State estimation of lithium-ion batteries via electrochemical features and self-attention networks

1 Introduction

The rapid electrification of the automotive industry and the growing demand for stationary energy storage systems have positioned Lithium-ion batteries (LIBs) as a cornerstone technology for modern society (Wang Z. et al., 2025). However, the performance of LIBs inevitably degrades over time due to complex internal electrochemical side reactions, such as the growth of the solid electrolyte interphase (SEI) and active material loss (Zhang et al., 2023). Consequently, the accurate estimation of the State of Health (SOH) is not merely a metric of performance but a critical requirement for safety and reliability. Precise SOH estimation is paramount for the Battery Management System (BMS) to execute fault early warning, optimize charging protocols, mitigate thermal runaway risks, and determine the optimal point for battery retirement or secondary utilization (Lin et al., 2025).

Historically, SOH estimation methods have been categorized into two primary streams: model-based approaches and data-driven approaches (Stetson et al., 2021). Model-based methods, such as Equivalent Circuit Models (ECM) and Electrochemical Models (EM), rely on mathematical equations to describe the internal physical and chemical behaviors of the battery (Hmidi et al., 2026). While these methods offer high interpretability, they face significant challenges in parameter identification and adaptability (Hossain et al., 2022). They often struggle to generalize across different operating conditions and battery chemistries without extensive recalibration (Wang et al., 2021; Madani et al., 2025).

Conversely, data-driven approaches, particularly Machine Learning (ML), have gained prominence due to their ability to map non-linear relationships between accessible battery features (voltage, current, temperature) and SOH without requiring deep knowledge of internal electrochemical mechanisms (Anuj et al., 2026; Terala et al., 2022). Early implementations utilized Support Vector Machines (SVM) and Gaussian Process Regression (GPR). However, the advent of Deep Learning has shifted the research focus toward neural networks capable of handling high-dimensional time-series data (Sadabadi et al., 2021).

Recurrent Neural Networks (RNNs) and their variants, such as Long Short-Term Memory (LSTM) and Gated Recurrent Units (GRU), are considered the state-of-the-art (SOTA) in many battery prognostics studies (Tang et al., 2025; Madani et al., 2026). These architectures are explicitly designed to process sequential data, making them intuitively suitable for battery aging time series (Zhang et al., 2024).

However, a diverging hypothesis has emerged regarding the efficacy of RNNs for long-term degradation prediction (Severson et al., 2019). While LSTMs effectively mitigate the gradient vanishing problem found in standard RNNs, they still process data sequentially. Critics argue that for long-cycle battery data (often spanning thousands of cycles), LSTMs suffer from “information dilution” or “catastrophic forgetting,” where the influence of early-stage aging features diminishes as the sequence length increases (Wang et al., 2023; Meng et al., 2023). Furthermore, the sequential nature of RNNs limits parallel computation capabilities, increasing training time for large datasets.

To address the limitations of sequential processing, the academic community is increasingly looking toward the Transformer architecture and Self-Attention mechanisms, originally revolutionized in Natural Language Processing (NLP) (Sun et al., 2022). Unlike LSTMs, Self-Attention networks calculate the correlation between every time step in a sequence simultaneously, allowing the model to capture global dependencies regardless of the distance between time steps (Yang, 2021).

Despite their potential, applying pure self-attention mechanisms to battery SOH estimation is not trivial. Standard attention mechanisms may overlook local feature extraction (e.g., subtle voltage fluctuations within a specific charge curve) which are effectively captured by Convolutional Neural Networks (CNNs) (Wei et al., 2024; Wang S. et al., 2025). Therefore, a hybrid hypothesis suggests that combining the local feature extraction of CNNs with the global context awareness of Attention networks yields superior performance (Gong et al., 2022).

Building upon this context, this paper identifies a gap in current attention-based SOH estimation: the need to explicitly weight the contribution of different aging stages across cycles. While global attention captures long-term dependencies, it does not necessarily prioritize the specific “critical segments” of voltage or current curves that are most indicative of degradation.

To address this, we propose a novel Self-Attention Network based approach for LIB SOH estimation. The contributions of this study are as follows:

• Hybrid Architecture: We integrate a Convolutional module for local feature extraction with a Self-Attention mechanism to capture long-range temporal dependencies, effectively solving the information dilution problem inherent in LSTM-based methods.
• Cross-Cycle Attention Submodule: We introduce a specialized attention mechanism designed to identify and highlight data segments across different cycles that contribute most significantly to the degradation state.
• Robust Validation: Utilizing a laboratory-measured dataset of 8 batteries under varying aging protocols, we demonstrate that the proposed method achieves an RMSE of less than 0.0033, significantly outperforming traditional LSTM baselines and enhancing the representation capability of multi-stage aging behaviors.

2 Methods and experiments

2.1 Experimental setup and data acquisition

All aging experiments were conducted on Delip 18,650 lithium-ion batteries (Rated Capacity: 1,500 mAh; Nominal Voltage: 3.7 V; Cathode: Li(NiCoMn)O₂; Anode: graphite). To systematically investigate battery aging mechanisms and validate the proposed estimation method, a comprehensive experimental platform was established. The core testing apparatus consisted of a battery testing system controlled via a dedicated intermediate machine for high-frequency data acquisition f. Electrochemical analysis was conducted using an electrochemical workstation.

The test subjects were commercial lithium-ion batteries. Each cell had a nominal voltage of 3.7 V and a rated capacity of 1,500 mAh. These batteries were selected to represent typical consumer-grade energy storage units, with an expected cycle life of approximately 1,000 cycles.

2.2 Accelerated aging protocols

Aging experiments were designed to simulate complex, real-world operating environments rather than relying solely on ideal laboratory conditions (Tian et al., 2023). The baseline aging cycle followed a standard Constant Current-Constant Voltage (CC-CV) protocol (Panchal et al., 2025):

Charging: Constant current (CC) charging at 1C (it represents the charge/discharge current relative to the battery’s nominal capacity (1.5 Ah), 1C = 1.5 A) until the voltage reached 4.2 V, followed by constant voltage (CV) charging until the current dropped below 0.1 A.

• Rest: A 5-min rest period to allow for thermodynamic equilibrium and cooling.
• Discharging: Constant current (CC) discharging at 1C until the cutoff voltage of 2.7 V was reached.
• Rest: A final 5-min rest period before the next cycle.

To introduce variability and capture non-linear aging behaviors, Table 1 shows eight specific cells were subjected to different stress conditions.

TABLE 1. Experimental setup.

Pulse Conditions (C07–C09): Included pulse charging (C07), combined pulse charge/discharge (C08), and random pulse discharging (C09) to mimic dynamic load fluctuations typical of electric vehicles.

In the 8-cell battery aging test conducted for this experiment, three cells—C02, C04, and C07—failed. Data from five cells remained relatively complete. This experiment will use the data from these five cells, along with partial data from the remaining three cells, as the test dataset. Figure 1 shows these five cells aging process. It is evident that under high-rate charging/discharging and pulsed operating conditions, battery capacity degrades more rapidly and becomes unstable.

2.3 Electrochemical modeling and feature extraction

To probe the internal electrochemical evolution of the batteries, EIS measurements were performed every 50 aging cycles. The Ivium workstation applied a small-amplitude sinusoidal voltage perturbation across a frequency sweep, generating a current response that characterized the system’s impedance (Kasper et al., 2022). Figure 2 shows the EIS results of C03.

The resulting Nyquist plots exhibited two distinct regions: a high-frequency semi-circle representing ohmic and polarization resistance, and a low-frequency linear tail representing diffusion (Lai et al., 2022). To quantify these physical phenomena, an Equivalent Circuit Model (ECM) in Figure 3.

The calculation methods and meanings of relevant parameters are as follows (Mattia et al., 2024). Equations 1–3 shows the Model Parameter Calculation Formula.

1 Z = 1 Z R c t + 1 Z C = 1 R + j ω C (1)

Z ω = R 1 + ω R C 2 − j ω R 2 C 1 + ω R C 2 (2)

Z = R Ω + 1 j ω C d + 1 R C T + σ ω − 1 / 2 1 − j (3)

Ohmic Resistance (R_Ω): representing electrolyte and contact resistance. Electrochemical Polarization: modeled by a charge transfer resistance (R_CT) in parallel with a constant phase element (C_d). The CPE was utilized instead of an ideal capacitor to account for the non-ideal porous electrode surfaces. Warburg Impedance (Z_W): a frequency-dependent component representing lithium-ion diffusion (concentration polarization) in the low-frequency region.

Figure 4 shows the correlation analysis using Pearson correlation coefficients between the extracted circuit parameters and the cycle number revealed that the R_Ω and Warburg impedance coefficients W_b-T and W_b-T (which are two part of Z_W) had the strongest correlation with battery aging. Consequently, these three parameters were selected as physics-based inputs for the machine learning model.

2.4 Self-attention LSTM framework

A hybrid deep learning architecture was developed for State of Health (SOH) estimation, combining Long Short-Term Memory (LSTM) networks with a self-attention mechanism (Teki et al., 2024).

2.4.1 LSTM network

LSTM is utilized to capture macroscopic, long-term temporal dependencies and degradation trends from the battery’s historical cycling data. Model sequences while avoiding vanishing gradients by using a gated memory cell (Jafari et al., 2022). Equations 4–9 demonstrates the state update calculation methods for each component of the LSTM. where, t is time step index; x _*t* refers to input vector at time t; h _*t-1* and h _*t* are previous and current hidden state; c _*t-1* and c _*t* are previous and current cell (memory) state; f _*t* is forget gate: how much old memory to keep; i _*t* is input gate: how much new information to write; c ∼ t is candidate memory content; o _*t* is output gate: how much memory to expose; W*, U* are learnable weight matrices; b* is bias vectors.

f t = σ W f x t + U f h t − 1 + b f (4)

i t = σ W i x t + U i h t − 1 + b i (5)

c ∼ t = tanh W c x t + U c h t − 1 + b c (6)

c t = f t ⊙ c t − 1 + i t ⊙ c ∼ t (7)

o t = σ W o x t + U o h t − 1 + b o (8)

h t = o t ⊙ tanh c t (9)

2.4.2 Self-attention mechanism

Self-Attention mechanism is integrated to address the limitation of traditional RNNs in distinguishing critical information from redundancy (Huang et al., 2018). This mechanism dynamically assigns weights to input sequences, allowing the model to focus on micro-scale features within cycles (e.g., instantaneous voltage drops or capacity fluctuations) that are most indicative of aging anomalies (Dey and Salem, 2017). Equations 10–11 demonstrates the calculation method for self-attention weights. where, A is attention weight matrix; Q, K, V are query, key, and value matrices; W* is learnable projection matrices; QK ^*T* is pairwise similar between tokens; d _*k* is key (and query) dimension which is used for scaling to stabilize gradients; X is input sequence.

A Q , K , V = s o f t m a x Q K T d k V (10)

Q = X W Q , K = X W K , V = X W V (11)

While pure Transformer architectures are powerful, they are highly parameter-heavy and typically require massive datasets to prevent overfitting. Furthermore, standard Transformers scale quadratically with sequence length, making them computationally expensive for real-time BMS embedded systems. Our proposed hybrid approach leverages the LSTM for efficient sequential memory and the Self-Attention mechanism for targeted feature weighting, achieving a practical balance between high precision and lower computational overhead.

2.5 Model training

In addition to the time-series data that changes with cycles during lithium-ion battery aging, the equivalent circuit parameters of the battery—namely R_Ω, W_b-T, and W_b-P—can also be used for training features. For the time-series data, this project defines aging data as a vector of length 10, meaning a 10-cycle aging sequence is selected as part of the label. Combining the aging sequence with battery parameters yields a feature dimension of 13 for the lithium-ion battery input sequence. This includes one set of aging sequences of length 10 and battery parameters of length 3. The data label represents the discharge capacity of the lithium-ion battery during the current cycle, with a dimension of 1. This project selected batteries C02, C06, and C09 as the test set. Among these, C02, being a faulty battery, possesses relatively sufficient data. C06 and C09, exhibiting similar operating conditions to other batteries, were used for testing. Figure 5 shows the structure of the network.

The network was trained using the Adam optimizer with Mean Squared Error (MSE) as the loss function. The calculation method of MSE is shown in Equation 12.where, y _*i* is the real value; y ^ i is the predicted value.

M S E = 1 n ∑ i = 1 n y i − y ^ i 2 (12)

3 Results and discussion

3.1 Comparative performance analysis

The predictive performance of the proposed Self-Attention LSTM model was evaluated against three baseline methods: a standard Recurrent Neural Network (RNN), a standalone Long Short-Term Memory (LSTM) network, and an Extended Kalman Filter (EKF) based approach. The models were tested on batteries C02, C06, and C09, which correspond to standard cycling, fast discharging, and random pulse discharging conditions, respectively.

Figures 6–8 show the training loss and SOH estimation results for C02 batteries under the aforementioned four operating conditions and errors of different cells.

To quantify the estimation accuracy, the Root Mean Square Error (RMSE) was calculated for the State of Health (SOH) predictions. The calculation method of RMSEis shown in Equation 13.

R M S E = M S E (13)

The experimental results demonstrated a clear hierarchy in performance, with the proposed method achieving the lowest error rates across all test cases, following the trend: Self-Attention + LSTM > LSTM > RNN > EKF.

The specific RMSE values indicated a significant improvement in precision for the proposed hybrid model. Table 2 shows the RMSE of different methods.

TABLE 2. RMSE of different batteries SOH prediction using different methods.

These results confirm that while the standard LSTM improves upon the basic RNN by managing long-term dependencies, the integration of the self-attention mechanism further reduces the estimation error by approximately 30%–40% compared to the standalone LSTM. The proposed model achieves an R² > 0.97 across all tested conditions, indicating a high degree of fit.

3.2 Capturing non-linear aging and capacity dives

A critical challenge in battery SOH estimation is accurately tracking the non-linear degradation trajectory, particularly the “capacity diving” phenomenon where performance drops precipitously after a certain inflection point.

Qualitative analysis of the prediction curves reveals that the proposed model exhibits superior sensitivity to these critical aging phases. While the EKF and standard RNN models tended to smooth out sudden changes or lag behind the actual degradation curve, the Self-Attention LSTM model closely tracked the ground truth data. The self-attention mechanism successfully identified and weighted the micro-features within the voltage and current sequences that precede these capacity drops, allowing the model to respond almost instantaneously to the acceleration in aging. This capability is vital for providing timely failure warnings in practical Battery Management Systems (BMS).

3.3 Generalization across complex operating conditions

The robustness of the proposed framework was validated by its consistent performance across the diverse datasets constructed for this study. The low error rates observed for C06 (Fast Discharge) and C09 (Random Pulse) confirm that the model effectively generalizes beyond standard laboratory conditions. By fusing the physics-based information from the EIS parameters (Ohmic resistance and Warburg impedance) with the data-driven time-series inputs, the model successfully decoupled the impact of varying load profiles from the underlying material degradation.

4 Conclusion

This study successfully developed a hybrid State of Health estimation method that integrates electrochemical principles with deep learning. The results validate that the fusion of Self-Attention mechanisms with LSTM networks significantly enhances estimation accuracy and stability compared to traditional methods. The core innovations of this work are threefold:

• Data-Driven Robustness: The construction of a multi-condition dataset (encompassing fast charging/discharging and random pulses) proved that the model can generalize to realistic, complex scenarios.
• Physics-Informed Inputs: The integration of EIS-derived parameters (R_Ω, Z_W) provided the neural network with interpretable physical constraints, improving reliability.
• Macro-Micro Synergies: The architecture successfully combined LSTM’s ability to model macroscopic long-term decay trends with the self-attention mechanism’s ability to focus on microscopic, high-impact data segments within individual cycles.

Future work will focus on compressing the model for deployment on resource-constrained embedded systems and exploring explainable AI techniques to further visualize the specific features driving the attention weights.

The proposed Self-Attention LSTM model demonstrates high accuracy for the tested 18,650 Li-ion cells, the relatively small sample size necessitates further validation. We have outlined our future research plan to evaluate the framework’s generalization capabilities across different cell chemistries and formats using larger, public datasets to ensure broad applicability.

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Footnotes

Edited by: Mohammad Waseem, Jamia Millia Islamia, India

Reviewed by: Satyam Panchal, University of Waterloo, Canada

Walid Mchara, Higher National Engineering School of Tunis, Tunisia