An end-cloud collaboration approach for state-of-health estimation of lithium-ion batteries based on bi-LSTM with collaboration of multi-feature and attention mechanism

ABSTRACT This study develops an end-cloud collaboration method for estimating the State-of-Health (SOH) of batteries. It fuses a cloud-based deep learning model for detailed analysis and an end-side model for swift evaluation, employing Bidirectional Long Short Term Memory networks and an attention mechanism for precise feature identification. A comprehensive feature extraction methodology, incorporating incremental capacity and differential thermal analyses, ensures robust correlation with battery degradation. The Extended Kalman Filter integrates these models, providing accurate and timely SOH estimations. Tested against NASA’s dataset, the method achieved SOH estimation with errors around 1%, suggesting potential for real-time battery health monitoring and broader multi-state estimation applications.


Introduction
Lithium-ion batteries are widely used in the power system of new energy vehicles due to their advantages of high energy density and low cost (Gao et al. 2021;Liu et al. 2022;Zhang et al. 2022).However, with the irreversible side reactions within the lithium-ion battery, they will gradually degrade with use, which is usually manifested as a decrease in capacity or an increase in internal resistance (Zhang et al. 2022).Battery degradation leads to reduced battery performance and safety hazards, so accurate and timely estimation of the state of health (SOH) is essential to ensure the lithium-ion battery operates in a high-performance and safe operating range.The SOH of a lithium-ion battery can be determined by measuring its capacity or internal resistance, but this method requires high equipment and environment, and usually can only be done in the laboratory (Ma et al. 2023).In practice, the SOH of lithium-ion batteries cannot be measured directly and needs to be estimated based on macroscopic collectible signals such as voltage, current and temperature (Tian et al. 2022;Zhou et al. n.d.).
Currently, the estimation of SOH for batteries can usually be categorized into model-based and data-driven methods.Modelbased methods mainly include those based on electrochemical mechanism (EM) models and those based on equivalent circuit models (ECM) (Gu et al. 2023;Wang et al. 2020).The EM-based approach considers the microscopic changes within the lithiumion battery during the degradation process.The ECM-based approach models the battery by constructing a circuit model by analogizing the behavior of the battery to the series-parallel connection of different electrical components.For extreme or unusual operating conditions, model-based approaches often lack generalizability and are very limited in practical applications.
In recent years, with the development of big data technology and cloud computing technology, data-driven methods have become increasingly hot (Hannan et al. 2021).Datadriven methods have a strong nonlinear modeling capability and can effectively capture the nonlinear mapping relationship between input features and battery SOH.Lin et al. (2022).used three traditional machine learning algorithms, multiple linear regression (MLR), gaussian process regression (GPR), and support vector regression (SVR), to achieve high-accuracy SOH estimation, and fused models based on the random forest algorithm.In deep learning, long short term memory (LSTM) and convolutional neural network (CNN) are widely used for SOH estimation of batteries because the battery aging problem is a typical time series problem.Zhang et al. (2018).implemented SOH and remaining useful life (RUL) estimation based on LSTM.Shen et al. (2020)).implemented SOH estimation with high generalization using CNN based on transfer learning and integrated learning techniques.
For data-driven methods, the correlation between input features and cell SOH significantly impacts the results.Many signal analysis methods are also used to assist data-driven methods to extract highly correlated features.Signal analysis methods characterize battery aging by further processing the macroscopic signals with features such as the magnitude, location, and area of peaks and valleys in the curve (Zhou et al. 2022).The extracted features usually have a high correlation with battery aging, and at the same time, to a certain extent, they make up for the disadvantage of poor interpretability of data-driven methods (Chen et al. 2022).Commonly used signal analysis methods include incremental capacity analysis (ICA) and differential thermal voltammetry (DTV) analysis methods.Wen et al. (2022) performed feature extraction based on ICA, established its mapping relationship with temperature and implemented SOH estimation at different temperatures using a backpropagation (BP) neural network.Wang, Yuan, and Li (2021).extracted features based on DTV analysis method and performed SOH estimation using GPR.Signal analysis methods have higher requirements for data processing, and many studies also use simpler direct features, sacrificing certain interpretability and correlation to improve model efficiency.Many methods of automatically extracting features from the raw signal have also been used to further optimize the model.Lin et al. (2023).divided the voltage curve into 25 segments and used the starting point of each segment as a feature for SOH estimation.Wang et al. (2022) used a modified GPR model and used the time between equal voltage intervals and equal temperature change intervals as features for SOH estimation.Gao et al. (2023).estimated SOH based on Hierarchical Feature Coupled Module (HFCM)-LSTM by automatically extracting features from raw data.
Although many existing methods are able to realize highaccuracy SOH estimation, they still face many problems in practical applications.First, there is a contradiction between accuracy and real-time performance during online estimation.The arithmetic power of on-board BMS is limited, while highaccuracy models are usually more complex, leading to an increase in computation (Yu et al. 2023).Meanwhile, onboard applications carry battery packs containing many monomers, further increasing computational consumption and exacerbating the contradiction between accuracy and real-time.Second, it is difficult to balance relevance and robustness for feature extraction.Although signal analysis methods can extract highquality features, signal analysis methods have higher requirements for data processing and a more cumbersome process, which may lead to the amplification of errors or even produce significant errors.In addition, deep learning models suffer from the problem of distraction and cannot fully mine the information embedded in important features and significant sequences (Tang et al. 2023).
In recent years, with the development of cloud platform technology, end-cloud collaboration has gradually become a new idea to solve problems.Cloud computing offers unparalleled scalability, which is essential for BMS as the number of electric vehicles (EVs) and consequently the batteries in use continue to grow.The cloud infrastructure can handle vast amounts of data generated by these batteries, enabling more comprehensive SOH assessments (Tian et al. 2023).The cloudbased deep learning model provides advanced computational capabilities that are not typically available in on-board systems (Galiounas et al. 2022).This allows for the employment of complex algorithms like Bi-LSTM and attention mechanisms which are central to achieving high accuracy in SOH prediction (Ruan et al. 2022).While initial setup costs for cloudbased systems can be significant, the long-term operational costs are reduced through economies of scale.Furthermore, the reduction in costs associated with battery failure and maintenance due to improved SOH estimation can offset these initial expenses.Cloud platforms allow for continuous model improvement without the need for physical updates to the BMS hardware.As new data is accumulated, the model can be retrained and updated remotely, ensuring that the SOH estimation remains accurate over time (Xiao et al. 2023).Based on this, this paper proposes a SOH estimation method based on end-cloud collaboration.Specifically, the whole endcloud collaboration method includes three parts.Cloud-based high-accuracy deep learning model, end-based high-real-time fast model, and end-cloud collaboration algorithm.The cloud deep learning model is constructed with a bidirectional-LSTM (Bi-LSTM) as the core, which is good at solving temporal problems.The attention mechanism (AM) is added to the model on the temporal and spatial scales to capture different features and important positions in different sequences.The input features of the deep learning model are based on multiple feature analyses for feature extraction.Two signal analysis techniques, ICA and DTV, are used to extract features that are strongly correlated with battery degradation.Also, the direct feature of equal discharge voltage interval time is used for robustness reasons.The end-side fast model is built based on a double-exponential empirical model.The end-cloud collaboration algorithm is deployed on the end side.The end-cloud collaboration strategy uses an extended Kalman filter (EKF) algorithm to fuse the results from the end-side result and the cloud-side result for results fusion and iterative updating, and also flexibly sets the updating period to balance the accuracy and the transmission resources between the end and the cloud.
The proposed SOH estimation method based on end-cloud collaboration is able to realize SOH estimation that balances accuracy and real-time performance.Under the cyber hierarchy and interactional network (CHAIN) framework, it has the potential to realize the full lifecycle health monitoring and management of batteries (Yang et al. 2020(Yang et al. , 2021)).Overall, the main contributions of this paper can be summarized as follows: (1) An end-cloud collaboration SOH estimation method is proposed.By arranging the high-accuracy deep learning model with a large computation volume on the cloud side and the high-real-time empirical model with a small computation volume on the end side, the EKF is used as the end-cloud collaboration algorithm to realize the online estimation of SOH that takes into account both accuracy and real-time performance.(2) The AM is added in the spatial and temporal scales in the cloud deep learning model, which can better mine the important information in different features and sequences.(3) Feature extraction is performed based on multi-feature analysis, ICA and DTV analysis are performed based on current and temperature signals, respectively, which provides a backup plan in the event of an error in a single signal.The feature of equal voltage interval discharge time requires less data processing and avoids further amplification in the event of an error in sampling.The strong correlation between the feature and battery degradation is guaranteed while robustness is improved.
Our method's theoretical competence for battery SOH estimation stems from the Bi-LSTM's inherent proficiency in processing time-series data, essential for capturing the dynamic behavior of battery degradation.The inclusion of an attention mechanism allows our model to discern and prioritize significant temporal and spatial features that directly correlate with SOH, a distinct advantage over traditional ANNs which may treat all input features with equal importance.This targeted approach ensures that our system adapts to the nuanced variances in battery performance data, enhancing prediction accuracy and robustness.Moreover, the end-cloud collaborative architecture is designed to balance the computational intensity of deep learning models with the practical constraints of onboard battery management systems.This results in a system that not only provides high-accuracy SOH estimations but also maintains the requisite real-time performance for in-situ applications, addressing a critical gap in current methodologies.In a comparative study against standard ANN models, our method achieved a reduction in Root Mean Square Error (RMSE) by approximately 15% and an enhancement in Mean Absolute Error (MAE) by roughly 20%, substantiating its precision and reliability.These statistical outcomes underscore the method's efficacy, making a compelling case for its adoption in advanced battery management systems.
The remaining sections of this paper are laid out as follows: Section 2 describes the battery dataset used in this paper and the feature extraction.Section 3 elaborates on the principles of the vehicle model, the cloud model, and the vehicle-cloud collaboration algorithm.Section 4 discusses and analyzes the results.Section 5 summarizes the main conclusions of this paper.

Degradation data and feature extraction
This section first describes the basic information of the dataset used in this paper.Then, the feature extraction process and correlation analysis results of multiple features are introduced.
The extracted features are used for training and testing the Bi-LSTM model on the cloud side.
The data collection process leveraged a controlled test environment simulating real-world operating conditions of lithium-ion batteries.The batteries were subjected to a series of charge, discharge, and Electrochemical Impedance Spectroscopy (EIS) operations, with data points recorded for voltage, current, and temperature at fixed intervals throughout each cycle.The preprocessing phase involved multiple steps to ensure the quality and relevance of the data: (1) Noise filtering -we employed Savitzky-Golay filters to smooth the time-series data, thereby reducing the impact of transient noise on the signal quality.
(2) Data normalization -We normalized the collected data to a consistent scale, which is crucial for the subsequent deep learning processes and to avoid biases toward certain features.
(3) Feature engineering: The ICA and differential thermal voltammetry DTV techniques were implemented to extract features that strongly correlate with battery degradation, ensuring that the input features used in the model were robust and informative.

NASA dataset
This paper uses the public dataset of lithium-ion battery degradation provided by NASA PCoE (Goebel et al. 2008).The detailed operating conditions are shown in Table 1.The dataset used 18,650 cells for three different operations, including charging, discharging and EIS testing.shows the capacity change for the whole cycle degradation operation.

Ica
ICA technology describes battery degradation by analyzing the relationship between voltage and capacity changes.ICA can reflect the process of ion detachment within the battery, thereby reflecting the degradation of the battery.In recent years, it has been widely used in the study of battery degradation.Figure 2(a) shows the variation of the ICA curve with battery degradation.The changes in the curve are closely related to battery degradation.As the battery ages, the peaks and valleys of the ICA curve gradually move downwards to the left.Therefore, by extracting peak features, features that are strongly related to battery degradation can be extracted.This paper extracts the peaks and peak positions in the curve as features.The ICA can be described as follows: Where I represents the current, Q the capacity and V the voltage.
ICA can reflect the process of ion detachment within the battery, thereby reflecting the aging of the battery.In recent years, it has been widely used in the study of battery degradation.Therefore, the data is first filtered using a Savitzky-Golay (SG) filter.The SG filter has a strong ability to handle peaks and valleys in curves, making it suitable for application to extract peak features.The SG filter can be calculated as follows: Where y represents the output signal after smoothing C j the coefficient and x the input signals.

Dtv
DTV analysis is based on two macroscopic signals: voltage and temperature.By analyzing the entropy change during battery aging, the energy change during the phase change process is captured, thereby reflecting the aging of the battery.The DTV analysis was performed under natural convection to reflect standard operational conditions.The temperature data captured during the battery's discharge phase provided the basis for our analysis, aligning with the typical use case scenarios of lithium-ion batteries where SOH estimation is most critical.
The DTV is calculated as follows: Where dT and dV represent the differential of temperature and voltage, respectively.
When conducting DTV analysis, the differential operation is performed, so the data is first preprocessed using the SG filter.Figure 2(b) shows the changes in the DTV curve as the battery ages.The changes in peaks and valleys in the DTV curve reflect battery degradation, and as the battery ages, it shifts to the left.Therefore, this paper extracts the peak and valley positions in the DTV curve as features.

Duration of the same discharging voltage range
Although the ICA and DTV methods have been able to obtain a sufficient number of features that are closely related to battery degradation, the relatively cumbersome data processing process of these two signal analysis methods means that, in practice, there is an increased likelihood of significant errors due to mistakes in one of the processes.Therefore, in this paper, a simple direct feature has also been chosen to provide a backup in the event of such a situation.Figure 2(c) shows the voltage profile of a battery as it is discharged during the degradation process.The voltage curves can be categorized into early and late stages based on their steepness.In the early stages of discharge, the curve is relatively flat.As the battery ages, the flat period will gradually shorten, and the curve will gradually shift to the left when it enters the steep nonlinear region of the final discharge stage earlier.This change is closely related to battery degradation.Considering that in practice, the operating range of the battery is more covered by an early leveling off phase, the extracted feature is the duration of the voltage leveling off phase during battery discharge.The duration of the same discharging voltage range can be described as follows: Where t represents the duration of the same discharging voltage range, t Vlow and t Vhigh represent the time point of maximum and minimum voltage during this period, respectively.

Correlation analysis
The features extracted in this paper are analyzed for correlation using the Pearson correlation analysis method.The Pearson correlation analysis is calculated as follows: where x and y are the variables.The results of the correlation analysis of the final selected features, using battery B18 as an example, are shown in Figure 2(d).The battery degradation can be effectively reflected as all the correlation coefficients between the extracted features and SOH are above 80%.The extracted multi-features will be input into the deep learning model for training and testing, and the collaboration of multi-features helps to further improve the robustness of the model while ensuring correlation.

Methodology
This section provides a detailed introduction to the various parts of the designed end-cloud collaboration system for battery degradation estimation, including a cloud-based highaccuracy deep learning model, an end-side high real-time double exponential empirical model, and end-cloud collaboration algorithms.The end-cloud collaboration algorithm includes fusion and iterative update of results on both sides of the end and cloud based on the Kalman filter, as well as online parameter identification based on UKF.

Bi-LSTM network
Recurrent neural network (RNN) is a deep learning model specialized in solving time series problems.LSTM is an improvement on RNN.When facing the long-term dependency problem, its hidden layer adds two processes of eliminating useless information and adding useful information, which is able to avoid problems such as gradient vanishing and gradient explosion.The structure of a typical LSTM cell are shown in Figure 3(a).The computation of LSTM can be described as follows: Firstly, the LSTM units receive the x j and h jÀ 1 and the forgetting gate is used to control which information to be forgotten in the cell state: Where σ is Sigmoid function.The sigmoid function will limit the value to the range of 0 to 1, which represents the forgotten ratio.
The input gate then processes the input sequence data for the current position, and the input gate will determine which information to be updated and added to the cell state through the sigmoid function.The input gate is calculated as follows: Next, the unit state update from c jÀ 1 to c j : Where c jÀ 1 � f j is the information to be reserved and i j � g j is the new information to be added.The sum of the two information is the cell state of the current sequence.
Finally, the sigmoid function determines which part of the information to be output, and the cell state is processed by the tanh function.The result of multiplying the two parts is the final output: Where h j is the new hidden state, and the c j is the unit state.
Bi-LSTM is based on LSTM and consists of two independent LSTM networks.The structure of Bi-LSTM is shown in Figure 3(b).Bi-LSTM works by capturing the information in the input sequence in forward and backward order respectively.The final output of the model is a splice of the outputs of the two LSTMs.Bi-LSTM is capable of capturing bidirectional temporal correlations from the input sequence.It has better performance compared to single LSTM.Therefore, in this paper, Bi-LSTM is used as the core of the deep learning model of the cloud-side.

Attention mechanism
While correlation analysis methods can identify features that are strongly correlated with SOH, they tend to select these features over the entire battery life cycle.However, these features may have different effects on the predicted results at different spatial and temporal locations.To solve this problem, this study introduces the AM to the deep learning model to improve its performance.AM stems from the ability of humans to focus their attention on the important parts of things when recognizing them.AM achieves the effect of making the model focus on the important parts of them by setting different weights for different features or sequences.The determination of the weights is realized through a neural network.By setting the number of neurons in the neural network to the same value as the dimension of the input features or sequences, different weights are automatically determined by the neural network during the training process.With the inclusion of AM, the model can fully utilize the important information in the data, thus solving the problem of distraction.The structure of the AM is shown in Figure 4(a).The AM can be described as follows:  Where u and w are the weight, b the bias, a t the attention weight, h t the input vector of the attention layer, e t the value of the hidden layer and s t is the output.The trained network will be used for high accuracy estimation of SOH based on the data collected at the end-side.During the training and testing of the model, a cross validation method is used.The data from the other three batteries is used as the training set, while the data from the battery to be tested is used as the testing set.

Double exponential empirical model on the end-side
It is difficult to develop a fast and suitable model to reflect battery degradation due to the highly complex, nonlinear, and time-varying nature of batteries.The battery degradation process is characterized by the double exponential empirical model, which fits the relationship between degradation and cycle count.The double exponential model is calculated as follows: Where k represents the cycle number and a, b, c and d are parameters of the model.The parameter a characterizes the health of the battery of the initial state.Parameter c characterizes the decay trend of the battery.Parameter b and Parameter d characterize the decay rate of the battery.When testing each battery using the method proposed in this article, the parameters of each battery are determined by fitting the capacity decay curves of the other three batteries, that is, using a cross validation method for validation.Specifically, the parameters are determined through a fitting process that uses historical degradation data from the batteries.Initially, the parameters are inferred by fitting the model to the capacity decay curves observed from multiple chargedischarge cycles.This process is executed through the application of optimization algorithms aimed at minimizing the discrepancy between the model's estimations and the actual observed data.Note that battery behavior and degradation patterns can evolve over time as the battery ages.Consequently, the model parameters are not strictly invariant; they are subject to updates to reflect the changing state and health of the battery.In practice, this is achieved by periodically reassessing the model with fresh data to adjust the parameters, ensuring the model remains accurate throughout the battery's lifecycle.To facilitate a dynamic adaptation to the battery's aging, the end-cloud collaboration framework incorporates mechanisms of online parameter identification for continual recalibration of model parameters in response to new data.Namely, the end-cloud collaboration framework encompasses both the initial parameter estimation and the subsequent updates necessary to maintain model accuracy as the battery degrades.

Extended Kalman filter algorithm
Kalman filter is a method for estimating the optimal state of a system.But Kalman filter is only applicable to linear systems.In nonlinear systems, many methods have been proposed to approximate the nonlinear system to a linear system, thus making it suitable for Kalman filter system.Among them, EKF is the most commonly used method due to its robustness, simplicity and speed etc. EKF makes the nonlinear system suitable for Kalman filtering system by expanding the nonlinear system in Taylor series at the reference point.
For a nonlinear system: where x t represents the current state, x tÀ 1 the previous state, u t the input, w t the process noise, f and h the nonlinear mapping relationship, z t the measured variables and v t the measurement noise.The noise satisfies Gaussian distribution.
First, perform prior estimation: Where xÀ t is the prior estimation value of x t .Then perform Taylor expansion at point xÀ t : After Taylor expansion, a linear approximation of the nonlinear system is obtained.Then, using Kalman filtering theory, time update and measurement update can be performed: Prediction equation and state covariance matrix: Where P À t is the error covariance matrix of a prior state.

Update equation and Kalman gain:
Where P þ t is the error covariance matrix of a posteriori state, xþ t is the posteriori estimation and K t is the Kalman gain.

End-cloud collaboration process
In this section, the overall framework of the end-cloud collaboration method proposed in this paper is elaborated.Figure 5 shows the architecture of the entire end-cloud collaboration system.It consists of three parts, the end-side high real-time double exponential empirical model, the cloud-side highaccuracy deep learning model and the end-cloud collaboration algorithm deployed on the end-side.
When integrating and iteratively updating the results from both ends of the end and cloud, the constructed state space function is as follows: state function: preprocessing and feature extraction on the collected data, which is subsequently input into the deep learning model for estimation, outputs a high-accuracy estimation result and returns the result to the end-side.The double exponential empirical model at the end-side performs high real-time estimation based on the current number of cycles.The EKF deployed on the end-side receives the estimation results from the end-side and cloud-side at the same time and iteratively updates the results, and ultimately outputs the high-accuracy and high realtime estimation of the end-cloud collaboration SOH result.At the same time, due to the requirement of the accuracy in practical applications and the balanced transmission resources, the EKF is set up so that the results can be updated and fused in certain time steps according to a fixed time interval.

Result and discussion
In this section, the method proposed in this paper is validated and the results are discussed.Subsection 4.1 compares the cloud models.The SOH estimation results using different features and different models are compared.In subsection 4.2, the end-side estimation results and the end-cloud collaboration estimation results are shown.The estimation results for setting different update steps are also compared and discussed.Subsection 4.3 validates the proposed method on other batteries of the NASA dataset.MAE andRMSE are used as evaluation metrics to assess the estimation results.And for the training of the deep learning model and the determination of the initial values of the parameters of the empirical model, leave-one-out cross-validation is used.

Estimation result of cloud-side with different features and different models
In this subsection, the estimation results of deep learning models using different features are compared using the battery B5 as an example.The effect of whether to add AM or not on the results when estimating based on multiple features is also compared.The estimation results are shown in Figure 6, where the upper dot plot represents the actual SOH value, the line plot represents the estimated value of the deep learning model, and the lower dot plot represents the relative error.Figure 6(f) shows a bar chart summarizing the errors.It can be seen that the errors of the estimation results using features extracted based on ICA and DTV are lower than those using direct features.The RMSE and MAE of the estimation results are only about 0.9% and 0.6%, respectively.This indicates that the signal analysis technique can be more effective in extracting features that are strongly correlated with battery degradation.The errors of the estimation results using single features are all larger than the errors of the estimation results using multiple features.Different features are extracted based on different macro signals, which reflect the information related to battery degradation from different perspectives.The collaboration of multi-features can provide more comprehensive information about the strong correlation with battery degradation for the deep learning model.Thus, high-accuracy SOH estimation can be realized.The RMSE and MAE of the prediction results are only 0.882% and 0.601%, respectively, and the collaboration of multi-features and AM further improves the estimation accuracy.
The RMSE and MAE of the estimation results are only 0.864% and 0.585%, respectively.This indicates that adding AM to the deep learning model can effectively solve the distraction problem.Adding AM on temporal and spatial scales respectively can make the model focus on important features in important sequence locations.The nonlinear mapping between multiple features and battery degradation is established more effectively.

End-cloud collaboration estimation results with different update step
In this subsection, the estimation results of the end-side empirical model and the final end-cloud collaboration estimation results with high accuracy and high real-time are shown using the battery B5 as an example.And the estimation results with different update steps are compared respectively.The estimation results are shown in Figure 7, and for each figure the description is as described in subsection 4.1.It can be seen that Figure 7(a) illustrates the results of the end-side fast empirical model.The error in the estimation results of the end-side fast empirical model is large.Although the empirical model can follow the trend of battery degradation, it is unable to capture the capacity rebound phenomenon that is strongly nonlinear.Meanwhile, due to the inconsistency between the batteries used in determining the parameters and the batteries to be verified, there is a certain gap between the estimated capacity degradation curve and the actual capacity degradation curve.Figure 7(b-e) show the estimation results of the end-cloud collaboration system by setting the update step size to 1, 5, 10 and 15, respectively.It can be seen that the end-cloud collaboration system updates and fuses the high real-time estimation results at the endside by the high-accuracy estimation results of the cloudside, and finally realizes the high-accuracy and high-realtime SOH estimation results.The RMSE and MAE of the estimation results are around 1% and 0.7%, respectively.The accuracy is much higher than the end-side model and slightly lower than the cloud-side model.Some accuracy is sacrificed in order to take into account real-time performance.The error of the estimation results gradually increases as the update step increases.In practical applications, the update step size can be adjusted according to the transmission resources and the demand for estimation accuracy.
Even though the end-side model has relatively larger errors compared to the cloud-side model, it still plays a critical role in our proposed end-cloud collaboration approach, primarily due to its ability to provide rapid, real-time estimates, which are invaluable in operational settings where immediate data processing is paramount.Although the cloud-side model exhibits superior accuracy owing to its more complex algorithms and the abundance of computing resources, it lacks the immediacy of the end-side model.The collaboration between the two models is designed to leverage their respective strengths: the cloud side's accuracy and the end side's speed.By fusing the rapid estimations from the end side with the precise calculations from the cloud side, our method achieves a synergistic balance, delivering real-time and accurate SOH estimations.This dual-model approach ensures that the system is not only effective under ideal conditions but also robust and adaptable in real-world applications where latency and computational power are often constrained.

End-cloud collaboration estimation results of all batteries
In this subsection, the end-cloud collaboration method proposed in this paper is validated on all cells of the NASA dataset, as shown in Figure 8.The description of the curves in the figure is the same as described in subsection 4.1.Table 2 summarizes the errors.Considering the transmission resources and accuracy, 5 is selected as the update step for validation.It can be seen that the endcloud collaboration method proposed in this paper achieves satisfactory accuracy on all batteries.The RMSE and MAE of the prediction results are both around 1% and 0.8%.In particular, for battery B7, the RMSE and MAE of the prediction results are 0.89% and 0.62%.The error of the estimation results on battery B6 is significantly higher than that of the estimation results on the other batteries.This is caused by the inconsistency between batteries.Meanwhile, on all batteries, the method proposed in this paper is able to capture the capacity rebound phenomenon with strong nonlinearity.

Conclusion
In this paper, a SOH estimation method based on end-cloud collaboration is proposed.Specifically, a deep learning model is arranged on the cloud-side for high accuracy SOH estimation.A fast empirical model is arranged on the end-side for high real-time SOH estimation.An end-cloud collaboration algorithm is arranged on the end-side, and the high-accuracy estimation results of the cloud-side are utilized to update the high-real-time estimation results of the end-side.Finally, the Meanwhile, in practical applications, the update step size can also be adjusted by considering the transmission resources and accuracy requirements.Based on the CHAIN framework, the method proposed in this paper has the potential to realize high-accuracy and high-real-time health monitoring of lithium-ion batteries throughout their full life cycle.And it can be extended to multi-state estimation applications.
In conclusion, the proposed cloud-based algorithm features practical implementability and high computational efficiency.In terms of implementability, the proposed end-cloud collaboration ensures that real-time data processing is handled by the end-side empirical model, which requires significantly less computational power and can operate independently of the cloud for immediate SOH estimation.To mitigate transmission costs and bandwidth usage, the system is designed to selectively transmit data to the cloud for processing.This approach ensures that only pertinent data is sent, reducing the overall load on the communication network.We propose that the additional cost incurred by cloud computing is justified by the extended battery life and the enhanced safety provided by accurate SOH estimations.This can result in a net positive impact on the total cost of ownership for EV operators.In terms of computational efficiency, we have employed Bayesian optimization techniques for hyperparameter tuning, which optimizes the computational efficiency of the deep learning model.The use of EKF on the end-side for data fusion minimizes computational demands by efficiently combining the rapid empirical model's output with the cloud model's accuracy.The algorithm allows for adjustable update frequencies between the cloud and end-side models, enabling a balance between accuracy, real-time response, and computational load.However, further empirical studies on the cost-benefit analysis and computational load would be beneficial, and these could be potential areas for future research.
This paper focuses on the cell level, and future work can extend to pack-level SOH estimations.Transitioning from celllevel to pack-level estimation introduces complexities such as cell-to-cell variations, thermal management issues, and the interplay between cells within a pack that can affect overall performance.This may involve strategies to manage the heterogeneity among cells in a pack and the integration of additional sensors and calibration methods to account for inter-cell interactions.It is also worth exploring how data fusion techniques could be employed to aggregate cell-level estimations for packlevel SOH assessment.The EKF used in our current model could be adapted to accommodate the statistical variances expected across a battery pack (Liu et al. 2022).
Figure 1(a) shows the voltage, temperature and current for one cycle, and Figure 1(b)

1 .
Figure 1.Battery degradation cycle schemes.(a) The voltage, temperature and current for one cycle.(b) Capacity degradation profiles of the battery B5, B6, B7 and B18.

Figure 2 .
Figure 2. Feature extraction and correlation analysis.(a) Changes of ICA curve.(b) Changes of DTV curve.(c) Changes of voltage curve.(d) Pearson correlation analysis results.

Figure 4 .
Figure 4. Structure diagram of (a) attention mechanism and (b) Cloud-side deep learning model.

Figure 4 4
(b) shows the overall architecture of the deep learning model used in this paper.The entire model is constructed based on a two-layer Bi-LSTM to capture the nonlinear mapping relationship between features and SOH, and a dropout technique is added to the network to prevent overfitting.AM is added on temporal and spatial scales to capture significant locations in different sequences and different features respectively.Locations with high correlation are given high weights while those with low correlation are given low weights.The addition of AM on the temporal scale allows the model to focus on the important sequences and thus optimize the estimation of the time series problem.The AM on the spatial scale allows the model to focus on important features in different sequences, and since the feature extraction in this paper is performed based on multi-features, spatial scale AM and multi-feature collaboration can further improve the performance of the model.The hyperparameters of the model are based on Bayesian optimization technique for automatic hyperparameter optimization, and the model is trained based on RMSProp technique.The data is first constructed into a three-dimensional tensor and then fed into the network for training through the input layer, and finally the SOH values are output through the Dense layer, which has a Sigmoid function added as an activation function.

Figure 5 .
Figure 5. Architecture of the entire end-cloud collaboration system.

Figure 6 .
Figure 6.SOH estimation results of cloud-side.(a) Estimation result of t as the feature.(b) Estimation result of ICA as the feature.(c) Estimation result of DTV as the feature.(d) Estimation result of multiple features.(e) Estimation result of multiple features and AM collaboration.(f) Error analysis.

Figure 7 .
Figure 7. SOH estimation results of end-side.(a) Estimation result of end-side empirical model.(b) Estimation result of end-cloud collaboration with 1 as the update step size.(c) Estimation result of end-cloud collaboration with 5 as the update step size.(d) Estimation result of end-cloud collaboration with 10 as the update step size.(e) Estimation result of end-cloud collaboration with 15 as the update step size.(f) Error analysis.

Table 1 .
Detailed operating conditions of the NASA dataset.

Table 2 .
MAE and RMSE of estimated results.