporal features mined by temporal neural networks as prior knowledge and physical laws to correct the battery prediction model, further constraining the model, thereby solving the overfitting problem of small-sample datasets and enhancing the model's generalization ability. This invention further improves the dynamic model of battery prediction using the chain rule. Each input of the DeepHTPM module is divided into a predictable part and an unknown part. For the unknown part, this invention puts it into the parameters to be learned and obtains it through training with a temporal neural network, while the known part is used as a new input to the DeepHTPM module. This makes each input value of the module originate from the predicted output value of the temporal neural network at each time step. Compared with previous studies where the input of the prediction model originated from the final predicted output of the temporal neural network, the method proposed in this invention guides the model's learning based on the features mined at each time step, thus greatly enhancing the prediction ability and model stability. The battery health state prediction method proposed in this invention can be used to predict the SOH and RUL of lithium battery datasets with various negative electrode materials. It provides a practical solution for predicting the health status of lithium batteries when the data sample is limited, which can greatly save the testing time of cycle life of new material batteries and promote the industrialization process of new material batteries. Attached Figure Description

[0035] Figure 1 This is an architecture diagram of the TNPINN fusion model of this invention;

[0036] Figure 2 This is a distribution diagram of the mean absolute error (MAE) and root mean square error (RMSE) of different models for SOH prediction in the embodiments of the present invention;

[0037] Figure 3 This is a distribution diagram of the mean absolute error (MAE) and root mean square error (RMSE) of different models for RUL prediction in the embodiments of the present invention. Detailed Implementation

[0038] The proposed fusion architecture effectively fits the degradation process of small-sample lithium-ion batteries by integrating a deep hidden physical model with a time-series neural network. It utilizes hidden time-series features mined by the time-series neural network as prior knowledge and physical laws to correct the battery prediction model, further constraining the model and thus solving the overfitting problem of small-sample datasets, enhancing the model's generalization ability. Battery state prediction methods can be divided into three types: physics-based prediction, empirical, and data-driven methods. Physics-based methods use the battery's electrical and chemical properties to describe its behavior, establishing a dynamic model of the lithium-ion battery using physical characteristics and measurement data to describe its response under different operating conditions. Empirical methods use fixed mathematical relationships to characterize the long-term dependence between the degradation behavior of lithium-ion batteries and the number of cycles, thereby predicting the future health state of lithium-ion batteries. Both of these methods require rich prior knowledge in specific domains and complex programming, resulting in difficulties in obtaining data features, complex analysis processes, and high computational costs. In recent years, numerous researchers have proposed data-driven models, which are particularly suitable for complex systems that are difficult to explain using traditional dynamic models and scenarios lacking in-depth understanding. These models can uncover complex underlying relationships in data without requiring a deep understanding of the system's physical principles. However, while traditional neural networks have significant advantages in processing time-series data, their prediction performance is unsatisfactory in datasets with scarce data and high noise levels. For the prediction problem of small-sample lithium-ion battery datasets, some studies have proposed PINN-based prediction methods; however, existing PINN-based battery state prediction methods do not fully utilize and mine the temporal features of the data. Furthermore, previous studies have used the input of prediction models derived from the final prediction output of temporal neural networks. Compared to existing research, the method proposed in this invention guides model learning based on the features mined at each time step, thus significantly enhancing prediction capability and model stability. Moreover, unlike existing research, this paper introduces PINN fusion as prior information for the dynamic model and information extracted from monitoring data to jointly predict battery health status, enhancing model robustness and noise resistance, and greatly improving the model's predictive ability. In addition to predicting the battery's State of Health (SOH), the model of this invention can also predict the battery's Remaining Charge-Discharge Cycle (RUL), thus allowing for early prediction of the remaining charge-discharge cycles and battery performance. This eliminates the need for manual charge-discharge experiments to calculate RUL at the end of the battery's lifespan, thereby significantly shortening the delay period for new materials.

[0039] This invention proposes a small-sample lithium battery health status prediction method based on model fusion, comprising the following steps:

[0040] (1) Obtain the lithium battery capacity degradation dataset.

[0041] The dataset obtained was provided by the Novel Battery Research Laboratory of the School of Materials Science and Engineering, Tianjin Normal University. This battery utilizes a simple ultrasonic dispersion method to combine conductive agents with nano-silicon particles, preparing silicon, Si / CNTs, Si / Graphene, and Si / MXene composites. Electrochemical testing was performed using a VMP-300 potentiostatic / current-static meter (Bio-Logic, France). The test voltage range was set between 0.01V and 3V. The battery discharge experiment ended when the battery capacity decreased to 50%, yielding charge-discharge data. This dataset provides unique insights into the performance and degradation characteristics of silicon anode lithium-ion batteries and offers a valuable resource for evaluating the proposed method under different battery chemistry systems.

[0042] (2) The feasibility of predicting using a combined data-driven and temporal-series-based implicit dynamic model is analyzed through mathematical formulas.

[0043] A. Battery degradation model

[0044] In battery management, State of Health (SOH) and Remaining Usable Life (RUL) are used to describe the battery's health status and remaining usable life, respectively, and are two key concepts in battery management systems. SOH refers to the ratio of the battery's current capacity to its rated capacity. When the battery's usable capacity falls below a pre-specified SOH, the battery is considered to be in failure. RUL refers to the number of charge-discharge cycles the battery can withstand before reaching its time of failure. For battery n, let u... n If we represent its current capacity, then:

[0045]

[0046] Q Nom This represents the battery's nominal capacity, and Qt represents the usable capacity after the t-th charge-discharge cycle. t is called the cycle number. Generally, when the battery operates under the same conditions in each cycle, the observed results after each cycle are as follows:

[0047] u n =u(t)(2)

[0048] Where u is a function for calculating the remaining battery capacity. The rate of change of the battery capacity is:

[0049]

[0050] Equation (3) is an explicit ordinary differential equation (ODE) parameterized by the set θ, where F represents a nonlinear function of t and u. For example, based on the formation and initial surface of the solid electrolyte interphase (SEI) in lithium-ion batteries, as well as the growth process of crack surfaces, we have:

[0051]

[0052] Where t k This represents the k-th iteration, t l Indicates earlier than t k The monitoring time, θ={θ1,θ2,…,θ6} are composite parameters. Each of them must be set according to dozens of electrochemical parameters, including the geometric area of ​​the graphite electrode film, the crack propagation activation energy and the solid porosity of the electrode film, etc. Equation (4) describes the molecular-level aging mechanism of the battery in detail. However, since the electrochemical parameters of the battery are difficult to collect in experiments, this model is difficult to apply in practice. Based on the observed degradation trend of lithium batteries, a simplified semi-empirical model can be proposed using regression analysis, which is expressed as:

[0053]

[0054] Where β represents the basic linear degradation rate determined by the battery's state of charge, depth of discharge, and battery temperature. By integrating equation (5) to u, the exponential function solution with decreasing absolute value of the derivative can be obtained. However, since different batteries have different degradation modes and mechanical properties, this model cannot fit the trend of accelerated battery degradation in early cycles. Deep learning-based methods mine the degradation patterns of batteries based on historical data, without considering the complex electrochemical reactions of the battery. They can directly mine the hidden battery degradation patterns from historical battery data and achieve accurate prediction of battery state. Therefore, this invention aims to mine the hidden dynamic model of battery degradation through neural networks to predict battery SOH and RUL.

[0055] B. Implicit Dynamic Model Combining Data-Driven and Temporal Features

[0056] To uncover the hidden dynamic model of battery degradation using a time-series neural network, this invention sets SOH as a continuous time series variable X. n =[x1,x2,...,xk,...,x] n-1 A multivariable function, where x k Let be the remaining battery capacity after the k-th cycle. When the battery operates under the same conditions in each cycle, we have:

[0057] u n =u(x1,x2,x3,…,x) n-1 (6)

[0058] According to formula (6), we can obtain That is, x k For the remaining capacity u n The rate of change is:

[0059]

[0060] Where θ is a nonlinear function of G(.). is u n First-order partial differential with respect to x. This is a second-order partial differential equation. To balance accuracy and computational complexity, this invention omits the higher-order partial differential parts in the above equation, and... Approximately expressed as:

[0061]

[0062] Where G is the established estimate The function. To obtain By solving for the undetermined parameter θ using a neural network, we have:

[0063]

[0064] in For the pair obtained through the neural network model The estimated value.

[0065] By improving formula (9) using the chain rule of calculus, we can obtain:

[0066]

[0067] Where h i (i = 1, 2, ..., k-1, k+1, ..., n-1) are obtained from X through a neural network. n The hidden temporal features extracted from each cycle, h i Represented as:

[0068] hi=N(x i ,h i-1 (11)

[0069] In formula (11) This can be obtained through the automatic differentiator of a neural network, and among them... The weights of the neural network can be considered as being placed into the θ hyperparameter, obtained through neural network training. Based on the above analysis, this invention proposes a Deep Hidden Temporal Physical Module (DeepHTPM) for dynamic prediction of battery degradation:

[0070]

[0071] Where h′1,…,h′ k-1 ,h′ k+1 ,…,h′ n-1 They represent and Φ is the trainable network parameter of the neural network.

[0072] (3) Based on feasibility, a fusion model of time series neural network and physical information neural network is constructed, that is, a fusion model of time series neural network and deep physical information neural network is constructed for lithium-ion battery prediction.

[0073] The time-series data of lithium batteries in the dataset are processed using a time-series neural network to mine hidden time-series features of each time-series state. The mined hidden time-series features of each time-series state are used as prior knowledge and input into the deep hidden time-series physical module of the fusion model to guide the learning process of the deep hidden time-series physical module.

[0074] The deep hidden time series physical model simultaneously receives battery capacity data from various time series, SOH or RUL predictions from time series neural networks, and hidden time series features mined by time series neural networks as input information. Based on the above input information, the deep hidden time series physical model constructs an implicit physical model for predicting battery health status. The prediction loss of RUL or SOH, the loss obtained from the implicit PDE, and the gradient loss of the implicit PDE are used together as the final loss to constrain and optimize the fusion model of the entire fusion framework.

[0075] The fusion model TNPINN is composed as follows Figure 1 The diagram includes three modules: a surrogate neural network (temporal neural network), a deep hidden time series physical module (DeepHTPM), and an automatic differentiator.

[0076] The surrogate neural network, or time-series neural network, can be various common time-series neural networks such as LSTM, GRU, and RNN, or combinations thereof. The surrogate neural network receives the time-series variable X. n The initial hidden state h0 is used as input, and the input sequence is then processed step by step according to time steps. At each time step, the input x of the current time step is received. i The hidden state h of the previous time step i-1 Then, the hidden state h for the next time step is generated through a proxy neural network. i Then h i This process continues, using the new input as a reference, until the final predicted value is obtained. The above process can be represented as follows:

[0077]

[0078] The loss function of a surrogate neural network is used to minimize the predicted value. and the actual remaining battery capacity value u n The difference between them, the loss function L u Represented as:

[0079]

[0080] Figure 1 The DeepHTPM approximation formula (10) is used to establish an implicit physical model for predicting battery health status when no explicit dynamic prediction model is available. DeepHTPM consists of multiple fully connected layers. The intermediate data obtained after each fully connected layer must be processed by an activation function to introduce nonlinearity into the neural network. The hyperbolic tangent is used as the activation function of DeepHTPM due to its differentiability. The input of DeepHTPM is the original input X of the time-series neural network. n u n Predicted value And the partial derivatives of the hidden states at each time step in the temporal neural network with respect to the input values ​​at the corresponding time steps. Furthermore, the values ​​of all differentials involved in this module can be calculated by an automatic differentiator. Let H... x =[h′1,…,h′ k-1 ,g′ k+1 ,…,h′ n-1 ] T The parameters of DeepHTPM can be minimized. The training is based on the mean squared error loss between the predicted and actual values, expressed as:

[0081]

[0082] In addition, define the function f(X) n ;θ,Φ):

[0083]

[0084] in Let represent the first-order partial derivative of u with respect to x. This invention uses the gradient of the PDE residual as a loss constraint on DeepHTPM. Let X in formula (16) n For f(X) n The derivatives of θ and Φ. The gradient loss of the PDE residual is expressed as:

[0085]

[0086] L fx The extreme value of f should approach 0, while when f x The closer L is to 0 fxThe closer it gets to the extreme value. Combining the three types of losses mentioned above, the total loss function of TNPINN in this paper is:

[0087]

[0088] Where λ u , λ f and Represents the weight of different losses in the total loss and

[0089] (4) Introduce the Bayesian optimization algorithm to automatically adjust the initial hyperparameters of the fusion model in order to optimize the overall prediction performance of the model and improve the convergence speed of the model.

[0090] Experiments have shown that the weights of the loss terms have a significant impact on the prediction results. However, manually adjusting the weights is very time-consuming and labor-intensive. Therefore, this paper introduces a Bayesian optimization algorithm to automatically adjust the weights of each loss term. This algorithm guides the search process by establishing a probabilistic model of the objective function, thereby finding the parameter configuration that makes the objective function achieve its optimal value. Running this algorithm usually requires only a small number of sampling points to find the global optimum, and it can adaptively adjust the position and number of sampling points.

[0091] In the TNPINN training process, SSE(·) represents the three components of the total loss calculated using formulas (14), (15), and (17), respectively. This represents the training data.

[0092] The training process of the TNPINN model is as follows:

[0093] Input: Training data and model hyperparameters,

[0094] Output: Proxy neural network NN u(X) n ,h0;θ), dynamic model

[0095] 1: Initialize θ, Φ, λ u ,λ f , Equal hyperparameters;

[0096] 2: Begin the cycle training. The process of each cycle is described below:

[0097] 3: The predicted value u of SOH or RUL is calculated based on a time series neural network;

[0098] 4: Calculate X using an automatic differentiator n right The partial derivative;

[0099] 5: Calculate X using an automatic differentiator k right The partial derivative;

[0100] 7: The prediction of G was calculated using DeepHTPM;

[0101] 8: Build new functions

[0102] 9: Calculate X using an automatic differentiator k right The partial derivative;

[0103] 10: Calculate the loss function of the surrogate neural network using Formula 14;

[0104] 11: Calculate using formula 15 The mean squared error loss between the predicted and actual values;

[0105] 12: Calculate the gradient loss of the PDE residuals using Equation 17;

[0106] 13: Calculate the total loss Calculate the total loss using formula 18 (18);

[0107] 14: Update θ, Φon loss

[0108] 15: Update λ using Bayesian algorithm u ,λ f ,

[0109] It should be noted that the training process of the TNPINN model begins with the initialization of hyperparameters, including the neural network hyperparameters θ, Φ, and λ. u , λ f , Then, the training process begins, with each round of training first using a time-series neural network to calculate the predicted values ​​of the state of health (SOH) or remaining useful life (RUL). Next, the input data X is calculated using an automatic differentiation tool. n For predicted values The partial derivatives are obtained. Then X is further calculated. k right The partial derivatives are obtained. After obtaining these derivatives, the dynamic model G is used in conjunction with the input data, predicted values, and partial derivatives to calculate the predicted output of the dynamic model. Then, a new function f is constructed, whose value is and The difference is calculated again using automatic differentiation. About X k The partial derivatives are obtained. During the loss calculation phase, the predicted values ​​are calculated separately. The mean square error between the true value u and the actual value u is the loss. Calculation function The error from zero is obtained calculate The error from zero is obtained Finally, the total loss is calculated by combining these loss values; then, the hyperparameters of the neural network are updated based on the loss values, and the regularization coefficient λ is updated using a Bayesian optimization algorithm. u , λ f , The entire training process is repeated continuously until the preset convergence condition is met or the maximum number of training rounds is reached.

[0110] (5) The optimized fusion model is used to predict the SOH and RUL of lithium batteries.

[0111] Example:

[0112] A. Dataset Description

[0113] The experimental datasets for this invention are divided into two parts. The first dataset is a self-collected dataset, primarily acquired from the laboratory of the School of Materials Science and Engineering at Tianjin Normal University. This dataset contains 49 independent samples of novel material batteries, representing 20 different novel material battery models. Each battery has slight differences in composition, with a total of 276 battery samples. During the experiment, these batteries underwent constant current charging and discharging cycles at a certain current. The dataset records the maximum capacity that the batteries could retain in each cycle. The other dataset is the open-source NASA lithium-carbon battery dataset provided by NASA. This dataset is designed to study the lifespan and replacement patterns of general-purpose lithium-ion batteries for the development of new hybrid vehicles. This dataset uses 18650 lithium batteries as the research object and collects data using accelerated aging experiments.

[0114] Experiment 1: Analysis of Results from Self-Collected Datasets

[0115] To explore the performance of different models in predicting SOH and RUL, this experiment designed two sets of experimental cases, labeled Experiment A and Experiment B. Experiment A predicted the SOH of the battery, while Experiment B predicted the RUL. Since the surrogate neural network in PINPINN can be any type of temporal neural network, in both sets of experiments, RNN, PINN-RNN-DeepHTPM, Bayes PINN-RNN-DeepHTPM, and LSTM were trained respectively. PINN-LSTM-DeepHTPM and Bayes PINN-LSTM-DeepHTPM were used to predict the SOH of the battery. In Experiment B, these six architectures were trained to predict the RUL of the battery. PINN-RNN-DeepHTPM refers to the TNPINN fusion architecture of the surrogate neural network using RNN, PINN-LSTM-DeepHTPM refers to the TNPINN fusion architecture of the surrogate neural network using LSTM, and Bayes PINN-RNN-DeepHTPM and Bayes PINN-LSTM-DeepHTPM refer to the fusion architectures after adding Bayesian algorithms to optimize the weight system.

[0116] The model performance evaluation metrics are: 1) Root Mean Square Error (RMSE), also known as the root mean square deviation. RMSE is a commonly used measure of the difference between measured values; it is the square root of the ratio of the sum of the squares of the deviations of the observed values ​​from the true values ​​to the number of observations. The specific formula is:

[0117]

[0118] in and u i This represents the output of the prediction model and the actual data label corresponding to the i-th input sample.

[0119] 2) Mean Absolute Error (MAE): MAE is a key metric used to measure the accuracy of a forecasting model. It is calculated by summing the absolute differences between the actual and predicted values, and then averaging them. The specific formula is:

[0120]

[0121] The learning rate and epoch settings for each method in the experiment are shown in Table 1. Furthermore, to reduce the number of hyperparameters that need to be adjusted, this invention first adjusts the baseline model parameters, and then applies the obtained optimal baseline model parameters to the architecture of this invention.

[0122] 1) Experiment A: Experiment A presents the SOH estimation results for three architectures at different numbers of hidden layers, as shown in Table 2. The SOH prediction results and evaluation metrics for each architecture at the number of hidden layers achieving the best prediction performance are shown in Table 2. Figure 2 .

[0123] Table 1 shows that PINN-RNN-DeepHTPM and PINN-LSTM-DeepHTPM significantly reduce RMSE and MAE values ​​compared to traditional RNN and LSTM models. This indicates that using the hidden temporal features of each mined temporal state as physical constraints does indeed improve the model's feature extraction capability, thus significantly enhancing the model's prediction performance. After introducing Bayesian optimization to optimize the weights of the three losses, Bayes PINN-RNN-DeepHTPM and Bayes PINN-LSTM-DeepHTPM, compared to PINN-RNN-DeepHTPM, show lower prediction errors under the same number of hidden layers. This demonstrates the significant impact of loss weights on model performance and reflects the superiority of Bayesian optimization for hyperparameter optimization. Among the six compared models, Bayes PINN-LSTM-DeepHTPM has the best prediction performance, with an RMSE of only 0.646% and an MAE of 0.536 when there are 128 hidden layers.

[0124] To verify the stability of the models, each model was trained and tested 10 times on this dataset, and the experimental results are as follows. Figure 2 As shown. From Figure 2 As can be seen, compared with other models, the Bayes PINN-RNN-DeepHTPM and Bayes PINN-LSTM-DeepHTPM proposed in this invention have higher stability across various metrics, especially Bayes PINN-LSTM-DeepHTPM, which exhibits the least volatility and lower prediction error. This demonstrates that despite a small dataset, the model of this invention still achieves stable prediction performance.

[0125] 2) Experiment B: Experiment B tested the RUL estimation results of different architectures under different numbers of hidden layers. The experimental results are shown in Table 3. Furthermore, the RUL prediction results and evaluation metrics for each architecture at the optimal number of hidden layers are shown in [Table 3]. Figure 3 .

[0126] Experiment B compares six different neural network models to predict battery RUL. Table 3 shows that as the number of hidden layers increases, the prediction results of all methods first decrease and then increase. This is because when the number of hidden layers is too large, the model may experience gradient vanishing. Among the six methods, the RNN model performs the worst, mainly because simple RNN units may not be sufficient to capture complex sequential states, and the model has poor generalization ability when the dataset is small, making it difficult to capture potential hidden features. Experimental results show that Bayes PINN-RNN-DeepHTPM and Bayes PINN-LSTM-DeepHTPM exhibit lower prediction errors and better prediction performance compared to other models across all hidden layers. Table 3 shows that Bayes PINN-RNN-DeepHTPM achieves the best prediction performance with 64 hidden layers, with RMSE and MAE of only 2.5% and 1.884%, respectively, demonstrating the superiority of the proposed fusion architecture. Furthermore, Figure 3 This also demonstrates that the proposed fusion architecture is more stable, and even under small sample conditions, the proposed fusion architecture achieves stable prediction performance.

[0127] Experiment 2: Analysis of Results from the NASA Dataset Experiment

[0128] In the NASA dataset experiment, this invention used data from one of the batteries (B0005, B0006, B0007, and B0018) as the test set, and the remaining three as the training set for performance testing in rotation. The comparison models were EEMD-IHSSA-LSTM-TCN, TCN, LSTM, SSA-LSTM, and IHSSA-LSTM. The TCN model is a time series prediction model based on a convolutional neural network, combining the features of one-dimensional convolution and residual connections. The SSA-LSTM model is a prediction model combining the Sparrow Search algorithm (SSA) and LSTM, where the Sparrow Search algorithm is used to optimize the initial parameters of the neural network, and LSTM is used for SOH and RUL prediction. The IHSSA-LSTM model utilizes an improved Sparrow Search algorithm, combined with iterative chaotic mapping and variable spiral coefficients to optimize the hyperparameters of the LSTM. The EEMD-IHSSA-LSTM-TCN model is a prediction model obtained by combining the TCN model and ensemble empirical mode decomposition (EEMD) signal processing techniques on the basis of the IHSSA-LSTM model.

[0129] Table 4 shows that when using the model of this invention to predict the NASA dataset, the maximum MAE is only 1.3% and the RMSE is only 1.661%, with the best prediction results reaching an MAE of 0.82% and an RMSE of 1.102%. Experimental data demonstrate that the model of this invention is far superior to other comparative methods, indicating that the model of this invention has a significant advantage in predicting the SOH of lithium-ion batteries, proving that introducing prior knowledge into the proposed PINN network to constrain the model does indeed help improve the accuracy of model prediction. Furthermore, since the TCN model and the LSTM model are single models, their prediction accuracy is relatively low, with LSTM showing the worst prediction performance. The main reason may be the unique gate control mechanism of the LSTM network, which makes its model structure more complex compared to traditional time-series prediction algorithms. This complexity requires more time and computational resources for LSTM during training.

[0130] Table 1 Training parameters for each architecture

[0131] Method Learning Rate Epoch RNN 0.01 100 PIRNN 0.01 100 Bayes PIRNN 0.01 100 LSTM 0.01 100 PILSTM 0.01 100 Ours 0.01 100

[0132] Table 2 Prediction results of SOH for lithium-silicon batteries

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[0134] Table 3. RUL Prediction Results for Lithium-Silicon Batteries

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[0136] Table 4. NASA Dataset SOH Prediction Results

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[0138]

Claims

1. A battery state prediction method based on the fusion of temporal neural networks and physical information neural networks, characterized in that, Includes the following steps: (1) Obtain the lithium battery capacity degradation dataset; (2) Construct a fusion model of time series neural network and physical information neural network for lithium battery prediction; (3) Use a time series neural network to process the time series data of lithium batteries in the dataset, and mine the hidden time series features of each time series state through the time series neural network. The hidden temporal features of each time series state are extracted as prior knowledge and input into the deep hidden time series physical module of the fusion model to guide the learning process of the deep hidden time series physical module. The expression for the deep hidden time-physics module is: in, x represents the remaining battery capacity after the k-th cycle. k For the remaining capacity u n The rate of change, DeepHTPM represents the deep hidden temporal physics module. Represents the predicted values ​​of a temporal neural network; h′1,…,h′ k-1 ,h′ k+1 ,…,h′ n-1 They represent and Φ represents the trainable network parameters of the temporal neural network; Let H x =[h′1,…,h′ k-1 ,h′ k+1 ,…,h′ n-1 ] T The parameters of DeepHTPM are minimized. The training is based on the mean squared error loss between the predicted and actual values, expressed as: In addition, define the function f(X) n ;θ,Φ): in Let u be the first partial derivative of x; let the gradient of the PDE residual be used as a loss to constrain DeepHTPM; let X represents n For f(X) n The derivatives of θ and Φ; the gradient loss of the PDE residual is expressed as: L fx The extreme value of f should approach 0, while when f X The closer L is to 0 fx The closer to the extreme value; the more comprehensive the three losses L u L f and The total loss function of the fusion model is: Where λ u , λ f and Represents the weight of different losses in the total loss, and (4) The deep hidden time series physical model simultaneously receives battery capacity data from each time series, SOH or RUL prediction values ​​predicted by the time series neural network, and hidden time series features mined by the time series neural network as input information. The deep hidden time series physical model constructs an implicit physical model for predicting battery health status based on the input information; the prediction loss of RUL or SOH, the loss obtained by implicit PDE, and the gradient loss of implicit PDE are used together as the final loss to constrain and optimize the fusion model. (5) Introduce the Bayesian optimization algorithm to automatically adjust the initial hyperparameters of the fusion model in order to optimize the overall prediction performance of the fusion model and improve the convergence speed of the model; (6) The optimized fusion model is used to predict the SOH and RUL of lithium batteries.

2. The battery state prediction method based on the fusion of temporal neural network and physical information neural network according to claim 1, characterized in that, Before constructing a fusion model of time series neural networks and physical information neural networks, we analyze the feasibility of predicting using an implicit dynamic model that combines data-driven and time-series features through mathematical formulas.

3. The battery state prediction method based on the fusion of temporal neural network and physical information neural network according to claim 1, characterized in that, The time-series neural network receives time-series variables X. n Using the initial hidden state h0 as input, the input sequence is processed step by step according to time steps; at each time step, the input x of the current time step is received. i The hidden state h of the previous time step i-1 Then, the hidden state h for the next time step is generated using a temporal neural network. i Then h i This process continues, using the new input as a reference, until the final predicted value is obtained. Represented as: In the formula, θ is a nonlinear function; The loss function of a temporal neural network is used to minimize the predicted value. and the actual remaining battery capacity value u n The difference between them, the loss function L u Represented as:

4. The battery state prediction method based on the fusion of temporal neural network and physical information neural network according to claim 1, characterized in that, The training process of the fusion model is as follows: First, initialize the hyperparameters, including the neural network hyperparameters θ, Φ, and λ. u , λ f , Then, a cyclical training process begins, in which each round of training first uses a time-series neural network to calculate the predicted values ​​of the state of health (SOH) or remaining useful life (RUL). Next, the input data X is calculated using an automatic differentiation tool. n For predicted values The partial derivatives are obtained. Then X is further calculated. k right The partial derivatives are obtained. After obtaining these derivatives, the dynamic model G is used in conjunction with the input data, predicted values, and partial derivatives to calculate the predicted output of the dynamic model. Then, a new function f is constructed, whose value is and The difference is calculated again using automatic differentiation. About X k The partial derivatives are obtained. During the loss calculation phase, the predicted values ​​are calculated separately. The mean square error between the true value u and the actual value u is the loss. Calculation function The error from zero is obtained calculate The error from zero is obtained Finally, the total loss is calculated by combining these loss values; then, the hyperparameters of the neural network are updated based on the loss values, and the regularization coefficient λ is updated using a Bayesian optimization algorithm. u , λ f , The entire training process is repeated continuously until the preset convergence condition is met or the maximum number of training rounds is reached.

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