Research on Thermal Failure Characteristics and Prediction Methods of Lithium–Sulfur Batteries

Abstract

Lithium–sulfur (Li-S) batteries are promising energy storage solutions due to their high density and cost-effectiveness. However, the risk of thermal failure limits their widespread use. Understanding thermal failure characteristics and developing accurate prediction methods are crucial for ensuring battery safety and reliability. This study aims to analyze the thermal failure characteristics of Li-S batteries and offer machine learning-based prediction methods for the early detection of potential thermal failures. The research begins with collecting temperature data from sensors deployed over numerous planes of a Li-S battery module under varied operating conditions. The data are created using proven numerical models that simulate various failure conditions. To improve model stability and learning efficiency, temperature data are preprocessed using min–max normalization to scale them to a consistent range. We suggest using a machine learning algorithm, such as the Energy Valley Optimizer Muted Multilayer Perceptrons with Mutual Information (EneVO-MPMI) algorithm. These models are trained on temperature data which are combined with Multilayer Perceptrons (MPs) to capture complicated, nonlinear correlations in thermal failure predictions, whereas the Energy Valley Optimizer (EneVO) optimizes the model’s structure and hyperparameters to avoid overfitting. Mutual Information (MI) assists in the selection of relevant features, resulting in accurate prediction from sensor data. To assess the models’ generalizability, five-fold cross-validation is used and achieves an average F1-score of 97.2%, a recall of 97.6%, an accuracy of 97.3%, and a precision of 96.9%. The EneVO-MPMI method emerges as the most effective, delivering a higher accuracy in forecasting thermal failure while requiring less training and prediction time. It shows that the EneVO-MPMI method is the most accurate and efficient at forecasting thermal breakdown in Li-S batteries. The technique can be used to identify Li-S battery defects early on, reducing the possibility of thermal instability and improving battery safety in a variety of applications.

1. Introduction

The quick development of electric vehicles, consumer electronics, and renewable energy storage systems has created a steep increase in claims for energy-dense, lightweight batteries [1]. The emerging battery technologies—lithium–sulfur (Li-S) batteries—have gained particular interest because they are low in material cost, possess a high theoretical energy density of about 2600 Wh/kg, and are environmentally benign [2]. With sulfur being cheap and readily available, Li-S batteries could potentially become substitutes for traditional lithium-ion batteries, especially in applications that need greater energy delivery and less weight [3].

Challenges and Thermal Instability: Despite these benefits, Li-S batteries encounter various technological challenges that hamper their mass industrial usage [4]. The most important among them is thermal instability, which might lead to capacity degradation, thermal failure, and even safety risks like fire or explosion [5]. Thermal failure in Li-S batteries is mainly triggered by high temperatures during operations, internal short circuits, or unstable electrochemical reactions that produce extra heat. This heat build-up, which is above the safe dissipation level of the battery, usually results in thermal runaway—an irreversible and dangerous process [6].

Importance of Understanding Thermal Failure and Prediction: It is crucial to understand the thermal breakdown behavior of Li-S batteries to enhance battery design, guarantee safe operation, and increase battery lifespan [7]. In addition, the creation of efficient prediction methods to predict thermal problems in advance greatly improves the management of battery safety systems, especially for electric vehicles and aerospace technologies, where battery reliability is key [8]. The failure mechanisms, high-temperature material behaviors, and heat-generating mechanisms of Li-S batteries have been increasingly targeted [9]. Furthermore, the incorporation of sensors, machine learning algorithms, and thermal modeling methods has facilitated improved timing and accuracy in thermal failure predictions [10].

This area continues to be hampered by the unavailability of real-time thermal failure data, the inability to accurately simulate internal battery response, and the difficulty of generalizing predictive models over a wide range of battery designs. Safety and the expense of sophisticated diagnostic equipment also continues to restrict experimental validation under severe or hazardous conditions.

This study aims to investigate the thermal failure behavior of lithium–sulfur batteries and design a machine learning-based prediction method with high accuracy to assist in the early identification of likely thermal failures in order to improve battery safety and reliability. The main contributions are as follows.

Comprehensive Thermal Breakdown Analysis: Using simulated sensor-based temperature readings under various operating situations, we carefully investigate the thermal breakdown behavior of Li-S batteries.

Novel EneVO-MPMI Model: To effectively and precisely forecast thermal failure, we introduce a novel hybrid machine learning model called Energy Valley Optimizer-Muted Multilayer Perceptrons with Mutual Information (EneVO-MPMI). While machine learning models like MLPs have demonstrated potential in forecasting battery failures, their efficacy is often hampered by two inherent challenges—suboptimal hyperparameter configuration and the curse of dimensionality arising from redundant or irrelevant sensor features. Merely combining optimization algorithms with neural networks is not novel. The primary novelty of the proposed EneVO-MPMI model lies in the synergistic integration of a bespoke physics-inspired optimizer with an information–theoretic feature selection mechanism, specifically tailored to the characteristics of Li-S battery thermal dynamics. This integration is designed to address the aforementioned challenges in a uniquely effective manner. First, the Energy Valley Optimizer (EneVO) introduces a novel metaheuristic strategy inspired by particle decay processes, which facilitates a more efficient and global search of the solution space compared to conventional optimizers like PSO or GA, leading to a more robust and generalizable model architecture. Second, and crucially, the optimization process is not performed on the entire feature set. Instead, Mutual Information (MI) is employed a priori to rigorously quantify the nonlinear dependencies between each sensor input and the target failure indicator, effectively filtering out non-informative data streams. This pre-emptive dimensionality reduction not only curbs overfitting but also significantly alleviates the computational burden. Therefore, the strength of EneVO-MPMI is not solely in its individual components but in their orchestrated combination; the MI ensures the model learns from the most relevant signals, while the EneVO optimally tailors the model to these signals, resulting in a system that is both highly accurate and computationally efficient for real-time thermal safety applications.

Improved Forecasting Efficiency and Accuracy: By employing five-fold cross-validation, the proposed method demonstrates improved accuracy and reduced computing time, offering a reliable method for early failure identification for battery systems.

2. Literature Review

A sigmoid-based Recursive Least-Frequently (RLF) model and Direct Thermal Characteristics (DTCs) were combined in SRLF-CHI-AdaPSOELM, which is a novel State of Health (SOH) prediction method that utilized canonical correlation analysis to identify significant indicators [11]. The AdaBoost-Particle Swarm Optimization-Extreme Learning Machine (AdaBoost-PSO-ELM) framework enhanced generalizability, achieving a Mean Absolute Error (MAE) of less than 0.5%. However, despite improved accuracy, noise sensitivity and the complexity of DTC modeling remained significant challenges. This underscored the need for robust and interpretable models for monitoring lithium-ion battery health.

K-nearest neighbors (k-NN), Random Forest, Gradient Boosting, and Long Short-Term Memory (LSTM) algorithms were employed to predict the position of thermal runaway (TR) cells in 32-cell air-cooled lithium-ion battery modules [12]. Pearson’s correlation with a cutoff of 0.85 was used for feature selection. Random Forest required minimal training time and achieved 100% accuracy. However, the approach was based on simulated sensor data. It was concluded that machine learning has the potential to enhance safety by enabling early TR detection.

To enhance lithium–sulfur (Li-S) battery performance by mitigating polysulfide shuttling, slow reaction kinetics, and dendrite formation, a heterostructure-engineered adaptation of the separator was implemented [13]. The results indicated that synergistic interfacial effects improved electrochemical performance, wettability, and thermal stability. Nevertheless, scalability and material complexity posed significant challenges, highlighting the need for further investigation on robust and scalable separator architectures that are suitable for commercial Li-S battery applications.

Material optimization techniques were applied in recent studies on Li-S batteries, focusing on sulfur filling, the electrolyte-to-sulfur relation, and polysulfide shuttle mitigation [14]. These studies demonstrated enhanced stability and capacity through structural confinement methods. However, limitations such as electrolyte instability and insufficient cycle life persisted. Statistical models were not employed, indicating the necessity for predictive frameworks addressing material degradation and thermal responses in Li-S systems.

Advanced in situ characterization methods were used to investigate solid-state electrolyte/electrode interactions in all-solid-state lithium–sulfur batteries (ASSLSBs) [15]. It was revealed that lithium dendrite formation and high interfacial resistance were significant challenges. Although interfacial engineering improved performance, cycle stability issues remained unresolved. The study lacked quantifiable statistical validation, supporting the future implementation of machine learning-driven models to predict and optimize interfacial behavior in ASSLSBs.

An experimental examination measured cathode stress evolution in Li-S batteries across solid–liquid–solid, and quasi-solid phase transitions using optical fiber Bragg grating (FBG) sensors [16]. The results showed that cathode structural changes and volume variations were directly linked to internal stress fluctuations. However, poor characterization accuracy and limited understanding of chemo-mechanical coupling posed challenges. This emphasized the need for integrated predictive approaches that incorporate internal stress dynamics in Li-S batteries.

To examine reaction pathways, structural properties, and catalytic activity, atomically dispersed catalysts for Li-S batteries were explored both theoretically and experimentally [17]. Spectroscopic and electrochemical analyses revealed reduced polysulfide shuttling and enhanced lithium polysulfide conversion. Despite favorable numerical outcomes and improved capacity retention, the stability and scalability of the catalysts remained problematic. The optimization of catalyst design for realistic and durable battery performance continued to be a challenge.

The battery management systems in the investigation of second-generation electric and hybrid cars is significant [18]. It was important that technologies such as charging, state estimation, and modeling were examined; several battery models were considered. Additionally covered in the article were cell balancing circuit types, battery charging strategies and optimization techniques, control reliability, power loss, efficiency, and investigation needs in battery management systems.

Examination indicates that lithium–sulfur (Li-S) batteries have the potential for next-generation power storage due to their high energy density and low cost [19]. The shuttle effect, short lifetime, and sluggish reaction kinetics were disadvantages of practical Li-S batteries. High-sulfur-loading cathodes studied under low E/S and N/P ratios were the main topic, examining the cyclability of Li-S batteries with an aerial capacity of more than 5 mAh cm⁻². Electrochemical property thresholds were provided in the evaluation, along with viable devices for real-world and business applications.

The utilization of sulfur redox electrocatalysts to lower energy barriers in sulfur redox processes and attach polysulfides to cathodes was investigated [20]. Individual tuning is suggested as density functional theory studies show no scaling connection among polysulfide binding energies. The catalytic performance was dominated by Li₂S₄ anchoring. This also shows how the binding strength of Li₂S₄ is affected by charge transfer, electronegativity, and work function.

Dynamic Economic Supply System (DESS) planning was performed using a hybrid method that combined the Gaussian mutation technique with an improved Butterfly Optimization Algorithm with dynamic switching probability [21]. With reduced voltage variation and power loss, the model showed high convergence precision and economic savings of up to 783,000 RMB. Despite its effectiveness, the results rely on the location of the nodes, which means that grid-integrated energy storage systems need to be optimized in a scalable and flexible manner.

Across all three clusters, four critical gaps emerge that this work aims to address. These are as follows: (1) Existing ML models for thermal prediction [11,12] are either Li-ion-specific or lack targeted feature selection/global optimization, failing to adapt to Li-S batteries’ unique thermal behavior; (2) material optimization studies [13,14] ignore thermal failure prediction, leaving a disconnect between structural improvement and safety; (3) experimental characterization studies [15,16] provide failure mechanism insights but no predictive tools; and (4) no study has integrated feature selection tailored to Li-S thermal signatures and adaptive model optimization to enable early, accurate thermal failure detection. These gaps motivate the development of the EneVO-MPMI model, which combines Mutual Information (MI)-driven feature screening (to capture Li-S-specific thermal features) and Energy Valley Optimizer (EneVO)-based ML optimization (to avoid local optima) for robust Li-S battery thermal failure prediction.

3. Problem Context

Predicting the health of Li-S batteries is severely limited by current methods. Although the SRLF-CHI-AdaPSOELM model [11] is quite precise, it is difficult to simulate thermally and is susceptible to noise. Real-time application is hampered by machine learning models based on k-NN, Random Forest, Gradient Boosting, and LSTM [13], all of which are based on simulated sensor data. Predictive frameworks are not incorporated into stress-sensing models based on FBG sensors [17], which disregard chemo-mechanical effects. The early and accurate identification of thermal failure is hampered by these deficiencies. The proposed EneVO-MPMI model addresses these issues by combining efficient optimization, nonlinear modeling, and relevant feature selection to produce robust, real-time predictive functions for Li-S battery systems that are safer and more reliable.

4. Methodology

To ensure the early thermal failure prediction of lithium–sulfur batteries, this approach leverages sensor-driven temperature data simulated with varied operational conditions. The data are preprocessed with min–max normalization to provide consistent input scaling. The model, EneVO-MPMI, combining Energy Valley Optimizer, Multilayer Perceptrons, and Mutual Information, is trained and validated with five-fold cross-validation, providing accurate, efficient, and consistent failure predictions. The overall flow for the prediction methods of lithium–sulfur batteries is shown in Figure 1.

4.1. Dataset

To facilitate thermal failure prediction and battery safety improvement using machine learning approaches, the dataset provides sensor-based thermal data for lithium–sulfur (Li-S) battery modules. It replicates temperature data from several sensors on several Li-S battery modules, including labeled failure status, charge and discharge rates, and ambient temperature. The objective is to lower the danger of thermal escalation in Li-S batteries by enabling intelligent systems for the early identification of thermal abnormalities. As concerns the sample data, a pair plot is used to show how the sensor and ambient temperatures relate to each other and to help separate normal and failure conditions visually; this is shown in Figure 2.

4.2. Pre-Processing Using Normalization

The preprocessing of the sensor temperature data is required to predict temperature failures in Li-S batteries. The data are scaled into a consistent range $[D, C]$ with the use of min–max normalization, making it simpler for the model to learn from. It facilitates quicker and more precise model training while preserving the original variations in temperature observations. The normalized value B′ is calculated using Equation (1), as follows:

$$B^{\prime }={\displaystyle \frac{(A-\min \left(B\right))}{(mx\left(A\right)-\min \left(A\right))}}\times \left(C-D\right)+C$$

(1)

where $B^{\prime }$ is the output that has been normalized, $B$ is the initial data range, $A$ is a single piece of information, and the predetermined normalization border is $[D, C]$. This improves the model’s comprehension of temperature variations and increases the accuracy of its predictions of hazards like thermal runaway and overheating.

The max–min averaging approach is specifically applied in the preprocessing of temperature sensor time-series data (collected from the three-plane NTC sensors of the liquid–electrolyte Li-S battery module) to mitigate the impact of transient noise (e.g., electromagnetic interference from BMS and short-term vibration-induced sensor fluctuations) while preserving critical thermal trend information—directly contributing to the model’s prediction accuracy.

4.3. Energy Valley Optimizer Muted Multilayer Perceptrons with Mutual Information (EneVO-MPMI)

The Energy Valley Optimizer Muted Multilayer Perceptrons with Mutual Information (EneVO-MPMI) is a new hybrid model that has been specifically developed for precise thermal failure prediction in Li-S batteries. EneVO-MPMI utilizes the ability of Muted Multilayer Perceptrons (MPs) for nonlinear learning and the adaptive searchability of the Energy Valley Optimiser (EneVO), which tunes the model parameters and structure to operate optimally. To enhance prediction accuracy, the highest thermal properties from sensor data are selected and retained with the application of Mutual Information (MI). In contrast to traditional optimization algorithms, the hybrid model better represents early thermal abnormality detection under different working conditions. EneVO-MPMI considerably enhances real-time potential thermal failure detection, subsequently increasing the functioning, safety, and reliability of Li-S battery systems.

4.4. Multilayer Perceptrons

Li-S battery safety monitoring processes nonlinear interactions between temperature sensor inputs, while failure indications are described using the MLP structure. The architecture of a single-hidden Multilayer Perceptron (MLP) has an arbitrary number of inputs, hidden units, and outputs. Weighted connections ${\beta }_{ki}$ allow each input $w$ to enter into hidden units, and the weighted total is subjected to a sigmoidal activation function. Additional weighted connections ${\lambda }_{il}$are used to provide outputs $e_l$, usually with a linear activation for regression-based prediction, as shown in Equation (2), as follows:

$$e_l=g_l\left({\sum }_{i=1}^I{\lambda }_{il}{h}_i\right({\sum }_{k=1}^K{\beta }_{ki}{w}_k\left)\right)$$

(2)

To incorporate bias terms, $w_0=y_0=1$. Using a linear output and logistic activation function at the hidden node, the model takes on the following form in Equation (3), which is a simplified scenario where $L=I=K=1$.

$$e={\lambda }_0+{\lambda }_{1}o$$

(3)

When trained on thermal sensor data, this model aids in capturing Li-S battery failure risks and complicated thermal behaviors. Model weights may be estimated by minimizing the error function, which assumes that $z_j|w_j~M\left({\lambda }_0+{\lambda }_1{o}_j,{\sigma }^2\right)$corresponds to maximizing the likelihood. The scoring procedure, which is an iterative process that uses second derivatives of the log-likelihood, is used for model fitting. If $\underset{\_}{\theta }=\left({\lambda }_0,{\lambda }_1,{\beta }_0,{\beta }_1\right)$, the probability in Equation (4) is as follows:

$$K\left(\underset{\_}{\theta }\right)=\prod \left\{{\displaystyle \frac{1}{\sqrt{2\pi \sigma }}}\exp \left\{-{\displaystyle \frac{1}{{2\sigma }^2}}{\left(z_j-{\lambda }_0-{\lambda }_1{\displaystyle \frac{e^{{\beta }^{\prime }{w}_j}}{1+e^{{\beta }^{\prime }{w}_j}}}\right)}^2\right\}\right\}$$

(4)

The log-likelihood is shown in Equation (5), as follows:

$$\mathcal{l}\left(\underset{\_}{\theta }\right)=-m log\sigma -{\displaystyle \frac{1}{{2\sigma }^2}}{\sum }_j^m{(z_j-{\lambda }_0-{\lambda }_1{o}_j)}^2-{\displaystyle \frac{m}{2}}\log \left(2\pi \right)$$

(5)

When residuals $f_j=z_j-{\mu }_j, \underset{\_}{f}=(f_{1,}\dots .,f_m)$, the scaled objective function is as follows in Equation (6):

$$V=-{\displaystyle \frac{1}{{2\sigma }^2}} {\sum }_j^m{(z_j-{\mu }_j)}^2$$

(6)

Regarding parameters, the first derivatives of $V$ are shown in Equation (7), as follows:

$$\begin{array}{c}{\displaystyle \frac{\partial V}{\partial {\lambda }_0}}={\displaystyle \frac{1}{{\sigma }_2}}{\sum }_j^m{f}_j\hfill \\ {\displaystyle \frac{\partial V}{\partial {\lambda }_1}}={\displaystyle \frac{1}{{\sigma }_2}}{\sum }_j^m{o_j f}_j\hfill \\ {\displaystyle \frac{\partial V}{\partial {\beta }_0}}={\displaystyle \frac{1}{{\sigma }_2}}{\sum }_j^m{{{\lambda }_1 o}_j (1-o_j)f}_j\hfill \\ {\displaystyle \frac{\partial V}{\partial {\beta }_1}}={\displaystyle \frac{1}{{\sigma }_2}}{\sum }_j^m{{{\lambda }_1 o}_j (1-o_j)f}_j{w}_j.\hfill \end{array}$$

(7)

The anticipated information matrix (θ) in Equation (8) is as follows:

$$\mathcal{I}\left(\theta \right)={\displaystyle \frac{1}{{\sigma }^2}}\times \left[\begin{array}{cc}m{\sum }_j^m{o}_j& \begin{array}{cc}{\lambda }_1{\sum }_j^m{o}_j(1-o_j)& \begin{array}{cc}{\lambda }_1{\sum }_j^m{o}_j(1-o_j)w_j& \end{array}\end{array}\\ \begin{array}{c}{\sum }_j^m{o_j}^2\\ \begin{array}{c}\\ \end{array}\end{array}& \begin{array}{cc}\begin{array}{c}{\lambda }_1{\sum }_j^m{o_j}^2(1-o_j)\\ \begin{array}{c}{{\lambda }_1}^2{\sum }_j^m{o_j}^2(1-{o_j)}^2\\ \end{array}\end{array}& \begin{array}{c}{\lambda }_1{\sum }_j^m{o_j}^2(1-o_j)w_j\\ \begin{array}{c}{{\lambda }_1}^2{\sum }_j^m{o_j}^2(1-{o_j)}^2{w}_j\\ {{\lambda }_1}^2{\sum }_j^m{o_j}^2(1-{o_j)}^2{w_j}^2\end{array}\end{array}\end{array}\end{array}\right]$$

(8)

Assuming that the variables have been converted, we obtain Equation (9), as follows:

$$\begin{array}{c}{w}_{o_j}^{\prime }=1\hfill \\ w_{1_j}^{\prime }=o_j\hfill \\ w_{2_j}^{\prime }={\lambda }_1{o}_j(1-o_j)\hfill \\ w_{3_j}^{\prime }={\lambda }_1{o}_j\left(1-o_j\right)w_j;\hfill \end{array}$$

(9)

Then, Equation (10) is as follows:

$$\mathcal{I}\left(\underset{\_}{\theta }\right)={\displaystyle \frac{1}{{\sigma }^2}}{W}^{\prime } W$$

(10)

The scoring update rule in Equation (11) is as follows:

$$t\left(\underset{\_}{\theta }\right)={\displaystyle \frac{1}{{\sigma }^2}}{W}^{\prime } \underset{\_}{f}.$$

(11)

This results in the iterative least squares updated Equation (12), as follows:

$$\begin{array}{c}{\underset{\_}{\theta }}_{q+1}={\underset{\_}{\theta }}_q+{\mathcal{I}}^{-1}\left({\underset{\_}{\theta }}_q\right)t\left({\underset{\_}{\theta }}_q\right)\hfill \\ ={\underset{\_}{\theta }}_q+({W_q^{\prime }{W}_q)}^{-1}{W}_q^{\prime }{\underset{\_}{f}}_q\hfill \end{array}$$

(12)

where the “adjusted dependent variate” at iteration $q$ is denoted by $W_q$. Step-length control is necessary to guarantee an increase in the probability in each iteration, since $W_q^{\prime }$ is updated in each one. The modification may be scaled to do this easily, as shown in Equation (13), as follows:

$$\begin{array}{c}{W}_q^{\prime }{W}_q{\underset{\_}{\theta }}_{q+1}=W_q^{\prime }{W}_q{\underset{\_}{\theta }}_q+W_q^{\prime }{f}_q\hfill \\ \hspace{1em}\hspace{1em}\hspace{1em}= W_q^{\prime }\left({\underset{\_}{\eta }}_q+{\underset{\_}{f}}_q\right)\hfill \\ \hspace{1em}\hspace{1em}\hspace{1em} = W_q^{\prime }{\underset{\_}{v}}_q\hfill \end{array}$$

(13)

To ensure convergence and numerical stability, the scale factor $\varphi$ is set to 1 and is then systematically halved until the log-likelihood rises or stays constant. For uses such as the detection of temperature anomalies in Li-S battery systems, this step-length control is essential. When there are several hidden units, the model structure works well, as shown in Equation (14).

$${\underset{\_}{\theta }}_{q+1}=({W_q^{\prime }{W}_q)}^{-1}{W}_q^{\prime }{\underset{\_}{v}}_q$$

(14)

Thus, we obtain the mean prediction, as shown in Equation (15), as follows:

$${\underset{\_}{\theta }}_{q+1}={\underset{\_}{\theta }}_q+\varphi ({W_q^{\prime }{W}_q)}^{-1}{W}_q^{\prime }{\underset{\_}{f}}_q$$

(15)

Direct relationships between variables $w$ and $z$are possible by extending the sum of squares objective function to an indefinite number of explanatory variables $w$ in Equations (16) and (17).

$$\begin{array}{c}{z}_j|w_j~M\left({\lambda }_0+{\lambda }_{1 {O1}_j}+{\lambda }_{2 {O2}_j,}{\sigma }^2\right)\\ logit O_{ij}={\beta }_{0_j}+{\beta }_{1_j}{w}_j, i=\mathrm{1,2}\end{array}$$

(16)

$${\mu }_j=\mathbb{E}\left[z_j\right]={\lambda }_0+{\lambda }_1{\displaystyle \frac{f^{{\beta }_{01+}{\beta }_{11}{w}_j}}{1+f^{{\beta }_{01+}{\beta }_{11}{w}_j}}}+{\lambda }_2{\displaystyle \frac{f^{{\beta }_{02+}{\beta }_{12}{w}_j}}{1+f^{{\beta }_{02+}{\beta }_{12}{w}_j}}}$$

(17)

A variable called $o_j$ and two variables called ${\lambda }_1{o}_j\left(1-o_j\right) {\lambda }_1{o}_j\left(1-o_j\right)$ are added to the method to accomplish this, as shown in Equation (18), as follows:

$$\begin{array}{c}{z}_j|w_j~M\left({\lambda }_0+{\lambda }_{1 }{o}_j+\gamma w_j,{\sigma }^2\right)\\ logit o_j={\beta }_0+{\beta }_1{w}_j\end{array}.$$

(18)

Consequently, $w_{j }$may affect $z_j$ in both linear and nonlinear ways. The sum of squares of $w$and the cross-product$w_{j }$and $z_j$ extend the score vector and expected information. This design allows both the linear and nonlinear impacts of sensor data to be achieved efficiently, which makes it easy to identify likely thermal breakdowns early enough and greatly increases the dependability and safety of lithium–sulfur (Li-S) battery systems.

4.5. Mutual Information (MI)

MI is a concept from information theory and it is a helpful way to analyze the interdependence between thermal sensor values and potential failure indicators in the setting of lithium–sulfur battery safety. MI specifically quantifies the amount of information that one variable (like the temperature at a specific sensor location) conveys about another (like the occurrence of thermal failure). This is critical for system reliability and the early detection of anomalous thermal behavior.

When $W$ (sensor data) and $Z$(failure indication) are independent of one another, MI drops to zero, signifying no predictive potential. MI successfully detects significant dependencies, allowing for improved feature selection for predictive models. The definition of the Mutual Information between two random variables, $W$ and $Z$ is as follows:

$$J=\left(W;Z\right)=G\left(W\right)-G\left(W|Z\right)=G\left(Z\right)-G\left(Z|W\right)=G\left(W\right)+G\left(Z\right)-J\left(W;Z\right)$$

(19)

where the entropy is represented by $G\left(.\right)$; the conditional entropies are represented by $G\left(W|Z\right)$and $G\left(Z|W\right),$ as follows:

$$G\left(W\right)=-{\int }_w{O}_W\left(w\right)log{O}_W\left(W\right)dw$$

(20)

$$G\left(Z\right)=-{\int }_Z{O}_Z\left(z\right)log{O}_Z\left(W\right)dz$$

(21)

$$G\left(W;Z\right)=-{\int }_w{\int }_z{O}_{W,Z}\left(w,z\right)log{O}_{W,Z}\left(w,z\right)dwdz$$

(22)

where $o_{W,Z}\left(w,z\right)$is the marginal density function.$O_W\left(w\right)$ and $O_Z\left(z\right)$ are the marginal density functions in Equations (23) and (24), as follows:

$$o_W(w)={\int }_z{O}_{W,Z}\left(w,z\right)dz$$

(23)

$$o_Z\left(\mathrm{z}\right)={\int }_w{O}_{W,}W\left(w,z\right)dw$$

(24)

When Equations (20)–(22) are substituted into Equation (19), the MI is as follows:

$$J\left(W;Z\right)={\int }_W{\int }_Z\begin{array}{c} \\ \\ \end{array}{O}_{W,Z}\left(w,z\right)log{\displaystyle \frac{O_{W,Z}(w,z)}{O_W\left(w\right)O_Z\left(z\right)}}dwdz$$

(25)

In actuality, this is calculated in Equation (25), which is a discrete form for thermal data monitoring that adds up all of the recorded values, necessitating the calculation of $o_{W,Z}\left(w,z\right)$. Using MP statistics, we can compute entropy based on average distances between MP data points in multidimensional space. By assisting in identifying relevant parameters for thermal failure prediction, this technique instantly increases the safety and reliability of Li-S battery systems.

4.6. Energy Valley Optimizer (EneVO)

The EVO algorithm is an innovative solution to tough optimization problems; it has been inspired by leading physics concepts such as particle decay and stability. The enhancement of predictive models’ accuracy and effectiveness allows for the detection of thermal breakdowns early on and increases the dependability and safety of lithium–sulfur batteries. Although numerous metaheuristic algorithms may exist, the continuous development of new ones is necessary to maximize their effectiveness. This subsection explains the application of the EVO algorithm as an optimization-driven diagnostic method for thermal danger rating in lithium–sulfur (Li-S) battery systems based on the physics concepts outlined above. The duty ratios $\left(C_i^l\right)$, which establish the starting state of the jth candidate solution, are first assigned values at random to start the initialization phase. To determine the operational search limits for each variable, the bounds $C_{i, Minimum }^l$ and $C_{i, Maximum }^l$ are set to 0.1 and 0.9, respectively. The enrichment bound (EB), which compares particle thermodynamic state parameters, is introduced in the second phase. To evaluate early signs of thermal abnormalities, the overall enrichment bound of the universe is calculated using Equation (26) by averaging the neutron enrichment level (NEL) of each candidate.

$$Enrichment Bound={\displaystyle \frac{\sum _{i=1}^{h}NE{L}_i}{h}},i=\mathrm{1,2},3,\dots h$$

(26)

The objective value (thermal signature), which is determined by Equation (27), is used in the third step to assess each prospective solution’s relative stability, as follows:

$$S{L}_i={\displaystyle \frac{NE{L}_i-BSL}{WSL-BSL}},i=\mathrm{1,2},3,\dots h$$

(27)

The best and worst thermal stability levels (i.e., the lowest and highest thermal risk) are indicated by BSL and WSL, respectively, whereas $S{L}_i$ represents the thermal stability status of the $i^{th}$ candidate, as shown in Equation (28), as follows:

$$C_i^{New 1}=C_i\left(C_{BSL.}\left(F_i^l\right)\right),\left\{\begin{array}{c}i=\mathrm{1,2},3,\dots h.\\ l=Alpha Index II\end{array}\}\right.$$

(28)

During the EVO exploration phase, decay-based techniques (alpha, beta, and gamma) are employed to reorient the solution space if a candidate’s thermal anomaly level is beyond the enrichment threshold. These tactics create new candidate states by simulating the dissipation of thermal stress and are triggered according to the stability of the candidate, as shown in Equation (29), as follows:

$$C_i^{New 1}=C_i\left(C_{BSL.}\left(F_i^l\right)\right),\left\{\begin{array}{c}i=\mathrm{1,2},3,\dots h.\\ l=Alpha Index II\end{array}\}\right.$$

(29)

This enhances safety by simulating ray emission by stable thermal states. Equation (30) illustrates how gamma decay-inspired motions involving nearest neighbors are used to create a second new candidate, as follows:

$$C_i^{New 2}=C_i\left(C_{at}\left(C_i^l\right)\right), \left\{\begin{array}{c}i=\mathrm{1,2},3,\dots h.\\ l=Gamma Index II.\end{array}\}\right.$$

(30)

Beta decay is thought to indicate less-stable thermal behavior if the stability threshold is low ($S{L}_{j }>Stability Bound$). Equations (31) and (32) are used to move in the direction of the optimal thermal profile and the operational data space center, as follows:

$$C_{COP}={\displaystyle \frac{\sum _{i=1}^h{W}_j}{h}},i=\mathrm{1,2},3,\dots h.$$

(31)

$$C_i^{New 1}=O_i+{\displaystyle \frac{(v_1\times C_{BSL}-v_2\times C_{COP})}{S{K}_i}}$$

(32)

When realigning towards safer operating standards, this simulates a thermally unstable state. Furthermore, the focused movement towards an ideal and nearby stable thermal state improves exploration, as shown in Equation (32), as follows:

$$C_i^{New 2}=C_i+\left(v_3\times C_{BSL}-v_4\times C_{NP}\right),i=\mathrm{1,2},3,\dots ,h.$$

(33)

Similarly to ambiguous or uncertain thermal events, as shown in Equation (33), random exploration is initiated when enrichment falls below the threshold ($NE{L}_{i }\le EB$), as follows:

$$C_i^{New}=C_i+v,i=\mathrm{1,2},3,\dots ,h$$

(34)

High-enrichment threshold candidates merge with the current population to generate two new positional vectors. Top-performing applicants move on to the following round, while boundary infractions are noted and dismissed by assessments. The most dependable thermal operating point is indicated by the ideal duty ratio or $\left(C_{best}\right)$. The EVO approach outperforms more conventional techniques in terms of computing efficiency when it comes to real-time anomaly identification in battery systems. Navigating intricate temperature distributions improves battery safety and operational dependability by facilitating the early detection of possible thermal breakdowns in order to increase the dependability of lithium–sulfur battery systems and detect likely heat problems early.

4.7. Interpretive Analysis of the EneVO-MPMI Model: How It Identifies Thermal Failure Characteristics

The EneVO-MPMI model identifies Li-S battery thermal failures via three transparent steps.

First, the MI module (Section 4.5) filters raw data to retain features with MI > 0.7 (validated by five-fold cross-validation) for the target liquid–electrolyte Li-S module. The top retained features are as follows: (1) Sensor 2 (center)–Sensor 1 (edge) temperature gradient (MI = 0.92); (2) Sensor 2’s temperature rise rate (MI = 0.88); and (3) Sensor 3 (edge) ambient temperature difference (MI = 0.75). Low-relevance features (ambient temperature, MI = 0.15; static charge rate, MI = 0.21) are discarded, focusing on dynamic thermal propagation (e.g., center–edge gradients) that reflects Li-S battery physics (polysulfide shuttle heats the center faster).

Second, the EneVO module (Section 4.6) tunes MLP hidden-layer weights, whereby high-MI features obtain higher weights (e.g., Sensor 2–Sensor 1 gradient from 0.32 to 0.68), while a residual low-MI feature’s weight drops from 0.18 to 0.05, aligning model attention with thermal failure mechanisms.

Finally, weighted features are combined for prediction. The case in overheat scenarios is as follows: 7 °C center–edge gradient (weight 0.68) + 1.8 °C/min rise rate (weight 0.55) = normalized score 0.82 (>0.7 threshold, failure). Under normal conditions, the following is true: <2 °C gradient + <0.3 °C/min rise rate = score < 0.4 (normal).

5. Results and Discussion

The performance of the proposed EneVO-MPMI model is compared with more traditional approaches. When implemented in Python 3.13, the EneVO-MPMI model efficiently detected significant thermal trends for early failure prediction in lithium–sulfur (Li-S) batteries and achieved better prediction accuracy.

Evaluation of the Suggested EneVO-MPMI Model

The average charge and discharge currents of lithium–sulfur batteries during the Normal, Overheat Alert, and Thermal Runaway thermal failure modes are illustrated in Figure 3. Higher stress leading to failure is reflected by the increased discharge current under Overheat Alert conditions. Using the new EneVO-MPMI model, it can better identify these trends early on, enhancing battery thermal safety through the prevention of catastrophic thermal failures.

The thermal patterns of sensors from planes P2, P3, and P1 display distinct thermal peaks in Figure 4, which is indicative of lithium–sulfur battery failure. The EneVO-MPMI model can anticipate these deadly heat events well in advance of their occurrence by identifying these distinct patterns. By allowing for a timely response, minimizing danger, and increasing operational stability in battery systems that are subjected to thermal stress conditions, early and correct diagnosis enhances battery reliability.

The estimation of lithium–sulfur battery charge and discharge rates over time is critical to recognizing thermal behavior patterns, as shown in Figure 5. These changing rate profiles are utilized by the EneVO-MPMI model to predict thermal breakdowns accurately. The model enhances battery safety by detecting initial thermal instability indications via charge/discharge rate variation analysis and correlations. In practical applications, this enables early intervention, lowers risk, and extends battery life.

The crucial significance that temperature data play in identifying thermal failure is highlighted by this correlation matrix, which, as shown in Figure 6, displays strong positive correlations between temperature sensors (0.98–1.00) and between the failure label and the high correlation with them (~0.97). Low predictive capability is implied by the poor association between failure and ambient temperature, charge, and discharge rates. These results support the proposed EneVO-MPMI model’s emphasis on sensor data and thermal gradients in precise early prediction, improving battery thermal safety and operational stability by precisely identifying potential thermal failures.

The effectiveness of the created EneVO-MPMI model for predicting early thermal failure in lithium–sulfur (Li-S) batteries is displayed in Figure 7. With a 12.5% reduction in training time and a 15.2% reduction in inference time, the model greatly improves, enabling faster and more effective prediction. The training time of the EneVO-MPMI model is reduced by 12.5% compared to the traditional MLP model without EneVO optimization (same dataset, same number of features, only without EneVO structure optimization). With a high detection rate of 97.8% for thermal failure, the model enables accurate anomaly diagnosis. Additionally, the model contributes to a 22% increase in battery life, demonstrating its practical use in enhancing the safety, durability, and dependability of Li-S battery systems. After applying the EneVO-MPMI model to achieve early thermal failure warning in liquid–electrolyte Li-S battery modules, three-plane sensors, and low-noise target scenarios, the battery life was improved by 22% compared to the benchmark scenario of no monitoring by this model, relying only on traditional BMS (without early thermal failure warning function).

To achieve early and accurate thermal failure detection in lithium–sulfur batteries, the five-fold cross-validation performance of the newly released EneVO-MPMI model is displayed in

Table 1. Five-fold cross-validation results of the EneVO-MPMI model for thermal failure prediction in Li-S batteries.

Fold	Accuracy (%)	Accuracy SD (%)	Precision (%)	Precision SD (%)	Recall (%)	Recall SD (%)	F1-Score (%)	F1-Score SD (%)
1	97.2	0.14	96.8	0.11	97.5	0.19	97.1	0.16
2	97.5	0.16	97	0.13	97.8	0.22	97.4	0.19
3	97.1	0.15	96.7	0.10	97.3	0.20	97	0.18
4	97.4	0.17	97.1	0.12	97.7	0.23	97.4	0.19
5	97.3	0.15	96.9	0.11	97.6	0.21	97.2	0.18

. The model’s stability and consistency in predicting early thermal failure are demonstrated by the assessment criteria that were used: accuracy, precision, recall, and F1-score. The F1-score varied from 97.0% to 97.4% across folds, recall varied from 97.3% to 97.8%, accuracy varied from 97.1% to 97.5%, and precision varied from 96.7% to 97.1%. These high results verify that EneVO-MPMI is appropriate for real-time battery safety monitoring by validating the model’s capacity to capture intricate thermal patterns, guaranteeing accurate fault diagnosis while reducing false positives and negatives.

The average performance of the suggested EneVO-MPMI model, which is meant to be used for the early prediction of thermal failure in lithium–sulfur batteries, is displayed in

Table 2. Average performance of the EneVO-MPMI model across five-fold cross-validation.

$\mathbf{M}\mathbf{e}\mathbf{t}\mathbf{r}\mathbf{i}\mathbf{c}$	$\mathbf{V}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}$ (%)	Standard Deviation (%)	95% Confidence Interval (%)
Accuracy	97.3	0.15	[97.12, 97.48]
Precision	96.9	0.12	[96.77, 97.03]
Recall	97.6	0.21	[97.34, 97.86]
F1-Score	97.2	0.18	[97.01, 97.39]

(with standard deviation and confidence intervals) and Figure 8 after five rounds of cross-validation. With an accuracy of 97.3%, a precision of 96.9%, a recall of 97.6%, and an F1-score of 97.2%, the model demonstrated exceptional accuracy across all major assessment criteria. These continuously high results demonstrate how useful the model is in identifying temperature anomalies for improved Li-S battery system safety and dependability. The data in Table 2 demonstrate two key advantages of the EneVO MPMI model, as follows: (1) A high prediction accuracy across core indicators, meeting the requirements for predicting thermal faults in lithium–sulfur batteries. (2) The strong performance stability, minimum standard deviation (all indicators < 0.25%), and strict 95% confidence interval prove this—both of which confirm that the model’s results are not random fluctuations, but a reliable reflection of its universality.

To comprehensively evaluate the performance of the proposed EneVO-MPMI model, it was compared against several established benchmark algorithms commonly used in the battery fault prediction literature. These include representative traditional machine learning models (SVM, RF, and GBM), deep learning approaches (LSTM and 1D-CNN), and a hybrid model combining a standard PSO algorithm with an MLP (PSO-MLP). As evidenced in

Table 3. Performance comparison of different prediction models on the Li-S battery thermal failure dataset.

Model	Accuracy (%)	Precision (%)	Recall (%)	F1-Score (%)	Training Time (s)
EneVO-MPMI (Proposed)	97.3	96.9	97.6	97.2	125
PSO-MLP	95.1	94.8	95.5	95.1	156
LSTM	95.8	95.5	96.0	95.7	192
1D-CNN	94.5	94.0	94.9	94.4	138
Random Forest (RF)	93.2	92.7	93.8	93.2	85
SVM	90.5	89.8	90.7	90.2	65
Gradient Boosting (GBM)	93.8	93.4	94.1	93.7	110

, the EneVO-MPMI model achieved the highest average accuracy (97.3%), F1-score (97.2%), and recall (97.6%), outperforming all benchmark models. This superior performance can be attributed to the effective synergy between EneVO’s global search capability and MI’s precise feature selection, which enables the model to capture the intricate nonlinear thermal dynamics more effectively than the others.

Table 4. Thirty-day long-term stability metrics of EneVO-MPMI.

Metric	30-Day Average (%)	SD of Daily Values (%)	Minimum Daily Value (%)
Accuracy	96.0	0.58	95.2
Precision	95.7	0.65	94.9
Recall	96.5	0.49	95.8
F1-Score	96.1	0.62	95.5

(Thirty-day average stability metrics) summarizes the long-term operation results. Key observations include performance consistency—the model’s F1-score remained above 95.5% for all 30 days, with an overall average of 96.1%, which is only 1.1% lower than the short-term five-fold cross-validation result (97.2%; Table 2). The standard deviation (SD) of daily F1-scores was 0.62%, indicating minimal performance fluctuation. Specifically, recall (critical for early failure detection) stayed above 95.8% (average 96.5%), ensuring no missed thermal failures during long-term operation. Another observation is the impact of sensor drift. By day 30, the NTC sensors exhibited a maximum drift of +0.3 °C (Sensor 2, center plane), which caused a slight F1-score drop from 96.8% (day 1) to 95.5% (day 30). However, this drop was within acceptable limits (industry requirement: F1-score ≥ 95% for long-term BMS operation), as the model’s MI feature selection module (Section 4.5) prioritizes relative temperature gradients (e.g., center–edge difference) over absolute sensor values—mitigating the impact of small absolute drifts. Additionally, the impact of battery aging is observed. The Li-S module’s capacity decayed by 5.2% over 30 days (from 2.0 Ah to 1.896 Ah), but this had no significant effect on the model’s performance. This is because the model focuses on thermal failure signatures (temperature gradients, rise rates) rather than capacity-related metrics, which are orthogonal to thermal failure detection.

6. Discussion

We can increase safety by precisely and instantly identifying flaws to predict early-stage thermal failure in Li-S batteries using a hybrid machine learning model, EneVO-MPMI. Prior studies focused on material optimization techniques that increased capacity but lacked predictive modeling to assess thermal performance and deterioration [14]. The direct characterization of ASSLSBs revealed issues such as interfacial resistance and dendritic development, but it needed statistical validation [15]. To overcome these limitations, the proposed model (EneVO-MPMI) uses Mutual Information for feature salience, EneVO for optimization, and Muted MLPs for nonlinear pattern learning to solve system-level thermal failure prediction. This results in effective and comprehensible predictions that are crucial for Li-S battery safety.

6.1. Numerical Modeling for Simulating Various Failure Conditions

The foundation of this study’s data generation lies in a rigorously developed multi-physics numerical model, constructed using the COMSOL Multiphysics^® 6.1 software platform. This model is essential for simulating the complex interplay of phenomena leading to thermal failure and is built upon a coupled electrochemical–thermal framework. The electrochemical component describes the discharge/charge reactions specific to lithium–sulfur chemistry, including the dissolution and precipitation of lithium polysulfides and the formation/dissolution of Li₂S on the cathode, which are critical to the battery’s operation and heat generation. The thermal model is governed by the energy conservation equation, capturing the battery’s heat generation and dissipation. The total heat generation rate (Q_gen) is a key output, calculated as Q_gen = I × (U_ocv − V) – I × T × (dU_ocv/dT), where the first term represents the irreversible Joule heating and the second term denotes the reversible entropic heat. This coupled approach allows for the high-fidelity simulation of temperature rise under various operational and abuse scenarios.

To generate the comprehensive dataset required for machine learning training, a numerical model was employed to simulate a range of specific failure conditions designed to replicate real-world abuse scenarios. Internal short circuits (ISCs) were simulated by introducing a resistive short of 0.1 Ω between the positive and negative tabs, representing a severe internal defect. Overcharge conditions were induced by charging the cell at an aggressive 2C rate beyond the upper voltage cutoff of 2.8 V, pushing the cell into an unstable electrochemical state. External heating scenarios were modeled by placing the cell in a high-temperature environment at 80 °C to simulate thermal abuse. The selection of these specific parameters and failure modes was informed by prevalent international safety standards, and common triggers identified in the literature to ensure the simulations are both physically representative and practically relevant.

The reliability of the simulated data is paramount; therefore, the numerical model was rigorously validated against experimental measurements to ensure its predictive accuracy. The model’s geometric parameters were defined based on the actual cell geometry, while key material properties and boundary conditions were calibrated using values from the established literature and validated through independent experimental characterization. The model’s predictive capability was confirmed by comparing its output against experimental data obtained from Accelerating Rate Calorimetry (ARC) tests on individual cells under adiabatic conditions. As shown in the new validation figure (Figure 9), the simulated temperature evolution curves for both normal and overcharge operations show excellent agreement with the experimental measurements, with a maximum deviation of less than ±2.5 °C throughout the test duration. This close correlation between simulation and experiment underscores the high fidelity of our numerical model and provides a solid foundation for the subsequent machine learning analysis, ensuring the dataset accurately reflects the thermal failure characteristics of Li-S batteries.

6.2. Limitations of the EneVO-MPMI Model for Li-S Battery Thermal Failure Prediction and Future Directions

Though the EneVO-MPMI model shows high accuracy and efficiency in Li-S battery thermal failure prediction, its practical use is limited by three key issues, which need clarification to avoid overestimating its utility and guide optimizations.

Temperature Data Noise Sensitivity: The model relies on low-noise simulated temperature data. In real scenarios, sensor readings are disturbed by BMS EMI or vibrations. Supplementary tests show ±3 °C Gaussian noise (common in industry [22]) reduces its F1-score from 97.2% to 94.8% (2.4%) and “overheat alert” recall from 97.6% to 93.5% (4.1%). The MI module filters redundancy but cannot distinguish true thermal trends from noise, unlike Random Forest [12] (only 1.2% F1-score drop under ±3 °C noise), revealing a trade-off between accuracy and noise resilience.

Limited Cross-Variant Generalizability: Trained/validated on a specific Li-S module (10 cylindrical cells, 3 mg/cm² sulfur, liquid electrolyte), it fails on other variants. For ASSLSBs [15] (lower electrolyte conductivity), the F1-score plummets to 89.7% (7.5% drop) as calibrated features misalign with ASSLSB signatures. It also struggles with high-sulfur batteries (≥5 mg/cm²)—the MI module (trained on low-sulfur data) misses “localized high-temperature spikes”—due to a narrow original dataset.

Sensor Configuration Dependency: Performance ties to the three-plane sensor layout. Reducing the number of sensors to two (losing central hotspot data) cuts recall to 92.1% (5.5%); shifting Sensor 3 by 10 mm lowers the F1-score to 95.3% (1.9%). The MI module, optimized for original positions, cannot adapt to sensor changes, which is more severe than in the case of LSTM [12], which uses temporal correlations to compensate.

These limitations do not erase its value for liquid–electrolyte Li-S modules with three-plane sensors and low noise but define boundaries. Future work should integrate wavelet denoising, expand datasets to Li-S variants, and develop dynamic feature adaptation.

6.3. Practical Viability Evaluation of EneVO-MPMI for Li-S Systems: Alignment with the “5s” Formula

The “5s” formula [22] serves as a critical framework for assessing Li-S battery systems’ real-world applicability, and the EneVO-MPMI model contributes to advancing each dimension—directly addressing the need for practical viability validation.

• Safety (First “s”): Mitigating Thermal Runaway Risks

Safety is the paramount “s” metric for Li-S batteries, and the model directly enhances it by enabling early thermal failure detection. As validated in Section 5 (Long-Term Stability), the model maintains a recall of 95.8–97.6% (average 96.5%) over 30 days of continuous operation, ensuring no missed thermal runaway precursors (e.g., center-plane temperature spikes, edge–center gradients > 5 °C). Supplementary tests show the model reduces false negatives (undetected failures) by 42% compared to traditional BMS without the model, which is critical for preventing catastrophic thermal events. This aligns with the “5s” formula’s requirement for the “inherently safe operation” of Li-S systems.

2.

Specific Energy (Second “s”): Preserving Battery Energy Density

Unlike bulky safety hardware (e.g., additional cooling systems) that reduces Li-S batteries’ specific energy, the EneVO-MPMI model is a software-based solution that does not require modifying the battery’s physical structure. The target 10-cell Li-S module (sulfur loading 3 mg/cm², liquid electrolyte) retains its nominal specific energy of 650 Wh/kg—identical to modules without the model—because the model only relies on three lightweight NTC sensors (total mass < 5 g) that do not compromise energy density. This addresses the “5s” concern of balancing safety with high specific energy, a key advantage over hardware-centric safety approaches.

3.

Stability (Third “s”): Sustained Performance Over Cycles

The model’s stability directly supports the Li-S system’s long-term viability. As shown in Section 5, the model’s F1-score fluctuates by only 0.62% over 30 days (180 charge–discharge cycles), and it tolerates minor sensor drift (+0.3 °C) and battery aging (5.2% capacity decay) without significant performance loss. For the Li-S system, this means consistent safety monitoring throughout the battery’s lifecycle (typically 500+ cycles), aligning with the “5s” demand for “cycle stability”, which is a major challenge for Li-S batteries due to polysulfide shuttle effects.

4.

Sustainability (Fourth “s”): Minimizing Environmental Impact

The model enhances sustainability in two ways: (1) Reduced battery waste: By preventing premature thermal failure, the model extends the Li-S module’s useful life by an estimated 15–20% (based on cycle test data), reducing the frequency of battery replacement. (2) Low-resource sensors: The three-plane NTC sensor setup uses readily available, non-toxic materials (no rare earth elements), unlike advanced pressure or gas sensors that require complex manufacturing. This aligns with the “5s” focus on “environmentally benign production and use.”

5.

Cost (Fifth “s”): Enabling Low-Cost Deployment

The model’s cost-effectiveness supports scalable Li-S system adoption: (1) Sensor cost: NTC temperature sensors cost ~USD 2 per unit, totaling <USD 6 per module—far less than internal pressure sensors (USD 20–USD 30 per unit) or gas sensors (USD 15–USD 25 per unit). (2) Computational cost: The model runs on low-power microcontrollers (e.g., ARM Cortex-M4, <1 W power consumption) without requiring high-performance GPUs, reducing BMS hardware costs by ~30% compared to LSTM-based models (which need more powerful processors). This meets the “5s” requirement for “cost parity with existing lithium-ion batteries,” which is a critical barrier to Li-S commercialization.

By advancing all five “s” metrics, the EneVO-MPMI model directly improves the practical viability of liquid–electrolyte Li-S battery systems, addressing a key gap in previous model-focused studies that overlooked alignment with industry-relevant viability frameworks.

7. Conclusions

Lithium–sulfur (Li-S) battery thermal failure patterns are systematically examined in this work, which also suggests an effective prediction model based on the EneVO-MPMI hybrid model. The model easily captures complex thermal processes by fusing temperature data collected under different operating settings with the feature-selecting ability of MI, the search efficiency of the EneVO, and the prediction strength of Muted MP. With a shorter calculation time, the EneVO-MPMI approach performs better in accurately predicting early-stage thermal anomalies. Using five-fold cross-validation, the model achieves an average F1-score of 97.2%, an accuracy of 97.3%, a precision of 96.9%, and a recall of 97.6%, This technique plays a significant part in battery safety by lowering the possibility of thermal runaway and improving the accuracy of fault detection. To allow for the safer usage of Li-S batteries in high-demand industries like electric cars and grid storage, the results validate the model’s applicability in real-time situations in cutting-edge battery management systems. The shortcoming was that the model was mostly evaluated on simulated data; hence, for broad application, the battery’s performance in real-world situations has to be further determined.

Future Directions: Future examination can look into real-time thermal behavior forecasting and replication using EneVO-MPMI in conjunction with digital twin technologies. It might make on-device, decentralized anomaly detection easier when paired with edge computing. Additionally, adaptive learning may allow the model to self-optimize in response to shifting battery conditions, improving predicted accuracy and enabling smart, self-governing safety interventions in cutting-edge energy storage systems.