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Frontiers in Mechanical Engineering ·

Volume 12 - 2026 | https://doi.org/10.3389/fmech.2026.1949090

Optimizing temperature prediction in automotive lithium-ion battery discharge cycles using machine learning and SHAP analysis

  • Anuj Prajapati1*corresponding author
  • Sandeep G. Thorat2
  • Gajanan Pradhan3
  • Swapnil Gund2
  • Prashant Paraye4
  • Vardan Singh5
  1. 1Department of Computer Engineering, Trinity Institute of Technology & Research, Bhopal, India
  2. 2Department of Mechanical Engineering, MIT Art Design and Technology University, Pune, India
  3. 3Kokuyo Workplace India Limited, Nagpur, India
  4. 4Department of Mechanical Engineering, PlastIndia International University, Mumbai, India
  5. 5Shree Jugal Kishore Structures Pvt Ltd, Bhopal, India
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Abstract

Effective thermal control is essential for lithium-ion batteries used in electric vehicles and energy storage systems, as uncontrolled heat generation accelerates degradation, reduces performance, and increases safety risk. Conventional temperature-prediction studies often report high accuracy using random data splitting; however, such evaluation may not adequately represent performance on unseen battery cells. This study aims to develop an accurate, stable, and interpretable machine-learning framework for predicting lithium-ion battery temperature during discharge cycles under unseen-battery conditions. The NASA lithium-ion battery ageing dataset was used to train and evaluate Linear Regression, Random Forest, and Light Gradient Boosting Machine models. Five input features were considered: measured voltage, measured current, power, cumulative discharged energy, and voltage drop, with measured temperature as the target. Battery-wise validation was performed using cells B0005, B0006, B0007, and B0018, where each battery was used once as an independent test set. Model performance was assessed using root mean square error, mean absolute error, and coefficient of determination. Uncertainty analysis, residual diagnostics, and SHapley Additive exPlanations were used to examine prediction stability, error behaviour, and feature influence. Light Gradient Boosting Machine achieved the strongest overall generalization, with a mean root mean square error of 1.070 °C and a mean coefficient of determination of 0.910. Random Forest showed closely comparable performance and achieved the lowest mean absolute error of 0.893 °C, while Linear Regression showed weaker predictive performance. SHAP analysis identified power, cumulative discharged energy, and measured voltage as the dominant predictors. The proposed framework provides a reliable and interpretable approach for battery temperature prediction and supports data-driven thermal monitoring in battery management systems. Future work should validate the model using broader datasets, real-time sensor data, ageing indicators, and physics-informed learning under dynamic operating conditions.

Keywords

1 Introduction

Lithium-ion batteries underpin consumer electronics, electric vehicles (EVs), and aerospace systems owing to their high energy density and long cycle life (Zolin and Zolin, 2017; Stan et al., 2014; Aifantis et al., 2022; Choe et al., 2024). In EVs, their specific capacity enables extended driving range and rapid power delivery (Wang et al., 2024; Radomski et al., 2013; Yu et al., 2024; Prajapati et al., 2025). However, Li-ion cells are highly temperature-sensitive; rapid charge/discharge induces heat that, if unmanaged, degrades capacity and can trigger thermal runaway (Demiryürek et al., 2022; Sun T. et al., 2025; Chinthalapudi et al., 2023; Li et al., 2025; Gund et al., 2026). Runaway events, often initiated by internal short circuits or overcharging, may escalate to fire or explosion, making thermal control a paramount safety concern (Kannan et al., 2021; Sonthalia et al., 2023; Yang et al., 2024). Elevated temperatures accelerate side reactions, causing marked capacity fade; tests at 55 °C report ∼36% loss after 350 cycles (Ke et al., 2024). Heat generation scales with discharge rate; at 2.5 C, the end-of-discharge heat density is approximately 1.8 times the initial value, and a 6 A load advances runaway onset by 7% (Mushtaq et al., 2024; Shivram and Harish, 2024; Maher and Boumaiza, 2025). Conversely, transient charging can provoke voltage drops linked to lithium plating, underscoring the interplay between electro-thermal dynamics and performance (Pilali et al., 2025). Real-time thermal monitoring mitigates these risks. Advanced sensors and estimation schemes, such as particle filters, electrochemical-impedance thermometry, and virtual thermal sensors, offer sub-degree accuracy (Du et al., 2019; Wang et al., 2022; Huang and Lai, 2019; Ren et al., 2022). Machine-learning frameworks, including LSTM and gated recurrent units, predict temperature trajectories within ±0.5 °C, enabling proactive cooling and capacity estimation (Tan et al., 2023; Ouyang et al., 2018; Li L. et al., 2021; Gulsoy et al., 2024). Real-time monitoring remains the primary defence against thermal incidents in lithium-ion batteries. Early signatures, such as rapid temperature rise and internal-gas pressure build-up, can be detected long before catastrophic failure, enabling immediate counter-measures such as current cut-off or active cooling (Zhang and Wei, 2025; Yin et al., 2023). Sequence-learning models such as the Informer localise thermal faults with ≤0.5 °C error, supporting pinpoint diagnosis under dynamic load profiles (Sun Y. et al., 2025). Broader machine-learning frameworks, from linear regression (LR) to deep recurrent networks, extrapolate future temperature trajectories, giving battery-management systems (BMS) sufficient lead-time to adjust cooling strategies (Mynavathi et al., 2024).

Uniform cell temperature is equally critical. Particle-filter algorithms and virtual thermal sensors estimate core temperatures in real time, mitigate cell-to-cell gradients, and thereby extend service life (Paccha-Herrera et al., 2024). Hierarchical capacity estimators that fuse core-temperature and heat-generation data further improve state-of-health (SOH) tracking throughout ageing cycles (Zhang et al., 2019). Sensor fusion enhances prediction precision. Electrochemical-impedance thermometry, combined with convolutional or transformer-based surface-temperature estimators, yields high-resolution thermal maps despite sparse physical sensors (Mc Carthy et al., 2022). When integrated into modern BMS architectures, gated-recurrent and LSTM-HMM models provide sub-second inference at low computational cost, making real-time deployment feasible in automotive platforms (Sun et al., 2024). Elevated discharge currents shorten the latency to thermal runaway and reduce total heat release because exothermic reactions initiate earlier (DONG et al., 2020). Temperature-induced voltage shifts can enhance performance at low ambient temperatures yet also signal safety-critical lithium plating during thermal transients (Carter et al., 2019). These considerations underscore the need for adaptive, data-driven thermal-management solutions that safeguard battery integrity across diverse operating regimes.

Machine learning (ML) has emerged as a powerful tool for analyzing the thermal behaviour of lithium-ion batteries, playing a critical role in enhancing their safety, efficiency, and reliability. Recent advancements have focused on combining ML with multiphysics models to predict thermal runaway events by simulating complex interactions between electrochemical processes, degradation mechanisms, and heat generation. Hybrid models that fuse physics-based simulations like the Single Particle Model with Thermal dynamics (SPMT) with neural networks have also demonstrated superior accuracy under high charge/discharge rates (Tu et al., 2021). ML is further utilized to optimize advanced cooling strategies, considering factors such as energy efficiency, economic cost, and environmental impact (Parsa et al., 2023). Recent studies have increasingly demonstrated the effectiveness of machine-learning and ensemble-based approaches for battery health and thermal-performance prediction. Sekhar et al. used the HNEI battery life-cycle dataset and reported that Random Forest (RF) achieved stronger remaining useful life prediction performance than linear regression, decision tree, Bayesian network, and gradient boosting models, confirming the suitability of tree-based learning for battery prognostics (Sekhar et al., 2023). Similarly, Sravanthi and Sekhar developed an optimized RF-XGBoost ensemble for remaining useful life, state of charge, and state of health prediction, showing improved accuracy for practical electric-vehicle battery-management applications (Sravanthi and Sekhar, 2026). In another comparative study, Sravanthi and Sekhar found that the Bagging Regressor provided the best remaining useful life prediction among gradient boosting, k-nearest neighbours, bagging, and extra-tree regression models, while maintaining reasonable computational efficiency (Sravanthi, 2025). A recent review further emphasized that data-dependent machine learning, deep learning, and ensemble models are promising for battery remaining useful life prediction; however, their practical deployment in battery management systems still requires robustness under dynamic operating conditions, noise, and limited computational resources (CL et al., 2025). These findings support the need for leakage-safe, interpretable, and computationally practical models for lithium-ion battery temperature prediction under discharge conditions. Collectively, these approaches underscore the vital role of ML in predicting and controlling the thermal behaviour of lithium-ion batteries across various operational scenarios.

Several machine-learning approaches have been reported for lithium-ion battery temperature prediction, including RF, GNN-LSTM, LR, GPR, SVM, LSTM, ARIMA, TDNN, and ANN-based models, as summarized in Table 1. These studies have mainly focused on predictive accuracy using input variables such as voltage, current, time, state of health, ambient temperature, and time-series operating data. However, relatively limited attention has been given to engineered electrothermal features, uncertainty evaluation, residual diagnostics, and feature-level explainability within a single battery temperature prediction framework. To address this gap, the present study develops a machine-learning-based framework for predicting lithium-ion battery temperature during discharge cycles using 169,766 samples from the NASA battery ageing dataset. Five input features were considered, namely, Voltage_measured, Current_measured, Power, Energy, and Voltage_drop, with Temperature_measured used as the target response. The novelty of this work lies in integrating engineered electrothermal features, leave-one-battery-out validation, uncertainty analysis, residual diagnostics, and SHAP-based interpretability. This approach evaluates not only prediction accuracy but also model stability, error behaviour, and feature influence under unseen-battery conditions. The objective of this study is to identify the most accurate, stable, and interpretable model for battery temperature prediction, thereby supporting safer and more reliable automotive battery thermal-management systems.

TABLE 1. Machine-learning models for lithium-ion battery temperature prediction.

ML modelFeaturesTargetFindingsPerformanceReferences
RFVoltage, current, time, SOHBattery temperatureIncorporates SOH for robust and precise estimationMAE = 0.1621; MSE = 0.0556; MAPE = 0.0504; R 2 = 0.9865(Ghodake et al., 2023)
GNN + LSTMSpatial and temporal temperature mapsThermal hotspots/battery temperatureIdentifies thermal-runaway zones via hotspot localizationMAE = 0.0720; RMSE = 0.1870(Goswami et al., 2024)
LR, GPR, SVMCurrent, voltage, temperatureBattery temperatureComparative analysis across models for accuracy profilingRMSE = 0.0746; MAE = 0.0423; R 2 = 1.0000(Zazoum, 2023)
LSTM, ARIMATime-series dataBattery temperatureLSTM outperforms ARIMA in precision and responsiveness<10% error; ∼8 min test time (ANN); SVM: similar accuracy(Zhou et al., 2017)
TDNNCurrent, voltage, ambient temperatureBattery temperatureCaptures nonlinear dynamics with strong correlationR 2 = 0.997; MSE = 0.514(Al Miaari and Ali, 2023)
ANNLarge multi-cycle datasetsBattery temperatureBalances high accuracy with manageable complexityR 2 = 0.9742(Örs and Javani, 2025)
LR, RF, LightGBMVoltage, current, power, cumulative discharged energy, voltage dropBattery temperatureLightGBM achieved the best overall generalization; SHAP identified power, cumulative discharged energy, and measured voltage as the dominant featuresLightGBM: RMSE = 1.070 °C, MAE = 0.898 °C, R2 = 0.910Present study

2 Methodology

2.1 Dataset description

The dataset used in this study was obtained from the Li-ion Battery Aging Dataset provided by the NASA Ames Prognostics Center of Excellence (PCoE) (NASA Prognostics Center of Excellence, 2025). The dataset was generated through controlled battery-degradation experiments on commercial 18,650-sized lithium-ion cells subjected to repeated charge–discharge cycling under controlled operating conditions. The original experiments were designed to simulate battery ageing until the cells reached the end-of-life threshold, defined by approximately 30% capacity loss from the nominal capacity of 2.0 A h to about 1.4 A h. The analysed dataset consisted of 169,766 discharge-cycle samples from four batteries, namely, B0005, B0006, B0007, and B0018. The discharge data were recorded at an ambient temperature of 24 °C with an approximately 2 A discharge current, corresponding to nearly 1C with respect to the nominal 2.0 A h capacity. The sampling interval was non-uniform and varied approximately between 9 and 20 s.

The recorded variables included measured voltage, measured current, measured temperature, charge current, charge voltage, capacity, time, cycle identifier, charge/discharge type, ambient temperature, and battery identifier. For model development, only discharge-cycle data were considered. Among the recorded variables, measured temperature was selected as the target thermal response, while measured voltage and measured current were retained as primary electrical predictors. Three engineered features, namely, Power, Energy, and Voltage_drop, were derived from the measured signals to represent instantaneous discharge power, cycle-wise cumulative discharged energy, and voltage-loss behaviour associated with internal resistance effects. The final input feature set consisted of Voltage_measured, Current_measured, Power, Energy, and Voltage_drop, while the battery identifier was used only for battery-wise validation grouping and was not included as a model input. This feature set was selected to capture the major electrical and operational factors affecting battery temperature during discharge cycles.

The use of this dataset assumes that controlled 18,650-cell discharge data provide a suitable basis for data-driven battery temperature prediction under the stated operating conditions. This assumption is supported by the availability of experimentally recorded voltage, current, temperature, capacity, time, and battery-level information. However, the limitations associated with unavailable cell chemistry, sensor accuracy, load-profile, and data-acquisition hardware details are explicitly acknowledged. Figure 1 presents the complete workflow adopted for battery temperature prediction, including data collection, preprocessing, feature engineering, model training, validation, evaluation, and result interpretation.

Prediction workflow.
Figure 1. Prediction workflow.

2.2 Descriptive data analysis

A comprehensive descriptive analysis was conducted to examine the statistical characteristics and interrelationships of the selected features before model development. The dataset comprised five input variables, namely, Voltage_measured, Current_measured, Power, Energy, and Voltage_drop, along with Temperature_measured as the target variable. Voltage_measured ranged approximately from 2.4 V to 4.2 V, reflecting the voltage response of lithium-ion cells during discharge operation. Current_measured represented the discharge-current behaviour in the selected discharge-cycle data. Energy, calculated as cycle-wise cumulative discharged energy using non-uniform time increments, showed a positively skewed distribution and increased with discharge progression. Voltage_drop, defined as the difference between the charge/reference voltage and the measured voltage, remained within a narrow range, indicating voltage-loss behaviour associated with internal resistance effects and cell-level operating variation.

Figure 2 shows the correlation matrix between the selected features and measured temperature. Voltage_measured and Power exhibited strong negative correlations with Temperature_measured, with correlation coefficients of approximately −0.92. In contrast, Energy showed a strong positive correlation with Temperature_measured, with a coefficient of approximately 0.90, indicating that temperature increased with cumulative discharged energy. Voltage_drop showed a weak positive association with temperature, whereas Current_measured showed negligible direct linear correlation. Although Current_measured had limited linear correlation, it was retained because nonlinear and interaction-based effects may still be captured by tree-based learning models.

Correlation matrix.
Figure 2. Correlation matrix.

Figure 3 presents the pairwise distributions and scatter relationships among the selected predictors. The Power–Voltage_measured relationship showed a nearly linear trend because Power was derived from measured voltage and the absolute discharge-current magnitude. The Energy-related plots showed nonlinear patterns, reflecting the progressive accumulation of discharged energy within each discharge cycle. The clustered patterns observed in Current_measured and Voltage_drop were attributed to discharge operating regions, battery-to-battery variation, and cycle-level differences within the discharge-only dataset.

Pairwise distribution and scatter plots.
Figure 3. Pairwise distribution and scatter plots.

Figure 4 illustrates the relationship between Temperature_measured and cumulative discharged energy. A clear increasing trend was observed, confirming that battery temperature rises as cumulative discharged energy increases. The broader spread at higher energy levels suggests that temperature evolution is influenced not only by cumulative energy but also by voltage response, power level, battery-specific behaviour, and cycle-level operating conditions.

Battery temperature versus cumulative discharged energy.
Figure 4. Battery temperature versus cumulative discharged energy.

Figure 5 shows the relationship between Temperature_measured and Power. The plot reveals a strong inverse nonlinear trend, where higher power values are generally associated with lower measured temperatures in the discharge dataset. This behaviour is consistent with discharge progression, where voltage and power decrease as the cell moves toward later thermal states. These nonlinear relationships support the use of ensemble-based machine-learning models for battery temperature prediction.

Temperature variation with power.
Figure 5. Temperature variation with power.

2.3 Feature engineering

To enhance the predictive capability of the models, feature engineering was performed using the measured electrical signals available in the discharge-cycle dataset. Instantaneous discharge power was calculated as the product of measured voltage and the absolute magnitude of measured current:where V i and I i represent the measured voltage and measured current of the i th sample, respectively. The absolute current magnitude was used because the discharge current follows a negative sign convention; therefore, this formulation represents discharge power as a positive quantity in watts.

P i = V i × I ᵢ (1)

Since the sampling interval was non-uniform, the Energy feature was calculated as cycle-wise cumulative discharged energy rather than by direct multiplication of power and elapsed time. For each discharge cycle, the time increment between two consecutive samples was calculated as:

Δ t i = t i − t i − 1 (2)

The incremental discharged energy was then obtained as:and the cumulative discharged energy was calculated as:where Δ t k = t k − t k − 1, and t k is the recorded discharge time in seconds. The cumulative energy calculation was restarted at the beginning of each discharge cycle for each battery to avoid energy carry-over between independent cycles. Since power is expressed in watts and time in seconds, Energy is expressed in Ws, equivalent to joules. In this study, Energy was used as a cumulative electrothermal descriptor representing the combined effect of discharge power and discharge duration.

Δ E i = P i Δ t i (3)

E i = ∑ k = 1 i P k Δ t k (4)

Voltage_drop was calculated as:where V charge , i represents the charge/reference voltage and V measured , i represents the measured voltage of the i th sample. This feature was used as a proxy for voltage-loss behaviour associated with internal resistance effects. The final input feature set consisted of Voltage_measured, Current_measured, Power, Energy, and Voltage_drop, while Temperature_measured was used as the prediction target.

V drop , i = V charge , i − V measured , i (5)

2.4 Model selection

This study employed three supervised machine-learning models, namely, LR, RF, and LightGBM, to develop a predictive framework for estimating the surface temperature of lithium-ion batteries. LR was implemented as the baseline model due to its analytical simplicity and interpretability. However, consistent with observations by Gangwar et al. (2024), its capacity to model nonlinear relationships and complex feature interactions was inherently limited, resulting in relatively lower predictive performance. To address these limitations, RF was adopted as a more robust alternative. As a non-parametric ensemble learning algorithm, RF constructs multiple decision trees using bootstrap aggregation and averages their outputs to enhance prediction accuracy and reduce overfitting. This approach has been shown to improve generalization in thermal and degradation modelling tasks (Alsubayhin et al., 2024). LightGBM, a state-of-the-art gradient boosting framework, was incorporated as the most advanced model in the comparative study. Known for its leaf-wise tree growth strategy and histogram-based optimization, LightGBM offers notable improvements in training speed, memory efficiency, and scalability. Studies by Huang and Airlangga (Airlangga, 2025; Huang et al., 2022) have demonstrated the strong performance of LightGBM and related machine-learning models on structured datasets, making it particularly well-suited for high-frequency thermal data encountered in battery diagnostics.

2.5 Model evaluation strategy

To evaluate the generalization capability of the developed temperature-prediction models, a battery-wise validation strategy was adopted. Unlike random five-fold splitting, this approach keeps one complete battery dataset unseen during testing and uses the remaining batteries for training. This design was selected because battery temperature prediction in practical battery management systems must work on new cells, not only on randomly mixed samples from the same cells. The validation was performed using four independent test batteries: B0005, B0006, B0007, and B0018. In each run, one battery was separated as the test set, while data from the other three batteries were combined for training. Thus, each model was evaluated four times under unseen-battery conditions. The number of training and testing samples changed according to the selected test battery; for instance, testing on B0005 used 124,644 training samples and 45,122 testing samples. Three models LR, RF, and LightGBM were assessed using RMSE, MAE, and R 2. RMSE measured the overall temperature prediction error and gave higher penalty to larger deviations. MAE represented the average absolute difference between measured and predicted temperature, while R 2 indicated how well the model explained the measured temperature variation. Mean values and standard deviations of these metrics were calculated across the four validation runs to compare both accuracy and stability. In addition, residual histograms and residual-versus-predicted-temperature plots were examined to identify bias, non-uniform error spread, and systematic prediction patterns. This combined strategy provided a realistic and reliable assessment of overall practical model performance for unseen battery cells.

Table 2 presents the dataset split used for leakage-safe battery-wise validation. In each validation run, one complete battery was kept as the unseen test battery, while the remaining three batteries were used for training. The training samples varied from 121,467 to 137,775, and the test samples varied from 31,991 to 48,299 depending on the selected test battery. This validation strategy avoids random mixing of samples from the same battery and provides a more realistic assessment of model generalization under unseen-battery conditions.

TABLE 2. Training and test sample distribution.

Training batteriesTest batteryTraining samplesTest samples
B0006, B0007, B0018B0005124,64445,122
B0005, B0007, B0018B0006125,41244,354
B0005, B0006, B0018B0007121,46748,299
B0005, B0006, B0007B0018137,77531,991

2.6 Mathematical modelling and optimization framework

In the present study, temperature prediction during lithium-ion battery discharge cycles is formulated as a supervised temperature-prediction problem. The measured battery temperature is considered as the output response, while the selected electrical and engineered features are used as input variables. For the i th data sample, the input vector is defined as:where V i is the measured voltage, I i is the measured current, P i is power, E i is cycle-wise cumulative discharged energy, and V drop , i is voltage drop. The target output is expressed as:where T i is the measured battery temperature, f X i represents the predictive model, and ϵ i is the prediction error.

X i = V i , I i , P i , E i , V drop , i (6)

T i = f X i + ϵ i (7)

The engineered features were mathematically defined from the measured battery signals. Power was calculated as:

P i = V i × I i (8)

Cumulative discharged energy was calculated by integrating instantaneous power over the time increment between consecutive samples:Here, Δ t k = t k − t k − 1, where t k is the recorded discharge time in seconds. The cumulative energy calculation was restarted at the beginning of each discharge cycle for each battery to avoid carry-over between independent cycles.

E i = ∑ k = 1 i P k Δ t k (9)

V drop , i = V charge , i − V measured , i (10)

Thus, the machine learning models predict the battery temperature as:where T i ^ is the predicted temperature and θ represents the model parameters learned during training. The optimization objective is to minimize the difference between measured and predicted temperature values. This can be expressed as:where n is the total number of training samples. For LR, the prediction function is represented as:where β 0 is the intercept, β j are regression coefficients, and m is the number of input features. For RF, the final prediction is obtained by averaging the outputs of multiple decision trees:where B is the total number of trees and h b X i is the prediction of the b th tree. For LightGBM, the prediction is formed by sequentially adding boosted decision trees:where M is the number of boosting iterations, η is the learning rate, and g m X i is the decision tree added at the m th iteration.

T i ^ = f θ X i (11)

θ * = arg min θ 1 n ∑ i = 1 n T i − T i ^ 2 (12)

T i ^ = β 0 + ∑ j = 1 m β j X ij (13)

T i ^ = 1 B ∑ b = 1 B h b X i (14)

T i ^ = ∑ m = 1 M η g m X i (15)

Model performance was evaluated using root mean square error, mean absolute error, and coefficient of determination. These metrics are defined as: where T ¯ is the mean measured temperature. This mathematical framework defines the complete data-driven optimization process used for battery temperature prediction, from feature construction to model training and performance evaluation.

RMSE = 1 n ∑ i = 1 n T i − T i ^ 2 (16)

MAE = 1 n ∑ i = 1 n ∣ T i − T i ^ ∣ (17)

R 2 = 1 − ∑ i = 1 n T i − T i ^ 2 ∑ i = 1 n T i − T i ^ 2 (18)

2.7 Model interpretability using SHAP

SHAP (SHapley Additive exPlanations) is a widely used method for interpreting the predictions of machine learning models. It is based on game theory and assigns each feature an importance value by estimating its contribution to the model’s output. SHAP values provide both local (individual prediction) and global (model-level) explanations, ensuring transparency and trust (Mosca et al., 2022). SHAP is especially valued for its solid theoretical foundation and consistency with human intuition in feature attribution (Pezoa et al., 2023; Ponce‐Bobadilla et al., 2024).

3 Results

3.1 Cross-validation metrics

The predictive performance of LR, RF, and LightGBM was evaluated using leave-one-battery-out validation. In this validation scheme, one complete battery dataset was kept as an independent test set, while the remaining three battery datasets were used for model training. This approach provided an assessment of model generalization under unseen-battery conditions. The models were evaluated using RMSE, MAE, and R 2, and the battery-wise results are summarized in Table 3.

TABLE 3. Cross-validation performance metrics.

ModelTest batteryRMSE (°C)MAE (°C)R2
LightGBMB00050.9850.8380.930
B00061.3741.1670.878
B00070.6780.5220.967
B00181.2401.0640.866
Average1.0700.8980.910
LRB00051.6681.4200.799
B00061.6121.3580.833
B00072.6002.3790.520
B00181.4231.1480.824
Average1.8261.5760.744
RFB00050.9010.7180.941
B00061.4311.1850.868
B00070.7410.6000.961
B00181.2511.0670.864
Average1.0810.8930.909

Table 3 indicates that the ensemble-based models provided substantially better prediction performance than the linear baseline. LightGBM produced the lowest mean RMSE of 1.070 °C and the highest mean R 2 of 0.910, indicating strong predictive accuracy and explanatory capability across the unseen battery cells. RF showed closely comparable performance, with a mean RMSE of 1.081 °C and R 2 of 0.909, and recorded the lowest mean MAE of 0.893 °C. In comparison, LR resulted in a higher mean RMSE of 1.826 °C, MAE of 1.576 °C, and lower R 2 of 0.744, reflecting its limited ability to capture nonlinear electrothermal behaviour during discharge operation. The battery-wise results also show that model performance varied across individual test cells. For the ensemble models, the lowest prediction errors were obtained for B0007, whereas relatively higher errors were observed for B0006 and B0018. This variation suggests that cell-specific ageing behaviour and cycle-level operating differences influenced the prediction response under unseen-battery validation. Overall, LightGBM provided the most favourable balance between RMSE and R 2, while RF remained highly competitive and achieved the lowest average absolute error.

3.2 Uncertainty analysis of temperature-prediction performance

Uncertainty analysis was performed to evaluate the stability of temperature-prediction performance across unseen battery cells and different thermal operating regions. The uncertainty was quantified using the standard deviation of performance metrics obtained from the four leave-one-battery-out validation runs. In each validation run, one complete battery was used as the unseen test cell, while the remaining batteries were used for training. Therefore, the mean value represents the average predictive performance of each model, whereas the standard deviation indicates the variability in model performance across different unseen battery cells.

Figure 6 presents the overall predictive performance of LR, RF, and LightGBM in terms of mean RMSE and mean R 2. LightGBM achieved the lowest mean RMSE of 1.070 °C and the highest mean R 2 of 0.910, indicating strong generalization capability under unseen-battery validation. RF showed closely comparable performance, with a mean RMSE of 1.081 °C and R 2 of 0.909. In contrast, LR exhibited a higher mean RMSE of 1.826 °C and a lower R 2 of 0.744. The larger error bars observed for LR indicate higher performance variability across the test batteries, whereas the ensemble-based models showed comparatively more stable prediction behaviour.

Overall temperature-prediction performance with error bars.
Figure 6. Overall temperature-prediction performance with error bars.

To further examine prediction stability across different thermal regions, the measured temperature data were divided into four ranges: 20 °C–30 °C, 30 °C–35 °C, 35 °C–40 °C, and above 40 °C. Figure 7 shows the temperature-range-wise RMSE comparison, while Figure 8 presents the corresponding MAE comparison. The error bars represent the standard deviation across the four leave-one-battery-out validation runs and indicate the variation in model performance under unseen-cell conditions.

Temperature-range-wise RMSE comparison with error bars.
Figure 7. Temperature-range-wise RMSE comparison with error bars.
Temperature-range-wise MAE comparison with error bars.
Figure 8. Temperature-range-wise MAE comparison with error bars.

The RMSE results in Figure 7 show that LightGBM and RF maintained lower prediction errors than LR across most temperature ranges. In the 20 °C–30 °C and 30 °C–35 °C ranges, both ensemble models produced relatively low and stable RMSE values, indicating reliable prediction in the lower and moderate temperature regions. Prediction error increased in the 35 °C–40 °C and above 40 °C ranges for all models, suggesting that temperature prediction becomes more challenging at elevated battery temperatures. A similar trend is observed in Figure 8, where MAE values increased with temperature range, particularly above 40 °C. Although RF showed slightly lower MAE in some ranges, LightGBM maintained a favourable overall balance between RMSE, MAE, and R 2. Uncertainty analysis confirms that the ensemble-based models provide more stable and accurate temperature-prediction performance than the linear baseline. The increased error variation at higher temperature levels indicates that elevated thermal regions involve stronger nonlinear behaviour and cell-specific effects, which are more difficult to model under unseen-battery conditions. The uncertainty analysis was further supported by Breusch–Pagan and White heteroscedasticity tests. As shown in Table 4, both tests produced p-values below 0.001 for LR, RF, and LightGBM, indicating statistically significant non-constant residual variance. This confirms that prediction errors were not uniformly distributed across the prediction range and supports the use of temperature-range-wise RMSE and MAE analysis for evaluating temperature-prediction stability.

TABLE 4. Breusch–Pagan and White test results.

ModelBreusch–Pagan p-valueWhite test p-value
LRp < 0.001p < 0.001
RFp < 0.001p < 0.001
LightGBMp < 0.001p < 0.001

3.3 Residual diagnostics

Residual diagnostics were performed to examine the distribution, bias, and error structure of the three evaluated models, namely, LR, RF, and LightGBM. For each model, residual distribution histograms and residuals-versus-predicted-temperature plots were used to evaluate central tendency, error spread, heteroscedasticity, and systematic prediction behaviour. The residual behaviour of LR is shown in Figure 9. The residual histogram in Figure 9a exhibited a broad and uneven distribution, with residuals extending approximately from −9 °C to +6 °C. The distribution was not closely centred around zero and showed a clear bimodal tendency, indicating higher error dispersion and prediction bias. The residuals-versus-predicted-temperature plot in Figure 9b showed a strongly structured pattern, with curved residual bands and a widening spread across the prediction range. At higher predicted temperatures, the residuals shifted increasingly toward negative values, indicating systematic underprediction in the elevated-temperature region. This behaviour confirms that the linear model was unable to adequately capture the nonlinear thermal response of lithium-ion batteries under unseen-battery conditions.

**(a)** Residual distribution for LR, **(b)** residuals versus predicted temperature plot for LR.
Figure 9. (a) Residual distribution for LR, (b) residuals versus predicted temperature plot for LR.

The RF model showed improved residual behaviour compared with LR, as presented in Figure 10. The residual histogram in Figure 10a was narrower and more concentrated around zero, with most residuals lying within approximately ±3 °C. The residuals-versus-predicted-temperature plot in Figure 10b showed a more compact residual band than LR, although some structured variation remained across the prediction range. A mild downward residual trend was visible at higher predicted temperatures, suggesting limited underprediction in elevated thermal regions. Despite this pattern, RF reduced the overall residual spread and provided more stable predictions than the linear baseline.

**(a)** Residual distribution for RF, **(b)** residuals versus predicted temperature plot for RF.
Figure 10. (a) Residual distribution for RF, (b) residuals versus predicted temperature plot for RF.

Figure 11 presents the residual diagnostics of the LightGBM model. The residual histogram in Figure 11a was concentrated near zero and showed a comparatively controlled error distribution, with most residuals remaining within approximately ±3 °C. The residuals-versus-predicted-temperature plot in Figure 11b showed a dense residual cloud across most of the predicted temperature range. Although the residual spread increased slightly at higher predicted temperatures, the overall error pattern remained more controlled than LR and comparable to RF. This indicates that LightGBM was able to capture the nonlinear discharge-temperature behaviour more effectively than the linear model while maintaining strong generalization under battery-wise validation.

**(a)** Residual distribution for LightGBM, **(b)** residuals versus predicted temperature plot for LightGBM.
Figure 11. (a) Residual distribution for LightGBM, (b) residuals versus predicted temperature plot for LightGBM.

The residual diagnostics are consistent with the cross-validation results. LR produced wider and more biased residuals, whereas the ensemble-based models showed lower error dispersion and more stable prediction behaviour. Among the evaluated models, LightGBM provided the most favourable overall balance between prediction accuracy, residual control, and explanatory performance, while RF remained closely competitive.

3.4 Smoothed trend analysis

To complement the residual-based evaluation, smoothed trend analysis was performed to examine the underlying physical relationships between battery temperature and the dominant electrothermal variables. While residual diagnostics assess prediction error behaviour, smoothed curves provide clearer insight into how temperature changes with cumulative discharged energy and power during discharge operation. This analysis reduces the visual effect of scattered cycle-level data and highlights the overall nonlinear thermal response of the cells.

Figure 12 shows the smoothed relationship between average battery temperature and cumulative discharged energy. The curve indicates a consistent increase in temperature with increasing cumulative energy, confirming the role of energy accumulation in thermal build-up during discharge operation. Since cumulative energy was calculated using the non-uniform time increment, the x-axis is expressed in Ws, equivalent to joules. The gradual flattening of the curve at higher energy levels suggests that the temperature rise becomes less steep near the later stage of discharge, although the overall trend remains increasing.

Smoothed temperature trend with cumulative discharged energy.
Figure 12. Smoothed temperature trend with cumulative discharged energy.

Figure 13 presents the smoothed temperature response with respect to power. The curve shows a nonlinear decreasing trend, where average temperature remains higher at lower power levels and decreases as power increases. This inverse relationship is consistent with the discharge process, in which voltage and power are higher during earlier, cooler stages and decrease as the cell progresses toward later, warmer discharge states. The nonlinear behaviour observed in Figures 12, 13 further supports the use of ensemble-based models for battery temperature prediction.

Smoothed temperature response to power.
Figure 13. Smoothed temperature response to power.

3.5 SHAP analysis

SHAP analysis was performed to interpret the predictions of the LightGBM model and quantify the contribution of each input feature to the predicted battery temperature. The mean absolute SHAP value plot in Figure 14 ranks the features according to their overall influence on the model output. Power showed the highest mean absolute SHAP value, followed by Energy and Voltage_measured. Voltage_drop showed a moderate contribution, while Current_measured had the lowest influence. This ranking indicates that instantaneous discharge power, cumulative discharged energy, and voltage response were the dominant predictors governing the temperature-prediction behaviour of the LightGBM model.

Mean absolute SHAP values for LightGBM input features.
Figure 14. Mean absolute SHAP values for LightGBM input features.

The SHAP summary beeswarm plot in Figure 15 provides further insight into both the magnitude and direction of feature influence. Power exhibited the widest SHAP distribution, confirming its strong contribution to the model output. Lower Power values were mainly associated with positive SHAP values, indicating an increase in predicted temperature, whereas higher Power values were mostly associated with negative SHAP values. This behaviour is consistent with the discharge process, where power decreases as the cell progresses toward warmer later-stage discharge conditions. Energy also showed a strong influence, with higher cumulative energy values generally shifting predictions toward higher temperature. In contrast, lower Energy values were associated with negative SHAP contributions, corresponding to lower predicted temperature during earlier discharge stages.

SHAP summary beeswarm plot for LightGBM model.
Figure 15. SHAP summary beeswarm plot for LightGBM model.

Voltage_measured also had a strong and physically meaningful effect on the predicted temperature. Higher voltage values were mainly distributed on the negative SHAP side, while lower voltage values shifted toward positive SHAP values. This indicates that reduced voltage during discharge is associated with higher predicted temperature. Voltage_drop showed a smaller but noticeable contribution, reflecting additional voltage-loss-related information associated with cell operating behaviour and internal resistance effects. Current_measured remained closely clustered near zero, indicating limited independent contribution to the LightGBM prediction compared with the other engineered features.

Figure 16 presents the SHAP dependence relationship between Power and Voltage_measured. At lower and moderate Power values, the SHAP values were predominantly positive, indicating an increase in predicted battery temperature. As Power increased beyond approximately 7 W, the SHAP values shifted toward zero and then became negative, suggesting a reduced contribution to predicted temperature. The colour gradient further indicates that this response was influenced by Voltage_measured. Lower voltage conditions were mainly associated with positive Power-related SHAP values, whereas higher voltage conditions were more closely associated with negative SHAP contributions at higher power levels. This confirms that the influence of Power on temperature prediction was not independent, but depended on the simultaneous voltage condition of the cell.

SHAP interaction of Power and Voltage_measured.
Figure 16. SHAP interaction of Power and Voltage_measured.

SHAP results confirm that the LightGBM model captured meaningful electrothermal relationships within the discharge-cycle dataset. Power, Energy, and Voltage_measured were identified as the most influential predictors, showing that instantaneous electrical loading, cumulative discharged energy, and voltage response jointly control the predicted thermal behaviour. Voltage_drop provided additional supporting information related to voltage-loss behaviour, whereas Current_measured contributed comparatively less as an independent predictor. These findings improve the interpretability of the proposed temperature-prediction framework and support its potential application in battery thermal monitoring and intelligent battery-management systems.

4 Discussion

Tran et al. (2022) evaluated four machine learning models LR, k-NN, Decision Trees, and RF for predicting lithium-ion battery temperature. RF showed superior performance (R 2 = 0.989), highlighting its ability to capture nonlinear thermal behaviours using real-world operational data. Fang et al. (2012) and Chen et al. (2013) applied feed-forward neural networks (FFNNs) to estimate battery surface temperature, replacing complex electrochemical models. Both studies demonstrated ANN’s capability to simulate thermal dynamics under varying ambient conditions. Ströbel et al. (2021) utilized real and imaginary impedance data with an ANN to estimate state-of-charge (SOC), state-of-health (SOH), and temperature. Their model required only a single impedance spectrum, reducing complexity while maintaining high accuracy. Jiang et al. (2021) compared LSTM-RNN and GRU networks, revealing LSTM’s higher sensitivity and predictive accuracy. Zhu et al. (2021) introduced a dual-function LSTM model for both temperature prediction and heat-type classification, thereby improving understanding of thermal-response behaviour. Ojo et al. (2020) developed a GRU-based model using RMSProp to handle temperature fluctuations under real-world loads. Kopp et al. (2022) compared ANN, CNN, and LSTM architectures, identifying LSTM as most effective, especially when using first-derivative inputs. Jiang et al. (2022) enhanced LSTM with elitist preservation and genetic algorithms for robust prediction under segmented input. Li M. et al. (2021b) designed an LSTM model to forecast temperature 5–10 s in advance, offering early-warning benefits for thermal management. Wang et al. (2021) applied CNNs with virtual sensors for internal temperature prediction, achieving better results than linear models due to spatial learning. Yang et al. (2021) simplified thermal analysis using a Single Hidden Neural Network, while Liu and Li (2015) pioneered SHNN with extreme learning for fast, real-time predictions.

Yang et al. (2020) hybridized FFNN with a 3D COMSOL model to capture both internal and surface temperatures. Tang et al. (2018) included Joule heating effects in long-term surface temperature modelling using SHNN. Feng et al. (2020) integrated current, voltage, and temperature in an electrochemical–thermal neural network, outperforming traditional models. For long-horizon forecasting, Hasan et al. (2020) used a NARX model with Levenberg–Marquardt training to predict temperature 24 h ahead. Kleiner et al. (2021a) and Behdad Jamshidi and Rostami (2017) optimized NARX architectures for dynamic accuracy. Kleiner et al. (2021b) found NARX more adaptive than physics-based models under varying load conditions. Fan et al. (2018) employed ANFIS, blending neural and fuzzy logic to model diverse operating states. The present study builds upon these advancements by evaluating three machine-learning regression models, namely, LR, RF, and LightGBM, for lithium-ion battery temperature prediction during discharge cycles. Under leave-one-battery-out validation, LightGBM achieved the strongest overall generalization, with the lowest mean RMSE of 1.070 °C and the highest mean R 2 of 0.910. RF showed closely comparable performance, with a mean RMSE of 1.081 °C and R 2 of 0.909, and achieved the lowest mean MAE of 0.893 °C. In contrast, LR showed comparatively weaker prediction performance, indicating that linear modelling was less effective in capturing the nonlinear electrothermal response of lithium-ion batteries under unseen-battery conditions. By combining battery-wise validation, residual diagnostics, uncertainty assessment, and SHAP-based interpretability, the proposed framework provides a practical route for identifying dominant thermal predictors and supporting data-driven battery thermal-management decisions.

Table 5 summarizes the practical design and manufacturing benefits of the proposed temperature-prediction framework. The framework supports sensor selection, model choice, reliability assessment, thermal interpretation, and BMS-level integration. These outcomes indicate that the proposed approach can assist battery designers and system engineers in identifying relevant operating parameters, evaluating model reliability, and supporting safer thermal-control strategies before physical deployment.

TABLE 5. Practical benefit of the proposed temperature-prediction framework for design and manufacturing.

Design/manufacturing needSupport from present studyReal benefit to designer
Selection of important monitoring parametersThe model uses Voltage_measured, Current_measured, Power, Energy, and Voltage_drop as input features for predicting battery temperatureA designer can focus sensor selection and data acquisition on relevant electrical and electrothermal parameters instead of relying on unnecessary variables
Model choice for thermal predictionBattery-wise validation shows that LightGBM achieved the best overall balance of prediction accuracy and explanatory capability, with RMSE of 1.070 °C and R2 of 0.910The designer can consider LightGBM as a practical prediction model for estimating battery temperature in new or unseen cells
Reliability before real deploymentResidual diagnostics showed that LightGBM and RF provided more controlled residual behaviour than LR, with lower error dispersion under unseen-battery validationThe designer can assess prediction reliability before integrating the model into a battery management system
Understanding thermal causesSHAP analysis identified Power, Energy, and Voltage_measured as the dominant predictors of battery temperatureThe designer can understand how instantaneous electrical loading, cumulative discharged energy, and voltage response influence thermal behaviour
Manufacturing-level applicationThe framework supports data-driven battery thermal monitoring, model-based validation, and safer battery-management decisionsThe designer can use the model output as a decision-support tool for sensor planning, control logic, and validation before prototype testing

5 Limitation and future scope

The present study is limited to the NASA lithium-ion battery ageing dataset, which includes four 18,650 cells tested under controlled experimental conditions. Therefore, the generalization of the developed framework to other battery chemistries, cell formats, nominal capacities, pack configurations, and real vehicle operating environments remains unverified. Although the dataset provides useful discharge-cycle measurements, complete details regarding exact cell chemistry, temperature sensor accuracy, sensor model, and data-acquisition hardware are not available, which restricts deeper experimental interpretation. The model was developed using selected electrical and engineered features, namely, Voltage_measured, Current_measured, Power, Energy, and Voltage_drop. Other potentially relevant variables, such as ageing indicators, impedance response, internal temperature, coolant behaviour, thermal-management control signals, and real driving-load profiles, were not included. In addition, the Energy feature was calculated as cycle-wise cumulative discharged energy using the available time and power measurements; therefore, further validation with datasets having higher sampling resolution and more detailed electrothermal measurements would strengthen the physical interpretation. Future work should validate the proposed framework using broader experimental datasets covering different chemistries, C-rates, ambient temperatures, ageing stages, and dynamic drive cycles. Real-time implementation in battery management systems should also be examined using onboard sensors, embedded hardware constraints, and practical computational limits. Hybrid physics-informed machine-learning models may further improve reliability, robustness, and deployment readiness by combining data-driven prediction with electrochemical and thermal-domain knowledge.

6 Conclusion

This study developed a quantitative and interpretable machine-learning framework for predicting lithium-ion battery temperature during discharge cycles using 169,766 samples from NASA battery cells B0005, B0006, B0007, and B0018. A leave-one-battery-out validation strategy was adopted, in which each battery was tested once as an unseen cell while the remaining cells were used for training. This approach provided a more realistic assessment of model generalization than random sample splitting. The final feature set consisted of five physically meaningful predictors, namely, Voltage_measured, Current_measured, Power, Energy, and Voltage_drop. Among the evaluated models, LightGBM achieved the strongest overall predictive performance, with a mean RMSE of 1.070 °C and R 2 of 0.910. RF remained closely competitive, with a mean RMSE of 1.081 °C and R 2 of 0.909, and achieved the lowest mean MAE of 0.893 °C. In comparison, LR showed weaker prediction capability, with a mean RMSE of 1.826 °C, MAE of 1.576 °C, and R 2 of 0.744. Relative to LR, LightGBM reduced RMSE by approximately 41.4%, reduced MAE by 43.0%, improved R 2 by 22.3%, and reduced unexplained variance by approximately 64.8%. These results confirm the advantage of ensemble-based models for capturing nonlinear thermal behaviour during lithium-ion battery discharge operation.

Residual diagnostics further supported the quantitative findings. LR showed wider and more biased residual patterns, whereas the ensemble models produced more compact and stable error distributions. LightGBM provided the most favourable overall balance between prediction accuracy, residual control, and explanatory capability, while RF remained a strong alternative with slightly lower average absolute error. SHAP analysis identified Power, Energy, and Voltage_measured as the dominant predictors, indicating that instantaneous discharge power, cumulative discharged energy, and voltage response jointly govern the predicted thermal behaviour. Voltage_drop provided additional supporting information related to voltage-loss behaviour, while Current_measured showed limited independent influence. The main contribution of this work lies in integrating engineered electrothermal features, corrected cumulative-energy calculation, unseen-cell validation, uncertainty assessment, residual diagnostics, and SHAP-based interpretation within a single practical battery temperature-prediction framework. However, the study remains limited to the NASA ageing dataset and selected electrical features. Future work should extend the framework to broader battery chemistries, cell formats, C-rates, ambient conditions, ageing stages, real-time sensor data, and dynamic drive-cycle profiles. Hybrid physics-informed machine-learning approaches may further improve robustness, physical interpretability, and deployment readiness for practical battery-management systems.

Generative AI statement

The author(s) declared that generative AI was used in the creation of this manuscript. During the preparation of this manuscript, AI-assisted tools were used only to improve language, grammar, and flow. All research design, data analysis, interpretation of results, scientific conclusions, and final content were developed, verified, and approved by the authors.

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Footnotes

Edited by: Anatoliy Levin, Melentiev Energy Systems Institute (RAS), Russia

Reviewed by: Rajesh G, IDK Institution, India

J N Chandra Sekhar, Sri Venkateswara College of Engineering, Tirupati, India

Footnotes

LR, Linear Regression; RF, Random Forest; LightGBM, Light Gradient Boosting Machine; SHAP, SHapley Additive exPlanations; RMSE, Root Mean Square Error; MAE, Mean Absolute Error; R2, Coefficient of Determination; SOH, State of Health; LSTM, Long Short-Term Memory; GNN, Graph Neural Network; TDNN, Time-Delay Neural Network; ANN, Artificial Neural Network; GRU, Gated Recurrent Unit; CNN, Convolutional Neural Network; SHNN, Single Hidden Neural Network; NARX, Nonlinear Autoregressive with Exogenous Input; BMS, Battery Management System; PCoE, Prognostics Center of Excellence; NASA, National Aeronautics and Space Administration; EV, Electric Vehicle; EOL, End of Life.

Statements

Conflict of interest

Author GP was employed by Kokuyo Workplace India Limited. Author VS was employed by Shree Jugal Kishore Structures Pvt Ltd.

The remaining author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Funding

The author(s) declared that financial support was received for this work and/or its publication. The article processing charges are funded by MIT Art Design and Technology University, Pune, India.

Data availability

The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding authors.

Author contributions

AP: Writing – review and editing, Writing – original draft. ST: Writing – review and editing. GP: Writing – original draft, Writing – review and editing. SG: Writing – original draft, Writing – review and editing. PP: Writing – review and editing, Writing – original draft. VS: Writing – review and editing, Writing – original draft.

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Citation

Prajapati, A., et al. (2026). Optimizing temperature prediction in automotive lithium-ion battery discharge cycles using machine learning and SHAP analysis. Frontiers in Mechanical Engineering, Volume 12. https://doi.org/
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12 - 2026

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Copyright © 2026 Prajapati, Thorat, Pradhan, Gund, Paraye and Singh.

License: https://creativecommons.org/licenses/by/4.0/

*Correspondence: Anuj Prajapati

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