A data-driven identification method for reaction rate constant and diffusion coefficient in the P2D model

doi:10.1016/j.cjche.2025.05.045

中国化学工程学报 ›› 2025, Vol. 88 ›› Issue (12): 188-197.DOI: 10.1016/j.cjche.2025.05.045

A data-driven identification method for reaction rate constant and diffusion coefficient in the P2D model

Gaoyang Li¹, Xiaoyu Guo¹, Yongshuai Li³, Jialong Huang¹, Zhirui Wang³, Yizheng Ma¹, Litao Zhu⁴, Hui Pan¹, Feng Shao², Hao Ling³, Yulin Min¹

1. Shanghai Key Laboratory of Materials Protection and Advanced Materials in Electric Power, Shanghai University of Electric Power, Shanghai 200090, China;
2. School of Chemistry and Chemical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China;
3. State Key Laboratory of Chemical Engineering, East China University of Science and Technology, Shanghai 200237, China;
4. College of Smart Energy, Shanghai Jiao Tong University, Shanghai 200240, China

收稿日期:2025-02-13 修回日期:2025-04-30 接受日期:2025-05-07 出版日期:2026-02-09 发布日期:2025-08-22
通讯作者: Hui Pan,E-mail:fiona_panhui@shiep.edu.cn;Feng Shao,E-mail:shaofeng0824@sjtu.edu.cn;Hao Ling,E-mail:linghao@ecust.edu.cn;Yulin Min,E-mail:minyulin@shiep.edu.cn
基金资助:
This work is supported by National Natural Science Foundation of China (22478239), Science and Technology Commission of Shanghai Municipality (19DZ2271100) and National Natural Science Foundation of China (22208208).

A data-driven identification method for reaction rate constant and diffusion coefficient in the P2D model

Gaoyang Li¹, Xiaoyu Guo¹, Yongshuai Li³, Jialong Huang¹, Zhirui Wang³, Yizheng Ma¹, Litao Zhu⁴, Hui Pan¹, Feng Shao², Hao Ling³, Yulin Min¹

1. Shanghai Key Laboratory of Materials Protection and Advanced Materials in Electric Power, Shanghai University of Electric Power, Shanghai 200090, China;
2. School of Chemistry and Chemical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China;
3. State Key Laboratory of Chemical Engineering, East China University of Science and Technology, Shanghai 200237, China;
4. College of Smart Energy, Shanghai Jiao Tong University, Shanghai 200240, China

Received:2025-02-13 Revised:2025-04-30 Accepted:2025-05-07 Online:2026-02-09 Published:2025-08-22
Contact: Hui Pan,E-mail:fiona_panhui@shiep.edu.cn;Feng Shao,E-mail:shaofeng0824@sjtu.edu.cn;Hao Ling,E-mail:linghao@ecust.edu.cn;Yulin Min,E-mail:minyulin@shiep.edu.cn
Supported by:
This work is supported by National Natural Science Foundation of China (22478239), Science and Technology Commission of Shanghai Municipality (19DZ2271100) and National Natural Science Foundation of China (22208208).

摘要/Abstract

摘要： To ensure the safe operation of batteries, accurately obtaining key internal state parameters is essential. However, traditional parameter measurement methods either require opening the battery or long-term measurements, which are impractical. Therefore, the fixed values are commonly used for these parameters in electrochemical models and have significant limitations. To overcome these limitations, this paper proposes a deep neural network (DNN) based data-driven evaluation method to determine model parameters. By coupling an improved one-dimensional isothermal pseudo-two-dimensional (P2D) model with DNN, this study identified concentration-dependent parameters through detailed discharge curve analysis. The results show that the data-driven method can effectively obtain the change trend of concentration-dependent parameters through the charge and discharge curve, and the method can be extended to different battery systems in different discharge rates and aging applications. This work is expected to provide new parameter selection insights for data-driven battery prediction and monitoring models.

关键词: Internal state parameters of batteries, P2D model, Parameter identification, Deep neural network (DNN), Data-driven evaluation method

Abstract: To ensure the safe operation of batteries, accurately obtaining key internal state parameters is essential. However, traditional parameter measurement methods either require opening the battery or long-term measurements, which are impractical. Therefore, the fixed values are commonly used for these parameters in electrochemical models and have significant limitations. To overcome these limitations, this paper proposes a deep neural network (DNN) based data-driven evaluation method to determine model parameters. By coupling an improved one-dimensional isothermal pseudo-two-dimensional (P2D) model with DNN, this study identified concentration-dependent parameters through detailed discharge curve analysis. The results show that the data-driven method can effectively obtain the change trend of concentration-dependent parameters through the charge and discharge curve, and the method can be extended to different battery systems in different discharge rates and aging applications. This work is expected to provide new parameter selection insights for data-driven battery prediction and monitoring models.

Key words: Internal state parameters of batteries, P2D model, Parameter identification, Deep neural network (DNN), Data-driven evaluation method

Gaoyang Li, Xiaoyu Guo, Yongshuai Li, Jialong Huang, Zhirui Wang, Yizheng Ma, Litao Zhu, Hui Pan, Feng Shao, Hao Ling, Yulin Min. A data-driven identification method for reaction rate constant and diffusion coefficient in the P2D model[J]. 中国化学工程学报, 2025, 88(12): 188-197.

参考文献

[1] G. Zubi, R. Dufo-Lopez, M. Carvalho, and G. Pasaoglu, The lithium-ion battery: State of the art and future perspectives, Renew. Sust. Energ. Rev. 89 (2018) 292-308.
[2] B. Nykvist, F. Sprei, M. Nilsson, Assessing the progress toward lower priced long range battery electric vehicles, Energy Policy 124 (2019) 144-155.
[3] C. Grosjean, P.H. Miranda, M. Perrin, P. Poggi, Assessment of world lithium resources and consequences of their geographic distribution on the expected development of the electric vehicle industry, Renew. Sustain. Energy Rev. 16 (3) (2012) 1735-1744.
[4] H.S. Hirsh, Y.X. Li, D.H.S. Tan, M.H. Zhang, E.Y. Zhao, Y.S. Meng, Sodium-ion batteries paving the way for grid energy storage, Adv. Energy Mater. 10 (32) (2020) 2001274.
[5] V. Ramadesigan, V. Boovaragavan, M. Arabandi, K.J. Chen, H. Tsukamoto, R. Braatz, V. Subramanian, Parameter estimation and capacity fade analysis of lithium-ion batteries using first-principles-based efficient reformulated models, ECS Trans. 19 (16) (2009) 11-19.
[6] X.Y. Li, C.G. Yuan, X.H. Li, Z.P. Wang, State of health estimation for Li-Ion battery using incremental capacity analysis and Gaussian process regression, Energy 190 (2020) 116467.
[7] X.N. Feng, C.H. Weng, X.M. He, X.B. Han, L.G. Lu, D.S. Ren, M.G. Ouyang, Online state-of-health estimation for Li-ion battery using partial charging segment based on support vector machine, IEEE Trans. Veh. Technol. 68 (9) (2019) 8583-8592.
[8] L. Cai, J.H. Meng, D.I. Stroe, G.Z. Luo, R. Teodorescu, An evolutionary framework for lithium-ion battery state of health estimation, J. Power Sources 412 (2019) 615-622.
[9] J. Kim, H.Y. Chun, M. Kim, J. Yu, K. Kim, T. Kim, S. Han, Data-driven state of health estimation of Li-ion batteries with RPT-reduced experimental data, IEEE Access 7 (2019) 106987-106997.
[10] C. Rojas, L. Oca, I. Lopetegi, U. Iraola, J. Carrasco, A critical look at efficient parameter estimation methodologies of electrochemical models for Lithium-Ion cells, J. Energy Storage 80 (2024) 110384.
[11] C. Rojas, L. Oca, I. Lopetegi, U. Iraola, J. Carrasco, A critical look at efficient parameter estimation methodologies of electrochemical models for Lithium-Ion cells, J. Energy Storage 80 (2024) 110384.
[12] J. Newman, W. Tiedemann, Porous-electrode theory with battery applications, AlChE. J. 21 (1) (1975) 25-41.
[13] M. Ecker, T.K.D. Tran, P. Dechent, S. Kabitz, A. Warnecke, D.U. Sauer, Parameterization of a physico-chemical model of a lithium-ion battery, J. Electrochem. Soc. 162 (9) (2015) A1836-A1848.
[14] M. Ecker, S. Kabitz, I. Laresgoiti, D.U. Sauer, Parameterization of a physico-chemical model of a lithium-ion battery, J. Electrochem. Soc. 162 (9) (2015) A1849-A1857.
[15] L. Oca, E. Miguel, E. Agirrezabala, A. Herran, E. Gucciardi, L. Otaegui, E. Bekaert, A. Villaverde, U. Iraola, Physico-chemical parameter measurement and model response evaluation for a pseudo-two-dimensional model of a commercial lithium-ion battery, Electrochim. Acta 382 (2021) 138287.
[16] J. Schmalstieg, C. Rahe, M. Ecker, D.U. Sauer, Full cell parameterization of a high-power lithium-ion battery for a physico-chemical model: part I. physical and electrochemical parameters, J. Electrochem. Soc. 165 (16) (2018) A3799-A3810.
[17] J. Schmalstieg, D.U. Sauer, Full cell parameterization of a high-power lithium-ion battery for a physico-chemical model: part II. thermal parameters and validation, J. Electrochem. Soc. 165 (16) (2018) A3811-A3819.
[18] S. Santhanagopalan, Q.Z. Guo, R.E. White, Parameter estimation and model discrimination for a lithium-ion cell, J. Electrochem. Soc. 154 (3) (2007) A198.
[19] J. Vazquez-Arenas, L.E. Gimenez, M. Fowler, T. Han, S.K. Chen, A rapid estimation and sensitivity analysis of parameters describing the behavior of commercial Li-ion batteries including thermal analysis, Energy Convers. Manag. 87 (2014) 472-482.
[20] M.A. Rahman, S. Anwar, A. Izadian, Electrochemical model parameter identification of a lithium-ion battery using particle swarm optimization method, J. Power Sources 307 (2016) 86-97.
[21] L.Q. Zhang, L.X. Wang, G. Hinds, C. Lyu, J. Zheng, J.F. Li, Multi-objective optimization of lithium-ion battery model using genetic algorithm approach, J. Power Sources 270 (2014) 367-378.
[22] A. Jokar, B. Rajabloo, M. Desilets, M. Lacroix, An inverse method for estimating the electrochemical parameters of lithium-ion batteries, J. Electrochem. Soc. 163 (14) (2016) A2876-A2886.
[23] S.C. Ding, Y.D. Li, H.F. Dai, L. Wang, X.M. He, Accurate model parameter identification to boost precise aging prediction of lithium-ion batteries: a review, Adv. Energy Mater. 13 (39) (2023) 2301452.
[24] J.F. Li, L.X. Wang, C. Lyu, E.H. Liu, Y.J. Xing, M. Pecht, A parameter estimation method for a simplified electrochemical model for Li-ion batteries, Electrochim. Acta 275 (2018) 50-58.
[25] B. Rajabloo, A. Jokar, M. Desilets, M. Lacroix, An inverse method for estimating the electrochemical parameters of lithium-ion batteries, J. Electrochem. Soc. 164 (2) (2017) A99-A105.
[26] Z.X. Sun, W.L. He, J.L. Wang, X. He, State of health estimation for lithium-ion batteries with deep learning approach and direct current internal resistance, Energies 17 (11) (2024) 2487.
[27] X.D. Xia, W. Wu, Z.C. Li, X.L. Han, X.B. Xue, G.Z. Xiao, T. Guo, State of charge estimation for commercial Li-ion battery based on simultaneously strain and temperature monitoring over optical fiber sensors, IEEE Trans. Instrum. Meas. 73 (2024) 2516411.
[28] U. Khan, S. Kirmani, Y. Rafat, M.U. Rehman, M.S. Alam, Improved deep learning based state of charge estimation of lithium ion battery for electrified transportation, J. Energy Storage 91 (2024) 111877.
[29] M. Kim, H.Y. Chun, J. Kim, K. Kim, J. Yu, T. Kim, S. Han, Data-efficient parameter identification of electrochemical lithium-ion battery model using deep Bayesian harmony search, Appl. Energy 254 (2019) 113644.
[30] H.Y. Chun, J. Kim, J. Yu, S. Han, Real-time parameter estimation of an electrochemical lithium-ion battery model using a long short-term memory network, IEEE Access 8 (2020) 81789-81799.
[31] L. Xu, X.K. Lin, Y. Xie, X.S. Hu, Enabling high-fidelity electrochemical P2D modeling of lithium-ion batteries via fast and non-destructive parameter identification, Energy Storage Mater. 45 (2022) 952-968.
[32] J. Kim, H.Y. Chun, J. Baek, S. Han, Parameter identification of lithium-ion battery pseudo-2-dimensional models using genetic algorithm and neural network cooperative optimization, J. Energy Storage 45 (2022) 103571.
[33] J. Kim, H.Y. Chun, H. Kim, M. Lee, S. Han, Strategically switching metaheuristics for effective parameter estimation of electrochemical lithium-ion battery models, J. Energy Storage 64 (2023) 107094.
[34] G. Di Luca, G. Di Blasio, A. Gimelli, D.A. Misul, Review on battery state estimation and management solutions for next-generation connected vehicles, Energies 17 (1) (2024) 202.
[35] R.B. Smith, E. Khoo, M.Z. Bazant, Intercalation kinetics in multiphase-layered materials, J. Phys. Chem. C 121 (23) (2017) 12505-12523.
[36] K. Chayambuka, G. Mulder, D.L. Danilov, P.H.L. Notten, Physics-based modeling of sodium-ion batteries part II. Model and validation, Electrochim. Acta 404 (2022) 139764.
[37] K. Chayambuka, M. Jiang, G. Mulder, D.L. Danilov, P.H.L. Notten, Physics-based modeling of sodium-ion batteries part I: Experimental parameter determination, Electrochim. Acta 404 (2022) 139726.
[38] C.H. Chen, F. Brosa Planella, K. O’Regan, D. Gastol, W.D. Widanage, E. Kendrick, Development of experimental techniques for parameterization of multi-scale lithium-ion battery models, J. Electrochem. Soc. 167 (8) (2020) 080534.
[39] M.M. Loghavi, A. Nahvibayani, M.H. Moghim, M. Babaiee, S. Baktashian, R. Eqra, Electrochemical evaluation of LiNi0.5Mn0.3Co0.2O₂, LiNi0.6Mn0.2Co0.2O₂, and LiNi0.8Mn0.1Co0.1O₂ cathode materials for lithium-ion batteries: from half-coin cell to pouch cell, Monatsh. Fur Chem. Chem. Mon. 153 (12) (2022) 1197-1212.

A data-driven identification method for reaction rate constant and diffusion coefficient in the P2D model

A data-driven identification method for reaction rate constant and diffusion coefficient in the P2D model

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 1

编辑推荐

Metrics

本文评价