Hybrid Electro-Thermal and FNN Framework for Joint SoC, SoH Estimation and Lifetime Prediction of Lithium-Ion Batteries in Electric Vehicles

Abstract

Improving the performance and lifespan of lithium-ion batteries is a key challenge for the development of electric vehicles. However, accurately estimating the state of charge (SoC), state of health (SoH), and life cycle remains complex due to the electrical, thermal, and aging phenomena associated with these energy storage systems. Against this backdrop, this study proposes a hybrid approach combining an electro-thermal model with a feedforward neural network (FNN) to improve the estimation of key lithium-ion battery performance indicators within a temperature range of 0 °C to 40 °C. The developed methodology was implemented in MATLAB/Simulink and applied to the analysis of the vehicle’s power profile, as well as the evolution of SoC, SoH, and battery life cycle. The results demonstrate an accuracy of 95.3% for state of charge (SoC) estimation, with a mean absolute error of 4.7%. For state of health (SoH) estimation, the accuracy is 95.8% accompanied by a mean absolute error of 4.2%. Lastly, for life cycle prediction, the accuracy is 92.5% with a mean absolute error of 7.5%. The performance results demonstrate the robustness of the proposed approach and its ability to replicate battery dynamic behavior under climatic conditions representative of the African context. This contribution opens up promising avenues for optimizing battery management systems and advancing the sustainable development of electric mobility.

1. Introduction

Advancements in electric vehicles are addressing current energy and environmental challenges. In these systems, lithium-ion batteries play a pivotal role by storing and supplying the energy required for vehicle operation. However, their performance is significantly influenced by operating conditions and aging processes [1,2]. Reliable estimation of state of charge (SoC), state of health (SoH), and life cycle has become essential for enhancing battery safety, driving range, and durability [3]. Given the complexity of the underlying electro-thermal phenomena, integrating artificial intelligence techniques offers a promising solution. This study proposes an approach combining an electro-thermal model with a feedforward neural network (FNN) to estimate key performance indicators for lithium-ion batteries within an African climatic context [4,5].

1.1. Motivation and Background

Several studies address the estimation of the state of charge (SoC) of lithium-ion batteries using methods based on metaheuristic algorithms and Kalman filter algorithms. However, several major challenges remain [6]. This study is motivated by: (a) the complex, nonlinear behavior of lithium-ion batteries, (b) the need to improve battery management system performance, (c) the economic significance of high battery costs, (d) the environmental issues associated with their lifespan, and (e) the lack of models specifically adapted to African climatic conditions, which are characterized by high temperatures.

1.2. Previous Works

Existing research relies primarily on electrochemical models, equivalent circuit models, and artificial intelligence-based approaches. Although these methods continue to improve SoC and SoH estimation, they are generally developed under temperate climate conditions and often focus on a single performance indicator. The joint estimation of SoC, SoH, and cycle life within an African context remains largely unexplored. The work presented in [7] on battery–ultracapacitor hybridization for electric vehicle applications introduces component modeling, dynamic energy management, and a nonlinear state-feedback controller, along with an adaptive energy strategy and power control. The results show significant performance improvements over a PI controller, including a reduction in steady-state error (SSE) from 3.51% to 0.43%, more efficient regenerative braking energy recovery (with a power-sharing ratio of 0 for the battery and 1 for the ultracapacitor when the latter’s SoC is below 0.99), and optimal use of energy sources by accounting for power profiles and source dynamics. Unlike other commonly used batteries, lithium-ion batteries—discussed in [8]—are distinguished by their high energy and power density, long lifespan, and minimal environmental impact, which accounts for their extensive application in consumer electronics. However, lithium-ion batteries for vehicles have high capacity and a large number of cells in series and parallel, which, combined with safety, durability, uniformity, and cost concerns, limits their large-scale use in vehicles. The restricted range in which lithium-ion batteries operate safely and reliably requires effective control and management of the battery management system (BMS). This article, combining a review of the literature with our practical experience, briefly explores the composition and key aspects of BMSs, including cell voltage measurement, battery state estimation, uniformity and equalization, fault diagnosis, and more. Its goal is to inspire further design and research in the field of battery management systems. The study in [9] presents a comparative analysis and validation of state estimation algorithms for Li-ion batteries within battery management systems. The study evaluates state observers, estimation algorithms, the Coulomb counting method, and robustness, while analyzing code properties. The parameters monitored include charge/discharge current, battery voltage, cell parameters, and external disturbances. Results indicate that model-based algorithms achieved high accuracy in estimating battery state of charge (SoC) while adhering to specified requirements and constraints. They also demonstrated properties achieving higher precision and faster dynamic convergence compared to other approaches. The findings show that the higher the code complexity value, the lower the actual complexity, indicating superior algorithm performance. Work [10] provides a comprehensive comparative analysis of thermal management systems for battery electric vehicles (BEVs) operating under long-distance driving cycles. The variables in this study include ambient temperature, solar flux, vehicle speed, and ventilation load. The results evaluate the impact of cabin setpoints (ranging from 18 °C to 24 °C) on the performance of integrated BEV thermal management systems under various ambient conditions. The transient performance of the different architectures was analyzed, highlighting the systems’ ability to maintain stable thermal conditions during rapid transitions such as sudden changes in ambient temperature or abrupt demands for heating or cooling. Work [11] concentrates on enhancing the efficiency of vehicle-to-grid (V2G) systems for battery electric vehicles through intelligent management strategies and an artificial neural network–particle swarm optimization (ANN-PSO) algorithm, achieving rapid convergence. Conversely, work [12] conducts a parametric study on artificial intelligence techniques aimed at optimizing battery state of charge (SoC) management and renewable energy integration. The results indicate that applying the TGA and ICBO heuristic techniques yielded results approximately 13% and 17% better, respectively, than those obtained via the linear programming (LP) method regarding the ESS state of charge. The use of ICBO resulted in an average SoC of 0.365, which benefits battery lifespan and performance. Refs. [13,14,15,16] propose a method for estimating the state of charge across four battery models at various temperature levels, utilizing an improved version of the adaptive extended Kalman filter algorithm within a MATLAB/Simulink R2024b environment. This study demonstrates that dynamic behavioral variations exist between batteries sharing similar specifications but produced by different manufacturers. The proposed algorithm yields satisfactory results that comply with current standards. However, experimental validation is required to better analyze error margins. The manufacturers chosen for the study included Turnigy (Hong Kong, China), LG (Seoul, Republic of Korea), Samsung (Yongin-si, Republic of Korea), and Panasonic (Osaka, Japan).

1.3. Paper Contributions

Despite the numerous solutions presented in the current literature, several identified shortcomings remain a concern. The main contributions of this article are as follows:

• The development of a lithium-ion battery electro-thermal model suitable for the simultaneous estimation of state of charge (SoC), state of health (SoH), and battery cycle life.
• Integration of a feedforward neural network to improve the accuracy of SoC and SoH estimations within the 0 °C to 40 °C temperature range, which is representative of African climatic conditions.
• A contribution to extending battery lifespan and reducing maintenance costs for electric vehicles.

1.4. Paper Organization

The remainder of this article is organized as follows. Section 2 presents the methodology, which adopts a hybrid approach combining an electro-thermal model and a feedforward neural network (FNN) to estimate the SoC, SoH, and cycle life of a lithium-ion battery. Section 3 details the vehicle’s power profile model employed within the simulation environment. The results obtained are presented in Section 4 and subsequently discussed, alongside an outline of future research directions. Finally, the conclusion summarizes the article’s main contributions and their implications for sustainable development.

2. Methodology

2.1. General Methodological Framework

This study proposes a hybrid approach combining an electro-thermal model and a feedforward neural network (FNN) to estimate the SoC, SoH, and cycle life of a lithium-ion battery. The methodology encompasses data collection, preprocessing, neural network training, and model performance evaluation. Figure 1 illustrates the key steps of the proposed approach, ranging from battery characterization to the estimation of SoC, SoH, and cycle life.

2.2. Electrothermal Modeling Workflow

The implementation of the electro-thermal model follows a sequential procedure designed to reproduce the battery’s dynamic behavior under various operating conditions. After initializing the battery’s electrical and thermal parameters, the vehicle’s power profile is applied to calculate the required current. A second-order Thévenin electrical model is then used to estimate the terminal voltage, while the thermal model calculates the internal temperature by accounting for Joule heating and heat exchange with the environment. The calculated parameters are subsequently used to determine the SoC, SoH, and battery cycle life. Figure 2 illustrates the battery’s electrical model: a second-order Thévenin equivalent circuit.

• TERMINAL VOLTAGE EQUATION

$$V_t\left(t\right)=V_{OC}\left(SOC\right)-I\left(t\right)R_0-V_1\left(t\right)-V_2\left(t\right)$$

• STATE EQUATIONS

$${\displaystyle \frac{{dV}_1\left(t\right)}{dt}}=-{\displaystyle \frac{1}{R_1{C}_1}}{V}_1\left(t\right)+{\displaystyle \frac{1}{C_1}}I(t)$$

$${\displaystyle \frac{{dV}_2\left(t\right)}{dt}}=-{\displaystyle \frac{1}{R_2{C}_2}}{V}_2\left(t\right)+{\displaystyle \frac{1}{C_2}}I(t)$$

$${\displaystyle \frac{dSOC\left(t\right)}{dt}}=-{\displaystyle \frac{\eta }{Q_n}}I(t)$$

• SoC UPDATE

$$SOC\left(t\right)=SOC\left(t_0\right)-{\displaystyle \frac{\eta }{Q_n}}{\int }_{t_0}^{t}I\left(\tau \right)d\tau$$

• $SOC\left(t\right)$: instantaneous state of charge t;
• $SOC\left(t_0\right)$: initial state of charge;
• ${\mathrm{Q}}_{\mathrm{n}}$: rated battery capacity (Ah);
• $\eta$: coulombic efficiency;
• $I\left(\tau \right)$: instantaneous current.

Figure 3 presents the battery model in maximum detail to facilitate a better understanding of the system’s implementation.

2.3. Feedforward Neural Network Approach

A feedforward neural network is used to model the nonlinear relationships between battery operating parameters and the target performance indicators. The input variables are current, voltage, and temperature, while the outputs correspond to SoC and SoH estimates. Figure 4 shows the architecture of the neural network developed in MATLAB/Simulink for estimating the battery’s internal states. The data is used both experimentally and synthetically with an Arbin/BTS4000 cycling bench (Shenzhen, China) on 3–5 real MLS12/390 cells, allowing for validation and fine-tuning. A 2-RC electro-thermal model and an aging model calibrated over 2–3 real cycles are also used, with the ultimate goal of increasing the data and generating 2500 cycles without waiting 2 years. Reference SoC values are obtained by Coulomb counting with periodic OCV correction at C/20. Reference SoH values are obtained by periodic C/3 capacity testing every 50 cycles. It is also important to note that in this work, the FNN output is not considered a reference to avoid bias. Indeed,

Table 1. Characteristics of the battery studied.

Lithium-Ion Battery	Model MLS 12/390
Manufacturer Producer	Mastervolt (Amsterdam, The Netherlands)
Chemical composition	LiFePO4, lithium iron phosphate
Nominal voltage	12.8 V
Nominal capacity	30 Ah
Maximum charging/discharging current	30 A/30 A
Mass	4.9 kg
Cost	720 €
Theoretical life cycle	>2500 cycles
Security protection	Equipped with a BMS (passive balancing)

presents the characteristics of the battery studied in detail. Furthermore, the MATLAB architecture comprises a sequence input layer with 5 input features, two fully connected hidden layers of 55 neurons each, and one output neuron. The two hidden layers are followed by tanh and Leaky ReLU activation functions, respectively, and the output uses clipped ReLU activation. Therefore, there are 2 hidden layers, with 55 neurons per hidden layer and 1 output neuron for SOC prediction. Table 1 lists the characteristics of the battery used.

Simulations were performed in MATLAB/Simulink for a temperature range of 0 °C to 40 °C, representative of the climatic conditions under study.

3. Vehicle Power Demand Model

The system under study is an electric vehicle powered by a lithium-ion battery. The power profile constitutes the main input of the model and represents the vehicle’s energy demand during its operating cycle:

P(t) = V(t) × I(t)

where:

• P(t): vehicle instantaneous power (W).
• V(t): battery voltage (V).
• I(t): current supplied by the battery (A).

Figure 5 shows the power profile of the vehicle used in the simulation environment.

In order to assess the effectiveness of the network, both the mean squared error (MSE) and the root mean squared error (RMSE) were employed. These metrics enable us to measure how closely the network’s outputs align with the desired or reference values.

$$MSE={\displaystyle \frac{1}{N}}{\sum }_{i=1}^N(p_i-O_i{)}^2$$

where $P_i$ is the real value and $O_i$ is the predicted value

$$\begin{gathered} RMSE=\sqrt{{\displaystyle \frac{1}{N}}}{\sum }_{i=1}^N(p_i-O_i{)}^2 \\ \mathrm{MAE}=(1/\mathrm{N}){\sum }_{i=1}^N|\mathrm{y}\mathrm{i}-\hat{\mathrm{y}}\mathrm{i}| \\ \mathrm{MAE} (\%)=100 \times (1/\mathrm{N}){\sum }_{i=1}^N|\mathrm{y}\mathrm{i}-\hat{\mathrm{y}}\mathrm{i}| \\ {\mathrm{R}}^2=1-[{\sum }_{i=1}^N{(\mathrm{y}\mathrm{i}-\overline{\mathrm{y}})}^2]/[{\sum }_{i=1}^N({\mathrm{y}\mathrm{i}-\overline{\mathrm{y}})}^2] \end{gathered}$$

Feedforward Neural Network Model

To improve SoC and SoH estimation, a feedforward neural network (FNN) was developed in MATLAB/Simulink.

The operation of an artificial neuron is based on the weighted combination of input variables.

The output of the neuron is given by y = f(Σ(wi × xi) + b) where:

• y: neuronal output;
• xi: i-th input variable;
• wi: weight associated with the input xi;
• b: neuron bias;
• Σ: weighted sum of inputs;
• f(.): neuron activation function.

It is important to note that the network inputs are voltage, current, and temperature, while the outputs are the improved SoC and SoH. The synaptic weights are adjusted during the training phase to minimize the error between the predicted values and the reference values. Figure 6 shows the feedforward neural network architecture used for SoC and SoH estimation. Indeed, SoH quantifies the battery’s degradation compared to its new state. In this work, the SoH capacity is the primary reference. It is obtained from the ratio of the current capacity measured at C/3 at 25 degrees Celsius to the nominal Q. Furthermore, the end-of-life criterion is when the battery has ceased to be used. This value is reached when SoH < 80%. For safety reasons, below 80%, the internal resistance rises too high, leading to a risk of overheating. Finally, at 80%, the battery is placed in stationary storage. This explains why the actual data exceeds the 80% threshold. It is also crucial to note that cycle time and costs are better for 1000 cycles compared to 5000 cycles. All of this is in accordance with the requirements of the IEC62660-1 and SAE J2288 standards.

Table 2. Parameters of the second-order Thévenin battery model.

Parameter	Description	Unit	Typical Value (Li-Ion)
${\mathit{V}}_{\mathit{O}\mathit{C}}$	Open-circuit voltage (function of SoC)	V	3.0–4.2
${\mathit{R}}_0$	Ohmic internal resistance	mΩ	5–20
${\mathit{R}}_1$	Fast polarization resistance	mΩ	0.5–5
${\mathit{C}}_1$	Fast polarization capacitance	F	100–2000
${\mathit{R}}_2$	Slow polarization resistance	mΩ	1–15
${\mathit{C}}_2$	Slow polarization capacitance	F	1000–20,000
${\mathrm{Q}}_{\mathrm{n}}$	Nominal battery capacity	Ah	30
$\mathit{\eta }$	Coulombic efficiency	–	0.95–0.99

and

Table 3. Simulation parameters.

PARAMETERS	Description	Value/Condition	Standard
Rated capacity	Total battery capacity	30 Ah	GEL-UDLA Department
Rated voltage	Average operating voltage	12.8 V (4s1pLiFePo4)	GEL-UDLA Department
Maximum discharge current	Maximum permissible discharge current for 2500 life cycles (1C)	30 A	ISO 12405-4
Max peak discharge	Pulse < 30 s for VE acceleration (5C)	150 A	Manufacturer pulse spec
Maximum charging current	Maximum permissible load current	30 A	ISO 12405-4
Operating temperature	Operating temperature range	0 °C to 40 °C	Africa Zone
State of charge (SoC)	State-of-charge range for testing	20% to 80%	UNECE R100
Driving cycle	Driving profile used for the simulation	WLTP, NEDC, FTP-75	WLTP, UNECE R101
Simulation duration	Total duration of simulations	1000 charge/discharge cycles	SAE J2380
Conversion efficiency	Charge and discharge energy efficiency	95%	ISO 12405-4
Security protocol	Safety measures to be followed	Overheating and overcharge protection	UNECE R100, IEC 62660-2
Accelerated aging	Aging simulation for longevity assessment	1000 charge/discharge cycles	IEC 61982

present the system parameters for the battery model and the overall simulation used for the estimates. The details of the forward-propagating neural network (FNN) training parameters, used to reproduce the problem, are as follows: seed = 42; Min Max/Standard Scaler, architecture 8-64-32-16-1 and 10-128-64-32-2; LeaKyReLU α = 0.01; AdamWIr = 1 × 10⁻³; weight attenuation = 1 × 10⁻⁴; Huber δ = 0.1 + physical loss λ = 0.05; batch 64/32; early stopping patience = 20. The number of full cycles (70/15/15) was split to avoid memory leaks.

The best parameters retained during the variations of simulation scenarios in this work for the MLS12/390 model at BOL (250 °C, 50% SoC) are as follows: R0 = 12.5 mΩ; R1 = 8.2 mΩ; C1 = 1250 °F; R2 = 15.1 mΩ; C2 = 4500 °F; Cp = 850 J/K; Rth = 2.1 K/W; Ea = 24.5 kJ/mol for Arrhenius degradation. Identification was performed via WTLS (weighted total minus squares) with RMSE < 8 mV. Further details in this work specify that a hybrid dataset was constructed, and 1000 experimental cycles at 45 °C were used (real data, recorded at 1 Hz of V, I, and T). From cycle 1001 to cycle 2500, synthetic data were generated by a calibrated electro-thermal model (validated RMSE of 2.3% over the last 100 real cycles). The data were augmented by Gaussian noise of 2% on V, I, and T. The final dataset size was 2.5 million points. The 40% experimental/60% synthetic ratio is now indicated.

4. Results and Discussion

4.1. Vehicle Power Profile Analysis

One of the objectives of this study is to simulate the energy demand of an electric vehicle in order to evaluate the impact of operating conditions on the behavior of the lithium-ion battery.

Figure 7 shows the evolution of the power demanded by the vehicle during the driving cycle under consideration. Several variations are observed, corresponding to the different phases of acceleration, steady-state operation, and deceleration. These power fluctuations directly influence the current supplied by the battery, as well as the evolution of its internal parameters.

4.2. Battery Load Profile

Analyzing the load profile makes it possible to evaluate the demands placed on the battery during vehicle operation.

Figure 8a–c shows the evolution of the load applied to the battery. The recorded variations reflect the different levels of energy consumption imposed by the vehicle. These results constitute the input data used for estimating SoC and SoH.

4.3. State of Charge Prediction

SoC estimation is one of the most important indicators in battery management systems, as it allows for the assessment of the remaining energy available to the electric vehicle. Figure 9 presents the state-of-charge estimate for different temperature levels.

The results obtained show that the model developed in MATLAB accurately reproduces the evolution of the SoC during charge and discharge phases. The trend remains consistent with the expected physical behavior of a lithium-ion battery, characterized by a gradual decrease in available charge during operation.

Figure 10 illustrates the SoC prediction results obtained in Simulink, with the ultimate aim of confirming the numerical stability of the proposed model. The comparison between estimated and reference values reveals an overall accuracy of 95.3%, with a mean absolute error of 4.7%. These results demonstrate the hybrid model’s ability to accurately estimate battery state of charge under climatic conditions representative of the African context.

4.4. State of Health Prediction

The state of health (SoH) assessment shown in Figure 11a,b allows monitoring of battery aging and anticipation of its degradation over time.

The results show a gradual decrease in the battery’s available capacity over the course of its use. This trend reflects the natural aging phenomenon observed in lithium-ion batteries. Figure 11a,b shows how each method tracks changes in battery capacity. The dashed line represents the actual battery capacity, and the different colored lines show the predictions of the various algorithms. The results show that AWTLS provides the most accurate estimates, indicating superior performance in monitoring battery health. This curve shows the predicted capacity (Ah) of a battery over time using different weighted regression algorithms:

• WLS: weighted least squares regression.
• WTLS: weighted total least squares regression.
• TLS: total least squares regression.
• AWTLS: adaptive weighted total least squares regression.

The Simulink simulations shown in Figure 12 make it possible to reproduce degradation mechanisms while incorporating thermal effects associated with operating conditions. Model validation demonstrates an accuracy of 95.8%, with a mean absolute error of 4.2%. This performance confirms the validity of the approach combining electro-thermal modeling and artificial intelligence for SoH estimation. Figure 11b shows the SoH degradation trajectory for MLS12/390 as follows: solid line (experimental data up to 1000 cycles for 45 °C (average of 3 cells)), dotted line (extrapolation of the electro-thermal model to 2500 cycles calibrated on experimental data).

4.5. Battery Life Cycle Prediction

Life cycle prediction makes it possible to estimate the battery’s service life before it reaches its end-of-life threshold.

The results in Figure 13 show good agreement between the predicted values and the reference values. The developed model achieves an overall accuracy of 92.5% with a mean absolute error of 7.5%. Despite the complexity of aging phenomena, these results demonstrate the proposed model’s ability to provide reliable life cycle estimates within a temperature range of 0 °C to 40 °C.

4.6. Discussion

(a)

Case of SoC estimation

Accurate state-of-charge estimation is essential for ensuring the driving range and safety of electric vehicles. The results obtained in this study achieved an accuracy of 95.3% with a mean absolute error of 4.7%, thereby demonstrating the proposed model’s ability to faithfully reproduce the dynamic behavior of the lithium-ion battery.

Table 4. Validation of SOC estimation against the recent literature.

References	Method	SoC Accuracy (%)
[5]	Hybrid model	94.6
[8]	ANN	92.1
[13]	LSTM	93.4
Proposed method	Electro-thermal model + FNN	95.3

shows the comparison of SoC estimation performance with the recent literature.

This can be achieved by simultaneously integrating electrical and thermal parameters into the neural network’s learning process. Unlike many studies conducted in moderate thermal environments, the proposed model remains applicable within a temperature range of 0 °C to 40 °C, making it better suited to the climatic conditions found in several African regions.

(b)

Case of SoH Estimation

State-of-health assessment is a key indicator for managing lithium-ion battery aging. The results obtained show an accuracy of 95.8% with a mean absolute error of 4.2%; see

Table 5. Comparison of SoH estimation performance with the recent literature.

Reference	Method	SoH Accuracy (%)
[3]	Electro-thermal model	94.3
[4]	Machine learning	93.7
[11]	Neural network	91.5
Proposed method	Electro-thermal model + FNN	95.8

.

The observed performance shows that the combined use of the electro-thermal model and the feedforward neural network improves the quality of the estimates. This approach allows for better consideration of the effects of temperature on battery degradation mechanisms.

(c)

Case of battery life cycle prediction

Predicting cycle life poses a major challenge due to the complexity of electrochemical aging phenomena. Despite this difficulty, the proposed model achieved an accuracy of 92.5% with a mean absolute error of 7.5%.

Table 6. Comparison of battery cycle life prediction performance.

Reference	Method	Accuracy (%)
[2]	ANN	90.3
[3]	Hybrid model	91.2
[12]	Statistical model	88.6
Proposed method	Electro-thermal model + FNN	92.5

presents the comparison of battery life cycle prediction performance.

The results obtained confirm the model’s ability to predict long-term battery capacity evolution. The observed discrepancies are primarily attributable to thermal phenomena and complex aging mechanisms that remain difficult to model with absolute precision. These results are consistent with works [17,18,19,20,21], which propose a new reconfigurable dual-core thermal management system and compare it experimentally to a conventional configuration. The system’s performance was comprehensively assessed using energy and exergetic analyses, as well as vehicle range measurements. The system features a reconfigurable architecture that allows counter-current series operation of the cooling and heating cores, thus effectively improving heat transfer. The experimental results indicate that, compared to the conventional system, the system offers an average coefficient of performance improvement of 47.7%, demonstrating significant advantages in terms of cooling performance and energy efficiency. At the same time, the compressor discharge temperature and pressure are reduced by 10.9% and 21.8%, respectively, similar to the work in [22,23,24,25,26], which analyzes the characteristics, advantages, and disadvantages of various AIHAI methods and outlines future research directions. Refs. [27,28,29,30] also propose a method for jointly estimating the SoC and temperature of a lithium iron phosphate battery based on reflected ultrasonic waves. A piezoelectric transducer is affixed to the surface of the battery to facilitate ultrasonic electrical conversion. Ultrasonic waves are produced by the transducer, travel through the battery, and reflect back to the transducer when they reach the bottom surface. The timing of these signals, used to identify key indicators of the battery’s condition, is determined through sliding window correlation analysis. To enhance the dataset after extracting features, virtual samples are generated. Ultimately, a backpropagation (BP) neural network is employed to simultaneously estimate multiple battery states across a broad temperature spectrum. Experimental findings indicate that the root mean square error (RMSE) for estimating the state of charge (SoC) is 7.42%, and for temperature, it is 0.40 °C. The method is non-destructive and easily integrated into battery management systems. Combined with the detection of gas emissions within the battery, it contributes to improving system safety. Its results correlate positively with this article. Refs. [31,32,33] propose an index to quantify the SoH disparity between fuel cell stacks and integrate it into the objective function to be minimized. Subsequently, an ESAC (enhanced soft actor-critic) reinforcement learning framework is developed, incorporating a three-level rule-based strategy. The results of simulation tests clearly demonstrate that introducing a term that accounts for the SoH disparity in the objective function effectively mitigates the SoH imbalance phenomenon. Simultaneously, ESAC promotes long-term operation of the multi-stack system at constant and identical power levels, which mitigates fuel cell degradation and further reduces the SoH disparity between stacks. These results pave the way for intelligent energy management in next-generation fuel cell trucks.

Table 7. Positioning of the results obtained in relation to the current literature.

Ref	Theme/Title	Tools and Methods	Input Variables	Results
[12]	Parametric studies on artificial intelligence techniques for batteries: SoC management and renewable energy optimization	✓ Heuristic techniques ✓ Linear programming (LP) method ✓ Methods for measuring SoC ✓ Soft computing techniques ✓ Parametric studies	✓ Crossover probability ✓ Mutation probability (Pm) ✓ State of charge (SoC) ✓ Coefficient of restitution (COR)	The results show that applying the TGA and ICBO heuristic techniques yielded results approximately 13% and 17% better, respectively, than those obtained using linear programming (LP) in terms of the ESS state of charge. The use of ICBO led to average SoC values reduced to 0.365, which is beneficial for battery life and performance.
[9]	A comparative study and validation of state estimation algorithms for Li-ion batteries in battery management systems	✓ State observers ✓ State estimation algorithms ✓ Coulomb counting method ✓ Robustness and code property analysis ✓ Programming	✓ Charge/discharge current ✓ Battery voltage ✓ Cell parameters ✓ External disturbances	Model-based algorithms demonstrated good accuracy in estimating the state of charge (SoC) of batteries at 91.6%, while respecting the specified requirements and limitations. They also demonstrated properties achieving greater accuracy and faster dynamic convergence compared to other approaches over a temperature range of 0 to 26 degrees Celsius.
[3]	Artificial intelligence-based battery management solutions for Li-ion batteries	✓ Machine learning algorithms ✓ Neural network-based methods ✓ Use of random forest regression ✓ Comparative analysis of the capabilities of six AI models	✓ Current ✓ Temperature ✓ State of charge (SoC)	✓ Mean absolute error: 0.0035 ✓ Median absolute error: 0.0013 ✓ Root mean square error (RMSE): 0.0097 ✓ Over a temperature range of −10 to 25 degrees Celsius
In this work	Battery management for electric cars using artificial intelligence	✓ Impedance spectroscopy ✓ The equivalent electrical circuit ✓ Coulomb counting ✓ Dynamic estimation of the parameters of an equivalent model	✓ Voltage ✓ Current ✓ Temperature	✓ For SOC estimation, our simulations achieved an accuracy of 95.3%. Mean absolute error (MAE): 4.7% ✓ The results obtained for SoH prediction show an accuracy of 95.8%. Mean absolute error (MAE): 4.2% ✓ We obtained an accuracy of 92.5% for battery life prediction. Mean absolute error (MAE): 7.5% ✓ Over a temperature range of 0 to 40 degrees

provides a comparative summary of the results obtained in this article alongside those from other recent publications.

We would like to clarify the validation scheme as follows: a total of 15% of the cycles (2126 to 2500) were never observed during training nor used for early termination. Furthermore, we performed cross-validation at different temperatures: the model trained at 250 °C and 350 °C was tested at 40 °C on data not seen during training (MAE_SoC = 1.89%). This test is now considered independent. We also added cross-validation at k folds per temperature (k = 3).

4.7. Challenge and Future Scope

Future work will focus on the experimental validation of the model and the integration of more advanced artificial intelligence techniques to further improve prediction performance. BMS systems compliant with ISO 12405 standards feature enclosures rated for temperatures up to 550 °C. These systems could also be considered for optimization, while taking into account aging (SoH) and temperature-based self-calibration. A comprehensive comparative study regarding the control of the system’s dynamic behavior under varying temperatures would be highly valuable. Finally, a comparative study using intelligent methods to optimize LSTM and GRU model parameters—with the aim of proposing a hybrid version—would also be of great interest. We also suggest, for broader applicability to other chemical reactions, that future work should include more comprehensive validation using an independent laboratory dataset, extending up to a real-world end-of-life scenario of 80%.

5. Conclusions

This study proposed a hybrid approach combining an electro-thermal model and a feedforward neural network (FNN) to estimate the SoC, SoH, and cycle life of lithium-ion batteries used in electric vehicles. The key scientific contributions focused on the following:

• Developing an electro-thermal model adapted for the simultaneous estimation of lithium-ion battery SoC, SoH, and cycle life.
• Integrating a feedforward neural network to improve estimation accuracy.
• Accounting for a temperature range of 0 °C to 40 °C, representative of African climatic conditions.
• Performing cross-validation using MATLAB and Simulink to enhance model robustness.
• Contributing to extended battery lifespan and reduced maintenance costs for electric vehicles.

From a sustainable development perspective, this approach promotes more efficient use of energy storage systems, reduces premature battery replacements, and contributes to the advancement of electric mobility in hot-climate regions. Simulations conducted using MATLAB/Simulink achieved an accuracy of 95.3% for SoC, 95.8% for SoH, and 92.5% for cycle life prediction. These results demonstrate the proposed model’s ability to effectively replicate the battery’s dynamic behavior within a temperature range of 0 °C to 40 °C. The developed approach thus represents a significant contribution to the improvement of battery management systems and the sustainable development of electric mobility.