Lithium battery voltage time sequence prediction method based on GRU neural network fusion filtering algorithm

By combining the GRU neural network with the state estimation algorithm, the lithium battery voltage prediction error is corrected in real time, solving the problems of error accumulation and low computational efficiency in the existing technology, achieving efficient and accurate multi-step voltage prediction, and meeting the needs of real-time energy management.

CN120595151APending Publication Date: 2025-09-05DALIAN MARITIME UNIVERSITY
View PDF 0 Cites 0 Cited by

Patent Information

Application Number
CN202510627880.3
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-05-15
Publication Date
2025-09-05

AI Technical Summary

Technical Problem

The existing technology has serious error accumulation and low computational efficiency problems in lithium battery voltage prediction, which makes it difficult to meet the needs of real-time energy management.

Method used

The GRU neural network is combined with the state estimation algorithm to update the state variables and error covariance matrix through the state equation and observation equation, calculate the Kalman gain matrix, correct the battery voltage prediction error, and realize multi-step advance prediction.

Benefits of technology

Real-time correction of battery voltage prediction errors improves the accuracy and reliability of prediction results and meets the computational efficiency requirements of real-time energy management.

✦ Generated by Eureka AI based on patent content.

Smart Images

  • Figure CN120595151A_ABST
    Figure CN120595151A_ABST
Patent Text Reader

Abstract

The invention belongs to the technical field of voltage prediction, and relates to a GRU neural network fusion filtering algorithm-based lithium battery voltage time sequence prediction method, which comprises the following steps of: combining a GRU neural network model with a state estimation algorithm to obtain a state equation and an observation equation; updating the predicted value of the state variable; updating the estimated value of the error covariance matrix according to the estimated value and the actual value of the state variable; calculating a Kalman gain matrix; calculating an error between the measured voltage and the calculated voltage of the observation equation; and correcting the state variable and the error covariance matrix according to the state of charge SoC of the battery to realize the time sequence prediction of the voltage of the lithium battery. According to the method, the prediction error of the battery voltage can be corrected in real time by combining the state estimation algorithm and the GRU neural network, so that the problem that the error is gradually amplified in an open-loop mode is avoided, and the accuracy and the reliability of a prediction result are improved.
Need to check novelty before this filing date? Find Prior Art

Description

Technical Field

[0001] The present invention relates to the technical field of voltage prediction, and in particular to a lithium battery voltage time series prediction method based on a GRU neural network fusion filtering algorithm. Background Art

[0002] Lithium batteries, with their significant advantages such as high voltage, high energy and power density, and long cycle life, have become a core energy storage component for new energy vehicles. As electric vehicles evolve toward unmanned and intelligent driving, tasks such as path planning and energy management based on model predictive control algorithms are increasing significantly.

[0003] When using the model predictive control algorithm for path planning and energy management, it is necessary to calculate the point-by-point change trend of the lithium battery terminal voltage in the prediction time domain according to the algorithm iteration step based on the model, and provide input for the calculation of other battery status quantities in the prediction time domain. The main technical solution in current research is to directly calculate the point-by-point change trend of battery status quantities in the prediction time domain with the help of the battery model. This "open-loop" operation mode causes the cumulative error to continue to increase, and ultimately causes the prediction results to deviate seriously from reality. In addition, since the current voltage calculation method uses the battery model, it repeatedly solves the battery terminal voltage at the next moment through a series of control equations, which has low computational efficiency and is difficult to meet the task requirements of real-time energy management scenarios.

[0004] Therefore, how to correct the prediction error of battery voltage in real time and improve computing efficiency becomes an urgent problem to be solved. Summary of the Invention

[0005] In response to the technical problems raised above, a lithium battery voltage time series prediction method based on a GRU neural network fusion filter algorithm is provided. The present invention mainly utilizes a combination of a GRU neural network and a state estimation algorithm to achieve multi-step advance prediction of battery voltage, which can effectively solve the defects existing in the existing technology.

[0006] The technical means adopted in the present invention are as follows:

[0007] A lithium battery voltage time series prediction method based on a GRU neural network fusion filtering algorithm includes:

[0008] Combine the GRU neural network model with the state estimation algorithm to obtain the state equation and observation equation;

[0009] Update the predicted values ​​of state variables;

[0010] Update the error covariance matrix estimate based on the estimated and actual values ​​of the state variables;

[0011] Calculate the Kalman gain matrix;

[0012] Calculate the error between the measured voltage and the voltage calculated by the observation equation;

[0013] The state variables and error covariance matrix are corrected according to the battery's state of charge (SoC) to achieve time series prediction of the lithium battery voltage.

[0014] Furthermore, the state equation is the ampere-hour integral formula f1(·):

[0015] SoC k|k-1 =f1(SoC k-1|k-1 ;I app,k-1 )+e 1,k =SoC k-1|k-1 +I app,k-1 δ / Q all +e 1,k

[0016] Among them, SoC k|k-1 represents the predicted value of battery state of charge SoC at time k; e 1,k Represents state noise; SoC k-1|k-1 represents the estimated value of SoC at time k-1; I app,k-1 represents the working current of the battery; δ represents the algorithm iteration step, Q all Indicates the nominal capacity of the battery;

[0017] The observation equation is a voltage prediction model based on the GRU neural network:

[0018] U k =g1(SoC k|k-1 ,P,I app,k )+ε 1,k

[0019] Among them, U k represents the battery terminal voltage, P represents the parameter set of the voltage prediction model of the GRU neural network, ε 1,k represents the measurement noise;

[0020] Initialize the parameters:

[0021] x 1,k =SoC k

[0022] A 1,k =1

[0023]

[0024] Among them, A 1,k represents the system matrix at time k; C 1,k represents the observation matrix; ΔSoC represents the differential of the state of charge SoC.

[0025] Furthermore, the updating of the predicted value of the state variable specifically includes:

[0026] SoC k|k-1 =f1(SoC k-1|k-1 ;I app,k-1 )+e 1,k =SoC k-1|k-1 +I app,k-1 δ / Q all +e 1,k

[0027] Among them, SOC k / k-1 Represents the predicted value of battery state of charge SoC at time k, SoC k-1 / k-1 Represents the estimated value of the state of charge SoC at time k-1.

[0028] Furthermore, the error covariance matrix estimation value is updated as follows:

[0029] P k / k-1 =A k-1 P k-1 / k-1 Alpha T k-1 +M k-1

[0030] Among them, P k / k-1 is the estimated value of the prediction error covariance matrix at time k, A k-1 represents the system matrix at time k-1, M k-1 is the covariance matrix of the state of charge SoC at time k-1, which represents the error of the ampere-hour integral equation.

[0031] Furthermore, the Kalman gain matrix is ​​calculated as follows:

[0032] K k =P k / k-1 C T k (C k P k / k-1 C T k +N k ) -1

[0033] Among them, K k is the Kalman gain matrix at time k, C k is the output matrix of the voltage model, N k is the noise covariance matrix of the voltage observation value at time k, which represents the sensor error.

[0034] Furthermore, the error between the measured voltage and the voltage calculated by the observation equation is expressed as the observation error E k :

[0035] E k=U k -g1(SoC k|k-1 ,P,I app,k )

[0036] Among them, U k Indicates the battery terminal voltage.

[0037] Furthermore, the state variables and the error covariance matrix are corrected according to the state of charge (SoC) of the battery, including:

[0038] SoC k / k The correction method is as follows:

[0039] SoC k / k =SoC k / k-1 +K k E k

[0040] Among them, SoC k / k is the estimated battery SoC at time k;

[0041] The error covariance matrix is ​​modified as follows:

[0042] P k / k =(IK k C k )P k / k-1

[0043] After single-step iterative voltage and state of charge (SoC) correction, the GRU neural network model predicts multi-step voltage and state of charge.

[0044] Compared with the prior art, the present invention has the following advantages:

[0045] The lithium battery voltage time series prediction method using a GRU neural network fusion filtering algorithm, provided by this invention, combines a state estimation algorithm with a GRU neural network model to perform multi-step advance prediction of battery voltage in real time. By combining the state estimation algorithm with the GRU neural network, the battery voltage prediction error can be corrected in real time, thus avoiding the problem of gradual error amplification in the "open-loop" mode and improving the accuracy and reliability of the prediction results.

[0046] The present invention combines the GRU neural network with the state estimation algorithm, uses the advantages of the neural network to perform data-driven prediction, and optimizes the prediction results with the help of a filtering algorithm, thereby greatly improving the computing efficiency, achieving rapid prediction of battery voltage, and meeting the task requirements of real-time energy management systems.

[0047] Based on the above reasons, the present invention can be widely promoted in fields such as voltage prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0049] Figure 1 This is a flow chart of the lithium battery voltage time series prediction method based on the GRU neural network fusion filtering algorithm in the present invention.

[0050] Figure 2 This is a diagram of the multi-step time series iterative prediction model based on the GRU neural network model in the present invention.

[0051] Figure 3 Flowchart of a method in an embodiment of the present invention.

[0052] Figure 4 These are the measured data for a 6.4Ah lithium iron phosphate battery in an embodiment of the present invention.

[0053] Figure 5 This is the prediction result of a 6.4Ah lithium iron phosphate battery using the method of the present invention in an embodiment of the present invention.

[0054] Figure 6 This is the prediction result of a 6.4Ah lithium iron phosphate battery using only the GRU neural network model in the embodiment of the present invention. DETAILED DESCRIPTION

[0055] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments of the present invention can be combined with each other. The present invention will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0056] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. The following description of at least one exemplary embodiment is actually only illustrative and is in no way intended to limit the present invention and its application or use. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0057] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or combinations thereof.

[0058] Unless otherwise specifically stated, the relative arrangement of the parts and steps, numerical expressions and numerical values ​​described in these embodiments do not limit the scope of the present invention. At the same time, it should be clear that, for ease of description, the sizes of the various parts shown in the drawings are not drawn according to the actual proportional relationship. The techniques, methods and equipment known to ordinary technicians in the relevant fields may not be discussed in detail, but where appropriate, the techniques, methods and equipment should be considered as part of the authorization specification. In all examples shown and discussed here, any specific value should be interpreted as merely exemplary and not as a limitation. Therefore, other examples of the exemplary embodiments may have different values. It should be noted that similar numbers and letters represent similar items in the following figures, so once an item is defined in one figure, it does not need to be further discussed in subsequent figures.

[0059] In the description of the present invention, it should be understood that the directions or positional relationships indicated by directional words such as "front, back, up, down, left, right", "horizontal, vertical, vertical, horizontal" and "top, bottom" are usually based on the directions or positional relationships shown in the accompanying drawings. They are only for the convenience of describing the present invention and simplifying the description. Unless otherwise specified, these directional words do not indicate or imply that the device or element referred to must have a specific direction or be constructed and operated in a specific direction. Therefore, they cannot be understood as limiting the scope of protection of the present invention: the directional words "inside and outside" refer to the inside and outside relative to the outline of each component itself.

[0060] For ease of description, spatially relative terms such as "above", "above", "on the upper surface of", "above", etc. may be used herein to describe the spatial positional relationship of a device or feature to other devices or features as shown in the figures. It should be understood that spatially relative terms are intended to include different orientations of the device in use or operation in addition to the orientation described in the figures. For example, if the device in the drawings is inverted, the device described as "above other devices or structures" or "above other devices or structures" will be positioned as "below other devices or structures" or "below their position devices or structures". Thus, the exemplary term "above" can include both "above" and "below". The device can also be positioned in other different ways (rotated 90 degrees or in other orientations), and the spatially relative descriptions used here are interpreted accordingly.

[0061] In addition, it should be noted that the use of terms such as "first" and "second" to limit components is only for the convenience of distinguishing the corresponding components. Unless otherwise stated, the above terms have no special meaning and therefore cannot be understood as limiting the scope of protection of the present invention.

[0062] like Figure 1 As shown, the present invention provides a lithium battery voltage time series prediction method based on a GRU neural network fusion filtering algorithm, comprising:

[0063] The GRU neural network model is combined with the state estimation algorithm to obtain the state equation and observation equation.

[0064] In specific implementation, as a preferred embodiment of the present invention, in the multi-step advance prediction of voltage, the state equation is the ampere-hour integral formula f1(·):

[0065] SoC k|k-1 =f1(SoC k-1|k-1 ;I app,k-1 )+e 1,k =SoC k-1|k-1 +I app,k-1 δ / Q all +e 1,k

[0066] Among them, SoC k|k-1 represents the predicted value of battery SoC at time k; e 1,k Represents state noise; SoC k-1|k-1 represents the predicted value of battery SoC at time k-1; I app,k-1 represents the working current of the battery; δ represents the algorithm iteration step, Q all Indicates the nominal capacity of the battery;

[0067] The observation equation is a voltage prediction model based on the GRU neural network:

[0068] U k =g1(SoC t|t-1 ,P,I app,k )+ε 1,k

[0069] Among them, U k represents the battery terminal voltage, P represents the parameter set of the voltage prediction model of the GRU neural network, ε 1,k Indicates the measurement noise.

[0070] Initialize the parameters:

[0071] x 1,k =SoC k

[0072] A 1,k =1

[0073]

[0074] P 1,0|0 =0,M0=0.05,N0=0.025

[0075] Among them, A 1,k represents the system matrix at time k; C 1,k Represents the observation matrix; ΔSoC represents the differential of the state of charge SoC. In implementation, the state variable is the SoC of the battery. The initial value of the state variable can be roughly calculated based on the open circuit voltage curve. The error covariance matrix in this system is the error between the current estimated SoC and the actual SoC, and is taken as P 0|0 = 0. Furthermore, this step requires initializing the state noise covariance matrix and the observation noise covariance matrix. Their initial values ​​need to be adjusted based on the specific usage scenario. Based on the sampling accuracy of online current and voltage data, the state noise covariance matrix M0 is set to 0.05, and the observation noise covariance matrix N0 is set to 0.025.

[0076] Update the predicted values ​​of the state variables.

[0077] In specific implementation, as a preferred embodiment of the present invention, updating the predicted value of the state variable specifically includes:

[0078] SoC k|k-1 =f1(SoC k-1|k-1 ;I app,k-1 )+e 1,k =SoC k-1|k-1 +I app,k-1 δ / Q all +e 1,k

[0079] Among them, SOC k / k-1 Represents the predicted value of battery state of charge SoC at time k, SoC k-1 / k-1 Represents the estimated value of the state of charge SoC at time k-1.

[0080] Update the error covariance matrix estimate based on the estimated and actual values ​​of the state variables.

[0081] In specific implementation, as a preferred embodiment of the present invention, the method for updating the error covariance matrix estimate is as follows:

[0082] P k / k-1 =A k-1 P k-1 / k-1 Alpha T k-1 +M k-1

[0083] Among them, P k / k-1 is the estimated value of the prediction error covariance matrix at time k, A k-1 represents the system matrix at time k-1, M k-1 is the covariance matrix of the state of charge SoC at time k-1, which represents the error of the ampere-hour integral equation.

[0084] Compute the Kalman gain matrix.

[0085] In specific implementation, as a preferred embodiment of the present invention, the calculation method of the Kalman gain matrix is ​​as follows:

[0086] K k =P k / k-1 C T k (C k P k / k-1 C T k +N k ) -1

[0087] Among them, K k is the Kalman gain matrix at time k, C k is the output matrix of the voltage model, N k is the noise covariance matrix of the voltage observation value at time k, which represents the sensor error.

[0088] Calculate the error between the measured voltage and the voltage calculated by the observation equation.

[0089] In specific implementation, as a preferred embodiment of the present invention, the error between the measured voltage and the voltage calculated by the observation equation is expressed as the observation error E k :

[0090] Ek =U k -g1(SoC k|k-1 ,P,I app,k )

[0091] Among them, U k Indicates the battery terminal voltage.

[0092] According to the battery's state of charge (SoC) state variables and error covariance matrix, the lithium battery voltage time series prediction is achieved.

[0093] In a specific implementation, as a preferred embodiment of the present invention, the state variables and the error covariance matrix are corrected according to the state of charge (SoC) of the battery, including:

[0094] SoC k / k The correction method is as follows:

[0095] SoC k / k =SoC k / k-1 +K k E k

[0096] Among them, SoC k / k is the estimated battery SoC at time k;

[0097] The error covariance matrix is ​​corrected to:

[0098] P k / k =(IK k C k )P k / k-1

[0099] After single-step iterative voltage and SoC correction, the GRU neural network model predicts multi-step voltage and state of charge.

[0100] When implementing, first predict the state of charge SoC at the next moment 1|0 Next, estimate the error covariance matrix P0 and SoC0 based on the initial data; calculate the prediction error covariance matrix P at the next moment 1|0 , and then calculate the Kalman gain matrix K1 at the next moment; next, calculate the error E1 between the measured voltage value and the value calculated by the GRU model. Then calculate the estimated value SoC of the battery k|k , and finally update the estimated error covariance P1 at the next moment. The above process is a complete recursive process of the Kalman filter. The present invention includes but is not limited to the extended Kalman filter (EKF) and the particle filter (PF).

[0101] Example 1

[0102] like Figure 2As shown in Figure 2, in the multi-step advance prediction process in the prediction time domain, the terminal voltage and SoC are calculated by the GRU neural network model.

[0103] First, the current I app , voltage U k and state of charge SOC k As input data, it is input into the GRU neural network model. By processing these time series features, the GRU model can capture the dynamic behavior and internal laws of the battery system and predict the voltage U at the next moment. k+1 and state of charge SOC k+1 After obtaining the voltage and state of charge at the next moment, these predicted values, along with the current at that moment, are re-input into the GRU neural network for the next round of prediction. This process is repeated over and over again, predicting the future battery voltage and state of charge through multiple time series iterations.

[0104] The specific workflow in this embodiment is to first perform single-step iterative voltage and SoC calibration, then perform multi-step prediction and cyclic iteration, such as Figure 3 shown.

[0105] First, the initial value is substituted into the Kalman filter process for single-step iteration. The state variable is the SoC of the battery. The initial value of the state variable can be roughly calculated based on the open circuit voltage curve. The error covariance matrix in this system is the error between the current estimated SoC and the actual SoC. 0|0 = 0. This yields the corrected voltage and SOC. A multi-step prediction is then performed, where the current, voltage, and SOC are input into the GRU neural network to obtain the voltage and SOC at the next moment. This process is repeated repeatedly, predicting the future battery voltage and SOC through multi-step time series iterations.

[0106] The effectiveness of the proposed method is verified by using the online test data of lithium iron phosphate batteries provided by Zhuhai Guanyu Battery Co., Ltd. in the first "Guanyu Cup" battery design competition "Lithium iron phosphate battery SOC estimation". First, the voltage and current data measured in the online scenario are as follows: Figure 4 shown. Figure 4 (a) is the voltage data of the lithium iron phosphate battery measured in the online scenario, and (b) is the current data of the lithium iron phosphate battery measured in the online scenario.

[0107] Table 1 Hyperparameters used in GRU network training

[0108]

[0109]

[0110] According to the data reported in Table 1, the algorithm iteration step is 1s and the prediction time domain is 60s. The predicted value of the terminal voltage proposed by the algorithm is compared with the measured value. Figure 5 As shown, the error between the predicted value and the measured value is small.

[0111] The comparison between the predicted value and the measured value of the opposite terminal voltage using only the GRU neural network model is as follows: Figure 6 As shown, there is a large error between the predicted value and the measured value.

[0112] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A lithium battery voltage time series prediction method based on a GRU neural network fusion filter algorithm, characterized in that: include: Combine the GRU neural network model with the state estimation algorithm to obtain the state equation and observation equation; Update the predicted values ​​of state variables; Update the error covariance matrix estimate based on the estimated and actual values ​​of the state variables; Calculate the Kalman gain matrix; Calculate the error between the measured voltage and the voltage calculated by the observation equation; The state variables and error covariance matrix are corrected according to the battery's state of charge (SoC) to achieve time series prediction of the lithium battery voltage.

2. The lithium battery voltage time series prediction method based on the GRU neural network fusion filter algorithm according to claim 1 is characterized in that: The state equation is the ampere-hour integral formula f1(·): SoC k|k-1 =f1(SoC k-1|k-1 ;I app,k-1 )+e 1,k =SoC k-1|k-1 +I app,k-1 δ / Q all +e 1,k Among them, SoC k|k-1 represents the predicted value of battery state of charge SoC at time k; e 1,k Represents state noise; SoC k-1|k-1 represents the estimated value of SoC at time k-1; I app,k-1 represents the working current of the battery; δ represents the algorithm iteration step, Q all Indicates the nominal capacity of the battery; The observation equation is a voltage prediction model based on the GRU neural network: U k =g1(SoC k|k-1 ,P,I app,k )+ε 1,k Among them, U k represents the battery terminal voltage, P represents the parameter set of the voltage prediction model of the GRU neural network, ε 1,k represents the measurement noise; Initialize the parameters: x 1,k =SoC k A 1,k =1 Among them, A 1,k represents the system matrix at time k; C 1,k represents the observation matrix; ΔSoC represents the differential of the state of charge SoC.

3. The lithium battery voltage time series prediction method based on the GRU neural network fusion filter algorithm according to claim 1 is characterized in that: The predicted value of the updated state variable specifically includes: SoC k|k-1 =f1(SoC k-1|k-1 ;I app,k-1 )+e 1,k =SoC k-1|k-1 +I app,k-1 δ / Q all +e 1,k Among them, SOC k / k-1 Represents the predicted value of battery state of charge SoC at time k, SoC k-1 / k-1 Represents the estimated value of the state of charge SoC at time k-1.

4. The lithium battery voltage time series prediction method based on the GRU neural network fusion filter algorithm according to claim 1 is characterized in that: The method for updating the error covariance matrix estimate is as follows: P k / k-1 =A k-1 P k-1 / k-1 A T k-1 +M k-1 Among them, P k / k-1 is the estimated value of the prediction error covariance matrix at time k, A k-1 represents the system matrix at time k-1, M k-1 is the covariance matrix of the state of charge SoC at time k-1, which represents the error of the ampere-hour integral equation.

5. The lithium battery voltage time series prediction method based on the GRU neural network fusion filter algorithm according to claim 1 is characterized in that: The calculation method of the Kalman gain matrix is ​​as follows: K k =P k / k-1 C T k (C k P k / k-1 C T k +N k ) -1 Among them, K k is the Kalman gain matrix at time k, C k is the output matrix of the voltage model, N k is the noise covariance matrix of the voltage observation value at time k, which represents the sensor error.

6. The lithium battery voltage time series prediction method based on the GRU neural network fusion filter algorithm according to claim 1 is characterized in that: The error between the measured voltage and the voltage calculated by the observation equation is expressed as the observation error E k : E k =U k -g1(SoC k|k-1 ,P,I app,k ) Among them, U k Indicates the battery terminal voltage.

7. The lithium battery voltage time series prediction method based on the GRU neural network fusion filter algorithm according to claim 1 is characterized in that: The method of correcting the state variables and the error covariance matrix according to the state of charge (SoC) of the battery includes: SoC k / k The correction method is as follows: SoC k / k =SoC k / k-1 +K k IN k Among them, SoC k / k is the estimated battery SoC at time k; The error covariance matrix is ​​modified as follows: P k / k =(I-K k C k )P k / k-1 After single-step iterative voltage and state of charge (SoC) correction, the GRU neural network model predicts multi-step voltage and state of charge.