A Grey-box Approach for the Prognostic and Health Management of Lithium-Ion Batteries



Published Oct 26, 2023
Francesco Cancelliere Sylvain Girard Jean-Marc Bourinet Matteo Broggi


The Lithium-Ion Batteries (LIB) industry is rapidly growing and is expected to continue expanding exponentially in the next decade. LIBs are already widely used in everyday life, and their demand is expected to increase further, particularly in the automotive sector. The European Union has introduced a new law to ban Internal Combustion Engines from 2035, pushing for the adoption of electric vehicles and increasing the need for more efficient and reliable energy storage solutions such as LIBs. As a result, the establishment of Gigafactories in Europe and the United States is accelerating to meet the growing demand and partially reduce dependencies on China, which is currently the main producer of LIBs.

To fully realize the potential of LIBs and ensure their safe and sustainable use, it is crucial to optimize their useful life and develop reliable and robust methodologies for estimating their state of health and predicting their remaining useful life. This requires a comprehensive understanding of LIB behavior and the development of effective prognostic and health management approaches that can accurately predict battery degradation, plan for maintenance and replacements, and improve battery performance and lifespan.

This work, funded by the GREYDIENT project, a European consortium aiming to advance the state of the art in the grey-box approach, combines physical modeling (white box) and machine learning (black box) techniques to demonstrate the grey-box effectiveness in the Prognostic and Health Management. The grey-box approach here proposed consist in a combination of a physical battery model whose degradation parameters are estimated online at every cycle by a Multi-Layer Perceptron Particle Filter (MLP-PF).

An electrochemical degradation model of a Lithium-Ion battery cell has been derived by use of Modelica. The model simulates the output voltage of the cell, while the degradation over time is simulate through the variation of 3 parameters: qMax (maximum number of Lithium-Ions available), R0 (Internal Resistance) and D (Diffusion Coefficient). To validate the model we resorted to the well-known NASA Battery Dataset, which has also been used to infer the optimal values of the three hidden degradation parameters at every cycle, to obtain their Run-to-Failure history. Then, the physical model is combined the MLP-PF: a MLP
Artificial Neural Network is firstly trained on the Run-to-Failure degradation processes of the model parameters, allowing the propagation of the parameters in the future and the corresponding estimation of the battery Remaining Use ful Life (RUL). The MLP is then updated online by a Particle Filter every time a new measurement is available from the Battery Management System (BMS), providing flexibility to this method, needed for the electrochemical nature of the batteries, and allowing the propagation of uncertainties.

How to Cite

Cancelliere, F., Girard, S., Bourinet, J.-M., & Broggi, M. (2023). A Grey-box Approach for the Prognostic and Health Management of Lithium-Ion Batteries. Annual Conference of the PHM Society, 15(1). https://doi.org/10.36001/phmconf.2023.v15i1.3506
Abstract 337 | PDF Downloads 256



Lithium-Ion Batteries, Particle Filter, Modelica, Physical Model, Grey-Box

Arulampalam, M. S., Maskell, S., Gordon, N., & Clapp, T. (2002). A tutorial on particle filters for online nonlinear/nongaussian bayesian tracking. IEEE Transaction on Signal Processing, 50(2), 174–188. doi: 10.1109/9780470544198.ch73

BloombergNEF. (2022). Race to Net Zero: The Pressures of the Battery Boom in Five Charts, https://about.bnef.com/blog/race-to-net-zero-the-pressures-of-the-battery-boom-in-five-charts/.

Cadini, F., Sbarufatti, C., Cancelliere, F., & Giglio, M. (2019). State-of-life prognosis and diagnosis of lithium-ion batteries by data-driven particle filters. Applied Energy, 235(June 2018), 661–672. doi: 10.1016/j.apenergy.2018.10.095

Cancelliere, F., & Girard, S. (2022). Management of a free-floating electrical scooters fleet. Proceedings of the LambdaMu 22 Congrés.

Daigle, M., & Kulkarni, C. S. (2013). Electrochemistry-based battery modeling for prognostics. In Phm 2013 - proceedings of the annual conference of the prognostics and health management society 2013 (pp. 249–261).

Daigle, M., & Kulkarni, C. S. (2015). End-of-discharge and End-of-life Prediction in Lithium-ion Batteries with Electrochemistry-based Aging Models. American Institute of Aeronautics and Astronautics, 1–11. doi: 10.1002/0470011815.b2a07002

Dickerson, A., Rajamani, R., Boost, M., & Jackson, J. (2015). Determining Remaining Useful Life for Li-ion Batteries. SAE Technical Paper 2015-01-2584. doi: 10.4271/2015-01-2584

Doucet, A., Godsill, S., & Andrieu, C. (2000). On sequential Monte Carlo sampling methods for Bayesian filtering. Statistics and Computing, 10, 197–208. doi: 10.1023/A:1008935410038

FMI. (2010). Functional mock-up interface. Retrieved from https://fmi-standard.org/

Heiner, Heimes. (2022). BATTERY ATLAS 2022, Shaping the European Lithium-Ion Battery Industry (Tech. Rep.).

Hu, X., Xu, L., Lin, X., & Pecht, M. (2020). Battery Lifetime Prognostics. Joule, 4(2), 310–346. doi: 10.1016/j.joule.2019.11.018

IEA. (2022). Global EV Outlook 2022 - Securing supplies for an electric future. International Energy Agency.

Khaleghi, S., Hosen, M. S., Karimi, D., Behi, H., Beheshti, S. H., Van Mierlo, J., & Berecibar, M. (2022). Developing an online data-driven approach for prognostics and health management of lithium-ion batteries. Applied Energy, 308(December 2021), 118348. doi: 10.1016/j.apenergy.2021.118348

Li, W., Zhang, J., Ringbeck, F., Jöst, D., Zhang, L., Wei, Z., & Sauer, D. U. (2021). Physics-informed neural networks for electrode-level state estimation in lithium-ion batteries. Journal of Power Sources, 506(March). doi: 10.1016/j.jpowsour.2021.230034

Lyu, C., Lai, Q., Ge, T., Yu, H., Wang, L., & Ma, N. (2017). A lead-acid battery’s remaining useful life prediction by using electrochemical model in the Particle Filtering framework. Energy, 120, 975–984. doi: 10.1016/j.energy.2016.12.004

Michael James, D. P. (1994). A Direct search optimization method that models the objective and constraint functions by linear interpolation. Advances in Optimization and Numerical Analysis, p. 51-67.

Modelica. (1996). https://www.modelica.org.

Nascimento, R. G., Corbetta, M., Kulkarni, C. S., & Viana, F. A. (2021). Hybrid physics-informed neural networks for lithium-ion battery modeling and prognosis. Journal of Power Sources, 513(August), 230526. doi: 10.1016/j.jpowsour.2021.230526

OpenModelica. (2007). https://www.openmodelica.com.

Saha, B., & Goebel, K. (2007). Battery Data Set. NASA Ames Prognostics Data Repository.

Sbarufatti, C., Corbetta, M., Giglio, M., & Cadini, F. (2018). Adaptive prognosis of lithium-ion batteries based on
the combination of particle filters and radial basis function neural networks. Journal of Power Sources, 344, 128–140. doi: 10.1016/j.jpowsour.2017.01.105

Shi, J., Rivera, A., & Wu, D. (2022). Battery health management using physics-informed machine learning: Online degradation modeling and remaining useful life prediction. Mechanical Systems and Signal Processing, 179(January), 109347. doi: 10.1016/j.ymssp.2022.109347

Sun, P., Bisschop, R., Niu, H., & Huang, X. (2020). A Review of Battery Fires in Electric Vehicles (Vol. 56) (No. 4). Springer US. doi: 10.1007/s10694-019-00944-3

Tran, M.-K., Mevawalla, A., Aziz, A., Panchal, S., Xie, Y., & Fowler, M. (2022). A Review of Lithium-Ion Battery Thermal Runaway Modeling and Diagnosis Approaches. Processes, 10(6). doi: 10.3390/pr10061192

Wang, S., Jin, S., Bai, D., Fan, Y., Shi, H., & Fernandez, C. (2021). A critical review of improved deep learning methods for the remaining useful life prediction of lithium-ion batteries. Energy Reports, 7, 5562–5574. doi: 10.1016/j.egyr.2021.08.182

Zhang, Y., Xiong, R., He, H., & Pecht, M. G. (2018). Long short-term memory recurrent neural network for remaining useful life prediction of lithium-ion batteries. IEEE Transactions on Vehicular Technology, 67(7), 5695–5705. doi: 10.1109/TVT.2018.2805189

Zou, Y., Hu, X., Ma, H., & Li, S. E. (2015). Combined State of Charge and State of Health estimation over lithium-ion battery cell cycle lifespan for electric vehicles. Journal of Power Sources, 273, 793–803. doi: 10.1016/j.jpowsour.2014.09.146
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