Innovative strategies for assessing battery health in electric vehicles

Abstract

Energy generation, which promotes a nation's economic stability and advancement, is one of the most significant facets of modern society. Recent years have seen significant advancements in energy conversion and storage technology, particularly in mobile gadgets and electric vehicles. Lithium-ion batteries are utilized in energy storage and electric vehicles because of their low self-discharge rates, long cycle life, and high energy density. Therefore, precise evaluations of battery conditions are necessary for safe operation. This study proposes a hybrid model based on the Bidirectional Gated Recurrent Unit (Bi-GRU) with the Giant Trevally Optimizer (GTO) for state of health (SOH) prediction, which will help in improving the predictive accuracy. In the estimation of SOH, some key features of charge-discharge cycle characteristics are used based on the NASA lithium-ion battery dataset. The proposed GTO-Bi-GRU model outperforms Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU) models by incorporating the bidirectional learning abilities of Bi-GRU, which captures the complex trend in battery degradation more effectively. Meanwhile, GTO performs the hyperparameter tuning optimally, outperforming classical optimization techniques such as particle swarm optimization (PSO), genetic algorithm (GA), and Cuckoo search algorithm (CS). This comparative study demonstrates that GTO-Bi-GRU achieves the highest prediction accuracy among all with coefficients of determination values of 0.9969, 0.9917, 0.9948, and 0.9882 on B5, B6, B7, and B18 battery cells. These results depict that GTO-Bi-GRU outperforms PSO-Bi-GRU, GA-Bi-GRU, and CS-Bi-GRU by a great margin, hence establishing it as a very effective model for SOH estimation. The results prove that GTO-Bi-GRU is robust enough and scalable for battery health monitoring applications in electric vehicles.

Keywords

Lithium-ion batteries electric vehicles state of health bidirectional gated recurrent unit giant trevally optimizer

1 Introduction

In today's world, energy is essential as it powers almost all human activities.¹ Transportation, heating, electricity production, and industrial operations are all activities that necessitate energy.² Energy sources can be classified as renewable or non-renewable based on their environmental impact and availability.³ In general, renewable energy sources, including solar, wind, and hydropower, are more sustainable due to their capacity for natural renewal.⁴ Nuclear power and non-renewable energies (coal, oil, natural gas, and fossil fuels) are examples of finite resources.⁵ Nonrenewable energy sources have an adverse effect on the environment by destroying habitats, polluting the air and water, and releasing greenhouse gases that exacerbate climate change. The crisis surrounding the reduction of Nuclear products and the resulting distress of the urgency in finding pure and renewable energy resources, as well as innovative technologies for energy utilization and storage facilities has been heightened due to global warming.^6,7 Some efficient conversion and preservation of energy technologies have emerged in recent years and developed rapidly and extensively in mobile phones, electric cars, and other portable electronics.^8,9 Fuel cells, supercapacitors, and lithium-ion batteries are some of these technologies.^10–12 Lithium-ion batteries have demonstrated significant benefits such as high energy density, lightweight design, extended cycle life, and minimal self-discharge.¹³ Application potential in electric cars has become crucial for reducing environmental pollution. The aging of lithium-ion batteries occurs due to the depletion of active materials in the electrodes and the depletion of lithium reserves during continuous use.¹⁴ It reduces the driving range of electric vehicles, causing range anxiety, and poses safety risks to Electric vehicle drivers (EV).¹⁵ Sufficient power to the battery management system (BMS) is required to ensure the secure operation of electric vehicles.¹⁶ To guarantee the secure operation of electric cars, a precise state of health (SOH) estimate is an essential role of BMS.¹⁷ The SOH is an evaluative metric to assess a battery's service life, indicating its degree of aging and dependability. Nevertheless, the SOH cannot be determined owing to the batteries’ intricate internal degradation mechanism.¹⁸ The selection of novel methodologies for assessing the SOH of batteries is crucial. Currently, experimental analysis, model-based, and data-driven methods comprise the three kinds of SOH anticipation techniques.^19–21 Among the experimental methods are open circuit voltage (OCV), coulomb counting, and impedance spectroscopy. Typically, these methods forecast the SOH of the battery in real time by employing a determination system. Furthermore, the model-based methodologies achieve SOH estimation by applying the laws of internal physicochemical reaction and prior knowledge of the life cycle.^22,23 For estimating SOH, data-driven methods have been implemented extensively, benefiting from vast quantities of battery data and not requiring preexisting knowledge or model mechanisms. The estimation of battery SOH in data-driven approaches involves the extraction of feature vectors associated with the aging procedure.²¹ Voltage characteristics are among the most commonly selected to characterize the deterioration process of a battery. Wu et al.²⁴ implemented a method based on the differential geometry method for feature variable extraction from the output voltage profile in the course of constant-current charging, followed by the estimation of the battery SOH using a data processing aggregation method. For the SOH of a battery, Yang et al. constructed a Gaussian process regression (GPR) model by employing four battery health features that were extracted.²⁵ The gray correlation method and a charging curve were employed to investigate the correlation between the features and SOH. Another significant attribute that demonstrates a strong correlation with the battery's SOH is the incremental capacity (IC) curve.²⁶ Based on the variations in the IC peaks, Weng et al. predicted the SOH of the battery.²⁷

The single-source feature's limitations were discussed by Dai et al.²⁸ It is important to note that the chosen model in the Dai et al.²⁸ study received the IC and voltage characteristics as inputs. A neural network based on prior knowledge was implemented to estimate the SOH of the batteries. Wang et al.²⁹ implemented thermal differential voltammetry characteristics that incorporated temperature and voltage. Zhang et al.³⁰ have recently introduced a model fusion approach wherein the selection of the model is determined by various charging conditions. As a standard for choosing models for the estimate of SOH the IC peak was employed; nevertheless, it exhibits dynamic fluctuations according to the number of cycles, and the presence of local extreme points can result in imprecise estimations of the charging condition and impact the selection of models. It is prone to failure when the feature space is high dimensional. Prediction methods that rely on a single model may exhibit limited robustness. Wang et al.³¹ combined the voltage and IC features as inputs to the model to circumvent the shortcomings of the single-source technique. The SOH of the batteries was estimated utilizing a neural network based on prior knowledge. Combining the filtering with a surrogate model, Wei et al.³² presented a data-driven strategy. While advancements have been made to the model's accuracy, its practical applicability was constrained because the updating criteria for model parameters relied on the discrepancy between predicted and actual values. Aging profiles are derived from voltage, and current profiles to provide a more comprehensive description of Battery degradation characteristics. The motivation for applying machine learning (ML) models to SOH prediction in batteries largely emanates from their huge potential currently demonstrated in nonlinear and complex patterns across a wide range of fields.³³ Advanced models in ML are applied to the field of capturing intricate biological processes of metastasis detection, multi-swarm cooperative particle swarm optimization for complex optimization problems, and nonlinear relationships in textual data of sentiment analysis.³⁴ It will present how far the ML methods can do pattern extraction from datasets that can vary diversely and possess very similar properties as the nonlinear degradations occurring in lithium-ion batteries. These shall henceforth enable fast adaptation to solve SOH problems of current batteries. Drawing inspiration from these works, this study proposes the inclusion of ML models with some new features of their own toward SOH-related research.³⁵ As machine learning (ML) methods exhibit suboptimal performance Bi-Directional Gated Recurrent Unit (Bi-GRU) is employed for SOH prediction.³⁶ A Bi-GRU neural network is an augmentation of a Gated recurrent unit (GRU) neural network by the addition of a second layer. At any given time, this two-layer architecture imparts to the output layer all pertinent contextual information regarding the input data.³⁶ By using the principles of natural selection, these algorithms replicate the greatest levels of efficiency ever witnessed in the natural world. The current work integrated optimization technique, the Giant trevally optimizer (GTO).³⁷ The gigantic trevally's hunting habits served as the model for the metaheuristic GTO algorithm. The dataset used in this study is NASA's lithium-ion battery dataset, which is described in detail in Section 3.1. This paper's main contributions are as follows:

With the ability to learn features in both directions, the Bi-GRU model was unveiled. The model may more accurately represent the time-series characteristics in the data. Specifically, The Bi-GRU model can forecast more accurately when handling capacity rebound brought by recovering capacity while cycling the battery operations, which improves the predictive model's accuracy and performance. To get the best possible hyperparameter combination for the Bi-GRU model, hyperparameter tuning for the model was carried out using the GTO optimizer, which was introduced as a method of model optimization.

The NASA battery dataset is used, focusing on lithium-ion batteries, and characteristics of the charge-discharge cycle are employed to estimate SOH in the research.

Performances of SOH prediction by comprehensive comparisons between Bi-GRU, Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), and Giant Trevally Optimizer-Bidirectional Gated Recurrent Unit (GTO-Bi-GRU), Particle Swarm Optimization-Bidirectional Gated Recurrent Unit (PSO-Bi-GRU), Genetic Algorithm-Bidirectional Gated Recurrent Unit (GA-Bi-GRU), and Cuckoo Search Algorithm Bidirectional Gated Recurrent Unit (CS-Bi-GRU) are implemented. The experimental results confirm that Bi-GRU outperforms LSTM and GRU with the advantage of bidirectional learning for mapping the battery degradation trend more effectively, especially for capacity rebound scenarios. Unlike the very computationally expensive LSTM and GRU, which do not offer bidirectional processing, the Bi-GRU has a more computationally efficient yet accurate solution. Besides, GTO was selected for hyperparameter tuning because it strikes a better balance in exploration-exploitation compared to PSO and GA. Results confirm that the most accurate and robust model is GTO-Bi-GRU, which could be an optimal choice for SOH prediction in battery health monitoring.

The remainder of the paper is divided into the following sections: In Section 2, a background and the SOH is defined theoretically. Section 3 discusses feature extraction and the data set. The research materials and techniques are discussed in Section 3. The results of this study are presented in Section 4. The study's conclusion is given in section 5.

2 Background

2.1 Lithium-ion batteries

Batteries are electrical energy storage devices that may be utilized as a source of power for devices that need electricity to operate. To be more precise, a battery is made up of one or more electrochemical cells that have external connecting terminals.³⁸ These connections are the positive and negative terminals, which, when a battery is delivering electricity, function as the cathode and anode, respectively.³⁹ When a battery serves as a power source by being linked to an electrical circuit, a chemical reaction (depending on the kind of battery) induces an electrical current to flow. One subset of the battery family is lithium-ion batteries. Lithium batteries, like many other battery types, are made up of a positive and a negative electrode (cathode, current collectors, an electrolyte, a separator, and an anode.⁴⁰ The electrodes are the site of the chemical reaction that produces electrical current either oxidation (loss of electrons) or reduction (gain of electrons) occurs according to whether a battery is charging or draining. Lithium ions (Li+) and free electrons (e-) are released or bound by these chemical reactions. The foundation of rechargeable batteries is this oxidation/reduction duality.⁴¹ Through the electrolyte, which is usually dissolved lithium salt, the lithium ions diffuse throughout the battery, producing a voltage between the terminals that drives the movement of free electrons, or electrical current. The purpose of the final parts, the separators, is to isolate the electrodes to prevent internal battery discharge.

Figure 1 shows a representation of the charging and discharging operations of a lithium-ion battery to more clearly depict the two modes of operation. It shows exactly how electrons go through the wire that connects the terminals and how lithium ions migrate through the separator. Both the electrons and the lithium ions are traveling in distinct directions toward the negative current collector when the battery is charging. In contrast, both particles go in the direction of the positive current collector when the battery is discharging.

Figure 1.

Illustrating how lithium-ions and electrons go through a normal lithium-ion battery.

2.2 Definition of state of health

The four main parts of a lithium-ion battery are the separator, cathode, anode, and electrolyte. Consequently, the battery's performance is dependent on the characteristics of these components.⁴² The rise in cycling leads to the unavoidable deterioration of lithium-ion batteries, which involves both mechanical and chemical impacts. Deterioration of the cell's structure, such as volume reduction or enlargement induced by the deintercalation and intercalation of lithium ions throughout the charge and discharging procedure, is a significant contributor to power fading. Fractures or fissures may form on both the cathode and anode as a result, thereby diminishing the battery's performance.⁴³ The charging and discharging process of an electrochemical system can therefore lead to chemical degradations, such as the solid electrolyte interphase (SEI) layer forming on the anode surface and the decomposition of the electrolyte.⁴⁴ These irreversible phenomena have the potential to deplete electrolytes and active lithium ions, resulting in a reduction in battery capacity and an increase in resistance. Calendar aging behaviors may also contribute to battery degradation, along with cycling degradation. Unlike cycling aging, calendar aging manifests itself during battery life. It is in rest mode without charging or discharging, and during this period the battery capacity gradually decreases.⁴⁵ Batteries undergo extensive calendar deterioration Between their manufacture and actual implementation in a battery system. Calendar aging has been shown to lead to the depletion of the electrode, which contains both lithium and active materials.⁴⁶ As a result of the degradation process, certain battery characteristic parameters change, such as the utmost available capacity diminishing and the internal resistance increasing. An indication that a battery has reached its end of life (EOL) is typically the occurrence of twofold internal resistance or a capacity decline of 80% relative to its nominal value.⁴⁷ SOH is an important indicator of battery degradation. By detecting SOH, the Remaining Useful Life (RUL) of the battery can be determined, thereby ensuring its dependability and extending its lifespan.⁴⁸ It is worth noting that the battery SOH can be employed to gauge the overall degradation level and provide an alert when a replacement is necessary. The ratio of the present state to the original state of the capacity or internal resistance may be used to determine the battery SOH.⁴⁹

\begin{aligned} S O H = \frac{C_{a}}{C_{r a t e d}} \times 100 % \end{aligned}

(1)

where

C_{a}

and

C_{r a t e d}

represent, respectively, the actual and rated capacities. The selection of these two characteristic variables that undergo gradual changes makes it possible to establish the battery SOH. In practice, however, obtaining it directly through any commercially available sensors is not feasible.

3 Material and methods

3.1 Dataset description

The database of NASA is derived from the initial dataset utilized in this study. B5, B6, B7, and B18 are manufactured lithium-ion batteries. The NASA battery dataset's charge-discharge cycle (CC-CV) comprises a charging procedure distinguished by constant current and voltage; these attributes are utilized in this investigation. B5, B6, B7, and B18, lithium-ion batteries have a capacity of 18,650, which are the four batteries from the entire dataset selected for this paper. Voltage and capacity are both nominal at 3.7 V and 2 Ah, respectively. The NASA-obtained dataset depicted the battery aging process from inception to decommissioning by including data on charging time, voltage, current, temperature, and other relevant parameters. Figures 2 and 3 illustrate the voltage and current change profiles of the battery throughout an entire charge and discharge cycle.

Figure 2.

NASA voltage charging-discharging curves.

Figure 3.

NASA current charging-discharging curves.

The NASA battery dataset forms an established, accepted platform for studying aging and degradation in lithium-ion batteries. It encompasses all the data on lithium-ion battery charge-discharge cycles under a controlled laboratory environment, all of which are coupled with explicit voltage, current, capacity, and temperature details. Although comprehensive and available to the public, this dataset is worthwhile in terms of SOH prediction; some restrictions in the dataset are cited here about its practical application in the context of EV batteries. The first limitation is that the data most accurately reflects laboratory testing circumstances, which are quite different from the unpredictable and changing environment that batteries must endure in real-world EV applications. This dataset does not account for variability created by real factors such as charging behaviors, temperature fluctuations, and mechanical stress. Only a portion of the cells has been scrutinized for this research: B5, B6, B7, and B18. Such might not entirely reflect all possible lithium-ion battery chemistries and topologies used within EVs, restricting applicability for a broader purpose within the field of EVs. Despite these limitations, this dataset would provide insight into the battery aging processes, thereby providing an excellent starting point for developing and testing models. Field-tested EV batteries or data representing wide-ranging operating conditions would further provide realistic relevance to results from such an approach. The proposed methodology could then be complemented by strengths derived from the NASA dataset, hence validating its generalizability and practical applicability in various fields.

3.2 Voltage and current feature extraction

The NASA battery dataset's charge-discharge cycle is made up of a charging procedure that is described by CC-CV. A constant voltage (CV) discharge process with 1.5 A and less than 2 A. Initially, a current of 1.5 A (0.75C) was utilized to charge the battery until the terminal voltage attained its rated charging voltage of 4.2 V. Following that, CV charging was performed on the battery at a voltage of 4.2 V until the current fell 0.5 A. After the CC-CV charging procedure, the battery will discharge with a constant current of 0 A until the terminal voltage reaches the discharge cut-off voltage associated with the process.

3.3 Measured health indicators

Current and voltage are among the measured Health Indicators (HIs) readily obtainable from the BMS. Consequently, battery degeneration may be replicated and explained using HIs that are extracted during the charging and discharging processes.

3.3.1 Voltage-related HIs

Changes in internal physical and chemical processes during storage and operation result in notable variations in the voltage curve during both charging and discharging. Specifically, the capacity decreases during the aging process, while the internal resistance increases. The charging current (CC) decreases as the number of cycles in the voltage curve increases. During the charging phase, two features, named voltage-charging-p1 and voltage-charging-p2, were selected, as illustrated in Figure 4. As shown in Figure 5, the slope during the charging phase increases with each cycle.

Figure 4.

The scatters of voltage during the charging period.

Figure 5.

The slop scatter of voltage during the charging period.

During the discharging phase, two features were selected named voltage-discharging-p1, and voltage-discharging-p2, which are mentioned in Figure 6. The ascent of the slope during the discharging phase decreases with each cycle, as illustrated in Figure 7.

Figure 6.

The scatters of voltage during the discharging period.

Figure 7.

The slop scatter of voltage during the charging period.

3.3.2 Current-related HIs

The deterioration trends of lithium-ion batteries are readily discernible through the analysis of charging and discharging current curves. As the cycle number increases, the charging current shifts to the left. As the cycle goes on, CV mode's duration lengthens while CC mode's drops. Two features were selected during the charging and discharging period named charging-terminal-current-m1, and discharging-terminal-current-m1 mentioned in Figure 8.

Figure 8.

The scatter of the charging-discharging current terminal.

3.3.3 SOH-related HIs

As stated in the preceding sections of this study, it is essential to determine the SOH of a battery. Conducting this test reveals that as the number of cycles increases, the SOH decreases. The entire process is illustrated in Figure 9.

Figure 9.

The scatter of SOH.

3.4 Experimental steps

The selected features with the greatest impact on SOH prediction are used as input variables for further training of the model to determine which Health Indicator (HI) has a significant impact. In the data preprocessing phase, redundant or unnecessary data is eliminated following the extraction of the dataset containing information on HI. A sliding method was also used to separate the data into training and test sets to get them ready for additional modeling and analysis. To eliminate the spatial influence of the variable and hasten the agreement of the model, normalize the data. This minimizes training-related inconsistency brought on by varying numerical ranges, expedites model training, and guarantees scaling consistency across various features. Reduce the Root Mean Square Error (RMSE) model assessment metric by optimizing the unoptimized Bi-GRU model using the Cuckoo Search Algorithm (CS) and the GTO. To help the model avoid local optimal solutions and improve model performance, to identify the optimal set of hyperparameters, do a random search in the hyperparameter space. Establish an appropriate set of hyperparameters as the model's starting points, then use the backpropagation technique to continuously modify the Bi-GRU model's internal parameters to reduce the loss function. The study framework is mentioned in Figure 10.

Figure 10.

The study framework.

3.5 Model description

3.5.1 Combining GTO and Bi-GRU to forecast SOH

In this paper, the hyperparameter of the Bi-GRU model has been optimized with the GTO to achieve the best setting toward the most accurate estimation of SOH. This includes the major hyperparameters that GTO will tune in the search for an optimal learning rate, number of layers, and number of hidden units in the Bi-GRU, which define the capability of the model to learn temporal and nonlinear characteristics in battery degradation data. It also provides a loss function that calculates the error of this prediction and grounds the basis for its optimization process during training. The optimization is guided through evaluating the loss functions obtained from the error metrics, RMSE, and Mean Absolute Percentage Error (MAPE).

The GTO acts in three of the most important phases adapted to the SOH estimation tasks.⁵⁰

Extensive Search:

GTO makes the initial Lévy flights over the wide hyperparameter space, which then allows it to dive into that space with depth later. The candidate configuration of the next iteration is determined as:

\begin{aligned} X (t + 1) = B e s t_{p} \cdot R + (M a x i m u m - M i n i m u m) \cdot R + M i n i m u m \cdot l e v y (D i m) \end{aligned}

(2)

Here, R represents a random number between 0 and 1, and Levy (Dim) enhances the process of exploration to prevent the premature convergence of the optimizer in the suboptimal solutions.

Area Selection:

This step is dedicated to reducing the search around the areas of smaller RMSE and MAPE. The position update will be calculated as:

\begin{aligned} X (t + 1) = B e s t_{p} \cdot A \cdot R + M e a n i n f o_{0} - X_{i} (t) \cdot R \end{aligned}

(3)

Where

M e a n_{i n f o}

is the aggregated information from the previous iterations, A adjusts the position based on closeness to the promising solutions.

Attack Phase:

The last stage will then fine-tune the solution from exploration to exploitation by zooming in on the adjustments of the hyperparameters. The updated position is obtained with the formula:

\begin{aligned} X (t + 1) = L + V + H \end{aligned}

(4)

Where

L_{r} V

, and H are the launch parameters that are regulated by the performance metrics of Bi-GRU, namely RMSE and MAPE.

This is a three-stage process that systematically enables GTO to explore, refine, and fine-tune the hyperparameter configurations toward the optimal setting of Bi-GRU for SOH estimation. The inclusion of GTO guarantees that the Bi-GRU model provides high predictive accuracy while being able to adapt to the nonlinear and temporal dependencies in the dataset of batteries.

3.5.2 Models

Bidirectional Gated Recurrent Unit

A Bi-GRU neural network is an augmentation of a GRU neural network by the addition of a second layer.⁵¹ At any given time, this two-layer architecture imparts all pertinent contextual information regarding the input data to the output layer. The basic idea behind the Bi-GRU neural network is that an input sequence is processed by both a forward and a backward neural network, with the resulting outputs of both networks being aggregated within a single output layer.⁵¹ The Bi-GRU neural network with two layers and time series growth. Particularly, within the Bi-GRU neural network, the output of the hidden layer is computed at each time point from forward to backward in the forward layer, and from backward to forward in the backward layer. At each moment, the output layer presents the output results of the forward and reverse layers, which it normalizes.

\begin{aligned} \vec{h_{t}^{1}} & = f (\underset{x h^{1}}{w_{t} x_{t} + w_{h^{1} h^{1}} \to \vec{h_{t - 1}^{1}}} +_{h^{1}}) \end{aligned}

(5)

\begin{aligned} \overset{\leftarrow}{h_{t}^{1}} & = f (\underset{x h^{1}}{w_{t}^{\leftarrow} + x_{t} + w_{h^{1} h^{1}}^{\leftarrow} h_{t + 1}^{1}} + \underset{h^{1}}{\leftarrow}) \end{aligned}

(6)

\begin{aligned} \vec{h_{t}^{2}} & = f (w_{\vec{h^{1} h^{2}}} \vec{h_{t}^{1}} + w_{\vec{h^{2} h^{2}}} \vec{h_{t - 1}^{2}} + b_{\vec{h^{2}}}) \end{aligned}

(7)

\begin{aligned} \overset{\leftarrow}{h_{t}^{2}} & = f (w_{h^{1} h^{2}} \overset{\leftarrow}{h_{t}^{1}} + w_{h^{2} h^{2}} \overset{\leftarrow}{h_{t + 1}^{2}} + b_{h^{2}}) \end{aligned}

(8)

\begin{aligned} y_{t} & = g (_{w_{h^{2} y}} \vec{h_{t}^{2}} + w_{h^{2} y} \overset{\leftarrow}{h_{t}^{2}} + b_{y}) \end{aligned}

(9)

where

H

is the quantity of measures in the GRU cell and

\vec{h_{t}^{1}} \in R^{H}

and

\vec{h_{t}^{2}} \in R^{H}

are the signals of emission of the forward layer's hidden layer in the Bi-GRU neural network's first and second layers at the same time t, respectively. At time t,

a n d

\overset{\leftarrow}{h_{t}^{2}} \in R^{H}

represent the output vectors of the backward layer in the hidden layer of the Bi-GRU neural networks’ first and second layers, respectively.

y_{t} \in R^{T}

indicates the matching word's score on each label at a given time t.

x_{t}

represents the input to the neural network at the time

t, f (\cdot)

denotes the processing of the GRU neural network,

g (\cdot)

signifies the activation function (where

g (x)_{i} = \frac{e^{x_{i}}}{\sum_{k = 1}^{n} e^{x_{k}}}

), and

W

and

b

are the weight matrices that require learning.

Long Short-Term Memory

An artificial neural network (ANN) called LSTM can analyze sequential data, such as time series, audio, and text. Processing data with long-term dependencies where the output at a current time step requires knowledge from previous time steps benefits greatly from its use. For long periods, LSTM networks can preserve this information by using memory cells, input gates, output gates, and forget gates. These gates allow selective data storage and retrieval in the network by controlling information flow into and out of memory cells. The input gate controls the flow of data into the memory cell.⁵²

Gated Recurrent Unit

It was Cho et al.⁵³ who originally presented the GRU network. RNNs are based on the fundamental idea of determining outputs by considering inputs and the hidden state, which is found by squaring up previous outputs or hidden states. The GRU provides advanced data control in a hidden state with an update gate and a reset gate. Generally speaking, it can identify which data from the past may be removed from the concealed state and which data from the current inputs must be added. In contrast to long short-term memory, which has a cell structure and a unit consisting of three gates, the GRU has fewer parameters.⁵⁴

3.5.3 Optimizers

Giant Trevally Optimizer

The GTO technique, which is a metaheuristic algorithm, was inspired by the gigantic trevally's hunting behaviors.³⁷ Methods employed by the giant trevally to capture prey include patterned foraging, region selection for optimal hunting, and launching from the water. These strategies are implemented in a three-step procedure by the GTO algorithm: extensive search, area selection, and attack. The illustration of GTO is mentioned in Figure 11.

A)
Extensive Search

Figure 11.
The illustration of GTO.

To simulate the extensive journeys undertaken by gigantic trevallies in search of sustenance, the GTO method employs a computational model founded on Levy flights, which are a variation of the random stroll. This stage enhances the capability of the algorithm for exploration and assists in circumventing regional optimum. The equation utilized during this stage is visually represented as follows:
$\begin{aligned} X (t + 1) = B e s t_{p} \times R + (M a x i m u m - M i n i m u m) \times R + M i n i m u m \times l e v y (D i m) \end{aligned}$
(10)
where $X (t + 1)$ represents the big trevally's placement variable in the following iteration, $B e s t_{p}$ signifies the optimal position achieved, $R$ signifies an arbitrary number between 0 and 1, and $l e v y (D i m)$ signifies the Levy flight. B)
Choosing Area
The algorithm determines the optimal foraging region in this stage by considering the availability of sustenance within the search space. This behavior is mathematically replicated using the subsequent equation:
$\begin{aligned} x (t + 1) = B e s t_{p} \times A \times R + M e a n_{i n f o} - X i (t) \times R \end{aligned}$
(11)
where $A$ represents a position-changing parameter, $X i (t)$ represents the current position, and $R$ is an integer selected at random. $M e a n_{i n f o}$ denotes the efficient utilization of all information acquired from previous locations concerning these enormous trevallies. C)
Attacking
The final stage of the algorithm mimics the attack of its victim by the trevally. The trevally's behavior is influenced by light refraction, which also affects its vision. To mimic this manner, the program determines how distorted the image is. V using Snell's equation and then mimicking: Trevally's assault
$\begin{aligned} X (t + 1) = L + V + H \end{aligned}$
(12)
By setting $V$ for visual distortion, $X (t + 1)$ for the subsequent position, $X (t + 1)$ for the launch speed, and $H$ for the launching slope function, the algorithm can transition from the exploration phase to the exploitation phase. The framework of GTO has been demonstrated in Figure 12.
Cuckoo Search Algorithm

Figure 12.
The framework of GTO.

To elaborate on the CS algorithm, let us examine the reproductive customs of some intriguing cuckoo species. Following this, we will outline the stages and fundamental concepts of the CS algorithm. A.
Cuckoo breeding behavior
Cuckoos are captivating avian species due to their formidable vocalizations and predatory reproductive strategy. Certain species, such as Anthia cuckoos and Guira cuckoos, employ the strategy of extracting eggs from communal nests occupied by other birds to increase the probability of successful hatching. Many species use mandatory brood parasitism, which is a kind of reproduction whereby they lay their eggs in the nests of various host birds, frequently other species. Nest usurpation, intraspecific brood parasitism, and cooperative reproduction are the three main forms of brood parasitism. There might be a conflict between the intruding cuckoos and some of their hosts. As soon as the host avian discovers that the eggs do not belong to it, it will either abandon the nest and build a new one elsewhere or jettison the foreign eggs. Similar to the New World brood-parasitic Tapera, female parasitic cuckoos often exhibit a high degree of specialization in reproducing the hue and design of the eggs of a limited number of host species. This is owing to the evolutionary nature of certain cuckoo species. Due to the decreased probability of their embryos being abandoned, they are capable of reproductive freedom. Additionally, several species exhibit extraordinary egg-laying timing. Frequently, cuckoo parasites choose nesting sites where the host bird has recently laid eggs. Eggs of the cuckoo typically emerge slightly earlier than the eggs of the host. Upon hatching, the first cuckoo baby exhibits an instinctual behavior wherein it forcibly pushes the host eggs from the nest, thereby increasing the proportion of food provided by the host avian. Additionally, research indicates that cuckoo babies may imitate the calls of their hosts to secure additional feeding opportunities. B.
Levy flights
Wildlife engages in hunting behavior that is either quasi-random or random. As the likelihood of transitioning to the subsequent location and the animal's current position/state determine the subsequent movement, the foraging route of an animal is essentially a random walk. Its chosen course of action is dictated by an implicit probability that can be mathematically expressed. For example, several studies have demonstrated that the flying characteristics of various insects and animals exhibit the characteristic features of Levy flights. Reynolds and Frye recently conducted research that indicates that fruit flies, scientifically known as Drosophila melanogaster, investigate their surroundings by traversing a series of linear flight paths interspersed with abrupt 90-degree turns. Since then, this behavior has been implemented in optimization and optimal search, yielding promising initial results. C.
Cuckoo search
Presently, the three idealized principles listed below are used to succinctly delineate the new CS approach:
A single egg is laid by each cuckoo, which is subsequently deposited in a nest that is selected at random.

Nests that are of superior quality will generate eggs (solutions) that are of the utmost quality and transmit them to succeeding generations.

A predetermined number of host colonies are available, and the probability that a host will discover an extraterrestrial egg is denoted by $P_{a} \in [0, 1]$ . In this situation, the host avian is faced with a decision: either discard the egg or abandon the nest to build a new one in a different location.
Replace a proportion $P_{a}$ of the $n$ nests with new ones containing new random answers in novel places to simplify this final assumption. Simply put, the objective function can be used to represent the fitness or quality of a solution to a maximizing problem.

An instance of a Levy flight occurs when new solutions $X^{(t + 1)}$ are generated, such as for the cuckoo i.
$\begin{aligned} x_{i}^{(t + 1)} = x_{i}^{(t)} + α \oplus L\'{e}vy (λ) \end{aligned}$
(13)
The step size, denoted as $α > 0$ , should correspond to the scales of the interest problem. As a general rule, $α = o (1)$ a be employed. A product $\oplus$ represents multiplications performed on an entry-by-entry. In essence, Levy flights generate a random walk, and the random steps of large steps are derived from a Levy distribution.
$\begin{aligned} Levy \sim u = t^{- λ}, (1 < λ \leq 3) \end{aligned}$
(14)
It possesses an infinite variance and an infinite mean. In this case, the succession of leaps and steps executed by a cuckoo generates a random walk process that adheres to a power-law step-length distribution characterized by a substantial tail. The illustration and framework of CS may be observed in Figures 13 and 14.
Particle Swarm Optimization

Figure 13.
The illustration of CS.

Figure 14.
The framework of CS.

The goal of PSO is to replicate the cooperative behaviors of a school of fish or a flock of birds to get the best possible outcomes. Although the precise position of the food source may not be immediately apparent, the swarm will nonetheless adhere to a set of guidelines to reach it. For the swarm to find the food source, cooperation is essential. In the end, swarms of fish or birds will reach the almost ideal solution simultaneously. These three principles separation, alignment, and cohesiveness allow a bird swarm to effectively traverse the search space and find the correct answer.⁵⁵
Genetic Algorithm
To solve optimization and search issues, the genetic algorithm is a computational method that simulates the mechanism of natural selection. A group of possible answers known as individuals is produced using this method. Then, these individuals are subjected to genetic processes like selection, recombination, and mutation to produce new individuals. The evaluation method used in this study is iterative, meaning it is repeated over several generations until a workable answer is found. As a result, GA is widely used in several fields, such as research, engineering, and finance.⁵⁶
3.6 Evaluation metrics

To assess the model's ability to accurately predict output values from input data, regression models are evaluated using evaluation criteria.

The preciseness of a model is quantified as a percentage under the acronym MAPE. By multiplying the actual value by the total sum of the difference between the predicted and actual values, and subsequently aggregating the resulting percentages, it is determined. The precision of the model is assessed by utilizing this value, and the model is more accurate when the MAPE is lower.

\begin{aligned} M A P E = (\frac{1}{n} \sum_{i = 1}^{n} | \frac{y_{i} - {\hat{y}}_{i}}{y_{i}} |) \times 100 \end{aligned}

(15)

Where

y_{i}

and

{\hat{y}}_{i}

represent the actual and predicted values of SOH, respectively. In particular, MAPE is capable of providing an intuitive result for applications with specific accuracy needs for the predictions in practical terms.

A model's fit to the data is quantified by its Coefficient of Determination ( $R^{2}$ ) score. To compute the sum of the squares of the differences between the actual and predicted values, divide the total by the total of the dimensions of the difference between the actual results and the actual values’ mean. Subtract this amount from 1. The more closely this number approaches 1, the more accurate the model is considered to be.

\begin{aligned} R^{2} = 1 - \frac{\sum_{i = 1}^{n} {(y_{i} - {\hat{y}}_{i})}^{2}}{\sum_{i = 1}^{n} {(y_{i} - \bar{y})}^{2}} \end{aligned}

(16)

The term “root mean square error” refers to the square root of the mean square of the variations between the values that were anticipated and those that were observed. A decreased RMSE denotes a smaller variation between the actual readings and the predictions of the model, suggesting better prognostication effectiveness. The following is the calculating formula:

\begin{aligned} R M S E = \sqrt{\frac{\sum_{i = 1}^{n} {(y_{i} - {\hat{y}}_{i})}^{2}}{n}} \times 100 \end{aligned}

(17)

Where

y_{i}

denotes the real value of SOH, the estimated value of SOH is

{\hat{y}}_{i}

, and n signifies the overall number of observations. A vital advantage of RMSE is that in this approach, greater mistakes are highly penalized; thus, it will be appropriate to predict accuracy concerning various tasks such as SOH estimation.

4 Result and discussion

This study evaluates many algorithms, including Bi-GRU, CS-Bi-GRU, and GTO-Bi-GRU, using NASA battery datasets labeled B5, B6, B7, and B18 batteries. Then the results of these algorithms are carefully analyzed and recorded. The goal is to determine the most accurate and effective way to predict SOH. Among the evaluation criteria used were $R^{2}$ , MAPE and RMSE scores. Determining the optimal technique for battery SOH prediction requires knowledge of test results. The evaluation of the results of the model is shown in Tables 1 and 2. SOH estimation integration of multiple features and models necessitates integration and selection with care to ensure precision and robustness. SOH estimation techniques are susceptible to substantial influence from the models and characteristics they employ; therefore, a comprehensive assessment is required. It is critical to accurately assess the condition of batteries to guarantee their durability and dependability. The intricate internal degradation mechanisms of batteries, nevertheless, pose a significant challenge in estimating SOH. The investigators have proposed several strategies to enhance battery SOH forecasts and bring them closer to real results. The main goal of this research is to determine which hybrid algorithm best, predicts the SOH. The effectiveness of the Bi-GRU model has been evaluated both with and without an optimizer. The Bi-GRU neural network model is appropriate for battery life prediction, as evidenced by the RMSEs of the neural network in the SOH prediction results being all less than 3.6% and the MAPE being less than 1.3%. Utilizing optimizers such as GTO and CS improves the outcomes obtained from the model. Table 1 shows how the use of optimizers led to improved outcomes. It was found that using the CS optimizer reduced the RMSE score by comparing the results. CS-BI-GRU reduced RMSE scores to less than 3% and increased the $R^{2}$ score to 0.99. The comparative study investigation's findings show that the GTO-Bi-GRU model outperformed the CS-Bi-GRU model based on the RMSE value decreased. With a 0.9969 $R^{2}$ score, GTO-BI-GRU demonstrated high precision compared to other models. The GTO-BI-GRU model was shown to be a highly accurate, trustworthy, and performing model. 20% of the data were forecasted and 80% of the data were trained to get more accurate SOH prediction results. It was found that the training and assessment datasets had exceptional accuracy. When it comes to SOH prediction, the GTO-BI-GRU model is far more accurate than those that came before it. The strategy's efficacy has been linked to its transparent approach to forecasting developments, which raises the precision of model projections. For a more in-depth analysis and review, see Figures 15 to 18, which extensively examines the performance of the models. Examining the differences between these criteria helps to improve the evaluation of the effectiveness of the models as a whole. Analyzing any trends visible in the graphic below will help emphasize the stability of the model. Performance comparison for SOH prediction in lithium-ion batteries by three deep learning models, namely Long Short-Term Memory (LSTM) ated Recurrent Unit (GRU), and Bi-GRU, is shown in Table 1. The models are assessed on four different battery cells (B5, B6, B7, and B18) using three important performance metrics: $R^{2}$ , RMSE, and MAPE. These metrics will help evaluate the precision and predictive power of models.

Figure 15.

Comparing various models across significant metrics (RMSE, $R^{2}$ , and MAPE) in the results for cell B5.

Figure 16.

Comparing various models across significant metrics (RMSE, $R^{2}$ , and MAPE) in the results for cell B6.

Figure 17.

Comparing various models across significant metrics (RMSE, $R^{2}$ , and MAPE) in the results for cell B7.

Figure 18.

Comparing various models across significant metrics (RMSE, $R^{2}$ , and MAPE) in the results for cell B18.

Table 1.

The results of evaluation criteria for various models in 5, 6, 7, and 18 cells.

Models	LSTM			GRU			Bi-GRU
Metrics	$R^{2}$	RMSE %	MAPE %	$R^{2}$	RMSE %	MAPE %	$R^{2}$	RMSE %	MAPE %
B5	0.9734	2.6081	1.4937	0.9788	2.4492	1.3661	0.985	2.2608	1.2537
B6	0.9726	3.7349	1.2915	0.9757	3.6259	1.1614	0.9811	3.5838	1.1217
B7	0.9714	2.8276	0.9004	0.979	2.6509	0.8369	0.9824	2.422	0.7519
B18	0.9689	2.1928	1.1149	0.9773	2.018	1.0425	0.9799	1.9092	0.954

Table 2.

Evaluation criterion results for various hybrid models in cells 5, 6, 7, and 18.

Models	PSO-Bi-GRU			GA-Bi-GRU			CS-Bi-GRU			GTO-Bi-GRU
Metrics	$R^{2}$	RMSE %	MAPE %	$R^{2}$	RMSE %	MAPE %	$R^{2}$	RMSE %	MAPE %	$R^{2}$	RMSE %	MAPE %
B5	0.9903	1.9734	0.9276	0.9929	1.5843	0.6355	0.9931	1.5333	0.6276	0.9969	1.0282	0.5108
B6	0.9862	3.3295	0.9077	0.987	3.0273	0.849	0.9874	2.9293	0.8316	0.9917	2.3717	0.7419
B7	0.9887	2.0836	0.6954	0.9902	1.7639	0.6572	0.9909	1.7452	0.6227	0.9948	1.3124	0.5514
B18	0.9806	1.8694	0.9122	0.9817	1.8048	0.8636	0.9816	1.825	0.866	0.9882	1.4584	0.7319

These results indeed reflect that Bi-GRU tends to outperform the LSTM and GRU models on SOH predictions. This is because all cells produce high values of $R^{2}$ for the Bi-GRU, representing higher complexity as it learns more about the trend of battery degradations, while the results of the model have lower variance in evaluating the error metrics. This is attributed to the bidirectional architecture that captures dependencies on both the forward and backward directions, hence doing a better feature extraction and learning in sequences. Compared with LSTM, GRU performs much better, with larger $R^{2}$ values and smaller scores of RMSE and MAPE, respectively, testifying that it is effective for modeling SOH trends. For example, in Cell B6, GRU achieves an $R^{2}$ value of 0.9757, higher than that of LSTM (0.9726), while its RMSE is lower (3.6259% and 3.7349%), meaning higher accuracy. This is because GRU has a more simplified gating mechanism while keeping temporal dependencies well, which can learn faster. On the other hand, LSTM indicates the lowest prediction accuracy and higher values of RMSE and MAPE for all cells. This hence makes LSTM more sensitive in reflecting the SOH degradation trend efficiently. In this respect, Cell B5 is outstanding, with LSTM recording the highest RMSE of 2.6081% and MAPE of 1.4937%, thus being the least effective among the three models. This is because the complexity of gating mechanisms in LSTM made it less optimal for the given dataset. On the whole, the comparison revealed that Bi-GRU is chosen as the high-efficiency model in SOH estimation, which strikes the optimal balance between accuracy and efficiency. The optimization performance of PSO, GA, CS, and GTO for the Bi-GRU model is given in Table 2 for predicting SOH. From the outcomes, GTO-Bi-GRU ensures the best in $R^{2}$ values while guaranteeing the minimum values for the RMSE and MAPE estimation of all considered battery cells. This clearly established the fact that the proposed approach, GTO-BiGRU, had higher predictive accuracy for modeling a nonlinear degradation pattern of a battery.

GA-Bi-GRU surpasses PSO-Bi-GRU in accuracy, especially for B5 and B7, though GTO-Bi-GRU remains the most precise model by showing the minimum values of RMSE and MAPE. Contrarily, PSO-Bi-GRU represents the lowest predictive accuracy, with higher RMSE values of B6 (3.3295%) and B7 (2.0836%), which indicates poor convergence ability. The superiority of GTO-Bi-GRU in performance is attributed to the effective balancing between exploration and exploitation to provide the optimal hyperparameters of the model. These results validate the main contribution of optimization for enhancing SOH estimation and ascertaining GTO-Bi-GRU as the most reliable and accurate method; hence, this qualifies it to be one of the prominent approaches for battery health monitoring in electric vehicle applications.

Figures 15 to 18 represent the testing performed on cells B5, B6, B7, and B18, where three models are compared: Bi-GRU, CS-Bi-GRU, and GTO-Bi-GRU. The analysis is conducted with three significant metrics— $R^{2}$ , RMSE, and MAPE to determine which model achieves high efficiency in forecasting the battery SOH. Figure 15. indicates that the GTO-Bi-GRU model provides the lowest values in Cell B5 for all metrics and the best results for all the compared models. The reason is that it is possible to minimize the prediction error while forecasting the battery state with this model. Figure 16, the testing evaluation results for Cell B6, reflect similar behavior, in which the GTO-Bi-GRU model is significantly lower than the others in terms of error reduction, thus validating the robustness across the various cells. Figure 17 illustrates that in the case of Cell B7, the GTO-Bi-GRU performance still has lower error values when compared with those of the remaining cells. The adaptability and reliability of any configuration are further proved. Results for test evaluation of cell B18 are shown in Figure 18, showing well-maintained superior performance in the GTO-Bi-GRU model against time and consequently its capability with nonlinear and dynamic characteristics of battery degradation data. It can be observed that for all figures, the GTO-Bi-GRU model consistently outperforms Bi-GRU and CS-Bi-GRU, which further justifies that the fusion of GTO and Bi-GRU facilitates the improvement of predictive accuracies. The results indicate that the GTO-Bi-GRU model is robust and reliable, thus being practical and efficient for battery state prediction in different scenarios.

NASA's battery dataset has been selected because it is one of the most credible and widely accepted datasets in the research fraternity in the study of lithium-ion battery aging and degradation. This dataset contains comprehensive charge/discharge cycles, with minute records of voltage, current, capacity, and temperature, which are very important for model development and validation in predicting the SOH. Although the dataset reflects typical conditions in laboratory testing, it provides a controlled environment for studying key aging mechanisms and serves as a paradigmatic basis for initial studies in this area. Furthermore, being publicly available and well-documented, this dataset allows for reproducibility and benchmarking of the most important parts of any scientific research. Other areas where future research can be built on the knowledge learned from this work include commercial EV systems or on-field operation data. This will offer insight into how the batteries perform under real-world conditions, including wide ranges of charging behavior, dynamic temperature fluctuations, and mechanical stresses occurring in actual vehicle usage. These would minimize the difference between lab-generated datasets like those from NASA and complicated, uncontrollable environmental ones in field operation. Future work will also include integrating multi-source data that covers different chemistries, configurations, and lithium-ion battery use patterns. The resultant models will be able to generalize much better across various EV platforms and usage scenarios. Future studies can develop the predictive accuracy, scalability, and practical relevance of the proposed methodologies for SOH prediction in modern EV battery technologies by combining strengths from controlled laboratory datasets with field-tested data.

5 Conclusion

The significance of energy in driving human activities is paramount, impacting essential sectors such as transportation, power generation, heating, and industrial operations. However, the distinction between renewable and non-renewable energy sources underscores a clear divide in sustainability and environmental impact. While renewable sources offer the potential for a more environmentally friendly future, the finite nature of non-renewable fuels highlights the urgent need to transition to cleaner alternatives. Recent advancements in energy conversion and storage technologies, particularly in electric vehicles and mobile electronics, have led to significant improvements. Among these breakthroughs, lithium-ion batteries have emerged as leaders due to their high energy density, long lifespan, and potential to reduce environmental pollution.

This study carefully considers the effects of battery aging and internal responses on capacity degradation during charge and discharge cycles. The investigation was based on battery datasets (B5, B6, B7, and B18) provided by NASA. The features analyzed in this study include voltage-charging-p1, voltage-charging-p2, voltage-discharging-p1, voltage-discharging-p2, charging-terminal-current-m1, and discharging-terminal-current-m1, all extracted from voltage and current data.

The evaluation criteria results unequivocally demonstrate that Model GTO-Bi-GRU was chosen as the proposed approach in this paper for battery SOH prediction because of its high accuracy and efficient operation. Tables 1 and 2 show that for various testing sets, the RMSE was less than 2.4%, MAPE was less than 0.75%, and $R^{2}$ reached to 0.9969 score. This demonstrated how dependable the model was.

Statements and declarations

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

References

Tribus

McIrvine

. Energy and information. Sci Am 1971; 225: 179–190.

Khan

Dilshad

Khalid

, et al. Review of energy storage and transportation of energy. Energy Storage 2019; 1: e49.

Güney

. Renewable energy, non-renewable energy and sustainable development. Int J Sustain Dev World Ecol 2019; 26: 389–397.

Sayed

, et al. Renewable energy and energy storage systems. Energies (Basel) 2023; 16: 1415.

Adewuyi

Awodumi

. Renewable and non-renewable energy-growth-emissions linkages: review of emerging trends with policy implications. Renew Sustain Energy Rev 2017; 69: 275–291.

Abas

Kalair

Khan

. Review of fossil fuels and future energy technologies. Futures 2015; 69: 31–49.

Hassan

Algburi

Sameen

, et al. Green hydrogen: a pathway to a sustainable energy future. Int J Hydrogen Energy 2024; 50: 310–333.

, et al. Optimal battery thermal management for electric vehicles with battery degradation minimization. Appl Energy 2024; 353: 122090.

Almalki

. Exploring students’ perspectives on the implementation of a self-organised learning environment: SOLE via mobile devices. Int J Mob Blended Learn (IJMBL) 2024; 16: 1–19.

10.

Zheng

Che

, et al. Thermal state monitoring of lithium-ion batteries: progress, challenges, and opportunities. Prog Energy Combust Sci 2024; 100: 101120.

11.

Rashid

. Review of: Nano supercapacitors (supercapacitors or electrochemical nanocapacitors). Qeios 2024: 1–2. doi: 10.32388/67gwcf

12.

Abouemara

Shahbaz

Mckay

, et al. The review of power generation from integrated biomass gasification and solid oxide fuel cells: current status and future directions. Fuel 2024; 360: 130511.

13.

Kim

Song

Son

D-Y

, et al. Lithium-ion batteries: outlook on present, future, and hybridized technologies. J Mater Chem A Mater 2019; 7: 2942–2964.

14.

Omar

, et al. Aging and degradation of lithium-ion batteries. In: Rechargeable lithium batteries. Sawston, Cambridge: Elsevier, Woodhead Publishing, 2015, pp. 263–279.

15.

Smuts

Scholtz

Wesson

. A critical review of factors influencing the remaining driving range of electric vehicles. In: 2017 1st international conference on next generation computing applications (NextComp), 2017, pp.196–201. IEEE.

16.

Lawder

, et al. Battery energy storage system (BESS) and battery management system (BMS) for grid-scale applications. Proc IEEE 2014; 102: 1014–1030.

17.

Safavi

Bazmohammadi

Vasquez

, et al. The SOH is an evaluative metric utilized to assess the service life of a battery, serving as an indicator of its degree of aging and dependability. Nevertheless, the SOH cannot be determined owing to the intricate internal degradation mechanism of batteri. Electronics (Basel) 2024; 13: 587.

18.

Safavi

Bazmohammadi

Vasquez

, et al. Battery state-of-health estimation: a step towards battery digital twins. Electronics (Basel) 2024; 13: 587.

19.

Lipu

MSH

, et al. A review of state of health and remaining useful life estimation methods for lithium-ion battery in electric vehicles: challenges and recommendations. J Clean Prod 2018; 205: 115–133.

20.

Bian

Wei

, et al. A novel model-based voltage construction method for robust state-of-health estimation of lithium-ion batteries. IEEE Trans Ind Electron 2020; 68: 12173–12184.

21.

Oji

Zhou

, et al. Data-driven methods for battery soh estimation: survey and a critical analysis. IEEE Access 2021; 9: 126903–126916.

22.

Dunkel

Hänggi

. Relativistic Brownian motion. Phys Rep 2009; 471: 1–73.

23.

Wang

. Thermal-electrochemical modeling of battery systems. J Electrochem Soc 2000; 147: 2910.

24.

Lin

Meng

, et al. A multi-feature-based multi-model fusion method for state of health estimation of lithium-ion batteries. J Power Sources 2022; 518: 230774.

25.

Yang

Zhang

Pan

, et al. A novel Gaussian process regression model for state-of-health estimation of lithium-ion battery using charging curve. J Power Sources 2018; 384: 387–395.

26.

Liu

She

, et al. Comparative study of incremental capacity curve determination methods for lithium-ion batteries considering the real-world situation. IEEE Trans Power Electron 2022; 37: 12563–12576.

27.

Wen

Chen

, et al. SOH Prediction of lithium battery based on IC curve feature and BP neural network. Energy 2022; 261: 125234.

28.

Dai

Wang

Huang

, et al. Lightweight state-of-health estimation of lithium-ion batteries based on statistical feature optimization. Renew Energy 2024; 222: 119907.

29.

, et al. Remaining useful life and state of health prediction for lithium batteries based on differential thermal voltammetry and a deep-learning model. J Power Sources 2022; 548: 232030.

30.

Zhang

, et al. An adaptive battery capacity estimation method suitable for random charging voltage range in electric vehicles. IEEE Trans Ind Electron 2021; 69: 9121–9132.

31.

Wang

Zhu

Dai

. An efficient state-of-health estimation method for lithium-ion batteries based on feature-importance ranking strategy and PSO-GRNN algorithm. J Energy Storage 2023; 72: 108638.

32.

Wei

Dong

Chen

. Remaining useful life prediction and state of health diagnosis for lithium-ion batteries using particle filter and support vector regression. IEEE Trans Ind Electron 2017; 65: 5634–5643.

33.

Ahmad

Jun

, et al. Comparative study of deep learning models for automatic detection of metastases in H&E stained images. In: 2021 4th International Conference on Computing & Information Sciences (ICCIS), 2021, pp. 1–6. IEEE.

34.

Sun

, et al. Parallel multi-swarm cooperative particle swarm optimization for protein–ligand docking and virtual screening. BMC Bioinformat 2022; 23: 201.

35.

Ahmad

Jun

. Sentiment analysis of cancer patients about their treatment during the peak time of pandemic COVID-19. In: 2021 4th International Conference on Computing & Information Sciences (ICCIS), 2021, pp. 1–5. IEEE.

36.

, et al. Bidirectional gated recurrent unit neural network for Chinese address element segmentation. ISPRS Int J Geoinf 2020; 9: 635.

37.

Sadeeq

Abdulazeez

. Giant trevally optimizer (GTO): a novel metaheuristic algorithm for global optimization and challenging engineering problems. Ieee Access 2022; 10: 121615–121640.

38.

Crompton

. T. R. Crompton, Battery reference book. Newnes, 2000, isbn: 075064625X, 9780750646253. Oxford, United Kingdom: Newnes, 2000.

39.

Brinkley

. Typical oxidation-reduction reactions in general chemistry. J Chem Educ 1929; 6: 1894.

40.

Lauro

Burrow

Mullins

. Restructuring the lithium-ion battery: a perspective on electrode architectures. EScience 2023; 3: 100152.

41.

Blomgren

. The development and future of lithium ion batteries. J Electrochem Soc 2016; 164: A5019.

42.

Zubi

Dufo-López

Carvalho

, et al. The lithium-ion battery: state of the art and future perspectives. Renew Sustain Energy Rev 2018; 89: 292–308.

43.

Vennam

Sahoo

Ahmed

. A survey on lithium-ion battery internal and external degradation modeling and state of health estimation. J Energy Storage 2022; 52: 104720.

44.

Meda

Lal

Sushantha

, et al. Solid electrolyte interphase (SEI), a boon or a bane for lithium batteries: a review on the recent advances. J Energy Storage 2022; 47: 103564.

45.

Zhang

Wang

Schaltz

, et al. Lithium-ion battery calendar aging mechanism analysis and impedance-based state-of-health estimation method. J Energy Storage 2023; 64: 107029.

46.

Karger

Schmitt

Kirst

, et al. Mechanistic calendar aging model for lithium-ion batteries. J Power Sources 2023; 578: 233208.

47.

Feng

Liu

, et al. State estimation for advanced battery management: key challenges and future trends. Renew Sustain Energy Rev 2019; 114: 109334.

48.

M-F

Liu

Jiang

, et al. A review on state of health estimations and remaining useful life prognostics of lithium-ion batteries. Measurement 2021; 174: 109057.

49.

Zhang

Liu

. State of health estimation for lithium-ion batteries on few-shot learning. Energy 2023; 268: 126726.

50.

Sadeeq

Abdulazeez

. Giant trevally optimizer (GTO): a novel metaheuristic algorithm for global optimization and challenging engineering problems. Ieee Access 2022; 10: 121615–121640.

51.

Zhang

, et al. Epileptic seizure detection based on bidirectional gated recurrent unit network. IEEE Trans Neural Syst Rehabil Eng 2022; 30: 135–145.

52.

, et al. A review of recurrent neural networks: LSTM cells and network architectures. Neural Comput 2019; 31: 1235–1270.

53.

Cho

. On the properties of neural machine translation: Encoder-decoder approaches. arXiv preprint arXiv:1409.1259, 2014.

54.

Cho

. On the properties of neural machine translation: Encoder-decoder approaches. arXiv preprint arXiv:1409.1259, 2014.

55.

Reynolds

. Flocks, herds and schools: a distributed behavioral model. In: Proceedings of the 14th annual conference on Computer graphics and interactive techniques, 1987, pp.25–34.

56.

Gülmez

Korhan

. COVID-19 vaccine distribution time optimization with Genetic Algorithm. 2022.