Simulation and optimization of hybrid battery thermal management based on SVR-NSGA-Ⅱ algorithm

doi:10.16085/j.issn.1000-6613.2025-066

Abstract

Abstract:

Battery thermal management is critical to ensure the thermal safety of lithium-ion batteries. Although traditional finite element analysis methods have been widely applied in battery thermal management research, they have limitations, such as low computational efficiency and complex parameter settings. This paper presented a machine learning model that combines feature engineering with finite element analysis results. By employing an orthogonal design method, the required finite element simulation data volume was effectively reduced. The support vector regression (SVR) model was used to accurately predict the temperature characteristics of a hybrid battery pack. The non-dominated sorting genetic algorithm Ⅱ (NSGA-Ⅱ) was applied to systematically analyze the synergistic optimization relationship between battery structural parameters and cooling strategies, proposing an optimal solution that balanced heat dissipation performance and energy consumption efficiency. Compared with traditional methods, the proposed approach significantly enhanced computational efficiency while maintaining prediction accuracy, providing a novel approach for the intelligent design of battery thermal management systems. The “feature extraction-machine learning modeling-multi-objective optimization” framework constructed in this study not only accurately predicteed battery temperature characteristics but also provided decision support for optimizing thermal management solutions in various application scenarios. This method has significant engineering application value in fields such as electric vehicles and energy storage systems, contributing to the improvement of battery system safety and energy efficiency.

Key words: battery thermal management, finite element analysis, support vector regression, non-dominated sorting genetic algorithm Ⅱ(NSGA-Ⅱ)

摘要：

锂电池热管理是确保电池热安全的关键，虽然传统的有限元分析方法被广泛应用于锂电池热管理研究，但存在计算效率低、参数设置复杂等局限性。本文提出了一种结合特征工程和有限元分析结果的机器学习模型，通过正交设计方法有效减小所需的有限元仿真数据量；利用支持向量回归（SVR）模型准确预测混合电池包的温度特征；采用非支配排序遗传算法Ⅱ（NSGA-Ⅱ）系统分析了电池结构参数与冷却策略的协同优化关系，提出了兼顾散热性能与能耗效率的最佳方案。与传统方法相比，本方法在保持预测精度的同时大幅提升了计算效率，为电池热管理系统的智能化设计提供了新思路。本研究构建的“特征提取-机器学习建模-多目标优化”技术框架，不仅能够准确预测电池温度特性，还能为不同应用场景下的热管理方案优化提供决策支持。该方法在电动汽车和储能系统等领域具有重要的工程应用价值，有助于提升电池系统的安全性与能效。

关键词: 电池热管理, 有限元分析, 支持向量回归, 非支配排序遗传算法

CLC Number:

TQ-9

MO Wendi, WANG Sijing, LIN Yiting, LIAN Cheng, LIU Honglai. Simulation and optimization of hybrid battery thermal management based on SVR-NSGA-Ⅱ algorithm[J]. Chemical Industry and Engineering Progress, 2025, 44(8): 4795-4807.

莫文迪, 王思静, 林伊婷, 练成, 刘洪来. 基于SVR-NSGA-Ⅱ算法的混合电池热仿真优化[J]. 化工进展, 2025, 44(8): 4795-4807.

Figures/Tables 10

References 31

[1]	YANG Xiaofei, Kieran DOYLE-DAVIS, GAO Xuejie, et al. Recent progress and perspectives on designing high-performance thick electrodes for all-solid-state lithium batteries[J]. eTransportation, 2022, 11: 100152.
[2]	ZHANG Xu, WANG Boya, ZHAO Shu, et al. Oxygen anionic redox activated high-energy cathodes: Status and prospects[J]. eTransportation, 2021, 8: 100118.
[3]	BANDHAUER Todd M, GARIMELLA Srinivas, FULLER Thomas F. A critical review of thermal issues in lithium-ion batteries[J]. Journal of the Electrochemical Society, 2011, 158(3): R1.
[4]	WALDMANN Thomas, WILKA Marcel, KASPER Michael, et al. Temperature dependent ageing mechanisms in lithium-ion batteries—A post-mortem study[J]. Journal of Power Sources, 2014, 262: 129-135.
[5]	WANG Yusong, LIU Bin, HAN Peng, et al. Optimization of an air-based thermal management system for lithium-ion battery packs[J]. Journal of Energy Storage, 2021, 44: 103314.
[6]	CHEN Shin-Chih, WANG Yung-Yun, WAN Chichao. Thermal analysis of spirally wound lithium batteries[J]. Journal of the Electrochemical Society, 2006, 153(4): A637.
[7]	KALKAN Orhan, CELEN Ali, BAKIRCI Kadir. Experimental and numerical investigation of the LiFePO₄ battery cooling by natural convection[J]. Journal of Energy Storage, 2021, 40: 102796.
[8]	ZHUANG Yijie, CHEN Tianhua, CHEN Jintao, et al. Thermal uniformity performance of a hybrid battery thermal management system using phase change material and cooling plates arrayed in the manner of honeycomb[J]. Thermal Science and Engineering Progress, 2021, 26: 101094.
[9]	MADANI Seyed Saeed, ZIEBERT Carlos, MARZBAND Mousa. Thermal behavior modeling of lithium-ion batteries: A comprehensive review[J]. Symmetry, 2023, 15(8): 1597.
[10]	XIAO Shuliang, ZENG Zhigang, ZHOU Difan, et al. Analyzing dynamic resistance in high-temperature superconducting tapes by combining finite element method with machine learning[J]. Journal of Central South University, 2024, 31(3): 737-746.
[11]	PEREIRA Danilo R, PITERI Marco Antonio, SOUZA André N, et al. FEMa: A finite element machine for fast learning[J]. Neural Computing and Applications, 2020, 32(10): 6393-6404.
[12]	CHENG Liang, GUO Haijing, SUN Lingyan, et al. Real-time simulation of tube hydroforming by integrating finite-element method and machine learning[J]. Journal of Manufacturing and Materials Processing, 2024, 8(4): 175.
[13]	NATH Dipjyoti, ANKIT, NEOG Debanga Raj, et al. Application of machine learning and deep learning in finite element analysis: A comprehensive review[J]. Archives of Computational Methods in Engineering, 2024, 31(5): 2945-2984.
[14]	LI Gang, LUO Rui, YU Dinghao. A framework for developing a machine learning-based finite element model for structural analysis[J]. Computers & Structures, 2025, 307: 107617.
[15]	ZHANG Ning, ZHANG Zhiyuan, LI Jintao, et al. Performance analysis and prediction of hybrid battery thermal management system integrating PCM with air cooling based on machine learning algorithm[J]. Applied Thermal Engineering, 2024, 257: 124474.
[16]	CHEN Xianzhong, TU Rang, LI Ming, et al. Hot spot temperature prediction and operating parameter estimation of racks in data center using machine learning algorithms based on simulation data[J]. Building Simulation, 2023, 16(11): 2159-2176.
[17]	ZHOU Xianlong, GUO Weilong, SHI Xiangyu, et al. Machine learning assisted multi-objective design optimization for battery thermal management system[J]. Applied Thermal Engineering, 2024, 253: 123826.
[18]	TANG Xingwang, GUO Qin, LI Ming, et al. Performance analysis on liquid-cooled battery thermal management for electric vehicles based on machine learning[J]. Journal of Power Sources, 2021, 494: 229727.
[19]	AHMAD Shakeel, LIU Yanhui, KHAN Shahid Ali, et al. Modeling liquid immersion-cooling battery thermal management system and optimization via machine learning[J]. International Communications in Heat and Mass Transfer, 2024, 158: 107835.
[20]	WANG Dan, Masood Ashraf ALI, ALIZADEH As’ad, et al. A numerical investigation of a two-phase nanofluid flow with phase change materials in the thermal management of lithium batteries and use of machine learning in the optimization of the horizontal and vertical distances between batteries[J]. Case Studies in Thermal Engineering, 2023, 41: 102582.
[21]	XIE Shiwei, XU Chengshan, LI Wei, et al. Machine learning accelerated the performance analysis on PCM-liquid coupled battery thermal management system[J]. Journal of Energy Storage, 2024, 100: 113479.
[22]	DOYLE Marc, FULLER Thomas F, NEWMAN John. Modeling of galvanostatic charge and discharge of the lithium/polymer/insertion cell[J]. Journal of the Electrochemical Society, 1993, 140(6): 1526-1533.
[23]	DOYLE Marc, NEWMAN John. The use of mathematical modeling in the design of lithium/polymer battery systems[J]. Electrochimica Acta, 1995, 40(13/14): 2191-2196.
[24]	MAHESHWARI Arpit, DUMITRESCU Mihaela Aneta, DESTRO Matteo, et al. Inverse parameter determination in the development of an optimized lithium iron phosphate-graphite battery discharge model[J]. Journal of Power Sources, 2016, 307: 160-172.
[25]	WANG Wenhe, HE Tengfei, HE Sen, et al. Modeling of thermal runaway propagation of NMC battery packs after fast charging operation[J]. Process Safety and Environmental Protection, 2021, 154: 104-117.
[26]	Peizhao LYU, HUO Yutao, QU Zhiguo, et al. Investigation on the thermal behavior of Ni-rich NMC lithium ion battery for energy storage[J]. Applied Thermal Engineering, 2020, 166: 114749.
[27]	XU Meng, ZHANG Zhuqian, WANG Xia, et al. Two-dimensional electrochemical-thermal coupled modeling of cylindrical LiFePO₄ batteries[J]. Journal of Power Sources, 2014, 256: 233-243.
[28]	REN Honglei, JIA Li, DANG Chao, et al. An electrochemical-thermal coupling model for heat generation analysis of prismatic lithium battery[J]. Journal of Energy Storage, 2022, 50: 104277.
[29]	MO Wendi, LIN Yiting, LI Jiahui, et al. An optimized hybrid battery pack with high energy density and high safety[J]. Chemical Engineering Science, 2024, 297: 120290.
[30]	DEB K, PRATAP A, AGARWAL S, et al. A fast and elitist multiobjective genetic algorithm: NSGA-Ⅱ[J]. IEEE Transactions on Evolutionary Computation, 2002, 6(2): 182-197.
[31]	LIANG Yueji, REN Chao, WANG Haoyu, et al. Research on soil moisture inversion method based on GA-BP neural network model[J]. International Journal of Remote Sensing, 2019, 40(5/6): 2087-2103.

参数	数值
参数	组合1	组合2	组合3	组合4	组合5	组合6
进风温度/K	298.15	296.15	294.15	292.15	290.15	288.15
风速/m·s^-1	0.5	0.4	0.3	0.2	0.1	0.05
电池横向间距/mm	50	40	30	20	10	5
电池纵向间距/mm	50	40	30	20	10	5
放电倍率	3C	2.5C	2C	1.5C	1C	0.5C

参数	数值
参数	组合1	组合2	组合3	组合4	组合5	组合6
进风温度/K	298.15	296.15	294.15	292.15	290.15	288.15
风速/m·s^-1	0.5	0.4	0.3	0.2	0.1	0.05
电池横向间距/mm	50	40	30	20	10	5
电池纵向间距/mm	50	40	30	20	10	5
放电倍率	3C	2.5C	2C	1.5C	1C	0.5C

输入					输出
倍率	温度/K	风速/m·s^-1	横间距/m	纵间距/m	最大温度/K	温差/K	功耗/W
3C	296.15	0.3	0.03	0.03	319.26	12.47	12.07
3C	288.15	0.1	0.04	0.005	324.32	16.13	19.45
3C	294.15	0.05	0.05	0.01	327.04	13.65	7.24
3C	288.15	0.5	0.05	0.03	312.38	14.1	95.53
3C	290.15	0.1	0.005	0.02	317.55	12.34	9.41
3C	290.15	0.3	0.03	0.02	319.31	13.12	35.98
2.5C	294.15	0.2	0.005	0.05	313.54	10.64	9.61
2.5C	298.15	0.1	0.05	0.005	323.93	11.48	3.70
2.5C	290.15	0.5	0.04	0.02	312.73	10.52	67.48
2.5C	296.15	0.3	0.02	0.03	315.68	9.7	10.60
2.5C	298.15	0.05	0.05	0.01	324.69	12.22	3.60
2.5C	292.15	0.4	0.05	0.04	315.41	11.78	47.99
2C	290.15	0.4	0.01	0.05	302.42	7.11	31.07
2C	296.15	0.2	0.04	0.02	316.1	8.66	10.20
2C	296.15	0.05	0.02	0.005	318.61	8.82	4.68
2C	288.15	0.3	0.01	0.05	316.48	8.49	29.19
2C	292.15	0.2	0.04	0.01	316.48	9.17	10.20
2C	292.15	0.3	0.05	0.005	315.32	10.40	36.87
1.5C	290.15	0.4	0.03	0.05	301.94	6.88	46.81
1.5C	292.15	0.05	0.005	0.04	311.73	9.41	5.74
1.5C	288.15	0.1	0.01	0.02	304.41	7.68	12.06
1.5C	292.15	0.5	0.01	0.03	299.61	4.42	29.59
1.5C	288.15	0.05	0.02	0.04	309.47	8.44	9.01
1.5C	298.15	0.5	0.005	0.005	304.98	6.98	4.50
1C	292.15	0.4	0.005	0.05	314.82	13.32	21.42
1C	294.15	0.2	0.04	0.04	304.66	3.75	16.50
1C	298.15	0.2	0.005	0.05	303.85	3.12	3.90
1C	298.15	0.5	0.03	0.02	304.2	3.28	4.50
1C	292.15	0.4	0.01	0.04	303.49	4.59	24.38
1C	298.15	0.4	0.02	0.01	296.87	2.77	4.30
0.5C	294.15	0.5	0.02	0.03	295.11	1.37	26.15
0.5C	288.15	0.1	0.02	0.01	290.33	1.97	14.53
0.5C	298.15	0.2	0.04	0.005	292.09	2.44	3.90
0.5C	296.15	0.3	0.01	0.04	297.07	1.31	9.12
0.5C	294.15	0.1	0.03	0.03	296.4	1.98	9.01
0.5C	294.15	0.05	0.03	0.01	297.39	2.1	6.26

输入					输出
倍率	温度/K	风速/m·s^-1	横间距/m	纵间距/m	最大温度/K	温差/K	功耗/W
3C	296.15	0.3	0.03	0.03	319.26	12.47	12.07
3C	288.15	0.1	0.04	0.005	324.32	16.13	19.45
3C	294.15	0.05	0.05	0.01	327.04	13.65	7.24
3C	288.15	0.5	0.05	0.03	312.38	14.1	95.53
3C	290.15	0.1	0.005	0.02	317.55	12.34	9.41
3C	290.15	0.3	0.03	0.02	319.31	13.12	35.98
2.5C	294.15	0.2	0.005	0.05	313.54	10.64	9.61
2.5C	298.15	0.1	0.05	0.005	323.93	11.48	3.70
2.5C	290.15	0.5	0.04	0.02	312.73	10.52	67.48
2.5C	296.15	0.3	0.02	0.03	315.68	9.7	10.60
2.5C	298.15	0.05	0.05	0.01	324.69	12.22	3.60
2.5C	292.15	0.4	0.05	0.04	315.41	11.78	47.99
2C	290.15	0.4	0.01	0.05	302.42	7.11	31.07
2C	296.15	0.2	0.04	0.02	316.1	8.66	10.20
2C	296.15	0.05	0.02	0.005	318.61	8.82	4.68
2C	288.15	0.3	0.01	0.05	316.48	8.49	29.19
2C	292.15	0.2	0.04	0.01	316.48	9.17	10.20
2C	292.15	0.3	0.05	0.005	315.32	10.40	36.87
1.5C	290.15	0.4	0.03	0.05	301.94	6.88	46.81
1.5C	292.15	0.05	0.005	0.04	311.73	9.41	5.74
1.5C	288.15	0.1	0.01	0.02	304.41	7.68	12.06
1.5C	292.15	0.5	0.01	0.03	299.61	4.42	29.59
1.5C	288.15	0.05	0.02	0.04	309.47	8.44	9.01
1.5C	298.15	0.5	0.005	0.005	304.98	6.98	4.50
1C	292.15	0.4	0.005	0.05	314.82	13.32	21.42
1C	294.15	0.2	0.04	0.04	304.66	3.75	16.50
1C	298.15	0.2	0.005	0.05	303.85	3.12	3.90
1C	298.15	0.5	0.03	0.02	304.2	3.28	4.50
1C	292.15	0.4	0.01	0.04	303.49	4.59	24.38
1C	298.15	0.4	0.02	0.01	296.87	2.77	4.30
0.5C	294.15	0.5	0.02	0.03	295.11	1.37	26.15
0.5C	288.15	0.1	0.02	0.01	290.33	1.97	14.53
0.5C	298.15	0.2	0.04	0.005	292.09	2.44	3.90
0.5C	296.15	0.3	0.01	0.04	297.07	1.31	9.12
0.5C	294.15	0.1	0.03	0.03	296.4	1.98	9.01
0.5C	294.15	0.05	0.03	0.01	297.39	2.1	6.26

核函数	模型评估
核函数	MAE	RMSE	R²
Linear	0.3514	0.5928	0.7694
Polynomial，degree=3	0.5342	0.7309	0.8300
Polynomial，degree=5	0.7691	0.8770	0.8122
Polynomial，degree=10	3.571	1.890	0.7797
Sigmoid	0.5493	0.7411	0.4898
RBF	0.3455	0.5828	0.9272