Remaining useful life prediction of lithium-ion batteries based on FEEMD-LSTM-TAM-OKELM

In response to the needs of today’s new energy era, lithium-ion batteries are based on advanced manufacturing technology and have unique advantages such as high energy density, low self-discharge rate, and long life.^1–3 People’s demand for convenient battery storage, green environmental protection, long cycle life, etc., widely used in urban construction of energy storage equipment, electric power transport, renewable energy systems, and other areas play an indispensable role.⁴ 

However, due to the chemical reaction inside the lithium-ion battery and the influence of external environmental factors, the degradation of the battery is inevitable. If there is no human treatment, lithium-ion battery life will be significantly reduced, its power system will have functional failure problems, which may lead to significant safety accidents.⁵ In battery health detection and management, it is necessary to predict the future battery capacity and Remaining Useful Life (RUL). Timely and accurate RUL prediction can effectively avoid accident risks.⁶ 

Lithium-ion battery RUL prediction technology has high requirements and high demand. Currently, there are three primary battery RUL prediction methods: model-based prediction method, data-driven prediction method, and fusion method.⁷ The model-based method mainly analyzes the failure mechanism and capacity degradation of the battery and establishes chemical, physical, or mathematical models to describe the attenuation behavior of the battery. This method can be subdivided into electrochemical models, equivalent circuit models, and empirical models. For example, Khodadadi Sadabadi et al.⁸ used an electrochemical model to study a battery RUL prediction method based on State of Health (SOH) estimation. Feng et al.⁹ considered introducing a Moving Average (MA) noise into the resistance-capacity circuit model and adopted the Recursive Extended Least Squares (RELS) algorithm to identify the parameters in the equivalent circuit model. This method can improve the recognition accuracy of the dynamic characteristics of the battery. Lyu et al.¹⁰ proposed a novel Particle Filter (PF) method based on an electrochemical model, which simulated the relationship between the state variables and life criteria of battery performance to achieve battery RUL prediction. The model-based prediction method can deeply understand the mechanism of battery degradation, and the model accuracy of this method is high; however, the time cost of establishing the lithium-ion battery prediction model is high, the model is easily affected by noise and environment, and the generalization performance of the model is not good enough.¹¹ 

The data-driven method directly uses the existing historical degradation data to predict the future degradation trend of the battery, without understanding the aging mechanism and expansion law of the battery. At present, data-driven methods mainly include Support Vector Regression (SVR) and Gaussian Process Regression (GPR), Extreme Learning Machine (ELM), Neural Networks (NN), etc.¹² Zhao et al.¹³ combined feature vector selection and SVR to realize online prediction of battery capacity. The feature selection method is used to remove redundant data, reduce the search space of the SVR model, and improve the prediction efficiency of the model. Tagade et al.¹⁴ studied a RUL prediction method for lithium-ion batteries based on deep GPR, further enhanced the prediction ability of the GPR algorithm, and estimated formal sequences such as current and voltage, achieving good results. Ren et al.¹⁵ used autoencoders to increase data dimensions, and then Convolutional Neural Networks (CNN) and Long Short-Term Memory (LSTM) to mine spatial and temporal information in the data, respectively. The data-driven method has shown significant advantages in lithium-ion battery RUL prediction, including its convenience of not relying on an in-depth understanding of the internal mechanism of the battery, effective use of big data, real-time and dynamic prediction capabilities, cost-effectiveness, and easy integration and expansion.¹⁶ However, this method depends on the quality and quantity of degraded data.

The prediction method based on fusion can combine the advantages of the above two methods, and maintain high prediction accuracy while deeply mining data characteristics, which is the mainstream of RUL prediction research. For example, Zhang et al.¹⁷ used the PF algorithm to update the model parameters online and introduced NN to adapt to the degradation trend of battery capacity under different conditions. Compared with the traditional method, this can reflect the attenuation degree of capacity more accurately. Wu et al.¹⁸ proposed a RUL prediction model for lithium-ion battery cells based on Adaptive Levy Flight (ALF) to optimize particle PF and LSTM and introduced ALF to optimize traditional PF, effectively overcoming the deficiencies of weight degradation and particle poverty. At the same time, the LSTM model is used to learn the degradation sequence of lithium-ion batteries and the fusion model can accurately predict the RUL. Jiao et al.¹⁹ proposed an electrochemical theory-based Light Gradient Boosting Machine (Light GBM) framework to implement RUL prediction and use Adaptive Robust (AR) loss to achieve adaptive adjustment under different situations and reduce the impact of noise on RUL prediction. In contrast to the single approach, the hybrid approach provides more accurate RUL prediction results, and the adaptive capability has been improved to some extent. However, the hybrid approach also has some drawbacks, such as large computational effort, an excessive number of parameters introduced, and error accumulation.

Lithium-ion batteries have a severe capacity regeneration phenomenon in battery capacity degradation. Throughout the life cycle of lithium-ion batteries, the storage capacity of the battery decreases, as the operating time increases. However, the capacity of the battery occasionally increases spontaneously with respect to the previous cycle, and the degree of increase is influenced by the electrochemical performance of the battery. This phenomenon is known as battery capacity regeneration.^20,21 In some cases, the cyclic charge and discharge experiment of lithium-ion batteries will have a capacity regeneration phenomenon, which will seriously mislead the modeling process and affect the prediction accuracy of RUL. Some scholars use signal-processing algorithms to decompose the capacity sequence. For example, Yang et al.²² developed an Ensemble Empirical Mode Decomposition (EEMD) based on the Gray Wolf Optimizer (GWO) optimization of the SVR kernel parameter model to predict the remaining service life of lithium-ion batteries. EEMD was used to pre-process degradation data of lithium-ion batteries to extract features, which improved the prediction accuracy. Shi et al.²³ studied a complete EEMD algorithm with adaptive noise and a multi-mode decomposition combined prediction model with LSTM to solve the problem of inaccurate prediction results of lithium-ion battery life. Among the above methods, although EMD and EEMD methods can realize the decomposition of battery capacity, the EMD method suffers from modal aliasing, and the EEMD method increases the complexity and computation of the algorithm greatly due to the addition of Gaussian white noise. Based on this, we conclude that there is a higher demand for ever-improving forecasting methods, as follows:

1. The capacity regeneration phenomenon exists in the battery capacity degradation process, and its influence on the accurate prediction of battery RUL must be reduced as much as possible.

2. It takes a lot of time for some signal processing methods to decompose the battery capacity sequence, so the time for decomposing the capacity sequence must be reduced.

To solve the above problems, it is necessary to achieve effective decomposition of the battery capacity sequence and reduce the impact of the capacity regeneration phenomenon as soon as possible.²⁴ This paper proposes a RUL prediction method based on Fast Ensemble Empirical Mode Decomposition (FEEMD)-LSTM-Temporal Attention Mechanism (TAM)-Online Kernel Extreme Learning Machine (OKELM). The main contributions of this article are as follows:

1. In this paper, the FEEMD decomposition method was adopted to decompose the capacity degradation data sequence of lithium-ion batteries into a series of relatively stable Intrinsic Mode Functions (IMFs) sequences, which enhanced the stability and accuracy of data decomposition and reduced the time of capacity sequence decomposition.

2. The LSTM-TAM is used to predict the overall trend of the battery capacity data. The LSTM layer is good at processing time series information, and it can process the input vector through a recursive execution method, which relies on the past hidden state and the current input. TAM algorithm can automatically weight the critical features of time series data to effectively obtain the importance of different time points. Therefore, the network can better characterize the attenuation trend of battery capacity.

3. For the vibration signal data of the attenuation sequence, the OKELM algorithm is used to predict, which adopts the “accelerated version” of extreme learning machine algorithm. For large-scale lithium-ion battery capacity degradation data, real-time high-speed calculation, efficient modeling, automatic learning of optimal parameters, and adaptive adjustment model can be achieved, which can well adapt to the characteristics of the vibration signal data. The battery capacity prediction is achieved while maintaining high prediction accuracy.

4. The feasibility and effectiveness of the proposed method are verified on the NASA battery and CALCE dataset. The prediction error in the NASA dataset is no more than one cycle. The prediction error in the CALCE dataset should not exceed two cycles.

The structure of this paper is as follows: Sec. II describes the theory and structure of the FEEMD-LSTM-TAM-OKELM prediction method. Section III introduces the experimental dataset and the hardware and software setup for the experiments. Section IV presents the experimental process and the results of data analysis in detail, and compares them with other models. Section V provides the conclusion.

FEEMD is a signal-processing method based on empirical mode decomposition, which can decompose time series into a set of different IMFs, considering the fractal characteristics of the signal to enhance the decomposition effect of the signal.²⁵ 

FEEMD will first calculate the corresponding noise standard deviation of a set of signals using the fractal dimension of the signals, then add the noise based on the noise standard deviation to generate a set of signals containing noise, and finally decompose and average this set of signals using the EMD method to obtain the final decomposition of the signals. The two important parameters used in FEEMD are the amplitude of the additional white noise k, and the EMD’s maximum number of operations M, which are set to 0.1 and 100, respectively. The detailed steps of the FEEMD algorithm are as follows:

1. Initialize the amplitude of white noise k and the maximum number of operations N of EMD.

2. Random Gaussian white noise sequence X_n(t) is added to the original capacity time sequence X(t) to obtain a new time series,

   $Xn(t)=X(t)+Mn(t).$

   (1)
3. A series of IMF_i,m and residual sequences R_m,n(t) are obtained using the EMD algorithm to decompose the signal of the white noise sequence,

   $Xm(t)=∑i=1nIMFi,m+Rm,n(t).$

   (2)
   Repeat steps (2) and (3) with different white noise until the maximum number of operations is reached N. Calculate the ensemble mean of all components as

   $ci(t)=∑i=1mIMFi,mN.$

   (3)

   FEEMD algorithm introduces the fractal characteristics of the signal so that the addition of noise is more consistent with the actual change of the signal so that it can reflect the change characteristics of the signal itself more accurately. Due to the complexity and nonlinearity of battery capacity degradation data, the FEEMD algorithm can more accurately extract the degradation trend and periodic change characteristics of lithium-ion batteries, to better mine the signs of battery capacity decay and achieve RUL prediction.

LSTM is an optimized version of Recurrent Neural Network (RNN), which is mainly used to process time series data and make predictions. The LSTM model manages the information retained in the data through the input gate, the forget gate, and the output gate to improve the gradient disappearance problem that occurs in the training process of the RNN model. The LSTM model structure is shown in Fig. 1.

Here, f_t is the output value of the forgetting gate at the time; σ is the sigmoid activation function, h_t−1 is the output state at the previous moment, and x_t is the input state at the current moment, which consists of the sequence of the battery capacity and the number of cycles; W_f is the weight matrix of the forgetting gate; and b_f is the bias value of the forgetting gate.

Here, o_t is the output value of the output gate at moment t, W₀ is the weight matrix of the output gate, b₀ is the bias value of the output gate, and h_t denotes the current output value of a single LSTM neuron cell.

As a series data processing technique, the attention mechanism is mainly used in the application of time series prediction to deal with long-term dependent series data, which is highly relevant to the current prediction. This mechanism can help the model better focus on the part of the input sequence that is most relevant to the current prediction by calculating the attention weight to focus the model on the time step that is most relevant to the current prediction. Then, the scoring function is used to calculate the weight parameters, to achieve a reasonable allocation of the weight of the input data and improve the accuracy of the prediction.²⁶ 

To enable the model to process the historical state information adaptively and strengthen the influence of the relevant moment state information, this paper introduces the LSTM of the temporal attention mechanism as shown in Fig. 2.

Here, score scoring function uses dot product, a_t,i is the attentional weight of the implicit layer state of the historical input to the current input, c_t is the intermediate vector, and $ht∼$ is the value of the implicit layer state at the current moment of the final output.

Traditional neural network models can be trained by pre-determined training samples. With the continuous updating of samples, the prediction error will continue to increase through the conventional divine network model prediction. Therefore, to solve the model update problem in the process of sample updating and improve the prediction accuracy, the OKELM algorithm is used to predict the oscillating signal. The modeling steps of the OKELM method are as follows:

1. Calculate the initial one using l samples {(x_i, t_j)}^N+l−1 at the current moment,

   $EN=qNFNTFNWN,$

   (15)

   $qN=K(xN,tN)+C−1,$

   (16)

   $FN=[K(xN,xN+1)…K(xN,xN+l−1)]T,$

   (17)

   $DN=EN−1,$

   (18)

   $ε100(−1)=λkDN(k,k),$

   (19)

   $εN=∑i=1Nε100(−1).$

   (20)

   Here, W_N is a (l −1) * (l −1)−dimensional square matrix, and q_N is a constant.

2. Using x_N+1 as input, the predicted value t_N+1′ for its standard output t_N+1 is calculated according to Eq. (22),

   $Ωi,j=h(xi)∗h(xj)=K(xi,xj),$

   (21)

   $f(xp)=[K(xp,x1)…K(xp,xN)]λ,$

   (22)

   $λ=1c+Ω−1T.$

   (23)
3. After obtaining the true value of t_N+1, calculate the model’s prediction error e = |tN − tN’| for this sample. If Eq. (22) holds, then update the pair according to Eq. (23) to obtain D_N+1; otherwise, D_N+1 = DN.

   $tN+1−tN+1′>εNl,$

   (24)

   $DN+1=EN+1−1.$

   (25)

4. Using the updated D_N+1, λ_N+1 is calculated according to Eq. (23); the old samples (x_N, t_N) are deleted, and $WN+1−1$ is calculated from D_N+1 according to Eq. (25); ε_N+1 is calculated from D_N+1 and λ_N+1 is calculated according to Eq. (20).

5. Let N = N+1, return to step (2).

In the RUL prediction of lithium-ion batteries, the decay process of battery capacity is affected by various factors such as temperature, charge/discharge cycle, and current magnitude. Therefore, the decay sequence of battery capacity presents complex nonlinear and non-stationary time series data. However, traditional linear models, such as linear regression, time series analysis, exponential smoothing, and linear Kalman filtering, make it difficult to accurately capture this complex trend. The FEEMD method can decompose the complex capacity decay trajectory into several relatively simple IMFs, which helps to more accurately reveal the local features in the battery capacity decay sequence and, thus, improves the accuracy of the RUL prediction. The LSTM layer is good at processing time series information, which can process the input vectors through a recursive execution method that depends on the past hidden states and the current inputs. The TAM algorithm can automatically weigh the key features of the time-series data to efficiently obtain the significance of different time points in the sequence. Therefore, LSTM-TAM can better characterize the decaying trend of battery capacity; OKELM can well adapt to the characteristics of oscillatory signal data and achieve battery capacity prediction while maintaining high prediction accuracy.

The structural block diagram of the prediction model proposed in this paper is shown in Fig. 3, which is mainly divided into four stages.

1. Capacity degradation data were extracted from NASA and CALCE datasets.

2. The battery capacity decay sequence is divided into a training set and a test set and then decomposed using the FEEMD algorithm to obtain its intrinsic modal components.

3. The LSTM-TAM and OKELM methods were used to train and predict the overall trend data and shock data, respectively.

4. RUL prediction is realized, and the effectiveness of the proposed method is verified by the test set, which improves the adaptability and prediction accuracy of the model.

The first experimental dataset is from the NASA lithium-ion battery dataset.²⁷ The experimental data of four batteries, B0005, B0006, B0007, and B0018, were selected for simulation verification.²⁸ The dataset contains charging, discharging, and impedance data for these four batteries; the data were obtained at a temperature of 24 °C. The four batteries were charged in Constant-Current (CC) mode at 1.5 A. When their charge voltage reached 4.2 V, they were charged again in Constant-Voltage (CV) mode, and charging continued until the battery charge current reached 20 mA. The B0005, B0006, B0007, and B0018 batteries were discharged in CC mode at 2 A until their voltages dropped to 2.7, 2.5, 2.2, and 2.5 V, respectively. Table I gives the details of the above lithium-ion batteries.

Figure 4 shows the capacity attenuation curve with the number of cycles during the discharge of four lithium-ion batteries. It can be seen from the curve that different types of batteries will have capacity regeneration in the discharge process, and the capacity sequence of lithium-ion batteries presents non-stationarity and nonlinear.

The second experimental dataset studied in this paper comes from the Center for Advanced Life Cycle Engineering (CALCE).²⁹ CX2_33 and CX2_34 were selected for simulation verification. The cycling of the cells is conducted using an Arbin BT2000 battery test system. For testing, cells named CX2_33 and CX2_34 were subjected to a standard CC/CV protocol. During charging, the battery is charged at a CC rate of 0.5 C until the cell voltage reaches 4.2 V, then maintained at 4.2 V until the battery charge current drops below 0.05 A. Figure 5 shows the decay curves of the capacity with the number of cycles during the discharge process of CX2_33 and CX2_34 lithium-ion batteries.

Experiments were performed on a Windows 11 system with 16 GB of memory, an RTX3060 graphics card, and an AMD Ryzen 7 5800H CPU with Radeon Graphics. The software programs were PyCharm 2021.2.2. The models utilized in the study were constructed using the CPU version of the Keras framework and the Python 3.7 development environment.

In the above equation, C_t and C_t denote the actual and predicted capacity values, respectively; and n is the number of test samples. RMSE and MAE are used to evaluate the accuracy of the prediction of the capacity degradation trajectory; RUL_prediction and RUL_true represent the predicted and true value of RUL, respectively; and AE is used to evaluate the accuracy of the prediction of RUL. The smaller the values of these three indicators, the more accurate the prediction.

Figure 6 shows the decomposition results of B0005, B0006, B0007, B0018, CX2_33, and CX2_34 battery capacity attenuation data by the FEEMD algorithm. It can be seen from the figure that all of them contain IMF components of various frequencies. IMF1 reflects the global degradation trend of battery capacity, and the remaining components indicate that the battery capacity is degraded in the process of attenuation.

Due to the influence of the capacity regeneration phenomenon, there will be local fluctuations.

In this study, the B0005, B0006, B0007, and B0018 cells in the NASA dataset, as well as the CX2_33 and CX2_34 datasets were used to experiment with several related algorithm models. In this experiment, to test the performance of the FEEMD-LSTM-TAM-OKELM combined model, the OKELM, LSTM-TAM, FEEMD-OKELM, FEEMD-LSTM-TAM, and other models are selected for synchronous prediction, Then, the superiority of the proposed model is compared and analyzed. In this experiment, when training the above model, the battery capacity more minor than the predicted Starting Point (SP) in the NASA and CALCE datasets is used as the training set, and the data larger than SP is used as the test set.

To verify the performance of the proposed method in lithium-ion battery RUL prediction, Table II shows the evaluation indices of lithium-ion battery prediction results under different models. The smaller the AE, RMSE, and MAE, the higher the prediction accuracy of the prediction model.

Divide the training set and the test set with the set SP value as the limit. The prediction results are compared with those predicted by OKELM, LSTM-TAM, FEEMD-OKELM, FEEMD-LSTM-TAM, and other methods. The specific comparison results are shown in Fig. 7.

Figure 7 shows the single OKELM model and LSTM-TAM model that have large fluctuations in the prediction of battery capacity decay sequence in the NASA dataset. The prediction effect of different batteries is quite different, and the prediction effect is not stable enough. With the introduction of the FEEMD decomposition method, the accuracy of some lithium-ion battery capacity decay sequences is significantly improved, and the prediction effect is more consistent with the accurate data. This is because the FEEMD decomposition method has the advantages of enhancing noise suppression and reducing mode aliasing for non-stationary sequences.

The FEEMD decomposition method inherits the advantages of EMD, can deal with various types of sequences adaptively, and can decompose different battery decay sequences to get relatively stable results. By comparing the prediction effects of the FEEMD-OKELM model, FEEMD-LSTM-TAM model, and the FEEMD-LSTM- TAM-OKELM model proposed in this paper, it can be seen that the prediction effect of the proposed prediction model is closest to the true value under different batteries, and the prediction effect is the most stable, which reflects the superiority of this method.

The FEEMD-LSTM-TAM-OKELM model inherits the advantages of the FEEMD algorithm, and according to the characteristics of the series decomposed by FEEMD, the LSTM-TAM method is used to capture the long-term dependence of time series data for the low-frequency data of the series, and the OKELM model is used to deal with nonlinear problems for the high-frequency data. The cross-modal learning and adaptive ability of the LSTM model, and the fast learning ability of the OKELM model are fully utilized to provide a more accurate and stable prediction effect for dealing with complex nonlinear time series.

To verify the performance predicted by RUL under different lithium-ion batteries by the proposed method, the SP value was used as the limit to divide the training set and the test set. The battery degradation data of the decomposed CALCE data were used to train various models, and the battery degradation data of the CALCE data were used for testing.

Table III shows the evaluation indices of RUL prediction results of CX2_33 and CX2_34 batteries under different models, where more minor AE, RMSE, and MAE indicate higher prediction accuracy of the prediction model. The prediction results were compared with those predicted by OKELM, LSTM-TAM, FEEMD-OKELM, FEEMD-LSTM-TAM, and other methods. The specific comparison results are shown in Fig. 8.

As shown in Fig. 8, CALCE batteries have more cycles than NASA batteries, and the predicted curves obtained in this paper almost coincide with the actual capacity degradation curves. With the integration of the FEEMD decomposition method and other model methods, the prediction effect of battery RUL gradually approaches the natural impact, which can better deal with the problem of battery capacity regeneration. Compared with the prediction effect of other models, the FEEMD-LSTM-TAM-OKELM model proposed in this paper presents a stable prediction effect for the RUL prediction of different batteries, and the model effect is the most robust.

Neurons are randomly discarded by dropout in the training process of the neural network, and the parameters of the model can be regarded as obeying the Bernoulli distribution. Therefore, if the dropout is turned on in the test stage and the prediction is repeated T times, the mean value is the final prediction value, and the variance is uncertain. The experimental results of the four groups are shown in Fig. 9 and Table IV.

The smaller RMSE and MAE of the four cells in Table IV verify that the proposed approach has a better prediction ability for capacity prediction. In addition, the AE values of RUL prediction for the following four kinds of batteries are 2, 5, 2, and 2, showing high prediction accuracy. It can be seen that the proposed approach can obtain reliable prognostic results and provide constructive suggestions for decision makers in system security maintenance.

The FEEMD-LSTM-TAM-OKELM combination model proposed in this paper is superior to other models in all model evaluation indices. The AE values of RUL prediction for the following four kinds of batteries are 0, 0, 1, and 1, showing high prediction accuracy. Compared with the single OKELM model, the RMSE of the FEEMD-LSTM-TAM-OKELM combined model proposed in this paper is 0.011 88, which is reduced by about 35.2%; MAE was 0.006 04, which decreased by 59.8%. Compared with other models, the combined model has different degrees of improvement, and the optimization effect is remarkable.

To further demonstrate the superiority of the model proposed in this paper, other research results on the same dataset are collected in the following Table V. According to the analysis, it can be seen that the prediction model proposed in this paper has the best prediction effect on the RUL of lithium-ion batteries, and the prediction effect of different batteries does not fluctuate much. For B0005, B0006, B0007, and B0018 batteries, the difference between the maximum RMSE and the minimum RMSE predicted by the FEEMD-LSTM-TAM-OKELM model is only 0.0034. The difference between maximum MAE and minimum MAE is only 0.003 66, which shows that the proposed model has adaptive solid ability.

The capacity degradation of lithium-ion batteries seriously hinders their safe use in many applications. To improve the accuracy of RUL prediction for lithium-ion batteries, this study introduces a methodological framework based on FEEMD-LSTM-TAM-OKELM. The framework integrates signal-processing methods and machine-learning algorithms for predicting the RUL of lithium-ion batteries. In this paper, the battery capacity is selected as an indicator of the health state, which is decomposed using the FEEMD method to obtain a general trend component and multiple oscillatory fluctuation components, which are used to enhance the stability and accuracy of the data decomposition and to reduce the time taken in the decomposition of the capacity series. LSTM-TAM is used to predict the total trend component, LSTM is prone to information loss and gradient disappearance when dealing with long time series data. Therefore, a TAM method is introduced, which can adaptively deal with the degree of influence of the historical capacity information of each cell on the current cell capacity information. OKELM is used to predict the oscillatory signals. The experimental results show that the method can achieve more accurate RUL prediction for lithium-ion batteries compared to some other methods (including the method in this paper compared to the methods in recent years), with AE of no more than one cycle in the NASA dataset and no more than two cycles in the CALCE dataset.

In future work, we will explore using methods such as grid search and optimization algorithms to find the optimal model parameters. In addition, we will consider the impact of other battery health factors (e.g., charge/discharge current rate, temperature, cutoff voltage, and impedance) on the RUL prediction of LIBs.

This work was partially supported by the Project of Liaoning Provincial Department of Education (Grant No. LJKZ0367) and the Discipline Innovation Team Funding Project of Liaoning Technology University (Grant No. LNTU20TD-15).

The authors have no conflicts to disclose.

Jingmei Yu: Writing – review & editing (equal). Yaoyang Cai: Writing – original draft (equal). Yingxin Huang: Data curation (equal); Software (equal); Validation (equal). Xinle Yang: Funding acquisition (equal); Resources (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.