Remaining useful life prediction of sodium-ion batteries based on ICEEMDAN-CNN-GRU

A hybrid battery remaining useful life (RUL) prediction model based on ICEEMDAN-CNN-GRU(M1) is proposed to address the nonlinearity and complexity of capacity degradation in sodium-ion batteries. Firstly, capacity attenuation data and some indirect parameters easily obtainable by sensors are experimentally measured. The original capacity sequence is reconstructed into a new one using the ICEEMDAN method to effectively suppress the influence of capacity regeneration and noise signals. Secondly, a hybrid CNN-GRU prediction model is constructed by leveraging the advantages of convolutional neural networks (CNN) in the field of data mining and gated recurrent unit (GRU) in time series prediction. Three sets of indirect parameters are used as inputs, and the reconstructed capacity is used as the output for RUL prediction model training with different starting points. Finally, the effectiveness of the algorithm is verified through data from three different rates, and the predicted indicators are better than those of traditional algorithms such as GRU, LSTM, and SVM.


Introduction
Sodium-ion batteries are a new type of energy storage technology offering high energy density, low cost, and abundant resources [1][2][3].They are extensively utilized in electric automobiles and energy storage systems.Recent progressions in electrode materials, electrolytes, and mechanism research have ameliorated their performance and stability, diminished expenses, and stimulated pragmatic applications.Nevertheless, prolonged usage diminishes their capacity and performance, so a prompt evaluation of its remaining useful life (RUL) is mandatory to avoid equipment damage.Precisely evaluating battery RUL is crucial to guarantee smooth operations and enhance energy efficacy [4][5].
Predicting the RUL of batteries is difficult due to their complex and nonlinear behavior, as well as external stresses.However, monitoring battery performance and capacity and using data analysis and machine learning can help predict RUL.This enables a better understanding of battery life and performance, and more effective maintenance and management.
Battery RUL prediction methods can be divided into model-based and data-driven methods [6].Model-based methods require extensive knowledge and solving complex equations [7], while datadriven methods are more cost-effective and efficient, and have been widely used by researchers due to the complexity of internal battery reactions and the presence of noise in measured data [8].
A data-driven RUL prediction model explores the relationship between external measurement parameters and the internal state of batteries, without the need to study complex battery principles [5].They extract information across time steps from previous data and transfer them to the current state to model time series.
To address the capacity regeneration problem during the battery's lifetime degradation, some multiscale decomposition methods are applied to battery capacity sequences.Some scholars use the combination of EMD and neural networks to predict battery RUL.Lei et al. proposed a CNN-LSTMbased RUL prediction method and used an autoencoder to augment the raw data for more effective training of CNN and LSTM [9].
Based on the analysis above, this paper proposes a method for estimating the RUL of sodium-ion batteries using ICEEMDAN-CNN-GRU(M1). First, the capacity data during the degradation process of sodium-ion batteries and other parameters that can characterize capacity degradation were detected.Then, ICEEMDAN was used to synthesize a new reconstructed capacity sequence from the original capacity sequence, effectively reducing its non-smoothness, nonlinearity, and complexity.Next, a hybrid CNN-GRU model was built for the RUL prediction of sodium-ion batteries.Finally, the effectiveness of the proposed model was validated using self-test datasets.

Battery charge and discharge test
We conducted a long-term cycling aging experiment on Na 4 Fe 3 (PO 4 ) 2 P 2 O 7 batteries in a constant temperature chamber (30℃).The battery was cycled using a multi-step charging mode and a constant current discharging mode.Real-time monitoring of voltage, current, and other parameters was carried out at specified intervals.The battery was cycled at different rates (0.1C, 1C, 1.5C, and 2C) after the first three cycles.Figure 1 shows the details.
As shown in Figure 2, the capacity of sodium-ion batteries gradually decreases with increasing charge and discharge cycles, resulting in a corresponding decrease in the state of health (SOH) of the battery.

Input parameters
As sodium-ion batteries age, their performance can be affected, resulting in higher internal resistance, lower specific discharge energy, and median voltage.This is due to electrode material deactivation and the formation of a solid electrolyte interface layer, which occurs with increased battery cycling.To estimate the RUL of the battery, specific discharge energy, median voltage, and internal resistance are analyzed.Figures 3, 4, and 5 demonstrate that as the number of charge-discharge cycles increases for the data under a 2C rate, the battery's discharge specific energy and median voltage decrease, while the internal resistance increases.This indicates that the battery's capacity deteriorates with more cycles, and there is a positive correlation between the degradation of capacity and the discharge-specific energy and median voltage, but a negative correlation with the internal resistance.
We calculated Pearson correlation coefficients between the input parameters and the SOH of sodiumion batteries.A coefficient closer to 1 indicates a stronger correlation.All the parameters showed a strong correlation with the actual capacity of the battery.This confirms their suitability as input parameters.The results of the Pearson calculations are shown in Table 1.

Reconstruction of capacity sequences by ICEEMDAN
Incomplete chemical reactions inside batteries can cause the capacity regeneration phenomenon.This can restore the battery's capacity, making it higher than predicted, which may lead to overestimating the battery's remaining life for sodium-ion batteries.To solve this, a signal decomposition method is used to create a new capacity sequence.
ICEEMDAN is an improved version of CEEMDAN, which addresses mode mixing and reduces false components in decomposition results.It achieves this by using the difference between the residue from the previous step and the average residue of multiple added noise signals as the IMF for the current iteration.
Figure 6 shows that the battery capacity of the first group is separated into six IMFs and one R component, while the second and third groups have seven IMFs and one R.The R components indicate the main capacity trends, while the IMFs show local battery weakening.Table 2 displays correlation coefficients, where higher values suggest stronger correlations between components and capacity.We combined the residual component and the intrinsic mode function with the highest correlation coefficient to create a new capacity sequence.Figure 7 shows that the new capacity sequence is smooth without capacity regeneration.This approach improves the accuracy of predicting the lifespan of sodium-ion batteries by reducing errors from various factors such as measurement equipment, energy regeneration, battery load changes, and environmental interference.

CNN-GRU
The CNN consists of three layers -input, hidden, and output.The hidden layer, which extracts features, is composed of convolutional, pooling, and fully connected layers.The core of CNN is the convolutional layer, which has a set of learnable filters, with the number of filters set to 32.The convolution kernel C j identifies features accurately using an activation function, Rectified Linear Units (Relu).The pooling layer compresses data and removes unnecessary information, while the fully connected layer aggregates the extracted feature information to predict data.The hidden layers of CNN are used for feature extraction.The CNN structure is shown in Figure 8.
To analyze battery data collected during charging and discharging cycles, we need a neural network that can handle time series.Recurrent Neural Networks (RNNs) are ideal for this task due to their internal feedback and forward connections.However, RNNs can only store a portion of the sequence, making them less accurate on long sequences.As our data has thousands of time series, we opted for the GRU, which is better suited for processing long sequences.
GRU has two main components: the reset gate and the update gate.These gates help GRUs to selectively retain important information from the past and combine it with the input sequence of the next cell while disregarding irrelevant information.This makes GRUs well-suited for modeling sequential data.
Furthermore, in order to establish a robust RUL prediction model with strong generalization capabilities, the GRU architecture was enhanced with Dropout and L2 regularization techniques.A dropout rate of 0.25 was set to effectively prevent overfitting.The RNN structure consisted of four layers, comprising two GRU layers and two Dropout layers, arranged in the following sequence: [GRU, Dropout, GRU, Dropout].This specific network architecture was employed to achieve high prediction accuracy while minimizing the risk of overfitting.

NESP-2023 Journal of Physics: Conference Series 2592 (2023) 012046
The hybrid network architecture, composed of both CNN and GRU models, is illustrated in Figure 9.The input data is first processed by the convolutional layer, followed by compression in the pooling layer.The multidimensional input is then flattened using the unrolling layer before being fed into the GRU for time-series prediction.Finally, the output result is obtained through an end-to-end learning process using the fully connected layer.This specific network architecture was designed to achieve accurate predictions for time-series data while minimizing computational complexity.Figure 10.Structure of CNN.

Forecasting process
Step 1: Data Preparation.Sodium-ion batteries were subjected to aging experiments to obtain the battery's capacity degradation sequence.Parameters with a high correlation to the capacity were selected for analysis.
Step 2: Capacity Sequence Reconstruction.Using the ICEEMDAD decomposition process, the original capacity sequence was decomposed into several intrinsic mode functions (IMFs) and a residual (R).Subsequently, a new sequence was created by selecting the sequences with a high correlation to the capacity.
Step 3: CNN-GRU Model Training.The discharge-specific energy, median voltage, and internal resistance were used as inputs, and the reconstructed capacity was used as the output for model training.Different training starting points were used to the model.
Step 4: RUL Prediction.The trained CNN-GRU model was used to construct the prediction model, and its predictive performance was tested using a separate test dataset.
The overall forecasting process is shown in Figure 10.

Assessment indicators
In this study, the root mean square error (RMSE) and mean absolute error (MAE) were used to evaluate the predictive performance of the developed machine learning prediction models.RUL er and P er were used to measure the accuracy of the remaining useful life (RUL) predictions.The specific expressions are as follows: Ci represents the true capacity; i C represents the predicted capacity; n represents the number of samples.RUL er is the prediction error of RUL for sodium-ion batteries; RUL pr is the predicted value of RUL for sodium-ion batteries; RUL tr is the true value of RUL for sodium-ion batteries; P er is the relative error of capacity prediction for sodium-ion batteries.

Analysis of experimental results
In order to demonstrate the performance of the ICEEMDAN-CNN-GRU combined model, the ICEEMDAN-GRU (M2), ICEEMDAN-LSTM (M3) and ICEEMDAN-SVM (M4) models were selected for comparison in this experiment.The models were trained using the first 400 and 600 cycles of the dataset, and the remaining data were used to test the models.The final prediction results are shown in Figures 11 and 12. Compared with the M2, M3, and M4 models, the capacity prediction curve of the hybrid M1 combined model was closest to the true degradation trend, and the RUL calculation error was the smallest under different prediction conditions.This indicates that the prediction accuracy based on the hybrid M1 method is the highest.From the prediction results, it can be seen that the earlier the prediction starting point, the less effective information can be obtained, and the modeling difficulty is greater.As shown in Table 3 and Figures 13, 14, 15, and 16, the prediction errors of M2, M3, and M4 models increase as the prediction starting point moves earlier.In comparison, the variation of the training data has little impact on the M1 combination model.Under different testing data and starting points, the proposed method in this paper has the smallest MAE, RMSE, and Per values among the three methods, indicating that the prediction effect is very stable.
Overall, the results indicate that the method proposed in this paper can provide accurate RUL predictions for different batteries and training datasets.Based on the prediction results, the M1 method demonstrates good robustness and better battery life prediction ability compared to the other methods.Figure 16.Average RMSE at a starting point of 400.

Conclusion
In this paper, a new combined M1 life prediction model is proposed for effective prediction of the remaining life of sodium-ion batteries, with the following conclusions: (2) The ICEEMDAN algorithm effectively reduces the fluctuation of capacity during the decay of sodium-ion batteries to avoid the interference of noise components and reduce the prediction error.CNN can extract spatial features from the input data, while GRU is used to extract the hidden time-dependent features.
(3) The combined M1 model incorporating Dropout and L2 regularisation techniques has high accuracy for different sodium ion battery lifetime predictions, the reduction of training data has little effect on the prediction results, and the prediction model has certain generalization and robustness.By comparing with ICEEMDAN-GRU, ICEEMDAN-LSTM, and ICEEMDAN-SVM models, the prediction accuracy of the proposed combined model has been improved relative to other models, the average absolute error of the combined M1 algorithm is within 1.41, the root mean square error is within 1.92%, and the P er value does not exceed 0.0116.

Figure 11 . 7 Figure 12 .
Figure 11.Predicted results with 400 as the starting point.

Figure 14 .
Figure 14.Average RMSE at a starting point of 400.

Figure 15 .
Figure 15.Average MAE at a starting point of 400.

8 ( 1 )
The measured indirect parameters (discharge specific energy, median voltage, internal resistance) are verified to have a strong correlation with sodium-ion battery capacity by Pearson correlation coefficient calculation and can be used to predict RUL.

Table 1 .
Calculation results for input parameters of Pearson correlation coefficient