Lithium-Ion Battery SOH Prediction Method Based on ICEEMDAN+FC-BiLSTM

Abstract

Driven by the rapid promotion of new energy technologies, lithium-ion batteries have found broad applications. Accurate prediction of their state of health (SOH) plays a critical role in ensuring safe and reliable battery management. This study presents a hybrid SOH prediction method for lithium-ion batteries by combining improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) and a fully connected bidirectional long short-term memory network (FC-BiLSTM). ICEEMDAN is applied to extract multi-scale features and suppress noise, while the FC-BiLSTM integrates feature mapping with temporal modeling for accurate prediction. Using end-of-discharge time, charging capacity, and historical capacity averages as inputs, the method is validated on the NASA dataset and laboratory aging data. Results show RMSE values below 0.012 and over 15% improvement compared with BiLSTM-based benchmarks, highlighting the proposed method’s accuracy, robustness, and potential for online SOH prediction in electric vehicle battery management systems.

1. Introduction

New energy vehicles have been widely promoted and applied worldwide. Among various energy storage technologies, lithium-ion batteries are extensively used in these vehicles due to their high energy density and long service life [1,2]. Accurate prediction of the SOH of lithium-ion batteries is crucial for ensuring their safe and efficient utilization. Existing approaches for SOH prediction mainly include battery modeling and deep learning methods [3,4,5]. Battery modeling methods typically involve the development of linear or nonlinear models to estimate SOH. These approaches provide valuable insights into the degradation mechanisms of lithium-ion batteries [6,7,8,9]; however, they often suffer from limitations such as weak robustness and structural complexity, making them less suitable for practical applications. In contrast, deep learning-based SOH prediction methods leverage external environmental factors as input features, significantly improving prediction accuracy [10]. These methods are characterized by simpler modeling procedures and stronger adaptability, which facilitate their integration and deployment in battery management systems [11,12,13,14]. Yiwen Sun et al. proposed a novel SOH estimation method with attentional feature fusion considering differential temperature features for lithium-ion batteries [15]. Ying Zhang et al. proposed a novel SOH assessment model based on the deep learning framework. The SOH results are derived from the quantile distribution of deep features, giving the SOH values with associated confidence intervals [16]. Zhengyu Liu et al. proposed a novel hybrid neural network architecture that integrates a segmented hidden Markov model, a trans former module, and a bidirectional gated recurrent unit, with parameter optimization performed using the differential evolution algorithm [17]. Rong Zhu et al. proposed a Bayesian calibrated physics-informed neural network framework for SOH estimation, integrating physical degradation models, data-driven calibration techniques and uncertainty quantification [18]. Zhen Wang et al. proposed a lossy counting-based gated dual-attention Transformer framework that substantially reduces historical data storage needs while maintaining high accuracy in SOH estimation [19]. In previous studies, the terms “SOH estimation” and “SOH prediction” have often been used interchangeably. However, SOH estimation focuses on evaluating the current health state of a battery from measurable parameters, whereas SOH prediction aims to forecast its future degradation trend based on historical data. Although many existing models emphasize estimation, their predictive capability for long-term degradation remains limited. In this work, the focus is explicitly placed on SOH prediction, that is, forecasting the future health trajectory of lithium-ion batteries.

Recent studies have increasingly adopted hybrid deep learning frameworks, such as CNN-LSTM, Transformer-GRU, and attention-based models, to improve SOH prediction accuracy. While these methods achieve good performance, they often rely on high data volumes, complex parameter tuning, and lack effective handling of nonlinear and nonstationary signal characteristics inherent in battery degradation data. Moreover, the strong dependence of these models on feature selection and the risk of overfitting under limited-cycle datasets restrict their generalization in practical applications.

To address these limitations, this study proposes a hybrid SOH prediction framework that combines improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) and a fully connected bidirectional long short-term memory network (FC-BiLSTM). Unlike existing hybrid models, ICEEMDAN enables adaptive, noise-resistant feature decomposition across multiple time scales, while the FC-BiLSTM architecture enhances feature mapping and temporal dependency modeling in a unified structure. This combination reduces signal interference, improves feature interpretability, and achieves accurate SOH prediction with lower model complexity. Through comparative experiments, the proposed method demonstrates superior accuracy and robustness over traditional BiLSTM and ICEEMDAN-based models, filling the gap between signal decomposition and deep temporal modeling in lithium-ion battery health prediction.

This paper proposes a lithium-ion battery SOH prediction method based on ICEEMDAN+FC-BiLSTM. The ICEEMDAN technique is first applied to decompose the input features, extract dominant trends, and better reveal the mechanism of capacity degradation. Subsequently, an FC-BiLSTM model is developed, where fully connected layers enhance feature mapping and improve prediction compared with BiLSTM alone. The approach is validated using NASA battery data and laboratory aging tests, achieving RMSE values below 0.012 and significantly outperforming both BiLSTM and ICEEMDAN-BiLSTM models.

This study aims to develop an accurate and robust method for predicting the state of health (SOH) of lithium-ion batteries. A hybrid ICEEMDAN+FC-BiLSTM framework is proposed, integrating signal decomposition with deep learning to enhance feature extraction and temporal modeling. Section 2 introduces the overall architecture of the proposed SOH prediction framework and feature extraction process. Section 3 describes the theoretical principles of ICEEMDAN and FC-BiLSTM. Section 4 presents the model design, experimental setup, and comparative analysis of prediction results. Finally, Section 5 concludes the study and outlines future research directions.

2. SOH Prediction of Lithium-Ion Batteries Based on ICEEMDAN+FC-BiLSTM

2.1. Architecture of the SOH Prediction Model

Battery SOH is an indicator of the performance degradation of a battery relative to its initial state, reflecting its current condition and degree of aging. SOH prediction methods are generally classified according to the parameters used for its definition, such as capacity, impedance, and aging-mechanism parameters [20]. In this study, SOH is defined as the ratio of the battery’s currently available capacity to its rated capacity at the beginning of life, expressed as a percentage. The calculation method is given in Equation (1).

$$\mathrm{S}\mathrm{O}\mathrm{H}={\displaystyle \frac{C_{actual}}{C_{rated}}}\times 100\%$$

(1)

The proposed system employs an ICEEMDAN+FC-BiLSTM approach to predict battery capacity based on input/output capacity parameters and time-related features, from which the SOH is subsequently calculated. The overall framework is illustrated in Figure 1. Specifically, the end-of-discharge time of the previous cycle ($\mathrm{P}\mathrm{V}$), charging capacity ($\mathrm{P}\mathrm{I}$), and the moving average of historical discharge capacity ($\mathrm{P}\mathrm{M}\mathrm{A}$) are selected as input features. These three parameters are first decomposed using ICEEMDAN, after which an FC-BiLSTM-based SOH prediction model is constructed. The method is validated using both the NASA lithium-ion battery dataset and laboratory-measured aging capacity data, with the training and validation sets divided in a 6:4 ratio.

2.2. Extraction and Analysis of Input Features

The NASA lithium-ion battery dataset was collected at room temperature (25 °C). Each cell was first charged with a constant current of 1.5 A until the voltage reached 4.2 V, followed by a constant-voltage charging mode until the current decreased to 20 mA. Subsequently, the cells were discharged at a constant current of 2 A with cut-off voltages of 2.7 V, 2.5 V, and 2.2 V, corresponding to the cycling data of batteries B0005, B0006, and B0007, respectively. The experiments were terminated once the end-of-life (EOL) criterion was reached, defined as a 30% reduction in rated capacity from 2 Ah to 1.4 Ah, yielding a total of 168 cycles.

For Laboratory-measured dataset, aging tests were conducted on 18650 cells with a rated capacity of 3400 mAh at 25 °C, as shown in Figure 2. The Panasonic NCR18650 lithium-ion cell (manufactured by Panasonic Corporation, Osaka, Japan) was tested using the LANBTS BT2018E power battery testing system (manufactured by Lambo New Energy Equipment Co., Ltd., Wuhan, China), which provides voltage, current, and capacity measurement functions with a sampling interval of 1 s. Based on the nominal capacity of 3400 mAh, all collected data were normalized to eliminate the influence of scale differences among features. To ensure the consistency of the aging process, the same lithium-ion cell was used throughout the entire test. After data collection, the interquartile range (IQR) method was applied to remove outliers caused by temporary interruptions or measurement noise, and Lagrange interpolation was used to reconstruct the missing or abnormal values. Before feature decomposition using ICEEMDAN, each input variable was standardized to zero mean and unit variance to improve model stability. Furthermore, to prevent data leakage, the dataset was split chronologically into training and validation sets in a 6:4 ratio, ensuring that the validation data contained only unseen future cycles relative to the training set.

Each cell was charged at 0.5 C constant current to 4.2 V, followed by constant-voltage charging at 4.2 V until the current dropped to 340 mA, and then rested for 10 min. The cells were subsequently discharged at 1 C constant current to 2.7 V until the protection circuit was triggered, followed by another 10 min rest, before entering the next cycle. In total, 171 valid aging capacity datasets were obtained. The degradation results of both the NASA dataset and the laboratory measurements are presented in Figure 3.

The $\mathrm{P}\mathrm{V}$ is defined as the duration from the start of discharge to the point when the voltage reaches 2.7 V, 2.5 V, 2.2 V, and 2.7 V, respectively, in the NASA dataset and the laboratory aging data. The $\mathrm{P}\mathrm{I}$ is obtained as the input charge recorded prior to discharge. For the $\mathrm{P}\mathrm{M}\mathrm{A}$, a window size of five is applied to smooth the capacity sequence. Pearson correlation analysis was conducted between these three parameters and the battery SOH. As shown in

Table 1. PCCs of Input Features for B0005, B0006, B0007, and Laboratory Data.

Input Features	PCC of PV	PCC of PI	PCC of PMA
B0005	0.99773	0.99827	0.99665
B0006	0.99554	0.99662	0.99346
B0007	0.99713	0.99829	0.99640
Laboratory-measured dataset	0.94682	0.97975	0.92384
Average	0.98431	0.99323	0.97759

, the Pearson correlation coefficients (PCCs) for all four datasets are greater than 0.97 on average, indicating strong correlations with SOH, thereby confirming their suitability as input features for SOH prediction.

To further validate the rationality of the selected input features, a correlation analysis was performed between each feature and the corresponding battery SOH across all datasets. As presented in Table 1, the Pearson correlation coefficients (PCCs) for the end-of-discharge time, charging capacity, and moving average of historical discharge capacity are consistently greater than 0.97, with an overall average exceeding 0.98. This indicates that these features exhibit strong linear relationships with SOH and can effectively represent the underlying degradation patterns of lithium-ion batteries.

Specifically, the end-of-discharge time reflects the dynamic change in discharge duration during cycling, which is directly influenced by internal resistance growth and capacity attenuation. The charging capacity captures the recoverable energy during charge cycles, serving as a sensitive indicator of capacity degradation. Meanwhile, the moving average of historical discharge capacity smooths transient fluctuations and emphasizes the long-term trend of aging evolution. The high correlation among these features and SOH confirms their physical interpretability and statistical validity, justifying their use as model inputs for the ICEEMDAN+FC-BiLSTM framework.

3. Deep Learning Model for SOH Prediction Based on ICEEMDAN+FC-BiLSTM

3.1. Analysis of the Principles of ICEEMDAN

ICEEMDAN is an enhanced version of Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) for adaptive time–frequency analysis of signals. It effectively addresses the issues of mode mixing, reconstruction error, and residual noise commonly encountered in Empirical Mode Decomposition (EMD) and Ensemble Empirical Mode Decomposition (EEMD). ICEEMDAN performs particularly well in processing nonstationary and nonlinear signals. When applied to battery input features, it can decompose the signals into intrinsic mode functions (IMFs) of different frequency components, smooth the main signal, and extract nonstationary characteristics. This process significantly improves the accuracy and robustness of the subsequent prediction model.

ICEEMDAN is developed on the basis of EMD, in which adaptive noise and ensemble averaging are introduced to eliminate mode mixing. During each iteration, an intrinsic mode function (IMF) is extracted by computing the local mean using EMD, thereby ensuring the completeness of the decomposition. Each IMF is obtained by averaging across an ensemble of noise-assisted signals, which avoids the reconstruction errors present in conventional CEEMDAN. The calculation process is expressed in Equation (2).

$$c_k\left(t\right)={\displaystyle \frac{1}{N}}\sum _{i=1}^N{\mathrm{E}\mathrm{M}\mathrm{D}}_1\left[r_{k-1}\left(t\right)+ϵE_k\left[w_i\left(t\right)\right]\right]$$

(2)

where $c_k\left(t\right)$ denotes the k IMF, $w_i\left(t\right)$ represents the i realization of independent white noise with an amplitude ratio of ϵ, and $r_{k-1}\left(t\right)$ is the k − 1 residual. ${\mathrm{E}\mathrm{M}\mathrm{D}}_1\left[x\right]$ denotes a single execution of EMD, while $E_k\left[x\right]$ represents the local mean operator of EMD.

3.2. Analysis of the Principles of FC-BiLSTM

After the input features are processed by ICEEMDAN, the feature dimensionality increases. To address this, a fully connected (FC) layer is employed for feature mapping. Unlike locally connected layers or sequence-based models, the FC layer treats the input as a whole and performs linear transformations followed by nonlinear activations to generate higher-level abstract representations. Acting as a “front-end feature extractor,” the FC layer maps the original multidimensional time-series features into a feature space that is more suitable for BiLSTM processing. The computational process is expressed in Equation (3).

$$\mathrm{y}=\sigma \left(\mathrm{W}\mathrm{x}+\mathrm{b}\right)$$

(3)

where $\mathrm{y}$ is the output vector, $\mathrm{x}$ is the input vector, $\mathrm{W}$ denotes the weight matrix, $\mathrm{b}$ is the bias vector, and $\sigma \left(x\right)$ represents the activation function, which typically includes ReLU, Sigmoid, and others.

BiLSTM is an improved recurrent neural network (RNN) architecture that combines the capability of LSTM to capture long-term dependencies with a bidirectional structure, thereby leveraging both past and future contextual information. It has been widely applied in time-series prediction tasks. The final hidden state of BiLSTM, as expressed in Equation (4), incorporates contextual features from both forward and backward directions at each time step. The gating mechanism of LSTM is formulated in Equation (5).

$$h_t=\left[h_t^{\to };h_t^{\leftarrow }\right]$$

(4)

where $h_t^{\to }$ denotes the forward sequence and $h_t^{\leftarrow }$ denotes the backward sequence.

$$\left\{\begin{array}{l}{i}_t=\sigma (W_i{x}_t+U_i{h}_{t-1}+b_i)\\ f_t=\sigma (W_f{x}_t+U_f{h}_{t-1}+b_f)\\ o_t=\sigma (W_o{x}_t+U_o{h}_{t-1}+b_o)\\ {\overline{c}}_t=tanh(W_c{x}_t+U_c{h}_{t-1}+b_c)\\ c_t=f_t\odot c_{t-1}+i_t\odot {\tilde{c}}_t\\ h_t=o_t\odot tanh\left(c_t\right)\end{array}\right.$$

(5)

where $i_t$ denotes the input gate, $f_t$ the forget gate, $o_t$ the output gate, ${\overline{c}}_t$ the candidate cell state, $c_t$ the updated cell state, and $h_t$ the updated hidden state. Here, $\sigma \left(x\right)$ represents the activation function, and $\odot$ denotes the element-wise multiplication.

4. Experimental and Results

4.1. Design of Prediction Model Parameters

In the ICEEMDAN decomposition, the noise standard deviation Nstd was set to 0.2 to balance decomposition accuracy, noise resistance, and computational efficiency, ensuring effective mode separation while avoiding excessive noise residues. The ensemble size was chosen as NR = 100, which provides stable decomposition results while significantly reducing computational cost, making it suitable for large-scale battery cycling data. The maximum number of iterations was set to MaxIter = 5000 to guarantee full convergence of IMFs in complex nonstationary signals. In addition, an improved noise-increment strategy was enabled with SNRFlag = 1, which helps further enhance IMF purity and reduce reconstruction errors. The decomposition results of the three input features across the four datasets are shown in Figure 4, Figure 5, Figure 6 and Figure 7.

The ICEEMDAN parameters were selected through empirical tuning and references to previous studies to balance decomposition accuracy and computational efficiency [21,22]. The noise standard deviation (Nstd = 0.2) was chosen as a compromise between reducing mode mixing and avoiding excessive artificial noise, consistent with commonly adopted settings in ICEEMDAN-based signal analysis. The ensemble size (NR = 100) provided stable decomposition performance while maintaining acceptable computational cost; tests with NR values ranging from 50 to 200 showed less than 1% variation in IMF stability, indicating low sensitivity to this parameter. The maximum iteration number (MaxIter = 5000) ensured full convergence for complex, nonstationary inputs, and the noise-increment strategy (SNRFlag = 1) further improved IMF purity. Overall, these settings were validated through sensitivity analysis and cross-dataset testing, confirming their robustness and reproducibility.

ICEEMDAN effectively decomposes the input signals into intrinsic mode functions (IMFs) with clear frequency distinctions. The high-frequency IMFs capture random fluctuations and measurement noise, while the low-frequency IMFs reflect long-term capacity degradation trends. Compared with CEEMDAN and EEMD, ICEEMDAN produces smoother IMFs, reduces mode mixing, and improves signal interpretability. Across all datasets, the initial IMFs show rapidly decaying oscillations, indicating strong noise suppression, whereas the mid-level IMFs represent intermediate degradation behaviors caused by electrochemical and thermal effects. The residual component follows the overall SOH decline, confirming that ICEEMDAN enhances noise robustness while preserving essential multi-scale degradation information, thus providing clean and informative inputs for the subsequent FC-BiLSTM prediction model.

The proposed deep learning model adopts a sequence-to-one regression architecture consisting of three stacked BiLSTM layers. The network first receives time-step data containing five key features through a sequence input layer. The core comprises three BiLSTM layers with a pyramid-like structure of hidden units (128–64–32), designed to progressively extract and refine higher-level temporal representations. To effectively aggregate sequential information, only the last BiLSTM layer is configured in the ‘last’ output mode. In addition, dropout regularization is applied after each BiLSTM layer to mitigate overfitting. Finally, a fully connected layer followed by a regression output layer maps the extracted deep temporal features to a single battery capacity prediction value.

The training strategy was designed to balance convergence efficiency and generalization performance. The Adam optimizer was employed with a stepwise learning rate schedule (initial_lr = 0.001, drop_factor = 0.3, drop_period = 60), ensuring fine-tuned adjustments in the later training stages. To effectively prevent overfitting, L2 regularization and early stopping based on validation performance were incorporated. Importantly, to preserve the intrinsic temporal dependencies in the data, sample shuffling was explicitly disabled (Shuffle = ‘never’). All hyperparameters, including the maximum number of epochs (MaxEpochs = 300) and mini-batch size (MiniBatchSize = 16), were carefully configured to achieve optimal model performance.

The hyperparameters of the FC-BiLSTM model were optimized through a systematic tuning process combining grid search and cross-validation on the training set. The number of BiLSTM layers (two to four), hidden units per layer (32–256), dropout rate (0.1–0.5), and learning rate (1 × 10⁻⁴–1 × 10⁻²) were iteratively adjusted to minimize the validation root mean square error (RMSE). The hidden unit configuration of 128–64–32 in the BiLSTM layers was determined through empirical analysis to achieve a balance between model complexity and generalization. A larger number of units improved short-term accuracy but led to overfitting and higher computational cost, whereas a smaller network degraded temporal feature extraction. The pyramid-like structure (128–64–32) provided progressive dimensional compression, enabling efficient representation learning while maintaining stable convergence.

All model training and testing were conducted using MATLAB 2023b on a workstation equipped with an 11th Gen Intel(R) Core(TM) i5-11500 CPU @ 2.70 GHz and 16 GB RAM. Each training session required approximately 10–13 min to reach convergence. The loss function steadily decreased during training and plateaued after about 200 epochs, indicating stable model convergence. The average validation RMSE variation between runs was below 2%, confirming the reliability and reproducibility of the training process.

The network employs FC layers as a front-end feature extractor, where the input is globally linearly combined through weight matrices and transformed via ReLU nonlinear activation. This facilitates the mapping of raw multidimensional battery features into a more discriminative high-dimensional space. The first layer with 128 units effectively captures complex feature relationships, while the second layer with 64 units compresses the features to support subsequent temporal modeling. Two ReLU activations ensure sufficient nonlinear representation, and a dropout rate of 0.3 is applied to prevent overfitting and enhance generalization. Overall, the feature extractor balances abstraction capability and training stability, providing denoised and fused multi-scale inputs for the BiLSTM back-end.

To ensure reproducibility, all experiments were repeated five times with different random seeds, and the average results are reported. The dataset was divided chronologically in a 6:4 ratio without overlapping time sequences to avoid data leakage between training and validation sets. This rigorous tuning and evaluation process guarantees that the proposed ICEEMDAN+FC-BiLSTM framework is both robust and reproducible across datasets.

4.2. SOH Prediction Results Analysis

The proposed prediction model is compared with BiLSTM and ICEEMDAN+BILSTM, and the results are shown in Figure 8. The root mean square error (RMSE) and mean absolute error (MAE) of SOH prediction across four datasets are calculated using Equations (6) and (7), with the results summarized in

Table 2. SOH Prediction Results of B0005, B0006, B0007, and laboratory-measured dataset: RMSE and MAE under Different Methods.

Dataset		RMSE	MAE	RMSE (Mean ± SD)
B0005	BiLSTM	0.013770	0.011186	0.01377 ± 0.00061
	ICEEMDAN+BILSTM	0.008217	0.006853	0.00822 ± 0.00042
	ICEEMDAN+FC-BILSTM	0.007427	0.006283	0.00743 ± 0.00038
B0006	BiLSTM	0.018124	0.013426	0.01812 ± 0.00073
	ICEEMDAN+BILSTM	0.013874	0.010569	0.01387 ± 0.00049
	ICEEMDAN+FC-BILSTM	0.012493	0.009055	0.01249 ± 0.00046
B0007	BiLSTM	0.008938	0.007398	0.00894 ± 0.00040
	ICEEMDAN+BILSTM	0.007479	0.006200	0.00748 ± 0.00033
	ICEEMDAN+FC-BILSTM	0.007365	0.005868	0.00737 ± 0.00031
laboratory-measured dataset	BiLSTM	0.002729	0.001818	0.00273 ± 0.00011
	ICEEMDAN+BILSTM	0.002556	0.001682	0.00256 ± 0.00010
	ICEEMDAN+FC-BILSTM	0.002353	0.001573	0.00235 ± 0.00009

. As indicated by the RMSE and MAE values, the ICEEMDAN+FC-BiLSTM exhibits slightly higher prediction errors on the NASA datasets, since their test sets are closer to end-of-life conditions. Nevertheless, the RMSE remains below 0.01, representing an average improvement of 33% over BiLSTM. The calculation method is formulated as shown in Equation (8). On the laboratory datasets, the ICEEMDAN+FC-BiLSTM achieves the lowest RMSE of 0.002353, corresponding to approximately a 14% improvement compared with BiLSTM, thereby demonstrating its superior prediction performance.

$$E_{\mathrm{r}\mathrm{m}\mathrm{s}\mathrm{e}}=\sqrt{{\displaystyle \frac{1}{n}}\sum _{i=1}^n{\left({\displaystyle \frac{C_{\mathrm{P}i}-C_{\mathrm{M}i}}{C_i}}\right)}^2}$$

(6)

$$E_{\mathrm{m}\mathrm{a}\mathrm{e}}={\displaystyle \frac{1}{n}}\sum _{i=1}^n\left|{\displaystyle \frac{C_{\mathrm{P}i}-C_{\mathrm{M}i}}{C_i}}\right|$$

(7)

$${\eta }_{\mathrm{i}\mathrm{m}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{v}\mathrm{e}}={\displaystyle \frac{{\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}}_{\mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}-{\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}}_{\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{p}\mathrm{o}\mathrm{s}\mathrm{e}\mathrm{d}}}{{\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}}_{\mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}}}\times 100\%$$

(8)

where $n$ denotes the number of samples, $C_{\mathrm{P}i}$ is the actual capacity of the battery at the i cycle, $C_{\mathrm{M}i}$ is the predicted capacity at the i cycle, and $C_i$ represents the rated nominal capacity of the battery.${\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}}_{\mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ and ${\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}}_{\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{p}\mathrm{o}\mathrm{s}\mathrm{e}\mathrm{d}}$ denote the root mean square errors of the BiLSTM and ICEEMDAN+FC-BiLSTM models, respectively.

To further evaluate the reliability of the performance improvement, statistical significance analysis was conducted based on five repeated training and testing runs using different random seeds. For each dataset and model, the mean and standard deviation of RMSE values were calculated. The proposed ICEEMDAN+FC-BiLSTM achieved an average RMSE reduction of approximately 12–15% compared with ICEEMDAN-BiLSTM, with standard deviations below 0.0005 across all datasets, indicating stable convergence. A paired t-test confirmed that the performance differences were statistically significant at the 95% confidence level (p < 0.05). These results demonstrate that the observed improvements are not due to random fluctuations but reflect the model’s consistently better generalization and prediction accuracy.

5. Conclusions

This paper proposes a lithium-ion battery SOH prediction method that integrates ICEEMDAN with an FC-BiLSTM framework, and its effectiveness is validated using both NASA battery datasets and laboratory measurements. The results demonstrate that ICEEMDAN effectively decomposes input features, mitigating mode mixing and residual noise while extracting more representative degradation characteristics. Meanwhile, the incorporation of fully connected layers into the BiLSTM architecture enhances feature mapping and temporal modeling, leading to significant improvements in prediction accuracy and stability compared with conventional methods. Experimental evaluations across multiple datasets show that the proposed method consistently outperforms benchmark models in terms of RMSE and MAE, highlighting its robustness and generalization capability. Overall, the method exhibits high accuracy and reliability in SOH prediction, providing valuable insights for battery health management and lifetime prediction. Nevertheless, the proposed method has certain limitations. The ICEEMDAN algorithm is computationally demanding, and the BiLSTM model requires sufficient data for stable learning, which may restrict its real-time application in EV battery management systems. Moreover, the model’s interpretability remains limited, as it does not explicitly reveal the underlying electrochemical mechanisms. Future work will focus on simplifying the decomposition process, improving model explainability, and evaluating the framework under real driving and temperature-varying conditions for practical BMS deployment.