Uncertainty-Aware Quantile-GBRT Modeling and Robust Optimization of a Hybrid Air–Liquid Battery Thermal Management System

Merve Akkuş; Ferhat Akkuş

doi:10.54287/gujsa.1831336

Uncertainty-Aware Quantile-GBRT Modeling and Robust Optimization of a Hybrid Air–Liquid Battery Thermal Management System

Abstract

In recent years, with the advancement of technology and industry, electric vehicles have become widely used. These vehicles have evolved with the goals of environmental sustainability and energy efficiency, increasing demand for lithium-ion battery technologies that offer high energy density and long life. In this study, the maximum temperature and temperature increase of a lithium-ion battery module in a 4-series 3-parallel configuration were analyzed using experimental air and hybrid (air+water) battery thermal management system (BTMS) data with an artificial intelligence-based uncertainty modeling approach. Going beyond traditional deterministic regressions, quantile-based GBRT models were applied, and q10–q50–q90 probability bands were created for each experimental configuration. Thus, the system's temperature behavior was evaluated not only through average predictions but also with uncertainty intervals. Robust Pareto optimization conducted under the condition q90(Tmax) ≤ 30°C revealed safe design points that minimize both maximum temperature and temperature difference. The Pareto analysis determined the optimal region to be around q90(Tmax) ≈ 28.8°C and q90(ΔT) ≈ 2.1°C; even in this case, the temperature difference remained below 2.5°C. Explainable artificial intelligence tools such as SHAP and PDP analyses showed that air and refrigerant flow rates play a dominant role in the temperature response, and that hybrid cooling provides a significant improvement in both Tmax and ΔT values compared to air cooling. In conclusion, the study presents an uncertainty-aware and data-driven BTMS design framework that integrates quantile modeling, robust optimization, and explainable artificial intelligence approaches, contributing to the development of safe and efficient electric vehicle battery systems.

Keywords

References

Acar, E., Jain, N., Ramu, P., Hwang, C., & Lee, I. (2024). A survey on design optimization of battery electric vehicle components, systems, and management. Structural and Multidisciplinary Optimization. https://doi.org/10.1007/s00158-024-03737-7
Ait Mouloud, L., Kheldoun, A., Oussidhoum, S., Alharbi, H., Alotaibi, S., Alzahrani, T., & Agajie, T. F. (2025). Seasonal quantile forecasting of solar photovoltaic power using Q-CNN-GRU. Scientific Reports, 15(1). https://doi.org/10.1038/s41598-025-12797-8
Akkuş, F., & Işık, M. Z. (2023). Elektrikli araçlarda kullanılan lityum iyon bataryaların hava, sıvı ve ısı borulu termal yönetim sistemlerinin incelenmesi. Batman Üniversitesi Yaşam Bilimleri Dergisi, 13(2), 36–54. https://doi.org/10.55024/buyasambid.1339607
Alcántara, A., Galván, I. M., & Aler, R. (2023). Deep neural networks for the quantile estimation of regional renewable energy production. Applied Intelligence, 53(7), 8318–8353. https://doi.org/10.1007/s10489-022-03958-7
Alcibar, J., Aizpurua, J. I., Zugasti, E., & Peñagarikano, O. (2025). A hybrid probabilistic battery health management approach for robust inspection drone operations. Engineering Applications of Artificial Intelligence, 146, 110246. https://doi.org/10.1016/j.engappai.2025.110246
Billert, A. M., Erschen, S., Frey, M., & Gauterin, F. (2022). Predictive battery thermal management using quantile convolutional neural networks. Transportation Engineering, 10, 100150. https://doi.org/10.1016/j.treng.2022.100150
Fu, Z., Zhang, J., & Peng, Q. (2022). Robust design for the cooling performance of the battery pack fire extinguishing system. In Proceedings of CAD Conference (pp. 107–112). https://doi.org/10.14733/cadconfP.2022.107-112
Hassija, V., Chamola, V., Mahapatra, A., Singal, A., Goel, D., Huang, K., Scardapane, S., Spinelli, I., Mahmud, M., & Hussain, A. (2024). Interpreting black-box models: A review on explainable artificial intelligence. Cognitive Computation. https://doi.org/10.1007/s12559-023-10179-8

Khiari, J., & Olaverri-Monreal, C. (2022). Uncertainty-aware prediction of battery energy consumption for hybrid electric vehicles. In Proceedings of the IEEE Intelligent Vehicles Symposium (pp. 1005–1010). https://doi.org/10.1109/IV51971.2022.9827458
Kisomi, M. K. (2022). Thermal management of lithium-ion batteries: A comparative study of phase change materials and air-cooling systems equipped with fins (MSc Thesis).
Kim, J., Yoo, Y. S., Yang, H. S., & Choi, H. S. (2024). Robust uncertainty-aware control of energy storage systems using biased renewable energy forecast. Applied Energy, 367, 123309. https://doi.org/10.1016/j.apenergy.2024.123309
Li, S., Zhang, C., Zhao, Y., Offer, G. J., & Marinescu, M. (2023). Effect of thermal gradients on inhomogeneous degradation in lithium-ion batteries. Communications Engineering, 2(1). https://doi.org/10.1038/s44172-023-00124-w
Li, W., Wang, N., Garg, A., & Gao, L. (2023). Multi-objective optimization of an air cooling battery thermal management system considering battery degradation and parasitic power loss. Journal of Energy Storage, 58, 106382. https://doi.org/10.1016/j.est.2022.106382
Liang, B., Liu, H., Cressey, E. L., Xu, C., Shi, L., Wang, L., Dai, J., Wang, Z., & Wang, J. (2023). Uncertainty of partial dependence relationship between climate and vegetation growth calculated by machine learning models. Remote Sensing, 15(11), 2920. https://doi.org/10.3390/rs15112920
Liu, S., Wang, Y., Liu, Q., Panchal, S., Zhao, J., Fowler, M., Fraser, R., & Yuan, J. (2024). Thermal equalization design for the battery energy storage system (BESS) of a fully electric ship. Energy, 312, 133611. https://doi.org/10.1016/j.energy.2024.133611
Lundberg, S. M., & Lee, S.-I. (2017). A unified approach to interpreting model predictions. Advances in Neural Information Processing Systems. http://arxiv.org/abs/1705.07874
Molnar, C., Casalicchio, G., & Bischl, B. (2020). Interpretable machine learning: A brief history, state-of-the-art and challenges. In Explainable AI. Springer. https://doi.org/10.1007/978-3-030-65965-3_28
Pirotta, M., Parisi, S., & Restelli, M. (2014). Multi-objective reinforcement learning with continuous Pareto frontier approximation. http://arxiv.org/abs/1406.3497
Ponce‐Bobadilla, A. V., Schmitt, V., Maier, C. S., Mensing, S., & Stodtmann, S. (2024). Practical guide to SHAP analysis: Explaining supervised machine learning model predictions in drug development. Clinical and Translational Science, 17(11). https://doi.org/10.1111/cts.70056
Sarıkurt, T., & Balıkçı, A. (2018). Elektrikli araç uygulamalarında kullanılan lityum bataryalar için göreceli kapasite tahmin yöntemi. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi, 24(5), 809–816.
Sukkam, N., Katongtung, T., Suttakul, P., Mona, Y., Achariyaviriya, W., Tippayawong, K. Y., & Tippayawong, N. (2024). Machine learning prediction of a battery’s thermal-related health factor in a battery electric vehicle using real-world driving data. Information, 15(9), 553. https://doi.org/10.3390/info15090553
Tai, L. D., & Lee, M. Y. (2025). Advances in the battery thermal management systems of electric vehicles for thermal runaway prevention and suppression. Batteries. https://doi.org/10.3390/batteries11060216
Wu, S., Li, D., Xing, W., & Liu, Y. (2025). Quantitative prediction model for lithium-ion battery life uncertainty based on DAE-CNN-BiGRU quantile regression. Journal of Energy Storage, 123, 116771. https://doi.org/10.1016/j.est.2025.116771
Xu, L., Wang, S., Xi, L., Li, Y., & Gao, J. (2024). A review of thermal management and heat transfer of lithium-ion batteries. Energies, 17(16). https://doi.org/10.3390/en17163873
Yang, T., Liu, H., Zhang, W., Ding, A., & Wu, M. (2025). Multi-objective topology optimization of the cooling plate for battery thermal management. Batteries, 11(11), 406. https://doi.org/10.3390/batteries11110406
Ye, L., Li, C., Wang, C., Zheng, J., Zhong, K., & Wu, T. (2024). A multi-objective optimization approach for battery thermal management system based on BP neural network prediction and NSGA-II algorithm. Journal of Energy Storage, 99, 113212. https://doi.org/10.1016/j.est.2024.113212
Zhang, Q., Cao, G., & Zhang, X. (2023). Study of wet cooling flat heat pipe for battery thermal management application. Applied Thermal Engineering, 219, 119407. https://doi.org/10.1016/j.applthermaleng.2022.119407
Zhang, Z., & Jung, C. (2019). GBDT-MO: Gradient boosted decision trees for multiple outputs. arXiv. http://arxiv.org/abs/1909.04373
Zhang, Y., Tian, J., Guo, Z., Fu, Q., & Jing, S. (2025). Uncertainty-Aware Economic Dispatch of Integrated Energy Systems with Demand-Response and Carbon-Emission Costs. Processes, 13(6). https://doi.org/10.3390/pr13061906
Zhou, X., Guo, W., Shi, X., She, C., Zheng, Z., Zhou, J., & Zhu, Y. (2024). Machine learning assisted multi-objective design optimization for battery thermal management system. Applied Thermal Engineering, 253, 123826. https://doi.org/10.1016/j.applthermaleng.2024.123826

Details

Primary Language

English

Subjects

Energy Generation, Conversion and Storage (Excl. Chemical and Electrical), Hybrid and Electric Vehicles and Powertrains

Journal Section

Research Article

Authors

Merve Akkuş ^*
0000-0002-6648-0946
Türkiye

Ferhat Akkuş
0000-0002-4587-7039
Türkiye

Publication Date

March 31, 2026

Submission Date

November 27, 2025

Acceptance Date

February 5, 2026

Published in Issue

Year 2026 Volume: 13 Number: 1

DOI

https://doi.org/10.54287/gujsa.1831336

IZ

https://izlik.org/JA92DN93KF

Cite

RIS / Bibtex

APA

Akkuş, M., & Akkuş, F. (2026). Uncertainty-Aware Quantile-GBRT Modeling and Robust Optimization of a Hybrid Air–Liquid Battery Thermal Management System. Gazi University Journal of Science Part A: Engineering and Innovation, 13(1), 242-268. https://doi.org/10.54287/gujsa.1831336

AMA

1.Akkuş M, Akkuş F. Uncertainty-Aware Quantile-GBRT Modeling and Robust Optimization of a Hybrid Air–Liquid Battery Thermal Management System. GU J Sci, Part A. 2026;13(1):242-268. doi:10.54287/gujsa.1831336

Chicago

Akkuş, Merve, and Ferhat Akkuş. 2026. “Uncertainty-Aware Quantile-GBRT Modeling and Robust Optimization of a Hybrid Air–Liquid Battery Thermal Management System”. Gazi University Journal of Science Part A: Engineering and Innovation 13 (1): 242-68. https://doi.org/10.54287/gujsa.1831336.

EndNote

Akkuş M, Akkuş F (March 1, 2026) Uncertainty-Aware Quantile-GBRT Modeling and Robust Optimization of a Hybrid Air–Liquid Battery Thermal Management System. Gazi University Journal of Science Part A: Engineering and Innovation 13 1 242–268.

IEEE

[1]M. Akkuş and F. Akkuş, “Uncertainty-Aware Quantile-GBRT Modeling and Robust Optimization of a Hybrid Air–Liquid Battery Thermal Management System”, GU J Sci, Part A, vol. 13, no. 1, pp. 242–268, Mar. 2026, doi: 10.54287/gujsa.1831336.

ISNAD

Akkuş, Merve - Akkuş, Ferhat. “Uncertainty-Aware Quantile-GBRT Modeling and Robust Optimization of a Hybrid Air–Liquid Battery Thermal Management System”. Gazi University Journal of Science Part A: Engineering and Innovation 13/1 (March 1, 2026): 242-268. https://doi.org/10.54287/gujsa.1831336.

JAMA

1.Akkuş M, Akkuş F. Uncertainty-Aware Quantile-GBRT Modeling and Robust Optimization of a Hybrid Air–Liquid Battery Thermal Management System. GU J Sci, Part A. 2026;13:242–268.

MLA

Akkuş, Merve, and Ferhat Akkuş. “Uncertainty-Aware Quantile-GBRT Modeling and Robust Optimization of a Hybrid Air–Liquid Battery Thermal Management System”. Gazi University Journal of Science Part A: Engineering and Innovation, vol. 13, no. 1, Mar. 2026, pp. 242-68, doi:10.54287/gujsa.1831336.

Vancouver

1.Merve Akkuş, Ferhat Akkuş. Uncertainty-Aware Quantile-GBRT Modeling and Robust Optimization of a Hybrid Air–Liquid Battery Thermal Management System. GU J Sci, Part A. 2026 Mar. 1;13(1):242-68. doi:10.54287/gujsa.1831336