Capacity Prognostics of Marine Lithium-Ion Batteries Based on ICPO-Bi-LSTM Under Dynamic Operating Conditions

Abstract

An accurate prognosis of the marine lithium-ion battery capacity is significant in guiding electric ships’ optimal operation and maintenance. Under real-world operating conditions, lithium-ion batteries are exposed to various external factors, making accurate capacity prognostication a complex challenge. The paper develops a marine lithium-ion battery capacity prognostic method based on ICPO-Bi-LSTM under dynamic operating conditions to address this. First, the battery is simulated according to the actual operating conditions of an all-electric ferry, and in each charge/discharge cycle, the sum, mean, and standard deviation of each parameter (current, voltage, energy, and power) during battery charging, as well as the voltage difference before and after the simulated operating conditions, are calculated to extract a series of features that capture the complex nonlinear degradation tendency of the battery, and then a correlation analysis is performed on the extracted features to select the optimal feature set. Next, to address the challenge of determining the neural network’s hyperparameters, an improved crested porcupine optimization algorithm is proposed to identify the optimal hyperparameters for the model. Finally, to prevent the interference of test data during model training, which could lead to evaluation errors, the training dataset is used for parameter fitting, the validation dataset for hyperparameter adjustment, and the test dataset for the model performance evaluation. The experimental results demonstrate that the proposed method achieves high accuracy and robustness in capacity prognostics of lithium-ion batteries across various operating conditions and types.

1. Introduction

In recent years, lithium-ion batteries, as a primary representative of clean energy, have found widespread applications in various fields, including electric ships (which encompass all-electric propulsion systems, conventional fuel-driven systems, and, as an intermediate solution, hybrid drive systems) [1], as well as electric vehicles, owing to their high energy density, absence of a memory effect, and overall reliability. Moreover, with the development of new technologies for mobile systems, reducing the mass of batteries has become more and more important [2], and lithium-ion batteries have been widely used in applications requiring a light weight and high performance due to their high energy density. For comparison purposes,

Table 1. The key characteristics of several battery types used in electric ships and vehicles.

Battery	Capacity (Ah)	Energy Density (Wh/kg)	Mass (kg)	Dimensions (mm)	Charging Time (h)	Cycle Life (Cycles)
Lead Acid	50–200	30–50	20–60	200 × 300 × 200	6–8	300–500
Nickel–Metal Hydride	10–40	60–120	5–15	130 × 110 × 140	4–6	500–1000
Sodium Ion	10–50	90–160	3–12	120 × 100 × 150	2–5	500–1000
Flow Batteries	50–200	30–50	50–100	300 × 400 × 500	4–6	2000–5000

provides the key characteristics of several battery types used in electric ships and vehicles. However, over time, the aging mechanisms within the battery (e.g., loss of active substances) can result in performance degradation and may even lead to safety hazards. Therefore, there is an urgent need to establish an effective battery management system for the real-time monitoring of the lithium-ion battery lifespan [3]. Currently, battery capacity prediction methods can be broadly categorized into three types: experimental measurement-based methods, model-based methods, and data-driven methods.

Experimental measurement-based methods utilize battery parameters (e.g., resistance, impedance, and capacity) derived from direct measurements to predict the capacity [4]. This approach, however, is costly, time-consuming, and may damage the battery, making it unsuitable for real-time applications. Model-based methods, including equivalent circuit models, empirical models, and electrochemical models, focus on the internal mechanisms of the battery. These methods require the development of mathematical models to describe the capacity degradation and use the model parameters to predict the battery’s capacity [5]. However, accurately capturing battery characteristics and operating conditions is challenging, and the complex degradation behavior of lithium-ion batteries makes it difficult for model-based methods to fully characterize and quantify the degradation process.

With the accumulation of battery data and the rapid advancement of artificial intelligence, data-driven methods for battery capacity prediction have gained significant attention [6]. These methods primarily rely on capacity decay data and characterization data (e.g., current, voltage, and temperature) to train prediction models, which include techniques such as support vector machines [7], recurrent neural networks [8], least squares support vector machines [9], and long short-term memory networks [10]. These methods do not require an in-depth understanding of the battery’s internal mechanisms and are therefore well-suited for predicting the capacity of lithium-ion batteries [11]. In addition, more and more researchers are now applying machine learning to a technique called digital twins to build a model with high accuracy for battery capacity prognostics [2]. However, the accuracy of data-driven methods depends significantly on the features extracted from the data and the way the model is trained [12]. To improve the prediction accuracy, it is essential to optimize three aspects: feature extraction, feature processing, and model training.

A.

Feature Extraction

Simplifying battery charging and discharging data into a series of features can reduce the model’s training burden and enhance its efficiency. However, under certain dynamic operating conditions, extracting effective features from the discharge process is challenging, whereas the charging process typically follows a more predictable pattern, making it easier to analyze. As such, it is more effective to extract features from charging data that reflect the degradation of battery capacity [13]. Moreover, the variety of charging methods leads to diverse ways of extracting features. To enhance the versatility of the prediction model, a standardized approach for feature extraction is required. Peng [14] and others developed a series of features that accurately represent the capacity degradation using a unified standard based on time, energy, and incremental capacity (IC) features. To predict the battery capacity degradation in electric vehicles (EVs), Deng et al. [15] extracted statistical features from the charging data, ensuring both methodological consistency and a comprehensive feature set. Guo et al. [16] combined rational analysis and principal component analysis (PCA) to derive features from charging data that are adaptable to various operating conditions, thus strengthening the versatility of their capacity prediction method. For high-precision capacity prediction across different lithium-ion battery datasets, Dai et al. [17] extracted six statistical features from charging data, determining the optimal feature combination by comparing various combinations of these features and thus reducing computational complexity. When effective features can be consistently extracted from charging data according to a unified standard, the method’s versatility is proven, and the workload in feature extraction is minimized. However, extracting too few features may fail to capture the full degradation process, while too many features may result in redundancy, thereby increasing the computational burden and reducing model efficiency. Therefore, the extracted features must accurately reflect capacity degradation across different operating conditions while being computationally efficient.

B.

Feature Processing

Selecting feature sequences that are highly correlated with the battery capacity can significantly improve the prediction’s accuracy. In cases where two feature sequences are highly correlated with both the capacity and each other, redundancy can be reduced by eliminating one of the features, thus easing the computational burden. For example, in [18], Box–Cox transformation (BCT) was used to enhance the correlation between the extracted features and battery capacity. In [15], Pearson’s correlation coefficient and gray correlation were employed to identify and remove redundant features, leading to the optimal set of features. In [14], principal component analysis (PCA) and empirical mode decomposition (EMD) were applied to the experimental curves of battery charging and discharging, as well as the incremental capacity curves, to extract features that strengthened the correlation between features and capacity. Furthermore, ref. [19] employed a two-step feature engineering approach—feature dimensionality reduction and seasonal fluctuation decoupling—to select the most relevant features for the capacity prediction while eliminating interfering components, thereby improving the model’s prediction accuracy.

C.

Model Training

The battery capacity prediction based on data-driven methods is influenced not only by the effectiveness of the extracted features but also by the choice of machine learning algorithms and the configuration of their hyperparameters. In [16], an adaptive RVM model based on PSO optimization was proposed, demonstrating high robustness and effectiveness for estimating the remaining capacity of lithium-ion batteries. Gong et al. [20] developed a battery capacity prediction model by combining empirical mode decomposition (EMD) and backpropagation with a long- and short-term cyclic memory network. In [21], a hybrid capacity estimation model was proposed by integrating the Arrhenius degradation equation and a lightweight Transformer architecture tailored for different operating conditions. Zhang et al. [22] employed a temporal convolutional network combined with Gaussian process regression to establish a novel capacity estimation method capable of automatically extracting capacity decay features from partial charging segments. Furthermore, improper hyperparameter settings can significantly degrade the performance of machine learning algorithms, thereby reducing the accuracy of capacity prediction. To address this, ref. [23] adopted an improved dung beetle optimization (IDBO) algorithm to optimize the hyperparameters of temporal convolutional networks (TCNs), obtaining optimal hyperparameter combinations quickly and accurately, which notably enhanced the accuracy of battery capacity predictions. It is important to note that if the test set is involved in hyperparameter tuning during the model training process, the model’s performance on the test set may exceed its true capability, leading to evaluation errors. Thus, using the validation set for model tuning is recommended to preserve the independence of the test set.

Building upon these principles, this paper first extracts a series of features from battery data. The correlations between the extracted feature sequences, as well as between these features and the capacity sequences, are then analyzed. Features that exhibit a strong correlation with the capacity are retained, while redundant features are removed, resulting in an optimal feature set. Subsequently, the improved crested porcupine optimization (ICPO) algorithm is employed to optimize the hyperparameters of the bidirectional long short-term memory (Bi-LSTM) network, thus constructing the ICPO-Bi-LSTM model for accurate prognostics of the lithium-ion battery capacity. The dataset is divided into training, validation, and test sets in a specified ratio. The training and validation sets are used for model training, while the test set is reserved for the final performance evaluation. Finally, this paper investigates the impacts of working conditions, the dataset ratio, and the different models on the capacity prediction results by analyzing batteries discharged under complex and simple conditions, thus demonstrating the generality and robustness of the proposed ICPO-Bi-LSTM method.

The main contributions of this paper are as follows:

• A unified statistical feature extraction method is proposed, i.e., calculating the mean, sum, and standard deviation values of current, voltage, energy, and power in the charging data for each charging and discharging cycle of a battery. These features apply to different batteries under complex and simple operating conditions, which solves the difficulty of needing to adjust the feature extraction method according to changes in battery conditions. The voltage difference between the battery before and after the simulated operating conditions in each cycle is extracted as another type of feature to fully reflect the capacity decay trend of the battery. The above-extracted features show a strong correlation with the battery capacity.
• To overcome the challenge of determining the hyperparameters of the Bi-LSTM model, the improved crested porcupine optimization algorithm (ICPO) is proposed. This algorithm identifies the optimal hyperparameter combination and integrates the improved Chebyshev chaotic mapping initialization to ensure diversity within the initial population. This improves the algorithm’s early-stage search speed and introduces a random difference variance strategy to avoid local optima, thereby enhancing the algorithm’s overall efficiency.
• The ICPO-Bi-LSTM model is developed using the optimal feature set to predict the capacity of lithium-ion batteries accurately. The dataset is divided into training, validation, and test sets, with the validation set being used for model training along with the training set. The test set is reserved exclusively for the final performance evaluation, preventing evaluation errors.

The remainder of the paper is organized as follows: Section 2 describes the experimental apparatus and dataset; Section 3 details the feature engineering process; Section 4 presents capacity prognostics based on the ICPO-Bi-LSTM method; Section 5 provides the results of battery capacity prognostics; and Section 6 concludes the paper.

2. Battery Data Analysis

2.1. Experimental Equipment

To comprehensively analyze the operational characteristics of lithium-ion batteries under real-world conditions, an experimental platform was developed to collect data from various battery types. The experimental equipment used in this study is the NEWARE CTE-4008D-5V30A tester, which is a battery test equipment manufactured by NEWARE, and its main function is to test the capacity, efficiency, cycle life, and other performances of the battery by simulating the battery charging and discharging process. It consists of a battery testing system, a host computer with software (BTS Client 8.0.0.516), and a battery under test. The physical schematic of the experimental apparatus is shown in Figure 1. After experiments were conducted with the NEWARE CTE-4008D-5V30A tester to obtain battery charge/discharge data, both model construction and battery capacity prognostics were carried out using the Python 3.11 (64-bit) platform.

2.2. Description of Experimental Data

This experiment used A123 APR18650M1A LFP/C (the manufacturer is A123 Systems LLC, Waltham, USA) batteries (B1) and OXUN IFR26650 LFP/C (the manufacturer is OXUN Energy, Changzhou, China) batteries (B2) to simulate real-world operating conditions. The research focused on the “Jun Lv Hao”, a 300-passenger all-electric ferry operating in Wuhan. The ship’s battery system comprises multiple clusters connected in parallel, offering a total capacity of 2240 kWh. The specific topology of the battery system is illustrated in Figure 2. The battery system of the “Jun Lv Hao” ship is divided into two sections (left and right), with each section containing six battery clusters. Once the six battery clusters are connected in parallel, they supply power to the pod and other loads via the ship’s DMSB. The experiment was designed to replicate the actual operating conditions of the “Jun Lv Hao” and assess the capacity degradation of lithium-ion batteries under complex operational scenarios based on the rated capacity of the selected batteries. To verify the effectiveness of the battery capacity prediction method developed in this study, we also employed LISHEN LR18650LA NCM/C (the manufacturer is Tianjin Lishen Battery Joint-Stock Co., Ltd., Tianjin, China) batteries (B3) for a simplified discharge test under controlled conditions. Figure 3 displays the current variation curves observed during a typical “Jun Lv Hao” voyage and under simulated conditions. The specifications of the “Jun Lv Hao” are provided in

Table 2. The specifications of the “Jun Lv Hao”.

Parameter	Specification
Type	Passenger Ship
Length	55 m
Width	10 m
Draft Depth	1.6 m
Route	The Yangtze River in Wuhan City
Coordinates	114°17.414′ E″, 30°34.296′ N″
Operating Mode of the Propulsion System	All-Electric Propulsion System
Engaged Power of the Motor	1200 kW
Charging Time	2 h
Maximum Speed	10 knots/h
Cruising Range	118 km
Battery Capacity	2240 kWh
Battery Weight	25 tons
Number of Battery Clusters	12

.

The specific operation of the simulated working condition is as follows: Firstly, the capacity value released under the actual working condition is calculated by the ampere-time integration method, the capacity value is reduced by a certain number of times so that it does not exceed the rated capacity of the battery used in the experiment, and then the output current of the actual working condition is reduced by the same number of times. At the same time, the original sampling time of the working condition is 5 s, and this paper shortens the time to 1 s, which constitutes the simulated working condition. After that, the capacity released under the simulated condition is calculated again using the ampere–time integration method to ensure that the value is less than or equal to the rated capacity of the battery used in the experiment. Additionally, to ensure the safety and efficiency of the experiment, the charging currents and the duration of a single cycle were constrained. The specific charging and discharging protocols for the three batteries are outlined as follows:

B1,

① Charge the battery with a constant current of 7.7 A to a cut-off voltage of 3.26 V;

② Charge the battery with a constant current of 5.28 A to a cut-off voltage of 3.32 V;

③ Charge the battery with a constant current of 5.28 A to a cut-off voltage of 3.33 V;

④ Charge the battery with a constant current of 4.015 A to a cut-off voltage of 3.36 V,

⑤ Leave the battery to stand for 5 min;

⑥ Charge the battery with a constant current of 4 A at 3.6 V to a cut-off current of 0.4 A;

⑦ Leave the battery to stand for 5 min;

⑧ Apply the simulated working conditions shown in Figure 3b;

⑨ Discharge the battery with a constant current of 4.4 A to a cut-off voltage of 2 V;

⑩ Leave the battery to stand for 5 min;

⑪ Repeat the above steps (①–⑩) until 200 cycles are completed;

B2,

① Charge the battery with a constant current of 7.2 A at 3.65 V to a cut-off current of 0.72 A;

② Leave the battery to stand for 5 min;

③ Apply the simulated working conditions shown in Figure 3b;

④ Discharge the battery with a constant current of 14.4 A to a cut-off voltage of 2 V;

⑤ Leave the battery to stand for 5 min;

⑥ Repeat the above steps (①–⑤) until 276 cycles are completed;

B3,

① Charge the battery with a constant current of 8 A at 4.2 V to a cut-off current of 0.1 A;

② Leave the battery to stand for 10 min;

③ Discharge the battery with a constant current of 8 A to a cut-off voltage of 2.75 V;

④ Leave the battery to stand for 10 min;

⑤ Repeat the above steps (①–④) until 528 cycles are completed.

Figure 4 presents the capacity degradation curves for three types of batteries, as obtained from the experiments described earlier.

Table 3. Items of battery data.

Items	Unit	Resolution
Current	A	0.0001 A
Voltage	V	0.0001 V
Energy	Wh	0.0001 Wh
Power	W	0.0001 W
Cycle	Time	1 Time

provides the details of the battery data experimentally obtained, which are relevant to the capacity prediction of lithium-ion batteries.

3. Feature Engineering

To build a data-driven model capable of accurately predicting the capacity degradation of lithium-ion batteries, a series of feature sequences are extracted from battery charge and discharge data in this section. It also uses a correlation analysis to identify and remove feature sequences that have a low correlation with the capacity sequence and eliminate redundant features that may increase the computational burden of the model. Finally, the optimal set of features that are highly correlated with the capacity sequence is obtained.

3.1. Feature Extraction

Charging data, including the current (I), voltage (U), energy (E), and power (P), can be obtained experimentally. In each cycle, the mean, sum, and standard deviation values (denoted by the subscripts ave, sum, and std, respectively) of the current, voltage, energy, and power are calculated, resulting in 12 features.

The above series of statistical features extracted from the charging data belong to the same type of features. To ensure that the extracted features can comprehensively reflect the complex and nonlinear degradation trend of the battery, the voltage difference of the battery before and after the simulated working condition (abbreviated as U_dif) is extracted as a feature in each charging and discharging cycle as well. The 13 features extracted are shown in

Table 4. The features extracted.

Items	Charge Current	Charge Voltage	Charge Energy	Charge Power	Voltage Data Under Simulated Conditions
Features	Isum	Usum	Esum	Psum	Udif
	Iave	Uave	Eave	Pave
	Istd	Ustd	Estd	Pstd

.

3.2. Correlation Analysis

In this paper, two metrics are employed, Spearman’s correlation coefficient [24] and grey correlation [14], to assess the correlations between feature sequences and capacity sequences. The Spearman correlation coefficient reveals the strength of the monotonic relationship between the battery capacity sequence and the feature sequence, while the grey correlation more effectively distinguishes the degree of correlation between the capacity sequence and each feature sequence. Generally, the higher the correlation between the feature sequences and the capacity sequences, the greater the accuracy of the predicted capacity decay curves upon inputting the capacity sequences and the feature sequences into the data-driven model.

The Spearman correlation coefficient is calculated as follows:

$$r_s=1-{\displaystyle \frac{6{\displaystyle \sum _{i=1}^n{d}_i^2}}{n(n^2-1)}}$$

(1)

where $r_s$ is the Spearman correlation coefficient, $n$ is the length of the feature sequence, $d_i$ is the rank difference between $X_i$ and $Y_i$ (where $X_i$ and $Y_i$ are the values in the ith position in the feature and capacity sequences, respectively), and the rank of a number refers to its position after all the numbers in the sequence have been ordered from smallest to largest, with ranks assigned in ascending order, i.e., 1, 2, …, $n$. Note that if there are ties in the data, the rank of each tied value is the arithmetic mean of the positions where they occur.

The steps for calculating the gray correlation are listed below.

(1)

The capacity sequence and the feature sequence are normalized and the normalized expression is given as follows:

$$x\prime ={\displaystyle \frac{x-x_{\min }}{x_{\max }-x_{\min }}}$$

(2)

where x represents the original value, x′ represents the normalized value, and x_max and x_min represent the maximum and minimum values in the same original sequence, respectively.

(2)

Calculate the gray correlation coefficient between the normalized feature sequence and the capacity sequence using the following formula:

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

(3)

where ${\xi }_i(k)$ represents the gray correlation coefficient of the ith feature sequence concerning the capacity sequence at the kth position, and k = 1, 2, …, n represents the total number of charging and discharging cycles of the battery, y(k) represents the capacity sequence, x_i(k) represents the feature sequence, and $\rho$ is the distinguishing coefficient, which is typically set to 0.5.

(3)

The gray correlation degree of the ith feature sequence concerning the capacity sequence can be obtained by calculating the average of the gray correlation coefficient using the following formula:

$${\gamma }_i={\displaystyle \frac{1}{n}}{\displaystyle \sum _{k=1}^n{\xi }_i}(k)$$

(4)

3.3. Features Selection

Using Equations (1)–(4), the feature sequences related to the capacity sequences, along with the Spearman correlation coefficients and gray correlations between features, can be calculated for the batteries under the two complex conditions. Additionally, the number of charging and discharging cycles is considered as a feature, as shown in Figure 5.

Feature sequences that exhibit a strong correlation with the capacity sequence and a low degree of autocorrelation among different feature sequences are selected to form the optimal feature set. In this study, feature sequences with an absolute Spearman correlation coefficient and gray correlation greater than 0.8 with the capacity sequence are considered highly correlated. If the absolute correlation coefficient between any pair of these highly correlated feature sequences exceeds 0.9, the sequences are considered highly autocorrelated, and one of the sequences should be removed to reduce redundancy [15]. The optimal feature sets for the two batteries, B1 and B2, for the capacity sequence can be derived from Figure 5, as shown in

Table 5. The optimal feature sets of B1 and B2.

B1	Isum	Iave	Ustd	Esum	Eave	Estd	Psum	Pave	Udif
B2	Isum	Iave	Usum	Esum	Eave	Estd	Psum	Pave	Udif

. In the optimal feature set for both batteries, common features are retained, while differing features are discarded to obtain a universally applicable feature set, consisting of I_sum, I_ave, E_sum, E_ave, E_std, P_sum, P_ave, and U_dif. This set is then used as input to the data-driven model for both batteries. Figure 6 illustrates the optimal feature set extracted from the charging data of both batteries, normalized according to Equation (2).

4. Battery Capacity Degradation Prediction

4.1. Bidirectional Long Short-Term Memory Network (Bi-LSTM)

As an enhanced version of the traditional recurrent neural network (RNN), LSTM largely addresses the issues of gradient vanishing and gradient explosion that commonly occur in standard RNNs when handling time series data by introducing input gates, forget gates, output gates, and cell states [24]. Given that the behavior of the lithium-ion battery capacity over time is influenced by complex, dynamic patterns, LSTM is capable of modeling these temporal correlations more effectively than other algorithms, such as convolutional neural networks (CNNs) or simple recurrent neural networks (RNNs), which may struggle with long-term dependencies. The specific architecture of the LSTM model is illustrated in Figure 7.

The core steps of LSTM are as follows:

(1)

Decide which information is discarded by the cell state in the forget gate f_t

$$f_t=\sigma (W_f\cdot {[\mathrm{h}}_{t-1},x_t]+b_f)$$

(5)

where $\sigma$ is the sigmoid function, $W_f$ and $b_f$ are the weight matrix and bias vector of the oblivion gate, h_t−1 is the output of the cell state at the moment t − 1, and $x_t$ is the input of the cell state at the moment t.

(2)

Decide what information is stored in the internal state.

First, update the input gate i_t

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

(6)

where $W_i$ and $b_i$ are the weight matrix and bias vector of the input gate, respectively.

Next, a candidate vector $\stackrel{\sim }{C_t}$ is obtained.

$$\stackrel{\sim }{C_t}=\tanh (W_c\cdot [h_{t-1},x_t]+b_c)$$

(7)

where $W_c$ and $b_c$ are the weight matrix and bias vector of $\stackrel{\sim }{C_t}$, respectively.

(3)

Update the cellular state.

$$C_t=f_t*C_{t-1}+i_t*\stackrel{\sim }{C_t}$$

(8)

where C_t−1 is the cell state at the moment t − 1.

(4)

Obtain the output of LSTM.

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

(9)

$$h_t=o_t\ast \tanh (C_t)$$

(10)

where $o_t$ is the sigmoid layer of the output gate, $h_t$ is the output of the LSTM at time t, and $W_o$ and $b_o$ are the weight matrix and bias vector of the output layer, respectively.

Bi-LSTM is an improved LSTM, which enhances the model’s context-capturing capability by computing the input sequence in two directions (frontward and backward) separately [25]. In the capacity prediction of lithium-ion batteries, the performance of the battery does not only depend on the current charging and discharging state, temperature, voltage, etc., but is also affected by the historical state, as well as the future trend. Therefore, the bi-directional structure can better capture these long-term and short-term dynamic changes and improve the prediction accuracy. Moreover, Bi-LSTM can extract more features from complex data by considering forward and backward time series information. Especially for the battery capacity prediction when the aging trend of the battery needs to be modeled, the advantage of bi-directional information flow is even more obvious, which can capture the subtle changes and patterns in the time series more effectively than LSTM and thus improve the accuracy of prediction models. The specific structure of Bi-LSTM is shown in Figure 8. The input layer receives the input data and passes it to the forward layer and the backward layer. The forward layer processes the forward time series of the input data and the backward layer processes the reverse time series of the input data. These two layers learn the different contextual information of the sequence separately and merge their outputs. Eventually, the output layer generates the final prediction based on the forward and backward outputs.

The formula for the forward layer is as follows:

$$L_t^f=\sigma (w_1{x}_t+w_2{L}_{t-1}^f+b_{L^f})$$

(11)

where $L_t^f$ is the output value of the forward layer, ${\omega }_1$ and ${\omega }_2$ are the weight matrices of the forward layer, and $b_{L^f}$ is the bias vector of the forward layer.

The equation for the backward layer is as follows:

$$L_t^b=\sigma (w_3{x}_t+w_4{L}_{t+1}^b+b_{L^b})$$

(12)

where $L_t^b$ is the output value of the backward layer, ${\omega }_3$ and ${\omega }_4$ are the weight matrices of the backward layer, and $b_{L^b}$ is the bias vector of the backward layer.

The final output value $h_t$ is calculated as follows:

$$h_t=w_5{L}_t^f+w_6{L}_t^b$$

(13)

where ${\omega }_5$ and ${\omega }_6$ are two weight matrices.

The Bi-LSTM model employs a bi-directional structure that captures hidden information in time series data more efficiently, thereby enhancing the accuracy of lithium-ion battery capacity predictions. The Bi-LSTM model employed in this study consists of three layers, each containing two LSTMs, which extract deeper features from the data and thereby improve the prediction accuracy compared to the single-layer Bi-LSTM.

4.2. Crested Porcupine Optimizer (CPO)

The CPO algorithm mimics the four defense strategies of the crested porcupine, which are executed sequentially as the distance between the predator and the crested porcupine decreases, including sight, sound, odor, and physical attack, and accelerates the convergence of the algorithm by introducing a cyclic population reduction technique. The main steps of CPO are listed below.

(1)

Population initialization

$${\overrightarrow{X}}_i=\overrightarrow{L}+\overrightarrow{r}\times (\overrightarrow{U}-\overrightarrow{L})|i=1,2\dots ,N$$

(14)

where N denotes the number of populations, ${\overrightarrow{X}}_i$ denotes the ith candidate solution in the search space, $\overrightarrow{L}$ and $\overrightarrow{U}$ are the lower and upper bounds of the search, respectively, and $\overrightarrow{r}$ is a vector randomly initialized between 0 and 1.

(2)

Cyclic population reduction technique

The cyclic population reduction technique means that some CPs are allowed to leave the population during the optimization process to accelerate the convergence speed, and then some CPs are added to the population to improve the population diversity and avoid falling into local minima, which ultimately achieves the purpose of accelerating the convergence speed while maintaining the population diversity. The specific mathematical model is as follows:

$$N=N_{\min }+(N\prime -N_{\min })\times (1-({\displaystyle \frac{t\%\frac{T_{\max }}{T}}{\frac{T_{\max }}{T}}}))$$

(15)

where T is the number of cycles, t is the number of current function evaluations, T_max is the maximum number of function evaluations, % is the remainder operator, and $N_{\min }$ is the minimum number of individuals in the newly generated population. In the optimization search process, the number of populations N first reaches the maximum value and then gradually decreases until it reaches $N_{\min }$, which represents a cycle. Then, the above cycle is repeated many times throughout the optimality-seeking process until T times.

(3)

The first defense strategy

The first defense strategy is visual intimidation, and the mathematical model is as follows:

$${\overrightarrow{x}}_i^{t+1}={\overrightarrow{x}}_i^t+{\tau }_1\times \left|2\times {\tau }_2\times {\overrightarrow{x}}_{CP}^t-{\overrightarrow{y}}_i^t\right|$$

(16)

where ${\overrightarrow{x}}_i^t$ is the position of the ith CP at the tth function evaluation and ${\overrightarrow{x}}_{CP}^t$ is the position of the current best CP, ${\tau }_1$, ${\tau }_2$ are two random numbers. ${\overrightarrow{y}}_i^t$ is calculated as follows:

$${\overrightarrow{y}}_i^t={\displaystyle \frac{{\overrightarrow{x}}_i^t+{\overrightarrow{x}}_k^t}{2}}$$

(17)

where ${\overrightarrow{x}}_k^t$ is the randomly chosen position of another CP.

(4)

The second defense strategy

The second defense strategy is sound intimidation, which is mathematically modeled as follows:

$${\overrightarrow{x}}_i^{t+1}=(1-{\overrightarrow{U}}_1)\times {\overrightarrow{x}}_i^t+{\overrightarrow{U}}_1\times (\overrightarrow{y}+{\tau }_3\times ({\overrightarrow{x}}_{r_1}^t-{\overrightarrow{x}}_{r_2}^t))$$

(18)

where ${\overrightarrow{U}}_1$ is a random vector between 0 and 1, ${\tau }_3$ is a random number, and ${\overrightarrow{x}}_{r_1}^t$ and ${\overrightarrow{x}}_{r_2}^t$ are randomly chosen positions of the two CPs.

(5)

The third defense strategy

The third defense strategy is the odor attack, which is mathematically modeled as follows:

$${\overrightarrow{x}}_i^{t+1}=(1-{\overrightarrow{U}}_1)\times {\overrightarrow{x}}_i^t+{\overrightarrow{U}}_1\times ({\overrightarrow{x}}_{r_1}^t+S_i^t\times ({\overrightarrow{x}}_{r_2}^t-{\overrightarrow{x}}_{r_3}^t)-{\tau }_3\times \overrightarrow{\delta }\times {\gamma }_t\times S_i^t)$$

(19)

where $S_i^t$ is a fitness function, $\overrightarrow{\delta }$ is a random vector, ${\gamma }_t$ is a time-dependent factor, and ${\overrightarrow{x}}_{r_1}^t$, ${\overrightarrow{x}}_{r_2}^t$, and ${\overrightarrow{x}}_{r_3}^t$ are randomly selected positions of the three CPs.

(6)

The fourth defense strategy

The fourth defense strategy is the physical attack, and the mathematical model is as follows:

$${\overrightarrow{x}}_i^{t+1}={\overrightarrow{x}}_{CP}^t+(\alpha (1-{\tau }_4)+{\tau }_4)\times (\delta \times {\overrightarrow{x}}_{CP}^t-{\overrightarrow{x}}_i^t)-{\tau }_5\times \delta \times {\gamma }_t\times {\overrightarrow{F}}_i^t$$

(20)

where α is a control parameter, ${\tau }_4$ and ${\tau }_5$ are random numbers, $\delta$ is a random vector, and ${\overrightarrow{F}}_i^t$ is a fitness-based factor.

CPO was validated using three CEC benchmarks (CEC2014, CEC2017, and CEC2020), and its performance was compared against that of three categories of existing optimization algorithms [26] as follows: (i) the most highly cited optimizers, including the Gray Wolf Optimizer (GWO), Whale Optimization Algorithm (WOA), Differential Evolution (DE), and Salp Swarm Algorithm (SSA); (ii) recently published algorithms, including the Gradient-Based Optimizer (GBO), African Vultures Optimization Algorithm (AVOA), Runge–Kutta Method (RUN), Equilibrium Optimizer (EO), Artificial Gorilla Troops Optimizer (GTO), and Slime Mold Algorithm (SMA); and (iii) high-performance optimizers, such as SHADE, LSHADE, AL-SHADE, LSHADE-cnEpSin, and LSHADE-SPACMA. The statistical analysis revealed that CPO can be regarded as a high-performance optimizer due to its significantly superior performance compared to all competing optimizers across the majority of the test functions in the three validated CEC benchmarks. Quantitatively, CPO achieved an improvement over rival optimizers, with percentages of up to 83% for CEC2017, 70% for CEC2017, 90% for CEC2020, and 100% for six real-world engineering problems.

4.3. Improved Crested Porcupine Optimizer (ICPO)

No single algorithm can be applied to all application scenarios with efficiency. When applied to the prediction of battery capacity, the CPO algorithm can be specifically adapted to enhance its capability in addressing the complex, dynamic characteristics of lithium-ion battery behavior, thereby improving the prediction accuracy. In the original CPO algorithm, the initialized population distribution is relatively random and poorly positioned, which may result in a slower global search during the early stages of the algorithm’s iterations or lead to convergence at a local optimum in the later stages. Additionally, during the algorithm’s iterations, if the position of the current optimal individual differs from that of the global optimal individual, as the number of iterations increases, individuals in the population may mistakenly converge toward the locally optimal region, resulting in premature convergence and a decrease in the accuracy of the global search. These limitations of the original CPO algorithm contribute to a reduced capacity prediction accuracy for lithium-ion batteries. Consequently, this paper improves the original CPO algorithm in two key areas: enhanced population initialization and a refined variation strategy, thereby establishing the ICPO algorithm, which offers high lithium-ion battery capacity prediction accuracy.

4.3.1. Improved Chebyshev Chaotic Mapping Initialization

Chebyshev chaotic mapping [27] is a widely used chaotic mapping method for population initialization in optimization algorithms, which is computed as follows:

$$x_{k+1}=\cos (k{\cos }^{-1}(x_k))$$

(21)

where k is the order, which takes the value of 4 in this paper, and $x_0$ is a random number between −1 and 1.

However, the traditional Chebyshev chaotic mapping may still be unable to make the initial population fully cover the search space, which reduces the optimization effect, and so this paper makes the following improvements to the Chebyshev chaotic mapping [28]:

$$x_{k+1}=1-2{(\cos (2\arccos x_k))}^2$$

(22)

The initialization of the CP population after the introduction of the improved Chebyshev chaotic mapping is calculated as follows:

$${\overrightarrow{X}}_i=\overrightarrow{L}+{\displaystyle \frac{x_{k+1}}{2}}\overrightarrow{r}\times (\overrightarrow{U}-\overrightarrow{L})|i=1,2\dots ,N$$

(23)

The improved Chebyshev chaotic mapping enhances the population’s dispersion and diversity while ensuring the randomness of the initial population distribution, greatly improving the algorithm’s performance.

4.3.2. Random Differential Mutation Strategy

In each iteration of the CPO algorithm, a Random Differential Mutation strategy [29] is used to perform mutation operations on the population to generate candidate individuals with greater potential, thus increasing the diversity of the population, which can help the algorithm to jump out of the local optimum and optimize the effect of the optimization search. The formula for stochastic differential variation is as follows:

$${\overrightarrow{x}}_i^{t+1}=r_1({\overrightarrow{x}}_{CP}^t-{\overrightarrow{x}}_i^t)+r_2({\overrightarrow{x}}_k^t-{\overrightarrow{x}}_i^t)$$

(24)

where $r_1$ and $r_2$ are random numbers between 0 and 1.

4.4. Developed ICPO-Bi-LSTM

In this paper, the ICPO algorithm is employed to optimize the hyperparameters of the Bi-LSTM model, such as the number of neurons in each layer, the learning rate, the number of iterations, and the dropout rate. Compared to the original CPO algorithm, the ICPO algorithm enhances the global search speed during the pre-iteration phase and addresses the issue of premature convergence. The flowchart of the ICPO-Bi-LSTM method is illustrated in Figure 9, and the primary steps are outlined below.

(1)

Normalize both the capacity and the optimal set of battery characteristics according to Equation (2), and divide them into training, validation, and test sets based on a predefined ratio.

(2)

Set the parameters of the ICPO algorithm and define the optimization ranges for the Bi-LSTM parameters. For instance, in the ICPO algorithm, the population size, maximum number of iterations, and optimization-seeking dimension are set to 100, 100, and 6, respectively; for Bi-LSTM, the search ranges for the number of neurons in each layer, learning rate, number of iterations, and dropout rate are defined as [1, 500], [0.0001, 0.001], [1, 200], and [0, 1], respectively.

(3)

Introduce improved Chebyshev chaotic mapping to initialize the population, as described in Equation (23).

(4)

Calculate the fitness value for each individual in the population and rank them based on their fitness values. The fitness function is determined using the following formula:

$$fit={\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N({\widehat{y}}_i}-y_i{)}^2$$

(25)

where N is the number of validation set samples, $y_i$ is the actual value of the ith validation set sample, and ${\widehat{y}}_i$ is the predicted value of the ith validation set sample.

(5)

Obtain the fitness value and position corresponding to the individual with the lowest fitness value, as determined by sorting the fitness values of all individuals, and update these to the global best fitness and best position.

(6)

Apply the four defensive strategies of the ICPO algorithm, along with the cyclic population reduction strategy, to update the positions of the individuals. Subsequently, update the positions further after each iteration by introducing random difference variation, as described in Equation (24).

(7)

After each update, check the position of each individual and adjust it back within the boundaries using a random number if it exceeds the upper or lower limits.

(8)

Calculate the fitness value for each individual after the update, and update the global best fitness and best individual position.

(9)

Determine if the loop should terminate: if the maximum number of iterations is reached or the fitness value attains the minimum, output the optimal hyperparameter combination for the Bi-LSTM model. Otherwise, return to step (6).

4.5. Capacity Prognostics Based on ICPO-Bi-LSTM and Feature Extraction

In this section, we propose an integrated Li-ion battery capacity estimation framework based on the ICPO-Bi-LSTM method. As illustrated in Figure 10, the proposed framework for capacity prediction comprises three key components: data processing, model training, and capacity prediction.

Initially, a set of features is extracted from the data of the battery. Subsequently, the correlations between the features and the capacity, as well as the inter-feature correlations, are assessed using Spearman’s correlation coefficient and a gray correlation analysis. Features exhibiting stronger correlations are selected, while redundant features are discarded to form an optimal feature set. This optimal feature set is then used as input for the ICPO-Bi-LSTM method. To avoid introducing bias in the performance evaluation, which could lead to erroneous predictions during online testing, the experimental data are divided into training, validation, and test sets. The training set is used for model parameter fitting, while the validation set is employed for iterative hyperparameter tuning to identify the optimal parameters for the Bi-LSTM model. Finally, the test set is used for the capacity prediction and performance evaluation.

5. Results and Discussion

5.1. The Evaluation Criteria

In this paper, the mean absolute error (MAE) and root mean square error (RMSE) are used to evaluate the capacity prediction accuracy of the established ICPO-Bi-LSTM method, which are calculated as follows:

$$MAE={\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N\left|{\widehat{y}}_i-y_i\right|}$$

(26)

$$RMSE=\sqrt{{\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N{({\widehat{y}}_i-y_i)}^2}}$$

(27)

where N is the number of samples in the test set, ${\widehat{y}}_i$ is the predicted value of the ith capacity predicted by the model, and $y_i$ is the actual value of the ith capacity. If the values of MAE and RMSE are smaller, the model’s capacity prediction is better.

5.2. Capacity Prognosis Accuracy Using Different Batteries at Various Set Ratios

In this section, the B1 and B2 batteries are used to evaluate the accuracy of the ICPO-Bi-LSTM model’s capacity prediction under dynamic operating conditions, while the B3 battery is employed to assess the model’s generalizability under simple operating conditions. The training, validation, and test sets are split into ratios of 6:1:3 (case 1), 7:1:2 (case 2), and 8:1:1 (case 3) for all three batteries, respectively. Figure 11 illustrates the capacity prognosis results for the three batteries across different dataset ratios. It can be observed that the ICPO-Bi-LSTM method not only accurately predicts the capacity under varying training, validation, and test set ratios but also captures the capacity regeneration phenomenon during the aging process of the batteries with high precision. Furthermore, the predicted capacity closely matches the actual capacity for both simple and dynamic operating conditions, demonstrating that the method is robust and versatile in battery capacity prognostics under diverse discharge conditions.

Table 6. Capacity prognosis errors for different batteries at various set ratios.

Battery	Ratios	MAE (%)	RMSE (%)
B1	6:1:3 (case 1)	0.6827	0.8236
	7:1:2 (case 2)	0.4346	0.6027
	8:1:1 (case 3)	0.1841	0.2473
B2	6:1:3 (case 1)	0.8862	0.9541
	7:1:2 (case 2)	0.7627	0.8463
	8:1:1 (case 3)	0.5538	0.5973
B3	6:1:3 (case 1)	0.9145	0.9622
	7:1:2 (case 2)	0.6434	0.6912
	8:1:1 (case 3)	0.1314	0.1386

displays the capacity prognosis errors for the three batteries across various dataset scales. It is noted that all error metrics remain within 1%, with the maximum values of the root mean square error (RMSE) and mean absolute error (MAE) recorded at 0.9622% and 0.9145%, respectively. Additionally, the estimation errors for all three batteries decrease as the proportion of data in the training and validation sets increases. This improvement is attributed to the larger amount of historical data on battery capacity degradation available in the training and validation sets, which enhances the accuracy of capacity prognostics using the ICPO-Bi-LSTM method.

5.3. Results of Different Prediction Methods

To further validate the superiority of the proposed ICPO-Bi-LSTM method and the superiority of the ICPO algorithm over other algorithms, five models—LSTM, Bi-LSTM, CPO-Bi-LSTM, PSO-Bi-LSTM, and the developed method—are employed to predict the battery capacity and compare their performance. The dataset is divided into 80% for training, 10% for validation, and 10% for testing for all four methods. For CPO, PSO, and ICPO, the population size is set to 100, the number of iterations to 100, and the optimization dimension to six. The hyperparameters of the Bi-LSTM model without algorithmic optimization are configured with 200 neurons per layer, a learning rate of 0.0001, 150 iterations, and a dropout rate of 0.5. For the LSTM model without algorithmic optimization, the parameters are set as follows: 50 neurons in the hidden layer, a learning rate of 0.001, 50 iterations, and a dropout rate of 0.5.

Figure 12 presents the capacity prognosis results for the three types of batteries using the five methods described above. The capacity curves predicted by all five methods closely match the actual capacity curves, demonstrating that the feature set extracted in this study accurately reflects the capacity degradation process of lithium-ion batteries under varying operating conditions. Furthermore, the fitting accuracy of the capacity curves predicted by the five methods, ranked in descending order as ICPO-Bi-LSTM, CPO-Bi-LSTM, PSO-Bi-LSTM, Bi-LSTM, and LSTM, further highlights the superiority of the ICPO-Bi-LSTM model.

The MAEs and RMSEs of the five previously discussed methods for predicting the three cell capacities are presented as evaluation metrics in

Table 7. Capacity prognosis errors and training times for different batteries using different methods.

Battery	Method	MAE (%)	RMSE (%)	Training Time (min)
B1	LSTM	0.7922	0.8793
	Bi-LSTM	0.6827	0.7423
	PSO-Bi-LSTM	0.5246	0.6433	23
	CPO-Bi-LSTM	0.3977	0.4813	18
	ICPO-Bi-LSTM	0.2433	0.2758	11
B2	LSTM	0.9273	0.9827
	Bi-LSTM	0.8427	0.8817
	PSO-Bi-LSTM	0.7062	0.7423	27
	CPO-Bi-LSTM	0.6213	0.6527	21
	ICPO-Bi-LSTM	0.5348	0.5777	14
B3	LSTM	0.5612	0.5837
	Bi-LSTM	0.3633	0.3849
	PSO-Bi-LSTM	0.2527	0.2734	35
	CPO-Bi-LSTM	0.2203	0.2276	25
	ICPO-Bi-LSTM	0.1346	0.1408	18

. In addition, to further validate the advantages of the low computational effort and high efficiency of the present ICPO-Bi-LSTM framework in model training, the time required to train the models using different algorithms is also listed in Table 7 as an evaluation metric. It can be seen that the final MAEs and RMSEs of all models are less than 1%, which further verifies that the optimal set of features extracted in this paper can effectively reflect the complex degradation trend of lithium-ion batteries. Moreover, the ICPO-Bi-LSTM method not only accurately predicts the battery capacity under simple and dynamic operating conditions but also minimizes the error generated by the prediction compared with other methods. On the other hand, the LSTM model requires manual setting of hyperparameters and cannot be dynamically adjusted according to the battery data, which limits its prediction capability and leads to lower accuracy. In contrast, the Bi-LSTM model adopts bi-directional training, which can effectively capture the hidden patterns in the battery time series data and thus improve the prediction performance, which further illustrates the advantage of Bi-LSTM over LSTM in battery capacity prediction. However, it still has the limitation of not being able to determine the optimal hyperparameters based on the data; the PSO algorithm can search for the optimal hyperparameter combinations of the Bi-LSTM model based on the data, and so the optimized Bi-LSTM model using the PSO greatly improves the prediction accuracy compared with the original Bi-LSTM model. On this basis, the original CPO algorithm can not only dynamically adjust the hyperparameters of the Bi-LSTM model according to the prediction error, which solves the problem that the optimal hyperparameters are difficult to determine, but also has a better optimization effect compared with the PSO algorithm, thus further improving the prediction accuracy. However, the original CPO algorithm has difficulty in determining the optimal hyperparameter combinations of the model due to the uneven distribution of the population and the possibility of falling into the local optimum, which leads to premature convergence of the algorithm, resulting in the limited prediction accuracy of the model. In contrast, the ICPO-Bi-LSTM method developed in this paper employs an improved Chebyshev chaotic mapping initialization to ensure a more uniform initial population distribution. This improvement helps to speed up the search rate in the initial stages of the CPO algorithm, as well as to perform a more thorough search in the later stages. In addition, the introduction of the Random Differential Mutation strategy after each iteration of the CPO algorithm not only shortens the optimization search time but also helps to prevent premature convergence, which is more conducive to determining the optimal hyperparameter combinations for the Bi-LSTM model, and these improvements greatly enhance the accuracy of the model in predicting the battery capacity. Finally, for the three batteries, training the Bi-LSTM model using the original CPO algorithm not only has a higher model prediction accuracy but also takes less time to determine the optimal hyperparameters of the model compared to training the Bi-LSTM model using the original PSO algorithm, which demonstrates the superiority of the CPO algorithm. The ICPO algorithm used in this paper not only optimizes the search results but also effectively shortens the search time due to the introduction of the improved Chebyshev chaotic mapping initialization and the Random Differential Mutation strategy, and thus outperforms the PSO algorithm and the original CPO algorithm in terms of both the prediction accuracy and model training time. Since the separate LSTM and Bi-LSTM models are not trained with an algorithm, there is no training time.

6. Conclusions

Capacity prognostics using data-driven methods can be inaccurate when the extracted features fail to sufficiently capture the degradation trend of lithium-ion batteries or when the model’s hyperparameters are improperly specified. This paper proposes a capacity prognostic method for marine lithium-ion batteries, which extracts features from battery charging and discharging data collected under dynamic operating conditions and utilizes the ICPO-Bi-LSTM model for capacity prognostics. First, a series of features are extracted from the charging and discharging data to ensure the adequate capture of battery capacity degradation. Then, the gray correlation degree and Spearman correlation coefficient are calculated to select features that are strongly correlated with capacity, while eliminating redundant features to obtain an optimal feature set. Additionally, the issues of an uneven population distribution and slow search efficiency during the early stages of the original CPO algorithm are addressed. The tendency of the original CPO algorithm to prematurely converge and fall into local optima in later stages, which hinders the identification of the optimal hyperparameter combination, is also mitigated. To this end, an improved CPO algorithm is proposed, combining enhanced Chebyshev chaotic mapping and a Random Differential Mutation strategy, which improve the population initialization and iterative search strategies of the original CPO algorithm, respectively.

The accuracy of our method is validated by predicting the capacities of two battery models (B1 and B2), which are discharged under dynamic operating conditions but charged using different methods. Additionally, we evaluate the method’s generalization ability using a third battery model (B3), which is discharged under simpler conditions. The experimental results confirm the method’s capacity to predict battery capacity accurately across various training, validation, and test set ratios, as well as under different charging and discharging conditions, demonstrating both high accuracy and robustness. Specifically, the mean absolute error (MAE) and root mean square error (RMSE) of the predicted capacities for the different batteries across various dataset ratios are consistently below 1%. Furthermore, our method achieves the smallest MAE and RMSE values when compared to other methods (e.g., CPO-Bi-LSTM, PSO-Bi-LSTM, Bi-LSTM, and LSTM), and the ICPO algorithm used in our approach demonstrates the shortest model training time compared to the original CPO algorithm and the PSO algorithm, resulting in the most accurate and efficient capacity prediction. In all model comparison experiments, the maximum MAEs and RMSEs of the predicted capacities using this method remain consistently below 0.6%.

Future work will include extensive experiments using various marine battery models under diverse dynamic operating conditions to further validate the effectiveness of our proposed method. We will progress from controlled laboratory environments to real-world marine applications, assessing the method in increasingly complex and dynamic conditions. One major challenge is the variability in battery charging and discharging conditions, which could impact data integrity. To address this, we plan to enhance both data acquisition techniques and the robustness of the model. Furthermore, we will investigate the effect of ambient temperature on battery performance, particularly during the charging process. Additionally, we aim to integrate the proposed method into an online prediction system for continuous monitoring, with a focus on ensuring scalability and real-time performance.