# State-of-Health (SOH) and State-of-Charge (SOC) Estimation for Lithium-ion Battery under Fast-Charging Conditions

Xuelu Wang, Toufik Azib, Jianwen Meng, Khelil Sidi-Brahim

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Xuelu Wang, Toufik Azib, Jianwen Meng, Khelil Sidi-Brahim. State-of-Health (SOH) and State-of-Charge (SOC) Estimation for Lithium-ion Battery under Fast-Charging Conditions. The 26th European Conference on Power Electronics and Applications, GDR SEEDS France & EPE Association, Mar 2025, Paris, France. 10.34746/epe2025-0177. hal-05107522

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# State-of-Health (SOH) and State-of-Charge (SOC) Estimation for Lithium-ion Battery under Fast-Charging Conditions

Xuelu WANG, Toufik AZIB, Jianwen MENG, Khelil SIDI-BRAHIM

École supérieure des techniques aéronautiques et de construction automobile (ESTACA)

ESTACA'Lab S2ET

12 Avenue Paul Delouvrier

Montigny-le-Bretonneux, France

Tel.: +33 (0)1.75.64.50.41

E-Mail: {xuelu.wang, toufik.azib, khelil.sidi-brahim}@estaca.fr

URL: https://www.estaca.fr/

***Index Terms***—Lithium-ion battery, Deep learning, Degradation, Diagnostics.

***Abstract***—This paper presents two models for lithium-ion battery SOC and SOH estimation using a Toyota Research Institute dataset. A Random Forest Regressor predicts SOH after 10 cycles, while an LSTM neural network estimates real-time SOC. Both models show high accuracy, contributing to advanced health-aware energy management in electric vehicles.

## I. INTRODUCTION

Nowadays, the biggest challenge for the automobile industry is the energy crisis and environmental problems. In this context, electric vehicles (EVs), including battery-powered EVs (BEVs), hybrid electric vehicles (HEVs) and plug-in hybrid electric vehicles (PHEVs), are experiencing ever-increasing development in recent years [1] [2]. The increasing reliance on lithium-ion batteries in these electric vehicles needs advanced techniques for monitoring and managing battery health to ensure safety, efficiency, and longevity [3] [4] [5]. The effective management of these batteries is critical for both operational reliability of electric vehicles and battery life and performance optimization [6] [7]. As a result, immediate and actionable insights for Battery Management Systems (BMS), which address the dynamic and varied demands placed on batteries during vehicle operation, are crucial [8] [9].

This paper details the development and validation of two advanced estimation models designed to enhance the functionality of BMS through precise SOH and SOC estimations. Utilizing a rich dataset provided by the

Toyota Research Institute (TRI), which includes online measurable parameters such as voltage, temperature, and current measurements from various battery cycles, has enabled a comprehensive analysis and robust model training [10]. The Long Short-Term Memory (LSTM) neural network was chosen for SOC estimation due to its ability to capture temporal dependencies and nonlinear relationships in sequential data, which makes it well suited for dynamic SOC prediction [11] [12] [13]. Similarly, Random Forest Regressor (RFR) was selected for SOH estimation due to its robustness, low computational cost, and capability to handle high-dimensional data while avoiding overfitting [8] [14] [15].

The primary objective is to develop and refine models for reliable real-time estimation of SOH and SOC in lithium-ion batteries. These estimation modules are critical for effective BMS in EVs. Fig. 1 illustrates the methodology employed for SOH estimation, while Fig. 2 demonstrates the LSTM-based architecture used for SOC estimation. These figures are referenced at relevant points in the text for better alignment with the described methods. The SOH estimation model uses a RFR to estimate battery health using an iterative time series estimation strategy, with a fixed sliding time window. In Fig. 1, a sliding time window with a fixed value is utilized to iterate in cycles, providing clear insight into the process. This approach helps in early detection of potential premature battery aging process and assists in planning maintenance schedules. The selected dataset was first cleaned, normalized, and key features were extracted. Then the RFR model was trained and optimized. In the end, the model's accuracy was validated using cross-validation and tested on a separate dataset, with
different performance metrics.

The SOC model employs a neural network to provide real-time SOC estimations during battery charge and discharge cycles, crucial for real-time decision-making in BMS [7] [16] [17]. Same as SOH estimation, the TRI dataset was used, focusing on instantaneous voltage, temperature, and current measurements. Then, a LSTM neural network was trained and optimized for capturing the nonlinear relationships between inputs and SOC as is shown in Fig. 2. The evaluation process employed metrics such as relative error (RE) for RFR and root mean square error (RMSE) for LSTM to validate the models' performances.

<figure><img src="image_2.png" /><figcaption>Fig. 1. Iterative SOH estimation process.</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Fig. 2. SOC estimation input and output structure.</figcaption></figure>

## II. DATASET ANALYSIS, METHODOLOGY AND FEATURE ENGINEERING

### A. *Toyota Research Institute-MIT Battery Aging Dataset* under fast charging conditions

The used database is provided by Severson, et al, which contains the degradation variation data of 124 commercial lithium iron phosphate/graphite cells (A123 Systems, model APR18650M1A, 1.1Ah nominal capacity) [10]. The charging rate vary from 3.6C constant current-constant voltage (CC-CV), the manufacturer's

recommended fast-charging rate, to 6C, probing the performance of current-generation power cells under extreme fast-charging conditions (about 10 minutes charging). By varying the charging conditions, a dataset that captures a wide range of cycle lives, from approximately 150 to 2,300 cycles (average cycle life of 806 with a standard deviation of 377) is generated.

<table><caption>TABLE I
BATTERY SPECIFICATIONS USED IN THE SELECTED DATASET.</caption><thead><tr><td>Parameter</td><td>Specification</td></tr></thead><tbody><tr><td>Nominal capacity and voltage</td><td>1.1Ah, 3.3V</td></tr><tr><td>Recommended standard charge method</td><td>1.5A to 3.6V CC-CV, 45 min</td></tr><tr><td>Recommended fast charge current</td><td>4A to 3.6V CC-CV, 15 min</td></tr><tr><td>Maximum continuous discharge current</td><td>30A</td></tr><tr><td>Recommended charge and cut-off V at 25°C</td><td>3.6V to 2V</td></tr><tr><td>Operating temperature range</td><td>-30°C to +60°C</td></tr><tr><td>Storage temperature range</td><td>-50°C to +60°C</td></tr><tr><td>Core cell weight</td><td>39 grams</td></tr></tbody></table>

These cells were cycled in a temperature-controlled environmental chamber with a variation less than 10 °C within a cycle under varied fast-charging conditions but identical discharging conditions (4C to 2.0V, where 1C is 1.1A). All cells in this database are charged with a one-step or two-step fast-charging policy. This policy has the format "C1(Q1)-C2". Fig. 4 represents an example of charging/discharge cycle with a protocol of 5.2C(66%)-3.5C (C1 = 5.2, Q1 = 66% and C2 = 3.5). The cell is charged to 66% of SOC in 5.5 C and then in 3.5 C to 80%.

For each cell, the charging and discharging protocols remain unchanged. Meanwhile, all cells discharge at a uniform rate throughout all cycles, represented by a consistent downward slope. Voltage, current, and cell temperatures were continuously recorded, with temperature variations largely attributed to internal impedance and charging policies. This ensures that the dataset accurately represents real-world fast-charging scenarios and supports the development of reliable predictive models for lithium-ion batteries. Fig. 3 represents the capacity degradation of various cells in this dataset under different fast-charging conditions as a function of cycles. The End-of-Life (EOL) of cells in this dataset varies from around 250 to 2300. The capacity degradation trajectories of the cells in this dataset illustrated a clear decreasing trend, indicating an observable degradation in charging and discharging capacity over the course of multiple charging cycles.
<figure><img src="image_4.png" /><figcaption>Fig. 3. An illustration of battery capacity degradation from the selected database.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 4. Charging rate variation of two-step charging policy.</figcaption></figure>

## B. Feature engineering for SOH and SOC estimation model

a) Feature engineering for SOH estimation: In this paper, a real time data driven SOH estimation model is built. The model takes the latest *T* cycles of voltage, current, average temperature and SOH data to estimate the SOH at the end of the next cycle. As is shown in Fig. 5, online data from cycle k to cycle k+T where in our case T equals to 10 cycles, are selected as input training data and SOH as output. The SOH of cycle k+T+1 is estimated based on inputs of cycle k+T+1. The iterative estimation strategy utilizes a sliding window iteration approach. Features that describe different charging conditions also play an important role in estimating the SOH. Fig. 4 shows the charging policy and how we illustrate eight constant features from the charging protocol: C1 and C2 respectively represent the charging current rate of the two-step charging protocol, C3 equals to 1C, indicating the constant charging rate after SOC reaching 80%. T1 and T2 represent the charging period, i.e. time used to charge under C1 and C2, respectively, T3 is the charging period of 1C after SOC reaching 80% and T4 represents the charging period in CC-CV. The environment temperature is kept unchanged for each cell testing process and the fluctuation of temperature is also noted down. The average temperature, denoted as AT, was considered as the 8th feature. The mentioned features are listed in the Tab. II.

<table><caption>TABLE II
FEATURES USED FOR SOH ESTIMATION MODEL.</caption><tr><td>Feature</td><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td><td>8</td></tr><tr><td>Parameter</td><td>C1</td><td>C2</td><td>C3</td><td>T1</td><td>T2</td><td>T3</td><td>T4</td><td>AT</td></tr></table>

<figure><img src="image_6.png" /><figcaption>Fig. 5. Illustration of model input and output structure preparation for sliding window in SOH estimation.</figcaption></figure>

b) Feature engineering for SOC estimation: In order to build a real-time SOC estimation module, only data that are measurable online such as voltage, current and temperature can be used. As is shown in Fig. 2, a neural network model trained by selected existing cell data will be used to do online SOC estimation. In terms of selection of the training data that are representative enough considering battery aging, 46 cells with different charging protocols that span a range of high, medium, and low initial charging rates, as well as different secondary rates and SOC transition points are selected. This will ensure the neural network model gets a comprehensive understanding of the impact of various charging strategies on battery aging. Charging cycle selection of each cell is also important in order to illustrate the representative training data. Thus, different cycle intervals that are equally distributed from the first cycle to the last one are selected. This selection method allows us to establish the dataset for the training session. In order to reduce the training computation burden, all training data are downsampled into 1000 sampling points homogeneously, as is shown in Fig 6.
<figure><img src="image_7.png" /><figcaption>Fig. 6. Illustration of data resampling into 1000 points</figcaption></figure>

### C. Machine learning model for SOH and SOC estimation

#### a) Random forest regressor for SOH estimation:
The RFR model is an ensemble learning method that constructs multiple decision trees during training and outputs the mean prediction of the individual trees. The following steps and mathematical expressions illustrate the functioning of the RFR in our application: We use the last $T = 10$ cycles of charging rate $C1, C2, C3$, the charging period of $T1, T2, T3, T4$, and an average temperature $T$ during each cycle, along with the SOH values to form our feature set $X$. Thus, $X = [X_k, X_{(k+1)}, \dots, X_{(k+T)}]$, where each $X_i$ corresponds to a vector of features from cycle $i$. During the training session, the training dataset consists of pairs $(X, y)$ where $X$ represents the feature vector from the past $T$ cycles, and $y$ represents the SOH at the end of each cycle $k+T+1$. For each training instance, the RFR then learns the mapping $f: X \to y$.

<figure><img src="image_8.png" /><figcaption>Fig. 7. Illustration of RFR architecture with input $X$ and output $y$ [18]</figcaption></figure>

An RFR illustration is represented in Fig. 7, the model is composed by $n$ decision trees $T_1, T_2, \dots, T_n$. Each decision tree model is trained on a bootstrap sample

from the training dataset. For each tree structure $T_i$, a bootstrap sample $X_i^{\text{sample}}$ is drawn from the training data. A random subset of $m$ features is selected, and the best split is chosen based on an accuracy-related criterion at each node. Each decision tree $T_i$ makes a prediction $y_i$ for a given input dataset $X$. The prediction from each tree is thus given by:

$$ \hat{y}_i = T_i(X) \quad (1) $$

The RFR aggregates the predictions from all decision trees to produce the final prediction $\hat{y}$. The final prediction SOH at cycle $k+T+1$, is the mean of the individual tree predictions, given by:

$$ \hat{y}_{\text{res}} = \frac{1}{n} \sum_{i=1}^{n} T_i(X) \quad (2) $$

#### b) Neural Network model for SOC estimation:
In this study, we employed a LSTM neural network to estimate the SOC of a battery based on recent voltage, current, and temperature data. LSTM networks are a type of recurrent neural network (RNN) well-suited for sequence prediction problems due to their ability to capture long-term dependencies and avoid the vanishing gradient problem. The following steps and mathematical expressions illustrate the functioning of the LSTM in our application. Each LSTM cell consists of several components: an input gate, a forget gate, an output gate, and a cell state. The gates control the flow of information, and the cell state maintains the long-term dependencies. A schematic diagram of neurons is shown in Fig. 8 [19].

<figure><img src="image_9.png" /><figcaption>Fig. 8. LSTM Schematic diagram of neurons [19]</figcaption></figure>

In general, the whole LSTM structure can be represented by:
**Forget Gate:** Decides what information to discard from the cell state.

$$f_t = \sigma(W_f \cdot [h_{t-1}, x_t] + b_f) \quad (3)$$

**Input Gate:** Decides what new information to store in the cell state.

$$i_t = \sigma(W_i \cdot [h_{t-1}, x_t] + b_i) \quad (4)$$

**Cell State Update:** Updates the cell state with new information.

$$\tilde{C}_t = \tanh(W_c \cdot [h_{t-1}, x_t] + b_c) \quad (5)$$

$$C_t = f_t \cdot C_{t-1} + i_t \cdot \tilde{C}_t \quad (6)$$

**Output Gate:** Decides what part of the cell state to output.

$$o_t = \sigma(W_o \cdot [h_{t-1}, x_t] + b_o) \quad (7)$$

$$h_t = o_t \cdot \tanh(C_t) \quad (8)$$

where $\sigma$ represents the sigmoid function, $\tanh$ represents the hyperbolic tangent function, $x_t$ is the input at time $t$, $h_{t-1}$ is the hidden state from the previous time step, $W$ are the weight matrices, and $b$ are the bias vectors.

The LSTM network is trained using backpropagation through time (BPTT) and optimized. The loss function, typically mean squared error (MSE), measures the difference between the estimated SOC and the actual SOC:

$$MSE = \frac{1}{n} \sum_{i=1}^{n} (y_i - \hat{y}_i)^2 \quad (9)$$

<figure><img src="image_10.png" /><figcaption>Fig. 9. LSTM architecture configuration used for SOC estimation model.</figcaption></figure>

The architecture of the LSTM network used in our study is depicted in Fig. 9. The input features are normalized symmetrically to ensure consistent scaling across the data, followed by two LSTM layers. The first LSTM layer comprises 128 hidden units, which are

responsible for capturing long-term dependencies in the time-series data. The degrees of freedom for this layer, corresponding to the trainable parameters, are calculated using the formula $4 \times n \times (n + \text{Input Size} + 1)$, where $n$ is the number of hidden units. For this layer, the total number of trainable parameters is $4 \times 128 \times (128 + 3 + 1) = 67,584$. The second LSTM layer contains 64 hidden units, which help in modeling shorter-term patterns and refining the sequence learning. The degrees of freedom for this layer are similarly computed as $4 \times 64 \times (64 + 128 + 1) = 49,408$ trainable parameters. To mitigate the risk of overfitting and enhance the generalization capability of the model, dropout layers are introduced after each LSTM layer. Each dropout layer has a dropout rate of 0.2, which randomly sets 20% of the input units to zero during training, preventing the model from relying too heavily on specific paths. The batch size, indicated as None in Fig. 9, is dynamically defined, allowing the model to process a variable number of time-series sequences in parallel. This flexibility depends on the computational memory available during training, ensuring efficient utilization of hardware resources. The last step of the network is a sigmoid activation function layer that translates the learned features of the LSTM layers into the estimated SOC results.

### III. RESULTS AND ANALYSIS

In this section, we present and analyze the results of SOH and SOC estimations. Data from multiple cells and cycles are used to estimate the variations in SOH and SOC over time. The accuracy of each estimation is evaluated by calculating the relative error (RE) as a function of time, providing a quantitative measure of the precision of our estimation models, it is defined as:

$$RE = \frac{y_i - \hat{y}_i}{y_i} \quad (10)$$

where $y_i$ and $\hat{y}_i$ are the actual and estimated value at the $i$th cycle, respectively.

#### A. Results and analysis for SOH estimation

In Fig. 10, the SOH estimation results for three cells are presented in a series of figures. Each figure compares the real SOH (depicted in orange) with the estimated SOH (depicted in blue) along the battery lifespan. These figures demonstrate that the RFR model accurately follows the general trend of SOH degradation for each cell, capturing both the overall decline and the smaller fluctuations throughout the battery's lifespan. Generally, these results show a strong alignment between the real
and estimated SOH values. However, some deviations are observed between the real and estimated SOH values, particularly in the cycle range approaching the EOL. The right graph in each figure displays the RE of the estimations as a function of the cycle number. These RE plots consistently show that most errors fluctuate around zero and increase with larger cycle number while the model does not systematically overestimate or underestimate the SOH in the middle. Occasional spikes in the error plots suggest some variability in the model's estimation accuracy, likely due to the inherent complexity and variability in battery degradation processes. Across all cells, the RFR model demonstrates strong performance in estimating SOH even when faced with varying operational conditions and degradation rates among different cells.

<figure><img src="image_11.png" /><figcaption>Fig. 10. SOH estimation results (Blue: Estimated SOH, Orange: Real SOH) and error for cell EL150800465027, EL150800460481 and EL150800460613.</figcaption></figure>

## B. Results and analysis for SOC estimation

In this section, the results of the SOC estimation for three cells are presented and analyzed, as illustrated in Fig.11, Fig.12 and Fig.13. Three interval of five cycles which were homogeneously distributed from the first cycle to the end of life cycle are selected as an example to illustrate the results. This approach ensures that we capture the full range of the cell's behavior over its lifespan. The results represent the SOC estimation for fifteen

cycles selected during the lifespan of one cell using the LSTM model, comparing the estimated SOC with the actual SOC. The results show that the model tracks the SOC quite closely across all samples, demonstrating the LSTM model's capability to accurately estimate SOC over a wide range of operating conditions. The close alignment between the estimated and actual SOC curves indicates that the LSTM model is effective in capturing the dynamic behavior of the battery cells.

<table><caption>TABLE III
ROOT MEAN SQUARE ERROR (RMSE) VALUES FOR THE SOC ESTIMATION OF PART OF TESTED CELLS DURING THE WHOLE LIFESPAN.</caption><caption>RSME Estimation for each cell</caption><thead><tr><th>Barcode</th><th>Policy</th><th>RSME</th></tr></thead><tbody><tr><td>EL150800737329</td><td>5C(67%)-4C'</td><td>3.312%</td></tr><tr><td>EL150800737313</td><td>5.3C(54%)-4C'</td><td>3.789%</td></tr><tr><td>EL150800737280</td><td>5.6C(36%)-4.3C'</td><td>4.430%</td></tr><tr><td>EL150800739476</td><td>5.6C(19%)-4.6C'</td><td>3.790%</td></tr><tr><td>EL150800737229</td><td>3.7C(31%)-5.9C'</td><td>5.098%</td></tr><tr><td>EL150800737307</td><td>4.8C(80%)-4.8C'</td><td>3.648%</td></tr><tr><td>EL150800737233</td><td>5C(67%)-4C'</td><td>3.408%</td></tr><tr><td>EL150800737270</td><td>5.3C(54%)-4C'</td><td>3.154%</td></tr><tr><td>EL150800737277</td><td>4.8C(80%)-4.8C'</td><td>3.039%</td></tr><tr><td>EL150800737276</td><td>5.6C(19%)-4.6C'</td><td>3.323%</td></tr><tr><td>EL150800737387</td><td>5.6C(36%)-4.3C'</td><td>3.207%</td></tr><tr><td>EL150800737386</td><td>5.9C(15%)-4.6C'</td><td>3.420%</td></tr><tr><td>EL150800737345</td><td>4.8C(80%)-4.8C'</td><td>4.037%</td></tr><tr><td>EL150800737378</td><td>5.3C(54%)-4C'</td><td>4.251%</td></tr><tr><td>EL150800737320</td><td>5.9C(15%)-4.6C'</td><td>3.397%</td></tr><tr><td>EL150800737369</td><td>5.3C(54%)-4C'</td><td>3.248%</td></tr></tbody></table>

Tab. III shows that the RMSE varies across different cells and charging protocols, reflecting the model's performance under various conditions. Notably, some cells exhibit higher RMSE values, indicating a greater deviation between the estimated and actual SOC. This variation could be attributed to differences in cell aging, internal resistance, and other factors affecting cell performance. The RMSE values for the cells range from approximately 3% to 5%, with most cells exhibiting RMSE values below 4%. These results suggest that the LSTM model maintains a relatively low error rate in SOC estimation, highlighting its robustness and reliability for SOC estimation in lithium-ion batteries. The consistency of the low RMSE values across multiple cells and cycles underscores the model's effectiveness in different scenarios and its potential for application in real-world battery management systems.
<figure><img src="image_12.png" /><figcaption>Fig. 11. Results of SOC Estimation using LSTM architecture for cell EL150800453773 for different cycle intervals, which represent different life stage of the battery life: Cycle 54-58.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>Fig. 12. Results of SOC Estimation using LSTM architecture for cell EL150800453773 for different cycle intervals, which represent different life stage of the battery life: Cycle 330-334.</figcaption></figure>

Moreover, the analysis of the RMSE values in Tab. III reveals the model performs well across a variety of charging protocols. For example, cells with barcodes EL150800737329 and EL150800737313, which were subjected to different charging protocols, both show RMSE values around 3.3% and 3.8%, respectively. This indicates that the LSTM model can adapt to different charging conditions and still provide accurate SOC estimations. In conclusion, the results presented in Fig. 11-13 and Tab. III demonstrate the LSTM model's effectiveness in SOC estimation across a range of conditions. The low RMSE values achieved across different cells and charging protocols validate the model's accuracy and robustness, making it a viable tool for enhancing battery management systems. This thorough analysis provides a strong foundation for further research and development in SOC estimation techniques using machine learning models.

<figure><img src="image_14.png" /><figcaption>Fig. 13. Results of SOC Estimation using LSTM architecture for cell EL150800453773 for different cycle intervals, which represent different life stage of the battery life: Cycle 606-610.</figcaption></figure>

## IV. CONCLUSION

This paper presents real-time estimation models for SOH and SOC in lithium-ion batteries using a dataset from the Toyota Research Institute. The RFR demonstrated high accuracy in SOH estimation, enabling early detection of battery degradation for improved BMS reliability and proactive maintenance. The LSTM neural network effectively estimated SOC in real-time, ensuring optimal battery usage and longevity. Both models achieved low RE and RMSE, proving their accuracy across different conditions and contributing to machine learning applications in EV battery diagnostics.

While this study provides promising results, variance analysis using PCA will be explored to quantify key feature contributions, reduce redundancy, and address potential overfitting seen in dataset patterns. Future work will focus on integrating SOC estimation into BMS frameworks, leveraging real-time sensor data to optimize charge cycles and battery safety. To enhance model generalization, additional datasets with different battery chemistries (NMC, LTO) and operational profiles will be incorporated. Moreover, advanced techniques like transfer learning and physics-informed neural networks will be investigated to improve prediction robustness.

By addressing these directions, this research aims to develop more scalable and efficient battery state estimation models, supporting the evolution of intelligent EV battery management systems.

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