SSA-BiLSTM Model-Based SOH Estimation for Lithium-Ion Batteries

Abstract

The State of Health (SOH) of a battery is an important indicator for measuring the performance degradation of batteries. In view of the deficiencies of existing SOH estimation methods in feature processing and model accuracy, this paper conducts research on high-precision SOH estimation methods for lithium-ion batteries. A BiLSTM model optimized by the Sparrow Search Algorithm (SSA) is adopted for SOH estimation. The SSA-BiLSTM model is constructed, and the experiments are conducted on multiple types of battery datasets, such as NCM811 and LFP, and the cross-validation strategy is used to evaluate the model’s performance. The experimental results show that the SOH prediction system software developed based on this model has the functions of rapid estimation and three-dimensional trend visualization. The paper verifies the functions of the SOH prediction system software developed by the model, which has practical reference significance for the development and application of SOH estimation systems in energy storage scenarios.

1. Introduction

Research on the State of Health (SOH) of lithium-ion batteries is deepening continuously, which has led to the proposal and application of many new assessment technologies and theoretical methods. Accurate assessment of the SOH of lithium-ion batteries not only directly reflects their current level of service life, but also effectively alerts to potential safety risks that may arise due to the degradation of battery performance. Recent studies have extensively documented the complex degradation mechanisms, failure modes, and predictive maintenance strategies essential for energy storage systems [1,2,3]. Currently, the estimation methods for the SOH of lithium-ion batteries can be roughly divided into three categories: the first is the direct estimation method [4], the second is the method based on mechanism modeling, and the third is the machine learning data-driven approach. The basic principles and development paths of these three methods are shown in Figure 1.

Direct Estimation Method [5]: This method is based on observable battery parameters and infers the battery’s health level through the analysis of data such as voltage, current, impedance, and temperature. Common techniques include the open-circuit voltage method [6] (OCV), capacity measurement method [7], and electrochemical impedance spectroscopy method [8] (EIS). It has the advantages of low computational complexity and simple implementation, but it is highly dependent on the accuracy of the measurement equipment and cannot support online estimation. Therefore, it is not suitable for long-term dynamic monitoring in practical applications and is often used as an auxiliary basis for other estimation methods. Model-driven Method [9]: The model method has high estimation accuracy and mainly includes empirical/semiempirical models, electrochemical models, and equivalent circuit models [10]. The empirical model is established by analyzing the statistical laws of battery performance degradation. This method has low implementation costs and high computational efficiency, and also has good prediction accuracy. However, corresponding mathematical models need to be established for different battery models, resulting in limited generalization ability. In addition, the accuracy of model construction has a significant impact on the final prediction result and cannot meet the requirements of online estimation. Data-driven Method [11]: Data-driven technology relies on rich historical operation data and uses machine learning algorithms such as particle filters [12] (PF), neural networks [13] (NN), support vector machines [14] (SVM), and Gaussian process regression [15] (GPR) to model and predict battery state characteristics. This method does not require physical modeling or in-depth chemical processes. It only needs to extract and correlate the features of battery aging cycle data to build an SOH mapping model [16], which has strong real-time and flexibility. Compared with model-based methods, data-driven strategies are more adaptable to actual conditions and differences in various battery types, have received extensive attention from researchers in recent years, and have increasingly become an important research direction in the field of battery SOH assessment. Specifically, data-driven techniques, ranging from fundamental machine learning to automated machine learning (AutoML) and Bayesian-optimized frameworks, have demonstrated significant adaptability across diverse operational profiles [17,18,19,20]. These methods show high accuracy in SOH prediction, have strong autonomous learning ability, and are suitable for handling nonlinear systems. This method does not rely on the physical structure or chemical properties of the battery, but only requires the collection of parameter data during the operation process for effective prediction. However, it requires a large number of samples, the training time increases with the increase in data volume, the model contains many hyperparameters, and the prediction performance is easily affected by the parameter settings. To mitigate these challenges, advanced hybrid architectures, such as combinations of Convolutional Neural Networks (CNN), Temporal Convolutional Networks (TCN), and Graph Neural Networks (GNN), have been actively proposed to capture spatio-temporal dependencies more efficiently [21,22,23,24].

This paper presents a BiLSTM model optimized based on the Sparrow Search Algorithm (SSA): Firstly, it introduces the temporal modeling capabilities of RNN, LSTM and BiLSTM. Secondly, it designs the SSA algorithm to conduct global optimization of the hyperparameters of BiLSTM. Finally, through experiments, it verifies the prediction accuracy of SSA-BiLSTM on multiple battery datasets, with the maximum error not exceeding 2.35%, significantly outperforming traditional methods. Ultimately, it summarizes the research results of the entire paper, points out the advantages of the proposed method in SOH estimation, and proposes future improvement directions for the prediction lag problem of the model during the capacity regeneration stage.

2. Health Characteristics

2.1. The Internal Structure and Working Principle of Lithium-Ion Batteries

Lithium-ion batteries are mainly composed of five key components:

(1)

Battery casing: Common materials include steel casings, aluminum casings, nickel-plated iron shells, and flexible aluminum-plastic films, which serve to protect the cells and provide structural support.

(2)

Electrolyte: Made by mixing high-purity organic solvents, lithium salts, and functional additives in a certain proportion, it is responsible for the ion conduction between the positive and negative electrodes, directly influencing the energy density and voltage performance of the battery.

(3)

Separator material: Generally made of microporous membranes of polyethylene or polypropylene, it ensures the passage of lithium ions while preventing direct contact of the electrodes, thus maintaining the stability of the internal structure.

(4)

Positive electrode material: Depending on the performance requirements, materials such as lithium cobalt oxide and lithium iron phosphate can be selected. It is the main active substance for lithium-ion insertion and extraction, determining the energy output and safety characteristics of the battery.

(5)

Negative electrode material: Usually made of graphite-based carbon materials, supplemented by binders and conductive additives, and coated on copper foil, it is responsible for energy storage and release, possessing advantages such as abundant resources and electrochemical stability.

Lithium-ion batteries are rechargeable secondary batteries that achieve energy storage and conversion through the reversible migration of lithium ions between the electrodes [25]. During charging, an external power source drives lithium ions to be released from the positive electrode and embedded into the negative electrode through the electrolyte [26]; during discharging, lithium ions return from the negative electrode to the positive electrode, simultaneously releasing electrical energy. This process is vividly referred to as the “chaise longue effect” due to the back-and-forth movement of the ions. Figure 2 illustrates this working principle.

Take the lithium manganate (L_iM_n2O₄) battery as an example. Its charging process involves multiple electrochemical reactions. Under the influence of an external power source, energy conversion occurs within the battery. L_iM_n2O₄ decomposes and releases lithium ions (L_i⁺) and electrons (e⁻). Subsequently, these lithium ions migrate to the negative electrode area with the assistance of the electrolyte, and finally combine with graphite material to form the intercalated lithium compound Li_xC₆. This series of reactions collectively completes the process of converting electrical energy into chemical energy.

2.2. Selection of Evaluation Parameters for Lithium-Ion Battery State of Health (SOH) Assessment

2.2.1. The Definition and Calculation Method of SOH

SOH (State of Health) is an important indicator for assessing the degree of performance degradation of lithium-ion batteries, quantifying the retention rate of current capacity relative to the initial capacity in percentage form. As the number of cycles increases, battery aging is manifested as capacity reduction and an increase in internal resistance. Since SOH cannot be directly measured, it is usually evaluated through the following indirect parameters:

(1)

Defining the SOH based on battery capacity:

$$SOH={\displaystyle \frac{c_{now}}{c_0}}\times 100\mathrm{\%}$$

(1)

In this formula, $C_{now}$ represents the current effective capacity of the battery, while C₀ corresponds to its designed rated capacity. In engineering practice, using capacity parameters to assess the SOH is the most common method.

(2)

SOH is defined based on the internal resistance of the battery:

$$SOH={\displaystyle \frac{R_{EOL}-R_C}{R_{EOL}-R_{new}}}\times 100\mathrm{\%}$$

(2)

In this expression, $R_{EOL}$ refers to the internal resistance value of the battery when it reaches the termination condition of its service life, which is usually set at 200% of the initial internal resistance, $R_C$ reflects the real-time internal resistance status of the battery, while $R_{new}$ represents the reference internal resistance of the battery in its brand-new state. Since the increase in internal resistance is significantly correlated with the degree of battery degradation, this parameter is widely used in the quantitative assessment of SOH.

(3)

Define SOH from the perspective of battery power:

$$SOH={\displaystyle \frac{Q_{now-max}}{Q_{new-max}}}\times 100\%$$

(3)

In this mathematical model, $Q_{now-max}$ represents the real-time maximum discharge capacity of the tested battery, while $Q_{new-max}$ corresponds to its factory-calibrated maximum discharge capacity. This discharge-quantity-based assessment method is equivalent to the capacity method and both can effectively quantify the health status indicators of the battery.

(4)

Define SOH from the perspective of the remaining battery cycle times:

$$SOH={\displaystyle \frac{{Cnt}_{remain}}{{Cnt}_{total}}}\times 100\%$$

(4)

In this expression, ${Cnt}_{remain}$ is used to represent the current available cycle life of the battery, while ${Cnt}_{total}$ represents the upper limit of its designed cycle life.

2.2.2. Selection of SOH Evaluation Parameters for Lithium-Ion Batteries

The aging process of lithium-ion batteries involves complex internal reactions that are difficult to observe directly. To accurately evaluate SOH, it is necessary to select characteristic parameters with strong correlation, such as the number of cycles, temperature, charge–discharge curves, impedance spectra and other key indicators. There is a coupling effect among these parameters, which may lead to overfitting of the model. Therefore, choosing appropriate parameters with high correlation is crucial for the SOH assessment.

(1)

The number of charge and discharge cycles of lithium-ion batteries

The number of cycles is an effective indicator for evaluating the aging degree of lithium-ion batteries. As shown in Figure 3, although the SOH attenuation curves of different batteries vary, they all exhibit a decreasing trend with the increase in the number of cycles. This method is simple to operate, but is limited by the incompleteness of the actual charging and discharging conditions; therefore, it is difficult to achieve real-time monitoring of SOH.

(2)

Voltage, current and time of the battery

The charging process of lithium-ion batteries consists of two stages: constant current and constant voltage. With the increase in the number of cycles, the charging curve shows the following characteristic changes: The initial voltage in the constant current stage rises, the duration shortens, and the proportion of the constant voltage stage increases significantly. The discharge process is manifested as a decrease in the initial voltage and a reduction in the discharge time. The evolution trends of these charge and discharge parameters are closely related to the attenuation of battery SOH and are easy to obtain through conventional monitoring equipment, which can be used as effective indicators for evaluating the health status of the battery.

(3)

Internal resistance of the battery

The internal resistance of lithium-ion batteries shows a significant negative correlation with SOH. As the number of cycles increases, the internal resistance rises while SOH decreases. However, it should be noted that environmental factors can cause fluctuations in internal resistance, affecting its accuracy as an SOH index.

(4)

EIS impedance spectrum of the battery

Electrochemical impedance spectroscopy (EIS) is a testing technique based on a frequency-domain response. This method analyzes the frequency characteristics of the battery impedance by applying a micro-amplitude AC signal in the DC bias state. EIS can effectively identify the impedance changes caused by the aging of battery materials, providing an important basis for SOH assessment. In addition to voltage, current, and temperature, recent works have heavily relied on Incremental Capacity (IC) analysis, differential thermal voltammetry, and direct current internal resistance (DCIR) as potent health indicators [27,28,29].

2.2.3. Health Hazard

Moreover, differing cathode chemistries such as LFP and NCM exhibit distinct degradation trajectories; NCM typically shows highly nonlinear capacity fade while LFP maintains relatively linear decay under moderate conditions, requiring robust predictive models to handle such variance [30,31,32]. Furthermore, aggressive operational profiles like fast charging significantly accelerate aging, emphasizing the need for robust feature extraction under dynamic conditions [33,34]. It is critical to emphasize that the NASA dataset employed utilizes an accelerated aging protocol under severe operating conditions. Unlike industrial cells operating under moderate conditions that typically require 800 to 3000 cycles to degrade, these specific 18,650 cells naturally reach their End-of-Life (EOL)—defined as a 30% reduction from nominal capacity—within approximately 160 to 170 cycles. To comprehensively evaluate the model’s applicability across different chemistries and extended lifespans, commercial Nickel Manganese Cobalt (NCM) and Lithium Iron Phosphate (LFP) datasets with over 1000 long cycles are simultaneously introduced in this study for supplementary validation.

Lithium-ion batteries will experience capacity degradation during their repeated use. By analyzing the operating parameters such as voltage, current, and temperature during the charging and discharging process, characteristic quantities that reflect the battery’s health status can be extracted. This study is based on the battery dataset of NASA and selects five key degradation characteristic factors. Taking the B5 battery as an example, the charging voltage characteristics are first analyzed: Figure 4 shows the charging voltage curves for the 30th to 150th cycles (with an interval of 30 cycles), where the horizontal axis represents relative time and the vertical axis represents the charging voltage value.

The voltage curve analysis in Figure 4 shows two significant features:

(1)

The voltage rise rate in the constant current charging stage increases with the increase in the number of cycles.

(2)

When the constant voltage charging time is prolonged, the curve shows a left-shifting trend.

In particular, the curvature of the curve changes most significantly within the voltage range of 3.8–4.0 V. As shown in Figure 5, the voltage-rise charging time in this range shows a significant correlation with SOH, and thus can be used as an effective characteristic indicator of health status.

Studies show that the duration of constant voltage charging (CV) is closely related to the health status of the battery. Experimental data show that as the number of cycles accumulates, the CV charging time presents a monotonically increasing characteristic, as shown in Figure 6. Through correlation analysis, it was found that the variation trend of this parameter was highly consistent with the SOH attenuation curve (correlation coefficient R² = 0.92), proving that it can be used as a reliable characterization index of SOH. Specifically, the average duration of the CV stage of the new battery is 42 ± 3 min; when the capacity decays to 80%, it is prolonged to 68 ± 5 min. The sensitivity of this parameter change reaches 0.26 min/cycle.

The charging current characteristic analysis selected the test data of the 30th to 150th cycles (with an interval of 30 cycles) of the B5 battery. As shown in Figure 7, in the curve of the charging current varying with time, the horizontal axis represents the charging duration and the vertical axis shows the change in current value. By comparing the current curves of different cycle times, obvious changes in the characteristics of equal current drop charging time can be observed.

The current curve analysis in Figure 7 reveals three key characteristics: The duration of constant current charging shortens with the increase of the number of cycles. From 30 cycles to 150 cycles, the curve shows a systematic left shift. The curvature of the current curve gradually decreases in the CV stage.

It is particularly notable that the most significant curvature change was observed within the current range of 0.5A to 0.1A. As shown in Figure 8, the isocurrent drop charging time in this range has a clear correlation with SOH (Pearson coefficient r = 0.89), and thus can be used as an effective characteristic indicator of health status. The specific manifestations are as follows: The average duration of the new battery during this period is 25 ± 2 min. When the capacity decays to 80%, it is shortened to 15 ± 1 min. The sensitivity of parameter change reaches 0.08 min/cycle.

Discharge temperature characteristic analysis shows that the peak temperature in time (${Te}_{maxt}$) is associated with a significant role in the battery health status. The experiment selected the discharge temperature data of the B5 battery from the 30th to the 150th cycle (with an interval of 30 cycles), as shown in Figure 9. The horizontal axis represents the discharge duration and the vertical axis represents the real-time temperature value. Research shows that with the increase of cycling times, ${Te}_{maxt}$ showed a trend of decline in the new battery: about 45 ± 2 min. When the capacity decays to 80%, this shortens to 28 ± 1 min. The variation rate of this parameter is 0.12 min/cycle, and the correlation coefficient with SOH reaches 0.91. The advance of the temperature peak time can be used as an effective indicator parameter for battery aging, and its changing trend is highly consistent with capacity attenuation.

Studies show that during the cycle use of lithium-ion batteries, the time required for the discharge stage to reach the peak temperature is significantly correlated with the battery’s health status (SOH). As shown in Figure 10, by comparing the trend curves of these two parameters with the number of cycles, it can be found that there is a clear correlation between the two. Based on this finding, in this study, the time interval when the temperature reaches the maximum during the discharge process was determined as an important characteristic index for evaluating the health status of lithium-ion batteries. This characteristic parameter can effectively reflect the performance degradation of the battery, providing a new basis for the accurate assessment of SOH.

To study the relationship between the isobaric drop discharge time and the battery health state (SOH), this paper selects the discharge voltage data of a No. 5 battery under different cycle times (the 30th, 60th, 90th, 120th, and 150th times) for comparative analysis. Figure 11 shows the variation trend of battery voltage with discharge time. It can be observed that within the voltage range of 3.5 V to 3.0 V, the slope of the discharge curve changes significantly. This phenomenon indicates that the discharge time required for the voltage drop to the same extent may be correlated with the degree of battery degradation, and thus can be used as a potential characteristic parameter for evaluating SOH.

Through the analysis of the experimental data of the charge and discharge cycles of lithium-ion batteries, the study found that the moment when the battery reaches the peak voltage during the discharge stage changes with the increase in the number of cycles. As shown in Figure 12, the time parameter was compared and analyzed with the test data of battery health status (SOH), and the results showed that there was a significant correlation between the two. Based on this finding, this study proposes taking the time interval when the voltage reaches the maximum value during the discharge process as an effective characteristic index for evaluating the health status of lithium-ion batteries. The introduction of this parameter provides a new technical approach for the accurate evaluation of SOH in lithium-ion batteries.

Based on the five characteristic factors of the isobaric rise time during the charging stage, the CV stage duration, the isochoric drop time, as well as the peak temperature time (${Te}_{maxt}$) and the isobaric drop time during the discharge stage, and their relationships with the state of health (SOH) of lithium-ion batteries, their characterization capabilities were preliminarily verified. To further quantify the correlation between these factors and SOH, this paper adopts the grey correlation analysis method. This method is based on the grey system theory and evaluates the influence degree of each factor on the target indicator by calculating the correlation coefficient. Its core steps include:

(1)

In research on the performance of lithium-ion batteries, the first step is to obtain the characteristic parameters and cycle test data of the experimental samples. Specifically, if m key characteristic parameters are selected as the analysis indicators and n sets of test data under different cycle periods are collected, then the following feature matrix can be constructed:

$$X=\left[\begin{array}{cccc}{x}_{11}& x_{12}& \dots & x_{1m}\\ x_{21}& x_{22}& \dots & x_{2m}\\ ⋮& ⋮& \dots & ⋮\\ x_{n1}& x_{n2}& \dots & x_{nm}\end{array}\right]$$

(5)

(2)

During the analysis of system characteristics, a set of benchmark data is usually required as the basis for comparison. In this study, the health status (SOH) of lithium-ion batteries is selected as the key parameter for performance evaluation, and the standard value under new conditions is set as the benchmark sequence. This benchmark sequence is represented as $X_0$ in the subsequent analysis and is used to measure the degree of battery performance degradation.

Reference sequence:

$$X_0=\{X_0\left(1\right),X_0\left(2\right),X_0\left(3\right),\dots ,X_0\left(m\right)\}$$

(6)

(3)

Due to the different dimensions of each variable, standardization processing is required to enhance the reliability of the analysis. This paper adopts the mean value method to achieve dimensionless data. The calculation formula is as follows:

$$x_i^{\mathrm{\prime }}\left(k\right)={\displaystyle \frac{x_i\left(k\right)}{{\overline{x}}_i\left(k\right)}},i=\mathrm{0,1},2,\dots ,m;k=\mathrm{1,2},\dots ,n$$

(7)

(4)

The correlation coefficient is obtained by calculating the absolute difference values of each corresponding point between the reference sequence and the comparison sequence. The calculation formula is as follows:

$${\zeta }_i\left(k\right)={\displaystyle \frac{\underset{i}{\min } \underset{k}{\min }\left|x_0\left(k\right)-x_i\left(k\right)\right|+\rho ·\underset{i}{\max } \underset{k}{\max }\left|x_0\left(k\right)-x_i\left(k\right)\right|}{\left|x_0\left(k\right)-x_i\left(k\right)\right|+\rho ·\underset{i}{\max } \underset{k}{\max }\left|x_0\left(k\right)-x_i\left(k\right)\right|}}$$

(8)

In the formula, $x_0\left(k\right)-x_i\left(k\right)$ represents the absolute difference between the reference sequence and the comparison sequence, $\underset{i}{\min } \underset{k}{\min }\left|x_0\left(k\right)-x_i\left(k\right)\right|$ is the minimum range, and $\underset{i}{\max } \underset{k}{\max }\left|x_0\left(k\right)-x_i\left(k\right)\right|$ is the maximum range. The discrimination coefficient $\rho$ (usually taken as 0.5) is used to adjust the discrimination degree of the correlation coefficient: the larger the $\rho$, the higher the resolution; the smaller the $\rho$, the stronger the discrimination ability. The correlation coefficient takes values from 0 to 1, and the larger the value, the more significant the correlation.

(5)

The degree of correlation is obtained by calculating the mean of the correlation coefficients between each comparison sequence and the reference sequence. The calculation formula is as follows. This value directly characterizes the strength of the correlation between the characteristic factor and the SOH of lithium-ion batteries.

$$r_i={\displaystyle \frac{1}{n}}{\sum }_{k=1}^n{\zeta }_i\left(k\right)$$

(9)

(6)

The correlation degree value directly reflects the degree of closeness between the characteristic factor and the optimal index.

This study is based on the aging data of B5-B7 batteries from NASA Research centers. Five characteristic parameters (isobaric rise time, CV stage duration, isobaric drop time, Temax and isobaric drop time) are selected as the comparison sequence, and SOH is used as the reference sequence for calculation. As shown in

Table 1. Correlation coefficients of each characteristic factor with SOH of lithium-ion batteries.

Serial Number	B5	B6	B7
serial number	0.5222	0.5411	0.7589
CV stage duration	0.6202	0.7220	0.7752
CV stage duration	0.6000	0.7283	0.7624
${Te}_{maxt}$	0.9841	0.9946	0.9918
Constant voltage drop discharge time	0.6723	0.7612	0.8120

, the correlation between peak discharge temperature time (Temax) and SOH is the strongest (γ = 0.92), while the correlation between isobaric rise time is the weakest (γ = 0.63). The correlation degrees of all characteristic factors met the requirements of the model, verifying its effectiveness as an evaluation index for SOH.

3. Estimation Method of SOH of Lithium-Ion Batteries Based on SSA-BiLSTM Model

3.1. SSA Algorithm

In recent years, swarm intelligence optimization algorithms have shown significant advantages in solving complex engineering optimization problems due to their excellent global search ability, fast convergence characteristics and good adaptability. As a new type of bionic optimization algorithm, the Sparrow Search Algorithm (SSA) was proposed by scholars in 2020 based on the foraging mechanism and defense behavior of sparrow populations. Relevant studies show that this algorithm has outstanding performance in terms of optimization accuracy and convergence speed.

The SSA algorithm builds a mathematical model by simulating the foraging process of sparrow groups. The core mechanism lies in the fact that during the algorithm iteration process, the system will dynamically adjust the spatial positions of the population individuals according to the preset rules, thereby accurately locating the area where the individual with optimal fitness is located. This unique optimization strategy makes it particularly suitable for the automatic tuning of neural network hyperparameters and can effectively improve the overall performance of the model. Recent implementations of the Sparrow Search Algorithm and its variants (such as Gray Wolf Optimization) in hyperparameter tuning have consistently proven superior in avoiding local optima and accelerating convergence in complex neural networks [35,36,37]. In the Sparrow Search Algorithm (SSA), initially, an information matrix for representing the positions of individuals in the population needs to be constructed. This matrix is used to record the initial coordinates of each sparrow in the search space and can be expressed as:

$$X=\left[\begin{array}{cccc}{x}_{\mathrm{1,1}}& x_{\mathrm{1,2}}& \dots & x_{1,d}\\ x_{\mathrm{2,1}}& x_{\mathrm{2,2}}& \dots & x_{2,d}\\ ⋮& ⋮& \dots & ⋮\\ x_{n,1}& x_{n,2}& \dots & x_{n,d}\end{array}\right]$$

(10)

Among them, the parameter n represents the number of individual sparrows in the population and d represents the variable dimension of the problem to be optimized.

In the Sparrow Search Algorithm (SSA), the entire population is usually divided into two types of core individuals: discoverers and followers. Among them, the discoverer refers to the member with relatively high fitness who can lead the remaining individuals to explore efficiently in the solution space. Whether followers choose to follow the behavior of the discoverer is mainly determined by the relative changes in fitness. During the search process, the discoverer adjusts its position according to a specific update mechanism. This update strategy can be expressed by the following formula:

$$X_{i,j}^{t+1}=\{\begin{array}{c}{X}_{i,j}^t\cdot \mathit{exp}(-{\displaystyle \frac{i}{\alpha ·{iter}_{max}}})\\ X_{i,j}^t+Q\cdot L\end{array}\begin{array}{ccc} & if& R_2<S_T\\ & if& R_2\ge S_T\end{array}$$

(11)

In the formula, $X_{i,j}^{t+1}$ represents the position information of the i-th bird in the j-th dimension in the t-th generation. Here, t represents the current iteration number, j is the dimension index of the variable, j∈{1,2,3,...,d}; α∈[0,1] is a random factor following a uniform distribution, and ${iter}_{max}$ is the maximum number of iterations, which is a constant; $R_2$ and $S_T$ represent the warning threshold and the safety threshold, respectively; Q is a random variable following a normal distribution, L is a matrix of dimension 1 × d, and all elements in the matrix are set to 1.

When $R_2<S_T$, it indicates that the current environment is relatively safe and the sparrow population has not yet sensed the threat of predators. Therefore, the discoverers can conduct searches over a wider area. However, when $R_2\ge S_T$, it means that some sparrows have already detected potential risks in the foraging area and have issued warnings. In this case, all sparrows need to quickly move away from the current coordinates and turn to a new safe area to continue foraging.

In the Sparrow Search Algorithm, some followers continuously monitor the activity trajectory of the discoverer during the foraging process. Once the discoverer locates a better food source, the followers will immediately abandon the original foraging position and instead try to seize this more favorable resource. However, if these followers fail to obtain food during the competition, they will then choose other areas to continue searching for food sources in order to maintain the continuity of their foraging behavior. The position information update mechanism of the followers can be described by the following formula:

$$X_{i,j}^{t+1}=\{\begin{array}{c}Q\cdot exp\left({\displaystyle \frac{X_{\mathrm{worst}}^t-X_{i,j}^t}{i^2}}\right)\\ X_p^{t+1}+|X_{i,j}^t-X_p^{t+1}|\cdot A^{+}\cdot L\end{array}\begin{array}{cc} & \mathrm{if} i>n/2\\ & \mathrm{otherwise}\end{array}$$

(12)

Here, $X_p^{t+1}$ represents the optimal position of the discoverer in the $t+1$th iteration, while $X_{\mathrm{worst}}^t$ represents the position corresponding to the worst-performing sparrow in the global fitness at the t-th generation. Matrix A is a 1 × d random matrix, whose element values are randomly assigned as 1 or −1, and satisfies the symmetry condition $A^{+}=A^T{\left(A{A}^T\right)}^{-1}$. Variable n represents the total number of sparrows in the population. When the individual number i exceeds $n/2$, it means that the fitness of this follower is low and they have failed to obtain food, so they need to migrate to a new area to continue the foraging task.

This study adopts the swarm intelligence optimization strategy. In the algorithm initialization stage, some individuals are randomly selected from the sparrow population as reconnaissance units according to the preset proportion. When implemented specifically, this proportion is set at 15% of the total number of individuals. During the iterative optimization process, the system dynamically adjusts the spatial distribution of group members to gradually converge the fitness index of the objective function to a better value. The core computing model of this mechanism is expressed as follows:

$$X_{i,j}^{t+1}=\{\begin{array}{cc}{X}_{\mathrm{best}}^t+\beta \cdot |X_{i,j}^t-X_{\mathrm{best} }^t|& f_i>f_g\\ X_{i,j}^t+K\cdot \left({\displaystyle \frac{|X_{i,j}^t-X_{\mathrm{worst} }^t|}{(f_i-f_w)+\epsilon }}\right)& f_i=f_g\end{array}$$

(13)

The definitions of each parameter of this model are as follows: $X_{\mathrm{best}}^t$ represents $t$he spatial coordinates of the best individual in the population during the t-th iteration; $\beta$ is a random step size adjustment factor, whose value follows a standard normal distribution (with a mean of 0 and a variance of 1); k is a uniformly distributed random variable within the interval [−1, 1]; and $\epsilon$ is a minimal normal quantity used to ensure that the denominator is non-zero. In terms of fitness evaluation, $f_i$ represents the fitness level of the current individual, while $f_g$ and fw correspond to the best and worst fitness values of the population, respectively.

When the individual fitness $f_i$ exceeds the group’s optimal value $f_g$, it indicates that this individual is in the periphery of the population and is at a higher risk of being preyed upon; if $f_i$ is equal to $f_g$, it means that the core area individuals have sensed environmental threats and need to enhance their defense capabilities through group aggregation behavior.

While traditional metaheuristic algorithms such as Particle Swarm Optimization (PSO), Genetic Algorithm (GA), and Grey Wolf Optimizer (GWO) have been widely used for hyperparameter tuning, the Sparrow Search Algorithm (SSA) was selected in this study due to its superior global exploration and local exploitation capabilities. Compared to PSO and GA, which are prone to falling into local optima, and GWO, which may suffer from slow convergence in late iteration stages, SSA incorporates a dynamic discoverer–follower mechanism and an anti-predation behavior. This allows SSA to demonstrate faster convergence speed and higher stability when optimizing the high-dimensional hyperparameters of deep learning models like BiLSTM.

3.2. BiLSTM Model

The bidirectional long short-term memory neural network (BiLSTM) is an optimized improvement of the traditional LSTM. Its main feature is to enhance the neural network’s learning function for future information, thereby overcoming the deficiency of single-directional LSTM networks in insufficient data information mining. Compared with the traditional single-directional LSTM, BiLSTM includes a forward LSTM layer and a backward LSTM layer, which can learn both forward and backward features of the input sequence. Thus, the model can not only be trained from input to output, but also from output to input, fully obtaining the past and future information of the input time series data, effectively improving the model’s dependence and enhancing the model’s prediction accuracy. The structure of the BiLSTM neural network is shown in Figure 13.

Figure 13. BiLSTM network structure.

Figure 13. BiLSTM network structure.

$$A_i=f_1({\omega }_1{x}_i+{\omega }_2{A}_{i-1})$$

(14)

$$B_j=f_2({\omega }_3{x}_i+{\omega }_5{B}_{i+1})$$

(15)

$$Y_i=f_3({\omega }_4{A}_i+{\omega }_6{B}_i)$$

(16)

In the formula: $x_1,x_2,x_3,\dots ,x_t$, respectively, represent the corresponding input data at each moment within the range of $t_1\sim t_i\left(i\in \left[1\sim t\right]\right)$.

$A_1,A_2,A_3,\dots ,A_t,B_1,B_2,B_3,\dots ,B_t$, respectively, represent the corresponding forward and backward iterative LSTM hidden states; $Y_1,Y_2,Y_3,\dots ,Y_t$ represent the corresponding output data; ${\omega }_1,{\omega }_2,{\omega }_3,\dots ,{\omega }_6$ represent the corresponding weights of each layer; $f_1$, $f_2$, $f_3$ represent the activation functions between different layers.

3.3. The Model Design of SSA Optimizing BiLSTM and the Method for Estimating SOH

Scientifically, battery degradation is a highly complex, non-linear time-series process where the current State of Health (SOH) strictly depends on historical aging trajectories and implicitly influences future trends. BiLSTM was chosen because its bidirectional architecture captures these temporal dependencies more effectively than standard unidirectional RNNs or LSTMs. However, BiLSTM performance is extremely sensitive to its hyperparameters. Therefore, SSA is applied to utilize its robust discoverer–follower–scout mechanism, providing superior global exploration to accurately locate optimal configurations.

The BiLSTM model constructed in this paper adopts the bidirectional long short-term memory network (BiLSTM) as its main structure. The input data first enters the model through the input layer, then passes through the BiLSTM layer to extract the bidirectional dependency features in the time series, and finally goes through the fully connected layer and the output layer to generate the prediction result for the health status (SOH) of lithium-ion batteries. The main parameter configuration of the model is shown in

Table 2. Design of BiLSTM Network Structure.

Network Layer Number	Network Structure	Major Parameter
First layer	Input layer	Structure (1,2)
Second layer	Forward LSTM layer	Neure: 5~100
Third layer	Backward LSTM layer	Neure: 5~100
Fourth layer	Rulu layer	Input quantity: 1
Fifth layer	Fully connected layer	Neure: 5~100
Sixth layer	Dropout layer	Fitting prevention coefficient: 0.2
Seventh layer	Output layer	Neure: 1

.

Simulation Analysis of SOH Estimation Based on the SSA-BiLSTM Combined Model:

(1)

Feature extraction: Five key features were extracted from the B5, B6, and B7 lithium-ion battery datasets: the charging time during isobaric rise, the duration of the constant voltage (CV) stage, the charging time during isochronous flow drop, the time when the maximum temperature occurs during the discharge stage (Temaxt), and the discharging time during isobaric drop. The degree of correlation between each feature and the battery’s state of health (SOH) was evaluated using the Grey Relational Analysis method, and the first two principal components were extracted through the Principal Component Analysis (PCA) method to serve as the input variables for the model.

(2)

Data preprocessing: The input data are scaled to the range of 0 to 1 using the Min-Max normalization method to unify the scale and improve the training efficiency of the model. Subsequently, the data are divided into a training set and a test set according to the time sequence, with the first 70% used as the training set and the remaining 30% as the test set.

(3)

Hyperparameter optimization and model training: The SSA algorithm is used to optimize some hyperparameters of the BiLSTM model to enhance its fitting ability and generalization performance. Subsequently, the SSA-BiLSTM model is trained based on the training dataset to obtain the optimal model for SOH prediction.

(4)

Model Evaluation and Validation: Using the trained SSA-BiLSTM model, the test sets of batteries B5, B6, and B7 were used for SOH prediction. The output results of the model were compared with the actual SOH values, and the prediction errors were calculated to verify the prediction accuracy and generalization ability of the model.

The structural flowchart of the SSA-BiLSTM model for estimating the SOH of lithium-ion batteries is shown in Figure 14.

4. Simulation and Verification

Regarding computational requirements, feature extraction and model training were conducted on a workstation (Intel Core i7-11800H, 8-core processor, 16GB RAM, NVIDIA RTX 3060 GPU). The offline training phase takes approximately 15 min per cell dataset. However, the optimal BiLSTM model is highly lightweight. The online inference time is in the order of milliseconds, making it suitable for deployment on standard Battery Management System (BMS) microcontrollers.

To comprehensively evaluate the applicability and robustness of the proposed SSA-BiLSTM model under dynamic conditions, three public lithium-ion battery datasets with distinct chemical systems and operating protocols were utilized: the NASA dataset (LCO), the Tianjin University (TJU) dataset (NCM), and the Huazhong University of Science and Technology (HUST) dataset (LFP). As pointed out by recent degradation studies, the chemical degradation mechanisms under intense accelerated stress conditions are not entirely identical to those occurring during normal long-term operation. Real-life battery degradation is highly dynamic, involving variations in C-rates during each charge/discharge cycle and extended rest times between cycles, which introduce complex capacity regeneration effects. To address this and prevent any misinterpretation of the model’s generalization capabilities,

Table 3. Comparison of operating protocols and rest times across different battery datasets.

Dataset	NASA(B5-B7)	Tianjin University (TJU)	Huazhong Univ. of Sci. & Tech. (HUST)
Cathode Chemistry	LCO	NCM	LFP
Charge C-rate	Constant 0.75 C	Variable (0.25 C–0.5 C)	Multi-stage (1.0 C–5.0 C)
Discharge C-rate	Constant 1.0 C	Variable (0.5 C–1.0 C)	Multi-stage (0.5 C–5.0 C)
Rest Time Between Cycles	Varying (10 min–4 h)	30 min	60 min
Operating Characteristic	Accelerated aging with prominent capacity regeneration	Temperature-sensitive evaluation	Realistic dynamic load variation

summarizes the explicit operating protocols across the three datasets. The NASA accelerated aging dataset applies a constant C-rate (0.75 C charge/1.0 C discharge) but features varying rest times ranging from 10 min to 4 h, which induces prominent local capacity regeneration. In contrast, the TJU NCM dataset employs diverse C-rates (ranging from 0.25 C to 1.0 C) with a strictly controlled 30-min rest time between cycles. Furthermore, the HUST LFP dataset mimics realistic usage variability by applying dynamic multi-stage discharge protocols with varying C-rates (ranging from 0.5 C to 5.0 C), followed by a 60-min rest time. By incorporating these diverse dynamic C-ratios and rest time distributions, the validation effectively proves the model’s capacity to learn complex degradation patterns far beyond simple constant C-ratio profiles.

Simulation Analysis of the SSA-BiLSTM Combined Model: The first and second principal components extracted from the principal component analysis are used as the input variables of the model, and the health status (SOH) of lithium-ion batteries is used as the output variable. The data of each battery sample are divided according to the time sequence. The first 70% is used as the training set to train the BiLSTM model optimized by SSA, and the remaining 30% is used as the test set to evaluate the prediction accuracy of the model for the battery SOH.

The optimization of the model adopts the Adam gradient descent algorithm as the optimization function and uses ReLU as the activation function. The maximum number of training iterations is set to 500. The SOH estimation curves and prediction errors of the three types of lithium-ion batteries are shown in the following figure.

Figure 15, Figure 16 and Figure 17, respectively, show the comparison curves of the actual SOH values of three lithium-ion batteries (B5, B6 and B7) and the predicted values by the SSA-BiLSTM model. Among them, the black curve represents the actual SOH values, and the red curve represents the predicted results by the model.

To rigorously evaluate the consistency of the estimation quality across the entire battery lifetime, a Leave-One-Battery-Out Cross-Validation (LOOCV) strategy was implemented (as shown in Figure 15, Figure 16 and Figure 17). In this approach, the model is trained on the full lifecycles of two batteries and tested entirely on the unseen full lifecycle of the third battery. Furthermore, the lifecycle was segmented into three distinct phases: early cycles (0–50), mid-degradation (51–100), and end-of-life (101–150). As detailed in Table 3, the SSA-BiLSTM model demonstrates excellent consistency, maintaining extremely low RMSE values during the early and mid-life stages. The error slightly increases during the end-of-life stage strictly due to complex capacity regeneration phenomena, but remains well within highly accurate margins.

The prediction lag and increased error observed during the capacity regeneration stages are primarily driven by a combination of physical and data-driven factors. Physically, capacity regeneration typically results from the relaxation phenomenon during battery resting periods, where internal lithium-ion concentration gradients re-equilibrate. From a data-driven perspective, the extracted macroscopic health features exhibit a relatively smoothed degradation trend, which struggles to instantaneously mirror these high-frequency, transient physical recovery spikes. Consequently, the BiLSTM model, heavily reliant on historical sequence memory, exhibits a delayed response to these abrupt capacity rebounds.

Furthermore, to explicitly validate the proposed method’s applicability to industrial cells with extended lifespans, the model was tested on the supplementary NCM and LFP datasets. As depicted in the extended prediction charts (Figure 18 and Figure 19), the SOH estimation results reveal the model’s robust tracking performance over a prolonged lifespan exceeding 1000 cycles. Unlike the accelerated aging tests, where severe capacity regeneration causes prominent local fluctuations, the degradation trajectories of these commercial cells under moderate conditions are relatively smoother. The predicted SOH curves (red lines) tightly track the true SOH values (black lines) throughout the entire lifecycle. Although minor predictive deviations emerge in the extremely late stages, the overall estimation errors are significantly suppressed. This visual evidence further substantiates that the proposed SSA-BiLSTM framework is not constrained by specific battery chemistries or short-term aging protocols, but inherently possesses excellent generalization capabilities for long-cycle industrial applications.

Finally, to rigorously validate the superiority of the proposed SSA-BiLSTM model, an analysis was conducted. Based on recent advancements in the literature [38], two state-of-the-art hybrid models—CNN-LSTM-Attention and CNN-BiLSTM-Attention—were selected as benchmark models. These models were explicitly chosen because they represent the current advanced deep learning frameworks utilizing spatial–temporal feature extraction combined with attention mechanisms for battery SOH estimation. As demonstrated in

Table 4. Quantitative performance comparison with state-of-the-art baseline models.

Comparison Dimension	Proposed Model	Reference Baseline 1	Reference Baseline 2
Model Architecture	SSA-BiLSTM	CNN-LSTM-Attention	CNN-BiLSTM-Attention
Intuitive Health Features	Five macro-level operational characteristics based on time and temperature	Microscopic characteristics based on Incremental Capacity (IC) curve	Microscopic characteristics based on Incremental Capacity (IC) curve
Preprocessing Complexity	Very Low	Very High	Very High
RMSE (%)	0.42%	1.18%	0.92%
MAPE (%)	0.55%	1.34%	1.08%
Engineering Applicability	High	Low	Low

, the proposed SSA-BiLSTM achieves significantly lower RMSE and MAPE values, confirming its superior prediction accuracy and robustness.

Before presenting the comparative results in Table 4, it is necessary to define the term “Engineering Applicability”. In this context, it refers to the feasibility of deploying the model onto a standard Battery Management System (BMS) microcontroller in real-world scenarios, evaluating the trade-off between preprocessing complexity, hardware computational overhead, and estimation accuracy. Table 4 illustrates this comprehensive comparison in detail. While the baseline models achieve acceptable error margins, their reliance on highly complex microscopic feature extraction significantly increases computational load, resulting in “Low” engineering applicability. In contrast, the proposed SSA-BiLSTM model utilizes easily obtainable macro-level operational characteristics, ensuring “Very Low” preprocessing complexity while achieving superior accuracy, thereby demonstrating “High” engineering applicability for actual energy storage scenarios.

Based on the LSTM structure, a bidirectional long short-term memory network (BiLSTM) model was constructed to estimate the health status (SOH) of lithium-ion batteries. Subsequently, the Sparrow Search Algorithm (SSA) for hyperparameter optimization was introduced, and the application process of SSA in optimizing the parameters of the BiLSTM model was elaborated in detail. Finally, the SSA-optimized BiLSTM model (SSA-BiLSTM) was constructed and trained, and the SOH of multiple batteries was estimated using this model. The predicted results of the model were compared with the actual values for analysis to verify the accuracy and generalization ability of the model.

5. Conclusions

This paper addresses the high-precision estimation requirement of the health status (SOH) of lithium-ion batteries and proposes a data-driven estimation framework. Specifically, a bidirectional long short-term memory network (BiLSTM) model optimized by the Sparrow Search Algorithm (SSA) is adopted. It should be clarified that while the fundamental SSA and BiLSTM algorithms are established in the existing literature, our core contribution lies in successfully integrating them and using this optimized SSA-BiLSTM framework for the first time, specifically to address battery SOH estimation, achieving high prediction accuracy. By adaptively optimizing the hyperparameters of BiLSTM with SSA, the prediction accuracy and generalization ability of the model are significantly improved. Experiments show that the maximum prediction error of the proposed method on the NASA open-source dataset is no more than 2.35%, and it has the functions of fast estimation and visualization, which has practical engineering application value.

However, it also has the following shortcomings: insufficient data diversity, delayed prediction in the capacity regeneration stage, improvement in algorithm efficiency, and joint estimation of multiple states. Despite the high estimation accuracy achieved by the proposed SSA-BiLSTM model, the initial validation was primarily confined to the accelerated aging test of LiCoO₂ (LCO) cells from the NASA dataset. To explicitly validate the proposed method’s applicability to industrial cells with extended lifespans, supplementary validations on commercial long-cycle Nickel Manganese Cobalt (NCM) and Lithium Iron Phosphate (LFP) datasets (exceeding 1000 cycles) have been incorporated. Future research will continuously focus on expanding the model’s robust generalization under complex variable-temperature and highly dynamic load profiles.