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

Abstract

The invention discloses a battery state prediction method based on fusion of a time sequence neural network and a physical information neural network, which mainly comprises a fusion framework of the time sequence neural network and the physical information neural network, and comprises the following steps of: firstly, mining hidden time sequence characteristics of each time sequence state by using the time sequence neural network and predicting SOH and RUL of a battery; secondly, the mined hidden time sequence characteristics of all time sequence states serve as priori knowledge to be input into a deep hidden time sequence physical module DeepHTPM of the TNPINN to guide the learning process of the module, and the DeepHTPM also receives the battery capacity of all time sequences and a predicted value predicted by a time sequence neural network as input at the same time; the DeepHTPM module jointly establishes an implicit physical model for predicting the state of health of the battery according to the inputs, and effectively combines the prediction loss of RUL or SOH of the time sequence neural network with the loss obtained by the implicit physical model to serve as the final loss to constrain the model. The method can be used for predicting SOH and RUL of lithium battery data sets of various negative electrode materials.

Description

Technical Field

[0001] The present invention relates to the field of deep learning technology, in particular to battery management and life prediction technology, and is particularly suitable for the field of battery status monitoring and battery health management systems. Specifically, it relates to a battery status prediction method based on the fusion of a time series neural network and a physical information neural network. Background Art

[0002] Lithium-ion batteries are the most common rechargeable batteries and are widely used in various portable electronic devices, aerospace, and electric vehicles. The rapid development of the electric vehicle market has led to a growing demand for lithium-ion batteries. As the main energy source for electric vehicles, lithium-ion batteries have become one of the most important industrial consumption. Due to the high replacement cost after battery degradation and the serious impact of battery degradation on the safety and performance of electric vehicles, battery management systems (BMS) are currently widely developed for electric vehicles. The main tasks of BMS are battery state of health (SOH) estimation and remaining useful life (RUL) prediction. Accurate SOH and RUL estimation help to obtain relevant information about the battery status in advance, replace the battery in time before the battery power declines to the safety threshold, and ensure the safety of the working environment of the electric vehicle power system.

[0003] The research on SOH and RUL prediction of lithium batteries has received widespread attention. Many researchers have proposed various prediction methods, which can be divided into three categories: physics-based, experience-based, and data-driven methods. Among them, the data-driven method does not need to consider the complex physical and electrochemical reaction processes inside the lithium-ion battery. It can predict the state of lithium-ion batteries by directly mining the implicit battery degradation laws from the battery historical data. It has received widespread attention in recent years. In addition, with the in-depth development of artificial intelligence technology, more and more deep neural networks, including long short-term memory networks (Long Short-Term Memory, LSTM), convolutional neural networks (Convolutional Neural Networks, CNN) and recurrent neural networks (Recurrent Neural Network, RNN) are used for SOH and RUL estimation.

[0004] Although certain results have been achieved in battery SOH and RUL prediction, after a careful review of existing work, it was found that the existing work has the following challenges: 1) The attenuation period of lithium-ion batteries is long and the number of cycles is large. It takes a long time to test a complete battery attenuation process. Due to the difficulty in data collection, battery data samples are usually small. Using traditional deep learning methods to predict battery status on small sample data sets will lead to problems such as serious model overfitting, poor generalization ability, and low prediction accuracy; 2) Transfer learning is a feasible way to solve the small sample problem. However, there are significant differences in the electrochemical properties and battery characteristics of batteries with different negative electrode materials. It is difficult to guarantee the effect of using transfer learning to pre-train on a certain negative electrode material lithium-ion battery data set with relatively rich data and then apply the knowledge learned from it to other material data sets.

[0005] Physics-Informed Neural Network (PINN) overcomes the limitation of insufficient data samples in the data set by using physical laws as priors to guide various models during the learning process, and becomes an effective method to solve the prediction of small sample data sets. For example, the literature [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 leakagedefect size estimation," IEEE Trans.Ind.Informat., vol.18, no.3, pp.1629–1640, 2022.] proposes a battery state prediction method based on physical information neural network. The authors integrate known physical laws and equations into the neural network model to combine the advantages of traditional physical models and the flexibility of data-driven models. However, many physical laws and equations in this study require a large amount of accurate experimental measurement data support, and many physical properties are difficult to obtain.The literature [M.Raissi,"Deep hidden physics models:Deep learning of nonlinear partialdifferential equations,"J.Mach.Learn.Res.,vol.19,pp.932–955,2018.] and [S.Cofre-Martel,ELDroguett,and M.Modarres,"Remaining useful life estimation throughdeep learning partial differential equation models:A framework fordegradation dynamics interpretation using latent variables,"Shock Vib.,vol.2021,p.9937846,2021.] further proposed a deep hidden physics model (Deep Hidden Physics Model, DeepHPM), which uses the method of establishing a semi-empirical and semi-physical partial differential equation (Partial Differential Equation, PDE) to simulate the degradation dynamics of lithium-ion batteries and further enhance the model's prediction 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.] proposed a battery SOH dynamic prediction and modeling method based on PINN. However, this study only integrated the linear neural network with the dynamic model of battery state prediction, and did not fully explore the potential time series characteristics of battery data, resulting in model instability when processing time series data and unsatisfactory model prediction results.

[0006] In view of the above problems, in order to accurately predict the SOH and RUL of small sample silicon-based material batteries, the present invention proposes an integrated framework of temporal neural network and physics-informed neural network (TNPINN). The architecture first uses the time series neural network to mine the hidden time series features of each time series state and predict the SOH and RUL of the battery. Then, the mined hidden time series features of each time series state are input as prior knowledge into the deep hidden time series physical module DeepHTPM (Deep Hidden time series physical model, DeepHTPM) of TNPINN to guide the learning process of the module. DeepHTPM also receives the battery capacity of each time series and the predicted value predicted by the time series neural network as input. The DeepHTPM module jointly establishes an implicit physical model for battery health state prediction based on these inputs, and effectively combines the prediction loss of RUL or SOH by the time series neural network with the loss obtained by the implicit physical model as the final loss to constrain the model. Summary of the invention

[0007] The purpose of the present invention is to address the deficiencies of the prior art and provide a battery status prediction method based on the fusion of a time series neural network and a physical information neural network; by combining the advantages of the physical information neural network in guiding the network model using physical laws with the ability of the time series neural network to mine hidden time series features, the accuracy of RUL and SOH prediction under small sample lithium battery data sets is enhanced, and the generalization ability and stability of the model are improved. This provides a practical solution for predicting the health status of lithium batteries. This solution can greatly save the test time of the cycle life of new material batteries and promote the industrialization of new battery materials.

[0008] To achieve the above object, the present invention provides a battery state prediction method based on the fusion of a time series neural network and a physical information neural network, comprising the following steps:

[0009] (1) Obtain 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 data set are processed using a time series neural network, and the hidden time series features of each time series state are mined through 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 physics module of the fusion model to guide the learning process of the deep hidden time series physics module;

[0012] (4) The deep hidden time series physical model simultaneously receives the battery capacity data of each time series, the SOH or RUL predicted value predicted by the time series neural network, and the 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 battery health state prediction based on the input information; the prediction loss of RUL or SOH, the loss obtained by 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) Introducing the Bayesian optimization algorithm to automatically adjust the initial hyperparameters of the fusion model to optimize the overall prediction performance of the fusion model and improve the model convergence speed;

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

[0015] Furthermore, before constructing the fusion model of time series neural network and physical information neural network, the feasibility of implicit dynamic model prediction combining data-driven and time series features is analyzed through mathematical formulas.

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

[0017]

[0018] in, Represents the remaining battery capacity x after the kth cycle k For the remaining capacity u n The rate of change of DeepHTPM stands for Deep Hidden Time Physics Module. represents the predicted value of the time series neural network; h′1,…,h′ k-1 ,h′ k+1 ,…,h′ n-1 Respectively and Φ is a trainable network parameter of the temporal neural network.

[0019] Furthermore, the time series neural network receives the time series variable X n With the initial hidden state h0 as input, the input sequence is processed step by step according to the time step; at each time step, the input x of the current time step is received iand the hidden state h of the previous time step i-1 , and then generate the hidden state h of the next time step through the temporal neural network i , and then h i As a new input, continue in this way until the final predicted value is obtained It is expressed as:

[0020]

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

[0022] The loss function of the temporal neural network is used to minimize the predicted value and the actual remaining battery capacity value u n The difference between the loss function L u It is expressed 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 by The mean square error loss between the predicted value and the true value is used for training, which is expressed as:

[0025]

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

[0027]

[0028] in represents the first-order partial differential of u with respect to x; the gradient of the PDE residual is used as a loss to constrain DeepHTPM; let Represents X n f(X n ; θ; Φ) derivative; the gradient loss of the PDE residual is expressed as:

[0029]

[0030] L fx The extreme value of should be close to 0, and when f X The closer to 0, the higher the L fx The closer to the extreme value; the comprehensive 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, the hyperparameters are initialized, including the neural network hyperparameters θ, Φ, λ u ,λ f , Then it enters the cyclic training process. Each round of training first calculates the predicted value of the health state SOH or the remaining service life RUL through the time series neural network Next, use the automatic differentiation tool to calculate the input data X n For the predicted value The partial derivative of Then further calculate X k right The partial derivative of After obtaining these derivatives, the dynamic model G is used to combine the input data, predicted values ​​and partial derivatives to calculate the predicted output of the dynamic model Then, construct a new function f whose value is and and again use automatic differentiation to calculate About X k The partial derivative of In the loss calculation stage, the predicted values ​​are calculated separately The mean square error between the true value u and the loss is Calculation Function The error with zero gives calculate The error with zero gives Finally, the total loss is calculated by combining these loss values; finally, the hyperparameters of the neural network are updated based on the loss values, and the regularization coefficient λ is updated using the Bayesian optimization algorithm. u ,λ f ,λ fn The entire training process continues to cycle until the preset convergence condition is met or the maximum number of training rounds is reached.

[0034] The beneficial effects of the present invention are as follows: the present invention proposes a fusion architecture for predicting the battery health state of a small sample lithium battery data set, which is a new solution that seamlessly integrates the prior information of a physical or empirical model with the monitoring data in the data set. This solution uses the hidden time series features mined by the time series neural network as prior knowledge and physical laws to correct the battery prediction model, further constrain the model, thereby solving the overfitting problem of the small sample data set and enhancing the generalization of the model. The present invention further improves the dynamic model of battery prediction by using the chain rule. Each input of the DeepHTPM module is divided into a predictable part and an unknown part. For the unknown part, the present invention puts it into the parameters to be learned, obtains it through the time series neural network training, and the known part is used as the new input of the DeepHTPM module. This makes each input value of the module originate from the predicted output value of each time step of the time series neural network. Compared with the previous research in which the input of the prediction model is derived from the final prediction output of the time series neural network, the method proposed by the present invention guides the learning of the model according to the features mined at each time step, so the prediction ability and model stability are greatly enhanced. The battery health status prediction method proposed in the present invention can be used to predict the SOH and RUL of lithium battery data sets of various negative electrode materials. It provides a practical solution for predicting the health status of lithium batteries when data samples are limited, which can greatly save the testing time of the cycle life of new material batteries and promote the industrialization process of new material batteries. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is the architecture diagram of the fusion model TNPINN of the present invention;

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

[0037] Figure 3 It is a distribution diagram of the mean absolute error (MAE) and root mean square error (RMSE) of RUL prediction by different models in the embodiment of the present invention. DETAILED DESCRIPTION

[0038] The fusion architecture proposed in the present invention effectively fits the degradation process of small sample lithium batteries by fusing the deep hidden physical model with the time series neural network method, and uses the 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, thereby solving the overfitting problem of small sample data sets and enhancing the generalization of the model. Battery state prediction methods can be divided into three types: physics-based prediction, experience-based and data-driven methods. The physics-based method uses the electrical and chemical properties of the battery to describe the behavior of the battery, and establishes a dynamic model of the lithium-ion battery by using physical properties and measurement data to describe the response of the battery under different operating conditions. The experience-based method uses a fixed mathematical relationship to characterize the long-term dependence between the degradation behavior of the lithium-ion battery and the number of cycles, thereby predicting the future health status of the lithium-ion battery. Both of the above methods require rich prior knowledge and complex program design in specific fields, and there are problems such as difficulty in obtaining data features, complex analysis process and high computational cost. In recent years, many researchers have proposed data-driven models. Such models are particularly suitable for complex systems that are difficult to explain with traditional dynamic models and scenarios that lack in-depth understanding. They can mine complex potential relationships in data without having an in-depth understanding of the physical principles of the system. However, traditional neural networks have obvious advantages in processing time series data, but the prediction effect is not ideal for data sets with scarce data and more data noise. In response to the prediction problem of small sample lithium-ion battery data sets, some studies have proposed prediction methods based on PINN. However, the existing PINN-based battery state prediction methods have not fully utilized and mined the time series characteristics of the data. In addition, the input of the prediction model in previous studies is derived from the final prediction output of the time series neural network. Compared with existing studies, the method proposed in the present invention guides the learning of the model according to the features mined at each time step, so the prediction ability and model stability are greatly enhanced. In addition, unlike existing studies, this paper introduces PINN fusion as the prior information of the dynamic model and the information extracted from the monitoring data to jointly predict the battery health state, so that the model robustness and noise resistance are enhanced, and the prediction ability of the model is greatly improved. In addition to predicting the battery SOH, the model of the present invention can also predict the battery RUL, so that the remaining charge and discharge times and battery performance of the battery can be predicted in advance at an early stage, without the need to manually conduct charge and discharge experiments until the end of the battery life to perform RUL statistics, thereby greatly shortening the delay period of new materials.

[0039] The present invention proposes a method for predicting the health status of a small sample lithium battery based on model fusion, comprising the following steps:

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

[0041] The acquired data set is provided by the New Battery Research Laboratory of the School of Materials Science and Engineering of Tianjin Normal University. The battery uses a simple ultrasonic dispersion method to combine the conductive agent with nano-silicon particles to prepare silicon, Si / CNTs, Si / Graphene and Si / MXene composites. The electrochemical test used a VMP-300 potentiostatic / galvanostatic instrument (Bio-Logic, France). The test voltage range was set between 0.01V and 3V. When the battery capacity dropped to 50%, the battery discharge experiment ended and the charge and discharge data were obtained. This data set provides unique insights into the performance and degradation characteristics of silicon negative electrode lithium-ion batteries, and provides a valuable resource for evaluating the proposed method under different battery chemical systems.

[0042] (2) The feasibility of implicit dynamic model prediction based on combined data-driven and time series features is analyzed through mathematical formulas.

[0043] A. Battery Degradation Model

[0044] In the field of battery management, SOH and RUL are used to describe the health status of the battery and the remaining useful life of the battery, respectively. They are two key concepts in battery management systems. SOH refers to the ratio of the current capacity of the battery to its rated capacity. When the available capacity of the battery is lower than the pre-specified SOH, the battery is considered to be failed. RUL refers to the number of times the battery can be charged and discharged before reaching the failure time. For battery n, let u n Represents its current capacity, then:

[0045]

[0046] Where Q Nom represents the nominal capacity of the battery, Qt represents the available capacity after the tth charge and discharge cycle, and t is called the number of cycles (cycles). In general, when the battery operates under the same conditions in each cycle, the observed results after each cycle are:

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

[0048] Where u is the function to find the remaining battery capacity. The rate of change of the battery capacity is:

[0049]

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

[0051]

[0052] where t k represents the kth cycle, t l Indicates that it is earlier than t k The monitoring time, θ = {θ1, θ2, …, θ6} is a composite parameter. 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 phase porosity of the electrode film. Formula (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, the 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 linearized degradation rate determined by the battery charge state, discharge depth and battery temperature. By integrating formula (5) to u, an exponential function solution with decreasing absolute value of the derivative can be obtained. However, due to the different degradation modes and mechanical properties of different batteries, the model cannot fit the trend of accelerated battery degradation in early cycles. The deep learning-based method mines the degradation law of the battery according to the historical data of battery degradation. It does not need to consider the complex electrochemical reactions of the battery. It can directly mine the implicit battery degradation law from the historical data of the battery to achieve accurate prediction of the battery state. To this end, the present invention intends to mine the hidden dynamic model of battery degradation through a neural network to achieve the prediction of battery SOH and RUL.

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

[0056] In order to mine the hidden dynamic model of battery degradation through time series neural network, the present invention sets SOH as a continuous time series variable X n =[x1,x2,...,xk,...,x n-1 ] is a multivariable function, where x k is the remaining capacity of the battery after the kth cycle (battery capacity). When the battery operates under the same conditions in each cycle, there is:

[0057] u n =u(x1,x2,x3,…,x n-1 )(6)

[0058] According to formula (6), we can get 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 The first partial differential with respect to x. is the second-order partial differential. In order to balance accuracy and computational complexity, the present invention omits the high-order partial differential part in the above formula and converts Approximately expressed as:

[0061]

[0062] Where G is the estimated To obtain Solve the unknown parameter θ through the neural network, then we have:

[0063]

[0064] in is the pair obtained by the neural network model The estimated value of .

[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) is obtained from X by neural network n The hidden temporal features of each cycle round extracted from i It is expressed as:

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

[0069] In formula (11) can be obtained through the automatic differentiator of the neural network, where The weight of the neural network can be regarded as being put into the θ hyperparameter, which is obtained by training the neural network. Based on the above analysis, the present invention proposes a deep hidden temporal physical module (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 Respectively and Φ is the trainable network parameter of the neural network.

[0072] (3) Based on the 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 model and deep physical information neural network is constructed for lithium-ion battery prediction.

[0073] The time series data of lithium batteries in the data set are processed using a time series neural network, and the hidden time series features of each time series state are mined through 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 physics module of the fusion model to guide the learning process of the deep hidden time series physics module.

[0074] The deep hidden time series physical model simultaneously receives the battery capacity data of each time series, the SOH or RUL predicted value predicted by the time series neural network, and the 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 battery health state prediction based on the above input information; the prediction loss of RUL or SOH, the loss obtained by 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 composition of the fusion model TNPINN is as follows Figure 1 The shown system includes three modules, namely, agent neural network (temporal neural network), deep hidden time series physics module DeepHTPM and automatic differentiator.

[0076] The proxy neural network is a time series neural network, which can be various common time series neural networks such as LSTM, GRU and RNN, etc. or their combination. The proxy neural network receives the time series variable X n The initial hidden state h0 is used as input, and then the input sequence is processed step by step according to the time step. At each time step, the input x of the current time step is received. i and the hidden state h of the previous time step i-1 , and then generate the hidden state h of the next time step through the proxy neural network i , and then h i As a new input, continue in this way until the final predicted value is obtained The above process is expressed as:

[0077]

[0078] The loss function of the proxy neural network is used to minimize the predicted value and the actual remaining battery capacity value u n The difference between the loss function L u It is expressed as:

[0079]

[0080] Figure 1 The Deep Hidden Time Series Physics Module DeepHTPM approximates formula (10) in the paper, which is used to establish an implicit physical model for battery health status prediction when there is no explicit dynamic prediction model available. DeepHTPM consists of multiple fully connected layers. The intermediate data obtained after each fully connected layer must pass through an activation function to introduce nonlinear factors into the neural network. The hyperbolic tangent is used as the activation function of DeepHTPM because of its differentiability. The input of DeepHTPM is the input X of the original time series neural network. n ,u n The predicted value of And the partial derivatives of the hidden state of each time step in the sequential neural network with respect to the input value of the corresponding time step. In addition, the values ​​of all differentials involved in this module can be calculated by the automatic differentiator. Let H x =[h′1,…,h′ k-1 ,g′ k+1 ,…,h′ n-1 ] T , the parameters of DeepHTPM can be minimized by The mean square error loss between the predicted value and the true value is used for training, which is expressed as:

[0081]

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

[0083]

[0084] in represents the first-order partial differential of u with respect to x. The present invention uses the gradient of the PDE residual as a loss to constrain DeepHTPM. Indicates that X in formula (16) n f(X n ; θ; Φ). The gradient loss of the PDE residual is expressed as:

[0085]

[0086] L fx The extreme value of should be close to 0, and when f x The closer to 0, the higher the L fxCombining the above three losses, 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) The Bayesian optimization algorithm is introduced to automatically adjust the initial hyperparameters of the fusion model to optimize the overall prediction performance of the model and improve the model convergence speed.

[0090] Experiments have found that the weight of the loss term has a great impact on the prediction results. However, manually adjusting the weight is very time-consuming and labor-intensive. Therefore, this paper introduces the Bayesian optimization algorithm to automatically adjust the weight of each loss term. The algorithm guides the search process by establishing a probability model of the objective function to find the parameter configuration that makes the objective function achieve the optimal value. Running the algorithm usually requires only a few sampling points to find the global optimal solution, and can adaptively adjust the location and number of sampling points.

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

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

[0093] Input: Training data and model hyperparameters,

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

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

[0096] 2: Start the cycle training. The following describes the cycle process of each round:

[0097] 3: Calculate the predicted value u of SOH or RUL based on the time series neural network;

[0098] 4: Compute X using the automatic differentiator n right The partial differential of

[0099] 5: Compute X using the automatic differentiator k right The partial differential of

[0100] 7: Use DeepHTPM to calculate and predict the results of G;

[0101] 8: Building new functions

[0102] 9: Compute X using the automatic differentiator k right The partial differential of

[0103] 10: The loss function of the proxy neural network is calculated using formula 14;

[0104] 11: Calculate using formula 15 The mean square error loss between the predicted value and the true value;

[0105] 12: Use formula 17 to calculate the gradient loss of the PDE residual;

[0106] 13: Calculate the total loss by(18) calculates the total loss according to formula 18;

[0107] 14: Update θ,Φ on loss

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

[0109] It should be noted that the training process of the TNPINN model starts with initializing the hyperparameters, including the neural network hyperparameters θ, Φ, and λ. u ,λ f , Then, the training process begins. Each round of training first uses a time series neural network to calculate the predicted value of the health state SOH or the remaining service life RUL. Next, use the automatic differentiation tool to calculate the input data X n For the predicted value The partial derivative of Then further calculate X k right The partial derivative of After obtaining these derivatives, the dynamic model G is used to combine the input data, predicted values ​​and partial derivatives to calculate the predicted output of the dynamic model Then, construct a new function f whose value is and and again use automatic differentiation to calculate About X k The partial derivative of In the loss calculation stage, the predicted values ​​are calculated separately The mean square error between the true value u and the loss is Calculation Function The error with zero gives calculate The error with zero gives Finally, the total loss is calculated by combining these loss values; finally, the hyperparameters of the neural network are updated based on the loss values, and the regularization coefficient λ is updated using the Bayesian optimization algorithm. u ,λ f , The entire training process is repeated until the preset convergence condition is met or the maximum number of training rounds is reached.

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

[0111] Example:

[0112] A. Dataset Description

[0113] The experimental data sets of the present invention are divided into two. The first data set is a self-collected data set, which is mainly collected in the laboratory of the School of Materials Science and Engineering of Tianjin Normal University. This data set contains 49 independent new material battery samples, which represent 20 different new material battery models. The composition of each battery has slight differences, and there are a total of 276 battery samples. During the experiment, these batteries were subjected to constant current charging and discharging cycles under a certain current, and the data set recorded the maximum capacity value that the battery can maintain for each cycle. The other data set is the open source NASA lithium-carbon battery data set provided by the National Aeronautics and Space Administration of the United States. This data set is to study the life replacement mode of general-purpose lithium-ion batteries and develop new hybrid vehicles. This data set takes the 18650 lithium battery as the research object and collects data in the form of accelerated aging experiments.

[0114] Experiment 1: Analysis of experimental results of self-collected data sets

[0115] In order to deeply explore the performance of different models in SOH and RUL prediction, this experiment designed two groups of experimental cases, marked as Experiment A and B, where Experiment A predicts the SOH of the battery and Experiment B predicts the RUL of the battery. Since the proxy neural network in TNPINN can be any type of temporal neural network, in the two groups of experiments, RNN, PINN-RNN-DeepHTPM, Bayes PINN-RNN-DeepHTPM and LSTM are trained respectively, and PINN-LSTM-DeepHTPM and Bayes PINN-LSTM-DeepHTPM are used to predict the SOH of the battery. In experiment B, these six architectures are trained separately to predict the RUL of the battery, among which PINN-RNN-DeepHTPM refers to the TNPINN fusion architecture in which the proxy neural network adopts RNN, PINN-LSTM-DeepHTPM refers to the TNPINN fusion architecture in which the proxy neural network adopts LSTM, Bayes PINN-RNN-DeepHTPM and Bayes PINN-LSTM-DeepHTPM refer to the fusion architecture after adding the Bayesian algorithm to optimize the weight system.

[0116] The model performance evaluation indicators are: 1) Root mean square error (RMSE), that is, 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 square of the deviation between the observed value and the true value and the number of observations. The specific formula is:

[0117]

[0118] in and u i 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 main indicator used to measure the accuracy of the prediction model. The calculation principle is to sum and average the absolute value of the difference between the true value and the predicted value. The specific formula is:

[0120]

[0121] The learning rate and epoch settings of each method in the experiment are shown in Table 1. In addition, in order to reduce the number of hyperparameters that need to be adjusted, the baseline model parameters are first adjusted in the present invention, and then the obtained optimal parameters of the baseline model are applied to the architecture of the present invention.

[0122] 1) Experiment A: Experiment A is the results of SOH estimation for three architectures with different numbers of hidden layers, as shown in Table 2. The SOH prediction results and evaluation index results of each architecture with the number of hidden layers that achieves the best prediction effect are shown in Figure 2 .

[0123] Table 1 shows that the RMSE and MAE values ​​of PINN-RNN-DeepHTPM and PINN-LSTM-DeepHTPM are significantly reduced compared with the traditional RNN and LSTM models, which indicates that taking the hidden time series features of each time series state mined as physical constraints does improve the feature extraction ability of the model, and the prediction performance of the model is significantly enhanced. After introducing the Bayesian optimization algorithm to optimize the weights of the three losses, Bayes PINN-RNN-DeepHTPM and Bayes PINN-LSTM-DeepHTPM compared with PINN-RNN-DeepHTPM, PINN-LSTN-DeepHTPM showed lower prediction errors under the condition of the same number of hidden layers, showing the important influence of the weight value of the loss on the model performance, and also reflecting the superiority of the Bayesian optimization algorithm for hyperparameter optimization. Among the six comparison models, Bayes PINN-LSTM-DeepHTPM has the best prediction effect, with an RMSE of only 0.646% and a MAE value of 0.536 when the hidden layer is 128.

[0124] In order to verify the stability of the model, each model was trained and tested 10 times on this dataset. The experimental results are as follows: Figure 2 As shown. Figure 2 It can be seen that compared with other models, the Bayes PINN-RNN-DeepHTPM and Bayes PINN-LSTM-DeepHTPM proposed in the present invention have higher stability in various indicators, especially Bayes PINN-LSTM-DeepHTPM, which has the smallest volatility and lower prediction error. This shows that despite the small data set, the model of the present invention still achieves a stable prediction effect.

[0125] 2) Experiment B: Experiment B tests the RUL estimation results of different architectures with different numbers of hidden layers. The experimental results are shown in Table 3. In addition, the RUL prediction results and evaluation indicators of each architecture with the optimal number of hidden layers are shown in Figure 3 .

[0126] Experiment B predicts the battery RUL by comparing 6 different neural network models. Table 3 shows that as the number of hidden layers of the model increases, the prediction results of various methods all show a state of first decreasing and then increasing. This is because when the number of hidden layers is too large, the model may experience gradient disappearance. The RNN model has the worst prediction effect among the six methods. The main reason is that the simple RNN unit may not be sufficient to capture complex sequence states, and the model has poor generalization ability when there is less data in the data set, and it is difficult to capture potential hidden features in the data. The experimental results show that Bayes PINN-RNN-DeepHTPM and Bayes PINN-LSTM-DeepHTPM show lower prediction errors than other models at all hidden layers, and the prediction effect is more ideal. It can be seen from Table 3 that Bayes PINN-RNN-DeepHTPM has the best prediction effect when the hidden layer is 64, and the RMSE and MAE are only 2.5% and 1.884%, which reflects the superiority of the fusion architecture proposed in this article. In addition, Figure 3 It also shows that the fusion architecture proposed in this paper is more stable, and even under small sample conditions, the fusion architecture proposed in this paper has achieved stable prediction performance.

[0127] Experiment 2: Analysis of NASA dataset experimental results

[0128] In the NASA data set experiment, the present invention uses the data of one of the batteries B0005, B0006, B0007, and B0018 in the data set as a test set, and the remaining three are used as training sets to perform performance tests in turn. The comparison models of the group are EEMD-IHSSA-LSTM-TCN model, TCN model, LSTM model, SSA-LSTM model and IHSSA-LSTM model. Among them, the TCN model is a time series prediction model based on a convolutional neural network, which combines the characteristics of one-dimensional convolution and residual connection. The SSA-LSTM model is a prediction model that combines the sparrow search algorithm (SSA) and LSTM, wherein the sparrow search algorithm is used to optimize the initial parameters of the neural network, and LSTM is used to perform SOH and RUL predictions. IHSSA-LSTM is a prediction model that uses an improved sparrow search algorithm, combined with iterative chaotic mapping and variable spiral coefficients to optimize the hyperparameters of 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 technology on the basis of the IHSSA-LSTM model.

[0129] It can be seen from Table 4 that when the model of the present invention is used to predict the NASA data set, the maximum MAE is only 1.3%, and the RMSE is only 1.661%. In the best case, the prediction effect can reach a MAE of 0.82% and a RMSE of 1.102%. The experimental data show that the model of the present invention is far superior to other comparative methods, indicating that the model of the present invention has significant advantages in predicting the SOH of lithium-ion batteries, and proves that the introduction of prior knowledge in the proposed PINN network to constrain the model does help improve the accuracy of model prediction. In addition, since the TCN model and the LSTM model are single models, the prediction accuracy of the two models is low, among which the LSTM prediction performance is the worst. The main reason may be the unique gate control mechanism of the LSTM network. Compared with the traditional time series prediction algorithm, its model structure is more complex. This complexity requires more time and computing resources for LSTM during training.

[0130] Table 1 Training parameters of 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 SOH prediction results of lithium-silicon battery

[0133]

[0134] Table 3 RUL prediction results of lithium-silicon battery

[0135]

[0136] Table 4 SOH prediction results of NASA dataset

[0137]

[0138]

Claims

1. A battery state prediction method based on the fusion of time series neural network and physical information neural network, characterized in that: The following steps are involved: (1) Obtain 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 the time series neural network to process the time series data of lithium batteries in the data set, and mine the hidden time series features of each time series state through 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 physics module of the fusion model to guide the learning process of the deep hidden time series physics module; (4) The deep hidden time series physical model simultaneously receives the battery capacity data of each time series, the SOH or RUL prediction value predicted by the time series neural network, and the hidden time series features mined by the time series neural network as input information; The deep hidden time series physical model builds an implicit physical model for battery health state prediction based on the input information; the prediction loss of RUL or SOH, the loss obtained by 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; (5) Introducing the Bayesian optimization algorithm to automatically adjust the initial hyperparameters of the fusion model to optimize the overall prediction performance of the fusion model and improve the model convergence speed; (6) Use the optimized fusion model to predict the SOH and RUL of lithium batteries.

2. The battery state prediction method based on the fusion of time series neural network and physical information neural network according to claim 1 is characterized in that: Before constructing the fusion model of time series neural network and physical information neural network, the feasibility of implicit dynamic model prediction combining data-driven and time series features is analyzed through mathematical formulas.

3. The battery state prediction method based on the fusion of time series neural network and physical information neural network according to claim 1 is characterized in that: The deep hidden time physics module expression is: in, Represents the remaining battery capacity x after the kth cycle k For the remaining capacity u n The rate of change of DeepHTPM stands for Deep Hidden Time Physics Module. represents the predicted value of the time series neural network; h′1,…,h′ k-1 ,h′ k+1 ,…,h′ n-1 Respectively and Φ is a trainable network parameter of the temporal neural network.

4. The battery state prediction method based on the fusion of time series neural network and physical information neural network according to claim 3 is characterized in that: The time series neural network receives the time series variable X n With the initial hidden state h0 as input, the input sequence is processed step by step according to the time step; at each time step, the input x of the current time step is received i and the hidden state h of the previous time step i-1 , and then generate the hidden state h of the next time step through the temporal neural network i , and then h i As a new input, continue in this way until the final predicted value is obtained It is expressed as: In the formula, θ is a nonlinear function; The loss function of the temporal neural network is used to minimize the predicted value and the actual remaining battery capacity value u n The difference between the loss function L u It is expressed as:

5. The battery state prediction method based on the fusion of time series neural network and physical information neural network according to claim 4 is characterized in that: Let H x =[h′1,…,h′ k-1 ,h′ k+1 ,…,h′ n-1 ] T , the parameters of DeepHTPM are minimized by The mean square error loss between the predicted value and the true value is used for training, which is expressed as: In addition, define the function f(X n ; θ, Φ): in represents the first-order partial differential of u with respect to x; the gradient of the PDE residual is used as a loss to constrain DeepHTPM; let Represents X n f(X n ; θ; Φ) derivative; the gradient loss of the PDE residual is expressed as: L fx The extreme value of should be close to 0, and when f X The closer to 0, the higher the L fx The closer to the extreme value; the comprehensive 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 6. The battery state prediction method based on the fusion of time series neural network and physical information neural network according to claim 5 is characterized in that: The training process of the fusion model is as follows: First, initialize the hyperparameters, including the neural network hyperparameters θ, Φ, λ u ,λ f , Then it enters the cyclic training process. Each round of training first calculates the predicted value of the health state SOH or the remaining service life RUL through the time series neural network Next, use the automatic differentiation tool to calculate the input data X n For the predicted value The partial derivative of Then further calculate X k right The partial derivative of After obtaining these derivatives, the dynamic model G is used to combine the input data, predicted values ​​and partial derivatives to calculate the predicted output of the dynamic model Then, construct a new function f whose value is and and again use automatic differentiation to calculate About X k The partial derivative of In the loss calculation stage, the predicted values ​​are calculated separately The mean square error between the true value u and the loss is Calculation Function The error with zero gives calculate The error with zero gives Finally, the total loss is calculated by combining these loss values; finally, the hyperparameters of the neural network are updated based on the loss values, and the regularization coefficient λ is updated using the Bayesian optimization algorithm. u ,λ f , The entire training process is repeated until the preset convergence condition is met or the maximum number of training rounds is reached.

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